COMMISSIONING OF THE SEPARATOR FOR CAPTURE REACTIONS IN

ASTROPHYSICS

By

Sara Ayoub Miskovich

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Physics - Doctor of Philosophy

2021

COMMISSIONING OF THE SEPARATOR FOR CAPTURE REACTIONS

ABSTRACT

IN ASTROPHYSICS

By

Sara Ayoub Miskovich

The SEparator for CApture Reactions (SECAR) [6] is a next-generation recoil mass sep-

arator system at the National Superconducting Cyclotron Laboratory (NSCL) and Facility

for Rare Isotope Beams (FRIB) at Michigan State University. SECAR was designed for

precise and direct measurements of reaction rates relevant to the explosive synthesis of ele-

ments in astrophysical sites such as X-ray bursts and novae. Once SECAR is operational,

it will be utilized for precise measurements of low energy (p,γ) and (p,α) reactions in in-

verse kinematics with beams of proton-rich radioactive nuclei of masses up to A = 65. The

work discussed in this thesis was dedicated to the commissioning of the beamline, including

diagnostic devices, to characterizing the system, and defining operational approaches that

ensure reliable, reproducible, and optimal performance.

To maximize the performance of the device, careful beam alignment to the central ion

optical axis needs to be achieved, which can be difficult to attain through manual tuning in a

quantitative and reproducible way. Additionally, the ion optical settings need to be verified

and optimized to ensure adequate mass separation. In this thesis, the first development of an

online Bayesian optimization with a Gaussian process model to tune a nuclear astrophysics

recoil separator and improve its ion optical properties is reported. The method is shown to

improve recoil separator performance, increase objectivity and reproducibility, and reduce

setup and tuning time significantly. It is now used routinely for all separator tuning.

As precise knowledge of the beam energy is critical when measuring narrow resonances,

the energy calibration of the first bending dipole pair was performed to provide independent

incoming beam energy determinations in the SECAR system. This was achieved through the

measurement of the γ-ray yields of the 27Al(p,γ)28Si resonances at Ep = 992 and 1800 keV/u

with a BGO (Bismuth Germanate) array at the SECAR target chamber. Two measurements

were obtained for each resonance, one with a H+ beam and one with a H+

2 , to cover a larger

rigidity range. By fitting the observed γ-ray yields with a thick target yield curve, a dipole
calibration factor of k = 3.6501×10-3 ± 6.2×10-6 (0.17%) T/

keV amu was obtained. To

√

achieve higher accuracy when extrapolating to higher energies, the energy calibration was

also performed taking into account relativistic effects.

This commissioning work paves the way for SECAR to achieve its scientific goals of

improving our understanding of stellar explosions. By providing accurate thermonuclear

reaction rates, astrophysical models will in turn provide better understanding of explosions

such as novae and X-ray bursts.

Dedicated to Mounir Sholy.

iv

ACKNOWLEDGMENTS

First, I want to thank my advisor Hendrik Schatz, and Fernando Montes for all their support

and patience throughout my years in graduate school. This work would not have been

possible without the help of the entire nuclear astrophysics group and everyone who took

part in the many commissioning runs we had. Know that I thank you all for your help,

especially Louis Wagner, Rahul Jain, Kirby Hermansen, Nabin Rijal, April Garrity, Justin

Browne, Stephanie Lyons, and Konrad Schmidt. I am thankful for the SECAR collaboration,

and in particular Michael Smith, Manoel Couder, Georg Berg and Kelly Chipps for always

having an answer ready to my many questions. I also thank Elaine Yakura for her amazing

support in navigating this journey, and my committee members, Alex Brown, Ed Brown,

Brad Sherrill, and Kirsten Tollefson for their guidance over the years.

The commissioning of this complex beamline was a lab-wide effort, and I would like to

thank everyone that supported any work that helped the completion of this thesis. I cannot

possibly name everyone that was involved here, but know that I am grateful for your support.

I would especially like to thank the ReA3 group, in particular Tasha Summers, Daniel Crisp,

Antonio Villari, Sam Nash, and Ana Henriques for all their hard work.

Graduate school would not have been the same without the support and companionship of

my friends. Our pre-covid office was always fun, thanks to Mara Grinder, Dayah Chrisman,

and Aalayah Spencer. I would also like to thank Kristen Dage for being generous and helpful

in every way since the day we met. Last but not least, I thank Elsie Arayes for her unyielding

support and encouragement for many, many years.

I cannot thank my parents enough for their unwavering support as I pursued any dream

I had, and for always believing in me no matter what. My journey would not have been

v

possible without the support of my wonderful family, and for that I am grateful. I particularly

thank Rayane for always being there for me, and Rudy for providing support and reassurance

when I needed it. Finally, I thank my husband Andrew, for calming me down when I was

overwhelmed, for celebrating small victories with me, and for his never-ending support that

ultimately helped me complete this degree.

vi

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

LIST OF ALGORITHMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Chapter 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Importance of Radiative Capture Reactions
1.2
. . . . . . . . . . . . . . . . . .
1.2.1 Radiative Capture Reactions in X-ray bursts . . . . . . . . . . . . . .
1.2.2 Radiative Capture Reactions in Novae
. . . . . . . . . . . . . . . . .
1.3 Direct Measurement of Radiative Capture Reactions . . . . . . . . . . . . . .
1.3.1 Experimental Studies . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2
Inverse Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Recoil Separator Design Principles
. . . . . . . . . . . . . . . . . . .
1.3.4 Previous Recoil Separators . . . . . . . . . . . . . . . . . . . . . . . .
1.4 SECAR at FRIB and NSCL . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Machine Learning for Tuning Optimization . . . . . . . . . . . . . . . . . . .

Chapter 2 Experimental Determination of Astrophysical Stellar Rates

.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Stellar Reaction Rates
2.2 Narrow Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Narrow Resonance Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3

SECAR Design and Experimental Setup . . . . . . . . . . . . .
3.1 The NSCL and ReA3 Facility . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 The FRIB Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 The SECAR Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Design Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2
Ion Optical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Beam Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Gas Target Systems
3.5.1
JENSA Target System . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Extended Gas Target System . . . . . . . . . . . . . . . . . . . . . .
3.6 Detectors and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Gamma-Ray Detection . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Recoil Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.3 Digital Data Acquisition System . . . . . . . . . . . . . . . . . . . . .

1
1
3
4
7
9
9
10
13
18
22
23

25
25
28
31

38
38
39
40
44
45
52
57
58
61
62
63
65
72

vii

Chapter 4 Beamline Commissioning . . . . . . . . . . . . . . . . . . . . . . .
4.1 Separator Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Magnet Stability and Reproducibility . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
4.2.1 Magnet Cycling and Hysteresis
4.2.2 Long Term Stability Tests . . . . . . . . . . . . . . . . . . . . . . . .
Initial Tests with Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Diagnostic Devices Tests . . . . . . . . . . . . . . . . . . . . . . . . .

4.3

73
73
76
77
79
85
87

Chapter 5 Tuning and Bayesian Optimization . . . . . . . . . . . . . . . . .
5.1 Tuning Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Manual Tuning Procedure . . . . . . . . . . . . . . . . . . . . . . . .

97
97
99
5.2 Dipoles and WF Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 Bayesian Optimization for Beam Tuning . . . . . . . . . . . . . . . . . . . . 106
5.3.1 The Bayesian Approach . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.3.2 Gaussian Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.3.3 Hyperparameter Selection . . . . . . . . . . . . . . . . . . . . . . . . 114
5.3.4 Acquisition Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.3.5 Method and Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.3.6 Beam Incoming Angle Optimization . . . . . . . . . . . . . . . . . . . 121
5.3.7
Ion Optics Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 131

Chapter 6 Dipole Energy Calibration . . . . . . . . . . . . . . . . . . . . . . 141
6.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.2 Resonant Reactions and Target Properties . . . . . . . . . . . . . . . . . . . 143
6.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.3.1 Target Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.3.2 Gamma Detection Array . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.3.3
SECAR Beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.4 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.5 Analysis and Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.5.1 Beam Current Integration and Normalization . . . . . . . . . . . . . 152
6.5.2 Dipole Field Determination . . . . . . . . . . . . . . . . . . . . . . . 153
6.5.3 Gamma-ray Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.5.4 Yield Curve Fitting and Uncertainties
. . . . . . . . . . . . . . . . . 158
6.5.5 Energy Calibration Results . . . . . . . . . . . . . . . . . . . . . . . . 164

Chapter 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.1 Next Steps and Future Developments . . . . . . . . . . . . . . . . . . . . . . 174

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

viii

LIST OF TABLES

Table 3.1:

SECAR separator properties for optimized direct measurements of p-
and α-capture reactions on unstable proton-heavy nuclei.
. . . . . .

Table 3.2:

Pole tip magnetic fields for COSY INFINITY nominal tune at 0.8
Tm used in this work. . . . . . . . . . . . . . . . . . . . . . . . . . .

45

53

Table 3.3:

Beam requirements for optimal recoil separation in SECAR. . . . . .

53

Table 4.1:

SECAR commissioning runs.

. . . . . . . . . . . . . . . . . . . . . .

86

Table 4.2:

Faraday cup collector current readbacks up to FP2 after tuning the
20Ne8+ beam in July 2020.
. . . . . . . . . . . . . . . . . . . . . . .

91

Table 5.1:

Slit gaps needed to admit the 2σ beam width within dE/E for each
tune.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Table 5.2:

Beam spot diameter at FP2 calculated in COSY with a target width
of 1.5 mm (2σ), compared to the widths (± 2σ) measured experimen-
tally with the nominal beam settings and with the best settings after
optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Table 6.1:

Parameters of 27Al(p,γ)28Si resonances scanned for the dipole cali-
bration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Table 6.2:

Calibration factors, beam energy spreads and calibration dipole fields
obtained for the 27Al(p,γ)28Si resonance energies with their statistical
uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

ix

LIST OF FIGURES

Figure 1.1:

Simplified illustration of resonant radiative capture in the laboratory
frame.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.2: Maximum recoil half-angle in the laboratory frame as a function of
the center of mass energy for a number of reactions of astrophysical
interest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.1: Maxwell-Boltzmann factor (dashed line) and Gamow factor (dotted
line) versus energy for an arbitrary temperature T. The product
e−kbT e−2πη, representing the Gamow peak, is shown with the solid
line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.2: Yield curve normalized to Ymax for a thick target based on Equation
2.29 with a small beam energy spread δ = 0.005%. . . . . . . . . . .

Figure 3.1: The SECAR recoil separator layout in the ReA3 Hall at MSU. The
beam enters the hall from the middle left into the JENSA gas jet
target system, and the capture reaction recoils along with the unre-
acted projectiles enter the first section in SECAR that selects a single
charge state. Two subsequent sections each including a velocity filter
(WF1, WF2) serve to reject the remaining projectiles, and the final
cleanup section features a final pair of dipoles before particles enter
the focal plane detection system. . . . . . . . . . . . . . . . . . . . .

11

13

28

35

40

Figure 3.2:

SECAR in the ReA3 Hall showing B1 up to Hex3.

. . . . . . . . . .

41

Figure 3.3:

SECAR in the ReA3 Hall showing B5 up to the final focal plane. . .

41

Figure 3.4: The ion optics of SECAR for the layout explained in Section 3.3
corrected up to fourth order. The four sections are shown in different
colors. Traces of rays in the horizontal (a) and vertical (b) planes are
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
shown.

Figure 3.5: Example COSY INFINITY ion optics calculation up to the first mass
separation slits of a 65As(p,γ)66Se reaction in the x-plane. The Se
recoils are shown in black, unreacted As beam of similar Bρ is shown
in blue, and a beam of a nearby charge state is shown in red (δQ/Q
=1/21). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

51

Figure 3.6: Diagnostics along the SECAR beamline. . . . . . . . . . . . . . . . .

54

x

Figure 3.7: Faraday cup design for SECAR (left). Cup design in 3-in-1 device at
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

FP1 (right).

Figure 3.8: BCM design for SECAR shown on 3-in-1 device at FP1. Aluminum
.

nitride (AIN) ceramic plate serves to electrically isolate the plates.

Figure 3.9: CAD drawing of JENSA chamber and its differential pumping com-
ponents. The distance from the target location to the end of the final
downstream pumping stage is 73 cm. Beam direction is right to left.

Figure 3.10: The JENSA nozzle and receiver installed in the ReA3 Hall. Beam
direction is right to left. . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.11: JENSA gas target assembly in the ReA3 Hall upstream of SECAR.
SECAR elements up to Q5 shown. JENSA compressor shown in
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
white on the left.

Figure 3.12: Drawing of the extended gas cell designed for use with SECAR at the
. . . . . . . . . . . . . .

Colorado School of Mines. Scale is in mm.

Figure 3.13: Current γ-array comprised of 19 BGO crystals for use with the JENSA
gas jet (a,b), with a CAD showing the flange installed on the beamline
. . . . . . . . . .
left of the JENSA target looking downstream (c).

Figure 3.14: Drawing of BGO array around the extended gas cell as designed at
. . . . . . . . . . . . . . . . . . . . .

the Colorado School of Mines.

55

56

59

60

61

62

66

67

Figure 3.15: Schematic of the focal plane detection system at FP4.

. . . . . . . .

67

Figure 3.16: One of the accelerating grids and foil after assembly (left) and the
MCP detector installed in the beamline (right). Once installed, the
foil sits at 45◦ relative to the beam axis and parallel to the MCP
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
detector.

Figure 3.17: The ∆E-Si detector showing the grids and DSSD assembled before
. . . . . . . . . . . . . . . . . . . . . .

installation on the beamline.

Figure 4.1: The main global controls page for SECAR. Top left shows the magnet
light that controls the ReA3 Hall SECAR light when the magnets
are one, and to the right several buttons provide options to switch to
other pages. The general menu tabs below show the magnet controls
in this image.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.2: The vacuum summary page showing the controls and status of vac-
. . . . . . . . . . . . . . . . . . . . .

uum gauges and turbo pumps.

69

71

74

75

xi

Figure 4.3: The controls page for SECAR showing the tab for controls during
. . . . . . .

tuning. This was developed for use during experiments.

Figure 4.4: Dipole B1 magnetic field reproducibility measured with the NMR
probe after 1 cycle with 30 s pause time. N = 208. . . . . . . . . . .

Figure 4.5: Quadrupole Q6 magnetic field reproducibility using two different cy-
. . . . . . .

cling procedures, measured with a Group 3 Hall probe.

Figure 4.6: Dipole B1 magnetic field long term stability test as measured with
NMR (top) and Hall probe (bottom). The dot-dashed lines corre-
spond to ± 0.01% stability levels. The flat lines between July 26 and
July 29 correspond to a control system connection drop. . . . . . . .

Figure 4.7: Dipole B1 magnetic field long term stability test as measured with
NMR (top) and Hall probe (middle) in the presence of an external
heating source from from 25 to 37◦C. The dot-dashed lines correspond
to ± 0.01% stability levels and the black vertical line indicates the
onset of heating. Bottom plot shows the Hall probe’s temperature
sensor readback.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.8: Dipole B5 magnetic field long term stability test as measured with
a Hall probe. The dot-dashed lines correspond to ± 0.01% stability
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
levels.

Figure 4.9: Quadrupole Q1 magnetic field long term stability test as measured
with two Hall probes placed at different pole radii. The ambient
temperature near the power supply rack (mezzanine) is shown in red.
The overlayed dot-dashed lines correspond to ± 0.01% of the mean
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
of each reading.

75

78

79

80

82

83

84

Figure 4.10: First beam spot on the FP1 viewer in SECAR on July 13, 2018.

. .

85

Figure 4.11: FC1 assembled in the clean room.

. . . . . . . . . . . . . . . . . . .

88

Figure 4.12: The 3-in-1 diagnostic drive to be installed at FP1, assembled in the
clean room. From left to right: BCM, Faraday cup, and viewer plate
(uncoated). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

Figure 4.13: A P22 coat on the Viewer2 plate before installation.

. . . . . . . . .

89

Figure 4.14: Viewer1 installed and inserted in the beamline.

. . . . . . . . . . .

89

Figure 4.15: FC1 suppression voltage test. . . . . . . . . . . . . . . . . . . . . . .

90

xii

Figure 4.16: Viewer image analysis process. Left: CCD image of the image with
light on to find scale from the 5 mm dot markings. Center: Raw
TIFF image of the beam from CCD. Right: Background subtracted
beam image with the red lines marking the beam spot center, and
red dots indicating the center with 5 mm distance between each dot.
In this image, each pixel corresponds to approximately 0.15 mm.
.

Figure 4.17: Viewer image analysis at FP1: Red lines indicate beam center as
calculated from the median of the distribution, blue dashed lines in-
dicate the width in the x-direction defined as ±1σ. The locations are
indicated in pixels, and the scale is 5 mm to 16 pixels. . . . . . . . .

Figure 4.18: Top: Normalized currents on the left side (blue) and right side (or-
ange) as a function of time. The point where they cross is the center
region of the BCM. The uncertainty on the measurements is shown in
the shaded region. Bottom: Ratio of left current to right current on
the BCM. It should be equal to 1 when the beam crosses the center
of the BCM.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.19: Final results showing the left side current (blue) and right side current
(orange) as a function of dipole current. The shaded region of over-
lapping blue and orange between 110.67 and 110.71 A is the region
when the beam was centered. . . . . . . . . . . . . . . . . . . . . . .

92

93

95

95

Figure 5.1:

(a): SECAR layout with notable diagnostics used for tuning, includ-
ing the upstream ReA3 beamline with the two steerer sets used for
correcting the incoming angle. The first set is 7.2 m away from the
(b):
first SECAR quadrupole, and the two sets are 1.8 m apart.
JENSA viewer and slits used in the manual tuning procedure.
. . . 100

Figure 5.2: B1 - B2 dipole scan in steps of 0.06 A on FP1 to minimize steering
in Q3 - Q5. The steering does not reach zero in this case, and this
may be due to small deviations of the beam from the center that are
not corrected at FP1. Fine tuning downstream where sensitivity to
such small deviations is increased is often needed.

. . . . . . . . . . 105

Figure 5.3: B1 - B2 dipole scan in steps of 0.02 A on FP1 to minimize steering

in Q3/Q4.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Figure 5.4: WF1 dipole magnet scan to minimize steering in Q8 and Q9 measured
at D1688. The best field corresponding to the beam leaving the WF
at the center is shown by the red dashed line. . . . . . . . . . . . . . 107

Figure 5.5: Conditional probability of x2 given x1.

. . . . . . . . . . . . . . . . 111

xiii

Figure 5.6: The effect of the lengthscale hyperparameter on the SE kernel from
Equation 5.8 for (cid:96) = 0.2, 1, 2. For each hyperparameter value, the
function kSE = (0, x) is shown on the left and random samples from
the Gaussian process prior are shown on the right.

. . . . . . . . . . 115

Figure 5.7:

Sampling of an observation at the viewer. Four images taken at differ-
ent quadrupole tunes are shown with the beam center location with
respect to the central red dot in mm. The mean steering distance
between the four beam spots is 4.7 mm. . . . . . . . . . . . . . . . . 122

Figure 5.8: The posterior mean (left), standard deviation of the mean (middle)
and acquisition function (right) for three different 2D steerer opti-
mization runs. The observations are shown in the first left and mid-
dle columns by dots shaded by time of observation, with the darkest
shade of red being the most recent observation. The next sample
point is shown in the right column by the white cross indicating the
minimum of the acquisition function. The most recent mean value
for for lengthscale and noise variance priors are noted for each, as
well as the exploration weight used.

. . . . . . . . . . . . . . . . . . 127

Figure 5.9: Best steering distance reached as a function of number of GP iter-
ations, for 2D (vertical) and 4D optimizations during two different
beam commissioning runs.

. . . . . . . . . . . . . . . . . . . . . . . 128

Figure 5.10: Beam spot steering at FP1 before (a - d) and after (e - h) optimization
of the beam angle for a 4D run with a 20Ne beam. The steering
decreased from an average of 7 mm to an average of 0.2 mm. All axes
are in pixels, and 16 pixels correspond to 5 mm.

. . . . . . . . . . . 130

Figure 5.11:

(a) Nominal and (b) after the GP optimization at FP2 for the 133Cs
commissioning run. Red dots indicate 5 mm. X-axis scale is in pixels,
where 31 pixels is 5 mm.

. . . . . . . . . . . . . . . . . . . . . . . . 137

Figure 5.12: Minimum of the objective function defined in Equation 5.23, reached

as a function of number of GP iterations, for 8D and 9D optimizations.138

Figure 5.13: The 20Ne beam ± 1σ widths within the energy acceptance. Scale is

31 pixels to 5 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Figure 6.1: Effect of the beam energy spread on the maximum yield and on the
mid-point of the rise plotted for a resonance energy of 991.86 keV/u
(left) and 1799.75 keV/u (right). The energy at the mid-point is
shown in dashed lines at the different energy spreads.

. . . . . . . . 145

xiv

Figure 6.2:

JENSA drive setup as used for the dipole calibration runs showing
from left to right: Al target foil on 4 × 4 mm slit, empty 4 × 4 mm
slit, empty 1.5 × 1.5 mm slit, viewer (slanted at a 45° angle). In this
image, the drive is retracted out of the beam’s path.

. . . . . . . . 146

Figure 6.3:

Setup of the 14 BGO array used for the dipole calibration runs. The
flange is mounted on the JENSA chamber.

. . . . . . . . . . . . . . 147

Figure 6.4:

Scaling of two different target run beam currents using background
current readings, within error bars.

. . . . . . . . . . . . . . . . . . 153

Figure 6.5: B1 - B2 dipole scan on FP1 to minimize steering in Q3 - Q5. The
error on the steering distance is calculated from a 1.5 pixel error on
each beam spot location measurement. The dashed line indicates the
region where the best field value lies.

. . . . . . . . . . . . . . . . . 155

Figure 6.6: BGO array spectra of all runs scanning the 1800 keV/u resonance
with H2 beam. The incoming beam energy Ep corresponds to the
ReA3 energies reported. From left to right, the resonant contribution
of 27Al(p,p’)27Al at 844 and 1015 keV, the 27Al(p,α)24Mg peak at
1369 keV, and the 27Al(p,γ)28Si peak at 1779 keV are seen.

. . . . 156

Figure 6.7: The 1779 keV peak at the Ep = 1800 keV/u resonance with a Gaus-
sian (green) and a exponential (magenta) plus constant (cyan) back-
ground fits. On the left is the (p,α) peak with a Gaussian fit (blue).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Figure 6.8: The 27Al(p,γ)28Si resonance at 992 keV/u with an H+

2 beam. The
solid curve is the theoretical yield fit to the data. The dark gray
shaded area indicates the region of the magnetic field at ER within
the statistical error of the fit. The light gray shaded area is the total
error.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Figure 6.9: The 27Al(p,γ)28Si resonance at 992 keV/u with an H+ beam. . . . . 162

Figure 6.10: The 27Al(p,γ)28Si resonance at 1800 keV/u with an H+

2 beam.

. . . 162

Figure 6.11: The 27Al(p,γ)28Si resonance at 1800 keV/u with an H+ beam.

. . . 163

Figure 6.12: Calibration fit to the fields at the resonance energies and their cor-
responding errors and residuals. The slope is the dipole calibration
factor k.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

xv

Figure 6.13: Projected energy of a 20Ne8+ beam over the B range in keV (top)

and its projected error in keV (middle) and percent (bottom).

. . . 166

Figure 6.14: The difference between the reported energy (∆E/E ∼ 0.25%) at the

mid-point of each scanned curve and the known resonance energy.

. 167

Figure 6.15: Relativistic calibration fit to the fields at the resonance energies and

their corresponding errors and residuals. . . . . . . . . . . . . . . . . 169

Figure 6.16: Projected E∗ of a 20Ne8+ beam over the B range (top), its projected

error (middle), and percent error (bottom).

. . . . . . . . . . . . . . 170

Figure 6.17: The relativistic kinetic energy KE (top), the non-relativistic kinetic
energy KE0 (middle), and their ratio with its error shown with the
shaded region (bottom) for a 20Ne8+ beam over the B range.

. . . . 171

xvi

LIST OF ALGORITHMS

Algorithm 1: General Bayesian optimization algorithm for SECAR tuning. .

.

.

. 120

xvii

Chapter 1

Introduction

1.1 Motivation

The SEparator for CApture Reactions (SECAR) [6] at the National Superconducting Cy-

clotron Laboratory (NSCL) and the Facility for Rare Isotope Beams (FRIB) was designed

for precise and direct measurements of reaction rates relevant to the explosive synthesis of

elements in astrophysical sites such as X-ray bursts and novae, namely proton and α-capture

reactions on proton-rich radioactive nuclei. The present work focuses on the commissioning

of the device, a first step to developing the experimental approach and establishing device

operations to achieve the scientific goals.

As SECAR is a precision device, much of this work was dedicated to characterize the

system and define operational approaches that ensure adequate performance. In the initial

stages of the commissioning, a significant effort was made to define the beam properties and

initial conditions that need to be met at the start of each experiment to optimize SECAR

operations, and to implement the necessary diagnostics. To address challenges related to

the complexity of the system, tuning procedures were developed and ultimately improved

by implementing autonomous and machine learning (ML) based algorithms to achieve the

necessary reproducibility and precision. At the same time this novel approach reduces setup

and tuning time significantly enabling more efficient use of the system by future users.

This work presents a working concept of an ML-based online tuning method that can be

1

improved as needed to further optimize the performance of SECAR. The approach will

also be applicable to other ion optical devices and beamlines. Finally, the first two bending

magnets were calibrated to facilitate independent measurements of the incoming beam energy

in SECAR when measuring narrow resonant reactions that require precise knowledge of the

beam energy.

Ultimately this work paves the way for SECAR to achieve its scientific goals. Crucial to

understanding stellar explosions, accurate thermonuclear reaction rates will be determined

with SECAR. These determinations will help address the origin of the elements, use X-ray

bursts as probes of dense matter in neutron stars, and answer the many open questions

related to nova explosions that occur on the surface of accreting white dwarfs.

In the following section, the astrophysical motivation behind the study of radiative cap-

ture reactions is presented. An introduction to the inverse kinematics method and to recoil

separators employed in the direct measurement of radiative capture rates follows in in Sec-

tion 1.3. SECAR properties are introduced in Section 1.4, followed by an overview of the

ML tuning optimization in Section 1.5.

In Chapter 2, an overview of stellar reaction rate theory and its application in direct

resonant capture rate measurements is given. In Chapter 3, the SECAR recoil separator is

presented in detail, including its beamline components and ion optical design. The com-

missioning and testing of its beamline devices, namely magnets and diagnostic devices, is

presented in Chapter 4. Chapter 5 discusses the development of manual and autonomous

ML-based tuning methods. Finally in Chapter 6, the energy calibration of the first two

SECAR bending magnets is presented.

2

1.2

Importance of Radiative Capture Reactions

The many elements making up the universe were synthesized in various ways. The Big Bang

is responsible for light elements such as hydrogen, helium and lithium [27]. After the Big

Bang, a high abundance of hydrogen and helium was left over in the cosmos, enriching stellar

environments. This led to the majority of the rest of the elements being formed through

burning processes in stars, the latter harnessing their energy from such fusion reactions.

Most of hydrogen burning occurs inside stars during the hydrostatic equilibrium phase.

Fusion of light isotopes into heavier isotopes generates the energy necessary to maintain the

thermal pressure crucial to balancing the gravitational force. The two main processes that

can dominate hydrogen fusion at this stage are the pp-chain (for lower mass stars such as the

Sun), and the CNO-cycle (for higher mass stars that reach higher core temperatures). As a

star evolves, helium accumulates from hydrogen burning, however initially the core does not

reach a hot enough temperature to ignite helium fusion. Depending on the star’s mass, He

burning starts via the 3-α-process either explosively with a flash as the star leaves the red

giant branch, or as the core gradually reaches He burning temperature for heavier stars. The

H and He nuclei present in the outer layers of a star remain abundant as the temperatures

are not high enough to initiate burning even in massive stars during the final supernova

explosion. However, many stars are in binary systems. Once one of the stars has ended

its evolution and formed a compact remnant such as a white dwarf or a neutron star, these

compact remnants can accrete the outer layers of a companion star. The accreted matter

is compressed and heated on their surface, igniting explosive hydrogen and helium burning

at much higher temperatures and densities than encountered during hydrostatic hydrogen

or helium burning. These thermonuclear runaway events are observed as X-ray bursts and

3

novae in the case of neutron stars and white dwarfs, respectively, and constitute sites of

hot and and dense degenerate matter. In these high temperature and density environments,

radiative capture reactions of proton and α nuclei involve proton-rich heavy nuclei away from

stability.

These radiative capture processes are defined as two-body fusion reactions in stellar

plasma where a proton or α particle captures a heavier nucleus to form a new nucleus. In

a resonant capture, the nucleus and the captured particle form a compound nucleus in an

excited state that subsequently emits γ-rays to finally end up in its ground or stable state.

In the case of direct capture, a γ-ray is directly emitted in the capture process populating

a final state. If the final state is an excited state, subsequent γ-rays are emitted as in the

resonant capture. Stellar reaction rates typically have contributions from narrow and broad

resonances as well as direct capture reactions.

To determine the isotopes created and understand the physics behind X-ray bursts and

novae, these events must be modeled using reliable nuclear reaction data to enable valid com-

parisons to observations [76]. When reactions rates are known, comparisons between X-ray

burst models and observations can be used as probes of neutron star properties such as mass

and radius, e.g. see [38, 68, 100]. In addition to addressing questions regarding the outburst

mechanism itself, novae studies can shed light on some Galactic chemical abundances that

are believed to have some nova origins such as 7Li, the short-lived isotopes 22Na and 26Al,

and some CNO isotopes, particularly 15N and 17O [54].

1.2.1 Radiative Capture Reactions in X-ray bursts

The most frequently observable explosions in the galaxy, Type-I X-ray bursts, are flashes

on the surface of accreting neutron stars in low mass binary systems, recurring on a scale

4

of hours to days. First discovered in 1976 [5, 41], they are among the brightest and most

common thermonuclear explosions with about 60 galactic bursting systems known today.

For a review of X-ray bursts and their observables, see [60, 61, 78]. X-ray bursts provide

an excellent probing tool of compact neutron stars and the properties of matter under such

extreme conditions. System parameters such as mass accretion rate, accreted abundances of

hydrogen, helium, and CNO metals strongly affect the bursts’ observable parameters pro-

viding an avenue to constrain these parameters through observations if the nuclear reactions

are understood [8].

X-ray bursts are powered by three mechanisms, the 3-α-process, the αp-process, and

hydrogen burning via the rp-process until peak temperatures up to 2 GK are reached [85,97].

