DEVELOPMENT OF RADIOFREQUENCY CARPETS FOR ION TRANSPORT AT
THE NSCL
By
Gregory Keith Pang

A DISSERTATION
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Chemistry
2011

ABSTRACT
DEVELOPMENT OF RADIOFREQUENCY CARPETS FOR ION TRANSPORT AT
THE NSCL
By
Gregory Keith Pang
The low-energy research program at the NSCL is dependent on gas thermalization techniques to convert the energetic nuclear reaction products (100 MeV/u) from projectile fragmentation reactions into high quality low-energy beams (eV). The NSCL is currently developing a gas-ﬁlled reverse cyclotron to provide a high stopping eﬃciency for the incoming fast
beams at pressures that will allow rf ion-guiding techniques to be eﬀective. In this work, the
development and characterization of rf carpets for the eﬃcient ion-guiding and extraction
of projectile fragments from a cyclotron gas stopper was achieved. The transport of Rb ions
within the pressure range expected for cyclotron gas stopper operation of 40 - 110 torr and
over transport distances (up to 40 cm) were investigated. Ion extraction from the rf carpet
was also successfully demonstrated. This work shows that large rf carpets can be constructed
that will work in the cyclotron gas stopper.

ACKNOWLEDGMENTS
Before I thank anyone, I would like to give a special thanks to the graduate program in
nuclear chemistry (and physics) at the NSCL. I could not have asked for a better place to
do my graduate research with regards to personnel, opportunities, and resources.
In preparation of this thesis, many thanks have to go to my advisor Dave Morrissey for
giving his corrections and feedback. I would also like to thank my family and friends for all
their support during my graduate years. Thanks to all LEBIT/Gas Cell members past and
present. You have become some of my closest friends.
Upon leaving, I will certainly miss the intelligent discussion during the Cycstopper/Rf
carpet meetings. I will miss Dave Morrissey’s intuition, Georg Bollen’s enthusiasm, and Stefan Schwarz’s technical expertise.

Finally, I’d like to thank again my advisor Dave Morrissey and Georg Bollen for giving
me such sound advice throughout my graduate career.

You all have taught me more than I know.

iii

Table of Contents
List of Tables

vi

List of Figures

vii

1 Introduction
1.1 Gas thermalization methods . . . . . . .
1.2 Limitations of current gas thermalization
1.3 Proposed solution: cyclotron gas stopper
1.4 The need for RF carpets . . . . . . . . .

. . . . . .
techniques
. . . . . .
. . . . . .

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

2 Ion conﬁnement with radiofrequency (rf ) carpets & early simulations
2.1 Ion conﬁnement with inhomogeneous electric rf-ﬁelds . . . . . . . . . . . .
2.2 The eﬀective potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 The eﬀect of a damping force on the eﬀective potential . . . . . . .
2.3 Multipolar rf ion guides . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Extension: Stacked ring ion guides, rf funnels, rf carpets . . . . . . . . . .
2.5 The rf carpet eﬀective potential . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Stability of ion motion over rf carpets . . . . . . . . . . . . . . . . . . . . .
2.7 Rf carpet simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.1 Rf carpet simulation basics . . . . . . . . . . . . . . . . . . . . . . .
2.7.2 Rf carpet electrode grouping simulations . . . . . . . . . . . . . . .
2.7.3 Hard-sphere (HS) collisions . . . . . . . . . . . . . . . . . . . . . .
3 Rf carpet transport
3.1 The rf carpet test chamber . . . . . . . . . . . . . . . . . . . . .
3.2 Alkali ion source characteristics . . . . . . . . . . . . . . . . . .
3.3 Rf carpet design . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Material requirements . . . . . . . . . . . . . . . . . . .
3.3.2 Typical ﬂex pcb manufacturing constraints . . . . . . . .
3.3.3 General design elements of RF carpets for ion transport .
3.4 Applying rf & dc voltages on the rf carpet . . . . . . . . . . . .
3.4.1 Rf voltages for the rf carpet . . . . . . . . . . . . . . . .
3.4.2 DC voltages for the rf carpet . . . . . . . . . . . . . . . .
3.4.3 Combining the rf and dc voltages . . . . . . . . . . . . .
3.5 Push electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Calibration of the ion source current . . . . . . . . . . . . . . .
iv

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

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

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

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

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

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

.
.
.
.

1
2
4
5
8

.
.
.
.
.
.
.
.
.
.
.

10
10
12
12
13
15
16
19
20
21
25
27

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

30
30
37
41
41
41
42
46
46
49
50
54
56

3.7
3.8
3.9
3.10
3.11
3.12

Linear carpet transport . . . . . . . . . . . . . . . . . . . . . . .
Semi-circle transport and extended semi-circle transport . . . .
Discharge tests . . . . . . . . . . . . . . . . . . . . . . . . . . .
Setting voltages for transport measurements . . . . . . . . . . .
Uncertainty in the transport measurements . . . . . . . . . . . .
Transport measurements . . . . . . . . . . . . . . . . . . . . . .
3.12.1 The eﬀect of the applied rf voltage . . . . . . . . . . . .
3.12.2 Operating pressures of the rf carpet . . . . . . . . . . . .
3.12.3 Transporting ions over long distances . . . . . . . . . . .
3.12.4 Eﬀect of ion current and the push ﬁeld on ion transport .
3.12.5 Ion Extraction from the rf carpet . . . . . . . . . . . . .
3.12.6 Ion drift time measurements . . . . . . . . . . . . . . . .

4 Summary and Outlook

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

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

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

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

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

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

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

58
59
60
62
64
64
64
69
76
81
86
93
96

Bibliography

100

v

List of Tables
1.1

Stopping eﬃciencies for the cyclotron gas stopper at 100 mbar . . . . . . . .

7

2.1

RF carpet electrode grouping simulation workbench parameters. . . . . . . .

23

2.2

Rf carpet electrode grouping simulation LUA user program variables. . . . .

24

2.3

Rf carpet electrode grouping simulation parameters. . . . . . . . . . . . . . .

26

2.4

HS collisions cross-section simulation determinations. . . . . . . . . . . . . .

28

3.1

Pressure readout for rf carpet test chamber and roughing line. . . . . . . . .

35

3.2

Operating parameters for the Heatwave Labs (Model 101139) ion source in
vacuum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

Parameters for the extraction rf carpet used in extraction measurements. . .

87

3.3

vi

List of Figures
1.1

1.2
1.3

1.4

2.1

2.2

2.3

Compilation of the observed extraction eﬃciencies as a function of ionization
rate density (number of buﬀer gas ion-electron pairs (IP) per unit gas volume
per time) for linear gas stopping stations (adopted from [1]). For interpretation
of the references to color in this and all other ﬁgures, the reader is referred to
the electronic version of this dissertation. . . . . . . . . . . . . . . . . . . . .

4

Conceptual drawing of a cross-sectional view of the cyclotron gas stopper. The
ions are stopped close to the center of the device. Adopted from [2]. . . . . .

6

Left: Sample trajectory from simulations of a 79 Br ion passing through the
system at a gas pressure of 175 mbar. Solid degrader not shown. Right: The
ﬁnal distribution of 79 Br ions in the system at a gas pressure of 175 mbar.
The red circular dashed line has a radius of 50 cm and indicates the area in
which the ions are thermalized. . . . . . . . . . . . . . . . . . . . . . . . . .

6

Photograph of a ion collection system with a rf carpet from RIKEN [3]. The
top electrode system has a diameter of 29 cm with 280 electrodes and a central
hole of 10 mm. It is only biased with dc voltages [4] and is used to guide the
ions towards the rf carpet (insert). The rf carpet is located below the top
electrode system and has a diameter of 3 cm with 43 electrodes and an exit
hole of 0.6 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

Illustration of eﬀective force on an ion in an inhomogeneous electric rf-ﬁeld.
Left: Ion placed in between a set of parallel plates (solid) and curved plates
(dotted). Right: Ion’s position over time for the parallel plate (solid) case and
curved plate (dotted) case. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

(1) Resultant quadrupole potential produced by applying a voltage in between
a set of hyperbolic electrodes. (2) Scenario when reversing the polarity of the
potential in (1). (3) Parabolic pseudopotential well the ion experiences if a rf
potential is applied in between the electrodes. . . . . . . . . . . . . . . . . .

14

rf voltage schematic of a quadrupole ion guide. Blue and red hatched patterns
represent the two diﬀerent rf phases separated by 180◦ . . . . . . . . . . . . .

14

vii

2.4

Geometrical arrangement of electrodes and rf voltage schematic of a stacked
ring rf ion guide and a rf funnel. Similar to the quadrupole ion guide, blue
and red hatched patterns represent the two diﬀerent rf phases separated by
180◦ . (1) Schematic of an individual ring electrode. (2) Stacked ring rf ion
guide: the inner radius is held constant. (3) Rf funnel: the inner radius has a
decreasing inner diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

Geometrical arrangement of electrodes and RF voltage schematic for a rf
carpet. The electrodes are laid out in one plane and are typically plated on
printed circuit board (pcb) material. The blue and red stripes represent the
two diﬀerent rf phases separated by 180◦ . . . . . . . . . . . . . . . . . . . . .

16

Ion trajectory from a simulation of an ion with m = 85 u starting at x = 20, y
= 2 along a rf carpet with a = 0.38 mm and g = 0.19 mm run at 1.5 MHz at
200 VRF,pk−pk with a 10 V/cm push ﬁeld and a 8 V/cm drag ﬁeld at 100 mbar.
The carpet would lie along the lower x-axis and the push electrode would be
parallel but at y = 10 mm and are not shown. The trajectory output clearly
shows the ion oscillating up and down due to the frequency of the applied rf
(micromotion) and moving along the rf carpet (macromotion). . . . . . . . .

17

Calculated eﬀective potential for a rf carpet (a = 0.5 mm and γ = 0.5) as a
function of distance away from the carpet superimposed with the static potentials from an electric ﬁeld perpendicular to the carpet electrodes (2 V/mm).
For an ion with A = 85 amu ion at 2 MHz and a rf voltage of 200 VRF,pk−pk
Black Curve: 100 mbar. Red Curve: 10 mbar. . . . . . . . . . . . . . . . . . .

18

The region of ion motion stability over an rf carpet in the (Epr ,Ed /κ) plane
is represented by the area under the curve. . . . . . . . . . . . . . . . . . . .

20

Conceptual schematic of the workbench setup used for ion transport simulations. The blue and red hatch patterns represent the two RF phases of the rf
carpet separated by 180◦ . The push electrodes are represented by the vertical
black lines. The direction of the push ﬁeld and drag ﬁeld are also shown. . .

21

2.10 Simulation workbench for the rf carpet electrode grouping study. The two sets
of electrodes corresponded to the carpet and push electrodes. . . . . . . . . .

22

2.11 Trajectories from a rf carpet simulation with a=1.5, γ=0.7 with simulation
parameters shown in Table 2.3. The carpet electrodes (not shown) are located
at x=0 and the push electrodes (not shown) are located at x=20. Blue line:
No electrode grouping. Black line: Electrode grouping of 4. . . . . . . . . . .

26

2.12 Histogram showing the TOF distribution of 100 ions with a collision crosssection of 2.75E-19×10−19 m2 . The blue vertical line refers to the TOF according to the ion mobility. . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

2.5

2.6

2.7

2.8
2.9

3.1

Mechanical drawing of the rf carpet test stand used for ion transport (1) Front
view of closed test stand. (2) Side view of closed test stand. (3) Front view of
open test stand. The inner diameter of the chamber is 1.2 m. . . . . . . . . .
viii

31

3.2

Mechanical drawing of the rf carpet test stand and the original carpet and
push electrode supports. The (dot-dot-dash) lines show the rf carpet test stand
and the (solid) lines show the carpet and push electrode supports. . . . . . .

32

Mechanical drawing of the clamping method that allowed for easier modiﬁcation of the carpet electrodes without having to redo the clamping process.
The carpet electrodes are represented by the opaque grey rectangular sheets.
Left: Frame on the door side. Right: Frame on the chamber side. . . . . . . .

33

50 cm carpet mounted in a frame. The electrical connections between the
carpet electrodes and the ceramic terminal blocks are visible. . . . . . . . . .

34

Pressure reading inside the chamber during pump out after the chamber was
opened and modiﬁed on three diﬀerent dates. Black circles: 4/18/2008, Red
stars: 5/14/2008, Blue Triangles: 7/1/2008. Blue triangles overlap black circles
and red stars. The TMP was started at ∼22 minutes. . . . . . . . . . . . . .

36

3.6

Dimensions for the ion source given in inches. . . . . . . . . . . . . . . . . .

37

3.7

Results of simulations of the two electrode system for the ion source using
the SIMION code. Both cases were for a pressure of 100 mbar using viscous
damping. Equipotential lines shown in red. Ion trajectories shown in black.
E1 (electrode 1) is the ion source body and the electrode surrounding it at
the same potential. E2 (electrode 2) is the lens in front of the ion source
that eventually became the entire ion source housing. E3 (electrode 3) is a
collection plate. Left: E1 = 90 V, E2 = 80 V, E3 = 33 V. Right: E1 = 100 V,
E2 = 80 V, E3 = 33V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

Exploded view of ion source housing. 1) Lens face of the ion source housing
(electrode #2 in Fig. 3.7). 2) Ion source (electrode #1 in Fig. 3.7). The ions
exit to the left from the lens (1). . . . . . . . . . . . . . . . . . . . . . . . . .

39

Schematic circuit diagram of the revised current measurement setup that allowed measurement of the ion current leaving the ion source, the ion current
reaching the ion source housing, and the ion current reaching the collection
plate. Label (1), Black: Ion source. Label (2), Red: Ion source housing. Label
(3), Green: Collection plate. . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

3.10 A linear carpet design with straight (linear) stripes for the transport area.
The diﬀerent design elements are designated by the numbered areas that are
outlined outlined by the colored dashed lines. (1) Dashed black line: transport
area; (2) Dashed blue line: segmented ion collection area; (3) Dashed red line:
Rf & dc contacts; (4) Dashed green line: clamping area - Kapton (substrate)
border. The coin, included for scale, is a US penny. . . . . . . . . . . . . . .

43

3.11 Photograph of a large rf carpet with a 48 cm transport distance and a pitch of
0.38 mm. The collection electrode (center bottom of the transport area) has
a diameter of 1.8 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

3.3

3.4
3.5

3.8

3.9

ix

3.12 Photograph of surface mount resistors mounted on an rf carpet with a centimeter scale for reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

3.13 Schematic diagram of the LC circuit used to generate the rf voltages for the rf
carpet. CL is the capacitive load determined by the rf carpet. Typical ranges
for the components: Variable Capacitors = 15 - 150 pF, Air-core inductors =
3 - 10 µH, CL = 700 pF - 10 nF. . . . . . . . . . . . . . . . . . . . . . . . .

47

3.14 Schematic diagram of the initial resistive voltage division used to apply the
individual dc voltages to the rf carpet electrodes with the resistor chain located
outside the chamber. eouter and einner refer to the electrodes at the outer
radius and inner radius respectively. ecollect refers to the collection electrode.
g refers to the gap between the rf carpet electrodes. The items encompassed
by the dashed line were in the rf carpet test chamber. . . . . . . . . . . . . .

50

3.15 Schematic diagram of the resistive voltage division used to apply the individual
dc voltages to the rf carpet electrodes with the resistor chain located on the
inside of the chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

3.16 Schematic diagram of the method used for early rf carpet prototypes to apply
the dc voltages and rf voltages to the individual traces. The resistor chain and
capacitors were located on the outside of the test chamber. . . . . . . . . . .

51

3.17 Schematic of the method used to apply the dc voltages and rf voltages to the
individual traces. The resistor chain and capacitors are located on the inside
of the test chamber. The Kapton dielectric is shown in orange. The capacitors
are formed from the two Cu traces. . . . . . . . . . . . . . . . . . . . . . . .

52

3.18 Results from the study of capacitive coupling of the voltages to the individual
traces. The voltage ratio on the top trace to that on the bottom is shown as
a function of fractional overlap of the layers. . . . . . . . . . . . . . . . . . .

53

3.19 Schematic of the voltage designation for the push electrodes using the voltages
on the carpet electrodes as a reference. . . . . . . . . . . . . . . . . . . . . .

54

3.20 A photograph of the ion source located in between a 50 cm rf carpet (right)
and the push electrodes (left). . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.21 Calibration of the ion source output used for transport eﬃciency measurements. 56
3.22 A photograph of the setup used in the transport measurements with the linear
rf carpet. With this setup, the ion source could be moved to the collection
plate to verify the transport eﬃciency. . . . . . . . . . . . . . . . . . . . . .

58

3.23 Test setup for a large 50 cm rf carpet (a = 0.38 mm, γ = 0.5. Push electrodes
are shown on the chamber door. . . . . . . . . . . . . . . . . . . . . . . . . .

59

3.24 A photograph of the support structure and test pad used in the discharge
tests on a 6” conﬂat ﬂange. . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

x

3.25 Measured rf voltage breakdown voltage (frequency shown in plot) for an electrode gap spacing of 0.7 mm and an electrode width of 1 mm. . . . . . . . .

61

3.26 Measured rf breakdown voltage as a function of pd constructed from the rf
breakdown curves taken at three diﬀerent electrode gaps. . . . . . . . . . . .

62

3.27 Range of the measured rf (1.5 MHz) breakdown voltage as a function of the
number of purges at an electrode gap of 0.525 mm and a pressure of 60 torr.

63

3.28 Results from simulations of rf carpet ion transport indicating a pressure scaling
relationship by the collapse of the transport eﬃciency curves in VRF,pk−pk (V )/p(torr)
space. Rf carpet parameters: Rf = 2 MHz, Drag Field = 3 V/ cm, Push Field
= 30 V/cm, Transport Distance = 5 cm, Pitch = 0.38 mm, γ=0.5. Black
diamonds: 30 torr, Red stars: 60 torr. . . . . . . . . . . . . . . . . . . . . . . 65
3.29 Measured transport eﬃciency as a response to the applied rf voltage on the
carpet electrodes. Experimental parameters: Chamber pressure=20 torr, Rf =
3.47 MHz, Drag Field=3 V/cm, Push Field=3 V/cm, Transport Distance=16
cm, Pitch = 0.38 mm, γ=0.5, I(Carp) = 700 pA. . . . . . . . . . . . . . . .

66

3.30 Example of the predicted transport eﬃciency curves scaled from the data in
Fig. 3.29 as a function of the applied rf voltage on the carpet electrodes.
Rf carpet parameters: Rf = 3.47 MHz, Drag Field=3 V/cm, Push Field=3
V/cm, Transport Distance=16 cm, Pitch = 0.38 mm, γ=0.5. Red circles: 40
torr, Blue triangles: 60 torr. . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

3.31 Comparison of measured (open symbols) and predicted (closed symbols) transport eﬃciency curves as a function of the applied rf voltage on the carpet
electrodes. Rf carpet parameters: Rf = 3.47 MHz, Drag Field=3 V/cm, Push
Field=3 V/ cm, Transport Distance=16 cm, Pitch = 0.38 mm, γ=0.5. I(Carp)
= 700 pA Red circles: 40 torr, Blue triangles: 60 torr. Black dot-dash line: discharge limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

3.32 Measured (black squares) and predicted (red circles) transport eﬃciency of
the rf carpet over the operating pressure regime of the cyclotron gas stopper.
Rf carpet parameters: Rf = 3.47 MHz at discharge limit, Drag Field=3 V/cm,
Push Field=3 V/cm, Transport Distance=16 cm, Pitch = 0.38 mm, γ=0.5,
I(Carp) = 700 pA. Black squares: Measured, Red Circles: Predictions. . . .

70

3.33 Predicted transport eﬃciency as a function of pressure for the rf carpets. Rf
carpet parameters: Rf = 3.47 MHz at discharge limit, Drag Field=3 V/cm,
Push Field=3 V/cm, Transport Distance=16 cm, Pitch = 0.38 mm, γ=0.5,
I(Carp) = 700 pA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

3.34 Comparison of transport eﬃciency over the operating pressure regime of the
cyclotron gas stopper for a rf driving frequency of 2 MHz (blue triangles) and
3.47 MHz (black squares). Rf carpet parameters: Rf voltage at discharge limit,
Drag Field = 3 V/cm, Push Field = 3 V/cm, Transport Distance = 16 cm,
Pitch = 0.38 mm, γ = 0.5, I(Carp) = 700 pA. . . . . . . . . . . . . . . . . .

72

xi

3.35 Typical simulated trajectories of ions at 2 MHz (black line) and 3.47 MHz
(red line) showing that increasing the rf driving frequency increases the ion’s
minimum distance from the rf carpet surface (blue line) and therefore increases
the ion’s survivability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

3.36 Comparison of the transport eﬃciency for a pitch of 1.5 mm, γ = 0.7 (red
circles) and a pitch of 0.38 mm, γ = 0.5 (blue triangles). Rf carpet parameters:
Rf voltage at discharge limit, Drag Field = 3 V/cm, Push Field = 3 V/cm,
Transport Distance = 16 cm, I(Carp) ≥ 2.5 nA. . . . . . . . . . . . . . . . .