The thermal runaway lasts between 10 s up to 100 s. The rp-process dominates energy

generation at late times and plays a significant role in determining the light curve tail of the

burst. The nucleosynthesis via the rp-process at these high temperatures goes up to 56Ni and

beyond within the timescale of the bursts and reaches an end point at the Sn-Sb-Te cycle [84].

Beyond Fe, waiting-points created by long-lived β-decays at 64Ge, 68Se, 72Kr, and 104Sn can

slow the process down and extend the energy release of the burst, leading to a duration of

100 - 300 s. These findings were based on one-zone model calculations [84] that include

the full rp-process network. Subsequent one-dimensional multi-zone calculations performed

with the full rp-process have confirmed previous studies and provided new insight on ignition

conditions and hydrogen burning between bursts [99]. The ultimate test for these models

remains direct comparisons to observations [25] which demands accurate nuclear physics

input.

Most of the nuclei participating in the rp-process are unstable. In addition to proton

capture rates, their nuclear masses and β-decay half-lives are among the important nuclear

5

physics pieces that are crucial to building an accurate model. The instability of the isotopes

involved makes experiments challenging. Nevertheless, advances in radioactive beam facili-

ties have led to experimental determinations of the β-decay half-lives and most of the masses.

Measurements of proton capture rates on unstable nuclei are particularly challenging, lead-

ing to the dependence of stellar models on theoretical models to provide astrophysical rates

for key reactions. Methods such as Hauser-Feshbach and shell model calculations are widely

used [35, 45], however uncertainties can be a factor of 2 - 3 up to many orders of magnitude

for rates that depend on a few isolated resonances [20,50,80]. Experimental efforts involving

indirect methods [2,7] are important when the radioactive beam in need is not yet available,

when the resonances are too weak, or when the resonance energies are too uncertain. These

methods can reduce uncertainties by providing information about the properties of the nu-

clei involved, but in many cases the uncertainties are still too large. To obtain sufficiently

accurate reaction rates for rp-process models, direct measurement are required. Given that

the majority of the isotopes involved are radioactive, such measurements necessitate the use

of inverse kinematics. This technique is employed in recoil separators such as SECAR, and

will be explained in detail in Section 1.3.2.

Several sensitivity studies have identified the reactions that have the most effect on the

light curve of X-ray bursts and should therefore be the focus of direct experimental ef-

forts [26, 28, 36, 37, 55, 75, 93, 99].

In these studies, reaction rates are varied individually

within their large uncertainties, and the subsequent effects on the light curve and the com-

position are examined to identify critical reactions. The first study to use fully self-consistent

one-zone and multi-zone 1D models of X-ray bursts [26] highlighted reactions that impact

the burst light curve and the ashes composition the most. The majority of those reactions

are (α, γ) and (p, γ) radiative capture reactions, emphasizing the importance and necessity

6

of addressing these uncertainties with direct measurements at radioactive beam facilities.

Some of the high impact reactions common for one-zone and multi-zone models that had

changes in rates large enough to affect the interpretation of observational data themselves

include 15O(α,γ)19Ne, 59Cu(p,γ)60Zn, 61Ga(p,γ)62Ge, and 23Al(p,γ)24Si. SECAR repre-

sents a targeted approach to reduce the uncertainties and enable direct measurements of

these rates and arrive at a better understanding of the underlying physics of X-ray bursts

and ultimately, of neutron stars.

1.2.2 Radiative Capture Reactions in Novae

Classical novae are stellar explosions that occur in interacting binary systems where a com-

pact white dwarf star accretes proton rich matter from a low-mass main sequence compan-

ion [11]. The proton rich matter accumulates on top of the white dwarf and is gradually

compressed up to degenerate conditions, eventually leading to a thermonuclear runaway with

temperatures not exceeding 0.4 GK. This phenomena is the second most common type of

thermonuclear explosion in the galaxy after X-ray bursts, and is recurrent with a period

of 104 - 105 years [98]. Observational properties of novae include the light curve showing

the luminosity versus time in optical light, infrared radiation to study dust formation, and

spectra in optical, ultraviolet and infrared reflecting the abundances of chemical species in

the ejecta.

In this hydrogen rich environment, the most important reactions involve protons due to

the comparably small Coulomb barriers to overcome. The predominant nuclear reactions

that contribute to the runaway are (p,γ) or (p,α) operating within the mass region of A

< 40. The runaway is initiated by pp-chain fusion and also involves the hot CNO cycle.

Later stages of the explosion are partially powered by proton capture reactions on neon

7

that is mixed in from the white dwarf in some novae, and by the decay of the resulting

radioactive isotopes. The nuclear reaction pathway lies between the line of stable nuclei and

the proton drip line and involves stable and unstable nuclei. Masses, β-decay half lives and

reaction rates of such isotopes are thus crucial to modeling these outbursts. Comprehensive

sensitivity studies have been carried out [49] and important radiative capture reactions have

been identified.

Recent experimental measurements have focused on many of the isotopes that were shown

to play a significant role in the outburst. The remaining gaps in knowledge are mainly due

to inadequate beam intensities, leaving critical rates still uncertain such as 30P(p,γ)31S and

25Al(p,γ)26Si. The former rate is critical for the production of elements between mass 30

and 40, and determines the Si isotopic ratios that have been observed in presolar meteorite

grains with a nova origin [49, 53]. The latter is one of the remaining critical rates with a

large uncertainty that affects the synthesis of the 26Al γ emitter [44]. Constraining these

rates would answer some long-standing questions regarding novae nucleosynthesis and the

elemental abundances observed.

Given that the critical reactions relevant to novae are closer to stability than in X-ray

bursts, and thanks to the recent experimental effort at stable and radioactive beam facil-

ities, novae are on track to being the only stellar explosions with nucleosynthesis models

fully backed by experimental data [54]. Due to the scarcity of intense radioactive beams in

the past, most of the effort was directed to reactions involving stable nuclei. Only recently

have direct measurements of reactions involving radioactive isotopes relevant to novae been

enabled by recoil separators at facilities such as TRIUMF and Oak Ridge National Labo-

ratory [3, 9, 31, 40]. With recent advancements at radioactive beam facilities bringing high

intensity ion beams to nuclear astrophysics, the remaining rates in need of direct measure-

8

ments such as 30P(p,γ) and 25Al(p,γ) are within reach.

1.3 Direct Measurement of Radiative Capture Reac-

tions

While indirect methods are essential for the identification of resonances and the determi-

nation of their spins, parities, and energies, direct methods directly determine the quantity

needed to calculate the astrophysical cross sections and reaction rates at astrophysical en-

ergies. The direct measurement of capture reactions via inverse kinematics is currently in

use or proposed at radioactive facilities worldwide. This section presents an overview of

the inverse kinematics approach, delineates typical recoil separator designs and performance

metrics, and introduces the recoil separators that pioneered this method as well as those

currently available.

1.3.1 Experimental Studies

Measurements of radiative capture reactions come with several experimental complexities.

The cross sections tend to be very small at typical astrophysical energies of 0.3 - 3 MeV/u,

making their rates difficult to measure with currently available intensity beams and tradi-

tional techniques. Additionally, the involvement of many radioactive isotopes in important

radiative capture reactions make normal kinematics difficult to use as heavy radioactive iso-

topes made into a target might decay quicker than an experiment can gather sufficient data.

Another challenge is the difficulty to detect the γ-ray signature of the capture reactions with

high sensitivity due to efficiency limitations and background, including background from the

9

decay of stray radioactive beam.

As high luminosity radioactive beams become available, inverse kinematics experimental

techniques are the method of choice to directly measure capture reaction rates. In addition to

reducing beam induced background, the method allows the study of astrophysical reactions

involving short-lived isotopes that would not be possible otherwise. Devices such as recoil

separators can enable these direct measurements. SECAR at FRIB will facilitate the direct

measurements of the radiative capture reactions that answer many of the open questions

regarding the physics behind accreting neutron stars, white dwarfs, and other explosive

scenarios.

1.3.2 Inverse Kinematics

There are two methods to experimentally study nuclear reactions. One is using normal

(forward) kinematics, the other is using inverse kinematics. They simply reflect the two

possible choices of which particles are the projectiles and which are the target. Normal

kinematics is a popular configuration when proton and α-particle beams are readily available

and the target nucleus is stable, and can be easily manufactured into a suitable target. In

this configuration, a lighter beam impinges on a heavy target, resulting in heavy recoils

that stay mainly within the target while the lighter ejectiles pass through onto the detector

system. In radiative capture reactions, the ejectile is the γ-ray emitted from the capture.

For capture reactions on unstable nuclei with too short half-lives to form a target, an inverse

kinematics configuration using a light target such as proton or helium with a radioactive

beam impinging on such a gas target is the only choice.

In the center of mass reference

frame, the light particle is impinging onto the heavy nucleus against the beam direction.

The main ejectile collected is the heavy recoil, and for radiative capture, the γ-ray can also

10

Figure 1.1: Simplified illustration of resonant radiative capture in the laboratory frame.

be detected in coincidence with the heavy recoils, reducing background in the measurement.

Even for stable beams, an inverse kinematics approach can be beneficial when the isotope

abundance is small, the target has high impurities, is difficult to fabricate, or is unstable

under intense beams.

Inverse kinematics with stable beams can also be used to increase

sensitivity and reduce background, as recoil detection can produce a much cleaner signal,

especially in coincidence with reaction γ-rays.

Taking a projectile with mass m0 and momentum p0 impinging on a target with mass

m1 at rest as shown in Figure 1.1 (a), a target nuclei captures a projectile nuclei and forms a

nucleus with mass m3 in an excited state (b). The recoil can be the compound nucleus in a

resonant reaction, or the final de-excited state of a direct capture. An excited recoil decays

via emission of additional γ-rays each at some angle with respect to the beam direction.

The γ-rays carry away little momentum leaving the recoil with a momentum similar to the

incident projectile but slightly changing the recoil angle. The recoil thus emerges from the

target in a narrow cone centered on the beam direction with an opening angle that generally

depends on the beam energy and the energies of the emitted γ-rays. Figure 1.1 (c) shows

the case for a resonant capture with a single γ-ray emission with the recoil emerging at an

11

angle θ3 from the beam axis. Angular straggling in the target and the angular divergence

of the incoming beam can further broaden the angular distribution of the recoils. A recoil

separator’s purpose is to spatially separate these ions by mass with a high rejection rate

for unreacted beam particles that would otherwise overwhelm detectors and make recoil

detection impossible. The separator has to let through the full recoil cone, and ideally has to

have full transmission for recoils of a selected charge state to avoid systematic uncertainties.

The angle of the recoils is maximized when a single photon is emitted to the ground state

and is defined by the excitation energy of the compound nucleus state. Given a single photon

emitted perpendicularly to the beam direction, the maximum lab angle of the recoil θmax

and the magnitude of the momentum spread of the recoils about their central momentum

∆p/p are given in the non-relativistic approximation [83] by

∆p
p

= tan(θmax) ≈ Eγ,max

p0

(cid:112)2m0Elab

≈ Qm + Elab

(cid:113)

2

≈

Qm + E

m0
m1

(m0 + m1)E

(1.1)

where Qm is the reaction Q-value, Eγ,max is the maximum energy of the emitted γ-ray, m0

is the projectile mass, m1 is the target mass, and E is the center of mass energy. At energies

typical for astrophysical studies, the beam velocities are typically low enough that relativistic

effects can be neglected. Figure 1.2 shows the maximum recoil lab angle for several radiative

capture reactions that are of astrophysical interest for X-ray bursts, novae and supernovae

studies. Differentiating Equation 1.1 with respect to E, it is found that it has a minimum at

E = Qm. Moreover, the smaller the Q-value and the larger the ratio m0/m1, the smaller the

recoil cone, leading to smaller demands on recoil separator angular (and energy) acceptance

requirements. Taking for example a separator that is able to measure α-capture on 15O
at ECM = 0.2 MeV, an angular acceptance of at least ± 23 mrad is needed. In practice,

12

Figure 1.2: Maximum recoil half-angle in the laboratory frame as a function of the center of
mass energy for a number of reactions of astrophysical interest.

the angular straggling in the target and the incoming beam angular divergence will broaden

the recoil angular distribution and a slightly larger acceptance is needed. If more than one

γ-ray is emitted, each photon is emitted in some direction resulting in a recoil angle less

than θmax. The resulting recoil angle distribution for the reaction then has a mean angle

less than θmax.

1.3.3 Recoil Separator Design Principles

A beam impinging on a gas target undergoes atomic charge exchange reactions and capture

reactions. After the target, most of the beam emerges, together with a typically very low

rate of reaction recoils, both species with some charge state and momentum distribution.

A recoil separator aims at separating the unreacted beam and transporting the recoils for

a selected charge state to a detector station at the end of the beamline. When assessing

13

recoil separator performance, the beam suppression, defined as the ratio of the number of

projectiles incident on the target to the number reaching the final detector station, is an

important quantity. A high beam suppression allows for the utilization of more intense

beams and offers more protection for sensitive detectors. Typical suppression needed for

capture reactions is 1012, and the highest reported for radiative capture surpassed 1014 at

the 90% confidence level [90].

As seen in Section 1.3.2, a recoil separator has certain geometrical acceptance require-

ments to allow through the full recoil cone of reactions that are of interest. Moreover,

the separator needs to accommodate the momentum and energy distributions of the recoils

determined by the energies and properties of the reactions that the device aims to study.

The design requirements then include angular, energy and momentum acceptances that are

needed to directly measure those reaction rates. An ideal separator is able to transmit 100%

of the recoils for a selected charge state within those specified acceptances to avoid systematic

errors, while ensuring a high unreacted beam suppression.

To achieve an adequate amount of beam suppression, a recoil separator system combines

a separator based on ion optical elements with one or more detectors systems. The sepa-

rator itself serves to create a spacial separation between the unreacted beam particles and

the recoils, and does so through a series of charge and mass separation stages. As both

recoils and unreacted beam enter the separator with a charge state distribution, a single

charge state needs to be selected in the separator. In SECAR, this charge selection stage is

performed immediately after the target, preceding any mass selection, to reduce unreacted

beam leaking due to scattering when hitting inner chamber surfaces downstream. Movable

slits are employed at the charge focus to transmit one charge state and block the rest. More-

over, a mass separation stage with a mass dispersive focus is required to create separation

14

between the recoils and the unreacted beam of similar momentum. Slits are utilized at the

mass focus as well to block the beam and transmit the recoils. In SECAR, a second mass

separation stage is added to suppress any unreacted beam leaking through the first stage.

Along the entire separator system, focusing elements such as magnetic quadrupoles are used

to transmit the recoils and the beam and bring them to a focus.

Charge State Separation

The motion of a charged particle with charge Q in an external electric and magnetic field

E and B, respectively, is given by the non-relativistic Lorentz force equation

F = Q (E + v × B)

(1.2)

where v is the particle velocity. The magnetic rigidity of a charged particle, which quantifies

how difficult it is to bend the particle and change its trajectory in a uniform magnetic field,

is defined as

Bρ =

p
Q

(1.3)

where ρ is the radius of the particle’s circular trajectory, and p is the particle momentum.

By fixing the momentum p, separation by charge Q can be attained for a given field B.

Therefore creating momentum dispersion via magnetic dipole magnets at a focal plane where

slits are installed along the separator facilitates the selection of one charge state of the recoils.

However due to momentum conservation in a capture reaction, the recoil and the beam have

similar momentum but different velocities, making magnetic rigidity dispersion no longer

sufficient to separate all the beam from the recoils. Given the very large number of unreacted

beam leaving the target mixed with the recoils, separation by velocity is therefore critical to

suppress the beam with similar momentum and charge and achieve mass separation.

15

Mass Separation

A combination of magnetic and electric fields is necessary to achieve a mass dispersive

plane. Similarly to the magnetic rigidity, the electric rigidity is defined using Equation 1.2

given a constant electric field E

Eρ =

pv
Q

.

(1.4)

Thus for a given charge state Q, electric dipoles bend according to kinetic energy. The mass

dispersion can therefore be achieved by employing electric and magnetic bending dipole

magnets in such a way to provide zero energy dispersion at one or more foci where slits

are installed to separate out the recoils from the unreacted beam with a different mass.

Electrostatic dipoles can be used to generate electric fields, or a device combining electric

and magnetic dipoles, called a Wien filter (WF) or velocity filter, can be used instead. A WF

is a device with magnetic and electric fields perpendicular to each other on the ion optical

axis. The values of the fields are set in such a way to let particles with the selected velocity

vz equal to Ex/By pass through along the axis without deflection. This property is derived

from Equation 1.2 when the force felt by a particle with velocity v is zero. The combination of

magnetic fields and electric fields is necessary to achieve an achromatic (no energy dispersion)

focus where slits are installed to separate out the recoils from the unreacted beam with a

different mass.

Wien Filters

Several advantages come with the use of a WF instead of separate electric and magnetic

bending dipole magnets. In a WF, the ratio of electric and magnetic fields selects the velocity,

making it possible to operate with reduced field strengths to accommodate higher rigidities,

or if less rejection is required for example. This offers flexibility in the ion optics that is

16

not possible in a system with separate magnetic and electric bending dipoles where the field

strengths are fixed by the bending radii and recoil momentum. Another advantage is that

WFs can achieve high separation of particles without any bend, while separate electric and

magnetic bending dipoles require a higher bend for higher separation. It follows that beam

can be transported through a WF with the device turned off (e.g. if in a multistage system

only one mass separation stage is needed), while electric bending dipoles have to provide

the appropriate electric fields from the beam to pass through.

In SECAR, two WFs are

employed in sequential mass separation stages to achieve a higher mass separation. In both

WFs, the electric dipole is embedded in a magnetic dipole, resulting in a compact design.

To achieve the desired mass separation with a single WF, it would have to be significantly

larger in width and length. This poses multiple concerns with the space available in the

experimental hall, and other technical difficulties such as requiring an increased high volt-

age on the electrodes. While both separate electric dipoles and WFs require high voltage

conditioning, a disadvantage is introduced with WFs due to the magnetic field deflecting

electrons emitted during conditioning. This can lead to a more challenging conditioning pro-

cess. Moreover, a WF poses greater design problems. Careful shaping of both the electrodes

and the magnet poles, ensuring that the field ratio E/B remains uniform, and matching the

electric and magnetic fringe field regions are ways to minimize the design challenges that

come with WFs.

Focusing Elements

To achieve a focus at locations where slits are used for separation, and to transport

the beam through the system despite of its initial angular divergence as it exits the target,

magnetic quadrupole lenses are utilized.

Ion optical designs often set up quadrupoles in

doublets or triplets to achieve a net focusing force in the horizontal and vertical direction.

17

Since a perfect focus is difficult to achieve with only quadrupoles, additional higher-order

elements are needed. Quadrupoles can introduce spherical aberrations and coma aberrations

where the beam spot may be sharp in the center but become increasingly blurred toward

the edges. These can be corrected by insertion of hexapole and octupole magnets at defined

locations based on the ion optical design.

An ion optical design forming a proper combination of all these optical elements to

provide adequate mass separation is combined with recoils detectors at a final focal plane

to count the recoils transported to the end of the separator. The detectors can also be used

to identify and separate recoils from unsuppressed beam, e.g. by energy loss, energy, and

time-of-flight measurements. Additionally, γ-ray detectors can be placed at the target to

detect γ-ray emissions from the capture reactions in coincidence with the recoil counting to

further suppress background. The final beam suppression of the system is a combination of

the separator suppression from the mass separation and the suppression provided from the

detector systems. A recoil separator is characterized by its beam suppression capability, its

energy, angular and rigidity acceptances, as well as its mass resolving power, a concept that

will be introduced in Chapter 3 where the ion optics of such a device is explained in more

detail.

1.3.4 Previous Recoil Separators

In this section, an overview of early recoil separators and current separators at stable beam

and radioactive beam facilities is presented with a focus on systems designed or re-purposed

for studying reactions relevant to nuclear astrophysics. The different separators have unique

designs in how electromagnetic elements are combined, and the choice of targets, γ-array

detectors and focal plane detectors. Such choices are made based on the precision, and

18

the angular and energy acceptances required for the reactions planned for each scientific

program. Although beam suppression reported varied with beam energies and conditions, the

descriptions below offer a general comparison of the overall performance and achievements

of the different systems and highlights the novel opportunities that SECAR will bring to the

community as the first recoil separator to be optimized for high masses.

Caltech Recoil Separator

The concept of a recoil separator for astrophysical reaction rate measurements was first

realized at the California Institute of Technology (Caltech) in the 1980’s. The pioneering

experiment by Kremer et al. [58] measuring the cross section of 12C(α, γ)16O at low energies

served as proof of concept of the inverse kinematics technique to reduce background by

employing coincidences between γ-ray emissions and recoil particles. The effectiveness of a

recoil separator for direct measurements at radioactive beam facilities was further explored

a few years later by Smith et al. [91]. The system used a heavy ion beam with a windowless

differentially pumped gas target, and utilized a quadrupole to focus the beam after the

target. A WF served to separate the recoils with slits stopping the beam particles. A charge

state was subsequently selected by a magnetic dipole, leading the recoils and remaining leaky

beam particles into the focal plane detector system. An array of four large NaI scintillators

was detecting γ-rays at the target in coincidence. Beam suppression with this system was

shown to be up to 1010.

ERNA at Bochum

The European Recoil separator for Nuclear Astrophysics (ERNA) was installed at the

Bochum Dynamitron Tandem accelerator laboratory to measure low energy reactions with

stable beams in inverse kinematics. It has been used to measure 12C(α, γ)16O [29] and other

astrophysically relevant reactions at low energies. ERNA was built using components from

19

the Caltech separator with additional quadrupoles and an extra WF. The separator uses a

WF to create a mass separation, then selects a single charge state using a single magnetic

dipole, followed by a second WF before transporting the recoils to the focal plane.

It is

combined with an extended gas target. The full system has shown beam suppression of 1010

- 1012, surpassing the Caltech separator due to the early selection of a single charge state

before the use of the second WF that is set up directly upstream of the focal plane [81].

ARES at Louvain-la-Neuve

The Astrophysics Recoil Separator (ARES) was designed for proton and α-capture mea-

surements in inverse kinematics at the Cyclotron Research Center at Louvain-la-Neuve in

Belgium.

It utilized a CH2 plastic foil hydrogen target instead of a gas target, and fol-

lowed previous improvements shown in ERNA by creating a charge separation first using a

magnetic dipole then using a WF to separate the recoils by velocity. The facility’s beam

properties included a large emittance that prevented the quantification of the separator’s

acceptance [1]. The system was used to measure 19F(p, γ)20Ne in inverse kinematics and

resulted in a beam suppression of 107 due to the use of a foil target and to the beam qual-

ity [22]. Another measurement was attempted, of a 19Ne(p, γ)20Na resonance at 448 keV,

however no recoils were detected and an upper limit on the resonance was established [21].

No further ARES measurements were done.

DRS at ORNL

The Daresbury Recoil Separator (DRS), initially designed for measurements of fusion

evaporation reactions in nuclear structure research, was re-purposed to study capture re-

actions relevant to the explosive hot CNO cycles upon moving from the UK to Oak Ridge

National Lab (ORNL) and the Holifield Radioactive Ion Beam Facility. The system followed

the Caltech design with a supplemental WF added before the charge selection stage. The

20

separator had a single dipole magnet, three quadrupole triplets, and two magnetic hexapoles

to provide higher-order corrections to the ion optics. It employed a windowless hydrogen gas

target, and the focal plane detectors included position detection and an ionization cham-

ber for recoil identification. The DRS was tested using stable beams and measured 17F(p,

γ)18Ne and 7Be(p, γ)8B [4, 15]. The beam suppression was of order 109 - 1011.

DRAGON at TRIUMF

The Detector for Recoils And Gammas Of Nuclear reactions (DRAGON) was designed to

study proton and α-capture reactions relevant to classical novae and type-I X-ray bursts using

radioactive beams at the ISAC facility at TRIUMF. The device uses two magnetic dipoles and

two electrostatic dipoles for its momentum and energy selection, with an extended windowless

proton or He gas target. The system is optimized for isotopes up to mass 30. The design

was chosen to accommodate the measurement of 15O(α, γ)19Ne at ECM = 0.5 MeV which
requires a minimum acceptance of ∼ 16 mrad (see Figure 1.2). DRAGON was thus designed
with a moderately large angular acceptance of ± 21 mrad to account for a slightly broader
angular distribution and with an energy acceptance of ± 4% [47]. The first experiment was a

direct measurement of the 21Na(p,γ)22Mg reaction [31,34]. The suppression of the separator

alone is on the order 109 - 1013 [90]. A γ-array comprised of bismuth germanate (BGO)

crystals coupled with the recoil detection in coincidence increases the suppression by up to 3

orders of magnitude. DRAGON has been successfully measuring reactions with stable and

radioactive beam, including high mass measurements such as 58Ni(p,γ)59Cr demonstrating

its capabilities beyond its initial design limits [89].

St. George at the University of Notre Dame

The Strong Gradient Electromagnetic Online Recoil separator for capture Gamma-ray

Experiments (St. George) is a recoil separator at the Institute for Structure and Nuclear

21

Astrophysics at the University of Notre Dame designed for the study of astrophysical low

energy (α, γ) reactions for stable beams with mass up to A = 40 [23]. The separator has
design acceptance values of ±40 mrad in angle and ± 7.5% in energy [69], and consists of

six dipole magnets, eleven quadrupole magnets, and one WF. It utilizes the HIPPO (High-

Pressure Point-like target) supersonic gas jet target [57]. The system was designed to provide

a beam suppression of at least 1015. A first detection of 18F recoils from the 14N(α,γ)18F

was recently made with the St. George separator [72].

1.4 SECAR at FRIB and NSCL

SECAR is optimized for proton- and α-capture reactions for explosive nucleosynthesis using

radioactive beams up A = 65. The device’s design is based on the St. George separator with

an additional Wien filter [6]. The JENSA gas jet target [17] is used with SECAR combined

with an array of BGO crystals for γ-ray coincidence measurements with focal plane detectors

that include time-of-flight, silicon and ionization chamber detectors. An additional extended

proton or He gas windowless gas target will be available when resonance energies are not

precisely known. SECAR will operate in the 0.2 - 3 MeV center of mass energy range and
is designed to have an energy acceptance of ± 3.1% and an angular acceptance of ± 25

mrad to accommodate for large recoil cones as seen in the case of 15O(α, γ)19Ne (Figure

1.2). It is designed to provide a separator beam suppression of 1013 with an additional 104

contribution from the recoil detector system.

22

1.5 Machine Learning for Tuning Optimization

To achieve precision measurements, SECAR creates separation between unreacted beam and

recoil particle of different mass but similar momentum by bringing the latter to a focus in

two mass-dispersed planes along the separator. The separation goals require a carefully

tuned recoil beam that is centered along the separator’s ion optical axis, and finely tuned

quadrupole fields to maximize the mass resolution and unreacted beam suppression of the

device. This is achieved by tuning and establishing precise beam optics of a pilot beam prior

to scaling to the recoil rigidity settings.

As the pilot beam is transported along the accelerator facility to the recoil separator,

beam parameters such as energy spread, angular deviation, and size of the beam impinging

on the target can be adjusted. Precise beam characteristics need to be achieved to fulfill the

initial conditions required to ensure a centered and focused beam at the target. Obtaining a

centered beam (< 1 mrad deviation from the central axis) has proven to be difficult and time

consuming, as is discussed in detail in Chapter 5. Additionally within SECAR, quadrupole

settings need to be tuned to obtain an optimized separation at the mass-dispersive plane

thereby maximizing SECAR’s performance. The process of manual adjustments and itera-

tions to achieve such beam properties can significantly increase the device’s setup and tuning

time. Tasks such as visual checks of tune quality can be operator dependent, introducing

subjectivity and bias to the process and leaving the device below optimal performance and in

a possibly irreproducible state. A more robust solution is achieved with an automated tune

optimizer that enhances reproducibility, ensures objectivity when assessing tune quality, and

operates with an efficiency that surpasses the speed of manual tuning when searching for the

optimal parameters to achieve SECAR performance targets for each experiment.

23

Machine learning model-dependent optimization methods have been successfully applied

in other facilities to automate the tuning and controls of complex accelerators, for example at

the Linac Coherent Light Source free-electron laser at SLAC to tune quadrupole settings [30,

67] and at the Central Laser Facility to create the first autonomous laser wakefield accelerator

[87]. The use of Bayesian optimization [13, 86] in the tuning of a complex beamline is in

some cases motivated by the assumption that the function f being minimized or maximized

(e.g. beam size or transmission as a function of machine settings) is expensive to evaluate

due to computational limits of beam simulation codes, or due to the time consuming task of

operator-dependent machine adjustments until a suitable tune is found or until the changes

take effect. In the case of SECAR, beam physics simulations incorporating the accelerator

beamline upstream cannot be expected to have the required accuracy to provide an optimized

experimental system, and manually tuning the beam to achieve precise beam properties has

proven to be time consuming and unreliable. Given the high dimensionality of the system,

a robust optimization of the experimental system is needed to validate and improve on the

theoretical tune parameters obtained from beam simulations. With a proper model of the

beam response in SECAR to changes in beamline parameters (magnet settings in SECAR

and upstream), a Bayesian approach presents a good choice for addressing these issues while

decreasing the time spent tuning and providing reproducible results.

In this work, a first application of a Bayesian optimization with a Gaussian process model

[79] to the online beam tuning and ion optics optimization of a nuclear astrophysics recoil

separator is reported. The stringent requirements defined as the optimal beam conditions

for SECAR operation are guided by the ion optical design discussed in Chapter 3. Manual

and Bayesian tuning methods are presented in detail in Chapter 5 and the ML algorithm’s

ability to achieve those requirements while improving on traditional methods is examined.

24

Chapter 2

Experimental Determination of

Astrophysical Stellar Rates

2.1 Stellar Reaction Rates

In astrophysical models of stellar environments, one needs to provide the rate r of a nuclear

reaction between two particles

r =

NtNp vσ(v)

(1 + δtp)

,

(2.1)

where Nt and Np are the number densities of the target (t) and the projectile (p) particles,

respectively, v is the relative velocity of the two particles, σ(v) is the nuclear cross section,

and δtp is the Kronecker symbol. This rate represents the number of reactions per second per

volume of stellar plasma. When the plasma is at thermodynamic equilibrium, the relative

velocity v is not constant, rather there is a broad distribution of relative velocities. It can

be shown that the relative velocity between two particles in stellar plasma can be generally

described by the Maxwell-Boltzmann formalism [19, 48], and its probability distribution for

a certain temperature T can be written as

P (v)dv =

2πkbT

−µptv2/(2kbT ) 4πv2 dv,
e

(2.2)

(cid:16) µtp

(cid:17)3/2

25

where µtp is the reduced mass, kb is the Boltzmann constant, and T is the temperature. Fold-

ing the cross section with the velocity distribution of the reacting particles and generalizing,

one obtains

with

r =

NtNp < σv >

(1 + δtp)

(cid:90) ∞

0

< σv > =

P (v) vσ(v) dv.