74

3.37 Comparison of the calculated eﬀective potential a A=85 ion experiences from
a rf carpet with a pitch of 1.5 mm (red circles), 0.38 mm (blue triangles), and
0.25 mm (black squares) in 80 torr of He gas with a driving frequency of 2
MHz, Rf voltage at discharge limit and a push ﬁeld of 10 V/cm. . . . . . . .

75

3.38 Simulated stopping radii for 16 O, 79 Br, and 127 I ions stopped in the cyclotron
gas stopper at 60 torr. The stopping radii correspond to the distances the ions
would need to be transported along the rf carpet. . . . . . . . . . . . . . . .

77

3.39 Measured transport eﬃciency at 20 torr (black squares), 40 torr (red circles),
and 60 torr (blue triangles) over diﬀerent transport distances across the rf
carpet. Rf carpet parameters: Rf voltage at discharge limit at 2 MHz, Drag
Field = 3 V/cm, Push Field = 3 V/cm, I(Carp) = 500 pA. . . . . . . . . .

79

3.40 Measured transport eﬃciency at 80 torr over diﬀerent transport distances
across the rf carpet. Rf carpet parameters: Rf voltage at discharge limit at 2
MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm, I(Carp) = 1 nA. . . . .

80

3.41 Measured transport eﬃciency at 60 torr with I(Carp) = 2.0 nA over diﬀerent
transport distances across the rf carpet. Rf carpet parameters: Rf voltage at
discharge limit at 2 MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm. . . .

81

3.42 Measured transport eﬃciency at 30 torr with varying I(Carp) for a push
ﬁeld of 10 V/ cm (black squares), 15 V/cm (red circles), and 20 V/cm (blue
triangles). Rf carpet parameters: Rf voltage at discharge limit at 2 MHz, Drag
Field = 3 V/cm, Transport Distance = 8 cm. . . . . . . . . . . . . . . . . .

82

3.43 Measured transport eﬃciency at 30 torr (black squares) and 60 torr (red
circles) for varying push ﬁeld strengths. Rf carpet parameters: Rf voltage at
discharge limit at 2 MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm,
Transport Distance = 8 cm, I(Carp) = 2 nA. . . . . . . . . . . . . . . . . .

83

3.44 Transport eﬃciency at 30 torr for a varying push ﬁeld for experiment (black
squares), the ’no space charge limit’ inferred from experiment (red circles),
and HS-collision simulations (blue triangles). Rf carpet parameters: Rf voltage
at discharge limit at 2 MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm,
Experimental transport distance = 8 cm, Simulated transport distance = 5
cm, I(Carp) = 2 nA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

xii

3.45 Transport eﬃciency at 60 torr for a varying push ﬁeld for experiment (blue
triangles), space charge simulations (red circles), and HS-collision simulations
(black squares). Rf carpet parameters: Rf voltage at discharge limit at 2 MHz,
Drag Field = 3 V/cm, Push Field = 3 V/cm, Experimental transport distance
= 8 cm, Simulated transport distance = 5 cm, I(Carp) = 2 nA. . . . . . . .

85

3.46 Photograph of the extraction rf carpet from Wada [3] with an aperture used for
ion extraction measurements. The outer o-ring electrode was used to conﬁne
the ions on the rf carpet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

3.47 Photograph of the setup used for ion extraction. The extraction rf carpet is
mounted below the main (large) rf carpet and a collection electrode is mounted
below the extraction rf carpet (not shown). . . . . . . . . . . . . . . . . . . .

87

3.48 Schematic diagram of the setup used for ion extraction. The red and blue
hatched marks represent the electrodes in which rf was applied. The dotted
electrodes represent the electrodes in which dc voltages were applied. The
diﬀerent collection electrodes for the diﬀerent transport modes are labeled
with their appropriate number designation. Transport mode 1 collected on
the extraction rf carpet electrodes encompassed by the dash line. Transport
mode 2 collected on the o-ring electrode and is encompassed by the dot-dash
line. Transport mode 3 collected on the collection electrode mounted below
the extraction rf carpet encompassed by the dot-dot-dash line. . . . . . . . .

88

3.49 Measured transport eﬃciency for transport mode 2 (collection on the o-ring
electrode) as a function of the rf voltage applied to the extraction rf carpet at a
gas pressure of 40 torr. Main rf carpet parameters: Rf voltage at discharge limit
at 2 MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm, Transport distance
before large hole = 8 cm. Extraction rf carpet parameters: Frequency = 5.28
MHz, Drag Field = 8 V/cm, Push Field = 20 - 27 V/cm. . . . . . . . . . . .

90

3.50 Measured transport eﬃciency for transport mode 3 (collection through the
aperture) as a function of the rf voltage applied to the extraction rf carpet at
a gas pressure of 40 torr at an extraction rf carpet frequency of 5.28 MHz (red
circles) and 8.56 MHz (black squares). Main rf carpet parameters: Rf voltage
at discharge limit at 2 MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm,
Transport distance before large hole = 8 cm. Extraction rf carpet parameters:
Drag Field = 8 V/cm, Push Field = 20 - 27 V/cm, Collect Pull Field = 25
V/cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

3.51 Measured transport eﬃciency for transport mode 3 (collection through the
aperture) at Collect Pull Fields of 25 V/cm (black squares), 40 V/cm (red
circles), and 70 V/cm (blue triangles) as a function of the rf voltage applied to
the extraction rf carpet at a gas pressure of 40 torr. Main rf carpet parameters:
Rf voltage at discharge limit at 2 MHz, Drag Field = 3 V/cm, Push Field =
3 V/cm, Transport distance before large hole = 8 cm. Extraction rf carpet
parameters: Drag Field = 8 V/cm, Push Field = 20 - 27 V/cm. . . . . . . .

92

xiii

3.52 Schematic used for the timing measurements. . . . . . . . . . . . . . . . . .

93

3.53 Measured pulse train (black) and ﬁt curve (red) at 40 torr for rf carpet parameters: Frequency = 3.47 MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm,
Transport Distance = 14.4 cm. . . . . . . . . . . . . . . . . . . . . . . . . .

94

3.54 Comparison of the measured ion transport speed (open red circles) and the
predicted ion transport speeds (black squares) from ion mobility calculations.
Rf carpet parameters: Pressure = 20 torr, Frequency = 2 MHz, 3.47 MHz,
Push Field = 3 V/cm, Transport Distance = 24 cm. . . . . . . . . . . . . . .

95

4.1

Design and arrangement of a series of rf carpets that would allow for a rf
carpet coverage of 1 meter in diameter. . . . . . . . . . . . . . . . . . . . . .

xiv

97

Chapter 1
Introduction
The thermalization of fast ion beams is a proven technique to convert the energetic nuclear
reaction products (100 MeV/u) from projectile fragmentation reactions in to suitable low
energy beams (eV) for precision experiments at the NSCL [5–7]. The NSCL has demonstrated the thermalization through the success of its low-energy program originally centered
on precision mass measurements of exotic nuclei with the LEBIT [8] experimental setup and
is expanding the low-energy program at the NSCL to include colinear laser spectroscopy. In
addition to the low-energy experiments, the thermal ions will be used to provide ions for
further reacceleration. The eﬀectiveness of thermalization of fast ions in a buﬀer gas can
also be seen in the growing number of experimental programs around the world that are
developing the ability to thermalize a wide energy range of reaction products from projectile
fragmentation, fusion-evaporation reactions and nuclear ﬁssion. [3, 5, 9, 10]. As more experimental programs incorporate thermalization in gas, the technique will need to constantly
evolve and improve to satisfy the increasing demand to measure nuclei at the limits of stability. In the vein of improving this technique, the goal of this dissertation was to develop
techniques for the eﬃcient transfer of ions after thermalization in a buﬀer gas to a central
point for collection within the operating conditions of a cyclotron gas stopper [2, 11, 12].
This introductory chapter will ﬁrst cover the basic principles and limitations of linear gas
catchers and gas cells that are presently used to thermalize fast ion beams. Then, possibly
1

removing these limitations in the form of the cyclotron gas stopper will be described and the
need for the development of the ion-guiding techniques described will become apparent.

1.1

Gas thermalization methods

All of the currently used gas catchers utilize the same general techniques to thermalize fast
ion beams. After the fast fragments are slowed down using solid degraders, the ions are
thermalized in a chamber ﬁlled with high-purity He gas. Due to the high ionization potential
of He, the thermalized ions remain singly or doubly-charged and are guided towards the
extraction oriﬁce of a cylindrical gas chamber with electric ﬁelds. Once at the extraction
oriﬁce, gas ﬂow is used to sweep the ions out of the gas chamber. The diﬀerences in devices
lies in the gas pressure used and the diﬀerent combinations of dc and/or rf electric ﬁelds
used to guide the ions towards the extraction oriﬁce.
The two major diﬀerent approaches to thermalization have relied on 1) a high stopping
eﬃciency by having a high gas pressure (up to 760 torr) and a short stopping length, but with
limited ion-guiding with only dc ﬁelds due to the reduced eﬀectiveness of using rf electric
ﬁelds(discussed in Ch. 2). 2) A reduced gas pressure (∼80 torr) and a long stopping path in
the stopping chamber with a low stopping eﬃciency and a combination of dc and rf electric
ﬁelds to focus and collect the ions. The original NSCL linear gas cell [5–7] was operated
with the former approach, and the current RIKEN gas cell [3, 4] is operated with the latter
approach. The equivalent gas thickness is given by the product of the chamber pressure and
length of the chamber (p · l), and for example, a p · l of 0.5 bar-m of He gas is required to
thermalize 100% of energetic beams (A > 60) of approximately 100 MeV/u. Thus, a gas
catcher operated at 1 bar with a chamber length of 0.5 m and and another gas catcher
operated at 0.5 bar with a chamber length of 1 m would have an equivalent target thickness.
An important parameter in the gas thermalization of rare isotopes is the ion extraction time,
which is dependent on the p · l parameter and the strength of the electric ﬁeld used to guide
the ions towards the extraction oriﬁce. Taking a typical electric ﬁeld strength of 10 V/cm, the
2

typical reduced ion mobility of K = 20 cm2 /V·s for medium mass ions in He gas, a p · l of 0.5
bar-m and a chamber at room temperature (298 K), corresponds to an ion extraction time
of 230 ms for ions traveling from the entrance window of the gas chamber to the exit of the
gas cell. For the same parameters and a uniform stopping distribution in the gas chamber,
the average ion extraction time would be 125 ms. These extraction times impose a limitation
in the study of rare isotopes with the shortest half-lives. Reducing these extraction times
could be achieved by lowering p · l, but this would correspond to a lower stopping eﬃciency.
Lowering p · l would have an even greater impact on light ions because light ions require
a longer stopping range because the stopping power, dE/dx, is proportional to Z 2 . The
RIKEN gas cell (length of 2 m and a pressure of 80 torr) reports a stopping eﬃciency of
only 11% for incident 8 Li ions [4]. However, signiﬁcantly increasing p · l to thermalize 100%
of the light ions results in longer extraction times.
At this point, it is useful to introduce the stopping eﬃciency, extraction eﬃciency, and
the product of both eﬃciencies which results in the overall eﬃciency. The stopping eﬃciency,
stop ,

is given by the expression:

stop

=

Nstop
Nincoming

(1.1)

where Nstop and Nincoming refer to the number of stopped ions and the number of incoming
ions respectively. The extraction eﬃciency, extract , is given by the expression:

extract

=

Nextract
Nstop

(1.2)

where Nextract is the number of extracted ions. The overall or total eﬃciency, tot , is then
given by the ﬁnal expression:

tot

= stop × extract = Nextract /Nincoming .

(1.3)

In general, with linear gas catchers, there is a tradeoﬀ between stopping eﬃciency and
3

extraction eﬃciency because of the impact of the p · l parameter. A higher stopping eﬃciency
could be gained by increasing p · l at the cost of increasing ion extraction times and if applicable, reducing the eﬀectiveness of rf ion-guiding techniques. Thus, for linear gas catchers,
the total eﬃciency cannot be maximized.

1.2

Limitations of current gas thermalization techniques

With current gas catchers, there has been evidence of decreasing extraction eﬃciency with
increasing beam rate. These ion losses occur because of the ionization of the He gas during

For interpretation of
the references to
color in this and all
other ﬁgures, the
reader is referred
to the electronic
version of this
dissertation

Figure 1.1: Compilation of the observed extraction eﬃciencies as a function of ionization rate
density (number of buﬀer gas ion-electron pairs (IP) per unit gas volume per time) for linear
gas stopping stations (adopted from [1]). For interpretation of the references to color in this
and all other ﬁgures, the reader is referred to the electronic version of this dissertation.
the slowing down of the incoming ions. The free electrons have a drift velocity in He gas
approximately three orders of magnitude greater than the Helium ions, so the electrons are
4

removed quickly due to the applied ﬁelds in the gas cell, leaving the remaining positive charge
of He ions in the stopping volume. This large remaining positive charge, or space charge,
pushes the desired (positive) ions towards the walls of the gas cell. Without ion conﬁnement
in the radial direction, the desired ions would be lost by collisions with the electrodes. Thus,
the critical parameter of these devices is the ionization rate density, Q (number of buﬀer gas
ion-electron pairs (IP) per unit gas volume per time), that was introduced by Huyse [13].
The compilation of the extraction eﬃciency of various gas cells as a function of Q is shown
in Fig. 1.1 [1].
High-energy (100 MeV/u) beam rates of 105 /s into linear gas catchers have already
been observed in experiments [4, 6] and conﬁrmed through calculations [4] to result in a loss
in extraction eﬃciency of the thermalized ions. Reducing the space charge eﬀects that are
primarily responsible for this loss in eﬃciency can be achieved by operating rf ion-guiding
devices in a manner such that the He ions have an unstable motion and are lost by collisions
with the electrodes, whereas the typically heavier ions of interest have a stable motion and
are safely guided along the electrodes.

1.3

Proposed solution: cyclotron gas stopper

In order to confront the problems introduced in the previous section, the NSCL is developing
a new device to thermalize fast ion beams, called the cyclotron gas stopper [2, 11]. In this
device, the stopping chamber is located in a cyclotron magnet, that conﬁnes the incident
ions during the deceleration process. A conceptual drawing of such a device is shown in
Fig. 1.2. The energetic beam is injected into the system and encounters an adjustable solid
degrader to degrade the beam, so that the resultant beam follows an inwards spiral path and
is thermalized near the center of the magnet. A sample trajectory of an ion in the system
along with the distribution of stopped ions near the center of the system from simulations
is shown in Fig. 1.3.
The cyclotron gas stopper will provide a much longer stopping path length for the ions to
5

Pushing Electrodes

Injected beam

RF Carpet

Pumping

RFQ Ion Guide

Entrance Window

Extracted Beam
Figure 1.2: Conceptual drawing of a cross-sectional view of the cyclotron gas stopper. The
ions are stopped close to the center of the device. Adopted from [2].

-3
3

0
Stopping

-1

3

0
x-y Projection

1

11

3

Incoming Beam
2

0.5
y (m)

y (m)

0

0

y (m)

y (m)

1

00

-1

-0.5
-2

Vacuum Window

-3 -3
-3

-2

-1

0
x (m)

1

2

-1-1

3

-1

x (m)

-0.5

0
x (m)

0.5

1

x (m)

Figure 1.3: Left: Sample trajectory from simulations of a 79 Br ion passing through the system
at a gas pressure of 175 mbar. Solid degrader not shown. Right: The ﬁnal distribution of
79 Br ions in the system at a gas pressure of 175 mbar. The red circular dashed line has a
radius of 50 cm and indicates the area in which the ions are thermalized.
6

Table 1.1: Stopping eﬃciencies for the cyclotron gas stopper at 100 mbar
Ion
stop (no add. degraders)
stop (with add. degraders)
127 I
72%
n/a
79 Br
82%
n/a
16 O
47%
60%

decelerate than can be achieved in a linear gas catcher, therefore increasing the l component
in the p · l parameter, and allowing for higher stopping eﬃciencies at reduced pressures. The
stopping eﬃciencies from simulations performed by the NSCL to study the thermalization of
ions produced from projectile fragmentation in the cyclotron gas stopper for various species
based upon this baseline concept and also a more advanced concept of adding solid degraders
azimuthally around the gas-ﬁlled chamber is shown in Table. 1.1. Additional solid degraders
placed at large radii inside the chamber will allow for lower operating pressures to thermalize
the light ions. The stopping eﬃciencies were found to range from 60 - 90% at 100 mbar (80
torr) for the various species studied. At the same time, the reduced pressures will allow rf
ion-guiding techniques to be more eﬀective and should provide higher extraction eﬃciencies.
As opposed to traditional linear cells in which the collection path length is on the same scale
as the stopping path length, and are both limited by the same p · l, the cyclotron gas stopper
has a separate l component for the stopping path length and the collection path length.
The cycstopper simulations also show ions are typically thermalized within 50 cm of
the extraction oriﬁce that is located on the central axis. Located in the magnet yoke is
a rf quadrupole ion guide that will be used to guide the ions through the diﬀerentially
pumped region. Transport of the ions from the region in which they are thermalized to the
extraction oriﬁce will require a transport method to have the following properties: 1) Operate
eﬃciently in the pressure regime of the cyclotron gas stopper, 2) Eﬃciently transport ions
over distances approaching 50 cm, and 3) Eﬃciently transport ions through an extraction
oriﬁce. The transport method will require an electrostatic ﬁeld to push the ions (designated
throughout the text as the push ﬁeld) towards the half of the magnet yoke in which the
extraction oriﬁce is located. Another electrostatic ﬁeld (designated the drag ﬁeld) is required
7

to guide the ions in towards the central axis. The ions will be prevented from colliding with
the electrodes by a repelling force provided by an alternating-gradient focusing device.
Fast extraction times are still necessary to study rare isotopes with the shortest half-lives,
but will still be determined by the strength of the drag ﬁeld that guides the ions towards the
extraction oriﬁce and the pressure in the stopping chamber. Again, taking a typical electric
ﬁeld strength of 10 V/cm, the typical reduced ion mobility of K = 20 cm2 /V·s for medium
mass ions in He gas, and now a chamber pressure of 100 mbar and a distance of 50 cm,
results in ion extraction times of approximately 25 ms. The operation of rf carpets will be
described in detail in the following chapters. The details of such a device will be introduced
in the following section and discussed in detail throughout the remainder of this text.

1.4

The need for RF carpets

Once the ions are thermalized near the center of the cyclotron gas stopper, the ions must
be guided eﬃciently towards the extraction oriﬁce located on the central axis and then
extracted through the yoke. The advantages in the stopping characteristics of the cyclotron
gas stopper would be lost unless ions could be guided and extracted eﬃciently out of the
stopping chamber.
Given the geometry of the cyclotron gas stopper, electrostatic ﬁelds and the repelling
force provided by an rf carpet can be used to guide the ions towards the extraction oriﬁce.
Rf carpets were ﬁrst developed by M. Wada at RIKEN [3] and are currently in use in their
linear gas cell. A photograph of a rf carpet used by M. Wada is shown in Fig. 1.4. Rf
carpets consist of a planar arrangement of electrodes (M. Wada used concentric electrodes,
but the present study used a variety of electrode shapes) in which rf voltages 180◦ out of
phase on adjacent electrodes, provides a repulsive force that is related to the ion conﬁnement
properties of a quadrupole ion guide. A dc gradient, the drag ﬁeld, is superimposed on the
rf carpet electrodes to guide the ions towards the center of the system and the extraction
oriﬁce. A constant electric ﬁeld perpendicular to the rf carpet, the push ﬁeld, is responsible
8

Figure 1.4: Photograph of a ion collection system with a rf carpet from RIKEN [3]. The top
electrode system has a diameter of 29 cm with 280 electrodes and a central hole of 10 mm.
It is only biased with dc voltages [4] and is used to guide the ions towards the rf carpet
(insert). The rf carpet is located below the top electrode system and has a diameter of 3 cm
with 43 electrodes and an exit hole of 0.6 mm.
for pushing the ions towards the rf carpet and resulting in nice potential minima directly
above the rf carpet.
The motivation of this work was to develop, characterize, and demonstrate a method
using rf carpets to transport ions from the central region of a cyclotron gas stopper to the
extraction oriﬁce. One of the main challenges of the project was the size the system needed to
collect all the thermalized ions (1 meter in diameter based on simulations). The size was also
the main diﬀerence between the previous uses of rf carpets at RIKEN that were restricted
to short ion transport distances (∼5 cm). Transporting ions over a distance approaching 50
cm with a planar rf carpet and the characterization of this device was unique to this project.
In addition to the study being an essential component to the cyclotron gas stopper, any
information gained could also be applied to the development of next-generation linear gas
cell.

9

Chapter 2
Ion conﬁnement with radiofrequency
(rf ) carpets & early simulations
Radiofrequency (rf) carpets control the motion of low energy ions by using inhomogeneous
alternating electric ﬁelds. Devices that employ this method of ion transport and ion conﬁnement have been used extensively in physics, chemistry, and more recently in the study of
rare isotopes. Typical and ideal operating environments are in vacuum or in the presence of
a dilute buﬀer gas. The most prevalent of these devices are multipolar rf ion guides, with the
quadrupole ion guide being the most commonly employed. Since ion conﬁnement is achieved
with inhomogeneous alternating electric ﬁelds, it is instructive to begin the present discussion by introducing the diﬀerences between a homogeneous alternating electric ﬁeld and an
inhomogeneous alternating electric ﬁeld with regards to ion conﬁnement.