(2.3)

(2.4)

With E = µtpv2/2 and dE = µtpvdv, the velocity distribution can be written as an

energy distribution

P (E)dE =

2√
π (kbT )3/2

√

E e−E/kbT dE.

(2.5)

The broad energy distribution in stellar plasma plays into the reaction rate by introducing

an energy-temperature dependence term. The reaction rate in stellar environments is then

defined in terms of the energy dependent cross section as follows

E σ(E) e−E/kbT dE.

(2.6)

(cid:115)

< σv > =

(cid:90) ∞

8

1

πµtp

(kbT )3/2

0

The reaction rate describes the number of reactions within a given volume per unit time in

terms of the cross section σ(E). As charged particles are interacting, this cross section drops

off by orders of magnitude as the energy decreases due to the repulsion from the Coulomb

barrier. Describing the cross section only in terms of its energy-dependent component and

removing the trivial contribution from the Coulomb repulsion, the astrophysical S-factor

26

S(E) can be defined as

σ(E) ≡ 1
E

e−2πη S(E),

with the Sommerfeld parameter η defined as

η =

ZpZte2



(cid:114) µtp

2E

,

(2.7)

(2.8)

where Zt and Zp as the charge states of the interacting particles. The Gamow factor e−2πη

is an approximation for the s-wave transmission probability at energies below the height of

the Coulomb barrier. Consequently the S-factor is smooth-varying and has a much reduced

energy dependence compared to the cross section. To obtain the reaction rate, one must

experimentally obtain S(E), and therefore σ(E), over the relevant energy range defined by

the temperature in stellar interiors.

The reaction rate is most sensitive to the cross section at energies that are within the

Gamow energy distribution. This energy distribution at a certain temperature T can be

approximated by a Gaussian peak, with the peak central energy, the Gamow energy, given

by

(cid:17)2

(cid:104)(cid:16) π



(ZtZpe2)2(cid:16) µtp

2

(cid:17)

(kbT )2(cid:105)1/3

,

EGamow =

and Gamow peak width, called the Gamow window, given by

(cid:112)EGamowkbT .

∆Gamow =

4√
3

(2.9)

(2.10)

Figure 2.1 illustrates the Gamow window for an arbitrary reaction. For non-resonant reac-

tions, the direct capture reaction rate can be obtained by extrapolation of the experimentally

27

Figure 2.1: Maxwell-Boltzmann factor (dashed line) and Gamow factor (dotted line) versus
energy for an arbitrary temperature T. The product e−kbT e−2πη, representing the Gamow
peak, is shown with the solid line.

determined S-factor S(E) to lower energy ranges guided by the Gamow window.

The S-factor, and therefore the cross section, typically have contributions from narrow

and broad resonances and non-resonant reactions. Resonances can dominate the astrophys-

ical reaction rate due to their higher cross section even when the resonance energy falls

outside of the Gamow window. Isolated and narrow resonances, defined in more detail in

Section 2.2 are the focus of this work. The reaction rate can be simplified when narrow res-

onant contributions dominate, and can be obtained by determining the experimental yield

and consequently, the strength of the resonance, as is detailed in the following sections.

2.2 Narrow Resonances

In explosive astrophysical sites, reaction rates are often dominated by resonant contributions.

When two nuclei undergo a resonant capture reaction, the compound nucleus is formed at

28

a specific excitation energy that is the sum of the beam energy and reaction Q-value Qm.

If this energy matches the energy of an excited state with excitation energy Ex within its

energy width, the cross section can be significantly enhanced. This resonant enhancement

occurs when

Ex ∼ Ecm + Qm

(2.11)

where Qm is the mass excess and Ecm is the relative energy, which can be written as the

resonance energy ER. An isolated resonance implies a small enough level density in the

compound nucleus to avoid significant overlap between resonances. A narrow resonance

is defined as a resonance whose width is approximately constant over the total resonance

width. The single-level Breit-Wigner formalism can be used to describe with a semi-classical

approach the resonant behavior between two particles [10], and the cross section for a given

isolated resonance can be expressed as [48]

σBW (E) =

λ2
4π

ΓinΓout

(ER − E)2 + Γ2/4

ω

(2.12)

where the Broglie wavelength is λ = 2π/(cid:112)2µtpE. The second term is dependent on the

partial widths of the entrance Γin and exit Γout channels and gives the cross section its

Lorentzian shape with a FWHM of the total width of the resonance Γ and a maximum at

ER. The statistical factor ω accounts for the number of possible states in the compound

nucleus compared to the number of states in the entrance channel. This factor can be

expressed as

ω =

2J + 1

(2Jp + 1)(2Jt + 1)

(1 + δp,t),

(2.13)

29

where Jp and Jt are the incoming spins of the projectile and target, respectively, and J is the

angular momentum of the excited state Ex. An additional term containing the Kronecker

delta is included to avoid the double counting of identical particles in the entrance channel.

Therefore the probability of finding the compound nucleus in a state Ex with a specific J

out of 2J+1 possibilities and finding the projectile and target in specific Jp and Jt out of all

the possibilities allowed in the entrance channel is given by this spin statistical factor ω.

Quantum mechanical selection rules govern the the resonant behavior for different chan-

nels. The spin and parity of the nuclear states allowed are determined by the selection rules

involving the spin and angular momentum

|(cid:96)p − Jp − Jt| ≤ J ≤ |(cid:96)p + Jp + Jt|

and the parity

π(J) = π(Jp)π(Jt)(−1)(cid:96)p

(2.14)

(2.15)

where (cid:96)p is the orbital angular momentum of the projectile and π(J), π(Jp), and π(Jt) are

the parities of the resonant state, the projectile, and the target, respectively. In the single-

level Breit-Wigner formalism, it is assumed that the resonance levels of a given angular

momentum J and parity π(J) are widely spaced compared to their total widths.

In explosive hydrogen burning, proton- and α-capture reactions are often dominated by

narrow resonances.

It is assumed that for a sufficiently narrow resonance, the Maxwell-

Boltzmann factor e−E/kT and the partial widths of the entrance and exit channels Γin and

Γout are approximately constant over the total width of the resonance Γ. Taking these

quantities as their constant values at the resonance energy ER, the resulting integral over

the cross section can then be carried out analytically to get the astrophysical reaction rate

30

and one obtains for a single narrow resonance

< σv > =

=

=

√

2π2

(µtpkbT )3/2
√

2π2

(µtpkbT )3/2

(cid:16) 2π

µtpkbT

The resonance strength is defined as

ωγ ≡ ω

ΓinΓout

Γ

.

(cid:90) ∞

ω

0

ΓinΓout

(ER − E)2 + Γ2/4

e−E/kbT dE

ΓinΓout

e−ER/kbT ω 2π

(cid:17)3/2 2e−ER/kbT ωγ.

Γ

(2.16)

(2.17)

It can be seen from Equation 2.16 that once the resonance strength is known, the astrophys-

ical reaction rate can be determined. If several narrow and isolated resonances contribute

to the cross section, Equation 2.16 can be modified to incoherently sum over the individual

states with different resonance energies and strengths.

2.3 Narrow Resonance Yields

The astrophysical thermonuclear reaction rate from narrow resonances is solely determined

by the resonance strengths. The resonance strength of an individual resonance can be directly

determined with a single experimental measurement using a target that is thick enough to

allow for an energy loss that is much greater than the width of the resonance, while still

being low enough to avoid contributions from any lower lying resonances. Using this method,

the experimentally determined yield Yexp can be directly related to the resonance strength.
The yield is defined as the ratio of the total number of nuclear reactions that occurred Nr

31

and the total number of incident beam particles Np,

Yexp ≡ NrNp

.

(2.18)

To relate this yield to the cross section, two quantities need to be defined. The stopping

power describes the energy loss dE of the beam per distance dx travelled in the target per

target nucleus


(E) ≡ − 1
N

dE
dx

(2.19)

where N is the number density of the target and is related to the concentration of the target

nuclei by

n ≡ N d =

Nt
A

.

(2.20)

Here Nt denotes the total number of target nuclei in atoms per unit volume, d is the target

thickness in units of length, and n is the number target nuclei per unit area. The stopping

power is in units of eV cm2/atom, and all quantities are assumed to be determined in the

center of mass system.

Consider a beam of energy E0 is incident on a target that can be divided into slices of

thickness ∆xi. The energy lost by the beam in each slice is then ∆Ei and is assumed to be

small. The cross section σi and the stopping power 
i are then taken to be constant over

∆xi. The partial yield over ∆xi can then be written as

∆Yi = σiNi∆xi.

(2.21)

Integrating over the entire target and using the stopping power definition from Equation

32

2.19, the total yield is expressed as

Y (E0) =

(cid:90) E0

E0−∆E

σ(E)

(E)

dE

(2.22)

where ∆E is the total energy loss in the target. For narrow resonances, the Breit-Wigner

resonance σ, the stopping power 
, the de Broglie wavelength λ, and the partial widths Γi are

all assumed to be independent of energy and therefore constant over the resonance width.

Substituting Equation 2.12 for the cross section in Equation 2.22, taking the constant terms

out and integrating, an expression for the yield for a narrow isolated resonance is obtained

(cid:90) E0

Y (E0) =

=

=


(E)

1

ω

λ2
4π

(cid:90) E0
(cid:16)E0 − ER

E0−∆E

atan

Γ/2

E0−∆E
λ2
ωγ
R
2π

R
λ2
ωγ
R
2π

R

Γ
2

(cid:104)

ΓinΓout

(ER − E)2 + Γ2/4

(ER − E)2 + Γ2/4

dE

(cid:17) − atan

(cid:16)E0 − ER − ∆E

Γ/2

(2.23)

(cid:17)(cid:105)

.

The quantities λR and 
R denote the de Broglie wavelength and the stopping power at

the resonance energy ER, respectively. From this expression, it can be deduced [48] that the

value of the maximum of the yield is

Ymax =

λ2
R
π

ωγ

R

(cid:16)∆E

Γ

atan

and the FWHM of the resonance yield curve is

F W HM =

Γ2 + ∆E2.

(cid:112)

33

(cid:17)

(2.24)

(2.25)

The beam energy at the maximum yield E0,max and at one half of the maximum yield E0,50%

are

and

E0,max = ER +

∆E
2

E0,50% = ER +

∆E
2

± 1
2

(cid:112)

Γ2 + ∆E2.

(2.26)

(2.27)

For a thin target where ∆E << Γ, the shape of the yield curve is Lorentzian following the
cross section, and the maximum is located approximately at the resonance energy E0,max ∼
ER and the FWHM ≈ Γ. If the target thickness is much larger than the total resonance

width, ∆E >> Γ, the yield curve takes on an atan function shape as the atan term dominates.
A flat top is seen where the energy is E0,max = ER + ∆E/2 and the FWHM ≈ ∆E. As

∆E increases, Ymax and the FWHM increase as the cross section is integrated over a larger
region. For an infinitely thick target where ∆E −→ ∞, the atan term in Equation 2.24 is

equal to π/2, and the beam energy at 50% yield is then simply equal to the resonance energy

ER.

For a thick target, the energy loss ∆E will be much greater than the width Γ of the narrow

resonance, and the FWHM of the yield curve will simply be equivalent to ∆E, namely the

width of the target in energy units. The thicker the target, the closer the yield becomes

that of an infinitely thick target. For instance, a target thickness that is equal to the total

resonance width ∆E/Γ = 1 reaches 50% of the maximum yield of an infinitely thick target
and FWHM/∆ ≈ 0.5. Increasing that thickness to 10 times larger than the total resonance
width ∆E/Γ = 10 brings it up to 94% with a FWHM ≈ ∆E within 0.5% [48].

In addition to the target thickness, the beam energy spread and straggling can influence

the general shape of the resonance yield curve [48]. To take these effects into account, a

34

Figure 2.2: Yield curve normalized to Ymax for a thick target based on Equation 2.29 with
a small beam energy spread δ = 0.005%.

Gaussian term of the form

g(E − E0) =

1√
2πδ

e

− (E−E0)2

2δ2

(2.28)

where E0 is the mean energy of the incoming beam and δ is the beam energy spread is

defined. It follows that the final form of the yield over the entire target is

(cid:90) ∞

(cid:104)

Y (E0) =

λ2
R
2π

ωγ

R

0

atan

(cid:16) E − ER

(cid:17) − atan

Γ/2

(cid:16)E − ER − ∆E

(cid:17)(cid:105)

Γ/2

g(E − E0) dE.

(2.29)

Figure 2.2 shows a typical yield curve for a target that is sufficiently thick to include the

narrow resonance. The maximum yield is determined from differentiating Equation 2.29 and

can be directly related to the resonance strength. For an infinitely thick target, it is no

longer affected by the total resonance width and matches Equation 2.24 with the atan term

35

equal to π/2:

Ymax =

λ2
R
2

ωγ

R

.

(2.30)

Therefore, a single measurement of the yield at an energy within the plateau region of the

yield curve allows the determination of the resonance strength and therefore the determina-

tion of the astrophysical reaction rate contribution of the resonance.

Given a direct measurement, e.g. from a recoil separator, the total experimental yield is

given by

Yexp =

NrNp

N

Npηυτ

=

(2.31)

where N is the total number of detected recoils, η is the detection efficiency, υ is the selected

recoil charge state fraction for transmission, and τ is the transmission efficiency. For γ-

coincidence detection, the γ-detection efficiency will depend on γ-ray branching and angular

distributions. All measurements of resonance strengths require knowledge of the number

of beam particles incident on the target, Np. This quantity is typically determined by

measuring and integrating the incoming ion beam current continuously when no significant

losses are expected at the target as such

Np =

(cid:90) I

Qe

dt,

(2.32)

where I is the electrical beam current (e.g. as measured by a Faraday cup), Q is the charge

state of the beam ions delivered by the accelerator facility, and e is the elementary charge. In

inverse kinematics, as recoil separators are designed to transmit only recoils, elastic scattering

of beam ions on the gas target can be used to achieve beam normalization. Elastic scattering

monitors in the target chamber are planned for SECAR. In this case, the normalization factor

36

can be determined by taking the ratio of the beam current reading upstream of the target

chamber and the number of elastically scattered target particles detected. To measure the

charge state fraction transmitted in the recoil separator, a comparison of the absolute beam

current readings between a Faraday cup upstream of the target and a cup located just after

the charge selection in the recoil separator must be made.

Using the maximum yield Ymax given in Equation 2.30 for an infinitely thick target, the

resonance strength is calculated as

ωγexp =

NmaxNpηυτ

.

2
R
λ2
R

(2.33)

37

Chapter 3

SECAR Design and Experimental

Setup

3.1 The NSCL and ReA3 Facility

The NSCL, located on MSU’s campus, is a facility dedicated to the production of rare iso-

tope beams via projectile fragmentation to investigate the properties of nuclei and nuclear

reactions. Stable beams are accelerated to 80 - 160 MeV/u by two coupled superconducting

cyclotrons (K500 and K1200), also known as the Coupled Cyclotron Facility (CCF), and

fragmented on a solid target. The resulting cocktail of rare isotopes gets separated in the

A1900 achromatic fragment separator, and the fragments of interest are delivered to any of

the multiple experimental halls for nuclear physics research. While these fast rare isotope

beams can be used to investigate nuclear structure and some reaction properties, the study

of reactions relevant to astrophysical scenarios require low energy beams. To achieve that,

the fast beams are stopped in a He gas cell, re-extracted, and transported to the electron

beam ion trap (EBIT) for charge state breeding. Subsequently, the charged ions are ex-

tracted from the breeder and transported into an achromatic charge state (Q/A) separator

where the desired charge state is selected before the beam enters the accelerator section.

The re-accelerator includes a room temperature RFQ and a superconducting LINAC. The

combination of the gas-stopper cell and the re-accelerator (ReA3) is unique to the NSCL

38

and provides energies ranging from 300 keV/u to up to 6 MeV/u depending on the charge-

to-mass ratio. The ReA3 facility includes beam distribution lines that consist of two high

resolution achromatic sections with slit systems that can be used to limit the beam energy

spread. The beam can be transported from the accelerator to one of three target stations in

the ReA3 experimental hall, one of which is a dedicated SECAR experimental line.

The CCF was shut down on November 15 2020 preceding the reconfiguration of the A1900

in anticipation of the completion of FRIB. In this work, only stable beams produced at the

ReA3 facility were utilized for the purpose of the commissioning of SECAR.

3.2 The FRIB Facility

FRIB, currently under construction on MSU campus, will be the world’s leading rare isotope

and low energy nuclear science facility when it becomes operational in 2022. FRIB will

replace the CCF facility with a new 200 MeV/u LINAC, significantly increasing the variety

and intensity of rare isotope beams available. The short-lived species are produced by

fragmentation in a new high power target station, separated in a new fragment separator,

and then fed into the existing NSCL beam transport system, including the existing gas

stopper and ReA3 re-accelerator.

The beam species anticipated at FRIB overlap well with the proton-rich unstable nuclei

that play a major role in thermonuclear runaways occurring at astrophysical sites such as

novae and X-ray bursts. Once the facility is completed, the ReA3 facility will stop and re-

accelerate the fast beams produced by FRIB and transport them to the different end-stations

in the ReA3 Hall for low energy nuclear structure and reaction studies, including scientific

experiments with SECAR. SECAR was designed to utilize the high intensity radioactive

39

Figure 3.1: The SECAR recoil separator layout in the ReA3 Hall at MSU. The beam enters
the hall from the middle left into the JENSA gas jet target system, and the capture reaction
recoils along with the unreacted projectiles enter the first section in SECAR that selects a
single charge state. Two subsequent sections each including a velocity filter (WF1, WF2)
serve to reject the remaining projectiles, and the final cleanup section features a final pair
of dipoles before particles enter the focal plane detection system.

beams available at ReA3 and FRIB by providing direct measurements of capture reactions

that such isotopes undergo at low astrophysical energies.

3.3 The SECAR Design

SECAR was designed to simultaneously achieve high transmission of capture reaction recoils

and a high rejection of unreacted projectiles. The design consists of eight dipole magnets,

15 quadrupole magnets, three hexapole magnets, one octupole magnet and two WFs. The

complete layout of the system in the ReA3 Hall is shown in Figure 3.1, and Figures 3.2 and

3.3 show the beamline after installation. The ion optical design consists of four sections with

a focal plane at the end of each. The sections are described below.

40

Figure 3.2: SECAR in the ReA3 Hall showing B1 up to Hex3.

Figure 3.3: SECAR in the ReA3 Hall showing B5 up to the final focal plane.

41

WF1B1   B2Hex1   Q3 Q4Q5B3  B4Hex2Q6Hex3B5    B6WF2FP3FP4B7   B8Q12 Q13Q14Q15Q10  Q11Section 1: Charge State Selection

This section starts at the target up to the first focal plane (FP1) that is located imme-

diately downstream of Q5. The beam projectiles arriving at the target have a single charge

state. As the beam particles pass through the gaseous target, charge changing processes

such as ionization, excitation, and radiative and non-radiative electron capture take place

and cause multiple charge states to be produced. The variation of charge state fractions

versus charge state is called the charge state distribution of the beam. In this section, a

single charge state (the most abundant) is selected for the recoils and unreacted beam. The

quadrupoles in the first section of SECAR serve to refocus the diverging trajectories of par-

ticles exiting the target back towards the optical axis of the SECAR beamline. The first

two dipoles B1 and B2 provide the momentum dispersion required to select a charge state.

Separation by magnetic rigidity (refer to Equation 6.1) using the magnetic field generated by

B1 and B2 leads to the recoils and beam of different charge states to be focused at different

positions at FP1. The dipoles are used to center the desired charge state on the magnetic

axis, and the slits at FP1 are moved to create a gap width that transmits the recoils and un-

reacted beam at that charge state while suppressing the remainder of the beam and recoils,

eliminating about half of the unreacted projectiles. Higher order aberrations are corrected

by specially designed shapes of the entrance and exit pole faces of the dipole magnets. An

adjustable hexapole magnet in the first quadrupole (Q1Hex) along with a separate hexapole

magnet (Hex1) were included for flexible corrections of second order terms that might result

from imprecision in the higher order corrections from the dipoles. The Q1 magnet has a

combined design where the quadrupole (Q1), hexapole (Q1Hex), and a correcting dipole

(Q1Dipole) component can be set separately via independent power supplies. After setting

Q1Hex for second order corrections, Q1Dipole is set accordingly to compensate for the dipole

42

effect introduced.

Section 2: Mass Separation and Projectile Rejection

The section from FP1 to first mass dispersive focus (FP2, located right before Q8) serves

to separate the unreacted beam from the recoils that have similar momentum to charge ratios.

In capture reactions, the emitted γ-rays carry off little momentum, leaving the recoils and

beam particles with very similar momenta. The recoil will have a greater mass (by 1 amu

for proton capture, 4 amu for α capture) and therefore a slightly lower velocity than the

unreacted beam. The velocity filter WF1 in this section serves to separate these recoils

from the beam. The values of the E and B fields in the WF are set in such a way to let

recoils with the selected velocity v be equal to E/B pass through along the axis. Due to the

momentum spread of the beam, the combination of magnetic dipoles and the WF creates an

achromatic (no energy dispersion) focus at FP2 and is crucial to separate the particles by

mass. The movable slits installed at this location are closed around the mass focused recoil

to selectively stop the deflected beam. The magnets before and after WF1, quadrupoles Q6

and Q7 and hexapoles Hex2 and Hex3 along with the octupole Oct1, serve to optimize the

mass separation in WF1, correct for higher order aberrations, and provide focus at FP2.

Section 3: Second Mass Separation and Projectile Rejection

This section extends from FP2 to the second mass dispersive focus (FP3, located right

before Q12). It has a similar setup and function as Section 2, adding another two magnetic

bending dipoles along with a second velocity filter (WF2) that is identical to WF1 with a mass

focus at FP3 where movable slits serve to suppress the beam and only transmit the recoils

with the desired mass. This second WF separation section provides an improvement on the

unreacted beam suppression by increasing the mass resolution. It also provides additional

suppression of the leaky beam that could arise from scattering and charge-changing reactions

43

along the beamline and especially within WF1.

Section 4: Cleanup and Recoil Detection

The section between FP3 up to the final detector station (FP4) provides a momentum

analysis through B7 and B8 to clean up any remaining projectiles that have undergone one

or multiple scattering reactions and no longer have the same momentum as the recoils. With

that background reduced, the remaining particles are transported through the final detec-

tion area where a time-of-flight measurement is used to identify them. The final stopping

detectors will further identify and count the particles making it to FP4, adding a suppression

of 104 against background particles. The particles can also be detected in coincidence with

γ-ray detection at the target. More details describing these detectors is provided in Sections

3.6.1 and 3.6.2.

3.3.1 Design Properties

The properties of the SECAR recoil separator as designed for a broad range of capture

reactions [6] are summarized in Table 3.1. The design limits were chosen to provide optimal

measurements of the extreme cases of reactions of interest that are relevant to novae and

X-ray bursts which involve isotopes with masses up to A = 65 and atomic numbers up to Z

= 33. The center of mass energy range of interest is determined by the temperature of the

astrophysical environment, around 0.1 - 0.4 GK for novae and 0.2 - 3 GK for X-ray bursts.

The peak and width of the Gamow energy distributions corresponding to these temperatures

can be obtained using Equations 2.9 and 2.10, respectively, for proton capture on targets

with Z = 8 - 33 to find that the range of interest spans 0.2 to 3 MeV. This range dictated the

SECAR system’s design parameters, including the magnetic and electric rigidity limits and

the maximum high voltage needed in the WFs, using a number of reactions of astrophysical

44

Property

Mass Range

CM Energy Range

Rejection by Separator
Rejection by Detectors

Angular Acceptance
Energy Acceptance

Magnetic Rigidity Range
Electric Rigidity Range

Value for Optimal Separator Function

15 - 65 amu
0.2 - 3 MeV

10-13
10-4

± 25 mrad
± 3.1 %

0.14 - 0.8 Tm
1.25 - 19 MV

Table 3.1: SECAR separator properties for optimized direct measurements of p- and α-
capture reactions on unstable proton-heavy nuclei.

interest and assuming a probable optimal charge state.

In particular, the 15O(α, γ)19Ne

reaction at ECM = 0.5 MeV with a recoil charge Q = 3 established the lower limits on

magnetic and electric rigidity, while 65As(p, γ)66Se reaction at ECM = 3 MeV with a recoil

charge Q = 21 determined the upper limits. For a background free measurement during

a two week experiment at maximum beam intensity of 1011, the rejection requirement for

SECAR is 10-13 with an additional rejection of about 10-4 from the detection system for a

total of 10-17. The recoil energy spread is typically small for most of measurements, and is
designed to be up to ± 3.1% based on the extreme case of 15O(α,γ)19Ne. The maximum
angular acceptance of ± 25 mrad was adapted from the 15O(α,γ) at ECM = 0.5 MeV as well,

as it presents the largest scattering angle of the sampled reactions of interest (see Figure

1.2), with additional consideration to account for broadening of the angular range from beam

spot effects.

3.3.2 Ion Optical Design

Beam optics describe the effect of electric and magnetic fields on moving charged particles.

These particles can be focused and directed by these fields produced by different electromag-

netic elements such as dipoles and quadrupoles. The trajectory and behavior of such particles

45

moving through a system of these elements can be modeled and optimized to transport a

beam of particles with certain properties to a desired point along the beamline. SECAR is

the result of an ion optical design that was developed to meet the design requirements listed

in Table 3.1. In a recoil separator, the beam spot at different focal planes is important for

the beam suppression of the device. For SECAR, these are FP1 for charge state separation,

and FP2 and FP3 for mass separation. The ion optical code COSY INFINITY (v. 9.1) [64]

was used to define the foci characteristics and design the separator [6].

In this thesis, the standard coordinate system defined in COSY will be used: the x-axis

is perpendicular to the left and the y-axis is perpendicular up with respect to the beam axis.

The distance measurements in COSY are in meters. The parameters a and b are defined as

the angles of the ion velocity towards the x and y axis, respectively, in radian. The t, d, g,

and z parameters are the fractional time, energy, mass and charge difference compared to a

reference particle’s mean value, respectively. A transfer matrix can written to describe these

beam parameters in first order at a given focal plane j, given the parameters at an initial

plane i as such





x

a

y

b

t

d

g

z



(x|x)
(a|x)
(y|x)
(b|x)
(t|x)
(d|x)
(g|x)
(z|x)

(x|a)
(a|a)
(y|a)
(b|a)
(t|a)
(d|a)
(g|a)
(z|a)

(x|y)
(a|y)
(y|y)
(b|y)
(t|y)
(d|y)
(g|y)
(z|y)

(x|b)
(a|b)
(y|b)
(b|b)
(t|b)
(d|b)
(g|b)
(z|b)



(x|z)
(a|z)
(y|z)
(b|z)
(t|z)
(d|z)
(g|z)
(z|z)

j





x

a

y

b

t

d

g

z

i

(x|d)
(a|d)
(y|d)
(b|d)
(t|d)
(d|d)
(g|d)
(z|d)

(x|g)
(a|g)
(y|g)
(b|g)
(t|g)
(d|g)
(g|g)
(z|g)

(x|t)
(a|t)
(y|t)
(b|t)
(t|t)
(d|t)
(g|t)
(z|t)

46

.

(3.1)

=

j

Each matrix element (m|n) refers to the effect on m given the value of n at the initial
location. For example, the first element is the linear magnification denoted as (x|x) and
signifies the position x at location j given the initial value of x at i. Similarly, (x|z) describes

the particle’s distance x from the beam center at location j depending on its initial relative

charge z = dQ/Q at the plane i. Therefore given the initial beam parameters at the target,

the deflection of the unreacted beam from the central heavy recoils can be calculated to first

order at any plane by

x = (x|x)x0 + (x|a)a0 + (x|d)d + (x|g)g

(3.2)

where x0 is the initial beam position, a0 is the initial angular deviation in x, d is the energy

dispersion and g is the mass dispersion.

In a recoil separator, a mass dispersive focus is necessary in at least one location to

separate the unreacted beam from the recoils. The former is then suppressed using movable
slits. At a mass dispersive plane, the mass dispersion element (x|g) can not be equal to zero,
while the energy dispersion (x|d) is required to be zero, and (x|x) and (x|a) should be as
small as possible. Ideally, (x|a) is zero for a focus in the x-direction. The magnification term
(x|x) is always a constant, and a magnification greater than 1 indicates a spot larger than

the spot at the target. The mass separation properties of the separator are determined by
the mass dispersion (x|g), and a large value leads to a large separation between unreacted

particles and the recoils. The first order mass resolving power is defined as

Rm =

(x|g)
2x0(x|x)

47

(3.3)

where 2x0 is the full object size (spot size at the target). The mass resolution of the device
is defined similarly by replacing the first order image size 2x0(x|x) by the real object size

calculated by including the higher order aberrations.

To determine the best design for SECAR, ion optical calculations up to fourth order

were included in the design of the transport matrix, and from that the electromagnetic

elements, their properties and their specific order in the beamline were determined. For that

calculation, the following initialization of the beam properties at the target were set:

x0 = ± 0.75 mm
a0 = ± 25 mrad
y0 = ± 0.75 mm
b0 = ± 25 mrad
d0 = ± 3.1 %,

where the x and y spot sizes correspond to the anticipated 1.5 mm beam diameter size

delivered at the target from the ReA3 accelerator. The design of the elements and the

beamline followed from this optimization [6]. Figure 3.4 displays 99 characteristics rays in

the horizontal and vertical planes in the upper and lower panel, respectively, outlining the

full SECAR ion optical profile from a COSY calculation for the edge case of a 65As(p,γ)66Se

reaction at Bρ = 0.8 Tm. The characteristic rays were defined within an ellipsoid of phase

space given by the SECAR properties of maximum angular acceptance in the x- and y-
direction of ± 25 mrad, and a maximum energy deviation from the recoil energy of the
central ray of ± 3.1 %. Each section described in Section 3.3 is marked with a different

color and the foci can be seen at the end of each. Looking at the charge state selection

(section 1) and the first mass selection (section 2) only, Figure 3.5 shows additional rays to

further clarify the design separation properties. The red rays represent a case of an adjacent

48

charge state (δQ/Q =1/21) that is well separated at FP1. The blue rays correspond to the

unreacted beam of similar rigidity as the recoils that gets separated by mass. The system has
an achromatic focus where (x|d) = 0, (a|d) = 0 and (x|a) = 0 at FP2 and a zero dispersion
focus (x|d) = 0 at FP3. It is estimated to have a mass resolving power at the first mass

separation section FP2 of Rm = 740 and a resolution of 508. The second mass separation

section at FP3 provides a mass resolving power of Rm = 1300 and a resolution of 767. It
should be noted that the final detector plane FP4 is not a real ion optical focus (i.e. (x|a)

is not zero), but rather a location with a narrowed beam envelope where the beam size is

reduced sufficiently in horizontal and vertical direction to match the size of the focal plane

detectors along the entire length of the focal plane setup.