2.1

Ion conﬁnement with inhomogeneous electric rfﬁelds

The conﬁning force provided by these structures as introduced by Dehmelt [14] can be
illustrated by placing an ion with charge e and mass m in between a set of parallel plates
that create a homogeneous electric rf-ﬁeld as shown in Fig. 2.1. If a time-dependent potential
10

diﬀerence, Φ(t), between the plates is given by the following equation:

Φ(t) = V0 · cos(Ω · t)

(2.1)

the ion will oscillate about its original position given by the frequency Ω of the applied
rf voltage (called the micromotion). However, the instantaneous force giving rise to this
micromotion or displacement averaged over time is zero and the ion’s average position does
not change over time.
176

Georg Bollen

z

z
0

0

0

t

V cosΩt
0
Fig. 5. Illustration of the origin of the eﬀective force Fn in an inhomogeneous
electric ﬁeld. Top: ion placed between to parallel plates and two bent plates between
which an oscillating voltage is applied. Middle: One oscillation of ion about its local
position. Bottom: Force acting on the ion as a function of time for the parallel
plates (solid line) and the bend plates (dashed line) Right: long term eﬀect of the
oscillating ﬁeld on the ion’s position in both cases.

q = 0 .9

a x ia l p o s itio n

a .u .

q = 0 .3

Figure 2.1: Illustration of eﬀective force on an ion in an inhomogeneous electric rf-ﬁeld. Left:
Ion placed in between a set of parallel plates (solid) and curved plates (dotted). Right: Ion’s
position over time for the parallel plate (solid) case and curved plate (dotted) case.
0

5

1 0

1 5
0

5

t [m s ]

1 0

t [m s ]

Fig. 6. Motion of an ion in an RFQ trap for two diﬀerent rf amplitudes corresponding
Mathieu parameters q = 0.3 and q = 0.9.
By replacing the set toof parallel plates with a set of curved electrodes and therefore

and is described by

introducing an inhomogeneous electric rf-ﬁeld, the ion still undergoes a micromotion, but
U
e
Vpseudo (ρ, z) =

r

m

2ωrf d2
0

2

(ρ2 /4 + z 2 ).

(4)

the micromotion now follows a non-zero average force in the direction of the weaker electric
rf-ﬁeld and the ion slowly drifts (called the macromotion) towards this region of weaker
electric rf-ﬁeld strength.

11

2.2

The eﬀective potential

The conﬁning force provided by an inhomogeneous electric rf-ﬁeld has been described by the
eﬀective or pseudo-potential, Vef f in vacuum, given by:

Vef f =

e
(E 2 )
2 0
4mΩ

(2.2)

where e is the elementary charge, m refers to the mass of the ion, Ω refers to the frequency
of the rf, and E0 refers to the electric ﬁeld strength, respectively.

2.2.1

The eﬀect of a damping force on the eﬀective potential

The devices used to thermalize fast rare isotope beams must operate in the presence of a
buﬀer gas, which damps the micromotion of the ions by collisions and results in a lower
eﬀective potential and a modiﬁed form of Eq. 2.2 [3]:
Ω2
Vef f,damp = 2
V
Ω + D2 ef f

(2.3)

where the damping factor D has the form of:

D=

e
mK

(2.4)

where the K is the ion mobility and is a direct measure of the ion’s drift velocity, vd in gas
with a static electric ﬁeld of strength E:
v
K = d.
E

(2.5)

The ion mobility K is commonly reported as a reduced ion mobility K0 at standard temperature T0 = 273 K and standard pressure p0 = 1013 mbar. An ion traveling in a He buﬀer
gas has a typical reduced ion mobility of approximately 20 cm2 /V·s. Thus, the ion mobility
K from the reduced ion mobility K0 is:
12

p T
K = K0 0 .
p T0

(2.6)

From Eq. 2.3, we can see that the eﬀective potential decreases with 1/p2 and high gas
pressures renders rf techniques ineﬀective at conﬁning low energy ions.

2.3

Multipolar rf ion guides

The idea of the eﬀective potential can be extended to the most popular of the devices that
employ inhomogeneous electric rf-ﬁelds, the quadrupole ion guide [15]. Consider a set of
hyperbolic electrodes, in which a potential, V is applied in between the adjacent electrodes,
the resultant electric quadrupole potential is:

φ=V ·

x2 − y 2
2
r0

(2.7)

where 2r0 is the interelectrode spacing. The electric ﬁeld in x and y is then given by:

Ex = −

2V x
2
r0

,

Ey =

2V y
.
2
r0

(2.8)

Using static potentials, the ion conﬁnement is limited in only one direction. Applying an
alternating potential modulated with a frequency Ω (e.g., rf) and substituting into Eq. 2.2
provides the following eﬀective potential:

Vef f =

e V 2 x2 + y 2
4
m
Ωr0

(2.9)

where x2 + y 2 = r2 and results in a parabolic radial pseudopotential well. Disregarding
additional eﬀects that may lead to ion motion instability, the ions are conﬁned to the center
of the device where the potential minimum is located.
Conceptually, a quadrupole potential produced purely by static voltages produces a
saddle-shape potential that cannot conﬁne an ion in two directions. The application of an
13

(2)

(1)

(3)

Figure 2.2: (1) Resultant quadrupole potential produced by applying a voltage in between a
set of hyperbolic electrodes. (2) Scenario when reversing the polarity of the potential in (1).
(3) Parabolic pseudopotential well the ion experiences if a rf potential is applied in between
the electrodes.
oscillating potential alternately conﬁnes the ions in one dimension and then the other. Classically, this can be viewed as a rotation of the saddle-shape potential along its axis of symmetry
so the ion experiences the resultant parabolic pseudopotential well that conﬁnes the ion in
both directions. In order to achieve this in practical application, radiofrequencies (∼ MHz)
are used.

(V0cosΩt)

r0

(-V0cosΩt)

Figure 2.3: rf voltage schematic of a quadrupole ion guide. Blue and red hatched patterns
represent the two diﬀerent rf phases separated by 180◦ .
The application of rf voltages to operate multipolar rf ion guides requires rf voltages that
14

are 180◦ out of phase on adjacent electrodes. A schematic of this is shown in Fig. 2.3 for a
quadrupole ion guide with rod-shaped electrodes.

- V0cosΩt
V0cosΩt

r

2
z

r

r
3
z

1

Figure 2.4: Geometrical arrangement of electrodes and rf voltage schematic of a stacked ring rf
ion guide and a rf funnel. Similar to the quadrupole ion guide, blue and red hatched patterns
represent the two diﬀerent rf phases separated by 180◦ . (1) Schematic of an individual ring
electrode. (2) Stacked ring rf ion guide: the inner radius is held constant. (3) Rf funnel: the
inner radius has a decreasing inner diameter.

2.4

Extension: Stacked ring ion guides, rf funnels, rf
carpets

These principles of ion conﬁnement can be extended to stacked ring ion guides, rf funnels, and
rf carpets. The application of rf voltages is similar to that in multipole ion guides, in which
a rf voltage applied to each electrode is 180◦ out of phase with any adjacent electrodes. The
only diﬀerence is the electrode shape in these structures. The stacked ring ion guides, as the
name suggests, consists of a stack of rings with the same inner diameter. The rf funnel [16]
15

consists of the same axial arrangement as the stacked ring ion guides, but each electrode has
a decreasing inner diameter (hence the term: funnel). Both rf funnels and stacked ring ion
guides consist of discrete rings which must be fabricated individually and are on the order
of fractions of a ∼mm. Rf carpets [3] diﬀer in this respect, in which the electrodes are in a
planar arrangement of concentric circles laid out on a printed circuit board (pcb). See Fig.
2.4 and 2.5.
Since the principles of ion conﬁnement are identical for the diﬀerent electrode structures,
conﬁned ions exhibit the same characteristic micro- and macromotions. An example of the
ion motion along a rf carpet is shown in Fig. 2.6.

- V0cosΩt
V0cosΩt
y
x

Figure 2.5: Geometrical arrangement of electrodes and RF voltage schematic for a rf carpet.
The electrodes are laid out in one plane and are typically plated on printed circuit board
(pcb) material. The blue and red stripes represent the two diﬀerent rf phases separated by
180◦ .

2.5

The rf carpet eﬀective potential

By solving for Ex and Ey for a rf carpet electrode geometry, the eﬀective potential for a set
of rf carpet electrodes in a buﬀer gas can be calculated using Eq. 2.3. In future discussions,
the gap, g is deﬁned as the spacing between adjacent electrodes and the pitch, a, is deﬁned
as the sum of the electrode width and the gap. From [17],
16


548 22

















548 22
Figure 2.6: Ion trajectory from a simulation of an ion with m = 85 u starting at x = 20, y = 2
along a rf carpet with a = 0.38 mm and g = 0.19 mm run at 1.5 MHz at 200 VRF,pk−pk with
a 10 V/cm push ﬁeld and a 8 V/cm drag ﬁeld at 100 mbar. The carpet would lie along the
lower x-axis and the push electrode would be parallel but at y = 10 mm and are not shown.
The trajectory output clearly shows the ion oscillating up and down due to the frequency of
the applied rf (micromotion) and moving along the rf carpet (macromotion).

V
arctan
Ex =
γaπ

cos π[xr − γ ]
2
sinh (πyr )

− arctan

cos π[xr + γ ]
2
sinh (πyr )

(2.10)

and

Ey =

cosh (πyr ) + sin π xr +
V
ln
2γaπ
cosh (πyr ) − sin π xr +

γ
2
γ
2

where γ, xr , and yr are deﬁned as:

17

·

cosh (πyr ) − sin π xr −
cosh (πyr ) + sin π xr −

γ
2
γ
2

(2.11)

γ=

g
a

(2.12)

xr =

x
a

(2.13)

y
yr = .
a

(2.14)

110.9;0!49039, '


















89,3.0,,1742.,7509 59.

Figure 2.7: Calculated eﬀective potential for a rf carpet (a = 0.5 mm and γ = 0.5) as a
function of distance away from the carpet superimposed with the static potentials from an
electric ﬁeld perpendicular to the carpet electrodes (2 V/mm). For an ion with A = 85 amu
ion at 2 MHz and a rf voltage of 200 VRF,pk−pk Black Curve: 100 mbar. Red Curve: 10
mbar.
The eﬀective potential for a rf carpet with a = 0.5 mm and γ = 0.5 with a voltage setting
of 200 VRF,pk−pk at 2 MHz for a mass of 85 amu is shown in Fig. 2.7 for two diﬀerent
pressures. An electric ﬁeld with a strength of 2 V/mm in the direction perpendicular to the
carpet electrodes, the push ﬁeld, gives rise to the minima in the potentials.
18

2.6

Stability of ion motion over rf carpets

The parameters for stable ion motion along rf carpets can be found in a similar fashion to
the parameters for stable ion motion in a quadrupole ion guide. The criteria for stable ion
motion are stable ion trajectories along the length of the device that are not intercepted by
an electrode. In the case of the quadrupole ion guide, arrival at these parameters starts with
the equation of motion in the form of the Mathieu equation and ends in a ﬁnal parameterized
form of:
d2 u
+ (au − 2qu cos 2ξ)u = 0
dξ 2

(2.15)

where u represents the position and ξ, au , and qu represent the dimensionless parameters:

ξ=

Ωt
2

,

au =

8eU
2
mr0 Ω2

,

qu =

4eV
.
2
mr0 Ω2

(2.16)

In Eqn. 2.16, U represents the applied dc voltage, V represents the applied zero-to-peak
rf voltage, and the other variables have been previously deﬁned. Stable ion motion in a
quadrupole ion guide is dependent on the dimensionless parameters a and q and is represented
by a region (the stability region) in the (q, a) plane.
For rf carpets speciﬁcally [17], the stability parameters are found by including two additional terms that include the damping of the micromotion due to the presence of gas [18],
and the push ﬁeld term. In the case of the rf carpet, the electric ﬁeld in the y-dimension will
determine if an ion’s motion is unstable and the ion collides with an electrode. The resultant
Mathieu equation for an rf carpet is now:
dyπ
d2 y π
= Ed exp(−yπ ) cos(ξ) − Epr − κ
dξ
dξ 2

(2.17)

with the introduction of the term yπ = yπ/a and with now ξ = Ωt. The parameters Ed , Epr ,
and κ are:

19

Ed =

γ
q8V
sin(π ) ,
2 γa2
2
mΩ

Epr =

qπEp
mΩ2 a

,

κ=

D
.
Ω

(2.18)

The stability region for stable ion motion over the rf carpet in the (Epr ,Ed /κ) plane is
shown in Fig. 2.8.


&389,-0


57







$9,-0









/,55,
Figure 2.8: The region of ion motion stability over an rf carpet in the (Epr ,Ed /κ) plane is
represented by the area under the curve.

2.7

Rf carpet simulations

Simulations of the ion transport by rf carpets were performed in order to gain an understanding of the operating parameters for rf carpets. In addition, simulations served to conﬁrm
experimental results and also explore parameter spaces that could lead to a simpliﬁed op20

eration of the rf carpets. For a given simulation with a speciﬁc carpet electrode geometry,
SIMION [19] was used to solve for the electric ﬁeld and then to numerically integrate the
equations of motion. This section will introduce the rf carpet simulations and cover the
simulations preceding the experimental testing of rf carpets. The simulations compared to
speciﬁc experimental setups will be covered in the experimental sections.

2.7.1

Rf carpet simulation basics

Epush

Edrag
pitch

gap

ɸ1

(ɸ1+180 )

Figure 2.9: Conceptual schematic of the workbench setup used for ion transport simulations.
The blue and red hatch patterns represent the two RF phases of the rf carpet separated by
180◦ . The push electrodes are represented by the vertical black lines. The direction of the
push ﬁeld and drag ﬁeld are also shown.
Recall that the electrodes on a rf carpet have an applied rf voltage that is 180◦ out
of phase with an adjacent electrode. In addition to this, the drag ﬁeld is superimposed on
the electrodes to establish a dc gradient to move the ions in the desired direction typically
towards a collection electrode or extraction oriﬁce. The push ﬁeld, is established by another
21

set of electrodes to generate a constant electric ﬁeld perpendicular to the eﬀective repelling
force provided by the carpet electrodes over the entire length of the carpet. A schematic
layout of the electrodes is shown in Fig. 2.9.
The ﬁrst rf carpet simulations were carried out to determine the maximum number
of carpet electrodes that could be grouped at the same dc potential without signiﬁcantly
decreasing ion transmission. Grouping electrodes would signiﬁcantly reduce the number of
resistors and connections required to establish the drag ﬁeld. Two sets of identical symmetric
electrodes arranged in concentric circles one above the other served as the carpet electrodes
and push electrodes, respectively. The ions were transported from the outer electrodes toward
the inner electrodes. The electric drag ﬁeld was superimposed on both the carpet and push
electrodes to maintain a symmetric push ﬁeld on the carpet electrodes. A view of the electrode
geometry used in SIMION is shown in Fig. 2.10 and the parameters are given in Table 2.1.

Figure 2.10: Simulation workbench for the rf carpet electrode grouping study. The two sets
of electrodes corresponded to the carpet and push electrodes.
Through the use of fast scalable electrodes, only three voltages had to be adjusted to
22

Table 2.1: RF carpet electrode grouping simulation workbench parameters.
Parameter
Value
a
1.5 mm
g
1.05 mm
distance between carpet and push electrodes
20 mm
maximum transport length
35.55 mm
24
number of carpet electrodes
correctly apply all the voltages to the 48 electrodes in a given simulation called RF amp,
DC Drag, and DC Push. RF amp was the rf amplitude in volts (0 to pk) applied to the
carpet electrodes. It was conﬁgured to have the same magnitude but an alternating sign
(+/-) for adjacent electrodes. DC Drag set the highest voltage for the outermost electrodes
on both the carpet and push electrodes and decreased linearly to the innermost electrodes
on both the carpet and push electrodes. DC Push set the additional uniform voltage on the
push electrodes. Using the distances provided in Table 2.1, DC Drag and DC Push could
be translated into the desired electric ﬁelds.
The transport eﬃciency was determined from the simulations by the following simple
relation:

=

Ntrans
Ntotal

(2.19)

where Ntrans refers to the number of transported ions over a speciﬁed distance and Ntotal
refers to the total number of ions started in the simulation. Criteria for Ntrans was reaching
a position speciﬁed by Ymin from the ion’s initial position without colliding with the electrodes and by the ion’s time-of-ﬂight not exceeding the time constraint speciﬁed by MaxTOF.
Ymin was selected such that the transport eﬃciency was calculated only over the transport
length of the rf carpet and not the innermost electrodes near the center hole. This topic is
discussed in later sections. MaxTOF was necessary to identify any rf carpet parameters that
could lead to trapping potentials along the transport length.
The ions’ initial parameters in the simulation were set to the expected properties of
ions thermalized in He gas. A charge of +1e and an initial kinetic energy of 0.025 eV was
23

Table 2.2: Rf carpet electrode grouping simulation LUA user program variables.
Parameter Description (units)
f MHZ RF frequency (MHz)
RF amp RF amplitude (V) [see text]
DC Drag Drag voltage (V) [see text]
DC Push Push voltage (V) [see text]
Ymin Positional constraint in the y-dimension (mm) to stop simulation
Mobility Reduced ion mobility (K0 )
P mbar Pressure (mbar)
MaxTOF Time constraint in the ion’s time-of-ﬂight (µs) to stop simulation
used for an ion with a mass of 85 amu. The ions were generated four pitch units above the
carpet electrodes and three pitch units inside of the outermost electrode to ensure that the
ions drifted slowly towards the carpet electrodes and were not aﬀected by the boundary
conditions. The ions were also generated at 10 equally spaced time intervals over the period
of the RF phase to ensure that the entire rf phase was sampled. A summary of the LUA user
program variables are shown in Table 2.2.
To simulate the presence of a buﬀer gas, the implementation of Stokes’ Law, or viscous
drag force, to damp the ion trajectories was used. The drag force on a particle traveling in a
viscous medium acts in a direction opposite and proportional to the velocity of the particle.
Thus, the resultant acceleration, atot , is given by:

atot = aviscous + asimulation

(2.20)

where asimulation is the acceleration due to the instantaneous electric ﬁelds calculated by
SIMION and aviscous is:

aviscous = −c · v

(2.21)

where c is the damping term. This damping term for the ion can be calculated from the
reduced ion mobility and the buﬀer gas pressure, the adjustable parameters Mobility and
P mbar, respectively. The resultant acceleration is calculated according to Eq. 2.20 by applying a small correction factor suggested in the SIMION literature (see drag.lua) to increase
24

the speed and accuracy of the simulation.

2.7.2

Rf carpet electrode grouping simulations

For the ’electrode grouping’ simulations, Φ1 and Φ2 maintained their 180◦ phase diﬀerence,
but the number of adjacent electrodes that held at the same dc potential without degrading
ion transmission was investigated. A group implies equal numbers of carpet electrodes from
both phases. The dc-grouping was also applied to the push ﬁeld electrodes. The eﬀect of
grouping on ion transmission, only required changing the electrode designation and mapping.
Therefore, the physical characteristics of both the carpet and push electrodes did not change
throughout this part of the study. The initial parameters of ions and the user program for
each simulation workbench were also identical.
The initial simulations were conducted before any experimental work was conducted, and
made some naive assumptions. However, since these simulations drove the initial rf carpet
designs, it is important to present them. The parameters used in the simulations are shown
in Table 2.3 and used the expected values for the voltages that could be applied to the
electrodes.
The loss mechanism acting when having groups of adjacent electrodes on the same bias
comes from the larger local potential drop experienced by the ion when it transitions between
the potential steps. This can be seen in Fig. 2.11, where the ion trajectory with an electrode
grouping of 4 comes much closer to the carpet electrodes than the ion trajectory with no
electrode grouping also shown in Fig. 2.11. This eﬀect can be reduced by decreasing the drag
ﬁeld, but this would slow the overall transport time proportionally to the reduction in the
drag ﬁeld. In addition, large groupings of electrodes would result in ions being conﬁned (or
trapped) along a single potential step and not being transported to the desired location.
From the simulation results, an electrode grouping of 4 electrodes (2 from each rf phase)
did not diﬀer strongly with regards to ion transmission eﬃciency. Thus, a grouping of 4
electrodes was implemented into the rf carpet design.
Rf carpet simulations that employed viscous damping were much faster in terms of
25

Table 2.3: Rf carpet electrode grouping simulation parameters.
Parameter
Value (units)
RF frequency
1 MHz
(70 - 100) V
RF amplitude
Pressure
100 mbar
10 V/cm
Drag Field
Push Field
10 V/cm
85 amu
Mass of ion
2 /(V · s)
K0 20 cm
2.4 cm
Transport length in y-dimension
MaxTOF
10000 us
10
SIMION Trajectory Quality




 22

















 22







Figure 2.11: Trajectories from a rf carpet simulation with a=1.5, γ=0.7 with simulation
parameters shown in Table 2.3. The carpet electrodes (not shown) are located at x=0 and
the push electrodes (not shown) are located at x=20. Blue line: No electrode grouping. Black
line: Electrode grouping of 4.
26

calculation time than those that employed Monte-Carlo collisions with hard-spheres (HScollisions). However, this lack of microscopic detail later proved to be insuﬃcient to explain
experimental trends (as will be discussed in later sections). Even with that drawback, viscous
damping still allowed for us to gain a general understanding of the ion motion along the rf
carpet.