The dispersive elements, dipoles and WFs, serve to achieve the charge and mass dispersion

at the focal planes. The dipole magnets all are designed to have a bending radius of 1.25

m and a maximum field in the good field region (GFR) of 0.64 T. The bending angle varies

for each section and is 22.5 degrees for B1 - B4, 42.5 degrees for B5 and B6, and 55 degrees

for B7 and B8. The WFs are identical and have a GFR horizontal electrode gap of 22 cm,

a GFR vertical gap of 7 cm, a bending radius of 7 m, and the high voltage applied to the
electrodes can reach ± 300 kV for a maximum electric field of 2.73 kV/mm between the two

electrodes.

The COSY tune determined from these calculations was used in this work as the starting

point for all SECAR commissioning runs. The pole tip fields for all of the quadrupoles,

hexapoles and the octupole for a Bρ = 0.8 Tm is given in Table 3.2. The field settings

for the beams used in all runs in this work were determined by appropriately scaling the

optimized settings by the ratio of magnetic rigidities. Note that Q1 is a magnet with 3

components: a quadrupole component Q1, a hexapole component Q1Hex, and a dipole com-

49

(a)

(b)

Figure 3.4: The ion optics of SECAR for the layout explained in Section 3.3 corrected up to
fourth order. The four sections are shown in different colors. Traces of rays in the horizontal
(a) and vertical (b) planes are shown.

50

Figure 3.5: Example COSY INFINITY ion optics calculation up to the first mass separation
slits of a 65As(p,γ)66Se reaction in the x-plane. The Se recoils are shown in black, unreacted
As beam of similar Bρ is shown in blue, and a beam of a nearby charge state is shown in
red (δQ/Q =1/21).

51

66Se21+ 3.12 MeV/uΔQ/Q=1/21Unreacted 65As21+Charge selection Mass SelectionSlits ponent Q1Dipole. The Q1Hex strength is determined and scaled from the COSY simulation

value, while the Q1Dipole field is set as 28% of the scaled Q1Hex field strength. This stems

from the fact that activation of the hexapole will produce a steering of the beam owing to

the intrinsic dipole component of the forces. The dipole component is a result of the magnet

design and needs to be compensated. Since the COSY command defining the Q1 magnet

only includes higher order corrections such as the Q1Hex component, Q1Dipole is scaled

directly from that and does not go into the COSY definition of Q1. Higher order corrections

for other quadrupoles are not included in this table. In this theoretically optimized setup

at the maximum design rigidity of 0.8 Tm, the dipole magnets with bending radius of 1.25

m require fields of 0.64 T (the design maximum field of these magnets), and the optimum
settings of the WFs are 0.1143 T for the magnetic field and ± 308.3 kV for the high voltage

on the electrodes (E = 2.80 kV/mm).

To practically achieve a separation close to the COSY predictions, the experimental

beam parameters need to be as close as possible to the theoretical beam parameters set in

the COSY simulation. To that end, a set of stringent requirements, summarized in Table

3.3, were established as the optimal beam conditions for all SECAR beam runs in this work.

In Chapter 5, tuning procedures developed to achieve these requirement are discussed in

detail.

3.4 Beam Diagnostics

Tuning a complex system such as SECAR would not be possible without diagnostic equip-

ment installed along the beamline. In addition to aiding in tuning, devices such as slits serve

to suppress unwanted beam when positioned correctly. Figure 3.6 presents all diagnostic

52

Magnet B (T)

Q1

Q1Hex

Q1Dipole

Q2
Hex1
Q3
Q4
Q5
Hex2
Q6
Q7
Hex3
Oct1
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15

-0.39773
0.00468
0.00131
0.21935
0.01031
0.24287
-0.24756
0.11239
0.01051
0.18163
-0.03002
-0.00837
0.031283
-0.14822
0.23438
-0.03367
0.16158
-0.18200
0.19100
0.12900
-0.13800

Table 3.2: Pole tip magnetic fields for COSY INFINITY nominal tune at 0.8 Tm used in
this work.

Property

Beam size at target

Beam angular deviation
Beam width at mass slits
Transmission to final focus

Requirement
1.5 × 1.5 mm
0 - 2.5 mrad
minimized

100%

Table 3.3: Beam requirements for optimal recoil separation in SECAR.

53

Figure 3.6: Diagnostics along the SECAR beamline.

devices installed or planned to be installed in SECAR. All these devices are mounted on

isolated linear motor drives and thus can be positioned in or out of the beam’s path. Some

devices are mounted on the same drive for convenience, such as the 3-in-1 device at FP1

which includes the Faraday cup FC2, the viewer Viewer2 and the beam centering monitor

BCM1.

Faraday cups (FCs) are common diagnostic devices that consist of a voltage suppressed

beam stop that delivers a full absolute current measurement. They are the main current

measurement tool used to evaluate beam transmission along the beamline. All SECAR

cups consist of three electrically isolated parts: the cup itself, the suppression plate, and

an unsuppressed aperture, as seen in Figure 3.7. A high voltage bias is applied to the

54

Viewer 2Faraday Cup 2X Slits 1BCM 10° CameraViewer 1Collimator 1Faraday Cup 1Faraday Cup 3Viewer 3Faraday Cup 4X, Y Slits 2Viewer 4Viewer 5X Slits 3Faraday Cup 5Y Slits 3BCM 3Viewer 6Viewer 7Faraday Cup 6X Slits 4Figure 3.7: Faraday cup design for SECAR (left). Cup design in 3-in-1 device at FP1 (right).

suppression plate to suppress secondary electron emissions induced by the collision of beam

particles with the collector that can cause inaccurate measurements. The cups are designed
to have a 1 pA sensitivity (∼ 106 pps) and an electron suppression that provides a 1%

current reading accuracy. Each cup is connected to a CAEN TetrAMM picoammeter device

dedicated to accurate and fast low current measurements. The TetrAMMs are 4-channel 24

bit with an internal sampling rate of 100 kHz per channel. A configurable averaging rate

of the sampled data can be set to reduce the transmission data rate, reduce high frequency

noise and increase the signal-to-noise ratio. This rate must set to be a multiple of the EBIT

beam pulse period for accurate measurements. The device provides two standard measuring
ranges, ± 120 nA (15 fA resolution) or ± 120 µA (15 pA resolution). It also includes a low-

noise integrated bias voltage source (up to -500 V) that is used to provide the bias voltage

for the FCs and is generally set to -200 V.

While the FC serves to provide a complete measurement of the beam current hitting it,

the beam centering monitor (BCM) was designed to use current measurements as a tool to

center the beam. Since 100% transmission of a selected recoil charge state is necessary, the

centering of the pilot beam is crucial as any small misalignment will be magnified significantly

55

SuppressorCollectorCollectorSuppressorApertureBCMApertureViewerFigure 3.8: BCM design for SECAR shown on 3-in-1 device at FP1. Aluminum nitride
(AIN) ceramic plate serves to electrically isolate the plates.

at the final focal plane 40 m downstream. Made up of four identical electrically isolated

square plates as shown in Figure 3.8, the BCM reads four currents proportionally equal

to the amount of beam hitting each plate. The BCM current readings are sampled by a

TetrAMM device as well (described above). In order to center the beam, operators move

the beam in such a way to equalize the current readings over all four plates. For accurate

centering, the BCM must be well aligned with the ion optical axis of SECAR.

The slits offer an additional way to center the beam. When set to a small opening around

the center position, the beam can be centered in the direction perpendicular to the gap by

maximizing transmission. In addition, current is read from the slit blades, and balancing the

current provides an alternative approach for centering provided the beam is larger than the

slit gap. Monitoring transmission and blade currents while changing the gap size can provide

information on the shape of the beam spot. The slits, similarly to the BCM, are unsuppressed

and therefore are limited in their sensitivity compared to the Faraday cups. All slit systems

installed in SECAR are movable across the center, and each plate is independently controlled

providing the ability to create an asymmetric gap. Each system consists of two plates that

are slightly offset, allowing a small overlap to be able to completely block the beam without

56

AlN Plate4x Current Wire Attachments4x BCM PlatesBellow WeldmentFaraday CupWire Platethe plates colliding.

Some form of imaging diagnostic is often added to beamlines at different positions to aid

in tuning. In SECAR, viewers consisting of a copper plate coated with fluorescent phospho-
rus (P22) inserted at 45◦ in the beamline, along with a CCD camera installed perpendicular

to it, are used to image the beam location and shape at seven locations. The fluorescence

is dependent on the beam intensity, and beam attenuation is often necessary to avoid de-

struction of the coating material. The attenuation strength is adjusted based on the beam

intensity to reach currents that the viewer can withstand, typically in the 0.1 - 1 pA range.

The installation, testing and commissioning of the BCM, viewer and Faraday cup devices

are described in Chapter 4 (Subsection 4.3.1). The 0-degree camera and the collimator were

not yet installed during the commissioning presented in this work. The camera will be

mounted in a zero degree port of the first dipole to provide images of the beam at the

target, and the collimator will be installed between Q1 and Q2. Once available, they will

be integrated into the tuning procedures discussed in Chapter 5, and will serve to aid in the

centering of the beam along the optical axis of the beamline.

3.5 Gas Target Systems

To measure (p,γ) and (α,γ) capture reactions in inverse kinematics with SECAR, a hy-

drogen or helium target is needed. Solid targets come with several disadvantages, such as

degradation over time due to beam exposure, contamination buildup, and background from

reactions on other target components. Gas targets can eliminate some of these problems

while introducing others. For example, a gas cell’s thin windows can affect angular strag-

gling and energy resolution, which can be detrimental for low energy capture measurements,

57

and static gas targets can degrade with beam exposure. For these reasons, SECAR was de-

signed to employ a windowless gas target system. In the following subsections, the two main

windowless gas targets to be used with SECAR are introduced: a gas jet and an extended

gas cell.

3.5.1 JENSA Target System

The Jet Experiments in Nuclear Structure and Astrophysics (JENSA) is a windowless,

differentially-pumped recirculating gas jet target system that was initially constructed and
commissioned at ORNL [17]. It has an areal density up to 9 × 1018 atoms/cm2, a narrow jet

diameter of around 4 mm, and provides high purity and high stability gas jets. This target is

sufficiently thick to provide a yield curve with a plateau for narrow resonance measurements

as discussed in Chapter 2. Additionally since the target is localized, it provides a precise

location for reactions and effectively creates a point source along the ion optical axis for the

recoils entering SECAR, matching the requirements of the ion optical design. Along with

being immune to beam degradation, the gas is recycled in the system further minimizing gas

use and losses.

JENSA’s design involves a de Laval nozzle (or convergent-divergent nozzle) to create

the supersonic jet. A de Laval nozzle is a tube that is pinched in the middle, making

an asymmetrical hourglass shape, used as a means of accelerating the flow of gas passing

through it. Below the nozzle, two closely matched concentric cone-shaped receivers collect

the expanding gas flowing out of the nozzle. The receivers are pumped by a a series of high-

throughput roots blowers and multi-stage roots pumps to generate constant air compression

and exhaust into a high-throughput diaphragm compressor. The compressor operates with

an inlet pressure as low as 1 atm and can maintain a maximum pressure up to 30 atm

58

Figure 3.9: CAD drawing of JENSA chamber and its differential pumping components. The
distance from the target location to the end of the final downstream pumping stage is 73
cm. Beam direction is right to left.

to produce the jet. Figure 3.9 shows a CAD drawing of the differential pumping system.

There are four pumping stages upstream of the central chamber and four downstream, each

separated by a gas-flow limiting aperture and equipped with a turbomolecular pump. The

central chamber shows the nozzle and receivers. Any gas escaping from the receiver through

the aperture is pumped by the turbo pumps.

Different de Laval nozzle designs with varying internal diameters can be used along with

varying opening diameters of the receivers to control the amount of gas that is not collected

by the system and escapes into the rest of the chamber. The installation of one of those

nozzles along with the receivers in the ReA3 Hall is shown in Figure 3.10, and Figure 3.11

59

Figure 3.10: The JENSA nozzle and receiver installed in the ReA3 Hall. Beam direction is
right to left.

shows a drawing of the installation upstream of SECAR, including the JENSA compressor

and its pumping system.

A reduction in the pressure to the order of 10-6 Torr is achieved over the gas flow limiting

apertures and pumping stages upstream and downstream of the jet. On the ReA3 side, the

aperture dimensions are large enough to accommodate the beam. The smallest aperture,
located directly upstream of the target, has a 6 mm diameter and a ± 3.4 mrad acceptance.

On the separator side, the apertures are large enough to accommodate the recoil cone. The
smallest one, installed directly downstream of the target, has a 4.5 mm diameter and a ±

32 mrad acceptance, while the aperture furthest downstream of the target (directly before
Q1) has a diameter of 33 mm and a limiting acceptance of ± 25.4 mrad, large enough to
accommodate SECAR’s ± 25 mrad design acceptance.

In this work, all experimental runs were conducted with no gas in the JENSA target.

60

Figure 3.11: JENSA gas target assembly in the ReA3 Hall upstream of SECAR. SECAR
elements up to Q5 shown. JENSA compressor shown in white on the left.

3.5.2 Extended Gas Target System

In the case of reaction measurements where the resonance energy is uncertain, it would be

difficult to ensure the resonant reaction occurs well within the target thickness. An extended

target with a length of 10 - 15 cm, combined with γ-ray detectors, is then ideal to locate

the resonant reaction and ensure it occurs fully inside the target. The exact location of the

resonance in the extended cell determines the location of where the capture reaction recoils

are generated, which will then be the ion optical object for the device.

An extended gas target system with a gas cell length of 10 cm is being designed at the

Colorado School of Mines to be used with SECAR. A drawing of the gas cell is shown in

Figure 3.12. To minimize the effect of the extended target on the mass resolution of SECAR,

the main target volume will be centered on the gas jet target location as determined by ion

optics calculations. Scintillator crystals will be installed along the length of the target to

61

Figure 3.12: Drawing of the extended gas cell designed for use with SECAR at the Colorado
School of Mines. Scale is in mm.

enable the locating and centering of a resonance with uncertain energy. More information

about the scintillator array is given in Subsection 3.6.1. The extended target will operate

with up to 10 Torr of hydrogen or helium gas. To achieve good vacuum, the setup will use a

portion of the JENSA setup such as all the upstream and downstream differential pumping

stages, and several of the roots blowers, the turbomolecular pumps and the multistage roots

backing pumps.

3.6 Detectors and Data Acquisition

To detect the various particles taking part in the reactions happening at the target, the

SECAR system employs two detector stations. The first consists of an array of scintillator

detectors installed around the target chamber to detect the emitted γ-rays from radiative

62

capture. Additionally, silicon detectors can be used in the chamber for elastic scattering

measurements, however that system is beyond the scope of this work. The second is a

system of focal plane detectors used to identify and count the various recoils and projectiles

reaching the end of the system at FP4. Together the two systems can be used in coincidence

mode to further suppress background. In this section, the two stations are described, along

with the data acquisition system used to process the signals from the detectors.

3.6.1 Gamma-Ray Detection

Due to the low number of reactions per second at astrophysical energies of interest, a highly

efficient detector system is required. To achieve that, the proper detection material must

be employed. Photon interactions with matter are fundamentally different than charged

particle interactions, and the mechanisms vary with particle energy. A γ-ray can interact

through three possible processes: the photoelectric effect dominates for low-energy γ-rays (up

to several hundred keV), Compton scattering dominates for γ-rays with more than several

hundred keV but less than 5 - 10 MeV, and pair production dominates for higher energy rays

(above 5 - 10 MeV). All of these processes may partially or fully transfer the photon energy

to an electron in the absorbing matter in a single or in multiple interactions. The cross

sections of each process is different and depends on the atomic number Z of the interaction

medium. The photoelectric effect varies with Z4.5, the Compton scattering is proportional

to Z, and the probability for pair production follows Z2.

If an incident γ-ray is below

the value at which pair production is significant, the resulting spectrum is the combined

effects of Compton scattering and photoelectric absorption, and two prominent features are

distinguished: a Compton continuum of energies corresponding to the Compton scattered

electrons, and a narrow peak corresponding to photoelectrons (designated as the photopeak).

63

To maximize the efficiency, high-Z materials are required along with a reasonable efficiency

at high energies (around 10 MeV). While the energy resolution is important, it is a secondary

requirement to the efficiency especially since the recoils provide a clean identification of the

reaction. In most cases, the room and beam-induced background are the main sources of

background.

The SECAR γ-array for the target system utilizes bismuth germanate (Bi4Ge3O12 or

BGO) scintillation detectors placed around the target. BGO is a purely inorganic scintillation

material with a high intrinsic efficiency due to the material’s high density of 7.13 g/cm3. The

very high atomic number (Z = 83) of Bi leads to a high detection efficiency of γ-rays including

those at 10 MeV and above. Signals from the BGO arrays can be used in coincidence with

a focal plane detector to improve background suppression. It can also serve as a start signal

to measure the time-of-flight of a recoil ion through the separator. All of the BGO crystals

are hexagonal shaped with a 35 mm face-to-face diameter and are 75 mm long. The signal

from each detector is read out by a fast photomultiplier tube (1 -2 ns rise time) and each is

equipped with a high voltage source. The energy resolution is at least 15% FWHM at 662

keV [14].

In the present jet target chamber design, one side of the chamber is occupied by a

diagnostic drive comprised of a viewer and slits that are necessary for tuning the beam into

JENSA, leaving only one side available for a γ-array installation. Figure 3.13 shows the array

assembled in its rectangular flange, and an additional CAD image of the flange installation

on the left side of the chamber in the downstream direction. This aluminum flange is 14 cm

wide and 15.1 cm long, with a depth of 14.3 cm and a 0.5 cm thickness. The setup provides

a geometrical efficiency on the order of 5% and assuming an intrinsic efficiency of 70% at

662 keV [74], provides a detection efficiency of 3.5% at 662 keV. Tests with a 137Cs source

64

confirmed these calculations.

Another circular flange manufactured at the University of Notre Dame for the SECAR

dipole calibration measurement is able to bring 15 BGO detectors closer to the target loca-

tion, increasing the total efficiency of by about 2.5 times compared to the rectangular array

described above. This flange has a 18.4 cm diameter and a depth of about 22.4 cm (Figure

6.3). The reader is referred to Chapter 6 for additional details about this setup.

A different BGO arrangement is planned for the JENSA extended gas target. This

design includes 26 detectors as drawn in Figure 3.14, and is simulated to be 63% efficient at

662 keV, 49% at 1.274 MeV line, and at 27% at 5 MeV [14]. As this target configuration

will be used when the energy of a resonance has sufficient uncertainty to make it difficult

to reliably position inside the gas jet, the BGO crystals placed along the extended target

provide position information that enables the locating and centering of the resonant reaction

in the target.

3.6.2 Recoil Detection

At the final focal plane, two microchannel plate detectors (MCP) for time-of-flight (TOF)

measurements are installed, along with a gas ionization counter (IC) or a double-sided silicon

strip detector (DSSD) as stopping detectors. Figure 3.15 shows a schematic of the focal plane

detection system along the end of the SECAR beamline. The initial design and testing of this

detector system was carried out at Louisiana State University (LSU) [46]. In the summer of

2019, the system was moved to MSU and installed in the SECAR beamline. The installation

and testing of this system were completed as a part of the commissioning of SECAR, however

they are beyond the scope of this work.

65

(a)

(b)

Figure 3.13: Current γ-array comprised of 19 BGO crystals for use with the JENSA gas jet
(a,b), with a CAD showing the flange installed on the beamline left of the JENSA target
looking downstream (c).

(c)

66

Figure 3.14: Drawing of BGO array around the extended gas cell as designed at the Colorado
School of Mines.

Figure 3.15: Schematic of the focal plane detection system at FP4.

67

Position-Sensitive Timing Detectors

The recoils first encounter the two MCP detectors as they arrive to the final focal plane

section of SECAR. The MCP detectors are high resolution position-sensitive timing detectors

that provide non-destructive measurements suitable for low-energy heavy ions. As the heavy

ions pass through a metal foil, electrons are emitted and accelerated towards the MCP

detector where a signal can be read. Given the small velocity difference between recoils and

unreacted beam arriving at the focal plane, the time of flight of the particles between the

two MCP detectors that are 1.39 m apart is accurately measured to identify each species. A

magnet-focusing MCP design is adopted from [88] for use in the SECAR focal plane. This

system has been used in experiments at the HRIBF [56] and the NSCL [66], and was shown

to provide excellent position and timing resolution (around 1 mm and 1 ns, respectively)

and to tolerate high instantaneous rates (up to 106 pps).

As can be seen from Figure 3.4, the beam size at the detectors station (purple shade)

is dispersed in the horizontal direction. For that reason, a single tilted metal foil (mylar
with aluminum coating) at 45◦ from the horizontal beam axis is utilized to maximize the

acceptance in that direction. As ions pass through the foil, secondary electrons emitted are

accelerated through a potential difference of around 550 V by a grid of thin high voltage

gold-plated tungsten wires, located 3 mm from the foil, towards the MCP detector installed

in alignment with the foil in the y-axis. One of the accelerating grid and metal foil systems

and one of the installed MCP detectors are shown in Figure 3.16. A strong NdFeB permanent

magnet is placed behind the MCP detector, forcing the electrons, which start out with some

transverse momentum, into a helical motion along the magnetic field lines into the MCP

detector. The MCP detector consists of two thin ceramic electron-multiplying microchannel

plates stacked on top of each other. Each plate is made up of an array of tubes (channel

68

Figure 3.16: One of the accelerating grids and foil after assembly (left) and the MCP detector
installed in the beamline (right). Once installed, the foil sits at 45◦ relative to the beam axis
and parallel to the MCP detector.

multipliers) with a 12 µm diameter each acting as independent electron multipliers. The

pulse from an initial electron entering a channel gets multiplied and strikes a resistive anode

plate with four electrical contacts at each edge of the plate. Comparing the magnitude of

the signals from the four contacts determines the position. The total electron transit time

through a channel is a few nanoseconds, leading to the excellent timing properties of these

detectors.

Final Stopping Detectors

After passing through the MCP detectors, the ions are stopped by a gas ionization

chamber (e.g. for high energy measurements) or a silicon strip detector (e.g. at low energies).

In the case of the former, the ions enter the IC through a thin window and lose energy in the

gas filling the chamber, typically 50 - 500 Torr of isobutane due to its low ionization potential

(10.8 eV) and mean energy for electron pair creation (23 eV). As the ions pass through the

isobutane gas, they lose energy and slow down, ionizing the gas molecules along their paths.

The ionized charged particles created are accelerated towards an anode and a cathode, and

69

the electrons resulting from the ionization drift due to the applied the electric field. The

voltage induced is then measured on two collecting anodes and related to the initial energy

of the ionizing particle. A relative energy loss ∆E measurement between the two sections

provides particle identification to discriminate between the unreacted beam and recoils and

any possible beam contaminants.

The design of the IC uses a standard cross-field ∆E-E design similar to the one in DRS [16]

with added x-y position sensitivity using an electric field parallel to the motion of the heavy

ions. The position measurement happens as the ions enter the IC where they pass through

a series of five equipotential surfaces of thin gold-plated tungsten wires (25 µm diameter)

layered in alternating cathode (wires 2 mm apart) and anode (wires 3 mm apart) planes

and generating a uniform electric field parallel to the direction of motion. As the electrons

are produced by ionization, they are accelerated and collected on the horizontal or vertical

wires. The resulting signals as a function of position provide an x-y position measurement

with a resolution of 3 mm or less. The energy measurements follow the position measurement

section, utilizing a uniform electric field perpendicular to the direction of motion of the ions.

The transverse field is created by 10 field shaping electrodes supplied by a 10-stage PMT

tube voltage divider. As the ions pass through this section, the elections drift to two anode

plates while the positive ions drift towards the cathode in the opposite direction. The current

collected on each anode depends on the amount of energy lost by the ion in that section. The

first anode (7.5 cm length) provides a ∆E measurement followed by the second anode (22 cm

length) that provides the full residual energy E. Compared to lower Z ions, heavier ions lose

more energy in the first anode for the same total energy. Using this ∆E-E method, particles

passing through the gas can be identified through a ∆E vs. E plot. Given the SECAR

rejection and the expected radioactive beam intensities, the IC is expected to operate at

70

Figure 3.17: The ∆E-Si detector showing the grids and DSSD assembled before installation
on the beamline.

rates greater than 104 pps without significant pileup.

A silicon strip detector can instead be used to stop the ions when a better total energy

resolution is desired than what the IC can provide at the same energy. Silicon detectors

are compact detectors with good energy resolution in charged particle detection, and good

timing resolution due to a pulse rise time of around 10 ns. Additionally, by using a DSSD,

2D position resolution can be achieved by reading out the perpendicular strips on the front

and back of the detector. A Micron Semiconductor BB7 detector can be installed as the

final stopping detector. The BB7 DSSD design has 32 strips on each face with 2 mm pitch
resulting in a full reactive area of 64 mm × 64 mm, covering the expected beam spot size at

that plane.

While an IC is not required to be used with the silicon detector, a hybrid Si-gas stopping

detector was implemented that can be used to measure ∆E in the gas and stop the ions in

the DSSD. The assembled ∆E-Si detector is shown in Figure 3.17 before installation at MSU

on the SECAR beamline.

71

3.6.3 Digital Data Acquisition System

The NSCL Digital Data Acquisition System (DDAS) is used to process the signals from

all SECAR detectors [77]. The DDAS is a modular system composed of Pixie-16 (digital

gamma finder) modules manufactured by XIA LLC distributed across up to eight compact

PXI/PCI crates. Each Pixie-16 module has 16 channels that provide the signals from the

detectors. That signal is then digitized via Analog Devices ADCs which can be either 14

or 16-bit, and 100, 250 or 500 Mega-Samples Per Second (MSPS). The modules have two

hardware gain settings with 0.52 V and 1.2 V full-scale input ranges. A crate holds up to 13

of these modules, including a computer module, and the clocks can be synchronized between

crates when multiple are in use. Each DDAS crate is typically read out by a computer

through which the NSCL Data Acquisition software suite (NSCLDAQ) handles the data

flow produced by the particles going through the detectors. The ReadoutGUI is the main

interface with the NSCLDAQ where all experiment controls are generally handled.

For the SECAR system, a total of five Pixie-16 16-bit PXI Spectrometer with 250 MSPS

ADCs are installed for the BGO and the focal plane detectors over two crates (one at

the target and one at FP4). The two crates will have synchronized clocks when running

the system in coincidence mode, and the data streams can be merged on one main DAQ

computer to facilitate event building.

A subset of the BGO detectors presented in this chapter was used with the DDAS system

in the dipole energy calibration experiment described in Chapter 6.

72

Chapter 4

Beamline Commissioning

4.1 Separator Control System

The NSCL and FRIB have a large distributed control system based on the Experimental

Physics and Industrial Control System (EPICS) framework, integrating accelerator and ex-

perimental areas. EPICS is a set of software tools and applications that enable the use of

distributed control systems to operate devices such as beamlines, including vacuum, power

supplies, diagnostic support etc. As part of this thesis, this system was extended to SECAR

following FRIB procedures and conventions.

In the past five years, the NSCL has adopted Control System Studio (CS-Studio) as the

main graphical user interface tool for ReA3 controls to communicate with EPICS channels.

CS-Studio is a set of control system interface tools that include real-time monitoring and

controls for large scale systems such as accelerators. This includes high level applications such

as making use of live data or of data stored in databases in history plots, an alarm handler,

and save/restore options for device statuses, and more. In order to integrate SECAR with

the ReA3 beamline, the control system pages for SECAR were built in CS-Studio, and

customized based on current and future SECAR controls needs. Figures 4.1 and 4.2 show

the interface designed for the main magnet controls page (which is also the main page of

the SECAR controls), and the vacuum controls page in a separate tab, respectively. Figure

4.3 shows the tab that resulted from creating a shortcut to commands and overviews needed

73

Figure 4.1: The main global controls page for SECAR. Top left shows the magnet light that
controls the ReA3 Hall SECAR light when the magnets are one, and to the right several
buttons provide options to switch to other pages. The general menu tabs below show the
magnet controls in this image.

for tuning during experiments, which were determined from experience and updated after

each commissioning beam run. Clustering controls by type, task, or beamline section was

deemed helpful to save time during monitoring and tuning, and to minimize confusion when

operating the device.

As commissioning tasks evolved and tuning methods became more complex, Python

scripts were written to handle tuning tasks and algorithms that were not possible through

CS-Studio, such as dipole field matching and a Bayesian optimization of the beamline as

described in detail in Chapter 5. These tuning tasks were automated once procedures were

established and are handled through the command line. For such applications or other user-

specific tasks that may be useful in the future, scripts and applications can be embedded

into the user interface on CS-Studio to make them more accessible for scientific users.

74

Figure 4.2: The vacuum summary page showing the controls and status of vacuum gauges
and turbo pumps.

Figure 4.3: The controls page for SECAR showing the tab for controls during tuning. This
was developed for use during experiments.

75

4.2 Magnet Stability and Reproducibility

SECAR consists of 10 dipole magnets (including two Wien filter magnets), 15 quadrupole

magnets, and four higher order multipole magnets that need to be maintained within their

specified field tolerances in order to achieve the desired SECAR mass resolution. Addition-

ally, all of the SECAR magnets include an iron yoke to increase the magnetic field, making

the resulting fields strongly dependent on their hysteresis history. Proper procedures to

ensure a stable and reproducible magnetic field in all devices are needed.