2.7.3

Hard-sphere (HS) collisions

Since the macroscopic viscous damping model was unable to reproduce the results observed in
experiment, microscopic detail was added to the simulations in the form of collisions with the
neutral background gas using a hard-sphere (HS) collision model. A SIMION user program,
collision hs1.lua, contains a complete hard-sphere collision model and could be called from
within another user program (e.g. the main user program for the rf carpet simulations) to
handle every ion-neutral gas collisional event.
A quality check of the collisional model was carried out by comparing the ion’s average
velocity with that of the velocity from the experimentally measured ion mobility in He.
The adjustable parameter in the HS collisional model with the most impact on the ion’s
average velocity is the collision cross-section, which determines the frequency of collisions
between the ion and the background gas. By default, the collision cross-section is the crosssectional area with a diameter that corresponds to the sum of the diameters of the colliding
particles. In collision hs1.lua, this diameter was 17 angstroms that corresponds to the sum
of the diameters of a He atom and a mass 200 amu ion. For this work, a collision crosssection for a He atom and a mass 85 amu ion needed to be determined. Rather than using a
geometric cross-section, the collision cross-section that matched the average velocity given by
ion mobility in He was found by creating a SIMION workbench that consisted of two parallel
plate electrodes biased to generate a 10 V/cm electric ﬁeld. A test ion was placed between
the electrodes and migrated towards one plate in the presence of a He background gas. The
simulation parameters are shown in Table 2.4 and collision cross-section of 2.75×10−19 m2
matched the TOF according to the experimental ion mobility. The TOF distribution is shown
27

Table 2.4: HS collisions cross-section simulation determinations.
Parameter
Value (units)
Pressure
30, 60 torr
Electric Field
10 V/cm
85 amu
Mass of ion
2 /(V · s)
K0 20 cm
Transport distance
1.0 cm

in Fig. 2.12. This cross-section results in a lower collision frequency as calculated from the
geometric collision cross-section for a He atom and Rb ion (6.16×1019 m2 ).








434:39





















%  :8
Figure 2.12: Histogram showing the TOF distribution of 100 ions with a collision crosssection of 2.75E-19×10−19 m2 . The blue vertical line refers to the TOF according to the ion
mobility.
The HS collision model with the collision cross-section determined by the ion time of ﬂight
above was used throughout the rest of the simulations for comparison to the experimental
results. It was more computationally intense to include HS collisions rather than the viscous
damping approach, but the improved realism proved to be worth the additional calculation
28

time.

29

Chapter 3
Rf carpet transport
The primary focus of this dissertation project was to develop an ion transport device to
be used in the transport of thermalized rare isotopes, and speciﬁcally in the cyclotron gas
stopper. Thus, it was only natural for the bulk of the study to be comprised of ion transport measurements in the context of providing a future direction for the development of a
transport device for rare isotopes.

3.1

The rf carpet test chamber

In order to test ion transport over distances approaching 50 cm, a chamber had to be built
that would be large enough to house 50 cm rf carpet electrodes, all the necessary feedthroughs for the application of the necessary voltages, the ion source to generate the ions,
and the diagnostic tools for pressure readings and ion current collection. The design of the
test chamber was inﬂuenced by the geometrical arrangement of the rf carpets in the cyclotron
gas stopper. A modular design for the test stand was chosen to provide a device to allow
varying size, shape, and method of application of voltages.
The rf carpet test chamber that was constructed for this project is 1.2 m in diameter
with a 45 cm depth and is shown in Fig. 3.1. Three support legs are mounted to the ﬂoor
by bolting ﬁxtures to increase physical stability when the chamber door is opened. In total,

30

2

1

3
Figure 3.1: Mechanical drawing of the rf carpet test stand used for ion transport (1) Front
view of closed test stand. (2) Side view of closed test stand. (3) Front view of open test
stand. The inner diameter of the chamber is 1.2 m.

31

there are 19 x 6”, 9 x 2.75”, and 2 x 8” conﬂat ﬂanges on the chamber. Along the door, there
are 6 x 6” and 1 x 8” conﬂat ﬂanges primarily used for viewports and feed-throughs for the
push electrodes. Arranged along the edge of the chamber, are 7 x 2.75” and 7 x 6” conﬂat
ﬂanges used for mounting the turbomolecular pump, pressure diagnostic tools (cold cathode
gauge, pirani gauge), current measurement feedthroughs, dc voltage feedthroughs, and the
gas inlet for the high-purity He gas (99.999%). The backside of the chamber has exactly
the same ﬂange arrangement as the chamber door, except that there are 2 x 2.75” conﬂat
ﬂanges, one of which was used for the ﬂexible hosing for the roughing line. The central 8”
conﬂat ﬂange on the backside of the chamber was used to mount a special 2 x 2.75” adapter
to input the two phases of the rf. The remaining 6” conﬂat ﬂanges were used as viewports
and to house the rotary feedthrough for the ion source. Due to the various carpet electrodes
studied in the chamber, the exact purpose of each ﬂange assignment changed very often.

Figure 3.2: Mechanical drawing of the rf carpet test stand and the original carpet and push
electrode supports. The (dot-dot-dash) lines show the rf carpet test stand and the (solid)
lines show the carpet and push electrode supports.
32

A symmetrical set of slide holders in which support bars can be mounted to hold the
carpet electrodes and the push electrodes. On the inside of the chamber and the innerside of
the chamber door as can be seen in (3) of Fig. 3.1. The symmetry of the holders allowed the
easy alignment of the carpet and push electrodes by matching the positions of the supports on
each slide holder and on its mirrored partner. In addition, the supports could be adjusted to
change the distance between the carpet and the push electrodes. Unfortunately, the practical
size of the ion source body and arm did not allow for its height to be adjusted. Since the
carpet and push electrodes themselves were typically on the order of 1 - 2 mils and made
of ﬂexible pcb material, the clamping method shown in Fig. 3.2 was used for several of the
ﬁrst rf carpet prototypes. This clamping method was limited to only six contact points per

Figure 3.3: Mechanical drawing of the clamping method that allowed for easier modiﬁcation
of the carpet electrodes without having to redo the clamping process. The carpet electrodes
are represented by the opaque grey rectangular sheets. Left: Frame on the door side. Right:
Frame on the chamber side.
electrode and that each clamp only had 0.9 cm2 of surface contact with the ﬂex pcb material.
This resulted in surface non-uniformities in the electrode surface and especially in close
proximity of the clamps. Another diﬃculty with this clamping method was that any repairs
that needed to be done to the carpet electrodes required all the connections for applying
33

the voltages and current collection to be disconnected and the entire electrode system to be
unclamped from the individual clamps. Since special care was taken to establish a uniform
surface on the electrodes, this process could take several hours depending on the particular
set of electrodes. Electrical discharges occurred frequently between the stainless steel clamp
held at the same electrical potential as the test chamber (ground) and the biased carpet and
push electrodes. A stand-alone clamping system (a frame) that kept the carpet electrodes
clamped with insulators when dismounted from the test stand was developed in order to
make the connections easier to the carpet electrodes, anchor points could be established on
the clamping frame that retained the connection to the electrodes and allow for connectivity
to the feedthroughs. A photograph of a carpet held with this improved clamping method

Figure 3.4: 50 cm carpet mounted in a frame. The electrical connections between the carpet
electrodes and the ceramic terminal blocks are visible.
is shown in Fig. 3.3. The electrodes are clamped by Teﬂon blocks (white) which served to
minimize discharges between the frame and the electrodes. Ceramic terminal blocks (gray)
attached to the frame were used to connect the carpet electrodes to the feedthroughs on the
34

Table 3.1: Pressure readout for rf carpet test chamber and roughing line.
Device
Location
Pressure Observed (units)
Pirani Gauge 1 Roughing Line
1×10−3 mbar to 5 mbar
Pirani Gauge 2
Chamber
1×10−3 mbar to 5 mbar
Cold Cathode Ion Gauge
Chamber 1×10−5 mbar to 1×10−8 mbar
Baratron Gauge
Chamber
5 torr to 760 torr

chamber. Thus, if the carpet needed to be removed from the chamber, only the connections at
the terminal blocks and the bolts fastening the frame to the slide holders had to be removed.
The chamber was pumped down by a Oerlikon Leybold TW 290H turbomolecular (turbo)
pump backed by a Varian Triscroll 300 mechanical scroll pump. The pressure gauges included
two MKS convection pirani gauges, a MKS cold cathode ion gauge, and a MKS absolute
baratron gauge. A MKS 937A controller was used to readout the pressure from the two pirani
gauges and the cold cathode ion gauge. A MKS 250E pressure/ﬂow controller was used to
readout the baratron gauge. Table 3.1 shows the pressure gauges, their locations, and the
associated pressure observed in the system. A gate valve was used to isolate the test chamber
from the turbo pump during ion transport measurements when the test chamber was held at
a static pressure. The gas ﬂow into the chamber was controlled by a MKS 250E ﬂow controller
and a MKS 148J 30000 SCCM solenoid valve. The ﬂow option on the 250E ﬂow controller
was not used since the chamber was generally held at static pressure for these studies and did
not need to maintain a constant ﬂow rate. Each time the chamber was opened, the chamber
was purged three times and then pumped down with the turbomolecular pump. A purge
cycle consisted of pumping down the chamber to ∼ 8 × 10−2 mbar with the scroll pump and
ﬁlling the chamber with ∼5 mbar of He gas. This volume was then pumped back down to
∼ 8 × 10−2 mbar. The complete process was considered one complete purge. The purging
process had a signiﬁcant positive eﬀect on the pump out time of the chamber, resulting in
a ∼ 1 × 10−7 mbar base pressure after 16 - 24 hours as opposed to a ∼ 1 × 10−6 mbar base
pressure over the same time frame without purging. The pressure inside the chamber during
pump down was recorded to check for leaks after any modiﬁcation to the ﬂanges occurred.

35

These pump out rates were in good agreement with each other between modiﬁcations as can
be seen by three examples in Fig. 3.5. Since the chamber was held at static pressures, the





5 2-,7















           
920 23
Figure 3.5: Pressure reading inside the chamber during pump out after the chamber was
opened and modiﬁed on three diﬀerent dates. Black circles: 4/18/2008, Red stars: 5/14/2008,
Blue Triangles: 7/1/2008. Blue triangles overlap black circles and red stars. The TMP was
started at ∼22 minutes.
partial pressure of contaminants for a given transport study could be estimated. Closing oﬀ
the chamber after pumping for 12 - 24 hours and observing the pressure rise in the chamber
typically resulted in a pressure rise of 6.3 × 10−9 mbar/s. Approximating the time spent for
a transport study at one particular pressure to be 60 minutes with at an average chamber
pressure of 100 mbar, the partial pressure of contaminants would be 0.2 ppm. There would
be more contaminants in the He gas (99.999%) than from the equipment inside the chamber!