The first two SECAR dipoles B1 and B2 are equipped with four Caylar NMR probes

attached to a NMR20 Gaussmeter. These were used to run the tests presented in this

section. One high range and one low range probe are each installed in B1 and B2, the former

covering 0.16 to 0.8 T and the latter 0.037 to 0.18 T. The absolute precision of the field

measurement of the NMR probes is in the order of 10-6. These enable accurate absolute

magnetic field measurements as these magnets will be used to define the beam energy during

tuning (refer to Chapter 6 for the energy calibration). The remaining dipoles and the Wien

filter magnets are each equipped with a Group 3 Hall probe connected to a DTM-151 Group

3 teslameter. These Hall probes also provide a temperature reading which was advantageous

when studying temperature effects on the probes and magnets. Since the quadrupoles were

not equipped with any magnetic field measuring devices, several of the Hall probes were

removed from the dipoles and temporarily installed in the quadrupoles for the purposes of

the tests presented in this work.

76

4.2.1 Magnet Cycling and Hysteresis

To reduce the uncertainty in the magnet strength caused by the iron core hysteresis effects

and achieve adequately reproducible fields for scientific measurements, a standard procedure

for cycling, or ”degaussing”, of the magnets was devised. The procedure allows for setting

the magnet through setting the current on its hysteresis curve to reach its corresponding

magnetic field on the excitation curve in a reproducible manner independently of the starting

conditions, preventing differential hysteresis effects. Since magnets may need to be cycled

several times during an experiment, several cycling procedures were tested and compared to

balance the trade off between speed and performance.

The cycling procedures were developed to meet reproducibility specifications. To derive

these, beam physics simulations with COSY were performed to study the impact of magnetic

field variations on SECAR performance, setting a maximum limit of 2% on mass resolution

change at FP2 from a single magnetic element’s field variations. This resulted in a 0.01%

tolerance specification on the magnetic fields of the quadrupoles, and Q3 and Q6 turned

out to be the most critical, affecting the mass resolution by at least 2% when their fields

vary by 0.01%. Q5 was shown to be the least critical, allowing up to 0.16% variance for

mass resolution changes under 2%. From those results, a requirement of 0.01% was set for

reproducibility and long term stability. This requirement was applied to dipoles as well

to optimize the transmission for recoils. Figure 4.4 shows the reproducibility of B1 when

cycled once with a 30 second pause time at maximum excitation. The measurements were

recorded with the NMR probe set up in B1 using the following cycling procedure: The

current is increased from zero to its maximum recommended value and kept at that value

for 30 seconds. The current is then decreased to its final desired value.

If a new lower

77

Figure 4.4: Dipole B1 magnetic field reproducibility measured with the NMR probe after 1
cycle with 30 s pause time. N = 208.

magnetic field needs to be set, the current is decreased to its appropriate value. If the new

magnetic value is higher, the cycling procedure is repeated. For the test shown in Figure 4.4,

B1 was set to 25% excitation (45 A) following the described cycling procedure for different

randomly chosen starting points at 0%, 50% or 100% excitation. As shown, the magnetic
field is reproducible for all 208 tests well within ± 0.01%. Similar results were found for B2.

The same test was run for Q6. Since the quadrupoles do not have a permanent field

measuring device installed, a Hall probe was placed on one of its pole tips to perform these

measurements. Figure 4.5 shows the results of 208 cycling tests using the same cycling

procedure as described for B1 (blue histogram data), as well as 164 runs of a modified

procedure that included 3 full cycles to maximum excitation with a 60 second wait time

at each of the maximum and minimum excitation levels (orange histogram data). When
cycling once, approximately 11% of time the final current falls outside of the ± 0.01% of the

78

Figure 4.5: Quadrupole Q6 magnetic field reproducibility using two different cycling proce-
dures, measured with a Group 3 Hall probe.

mean magnetic field, compared to 0.6% when cycling 3 times with a wait time twice as long.

These results indicate that when running quadrupoles with mass resolution optimization as

a priority, cycling 3 times with a 60 second wait time is critical.

4.2.2 Long Term Stability Tests

Magnetic field stability in each of the magnets is primarily achieved by controlling the ex-

citing current. However, the magnetic field may be affected by additional effects such as

changes in the magnetization of the magnet material, or temperature effects affecting the

magnet. To be able to monitor the field stability to the accuracy required, sufficiently accu-

rate measuring devices are needed. B1 and B2’s magnetic fields are monitored by two Caylar

NMR probes while the rest (B3 - B8) are equipped with Group 3 Hall probes. The absolute

precision of the measurement of the magnetic field with the NMR probes is of the order of
10-6. The Group 3 Hall probes are specified to have ± 0.01% precision at 25◦C. This is of

79

Figure 4.6: Dipole B1 magnetic field long term stability test as measured with NMR (top)
and Hall probe (bottom). The dot-dashed lines correspond to ± 0.01% stability levels. The
flat lines between July 26 and July 29 correspond to a control system connection drop.

the order of the required stability. Tests of the performance of the Hall probes and their

sensitivity to the environment in the ReA3 Hall were therefore necessary.

Group 3 Hall Probe Accuracy and Specifications

A performance test for the Hall probe was done by temporarily installing one of the probes

along with the permanently installed NMR probe in B1. Figure 4.6 shows the results. The

flat lines between July 26 and July 29 correspond to a control system connection drop. It

can be seen that the B1 magnetic field is well within the specified 0.01% stability level

as measured by the NMR probe. The Hall probe measurement shows significantly larger

variations that can be attributed to the Hall probe precision. The measurement confirms

the manufacturers precision claim of 0.01%.

Due to air vents situated right above the SECAR beam line and to the proximity to the

80

0.109250.10926Jul 242019Jul 27Jul 30Aug 2Aug 5Aug 80.109050.10910.10915NMR Field (T)Hall Field (T)rolling door in the ReA3 Hall that occasionally is open to the cold outside Michigan air, a

study of the dependence of the Group 3 Hall probe on temperature was conducted using the

same setup as the NMR-Hall stability test. Using an external heat source, the aluminum
holder of the probes was heated by convection gradually from 25◦ to around 37◦C and kept

at that temperature for several days with B1 set to an arbitrary current. Figure 4.7, where

the onset of heating is indicated with the black vertical line, shows that the NMR probe
readings were not affected by the temperature rise and remained within ± 0.01%. The Hall

probe shows a sharp drop at the onset of heating, most likely due to the movement of the

system as it is very sensitive to any vibrations, then displays a slowly increasing magnetic
field reading until surpasses the ± 0.01% range four days later, right before the heating

source was turned off as indicated by the sharp drop-off in temperature in the bottom plot.

These tests confirmed the specifications of the device that state that under normal operating
conditions (typical room temperature ∼ 25◦) the Hall probe provides the 0.01% accuracy

needed for monitoring magnetic field drifts, but that large temperature variations in excess of

typical room temperature for long periods of time need to be avoided. It would be prudent

to monitor the behavior of the probes on hot summer days or seasons with high average

temperatures.

Dipole Field Long Term Stability

Similarly to the tests discussed in the previous section, magnetic field stability tests of

dipoles B1, B2 and B5 have been performed by keeping their respective magnet current

set for extended periods of time. For B1 and B2, the field was measured with the NMR

probes, while the Hall probes were used for the other magnets. The magnet current stability

is maintained by each magnet’s power supply internal feedback loops using the read back

current in the control system. Dipole tests for B2 and B5 showed similar results to B1

81

Figure 4.7: Dipole B1 magnetic field long term stability test as measured with NMR (top)
and Hall probe (middle) in the presence of an external heating source from from 25 to
37◦C. The dot-dashed lines correspond to ± 0.01% stability levels and the black vertical
line indicates the onset of heating. Bottom plot shows the Hall probe’s temperature sensor
readback.

82

0.109250.109260.109050.10910.10915Aug 82019Aug 9Aug 10Aug 11Aug 122025303540NMR Field (T)Hall Field (T)Hall Temp (°C)Figure 4.8: Dipole B5 magnetic field long term stability test as measured with a Hall probe.
The dot-dashed lines correspond to ± 0.01% stability levels.

shown in Figures 4.6. Figure 4.8 displays results from an 18 day stability test of B5, a

duration equivalent to a long SECAR reaction rate measurement at a single beam energy.

The magnetic field is stable within specification as indicated by the dot-dashed lines.

Quadrupole Field Long Term Stability

A similar setup used for the reproducibility tests with Q6 was also used in Q1 to study

the field stability. A Hall probe was installed in Q1 and the magnetic field, along with

the ambient temperature near the power supply rack and the temperatures of the inlet and

the outlet cooling water of Q1, were monitored for about 84 hours. The Hall field and the

ambient temperature are plotted over time in Figure 4.9. The magnetic field varied by at
least ± 0.05% during the test. Additionally, the Hall probe temperatures and the cooling

water outlet temperature showed a fluctuation similar to the ambient temperature (data
not included in this plot). While the cooling water warmed up to 27◦C, the Hall probe
experienced a temperature high of 33◦C as it was placed directly on the warm magnet.

The most likely explanation of the field measurement variations that coincide with sudden

83

+0.01%-0.01%Oct 102019Oct 13Oct 16Oct 19Oct 22Oct 25Oct 28−0.1529−0.152895−0.15289−0.152885−0.15288−0.152875−0.15287B5 Stability TestTimeField (T)Figure 4.9: Quadrupole Q1 magnetic field long term stability test as measured with two Hall
probes placed at different pole radii. The ambient temperature near the power supply rack
(mezzanine) is shown in red. The overlayed dot-dashed lines correspond to ± 0.01% of the
mean of each reading.

changes in temperature (such as around 6 pm on both days in Figure 4.9) is the temperature

sensitivity of the probe when the conditions surpassed typical room temperatures. However,

the overall slow drift over time past the stability requirements when the room temperature

was stable is attributed to the magnet itself. In order to address any slow drifts in the future,

a plan to install Hall probes in quadrupoles is being set in place. This will allow the SECAR

operators to identify and easily correct any magnetic field drift outside of the specifications

or any other issues that could arise with the magnetic field that could affect the ion optics

during experiments.

84

-0.01%+0.01%00:00Jun 7, 201912:0000:00Jun 8, 201912:00−0.3064−0.3066−0.3068−0.307−0.3072−0.3074−0.30762224262830G3 Hall Probe 1Ambient TempField (T)Temperature (°C)Figure 4.10: First beam spot on the FP1 viewer in SECAR on July 13, 2018.

4.3

Initial Tests with Beam

In July 2018, a proton beam was transmitted through SECAR up to FP1 for the first time.

The first image of a beam spot in SECAR is shown in Figure 4.10, along with some of the

SECAR team members that were present for that milestone. Since then, several test beams

have been transported through the system. Table 4.1 provides a list of beam times discussed

in this work with a summary of the main goal achieved during each run. A shutdown due

to COVID-19 ”stay-in-place” order by Michigan’s Governor interrupted the commissioning

schedule briefly. Nevertheless, experiments resumed in June 2020. These test beams were

selected by beam particle, energy, and charge state, which determine the magnetic rigidity.

A variety was chosen to test transmission and tuning of SECAR over its rigidity range (0.14 -

0.8 Tm). The energy uncertainty and energy spread of the ReA3 beams were approximately

0.5% (FWHM).

During the diagnostic tests detailed in Subsection 4.3.1 where the change in x-position
at FP1 as a function of the B1 and B2 magnetic fields was measured, a dispersion of 1363 ±
B was obtained for the dipoles. This is ∼ 8% lower than COSY predictions.

68 (5%) mm/ dB

85

Date

Jul. 13 2018

Jul. 19 2018

Jul. 25 - 27 2018

Feb. 12 - 14 2019

Feb. 21 - 23 2019

Mar. 10 - 12 2019

Mar. 25 - 28 2019

Apr. 4 - 5 2019

Aug. 26 - 29 2019

Sep. 3 - 12 2019

Mar. 2 - 9 2020

Jun. 8 - 11 2020

Jun. 15 - 20 2020

Jun. 20 - Jul. 2 2020

Jul. 20 - 24 2020

Jul. 27 - 30 2020

Beam
+
H2
H2
H2

+

+

40Ar14+
40Ar14+
40Ar14+
23Na8+
23Na8+
14N6+
+

H2
+, 1H+
H2
133Cs41+
133Cs41+
133Cs41+
20Ne8+
20Ne8+

E (MeV/u)

Bρ (Tm)

2.97

2.97

2.97

2.86

2.81

2.86

0.30

2.50

4.08

0.99

0.5000

0.5000

0.5000

0.6954

0.6893

0.6954

0.2266

0.6545

0.6799

0.2888

Goal

First Beam

Tuning to FP1, Ion Optics Studies

Diagnostics Testing, Automated Tuning Tests

Tuning to FP1, Ion Optics Studies

Tuning to FP1, Energy Scaling

Tuning to FP1, Energy Scaling

Tuning to FP1, Energy Scaling

Diagnostics Testing and Troubleshooting

Tuning to FP2 with WF1

Dipole Energy Calibration

0.99, 1.80

0.1444 - 0.3891 Dipole Energy Calibration, Automated Tuning Tests

0.96

1.00

1.00

0.4573

0.4667

0.4667

Tuning to FP2 with WF1, Quad Optimization

Tuning to FP3 with WF1

Tuning to FP4 with WF1

1.12, 1.16

0.3809, 0.3887

Tuning to FP4 with WF1 with He Jet

1.18

0.3911

Tuning to FP4 with WF1 with He Jet

Table 4.1: SECAR commissioning runs.

86

4.3.1 Diagnostic Devices Tests

In Chapter 3, the SECAR beamline was described including a detailed map of the diagnostic

devices installed along the instrument as shown in Figure 3.6. During the commissioning

discussed in this work, the collimator and the zero-degree camera were not yet installed, and

the beamline up to FP2 was the main focus of the work. In this section, the installation

and testing of the Faraday cups, viewers and BCMs are discussed as they pertain to the

commissioning of SECAR up to FP2.

Assembly and Installation

In June 2018, the diagnostic devices for the SECAR beamline up to FP1 were assembled

and installed, except for the slits which were installed the following year. The remainder of

the diagnostics up to FP2 were installed in 2019. Figure 4.11 shows the first Faraday cup

(FC1) installed in SECAR (located before the first set of dipoles) assembled in the clean

room. This is the main cup used when centering through JENSA into SECAR, and it is one

of the larger cups installed in this beamline. As described in Chapter 3, all Faraday cups in

SECAR are composed of a collector and an aperture that are electrically isolated from each

other and that independently read current. Only the collector is voltage suppressed, and

that is achieved by an isolated plate installed in front of the inner sides of the collector.

Throughout the beamline, some diagnostic devices were designed to share a drive as

shown for the 3-in-1 device at FP1 in Chapter 3. Figure 4.12 shows the 3-in-1 diagnostic

drive after assembly and before installation at FP1. From left to right, BCM1, FC2 and

Viewer2 are shown. The five dot markings in the center of the viewer plate indicate a 5 mm

distance between each two dots. All viewers in SECAR have similar marks in their center.

In this image, the viewer had not yet been coated with the phosphorus. Figure 4.13 shows

87

Figure 4.11: FC1 assembled in the clean room.

Figure 4.12: The 3-in-1 diagnostic drive to be installed at FP1, assembled in the clean room.
From left to right: BCM, Faraday cup, and viewer plate (uncoated).

Viewer2 after being coated, and Figure 4.14 shows Viewer1 after installation on its actuator

drive downstream of B2, inserted into position along the beamline.

Faraday Cup Beam Tests

The suppression voltage needed for the cups was determined during one of the July

2018 runs with an H+

2 beam impinging on FC1. The suppression was slowly increased and

the current readback of the collector was recorded. The results are shown in Figure 4.15.

Following that, the operating suppression voltage was established as -200 V for all SECAR

88

Figure 4.13: A P22 coat on the Viewer2 plate before installation.

Figure 4.14: Viewer1 installed and inserted in the beamline.

89

Figure 4.15: FC1 suppression voltage test.

cups. In later commissioning runs, a 10% to 25% discrepancy was occasionally observed in

some of the readings, notably with FC3 (BTS35:D1563, before WF1) when compared to the

ReA3 cup upstream of JENSA (BTS34:D1448) and to FC1. Table 4.2 displays the readings

from all cups up to FC2 with their ratio to the ReA3 cup before JENSA. The discrepancy

in most of the cups was occasional and did not exceed 10%, except for FC3 which did not

improve even with an increased the suppression voltage past -200 V. This may be explained

by the fact that FC3 is the largest of the cups to accommodate the large and unfocused beam

spot size at that location. The beam may be hitting the suppression plates or the aperture

and causing secondary electrons. This minor issue did not affect transmission estimates

during early commissioning, however it may be necessary in the future to address the issue

if it introduces any tuning problems.

Viewer Image Analysis

Each viewer plate along the beamline is paired with an adjustable CCD camera and a

manual light. From the viewer camera data stream, images can be saved in TIFF format.

90

Cup/Location

Current (pA) Ratio to ReA3 Cup

ReA/BTS34:D1448
FC1/BTS35:D1485
FC2/BTS35:D1542
FC3/BTS35:D1563
FC4/BTS35:D1638

62
60
65
75
66

1

0.97
1.04
1.21
1.06

Table 4.2: Faraday cup collector current readbacks up to FP2 after tuning the 20Ne8+ beam
in July 2020.

For beam centering and tuning, it was advantageous to create a way to objectively analyze

the viewer images and quantify the different beam spot parameters, as doing it by eye was

not sufficiently accurate especially with weak beams. To facilitate obtaining a scale for

the images, an image with the light on where the dots detailing the center region of the

viewer are visible was taken for each viewer. The dots are used to scale the beam position

and movements during experiments. Figure 4.16 shows an example of a processed image

of a beam spot. To achieve the final results, a Python program was written to subtract

a background image taken without beam on the viewer, and detect the center dots in the

image of the viewer with the light on to provide the scale in mm. The red vertical and

horizontal lines indicate the center of the beam spot. This image processing became a key

component in the automated tuning methods discussed in Chapter 5.

To achieve these results, the TIFF images were imported as a 2D array of numbers, and

the background image was subtracted element by element from the beam image. The data

was subsequently integrated column by column for each of the x and y axes resulting in a

1D beam profile in each axis. These distributions were then used to find the location and

the width of the beam spot. In this work, the center location was calculated by finding the

median of the beam profile distribution in each dimension. The median was defined as the

first point (pixel location) where the ratio of the cumulative integration of the beam profile

91

Figure 4.16: Viewer image analysis process. Left: CCD image of the image with light on to
find scale from the 5 mm dot markings. Center: Raw TIFF image of the beam from CCD.
Right: Background subtracted beam image with the red lines marking the beam spot center,
and red dots indicating the center with 5 mm distance between each dot. In this image, each
pixel corresponds to approximately 0.15 mm.

to the total integration over the entire axis is greater than or equal to 50%. Other methods

were considered such as fitting the beam spot shape with one or more Gaussian shapes or

finding the weighted mean of the distribution, however the median method was chosen due to

its robustness when handling any irregular beam shapes including heavy tails that occur due

to optical effects upstream. The beam spot width was needed for beam optics optimizations
and was defined as ±1σ of each beam profile distribution. This was found using the same

ratio of cumulative sum over total sum and taking the pixel location where the integral was

closest to 15.9% as -1σ, and 84.1% as +1σ. Figure 4.17 is an example of the full image

processing results.

Beam Centering Methods

The SECAR beamline includes two diagnostic devices, the BCM and the viewer, that are

crucial for centering the beam and ensuring optimal rejection and transmission. In the initial

stages of commissioning during the H2 beam run on July 27, 2018, a test of the performance

of the BCM and viewer devices was done to identify the most efficient and precise of the two

for beam centering during the initial tuning. Throughout this test, the currents in B1 and

92

Figure 4.17: Viewer image analysis at FP1: Red lines indicate beam center as calculated
from the median of the distribution, blue dashed lines indicate the width in the x-direction
defined as ±1σ. The locations are indicated in pixels, and the scale is 5 mm to 16 pixels.

93

B2 were increased slowly from 110.56 to 110.76 A in steps of 0.01 A, scanning the areas of

Viewer2 and BCM1 horizontally at FP1. This scan corresponded to a 13.5 pixel change in

position of the center of the beam on the viewer output, corresponding to approximately 2

mm along the viewer and BCM.

A viewer image was saved at each step for a total of 20 images during the scan. They

were each background subtracted and resulted in a background-free beam spot image. The

counts along the x-axis (long axis) were integrated to show a 1D Gaussian-looking peak. To

compare this centering method with the BCM, the median data point along the integrated

curve in the x-direction was taken as described above, with an error of 0.5 pixels, to find

that the beam center crosses the center of the viewer between 110.67 - 110.68 A.

During the BCM testing portion of the test, a significant amount of noise was recorded

on each plate, as seen in Figure 4.18. This issue contributed to a large error bar that

was derived from the fluctuations and deviation from linearity of the archived BCM data.

Moreover, the BCM plates occasionally read negative currents. Those current were divided

over the readings of the adjacent plates in the analysis. The results, shown in Figure 4.19,

indicate that within uncertainties, the BCM records the crossing of the sum of the left plates

and the sum of the right plates between 110.67 - 110.71 A.

Comparing the BCM’s ease of use and robustness in finding the center of any beam spot

with the viewer’s analysis method and results, it was determined that the viewer super-

sedes the BCM as the beam centering device of choice for initial tuning and optimizing the

beam trajectory in SECAR independently of alignment and beam spot shape. It was later

concluded that the noise seen in the BCM was partly due to the drive motor not shutting

off when the devices are in place, in addition to some electronic noise that required some

rewiring to resolve the issue. Nevertheless, the viewer remained the main choice for tuning in

94

Figure 4.18: Top: Normalized currents on the left side (blue) and right side (orange) as a
function of time. The point where they cross is the center region of the BCM. The uncertainty
on the measurements is shown in the shaded region. Bottom: Ratio of left current to right
current on the BCM. It should be equal to 1 when the beam crosses the center of the BCM.

Figure 4.19: Final results showing the left side current (blue) and right side current (orange)
as a function of dipole current. The shaded region of overlapping blue and orange between
110.67 and 110.71 A is the region when the beam was centered.

95

110.56110.58110.60110.62110.64110.66110.68110.70110.72110.74110.76Dipole Current (A)0.00.20.40.60.81.01.2Normalized BCM CurrentLeft sum and right sum of BCM currents vs dipole setting. Crosses between 110.67 and 110.71 A Left sumRight sumthis work. In Chapter 5, a detailed walk-though of the beam tuning procedures is given, the

methods of which will reinforce the decision of using the viewer as the initial beam centering

diagnostic device for tuning via quadrupole steering due to the need to monitor the beam

spot shape and location. In the future, the BCM may be useful for precision tuning of well

shaped beams in dipoles and steerers, or the centering of non-attenuated or low intensity

beams that can’t be easily tuned with a viewer, provided the magnetic elements and the

beamline are well aligned with the BCM center.

96

Chapter 5

Tuning and Bayesian Optimization

To achieve precision measurements, SECAR creates separation between unreacted beam and

recoil particles of different mass but similar momentum by bringing both to a focus in two

mass-dispersed planes along the separator. The separation goals require a centered recoil

beam and finely tuned quadrupole fields to maximize the mass resolution and unreacted

beam suppression of the device. The critical first step in establishing the correct ion optical

setting is to center a pilot beam along the optical axis and adjust the quadrupoles and

higher order elements to achieve the correct beam spot shapes, sizes, and foci at critical

locations. The separator can then be scaled from the pilot beam setting to the recoil setting

by scaling all magnets according to the Bρ change. This chapter discusses the methods

used to achieve an optimal tune that supports SECAR’s separation goals, and presents the

initial implementation of an efficient machine learning algorithm that allows for objective

and precise tuning of the device.

5.1 Tuning Methods

A properly centered pilot beam along the beam line’s ion optical axis is critical to achieve

good transmission and provide a starting point to scale to the recoil rigidity. Although all
SECAR electromagnetic elements were aligned to 0.2 mm and 0.01◦ to the nominal beam axis

in the facility’s alignment coordinate system, it is still necessary to experimentally confirm

97

that the beam is on the ion optical axis and not rely solely on space coordinates provided

by the diagnostics such as beam viewers. This section describes the steps taken to align

any incoming beam through the JENSA chamber into the SECAR beam line as well as the

methods to tune the dipole bending magnets to align the beam through FP4 at the end of

SECAR.

To ensure there is no deviation from the central optical axis, a tuning procedure was

established making use of existing diagnostic and magnetic devices to indirectly probe the

incoming beam angular deviation and center the beam in all SECAR magnets. This method

uses the steering observed due to quadrupole magnets as a probe of the beam’s deviation

from the magnetic axis.

In a quadrupole magnet, a particle feels a force proportional to

the distance from the central axis (Lorentz force, Equation 1.2), where the net force is zero.

When the incoming beam is aligned with the central optical axis of a quadrupole magnet,

changes in the quadrupole strength should only focus and de-focus the beam distribution in

the x- or y-direction depending on the polarity of the quadrupole. If there is some deviation

from the axis, the beam will feel imbalanced forces from the quadrupole fields and is caused

to steer in one direction or the other as the quadrupole strengths varies. Based on this

behavior, the tuning procedure for the incoming beam was developed using the SECAR

quadrupoles for probing deviations of the beam from the optical axis. The two ReA3 steerer

pairs at BTS34:D1413 and D1431 (see Figure 5.1) are employed to adjust the angle and

position of the beam impinging on the target. If the beam is deviated from the central ion

optical axis, movements of the beam spot are observed on one of the viewers installed at some

distance downstream when quadrupoles are varied upstream. The SECAR layout in Figure

5.1 displays all viewers used in this chapter for this purpose. In addition to centering the

beam, this method ensures quadrupoles can later be adjusted without shifting the beam’s

98

position and limiting transmission.

Prior requirements

Before initiating any beam tuning in JENSA/SECAR, the incoming beam tuned by the

ReA3 operators must meet certain requirements. The beam spot size at the JENSA target,

visible through the viewer installed in the target chamber as shown in Figure 5.1 (b), should
be restricted to 1.5 mm. This is accomplished by maximizing transmission through 2 × 2
mm and 1.5 × 1.5 mm apertures available on the same drive as the viewer. Transmission is

measured from the last ReA3 section upstream of SECAR using the last ReA3 Faraday cup

(FC D1448) and the first SECAR cup (FC1) after Q2. The copper apertures installed in the

upstream and downstream JENSA cubes as discussed in Chapter 3 (see Figure 3.9) can read

current when beam is hitting them, and they serve as further diagnostics for the operators as

they adjust the tune, minimizing any current reading on those apertures while maximizing

the transmission between the two cups on both sides of the chamber. The restrictions
imposed by those apertures guarantee a maximum incoming angle of ± 3.4 mrad. During

this part, the operators tune the ReA3 dipoles and multipoles, but leave the two horizontal

and vertical steerer pairs upstream of JENSA, shown in Figure 5.1, set to zero. Once these

requirements are met, the tuning using SECAR diagnostics and magnets begins, utilizing

those ReA3 steerers as needed.

5.1.1 Manual Tuning Procedure

In this section, the method is described as used with the first two quadrupoles, Q1 and

Q2, and the viewer at FP1. The same method applies for any suitable combination of

quadrupoles and downstream viewers along the SECAR beamline. The procedure below

outlines the steps taken to manually adjust the incoming beam angle, and subsequently tune

99

(a)

(b)

Figure 5.1: (a): SECAR layout with notable diagnostics used for tuning, including the
upstream ReA3 beamline with the two steerer sets used for correcting the incoming angle.
The first set is 7.2 m away from the first SECAR quadrupole, and the two sets are 1.8 m
apart. (b): JENSA viewer and slits used in the manual tuning procedure.

100

Viewer at FP1JENSAViewer Viewer at FP2 Viewer at D1688 Viewer at D1783 Viewer at D1836Viewer at D1879 H&V Steerers at D1431 H&V Steerers at D1413 the SECAR dipoles.

Step-by-Step Tuning Procedure

1. The quadrupoles are set to their nominal tune scaled from the standard COSY map

to the appropriate Bρ (see COSY map in Table 3.2).

2. The dipoles are scaled according to Bρ and the NMR probes in B1 and B2 are matched

to readback values within 10-5 T, while checking that the beam is approximately cen-

tered on the viewer at FP1. Then the dipole magnets are cycled to ensure reproducible

fields when setting them later on.

3. With Q1 and Q2 at their nominal values and Q3 to Q5 off, the location of the beam spot

center at the FP1 viewer is recorded (found either manually or through the automated

image analysis program discussed in Section 4.3.1).

4. Q1 is set to half its original value (this was chosen for convenience, however any value

away from the nominal that produces visible changes in the beam on the viewer is

acceptable and does not change the effectiveness of the method). If the beam moves

from its previously recorded position at FP1, the downstream ReA3 steerer set (D1431)

is adjusted so that the beam position at the FP1 viewer goes back to the position

recorded with the nominal Q1 setting.

5. Q1 is set back to nominal. Looking at the JENSA viewer, the upstream steerers

(D1413) are adjusted to re-center the beam on the JENSA viewer, if needed.

6. The beam current readings on the downstream and upstream JENSA apertures are

checked to verify that the previous step did not change the incoming beam angle too

101

much. If the apertures are reading current (more than 10% of the total beam current),

the last steerer changes are reversed step by step until the current is less than 3 pA.

7. Steps 3 - 6 are repeated until there is no steering at FP1 due to Q1 (or the minimum

possible steering) and no or minimal current readings on the target apertures.

8. The same steps are repeated with Q2, until both Q1 and Q2 do not steer (or steer

minimally).

9. If the procedure is not converging to a setting where steering is minimal or decreasing

without loss in transmission, the steerers are set back to zero and the procedure is

repeated using the steerers in reverse: downstream steerers to center on the JENSA

viewer and upstream steerers to center on FP1.

10. Once the beam is centered along the quadrupoles’ ion optical axis, the dipoles pair is

tuned. The steering effects in the x-direction of Q3, Q4 and Q5 after the dipoles are

checked using a similar procedure to the one used with Q1 and Q2. Going down in

current, B1 and B2 are adjusted simultaneously as needed until the beam does not

steer when Q3 - Q5 are varied in strengths. This ensures the beam leaves the dipole

pair and enters the quadrupoles along the ion optical center. If there is a need to go

back up in current, the dipoles are cycled again.

11. If there is steering due to Q3 - Q5 in the y-direction, this is corrected using only the

ReA3 vertical steerers following the same procedure as Q1 - Q2 utilizing the JENSA

and the FP1 viewer. No SECAR elements are able to provide vertical adjustments.

The procedure has to be repeated at every viewer to fine tune any small angular deviations

that are magnified downstream and each dipole pair has to be set in the same manner to

102

ensure a well centered beam up to the end of SECAR, making this manual procedure operator

dependent and very time consuming. A faster and more robust method was needed to tune

the entire separator. This led to the automation of most of the procedure as is described

next for horizontal beam centering using the dipoles and in Section 5.3 for adjustments of

the incoming beam position and angle using the ReA3 beamline steerers.

5.2 Dipoles and WF Tuning

Tuning dipoles in pairs is challenging as small field differences can introduce angles when

leaving the pair. Each pair in SECAR has to be carefully cycled and their field readbacks

matched to 10-5 T (using NMR probes for B1 - B2 and Hall probes for B3 - B8) before

finding the correct field setting to center the beam in the dipoles. To accelerate the tuning

procedure and make it more reproducible, a simple automated scan over the corresponding

viewer for each pair was implemented to find the least steering path through the quadrupoles

located between each dipole pair and a viewer downstream.

As an example, the steps below describe the automated scan for the case of B1 and B2

with the beam position monitored at the FP1 viewer:

1. The selected dipoles are set to a current that is significantly higher than the expected

setting and positions the beam near the low bending radius edge of the viewer.

2. The automated scan is run. This prompts the cycling of the dipoles following the

procedure outlined in Chapter 4.

3. Once settled, dipole field readbacks are matched by the automated script down to 10-5

T by decreasing the current in small steps as needed.

103

4. A series of images is taken of the beam spot at the FP1 viewer at four different

quadrupole tunes varying only Q3 - Q5, as these quadrupoles are downstream of B1

- B2 and upstream of FP1. The quadrupole strengths at the four different tunes are

selected beforehand with the only criterion being a change that keeps the beam spot

visible (not too unfocused) on the viewer. In this case the tunes typically are: Q3 -

Q5 at nominal, Q3 at -90 A with others at nominal, Q3 at two-thirds of its nominal

strength with others at nominal, and Q4 at two-thirds of its nominal strength with

other at nominal.

5. The steering distance is calculated from the mean distance between the beam centers

of the four tune images taken using the viewer image analysis tool described in Section

4.3.1.

6. The dipole currents are simultaneously decreased by a step size specified by the oper-

ator (typically 0.06 to 0.02 A).

7. Step 3 - 6 are repeated.

8. Once the beam reaches the other end of the viewer, the script is halted and the steering

distance as a function of dipole fields is plotted.

9. The curve is fit with a second degree polynomial, and the corresponding best magnetic

field range is found by the magnetic field corresponding to the lowest steering value of

the best fit and its corresponding uncertainty.

10. The dipoles are set to the best field values after cycling and matching the NMR probes

again.

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Figure 5.2: B1 - B2 dipole scan in steps of 0.06 A on FP1 to minimize steering in Q3 - Q5.
The steering does not reach zero in this case, and this may be due to small deviations of
the beam from the center that are not corrected at FP1. Fine tuning downstream where
sensitivity to such small deviations is increased is often needed.

Figure 5.2 shows the average steering distance due to Q3 and Q4 (varied as detailed

above) as a function of the NMR field value in B1 - B2. This scan was done in steps of

0.06 A to find the region of least steering, then fine tuned with smaller steps of 0.02 A as
shown in Figure 5.3. The error on this steering distance was calculated to be ∼ 10% from
propagating the ± 1.5 pixel error on each x and y position corresponding to the accuracy in

finding the median of the beam profile projected onto each axis (refer to the viewer image

analysis in Chapter 4). The error on the magnetic field took into account the difference in

field measurements between B1 and B2 which was at least 10-5 T and occasionally higher

when small drifts occurred after matching them.

The WF dipoles are tuned in a similar fashion after setting the electrodes to the appro-

priate high voltage settings for the beam being tuned. These are simpler to tune as there is

only one dipole magnet per WF. The quadrupoles Q8 and Q9 installed downstream of WF1

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Figure 5.3: B1 - B2 dipole scan in steps of 0.02 A on FP1 to minimize steering in Q3/Q4.

and before B5 - B6 are used to correct the angle of the outgoing beam from the WF1 mag-

net using the viewer at location D1688. The viewer at D1783 at a larger distance can also

be used when higher sensitivity is needed. Figure 5.4 shows the steering in the x-direction

measured in Q8 and Q9 as a function of the WF1 dipole field at the viewer at D1688. Any

vertical steering observed at this point has to be adjusted by fine tuning the vertical steerers

in ReA3 at these viewers. Only WF1 was installed during the commissioning discussed in

this work, however once installed WF2 will be tuned as described for WF1 using Q12 - Q13

at the viewer downstream of B8 (D1836).

5.3 Bayesian Optimization for Beam Tuning

Although the JENSA apertures allow the incoming angle of the beam to be limited to 3.4

mrad, SECAR requires smaller angles for optimal performance. As seen in the previous

section, having different operators tune SECAR to that requirement manually is a time

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Figure 5.4: WF1 dipole magnet scan to minimize steering in Q8 and Q9 measured at D1688.
The best field corresponding to the beam leaving the WF at the center is shown by the red
dashed line.

consuming task that introduces bias and often leaves the separator in a sub-optimal non-

reproducible state. An automated online Bayesian optimization was shown to efficiently tune

the beam in SECAR during commissioning operations in 2020 thereby ensuring objective

measures of tune quality and leaving the machine in a reproducible state that provides an

optimal beam for maximizing the separator’s performance.

In this section, the Bayesian

approach is described and results from the first beam tests are presented.

5.3.1 The Bayesian Approach

A Bayesian optimization is a gradient-free global maximizer (or minimizer) of an unknown

black-box function f . Each observation of f in the domain is unbiased and possibly noisy,

and constitutes a part of prior data collected that informs the decision of where to place

the next evaluation by applying Bayes’ theorem. The theorem describes the probability of

an event based on prior knowledge of conditions that might be related to the event. This

107

method is an iterative search for a better optimum, making it a sequential optimization

algorithm. It imposes a probabilistic distribution over the objective function values and its

corresponding input axes to find the distribution of the function value at any new point in the

domain. This is then used to choose a better optimum, and once the sample of observation is

collected at that point, the procedure is repeated. The Bayesian optimization is essentially

an interplay of two components. The first one is the underlying probabilistic model of the

objective function, e.g. a Gaussian process. The second key component is the choice of

acquisition function that places the criterion on how to choose the next point. Thorough

introductions to Bayesian optimization can be found in [13, 86].

This approach is often taken when the function f is expensive to evaluate, for example

due to computational limits of simulation codes.

In the case of SECAR, thorough beam

physics simulations incorporating the accelerator beamline upstream are not yet available

and may not be sufficiently accurate. Given the high dimensionality of the system, a robust

optimization of the experimental system is needed to validate and improve on the theoretical

COSY parameters. With a proper surrogate model of the beam response in SECAR to

changes in beamline parameters (magnet settings in SECAR and upstream), a Bayesian

approach presents a good choice for addressing these issues while decreasing the time spent

tuning and eliminating the bias introduced by operators.

Bayesian Priors

In the Bayesian formalism, samples from the true function are used to construct an

estimate of the probabilistic model, i.e. the surrogate model. This surrogate can be used to

model the true function and to select which observations are to be made next by applying

Bayes’ theorem. As there might be an infinite number of possible functions that could be

consistent with the data, priors need to be imposed to inform the model on what is known

108

about the true function, e.g. smoothness, or variability. Assuming a noisy observation y

that depends on an unknown parameter w given an input variable x

y = wx + 


(5.1)

with 
 ∼ N (0, σ2

n) as the stochastic noise in the observation y, a prior distribution p(w) is

defined on the parameter w. Probabilities based on the observed data are then computed as

such

following Bayes’ Rule

p(w|y, X) =

p(y|X, w) × p(w)

p(y|X)

,

posterior =

likelihood × prior
marginal likelihood

(5.2)

(5.3)

where p(w) represents the initial guess of the probability of w, and p(y|X, w) is the likelihood
that y is observed given X and w. The posterior p(w|y, X) then contains information from

both the data and prior distribution. Given a set of observations (y, X), the probability that

a new observation at position x∗ will result in observation y∗ can be calculated as

(cid:90)

p(y∗|x∗, y, X) =

p(y∗|x∗, w)p(w|y, X)dw.

(5.4)

This is referred to as the predictive distribution and it is given by weighting all possible

predictions by their calculated posterior distribution to find the function value at some

point x∗. Assuming the prior and the likelihood to be Gaussian, the predictive distribution

is also Gaussian with a mean and variance corresponding to the predicted value of y∗.

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5.3.2 Gaussian Processes

Gaussian processes are popular in Bayesian modeling for regression and classification. They

are easy to implement, flexible and conveniently provide uncertainty estimates along with

their predictions. A Gaussian process defines a distribution over functions, a generaliza-

tion of the Gaussian probability distribution which describes random variables (scalars or

vectors).

In this work, a Gaussian process method for regression is described as applied

to the tuning of SECAR. For a review on Gaussian processes, see [79]. Formally, a Gaus-

sian process is a stochastic process with all of its finite-dimensional distributions being joint

Gaussian distributions. In the bivariate case, taking a 2D joint Gaussian distribution with

two normally distributed and correlated variables x1 and x2 with covariance matrix elements

Σ12 = Σ21 = 0.7, the conditional probability of one of the variables can be derived given the

other, as a measurement in one dimension (x1 for example) will constrain the distribution

of the other (x2). This example is illustrated in Figure 5.5 where the 2D joint Gaussian

probability density function of x1 and x2 is shown in blue with mean µ1 = µ2 = 0 and

covariance Σ, and the probability of x2 given a measurement of x1 = 1 and given the distri-

bution parameters Θ = ([0, 0]T , Σ) is shown in the black solid line. Analogously to Bayes’

rule in Equation 5.3, this conditional probability can be expressed in terms of the marginal

distributions and the joint density distribution. In a Gaussian process, the posterior can be

similarly expressed from the prior and the observations at all sampled input values to find

the joint probability of all values of the unknown function f for all the input values in the

domain. The Gaussian process then returns the mean and variance of a normal distribution

over the possible values of f at any given input location in the domain.

Just as a Gaussian distribution is completely described by its mean and covariance, a

110

Figure 5.5: Conditional probability of x2 given x1.

Gaussian process is completely specified by its mean function m and covariance function k:

where

and

f (x) ∼ GP(m(x), k(x, x(cid:48)))

m(x) = E[f (x)]

k(x, x(cid:48)) = E[(f (x) − m(x))(f (x(cid:48)) − m(x(cid:48)))].

(5.5)

(5.6)

(5.7)

In this work, the covariance function defines the beam’s response to changes in the input

settings of different magnetic elements in the beamline and was selected to be the popular

squared exponential (SE) kernel. With this choice, the variance is close to unity for variable

with close inputs, and decreases with increasing distance between inputs. The SE function is

111

infinitely differentiable and thus is very smooth, a good model for beam response to magnetic

field changes. The covariance function was defined as

(cid:16) − |xp − xq|2

(cid:17)

,

(5.8)

kSE(xp, xq) = σ2

f exp

2(cid:96)2

where σ2

f is a scaling parameter that represents the output variance, and (cid:96) is the character-

istic lengthscale parameter, a positive constant that roughly describes the distance that can

be covered in the input space before points become correlated. Since experimental data rep-

resents a noisy version of the black box function, an independent and identically distributed

Gaussian noise term 
 with variance σ2

n is added as done in Equation 5.1, and the noisy

observations become y = f (x) + 
. The final form of the covariance function is given by

cov(yp, yq) = kSE(xp, xq) + σ2

nδpq,

(5.9)

where the Kronecker delta δpq is 1 for p = q and zero otherwise. The signal variance

σ2
f , the lengthscale (cid:96), and the noise variance σ2

n parameters are free parameters known as

hyperparameters. The covariance function learns them empirically from prior observed data

through maximizing the log marginal likelihood with respect to the hyperparameters. The

choice of hyperparameters is important as it has a significant effect on the quality of the

Gaussian process predictions, and is discussed more in Subsection 5.3.3.

Assuming a prior that expresses the known beliefs about these parameters given n noisy
observation points x = {x1:n}, taking the prior mean to be zero m(x) = 0 without any loss

of generalization, the prior covariance matrix is defined as

cov(y) = K(x, x) + σ2
nI

(5.10)

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following Equation 5.9. The matrix K is written as



k(x1, x1)

...

. . .
. . .

k(x1, xn)

K =



k(xn, x1)

k(xn, xn)

(5.11)

with k as the SE kernel given in Equation 5.8. Consequently, the prior given noisy data can

be expressed as

y ∼ N (0, K + σ2

nI).

(5.12)

Given a new observation at x∗, the prior y and the output f∗ are jointly Gaussian and the

joint prior distribution is  y

f∗

 ∼ N

(cid:32)

0,

where

K + σ2

kT

nI

(cid:33)

k

k(x∗, x∗)

(5.13)

k = [k(x∗, x1) k(x∗, x2)

. . .

k(x∗, xn)].

(5.14)

To get the posterior distribution over functions, the conditional distribution can be derived

from the joint prior distribution on the observations (see [79] for details):

p(f∗|x, y, x∗) = N (µ(x∗), σ2(x∗)),

where f∗ is the noise free predictions,

µ(x∗) = kT (K + σ2

nI)−1y

113

(5.15)

(5.16)

and

σ2(x∗) = k(x∗, x∗) − kT (K + σ2

nI)−1k.

(5.17)

The predictive distribution of the Gaussian process is completely described by the posterior

mean µ(x∗) and variance σ2(x∗). Note that the latter only depends on the inputs, as expected

for a Gaussian distribution.

5.3.3 Hyperparameter Selection

Since a Gaussian process model is a non-parametric model, its power lies in the crucial

choice of the covariance function k, also known as the kernel function, as it determines most

of the generalization properties of a Gaussian process model (e.g. smoothness, periodicity,

linearity, etc). Therefore the important model parameters are the quantities used to param-

eterize the covariance function. For the selected SE kernel function defined in Equation 5.9,

three parameters, the observation variance σ2

f , the noise variance σ2

n, and the lengthscale

(cid:96) can be freely varied and constitute the hyperparameters of this model. The settings of

these parameters ultimately determine how well the Gaussian process model will capture

the features of the objective function being optimized. For instance, Figure 5.6 shows the

effect of the lengthscale (cid:96) on the SE kernel, highlighting the importance of the choice of

hyperparameters based on the properties of the function being modelled - the smoothness

in this case. Typically the hyperparameter values are learned as samples are collected with

every iteration by maximizing the log-likelihood of the observations, essentially providing a

measure of the likelihood of the data given the model hyperparameters. To increase the effi-

ciency of this learning process, an informative prior on the hyperparameters can be defined

given some known properties of the function being sampled (function smoothness related to

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Figure 5.6: The effect of the lengthscale hyperparameter on the SE kernel from Equation
5.8 for (cid:96) = 0.2, 1, 2. For each hyperparameter value, the function kSE = (0, x) is shown on
the left and random samples from the Gaussian process prior are shown on the right.

the underlying beam physics for example). For an in-depth review on model selection for

Gaussian process regression and marginal likelihood for hyperparameter selection, see [79].

In this work, the observation variance σ2

f is set and optimized by maximizing the log

marginal likelihood with respect to the variance. For the lengthscale (cid:96) and the noise term

σ2
n, a Gaussian prior with an appropriate mean and standard deviation was initialized for

each at the beginning of every run. The initial values were set based on previous tuning

experience and empirical data which made apparent the localized and smooth nature of

the beam response to changes in the beamline. If the beam had some instability coming

from upstream of SECAR and was moving on the viewer while all SECAR magnets were

stable, the prior on the noise hyperparameter was increased accordingly (usually on the scale

of 0.5 - 1 mm). Similarly, the lengthscale prior was adjusted according to the beam spot

115

position’s sensitivity to changes in steerer currents. Subsequently the marginal likelihood

was maximized with respect to each parameter at every new iteration. As will be seen in

the next sections, both hyperparameters varied between tunes and at different locations in

the beamline, making an empirical optimization using the sampled data the best option

currently available to properly select the model’s hyperparameters.

5.3.4 Acquisition Functions

The goal of a Bayesian optimization is to find the globally optimal solution in as few function

evaluations as possible. This can be done through a utility function that, based on the

collected data, estimates which unobserved sample point has the most potential to result in

a maximum. The function determining at what point to evaluate the objective function next

is called an acquisition function a(x). High values in the acquisition function correspond to

high values of the objective function. Simply maximizing a(x) to find the next sampling

point,

xnext = argmax a(x),

(5.18)

is relatively easy to optimize as it depends only on the probabilistic model described by the

posterior distribution derived in Equation 5.15.

There are two methods of searching for the next point with the highest potential for

improvement on the current maximum. One method is to look near points with a high

posterior mean µ(x) - called exploitation, and the other is to prefer points with a high

posterior variance σ2(x) to explore away from known regions - called exploration. Exploiting

too much runs the risk of getting stuck in a local optimum, while exploring too much means

continuing to explore indefinitely even after finding a global optimum. The main property

116

that an acquisition function has to satisfy is the ability to trade-off between exploitation

and exploration when choosing the next sampling point. The three most common types of

acquisition functions are described briefly below.

Probability of Improvement

Initially introduced by Kushner et al. in 1964 [59], the probability of improvement (PI)

function was the first acquisition function to be suggested.

It selects the point with the

highest PI over the current maximum f (x+) as the next query point and is defined for a

normal posterior distribution characterized by µ(x) and σ2(x) as:

P I(x) = P (f (x) ≥ f (x+))

(cid:16) µ(x) − f (x+)

(cid:17)

= Φ

σ(x)

(5.19)

,

where Φ indicates the cumulative distribution function (CDF). The disadvantage of this

approach is that as given above, the PI is purely exploitative as P I(x) will be large when
σ(x) is small. This can be remedied by adding a user-defined trade-off parameter κ ≥ 0 to

the function evaluation f (x+). With this modification, the PI selects the point most likely

to provide an improvement of at least κ.

Expected Improvement

While the PI only looked at how likely is an improvement, a more complete function

would additionally consider the magnitude of the improvement. The expected improvement

function (EI) [71] chooses the next point as the point with the highest expected improvement

over the current max f (x+). The EI expression for a posterior distribution with mean µ(x)

117

and variance σ2(x) is

EI(x) =

(µ(x) − f (x+))Φ(Z) + σ(x)φ(Z)

0

if σ(x) > 0

if σ(x) = 0

with

µ(x) − f (x+)

σ(x)

,

Z =

(5.20)

(5.21)

where Φ and φ are the CDF and the probability density function (PDF) of the standard

normal distribution, respectively. Similarly to the modification suggested for P I(x), EI(x)

can be expressed in a more generalized form where a positive user-defined trade-off parameter

κ is added to f (x+) [63].

Lower Confidence Bound

A lower confidence bound (LCB) acquisition function [24] is constructed from the Gaus-

sian process posterior mean function µ(x) and its standard deviation σ(x) and is a simple

heuristic balancing of exploration and exploitation:

LCB(x) = µ(x) − ξσ(x),

(5.22)

where the term ξ is a positive user-defined exploration weight that defines the desired amount

of exploration in regions of large uncertainty. The LCB is minimized (instead of maximized

as in the case of the previously mentioned acquisition functions) and the next measurement

is chosen to be sampled at that minimum and added to the GP. An analogous acquisition

function, the upper confidence bound (GP-UCB), can be used for maximization problems

instead. One disadvantage with this method is that the choice of exploration weight ξ will

118

depend on each specific application and may not always be straightforward to set.

In this work, a lower confidence bound (LCB) acquisition function with user defined

exploration weight ξ was employed to select the next observation points. This choice presents

a direct way to balance exploitation and exploration and a simple bound on how close each

point is to the minimum.

5.3.5 Method and Algorithm

Implementing an online Bayesian approach to tuning SECAR required the integration of

several parts, including the control system for the magnets being tuned, extraction of ob-

servations through diagnostics devices, and running the optimization program online during

experiments. To facilitate communication between the optimization program and the control

system described earlier in Section 4.1, PyEpics, a Python interface to the EPICS Chan-

nel Access (CA) library for the EPICS control system [73], was used. The Python GPy

library [39] and the associated GPyOpt [92] tool were used for the Bayesian optimization

and the Gaussian process framework, respectively. The viewer analysis tool discussed in

Section 4.3.1 was used to generate the observations needed for the algorithm when sampling

the unknown function. Although the diagnostic device was the same, the evaluation of the

objective function at the viewer was different for each of the two optimizations described in

this work. The beam incoming angle optimization was concerned with the steering of the

beam measured at the viewer as is explained in detail in Subsection 5.3.6, and the ion optics

optimization was modeling an objective function that depended on the beam spot’s location

and width in the x- and y- direction as is presented in Subsection 5.3.7.

While the objective function and the implementation varied depending on the optimiza-

tion goal, the general algorithm remained the same and is described in Algorithm 1. Before

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Algorithm 1 General Bayesian optimization algorithm for SECAR tuning.

1: Randomly select initial sampling point and evaluate objective function
2: while some stopping criterion is not met do
3:

Maximize the acquisition function using the posterior mean and variance under the

set exploration weight set to find next sampling point

Evaluate the objective function at the selected point
Add new observation to set of samples

4:
5:
6: Select the minimum of the objective function evaluations to be the final tune

every optimization run, priors on the hyperparameters were defined before initializing the

algorithm. As the beam tune quality varied throughout the different experiments, the prior

on the noise term σ2

n in the covariance function was defined each time as a Gaussian with a

mean and standard deviation that best described the noise observed in the viewer images,
n ∼ N (1, 0.5) (in units of pixels2). The prior on the lengthscale of the kernel

typically σ2

chosen for the Gaussian process as defined in Equation 5.8 was also chosen to be of Gaussian

form with a mean and standard deviation that best described how quickly the beam optics

changed with changes in magnet settings, and varied from run to run. These parameters

were empirically defined after observing the behavior of the beam in previous tuning runs

and selecting the values that maximize speed of convergence to a global minimum. The

exploration weight ξ was typically around 0.5, up to 3 when the domain covered by the

magnets being optimized was large. After initializing the priors on the hyperparameters,

the GPy software package automatically updated the priors at each iteration based on past

observations.

In the early stages of developing this tuning code, the Gaussian process functions were

explicitly defined and the algorithm was developed without the use of any external package

for the framework. At that time, no automated marginal likelihood maximization was yet

implemented for updating the hyperparameters and it was necessary to manually adjust

120

the lengthscale and noise when needed. Later on, the GPy library was adapted due to the

ease of use of the frameworks and accessibility to useful features including setting priors

on the hyperparameters and the capability of automatically adjusting those priors as more

observations are sampled.

It also offered a higher computational efficiency, allowing for

hundreds of samples to be gathered in minutes, the only real bottleneck remaining being the

time it takes for the magnets to settle at new current values before images of the new beam

positions can be taken.

5.3.6 Beam Incoming Angle Optimization

The main drivers behind the need for an efficient automated solution that led to the imple-

mentation of a Bayesian approach to tuning were the subjectivity and the variable efficiency

and capabilities of each operator during manual tuning. A new procedure based on the

manual one detailed in Subsection 5.1.1 was devised based on Algorithm 1. The steps in-

cluding centering the beam on the JENSA viewer and the FP1 viewer, as well as checking

the transmission through the JENSA apertures (current readings) were not included in the

automated procedure but were always checked manually at the end. Although a feedback

from current readings along the system could be incorporated into the objective function,

there currently seems to be little evidence that such a check is needed based on the successful

experimental runs, as the algorithm is already able to find an optimum that allowed for full

transmission through the system.

This optimization utilizes the quadrupoles’ steering effects on the beam particles when

some incoming beam angle with respect to the magnets’ optical axis is present, similarly

to the manual tuning method. It can be done using any combination of quadrupoles and

downstream viewer. For simplicity, in the following discussion only Q1 and Q2 will be

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Figure 5.7: Sampling of an observation at the viewer. Four images taken at different
quadrupole tunes are shown with the beam center location with respect to the central red
dot in mm. The mean steering distance between the four beam spots is 4.7 mm.

considered paired with the FP1 viewer. A selection of four different quadrupole current

settings were chosen for Q1 and Q2 so the beam spot changes were visible on the viewer.

Typical settings were: both at nominal, both at zero, Q1 at half of the nominal while Q2 was

at nominal, and vice versa, while Q3 - Q5 remain at zero to avoid deflection due to B1 and

B2. However the current settings for Q1 and Q2 can be changed according to beam behavior

with no noticeable effect on the speed or effectiveness of the method. The algorithm samples

the objective function by taking four images at that viewer at the four different quadrupole

settings. The centers of the beam spot at each setting is then computed, and the average

distance between the four is returned as the value of the new observation y. This sampling

process is demonstrated in Figure 5.7. The unknown function that is being minimized is then

the average steering distance as a function of the four ReA3 steerer settings. The acquisition

function is computed and minimized using the posterior mean and variance that included

the new observation, and the next step (next four current values for the steerers) is selected

and sampled. This iterates continuously as the algorithm explores a defined phase space of

the steerer settings and samples the regions with highest probability of minimizing the mean

steering value. The full procedure for tuning into the SECAR beamline using Q1 and Q2 at

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(4.8, 10.5)(6.4, 2.0)(5.2, 5.5)(7.3, 0.2)Q1 - Q2 NominalQ1 - Q2 ZeroQ1 at Half - Q2 NominalQ1 Nominal - Q2 at HalfFP1 is outlined below.

Step-by-Step Automated Tuning Procedure

1. The ReA3 operators tune the beam through the target chamber by maximizing the

current read on FC1 through the JENSA 1.5 and 2 mm slits and keeping aperture

readings at minimum. They also use the ReA3 quadrupoles to ensure a small (ideally

1.5 mm) beam spot at the JENSA viewer. This is done while keeping the four upstream

horizontal and vertical ReA3 steerers at zero current.

2. Q1 - Q2 are set to their nominal tune scaling from the standard COSY map to the

appropriate Bρ, while the others are left at zero. The choice of the four settings used

to sample the steering function is defined and is typically the same as shown in Figure

5.7.

3. The dipoles are set to the value corresponding to the Bρ of the beam, however they are

not typically set to an accurate and calibrated tune yet and the x-position of the beam

is off from the true center - this has no effect on tuning the incoming beam angle.

4. The tuning script is initialized with the desired bounds on the currents for the four

steerers, defining the phase space for the parameters (typically -15 to 15 A, smaller

when fine tuning). The exploration weight of the acquisition function (around 0.5)

and the Gaussian priors for the noise and the covariance function’s lengthscale factor
are also initialized to the desired starting values, typically N (1,0.5) for the noise and
N (10,2) for the lengthscale (note that the lengthscale may have a mean as low as 1 A

at sensitive locations).

5. The optimization code is run following Algorithm 1.

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6. Once the average steering distance reaches a minimum (typically 1 - 2 mm), the code

is manually stopped and the steerers are set to the currents corresponding to the least

steering tune.

7. The steering effects due to Q1 and Q2, along with the beam spot position at the

JENSA viewer, and the transmission including JENSA aperture readings are checked

manually to confirm the quality of the tune.

If the steerer phase space is large, it can be narrowed down around the best settings

found and repeated to fine tune with a smaller exploration weight if needed. Typically this

is done at the next viewer along the beamline. Although much less decision making and

time is needed on the part of the operator compared to the manual tuning, a critical manual

task remains to make sure the images are of acceptable quality for useful data extraction,

including checking for proper background image subtraction and that the beam is hitting

the viewer. Early attempts suffered from the latter problem until a conditional limit on the

threshold was added to the algorithm to automatically check if beam was present at each

iteration. If the condition is not met, the algorithm skips the iteration and moves on to the

next best steerer settings. While this procedure highlighted the steps taken to tune all four

steerers concurrently, it is possible to tune any subset of those steers while keeping others

fixed by simply adjusting the magnet list that the algorithm takes as input. This was done

when steering along one of the axes (usually the vertical axis) only needed adjusting and a

2D optimization was sufficient.

A similar optimization procedure was performed at FP1, FP2 and at viewers downstream

of FP2 using different sets of quadrupoles as shown in Figure 5.1. This was especially

helpful when the steering on the vertical axis needed fine tuning, as the sensitivity to small

124

angles increases further downstream. A simple change in the script to indicate the desired

quadrupoles and correct viewer location can be made to switch the image acquisition to

whichever viewer is being used. The first step was always to adjust the beam angle into

the first section of SECAR at FP1, and the optimization was repeated at any subsequent

viewer where steering was observed as the beam was transported through SECAR with the

corresponding upstream quadrupoles as probes for the incoming angle. In many cases, it

was critical to optimize the steering in several quadrupoles at and past FP2 to obtain a good

tune at the mass slits at FP2.

The general process to tune up to FP2 was as follows: After an on-axis tune was obtained

at FP1, the dipoles pairs B1 - B2 and B3 - B4 and the WF1 were set following the tuning

procedure described in Section 5.1.1. Once the beam was transmitted to FP2, the steering

due to Q1 and Q2 was checked again at that location, in addition to any steering in the

vertical direction observed with any of Q5 - Q7 upstream of FP2.

If vertical steering is

observed, the automated procedure is repeated using only the vertical ReA3 steerers, and

varying the settings of the quadrupoles that steer while keeping the others at their nominal

currents. The steerers’ domain was constrained further when fine tuning to exploit the region
of low steering that was already found, and generally taken as around ± 2 A of the current

best tune. Steering in the x-direction at FP2 and beyond is generally dealt with by carefully

tuning the dipole and the WF1 magnetic fields.

Results

When the code is run, a first observation is made of the tune’s initial settings and the

first value of the objective function is calculated (total steering distance in 1D or 2D in pixels

or mm). This value is then used as the input to the first iteration of Bayesian optimization

in which the posterior mean and variance are computed to optimize the acquisition function.

125

Since computing these quantities is not costly, they are obtained for a large number of points

in the phase space of optimization defined for the steerer magnets as shown in Figure 5.8.

The left column shows a heatmap the posterior mean µ(x), the middle shows the posterior

standard deviation (SD) σ(x), and the right column shows the acquisition function for the

most recent observation with a constant exploration weight ξ. In the posterior mean and

SD heatmaps, the observations are overlayed as circular data points on the grid. The first

observation point is shown in white while the next observations are shown in gradually

darker shades of red, up to the most recent observation shown in dark red. The three rows

correspond to three different instances where a 2D optimization was performed on either the

vertical or horizontal steerers over different phase spaces as indicated by the axes. It can be

seen from the posterior mean maps that it is low where the observation mean is low. Whereas

for the posterior SD, it is low near the observed parts of the domain (near the sampled points)

and high further away from them. On the acquisition function plots, the white cross indicates

the next sample point, i.e. the minimum of the acquisition function. A good balance was

achieved with exploration weight ξ of at least 0.5. The values adopted allowed for enough

exploration to find the region of the global minimum after which exploitation was responsible

for the fine tuning of the minimum value.

Figure 5.9 shows the speed of convergence of the algorithm for different setups. The

domain varied in each case for each steerer magnet. The smallest domain shown in this

figure was (-3,3) A for the two vertical steerers corresponding to the 2D with 133Cs line,

while the largest domain was (-10,10) A for each of the four steerers, corresponding to the

4D with 133Cs line. In general all 2D optimizations converged within 15 to 20 iterations, while

4D optimizations took about double the number iterations, occasionally needing around 60

when the tune was particularly difficult and the phase space was large. The main criterion for

126

(a) (cid:96) = 10.8 A, σ2

n = 1.15 pixels2, ξ = 3

(b) (cid:96) = 1.2 A, σ2

n = 3.5 pixels2, ξ = 0.5

(c) (cid:96) = 5.1 A, σ2

n = 0.07 pixels2, ξ = 0.3

Figure 5.8: The posterior mean (left), standard deviation of the mean (middle) and acqui-
sition function (right) for three different 2D steerer optimization runs. The observations are
shown in the first left and middle columns by dots shaded by time of observation, with the
darkest shade of red being the most recent observation. The next sample point is shown in
the right column by the white cross indicating the minimum of the acquisition function. The
most recent mean value for for lengthscale and noise variance priors are noted for each, as
well as the exploration weight used.

127

Figure 5.9: Best steering distance reached as a function of number of GP iterations, for 2D
(vertical) and 4D optimizations during two different beam commissioning runs.

accepting a tune was reaching a minimum average steering distance from the initial nominal

tune of at most 5 mm, typically closer to 2 mm, to avoid having deflection outside of the slit

gaps that will be used at the focal planes while maximizing the transmission through the

JENSA apertures and to the SECAR focal planes.

Figure 5.10 shows the beam spot steering between four quadrupole tunes at FP1 before

(images a - d) and after (images e - h) optimization of the steerers where there was an order

of magnitude of improvement on the steering distance. All images were taken at FP1 before

the bending magnets were adjusted, so the x-position is not the final beam position. Only

the first two quadrupoles upstream of the first two bending magnets, Q1 and Q2, were varied

in strength in each image to create a deflection due to the incoming beam angle while Q3 -

Q5 were set to zero. These results were obtained in 16 iterations with an exploration weight
of 0.5 and initial priors for the lengthscale as N (6, 2) and for the noise variance as N (1, 0.5).

The currents of the four steerers were free to vary within limits constrained only by the

128

visibility of the beam on the viewer. It would not have been possible to achieve to this level

of precision with this efficiency with manual tuning.

This method was applied at every viewer up to the final focal plane along the SECAR

beamline utilizing the quadrupoles upstream of each viewer to fine tune the angular deviation

at each location. This was especially helpful to reduce small angular deviations whose effects

were negligible at the first viewer location but significant towards the last section of the

beamline. Full transmission was obtained after every run when the steerer domains were

properly selected, indicating that there is little need for the algorithm to check transmission

at every iteration. However such an addition to the objective function would help the

algorithm constrain the domain as it explores without much input from the operators.

Final Angular Deviation

While observing steering effects gives some direction as to how the angular deviation of

the beam from the optical axis is changing, quantifying these changes is not straightforward.

To understand how tuning is impacting the beam angle, ion optical calculations using COSY

INFINITY were used to determine the incoming angle that could create the observed level

of steering for several runs. Since the x-direction along SECAR is dependent on the dipoles

and the Wien filters, only the y-steering is discussed here.

Starting with an initial beam tune prior to optimization of the angular deviation, four

images of the beam spot location at FP1, FP2 and D1688 corresponding to four different

quadrupole tunes were taken with the viewers at each location. The beam spot location in

the x- and y-direction was found for each, and the beam was observed to be steering around

7 mm at all locations. To compare these experimental results with COSY, the transfer

matrix was calculated for each quadrupole setting, and the beam spot center in the x- and

y-direction was found at FP1, FP2 and D1688 for a large range of initial beam angles covering

129

Figure 5.10: Beam spot steering at FP1 before (a - d) and after (e - h) optimization of the
beam angle for a 4D run with a 20Ne beam. The steering decreased from an average of 7
mm to an average of 0.2 mm. All axes are in pixels, and 16 pixels correspond to 5 mm.

130

-3.4 to 3.4 mrad. The initial angular deviation in the y-direction that could lead to a 7 mm

steering was found to be 1.6 mrad.

The same comparison was repeated for the beam spot images after the incoming beam

angle was adjusted using the Bayesian optimization at each of those locations. The remaining

steering seen experimentally in the y-direction after optimization was 0.7, 0.4 and 0.6 mm

at FP1, FP2 and D1688 respectively. It was found using COSY that the incoming y-angle

explaining these results was 0.8 mrad.

These results highlight the effects of angular deviations as small as 1.6 mrad at the

target and the importance of minimizing that deviation at different locations in SECAR.

The tuning method presented is sensitive enough to ensure angles of <1 mrad on the target

that are needed for full recoil acceptance. The effectiveness of the tuning procedure is highly

dependent on the initial conditions of the beam, especially the upstream ReA3 beamline as

it affects the beam at the JENSA target location. From multiple beam tests and ion optics

comparisons, it was shown that the steering can be minimized to negligible levels, provided

that the initial starting tune’s angular deviation is not too large.

5.3.7 Ion Optics Optimization

For optimal separator performance, the unreacted beam particle suppression needs to be

maximized by minimizing the horizontal beam spot sizes at the mass selection focal planes

(FP2 and FP3). As only WF1 was installed at the time of these beam runs, optimization at

FP2 is discussed in this work. Having a well focused beam of recoils that is well separated

from the equally well focused unreacted beam is crucial for the mass resolution. To optimize

the beam rejection, the ratio of the width w of the beam spot to the horizontal distance

between the recoil focus and the unreacted beam focus ∆x needs to be minimized at FP2 (see

131

Figure 3.5 for reference, black and blue lines). This allows for the slits to be closed as tightly

as possible around the recoils and reduce transmission of any unwanted beam particles. Both

the width and the beam separation are characteristic of the specific beam optics for each

reaction: ∆x is related to the mass difference between the beam and the recoil, while for

given beam properties w depends solely on the quadrupoles Q1 - Q7, hexapoles Hex1 - Hex3,

and the octupole Oct1 settings upstream of the velocity filter (WF1). While the optimal ion

optical tune was determined through COSY INFINITY simulations, the best experimental

ion optical setting is likely to be different owing to imperfections in the simulation. Therefore

to minimize w/∆x, all focusing magnets upstream of FP2 need to be adjusted in such a way to

minimize the width w at the mass slits while keeping full transmission and the beam position

centered between the slits. This multidimensional optimization was tested during SECAR

commissioning operations using the Bayesian approach described in Subsection 5.3.1, and is

discussed here in detail.

The final ion optical settings need to transmit the beam fully within the angular (± 25
mrad) and energy (± 3.1%) acceptance of the device (see Chapter 3 or [6] for more details on

the SECAR design parameters). Along with a narrow beam spot width, having an ion optical

focus so that the beam spot does not move within the separator’s acceptance is crucial to

allow slit gaps as narrow as possible. In this work, the limits of the energy acceptance were
pushed by optimizing the focused beam spot position within an energy range of ± 4% and

ensuring the beam spot did not move significantly within that energy range. In the future,

a similar measurement needs to be done for the angular acceptance.

Method

Once a well-aligned beam was transmitted to FP2, and after the WF1 settings were opti-

mized, the quadrupoles (and some hexapoles) were optimized at the FP2 viewer. Algorithm

132

?? was adapted to this optimization goal. The unknown function f to be minimized now

represents the beam spot width in the x-direction (projected on the x-axis) as a function of

all seven quadrupole tune settings, as well as one or more of the hexapole magnets available

upstream of FP2 (Hex3 and Oct1 were not included in these tests). The observations sam-

pled in this case were simply the horizontal beam spot widths directly measured from the
viewer images at FP2, defined as ± 1σ from the median peak of the beam spot following

the viewer analysis method described in Section 4.3.1. The optimization takes the selected

magnet current setting parameters as inputs and iterates over possible combinations to guide

the selection of the next observation point.

As the optimization is being done at +4% and -4% dE/E as well at the nominal energy,

some sampled ion optical settings resulted in a very narrow beam, albeit away from the ion

optical center of the beamline (effect of quadrupole steering when the beamline is not at

the optimized initial energy tune). Additionally, depending on the tune being sampled, the

beam occasionally took a shape that is too long in the y-direction - the beam spot edges

could not be seen on the top and bottom of the viewers, raising concerns about losses in

the beamline. To avoid having to check the transmission at every iteration, the beam spot

widths in both x- and y-direction were checked by the optimizer at every iteration, a method

that has provided 100% transmission as checked manually at the end of each optimization.

To achieve that while keeping the beam centered, the objective function was weighted with

the width in the y-direction, keeping it at most the size of a third of the viewer height, and

penalized when the center location in the x-direction was far from the starting position by

more than the size of the width. The final form of the objective function for this ion optical

133

optimization took the form

f (xGP , winit,x, wGP,x, wGP,y) =

(cid:18)xGP + wGP,x − xinit,x

(cid:19)4

20

(cid:16)wy

70

+

(cid:17)4

,

(5.23)

where the measurements of the GP sample beam position xGP , initial width in the x-direction

winit,x, sample GP width in the x-direction wGP,x, and sample GP width in the y-direction

wGP,y were observed at the viewer installed at FP2. The function form and weights were

derived empirically after several tests runs to maximize transmission and minimize beam spot

movement from its initial starting point. With the updated objective function, Algorithm

?? was applied with the following details: f was sampled following Equation 5.23, and the

inputs were the magnet current settings being optimized.

Once the optimization is run, the magnet setting providing the smallest value of f over

the energy acceptance is selected as the final optimal tune. The procedure to optimize the

quadrupoles and hexapoles upstream of FP2 is described below.

Step-by-Step Ion Optics Optimization Procedure

1. After achieving a non-steering tune at FP2 and setting B1 - B4 and WF1 correctly,

all the quadrupoles and hexapoles are set to the nominal COSY settings scaled to the

corresponding Bρ (see COSY map in Table 3.2).

2. The initial position and width of the beam spot at FP2 are recorded at this energy.

The former is used in the objective function as shown in Equation 5.23.

3. SECAR is scaled down 4% in energy from the nominal tune. The initial position and

width are recorded at this energy as well.

134

4. The GP code is run to optimize the acquisition function at FP2 using Q1 - Q7 and
Hex1 - Hex2. The domain for all magnets is defined as ± 15 A of the initial nominal

values.

5. Once the algorithm has found a minimum for f in Equation 5.23 corresponding to a

beam spot within about 2 mm of the original beam spot position and with a width

smaller than the initial width, this best tune and width are recorded and called c1 1

(c* $ convention is followed where c stands for candidate, * denotes the iteration of

this procedure and $ is the scaling iteration within each procedure).

6. SECAR is scaled up 4% in energy from the nominal tune. The dipoles and WF1 are

cycled. The initial nominal width is recorded at this energy as well as the width using

the scaled c1 1 tune.

7. The GP code is run to optimize the acquisition function at FP2 using Q1 - Q7 and
Hex1 - Hex2. The domain for all magnets is defined as ± 2 A of the scaled c1 1 values.

8. Once a minimum is found again, the best tune and width are recorded and called c1 2

9. SECAR is scaled back to the initial (0%) energy from c1 2 and the width is recorded.

10. SECAR is scaled down 4% in energy again from c1 2 and the width is recorded.

11. The best tune between nominal and c1 2 is selected (or between nominal and all c* $

iterations done).

12. A transmission check is done at every Faraday cup after selecting the final tune.

The best tune is defined as the one that minimizes the horizontal width as well as the

deviation of the beam spot at FP2 from the initial position among all candidates. To quantify

135

that further, the slit gap settings to be used with each beam spot width to have ± 2σ of the
beam pass through with an energy acceptance of ± 4% is calculated, and the tune with the

narrowest slit gap is the final optimized tune.

Results

This method was first tested during the June 2020 commissioning run with a 133Cs41+

beam at 1 MeV/u. The above procedure was followed to optimize within an energy ac-
ceptance of ± 4%. The best tune achieved was labeled c4 2. In this run, the quadrupoles

Q1 to Q7 and the hexapoles Hex1 and Hex2 were optimized. In July 2020, a second op-

timization was run with a 20Ne8+ beam at 1.17 MeV/u where Q1 to Q7 and Q1Hex were

optimized, while Q1Dipole, Hex1 and Hex2 were off. The c4 2 settings were compared to

the last iteration c5 2 and to the nominal starting values. All these tunes were scaled to the

corresponding Bρ of each run. In both the 133Cs and 20Ne case, Hex3 and Oct1 were off.

Figure 5.13 displays the beam spot position (solid red lines) and width (dashed blue lines)

at FP2 for c4 2, nominal, c5 1 and c5 2, with the rows corresponding to +4%, 0%, and -4%

scaling in energy, respectively, for the case of the 20Ne8+ beam. For each tune, the slit gap

that has to be set to in order to let through 2σ of the beam distribution from the x-center

in both directions within the full energy acceptance was calculated. Table 5.1 summarizes

the results for both beam runs. Figure 5.12 shows the speed of convergence for 8D (Q1 - Q7

and Q1Hex) and 9D (Q1 - Q7 and Hex1 - Hex2) optimizations.

It is clear that the method offered an improvement in the width size with the 133Cs beam,

while no improvement was achieved on the nominal settings with the 20Ne beam where the

nominal tune still provided the best optics. A comparison of the beam spot before and

after optimization with the 133Cs beam is given in Figure 5.11. The total shift in x-position

between the two images is about 1.3 mm and no significant change in the length in the

136

133Cs41+,
Bρ =
0.4667 Tm

20Ne8+,
Bρ =
0.3887 Tm

Slits

Left (mm)
Right (mm)
Gap (mm)

Slits

Left (mm)
Right (mm)
Gap (mm)

60.08
66.53
6.45

57.66
65.40
7.74

59.76
65.89
6.13

Nominal C3 1 C4 1 C4 2
60.73
64.92
4.19
Nominal C4 2 C5 1 C5 2
55.40
67.66
12.26

341.5
417.5
12.26

62.02
70.24
8.22

63.79
72.66
8.87

Table 5.1: Slit gaps needed to admit the 2σ beam width within dE/E for each tune.

Figure 5.11: (a) Nominal and (b) after the GP optimization at FP2 for the 133Cs com-
missioning run. Red dots indicate 5 mm. X-axis scale is in pixels, where 31 pixels is 5
mm.

Beam Bρ (Tm) COSY (mm) Nominal (mm) Best (mm)
133Cs
20Ne

0.4667
0.3887

3.55
4.84

3.22
4.84

4.08
4.02

Table 5.2: Beam spot diameter at FP2 calculated in COSY with a target width of 1.5
mm (2σ), compared to the widths (± 2σ) measured experimentally with the nominal beam
settings and with the best settings after optimization.

137

(a)(b)Figure 5.12: Minimum of the objective function defined in Equation 5.23, reached as a
function of number of GP iterations, for 8D and 9D optimizations.

138

dE
E

Nominal

C4 2

C5 1

C5 2

+4%

0%

-4%

Figure 5.13: The 20Ne beam ± 1σ widths within the energy acceptance. Scale is 31 pixels to 5 mm.

139

y-direction is seen. The beam spot widths (± 2σ) were compared with COSY calculations
assuming a ± 1.5 mm radius in the x-direction at the target (2σ) and a negligible beam

angle at the target. The COSY widths were calculated at FP2 and corrected up to fourth

order. The results shown in Table 5.2 indicate that the nominal optics were sufficient to

achieve the nominal mass resolution in the case of the 133Cs beam. However with the 20Ne
beam, a beam size ∼ 20.6% larger than theoretically predicted, and therefore a reduced mass

resolution by the same amount, was observed experimentally. This may be due to higher

order effects since the hexapoles were not included in the 20Ne optimization.

The Bayesian optimization of the optics decreased the beam size by 9.2% in the case

of the 133Cs, but offered no improvement with the 20Ne beam. The latter results may be

attributed to the inclusion of Q1Hex in the optimization, which may have steering effects

on the beam that were not compensated by the Q1Dipole, possibly driving the optimization

away from the best optics.

These results have shown that it is beneficial to experimentally optimize the magnets

when there is room for improvement on the nominal settings as seen in the case of the

133Cs beam. The Bayesian approach taken using Gaussian processes was shown in these

preliminary tests to be an efficient and precise way to achieve that in order to provide the

best beam suppression possible. The 133Cs measurements confirmed the ion optical design.

While it is unclear why for the measurements with the 20Ne beam a larger beam spot size

than predicted was obtained, it may owed to higher order contributions that need to be

corrected to achieve the mass resolution.

In Chapter 7, improvements on the presented

tuning methods and Bayesian optimization are suggested to address this issue in the future.

140

Chapter 6

Dipole Energy Calibration

Astrophysical proton-induced reactions occur in narrow energy bands, and the precise energy

of narrow resonances plays a crucial part in the reaction rate formalism discussed in Chapter

2.

It is therefore necessary for the energy of the ion beams used in direct experimental

measurements of such resonances to be known within a few keV to ensure the energy of

the desired resonance is fully covered by the energy loss in the target. To that end, an

independent and precise determination of the incoming beam energy is needed for SECAR.

This chapter discusses the theory, method and results of the absolute energy calibration of

the first magnetic bend in SECAR.

6.1 Theory

The absolute energy of a beam can typically be determined by the calibration of a bending

magnet using energies of certain known resonances or thresholds.

In the non-relativistic

approximation, the magnetic rigidity of an ion with a total energy E is defined as

√
2AE
Q

,

Bρ =

(6.1)

where A is the ion mass and Q is the ion charge. The effective radius ρ of a dipole bending

magnet is dependent on the integration of the magnetic field along the reference beam

141

trajectory through the magnet, including any fringe fields, divided by the central field. The

central magnetic field needed to force an ion on the central trajectory can be expressed as

√

AE
Q

,

B = k

(6.2)

where k is a constant calibration factor. This factor is a characteristic of the magnet, but

can be dependent on the applied field due to the progressive saturation of the iron poles.

Therefore this factor needs to be experimentally determined for each magnet. Once a magnet

is calibrated and k is known, the energy of a beam on the central trajectory can be directly

related to the magnetic field.

This calibration becomes straightforward when centering on well-known particle energies,

a list of which is recommended in [65]. Proton induced reaction measurements can yield

high precision energy calibrations in the 0.3 - 3.5 MeV energy range. While the use of

(p,n) reaction thresholds is particularly useful for high proton energies (Ep = 4.2 - 9.5

MeV) [12, 95], a disadvantage arises from the lesser-known threshold energies and from high

neutron background at that energy range [94]. Therefore low-energy proton induced reactions

such as (p,γ) are generally employed to calibrate bending magnets. Several calibration

measurements are typically needed to cover different regions of the magnetic rigidity domain

of an instrument, however in most cases the absolute energy determination at higher energies

will still depend on extrapolations towards higher magnetic rigidities. In this work, two well-

known 27Al(p,γ)28Si resonances were used to directly measure the calibration factor at four

different magnetic rigidities covering a significant fraction of the lower half of SECAR’s

rigidity acceptance, from 0.14 to 0.4 Tm. The chosen resonances had narrow widths and

large resonances strengths, ideal for this application, and were suitable for ReA3’s energy

142

ER (keV/u)

1799.75
991.86

Ex (MeV)
13.321 (1+)
12.542 (3+)

ωγ (eV) Γ (keV) BR

Bρ (Tm)

1.94
1.15

0.45
0.10

0.94
0.97

0.3891, 0.1946 H+
0.2888, 0.1444 H+

Beam
2 , H+
2 , H+

Table 6.1: Parameters of 27Al(p,γ)28Si resonances scanned for the dipole calibration.

range (0.3 - 3 MeV/u).

6.2 Resonant Reactions and Target Properties

The magnetic calibration factor in Equation 6.2 was measured with two well-known 27Al(p,γ)

resonances using two different beams (H+ and H+

2 ) with different magnetic rigidities for

each resonance as listed in Table 6.1. The resonance energies ER and strengths ωγ were

adapted from [18], and the excited states Ex and widths Γ from [33]. An overview of narrow

resonance capture reactions and laboratory yield measurements can be found in Chapter 2.

The branching ratios BR taken from the decay schemes in [70] were added up from all the

contributions to the 1.779 MeV first excited state in each cascade. The magnetic rigidity Bρ

with the corresponding projectiles for each resonance scanned is also listed.

In the resonant 27Al(p,γ) reaction, a proton beam impinges on a 27Al target with an

energy that matches the resonance energy ER within its width, and is captured by a target

nucleus to produce an excited 28Si nucleus at a state Ex. At de-excitation, γ-rays are emitted

following the decay cascades described in [70]. The highest branching ratio of the decays in

each cascade corresponds to the dominant transition from Ex to the first excited state at

1.779 MeV (2+), then finally to the ground state (0+). The latter transition’s yield at each

energy was measured by γ-ray detectors installed at the target location. The observed yield

curve has an inflection point and a width corresponding to the resonance energy and the

beam energy spread, respectively. The energy width of the resonances is negligible in the

143

cases considered here.

The 27Al target foil used during these calibration measurements was fabricated at the

NSCL’s detector lab through the process of evaporation. The foil had a thickness 0.11
mg/cm2 (∼ 0.45 µm), falling under the category of semi-thick targets for resonance mea-

surements. The energy loss in the target ∆E, corresponding to 21.4 keV and 14.5 keV at

992 and 1800 keV/u, respectively, is large enough to exceed the width of the resonance and

to observe a thick-target yield curve while still being smaller than the energy distance to
the next lower resonance. At these ratios of ∆E/Γ, ∼ 32 and 214 at 1800 keV/u and 992

keV/u respectively, this semi-thick target yield is comparable to an infinitely thick target

yield. The difference of energies at which the yield is 50% of its maximum and the resonance

energy ER is at most 8×10−3Γ, which is only a 3.6 eV deviation at 1800 keV/u [48]. For
these values of ∆E/Γ, the width is FWHM ≈ ∆E, and the slope of both the low-energy and

high-energy edge of the yield curve is determined by the beam energy spread δ, decreasing
with increasing spread. More significantly, for ratios δ/∆E ∼ 0.5, the maximum yield and

the energy at 50% yield will be influenced by the beam energy resolution, decreasing the

height of the yield curve and shifting the mid-point energy below the resonance energy. Al-

though the beam energy spread was typically around 0.3% in this experiment, this effect was

significant especially with the H+ beam after going through the degrader described below
when the spread was up to 0.5% (∼ 5 keV and 9 keV for the 992 and 1800 MeV/u resonances,

respectively), resulting in a slight shift of the mid-point energy as shown in Figure 6.1. For

this reason, the energy calibration was done by fitting the data with a theoretical yield model

based on Equation 2.29 with the calibration factor k and the beam energy spread δ as fit

parameters, instead of simply finding the mid-point of the rise of the yield curve.

144

Figure 6.1: Effect of the beam energy spread on the maximum yield and on the mid-point
of the rise plotted for a resonance energy of 991.86 keV/u (left) and 1799.75 keV/u (right).
The energy at the mid-point is shown in dashed lines at the different energy spreads.

6.3 Experimental Setup

The dipole calibration experiment was performed in two parts at the NSCL’s ReA3 facility,

where an off-line stable ion beam injector provided a singly charged proton beam using a

small external filament.

In September 2019, the first resonance energy scanned was 992

keV/u with an H+

2 beam. In March 2020, the 1800 keV/u resonance was scanned with a

H+

2 beam, in addition to repeating both the 1800 keV/u and the 992 keV/u resonances with

a H+ beam. A carbon foil of 360 nm was used as a degrader to break the H2 molecule. It

was placed in the object of the horizontal separator (BTS30:D1256), with slits in the object

point closed to 1.5 mm in HO and VE. To provide a consistent energy profile, the energy
slits of ReA3 (BTS30:D1316) were closed to 7.5 mm in order to provide ± 0.5% maximum
energy dispersion (∼ 0.5% FWHM). The setup was identical in both runs except for the

target foil that was swapped for a new one before the March 2020 run.

145

Figure 6.2: JENSA drive setup as used for the dipole calibration runs showing from left to
right: Al target foil on 4 × 4 mm slit, empty 4 × 4 mm slit, empty 1.5 × 1.5 mm slit, viewer
(slanted at a 45° angle). In this image, the drive is retracted out of the beam’s path.

6.3.1 Target Installation

The aluminum foil was self-attached on a 4 × 4 mm stainless steel slit which was mounted
on the JENSA viewer drive along with an identical open 4 × 4 mm slit for background
measurements. Additionally, a 1.5 × 1.5 mm empty slit was mounted for tuning into SECAR

along with the permanent installation of the viewer on that drive. This setup is shown in

Figure 6.2. The drive and the drive motor are installed on the right side of the JENSA

chamber looking downstream.

6.3.2 Gamma Detection Array

An array of 14 Scionix BGO scintillation detectors was installed on the left side of the JENSA

target chamber (downstream direction) in a 7.25 inch diameter circular flange as shown in

Figure 6.3. Each detector is comprised of a hexagonal shaped crystal with a length of 75

mm and face to face diameter of 35 mm, encased in a 0.5 mm thick aluminum housing, and

read out by a 30 mm Hamamatsu photomultiplier tubes. Since the the right side port of the

146

Figure 6.3: Setup of the 14 BGO array used for the dipole calibration runs. The flange is
mounted on the JENSA chamber.

target chamber was taken up by the JENSA diagnostic drive that includes the target foil,

it was not possible to have an array covering both sides of the beamline. For that reason,

this flange was manufactured for this experiment at the University of Notre Dame to bring

the array as close as possible to the target foil. The depth of the flange was 8.8 inches

(accounting for its 0.125 inch thickness), maximizing the efficiency. The center of the flange

is approximately 1.9 inches away from the target when the latter is inserted into position

along the beam axis. The solid angle coverage of the array around the position of the target

foil (in front of the jet) was calculated using a Monte Carlo simulation to be 2.2 sr.

Data Acquisition

The NSCL DDAS system (see Chapter 3) was used to process the BGO array signals

in this measurement [77]. A single XIA digital gamma finder (Pixie-16) was used in a XIA

crate for the 14 detectors. The Pixie-16 module has 16 channels that take the signal coming

from the PMTs and converts them into their digital representation, employing 100 MSPS

147

ADCs. The DDAS crate was read out by a computer through which the NSCLDAQ handled

the data flow produced by the γ-rays in the detector array. The ReadoutGUI was the

main interface with the NSCLDAQ where all experiment controls were handled. A SpectTcl

implementation for unpacking the event data from the NSCLDAQ was used to export the

raw γ-ray spectra for analysis using Python scripts.

BGO Array Calibration and Efficiency

Each of the 14 BGO detectors processes the deposited energy from incoming γ-rays

differently which leads to the same γ-ray energy’s photopeaks showing up at different ADC

channels for each detector. It is thus necessary to individually calibrate each detector in

the array. Once that calibration is applied, the spectra from all detectors can be added

by energy and the array can be treated as one large detector, making low count peaks in

individual spectra more prominent when summed. This energy calibration was done using

the well-know γ-ray decays of a 137Cs and a 60Co radioactive sources. The former emits a

γ-ray at 661.7 keV and the latter emits two γ-rays at 1173.2 and 1332.5 keV. The sources

were placed in the JENSA chamber on the jet receiver, near the location of the target. The

recorded net peaks of known energies from the two calibration sources were fitted in each

detector spectrum with a Gaussian on top of an exponential function to determine the peak

centers. A linear fitting function of the form

energy = m × channel + b

(6.3)

was applied to the channel numbers corresponding to the center of each energy.

Using the net area under the Gaussian fits of the source photopeaks and the known

half-life and current activities of the sources, the array efficiency was determined at those

148

γ-ray energies. A 207Bi source was used in this test as well to determine the efficiency near

the γ-ray energy of interest, however inconsistencies found in the source activity documents

rendered these runs unusable. The 137Cs and 60Co source efficiency measurements were

8.8% at 662 keV and 6.8% for 1332 keV. The array’s efficiency at 1779 keV was varied when

fitting the final yield curve model to the experimental yield as will be described in Section

6.5.4 and resulted in a mean value of 5.7% at 1779 keV.

6.3.3 SECAR Beamline

The first two SECAR dipoles, B1 and B2, were calibrated in this experiment. Four Caylar

NMR probes connected to an NMR20 Gaussmeter are permanently installed in those dipoles.

One high range and one low range probe are in each of B1 and B2, the former covering 0.16

to 0.8 T and the latter 0.037 to 0.18 T. The absolute precision of the field measurement of

the NMR probes is in the order of 10-6. The reader is referred to Chapter 4 for details on

the stability of the NMR probes and the reproducibility of the magnetic fields in the dipoles.

The first part of the SECAR beamline up to FP1 was utilized for the purposes of this

calibration. Three Faraday cups were used to measure transmission through SECAR: the last

ReA3 cup upstream of JENSA (BTS34:D1448), the first cup after Q2 (FC1 at BTS35:D1485)

and the cup at FP1 (FC2 at BTS35:D1542). In order to obtain an accurate calibration, one

has to ensure the beam is on the ion optical axis. This was done by ensuring quadrupoles do

not steer the beam when their strengths are varied. The tuning methods described at length

in Chapter 5 for adjusting the incoming beam angle and setting the dipoles were used in this

calibration experiment. The viewer at FP1 was the main diagnostic tool used for minimizing

steering and tuning the entire setup. The quadrupoles Q1 and Q2, both upstream of B1

and B2, were used to probe the incoming angle of the beam through JENSA along with the

149

JENSA viewer and the ReA3 steerers upstream (BTS34:D1413 and D1431). The angle of

the beam outgoing from B1 and B2, and therefore the dipole NMR field values corresponding

to a centered beam, were adjusted by minimizing the steering in Q3, Q4 and Q5, all three

located between B2 and FP1.

6.4 Experimental Procedures

A properly aligned beam along the beamline’s ion optical axis is critical to achieve accu-

rate calibration of the dipoles. Careful assessment of the delivered beam quality and the

transmission at each energy change was necessary before moving on to data collection and

eventually the tuning of the two dipoles. Some requirements had to be met to confirm a

good starting tune upstream. Those metrics ensured a full beam on the target foil and the

ability to successfully achieve a well-tuned beam at FP1. Transmission from the last ReA3
cup at D1448 through the 4 × 4 slits in the JENSA drive read out on FC1 in SECAR had

to be at least 85%, and the FC1 aperture had to read at most 10% of the current read in the
collector (beam loss to aperture ≤ 10%). Failing to meet these requirements would warrant

a re-tune to adjust the incoming angle upstream or the beam size at the target. To help

constrain the incoming beam angle and keep the beam close to the dipoles’ center axis, the

ReA3 collimators at BTS34:D1435 and BTS34:D1448, each having a 5 mm diameter, were

inserted every time B1 and B2 were being tuned. However no constraints on the angle were

kept downstream of the target as the JENSA apertures (refer to Subsection 3.5.1) at that

location were removed for this experiment due to beam losses that could not be accounted

for in the beam current integration. Additionally as mentioned earlier, the beam energy

spread was fixed by setting the energy slits of ReA3 (BTS30:D1316) at a gap of 7.5 mm in

150

order to provide ± 0.5% maximum energy dispersion (∼ 0.5% FWHM).

After receiving a new beam energy and checking the quality of the tune, the next step
was to collect beam on target data with a subsequent background run through the 4 × 4 slit

at that energy. The current was integrated in FC1 for both those runs. Once the 27Al and

the background spectra were collected, the JENSA drive was removed, the ReA3 collimators

were inserted, and the beam tuning through JENSA using the ReA3 steerers and guided by

the steering in Q1 and Q2 began, until the beam was aligned to the optical axis. Following

that centering, the dipoles were ready to be tuned at that energy by adjusting the magnet

currents to ensure the beam is exiting the dipoles along the center as determined by the

absence of steering in Q3 - Q5.

The method with which the incoming beam angle was adjusted, determining how the

beam enters the dipole pair, varied between the run in September 2019 (the first resonance

energy scan at 992 keV/u with H2) and the remainder of the runs in March 2020.

In

2019, SECAR was still being tuned manually as described in Subsection 5.1.1. By the next

runs in 2020, the automated Bayesian optimization (Section 5.3) was being used to tune

the incoming beam angle coming into SECAR from the ReA3 beamline, and an automated

scanning script (Subsection 5.2) was used to find the dipole fields that centered the beam

along the optical axis of Q3 - Q5. The setup was otherwise identical for all runs.

Once B1 and B2 were set and the beam spot did not steer at FP1, the beam energy was

changed by 1 - 3 keV and the process was repeated until a yield curve was seen. Due to

time constraints and difficulties in obtaining a good tune at some energies, some resonances

could not be sampled sufficiently to observe the full yield curve shape. Additionally, as will
be apparent in the next sections, the beam energy spread (up to ∼ 0.5%) decreased the

maximum yield for some runs, leading to a shift in the energy at which the yield reached

151

50% of its maximum below the resonance energy ER by as much as 0.26% as shown in Figure

6.1. However as noted in Section 6.2, this effect did not introduce any issues in the analysis

presented.

It is important to note that the readings of the NMR probes in B1 and B2 were matched

to within 10-5 T during manual and automated tuning, as specified in Chapter 5, to ensure

no angle is introduced by the dipoles bending at slightly different strengths. Having both

magnets with the same field bending a beam coming in on the optical axis such that it

emerges as it entered, with no angle on the optical axis, allows for the calibration of a single

field parameter for the pair. The cycling method used at the start of each tune followed the

established procedures that were discussed in Chapter 4 to achieve reliable and reproducible

readings. The dipoles were always cycled three times at the beginning of each tune, were

always set by going down in current, and in the event of an increase, were cycled again. This

allowed for reproducible and matched field readings in B1 and B2, and the average of the

two measurements was taken as the calibration field at each scanned energy.

6.5 Analysis and Errors

6.5.1 Beam Current Integration and Normalization

FC1 was used for collecting the beam current during all target runs. In order to correctly
estimate how much beam was impinging on the foil, a background run with the 4 × 4 empty

slit (identical to the target mount) inserted was taken after each target run. The current

readings from each run were extracted from the data archive database for analysis. The

charge collected during the target run was scaled (down for H2 beam and up for H+) to the

background run to correct for losses due to the target widening the beam shape downstream.

152

Figure 6.4: Scaling of two different target run beam currents using background current
readings, within error bars.

The scale factor was determined by taking the ratio of the averages of the last 20% of the

recorded current during the target runs and the first 20% of the background run. The

ion source had some instabilities that included sudden drops in intensity on FC1 readings,

making it difficult to analyze some runs. To account for most of those variations especially
within the time interval between target and background run, a conservative ± 12% error on

the scale factor was introduced. Figure 6.4 shows two runs’ normalization scaling (green line

represents the scaled current) with the associated error shown in shaded blue. As absolute

currents were not needed for the purposes of this calibration, this was sufficient to obtain

relative currents from run to run.

6.5.2 Dipole Field Determination

As mentioned in Section 6.4, the dipole fields at each energy were determined by tuning B1

and B2 through minimizing the steering in Q3, Q4 and Q5. Since tuning was still being done

153

manually in 2019 during the first resonance scan, the fields values were taken as recorded

during each run. By the next runs in March 2020, SECAR tuning had moved to a more

efficient and objective automated scan that employs the steering minimization method.

The automated dipole scan recorded the beam spot center position and the steering

distance due to Q3 - Q5 at FP1 as a function of the average NMR field in B1 and B2. Refer

to Section 5.2 for more details on the scanning method. A parabola was fitted to the scanned

curve and the minimum of the parabola was taken as the calibration field. The error on the
field at the minimum was ∼ 0.05 - 0.07%, and was obtained from the error on the calculated
steering distance in the y-axis that is propagated from the ± 1.5 pixel uncertainty on each

of the four beam spot locations that quantified the steering. Figure 6.5 shows the results

of an automated scan for one of the runs. The steering distance of the beam spot with its

associated error as a function of the average of the NMR readings is shown in blue. The

orange line is a parabolic fit to the data and the dashed line indicates the region where the

best field value lies.

Although the manual and automated methods followed the same criteria for finding the

best tune (least steering region), it is likely some error was introduced in the former as

operators had to select the best tune visually without any objectively quantitative aid. The

subtle differences in steering along the minimum of the curve delineated by the dashed line

in Figure 6.5 are hardly noticeable to the human eye, making the error on the determined

field at least as large as those derived in the parabolic scans. To quantify the error on

the manually derived fields, the mean error and its standard deviation on the field values

from the automated scans (the areas delineated by the dashed line for all March 2020 runs)

was determined, and a σB of 0.05% was adapted for the 992 keV/u with H+

2 resonance scan

measurements.

154

Figure 6.5: B1 - B2 dipole scan on FP1 to minimize steering in Q3 - Q5. The error on the
steering distance is calculated from a 1.5 pixel error on each beam spot location measurement.
The dashed line indicates the region where the best field value lies.

6.5.3 Gamma-ray Spectra

The raw γ-ray data extracted for each individual detector from the NSCLDAQ were energy

calibrated using the calibration curves described in Subsection 6.3.2 then histogrammed and

binned in 5 keV bins. The spectra of all 14 detectors were summed for each run, after which

the Eγ = 1779 keV peak was prominent and easy to identify for all runs. The resonance

yields were obtained from the γ-ray yield of the 1779 keV peak. To do that, each run was
background subtracted after adjusting for the run time using the empty 4 × 4 slit runs,

followed by a Gaussian peak fitting with a χ2-minimization method around the 1.8 MeV

region in the spectrum. For the Ep = 992 keV/u resonance, the peak of interest was isolated

in that region. At Ep = 1800 keV/u, lower energy γ-rays were detected from 27Al(p,α)24Mg

at 1369 keV and from a resonant contribution of 27Al(p,p’)27Al at 844 and 1015 keV [52],

155

Figure 6.6: BGO array spectra of all runs scanning the 1800 keV/u resonance with H2 beam.
The incoming beam energy Ep corresponds to the ReA3 energies reported. From left to right,
the resonant contribution of 27Al(p,p’)27Al at 844 and 1015 keV, the 27Al(p,α)24Mg peak
at 1369 keV, and the 27Al(p,γ)28Si peak at 1779 keV are seen.

as shown in Figure 6.6.

Since this measurement does not aim at deriving absolute resonance strengths but rather

focuses on the relative change in yield between runs, consistency in fitting the data between

runs was emphasized. For all the runs during the 1800 keV/u scans, a Gaussian curve was

fitted to each of the four prominent peaks with an exponential and constant background.

The width was a free fitting parameter for the first peak at 844 keV only, and the other three

widths were each scaled from that width parameter σ844 according to their energy following

156

Figure 6.7: The 1779 keV peak at the Ep = 1800 keV/u resonance with a Gaussian (green)
and a exponential (magenta) plus constant (cyan) background fits. On the left is the (p,α)
peak with a Gaussian fit (blue).

(cid:112)E/844. An example of the resulting fit around the 1779 keV area of

the relation σ = σ844

interest is shown in Figure 6.7. Since the peak was isolated in the 992 keV/u scan spectra,

a single Gaussian with a width scaled from the average width of the 844 keV peak from the

1800 keV/u scans with a constant background was fitted to the data. Summing corrections

were determined to be negligible.

The total number of detected photons from the (p,γ) reaction, N , was extracted by

integrating the area under the Gaussian peak fitted at 1779 keV. The resonance yield at

157

each scanned energy was defined as

Yexp =

N
Np

(6.4)

where Np is the number of incident protons calculated from the total accumulated charge

and the elementary charge e, given the runtime ∆t and the normalization current I

Np =

I∆t

e

.

(6.5)

6.5.4 Yield Curve Fitting and Uncertainties

A thick target yield model was used to derive the magnetic field at the resonance energy,

and therefore the energy calibration factor at that energy. In this calibration, the fitting

parameters for the model were the calibration factor k and the beam energy spread δ. The

upper limit on the energy spread was set to 0.5% as the ReA3 beamline dispersion slits

upstream were adjusted to maintain that constraint at all energies. The theoretical yield

model used to fit the experimental data was adapted from Equation 2.29 and was defined as

Yth,lab =

η BR

ωγ



(cid:104)

λ2
2π

(cid:90) Ei+3δ

Ei−3δ

1√
2πδ

(cid:16)E − ER

(cid:17) − atan

(cid:16) E − ER − ∆E

(cid:17)(cid:105)

− (E−Ei)2
e

2δ2

dE

(6.6)

atan

Γ/2

Γ/2

where λ is the de Broglie wavelength at the resonance energy, ωγ is the resonance strength,


 is the stopping power at the resonance energy, BR is the branching ratio of the 1.779 MeV

γ-ray, ER is the resonance energy, η is the detection efficiency, δ is the energy spread, Γ

158

is the total resonance width, and ∆E is the total energy loss in the target. The resonance

parameters are given in Table 6.1. The stopping power 
 and the energy loss ∆E were

obtained from the SRIM code [101]. Ei, the total energy of the incoming beam, was defined
as B2

k2A2 , where B is the average NMR value of the tune at that energy, A is the total mass
of the incoming beam particle, and k is the dipole calibration factor. Since the BGO array

efficiency η in Equation 6.6 was not known at the γ-ray energies measured (see Section 6.3.2),

it was treated a free parameter in the fitting as well.

The fitting parameters k, δ and η were varied simultaneously within a defined grid space

in a χ2-minimization algorithm to fit the experimental data Yexp to the theoretical yield Yth

given by Equation 6.6. At each point in the three-dimensional space defined by the values

of k, δ, and η, the χ2 statistic was calculated for N data samples following

N(cid:88)

χ2 =

(Yth,i − Yexp,i)2

i

σ2
T,i

,

(6.7)

where the total two-dimensional variance is

σ2
T = σ2

Y +

(cid:16)dYth

dB

(cid:17)2

,

σB

and

(cid:17)2

(cid:16)σY

Y

(cid:17)2

(cid:16)σN

N

(cid:16)σI

(cid:17)2

I

.

+

=

(6.8)

(6.9)

For the choice of a 1σ (68%) confidence interval, the value of the critical χ2 statistic was

derived from the integration of the χ2 probability distribution at 68% or higher

(cid:90) ∞

χ2
υ,68%

f (χ2)dχ2 = 0.32

(6.10)

159

where υ is the number of degrees of freedom, and the probability distribution is defined as

f (χ2) =

1

2υ/2Γ(υ/2)

e−χ2/2(χ2)(υ/2)−1.

(6.11)

All k, δ and η parameters in the search grid that resulted in a χ2 that was less than or

equal than χ2

υ,68% were included in the final result. The mean of the values fallen within the

χ2
υ,68% contour region defined the best fit value for each parameter, and the statistical error

on that mean was the distance to the contour limit values.

A source of systematic uncertainty on this measurement was the SRIM derived stopping
power 
 for H in Al which has an associated ∼ 5% error [51], affecting the height and the

width of the curve. The stopping power was varied within its error to estimate the subsequent

effect on the fitting parameters and it was shown that its contribution to the error on the

calibration factor was at most 0.02%.

A larger source of systematic uncertainty was introduced by the tuning method itself,

and more specifically, how well the beam trajectory through the magnets is known. It was

observed over the tuning runs, including the commissioning runs to FP4 in June and July

of 2020 (see Chapter 5) when small residual angular deviations of the incoming beam angle

were corrected downstream, that the resulting beam spot positions after centering in B1 and
B2 have a spread of ± 1.25 mm at FP1. This measure represents the uncertainty on the

tuning method and the precision to which the ion optical axis is known after centering the

beam and tuning the SECAR beamline. Using the dipole magnets’ measured dispersion of

1363 mm/ dB

B , the effect on the magnetic field is ± 0.09%. This systematic error contribution
to σB was added to the final field values in this calibration, the results of which are presented

below.

160

Figure 6.8: The 27Al(p,γ)28Si resonance at 992 keV/u with an H+
2 beam. The solid curve is
the theoretical yield fit to the data. The dark gray shaded area indicates the region of the
magnetic field at ER within the statistical error of the fit. The light gray shaded area is the
total error.

In the following figures, the results for all of the yield curve fits are presented. The

resonance scans at 992 keV/u are shown in Figures 6.8 and 6.9, and the 1800 keV/u resonance

scans are shown in Figures 6.10 and 6.11. The red curve is the best fit of the theoretical

yield model defined in Equation 6.6 to the measured γ-yield data. The dark gray shaded

areas indicate the region of the magnetic field at ER within the statistical error of the fit,

and the light gray shaded areas are the total error after including the systematic sources of

uncertainty.

Since the yield curve shape is known and is dictated by the physics represented in Equa-

tion 6.6, it was clear that the additional scatter observed in the case of the 1800 keV/u

resonances was introduced by an unknown error in the horizontal direction, and that the

161

Figure 6.9: The 27Al(p,γ)28Si resonance at 992 keV/u with an H+ beam.

Figure 6.10: The 27Al(p,γ)28Si resonance at 1800 keV/u with an H+

2 beam.

162

Figure 6.11: The 27Al(p,γ)28Si resonance at 1800 keV/u with an H+ beam.

error on the NMR field was underestimated. This was likely due to the beam entering

the dipoles at different angles for this particular energy tune. The measured NMR fields

correspond to the beam exiting the dipoles at the center (least steering path through Q3

- Q7) regardless of the point of entrance of the beam into the dipoles. Therefore with an

improperly tuned beam upstream of B1 and B2, the NMR readings may not be providing

an accurate value of what the true field should be when the beam is properly centered. To

quantify the missing uncertainty, the error in the x-axis was increased for this scan to get a

reasonable χ2 value.

163

√

3.64357×10-3
3.65263×10-3
3.64193×10-3
3.63958×10-3

991.86
991.86
1799.75
1799.75

ER (keV/u) k (T

keV amu) dk/k (%)

δ (keV) dδ/δ (%) BR (T)
0.231368
0.115955
0.311478
0.155639

35.97
9.98
28.29
18.20

2.53
4.51
6.15
5.00

dBR/BR (%)

0.07
0.05
0.03
0.02

0.07
0.05
0.03
0.02

Table 6.2: Calibration factors, beam energy spreads and calibration dipole fields obtained
for the 27Al(p,γ)28Si resonance energies with their statistical uncertainties.

6.5.5 Energy Calibration Results

The final fitting parameters for each resonance and their corresponding statistical errors are

summarized in Table 6.2. The final uncertainty on the calibration field BR after adding the

systematic and statistical errors in quadrature was up to 0.12% for the Ep = 992 keV/u scan

and 0.09% for the 1800 keV/u scans. The final mean value for the BGO array efficiency was
5.7% ± 0.5% at 1779 keV.

Since the magnet may exhibit some residual field at zero excitation, a linear regression

with a non-zero intercept was applied to the data. From Equation 6.2, it is clear that the

calibration factor is the slope when looking at the magnetic fields at ER as a function of

the resonance energies. Figure 6.12 displays the resulting linear fit and its residuals from

the resonances measured. The uncertainties on the calibration factor k were derived by

bootstrapping the data: a sub-sample was randomly generated 10000 times with replacement

to compute the error contributions from the fitting and from the input calibration fields. The
resulting calibration factor was k = 3.6501×10-3 ± 6.2×10-6 (0.17%) T/

keV amu.

√

This energy calibration enables the determination of the energy of an incoming beam

from the NMR fields of B1 and B2 once the beam has been properly tuned following the

procedures outlined in Chapter 5. For instance, taking a 20Ne8+ beam (to be used in the final

commissioning experiment planned for SECAR), the projected energies within the magnetic

164

Figure 6.12: Calibration fit to the fields at the resonance energies and their corresponding
errors and residuals. The slope is the dipole calibration factor k.

165

Figure 6.13: Projected energy of a 20Ne8+ beam over the B range in keV (top) and its
projected error in keV (middle) and percent (bottom).

rigidity acceptance of SECAR that can be measured are shown in the top plot of Figure

6.13. The error on that energy estimate is shown in the middle plot, with the value as a

percentage of the beam energy in the bottom plot. For a 20Ne8+ beam with an estimated

energy around 1.18 MeV/u, the uncertainty on an energy measurement using the calibrated
magnets B1 and B2 is ∼ 0.24%.

Comparison to ReA3 Beam Energy Measurements

The beam energy delivered to SECAR is also reported by the ReA3 operations team

based on measurements using a calibrated magnetic beam analyzer with a beam energy
determination uncertainty of ∆E/E ∼ 0.25% [62]. The beam energies determined from

the best fit resonance yield curves in this experiment can be directly compared to these

reported energies. The most straightforward comparison is at the point corresponding to

166

Figure 6.14: The difference between the reported energy (∆E/E ∼ 0.25%) at the mid-point
of each scanned curve and the known resonance energy.

the well-known resonance energy ER. By interpolating the two closest reported energies

to that mid-point, the ReA3 energy at that point, labeled EReA, was determined. Taking

the difference between the resonance energies ER and EReA, it was found that the reported

energies were consistently overestimated.1 The results are visualized in Figure 6.14. This

solidifies the importance of the energy calibration described in this work as an independent

way of measuring the incoming beam energy during SECAR experiments.

Relativistic Calibration

For higher accuracy at higher energies, the energy calibration was also done relativisti-

cally. In this case, the location of the resonance energy ER on the yield curve at the inflection

point is assumed to be the same as the non-relativistic case. A relativistic relationship be-

tween B and E was derived, using the total energy ET and kinetic energy KE definitions:

1It was later found that the time-of-flight calibration of the ReA3 accelerator [96] provides a beam energy

(∆E/E = 0.24%) with deviations from the measured resonance energies of around 1 - 6 keV [43].

167

(cid:113)

(pc)2 + (E0)2

ET = γmc2 =

KE = (γ − 1)mc2,

(6.12)

(6.13)

and

where m is the rest mass, E0 is the rest energy, and γ is the Lorentz factor. Defining E∗ as
(pc)2 and using Equation 6.13, one can write

E∗ = (KE + E0)2 − E2
0 .

(6.14)

Using the results from Table 6.2 and the calculated E∗ at each resonance measurement, a

linear regression of the form

√

E∗
Q

B = krel

+ intercept

(6.15)

was fitted to the data to derive the relativistic calibration factor krel. Figure 6.15 displays

the resulting linear fit and its residuals from the measured data. The resulting calibration
factor was krel = 2.6664×10-6 ± 5.0×10-9 (0.19%) T/keV.

Taking the example of the 20Ne8+ beam again, the projected E∗ values within the mag-

netic rigidity acceptance of SECAR that can be measured are shown in the top plot of Figure

6.16. The error on the prediction is shown in the middle plot, with the value as a percentage
of the E∗ prediction in the bottom plot. For a 20Ne8+ beam with an estimated energy

around 1.18 MeV/u, the uncertainty on an energy measurement using this relativistic cali-
bration is ∼ 0.18%. The relativistic kinetic energy KE derived from E∗, the corresponding

168

Figure 6.15: Relativistic calibration fit to the fields at the resonance energies and their
corresponding errors and residuals.

169

Figure 6.16: Projected E∗ of a 20Ne8+ beam over the B range (top), its projected error
(middle), and percent error (bottom).

non-relativistic energy KE0 (total energy from the top plot of Figure 6.13), and their ratio

are shown in Figure 6.17.

170

Figure 6.17: The relativistic kinetic energy KE (top), the non-relativistic kinetic energy
KE0 (middle), and their ratio with its error shown with the shaded region (bottom) for a
20Ne8+ beam over the B range.

171

Chapter 7

Conclusions

In this thesis, stable beam commissioning of the new SECAR recoil separator was pre-

sented. First, the installation and testing of beamline components including the critical

diagnostics was achieved, in addition to establishing operational procedures necessary to at-

tain reproducible and stable machine states that meet the stringent scientific requirements.

Subsequently, beam tests allowed for the establishment of a tuning procedure and the im-

plementation of an automated online ML-based approach to optimizing magnet settings,

improving the efficiency of the method, the reliability of the results, and the performance

of the device. Additionally, the energy calibration of the first bending magnetic dipole pair

was achieved via measurements of the γ-ray yields of two 27Al(p,γ)28Si resonances.

Beginning with robust diagnostics and reliable electromagnetic components, tuning pro-

cedures were developed to properly transport pilot beams through the beamline. This con-

sisted of adjusting the incoming angle of the beam to center it along SECAR’s ion optical

axis by tuning the ReA3 steerers installed upstream of the JENSA chamber. After this was

achieved, each dipole pair was properly set as the beam was transported through the beam-

line. In an effort to increase objectivity, efficiency, and reproducibility, a ML-based approach

was implemented to optimize the incoming beam’s angular deviation. A viewer image anal-

ysis software was developed to provide the ML algorithm with precise beam spot locations,

facilitating online optimizations. The steering observed on the viewers due to quadrupole

magnet strength changes upstream was used to assess the beam’s deviation from the ion opti-

172

cal center as a function of the ReA3 steerer settings. A minimization of this steering ensures

the beam is on the ion optical axis. This method, previously used by operators tuning by

hand, was successfully implemented into a robust ML algorithm regardless of the beam spot

shape changes associated with quadrupole magnet changes. This first implementation of an

online Bayesian optimization of a nuclear astrophysics recoil separator was shown to increase

the efficiency and precision in achieving the stringent beam parameter requirements needed

for optimal separator performance as compared to manual tuning methods. The beam size

at the target is still manually checked and provided by the ReA3 operations team. While

for the SECAR performance it is critical that the incoming beam on the target has a small

angle (< 1 mrad), there is no diagnostics to ensure this. The gas target apertures restrict the

beam angle only to < 3.4 mrad. In this thesis, it was demonstrated that SECAR diagnostics

in connection with the Bayesian approach for tuning ReA3 beamline steerers can be effec-

tively employed to achieve the required small angles. With this method, negligible angular

deviation in the y-direction was found. A small remaining deviation in the x-direction can be

adjusted with bending optical elements. This method is now used routinely for all separator

tuning, and can generally be applied to other separators and accelerator beamlines.

The ion optical settings of the system are critical for the mass resolution. An optimization

of the quadrupoles and higher order elements was performed within an upper limit of the
energy acceptance of ± 4% using a Bayesian approach with Gaussian processes. A weighted

function incorporating the beam width and location was modeled as a function of the magnet

settings and minimized at FP2. The 133Cs beam measurements confirmed the ion optical

design and were improved by over 9% with the presented method. In the case of the 20Ne

beam measurements, a lower than predicted ion optical performance was observed with

the nominal settings and the approach presented did not succeed in improving it. This

173

may be attributed to higher order contributions that were not corrected in this run. More

measurements are needed to characterize the ion optics of the system.

The energy calibration of the first dipole pair has been completed by measuring 27Al(p,γ)

resonant reactions at Ep = 992 and 1800 keV/u using H+ and H+

2 beams. A BGO detector

array was utilized to measure the γ-ray thick target yield around the resonance energy and
√
resulted in a calibration factor k = 3.6501×10-3 ± 6.2×10-6 (0.17%) T/

keV amu. The

dominant uncertainty in this calibration is attributed to the inconsistent incident beam

angle into the dipole pair. This represents the limitation of the tuning method employed to

adjust the incoming beam angle using the ReA3 steerers. Additionally, a relativistic energy

calibration was done for higher accuracy when extrapolating to higher energies, and the
resulting relativistic calibration factor was krel = 2.6664×10-6 ± 5.0×10-9 (0.19%) T/keV.

7.1 Next Steps and Future Developments

This work constituted a significant portion of the SECAR commissioning. Tests with the

JENSA gas target, along with a verification of the angular and energy acceptances of the

system, remain to be done ahead of the measurement of a 20Ne(p,γ) resonance marking the

completion of the SECAR commissioning operations. Continued work on beamline tuning

procedures and optimizations will build upon the work presented in this thesis. Several

pathways for future developments and improvements are discussed below.

The alignment of the beamline elements arose as a critical issue during the commission-

ing. There are two parts to the alignment. First, the SECAR beamline ion optical center

must be aligned to the ReA3 accelerator beamline. Empirical evidence during tuning has

indicated that there is a slight misalignment in the y-direction (perpendicular to the beam

174

axis) between the ReA3 and the SECAR ion optical axis. This has proven to cause delays

in obtaining an acceptable starting tune for the optimization. Additionally, the last ReA3

quadrupoles installed downstream of the steerer magnets may cause steering in an otherwise

non-steering and centered tune in SECAR, and this makes setting the appropriate focus

and beam spot size that are critical for SECAR performance challenging. This issue may

be resolved by extending the Bayesian optimization to the beam spot size and transmission

through JENSA and the upstream ReA3 quadrupoles. Second, diagnostic elements along

SECAR should be aligned to the optical center. Devices such as BCMs need to be aligned

well in order to be useful for centering the beam. Other devices such as the viewers need not

be perfectly aligned as the methods with which the centering is done do not rely on visual

centers, but rather on the behavior of the steering on the viewers. Several of the viewers

currently installed have center locations that deviate from the optical center by as much as

7 mm. As more tuning experience will lead to better knowledge of the ion optical centers

at all viewer locations, it may be advantageous to align the physical centers of the viewers

with the ion optical center to make tuning more straightforward.

There are several paths to improve and build upon the initial implementation of the

Bayesian optimization to the tuning of the ReA3 steerers presented in this work to increase

the efficiency of the algorithm. Incorporating transmission measurements (at apertures and

Faraday cups) as well as beam position information at the target may increase the efficiency

with which the incoming angle is tuned by providing additional constraints on the steerer

phase space and reducing the number of observations needed. Additionally, expanding the

optimization to include more of the upstream ReA3 beamline or utilizing the extensive ReA3

archived data to inform on incoming beam parameters may be helpful in understanding the

properties of the beam. As stated earlier, extending the Bayesian optimization to include the

175

beam spot size and the transmission through JENSA and the upstream ReA3 quadrupoles

may reduce the complications introduced by any misalignment that exists between the ReA3

and the SECAR beamlines. As more tests are performed and more data is collected, a re-

lationship between beam species, beam rigidity and the hyperparameters of the Gaussian

process covariance function can be derived for each section of the beamline, possibly increas-

ing the efficiency of subsequent runs. Future work can also include thorough ion optical

comparisons of the beam angle in SECAR after the beamline is fully tuned and at different

stages of the optimization to gain a better understanding of the system.

The optimization of the ion optical settings was shown to be successful in the case of the

133Cs beam. Further measurements are needed to assess both the robustness of the method

and the ion optical characteristics of SECAR (i.e. mass resolution) compared to its design,

and to investigate why the method was insufficient in the case of the 20Ne. These measure-

ments should include the optimization of all the higher order corrective elements. Additional

optimizations are needed to confirm the settings within the angular acceptance, for example

by using a foil at the target to create angular straggling and repeating the method presented

in this thesis. The Bayesian optimization may be improved in several ways. As quadrupoles

are designed to work in pairs or triplets, a physics-informed correlation matrix can be added

to the covariance function of the Gaussian process model to arrive at better optics more effi-

ciently (e.g. see [42]). This can be obtained using the currently available COSY INFINITY

model of SECAR. Moreover, the algorithm can be expanded into a multi-objective optimiza-

tion [32] to efficiently improve the COSY model, and ultimately the experimental device,

in achieving a high mass resolution for different scientific experiments. By simultaneously

optimizing several transfer matrix elements including the distance from the beam center in

the x-direction given the initial fractional angle, energy and mass difference of the beam

176

particles compared to mean value at the mass slits, the full Pareto front of this optimization

can be reached with fewer observations. The multi-objective approach can also be useful in

online implementations such as the ones presented in this work where multiple optimization

goals are often being sought out (e.g. see [82]). Combining such methods will make achieving

the design mass resolution possible in an efficient and reproducible way, and may even lead

to further improvements.

Lastly, as tuning procedures improve and more data is available on the central ion optical

axis, it may be beneficial to perform additional measurements to increase accuracy of the

dipole calibration factor obtained in this work.

In the future, this calibration should be

extended to higher rigidities (Bρ = 0.4 - 0.8 Tm), for example using time-of-flight measure-

ments of high rigidity beams.

In conclusion, the work presented in this thesis made significant contributions to the

commissioning of SECAR. This included initial studies of the properties of the system, a

first demonstration of an online ML-based tuning in an astrophysics recoil separator, and

the energy calibration of the first bending dipole pair to provide independent measurements

of the incoming beam energy in SECAR. This work paves the way for SECAR to achieve its

scientific goals by establishing operational approaches that optimize the recoil separator’s

performance. As FRIB comes online, SECAR will be utilized for measurements to improve

our understanding of novae, X-ray bursts, and other explosive astrophysical environments.

177

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