36

3.2

Alkali ion source characteristics

The ion source used throughout the transport tests was an alkali aluminosilicate ion source
from Heatwave Labs (Model 101139). For this study, a Rb ion source was primarily used.
The source operates on the principle of thermionic emission of the alkali ions from an aluminosilicate ion emitter material. A schematic diagram of the ion source obtained from the
manufacturer is shown in Fig. 3.6. A table of the operating parameters in vacuum can be
found in Table 3.2. The ion source for the ion transport tests had to operate in the presence
of helium gas, whereas the intended operation of these ion sources is in vacuum. Thus, the
required heater current to produce an ion current leaving the source on the order of nA was
approximately 3 A in the presence of the He gas. Thus, the operation of these ion sources
diﬀered from the standard operating procedure as suggested in the literature.

.010 3% Re/W Heater Wire
with
.007 HT Mo Overwrap

.250
.015 Re
.39
Figure 3.6: Dimensions for the ion source given in inches.
In order to perform the ion transport measurements, the physical position of the ion
source had to move, the ions needed to be able to reach the carpet, and a method of measuring the current leaving the source had to be developed. Moving the ion source to diﬀerent positions was accomplished by placing the ion source on an arm attached to a rotary
37

feedthrough with a control knob with an integrated position indicator on the outside. This
allowed the ion source to be moved to the exact same location (diﬀerent transport distances)
when the chamber was closed. In order for the ions to reach the carpet electrodes reliably,
simulations were conducted to design an electrode system that would provide the best focusing for ions to reach the carpet. A simulation of the ion motion for the two electrode
system that was adapted into the ﬁnal design (exact dimensions) for the ion source housing
is shown in Fig. 3.7.

E1 E2

E3

Figure 3.7: Results of simulations of the two electrode system for the ion source using the
SIMION code. Both cases were for a pressure of 100 mbar using viscous damping. Equipotential lines shown in red. Ion trajectories shown in black. E1 (electrode 1) is the ion source
body and the electrode surrounding it at the same potential. E2 (electrode 2) is the lens in
front of the ion source that eventually became the entire ion source housing. E3 (electrode
3) is a collection plate. Left: E1 = 90 V, E2 = 80 V, E3 = 33 V. Right: E1 = 100 V, E2 =
80 V, E3 = 33V.
The ﬁnal design of the ion source housing allowed the mounting and biasing of the ion
source at a separate potential from the rest of the housing. It also incorporated a support
for the leads for the heater current.
Measuring the ion current reaching the carpet electrodes was important for this study
because it provided the basis for determining the transport eﬃciency. Transport eﬃciency was
determined by the ratio of the ion current on the collection electrode to the total ion current
38

Table 3.2: Operating parameters for the Heatwave Labs (Model 101139) ion source in vacuum.
Value
Parameter
Temperature 900 - 1200◦ C
6.3 V
Voltage
Current
1.8 A @ 1100◦ C

1

2

Figure 3.8: Exploded view of ion source housing. 1) Lens face of the ion source housing
(electrode #2 in Fig. 3.7). 2) Ion source (electrode #1 in Fig. 3.7). The ions exit to the left
from the lens (1).
interacting with the carpet electrodes. Initially, the only information on the ion current
leaving the ion source was the current observed on a collection plate located somewhat
away from the carpet electrodes. This was regarded as the total ion current from the ion
source. However, when ion transport eﬃciencies greater than 100% were observed on the rf
carpet, this simple method of determining the ion source output had to be rejected. The ion
source total output was found to be sensitive to not only the heater current, but also the
extraction voltage. If the electric ﬁelds at the lens when it was near the collection plate were
not identical to those experienced over the carpet electrodes, diﬀerent ion source currents
leaving the source would be produced at the carpet electrodes and at the collection plate.
Numerous attempts were made to mimic the electric ﬁelds that the ion source experienced
over the carpet electrodes at the collection plate, but this resulted in cooling/heating eﬀects in
39

the ion source and still rendered eﬃciency determinations to be diﬃcult with this technique.

1

A

V2

V1

A

2

A
3

Figure 3.9: Schematic circuit diagram of the revised current measurement setup that allowed
measurement of the ion current leaving the ion source, the ion current reaching the ion source
housing, and the ion current reaching the collection plate. Label (1), Black: Ion source. Label
(2), Red: Ion source housing. Label (3), Green: Collection plate.
A new conﬁguration was developed to give the greatest amount of dynamic control involving measurement of the total ion current leaving the ion source [I(IS)] and any ion current
impinging on the ion source housing [I(Lens)]. Then, [I(IS)] - [I(Lens)] = [I(Collect)],
where [I(Collect)] is the ion current impinging on the collection plate / carpet electrodes.
From these measurements, a transport eﬃciency is determined and is discussed in detail
in section 3.6 (Calibration measurements). A rechargeable car battery was used to provide
low-noise power to heat the ion source.

40

3.3
3.3.1

Rf carpet design
Material requirements

The requirements on the printed circuit board (pcb) material for the rf carpets include a low
outgassing rate, good signal transmission, and robust thermal properties. The low outgassing
rate is required because impurity ions can charge exchange with the He buﬀer gas ions created
during the slowing down process and can be extracted out of the stopping chamber. Good
signal transmission, or low signal attenuation, is important to make sure that the applied rf
signal was constant over the length of an electrode stripe over the desired frequency range.
Robust thermal properties are important because surface mount devices must be soldered
onto the ﬂex circuit without degrading the material or delaminating the Cu.
To fulﬁll these requirements, Kapton, a polyimide ﬁlm that is commonly used as an
insulator in UHV environments was chosen as the substrate for the rf carpets. In addition,
a Kapton based adhesive can be used to adhere the Cu to the Kapton substrate avoiding
the use of epoxy adhesives. An all-polyimide laminate available from Dupont (Pyralux AP)
was chosen to be the speciﬁc Cu-clad laminate because it fulﬁlled the material requirement,
had a low signal attenuation up to the GHz frequencies, and passed thermal stress tests for
soldering without any delamination of the Cu. The ﬂexible nature of the laminates has given
the resultant printed circuit boards the name of ’ﬂexible pcb’ or ’ﬂex pcb’.

3.3.2

Typical ﬂex pcb manufacturing constraints

Once the substrate material was chosen, a set of pcb manufacturers had to be found that
could do low-volume (prototype) work and be technically proﬁcient enough to manufacture
large size pcbs with a consistent Cu trace and gap size on the sub-mm level over the entire
area. The typical manufacturing limit with regards to size is a maximum panel area of 45 cm
x 60 cm and minimum trace and gap width of 0.125 mm. The ﬂex pcb manufacturers that
were used for this project were Innovative Circuits, Gigatek Inc., and Stevenage Circuits.

41

3.3.3

General design elements of RF carpets for ion transport

Taking into account the manufacturing constraints mentioned in the previous section for
ﬂex pcb manufacturing, early rf carpet prototypes used for ion transport required four main
design elements:
1. The transport area
2. The collection area
3. Rf & dc contacts
4. Clamping area for physical support
An example of a prototype rf carpet with these general design elements for all RF carpets
(arranged in a linear fashion) for ion transport is shown in Fig. 3.10.
The transport area, as its namesake suggests, is the area of the carpet electrodes responsible for transporting the ions. It generally consisted of a repeating electrode and gap
structure with a uniform spacing over the desired transport area. Due to the minimum areas
required for the other three design elements, the active area of the rf carpet was typically 40
cm x 50 cm or less.
The collection area contained an electrode array adjacent to the transport area that could
be biased and connected to an electrometer to measure the ion current. In the carpet design
with linear stripes, such as in Fig. 3.10, the collection area was segmented in order to observe
the distribution in the transverse direction of ions transported along the surface. For carpet
designs consisting of semi-circle stripes, the collection area was the innermost semicircular
electrode.
In order to apply the appropriate RF & DC voltages, a portion of the circuit board
was reserved to make the necessary connections to the carpet electrodes. The contacts had
various shapes depending on the nature of the connection method. An early connection
method used a clamping mechanism constructed of Teﬂon bars with the individual wires
from the 9-pin feedthroughs woven through the Teﬂon bars. The connection area shown
42

Figure 3.10: A linear carpet design with straight (linear) stripes for the transport area. The
diﬀerent design elements are designated by the numbered areas that are outlined outlined
by the colored dashed lines. (1) Dashed black line: transport area; (2) Dashed blue line:
segmented ion collection area; (3) Dashed red line: Rf & dc contacts; (4) Dashed green line:
clamping area - Kapton (substrate) border. The coin, included for scale, is a US penny.

43

in Fig. 3.10 is representative of the electrodes used for this clamping method. Connection
methods were simpliﬁed in later designs to be a square pad with suﬃcient surface area for a
hole that allowed a bolt to secure an individual wire to make a good electrical contact.
The clamping area refers to the available material of the substrate (Kapton) around the
border of the pcb by which the ﬂex pcb could be fastened and mounted inside the vacuum
chamber. Typically 1 cm between the pcb of the board and any Cu traces was provided for
clamping.

Figure 3.11: Photograph of a large rf carpet with a 48 cm transport distance and a pitch of
0.38 mm. The collection electrode (center bottom of the transport area) has a diameter of
1.8 cm.
Over the course of the present work, the transport area electrode shapes evolved from initially parallel linear stripes to semi-circular stripes. The semi-circle rf carpets had the feature
that they also guided the ions in towards the central electrode in a manner necessary for the
44

ﬁnal operation of rf carpets in the cyclotron gas stopper. However, given the manufacturing
limit of the maximum area, a design consisting of purely semi-circles would only have a
maximum transport distance of 20 cm. In order to take advantage of the maximum area for
one Kapton panel and extend the transport distance as far as possible, a semi-circle design
continued by a series of arcs allowed a maximum transport length of 48 cm. A photograph
of an example of such an rf carpet is shown in Fig. 3.11.
Later designs which moved the resistors onto the ﬂex pcb in order to establish the drag
ﬁeld. These pcb’s required an additional element that provided pads designated for speciﬁc
surface mount resistors. In addition to the resistor pads, the routing to the appropriate
electrode had to be present. The pads had to have enough space in between each resistor for
soldering, as well as leaving most of the area of the ﬂex PCB devoted to the transport of
ions. A photograph of surface mount resistors mounted on the rf carpet that satisﬁed these
requirements is shown in Fig. 3.12.

Figure 3.12: Photograph of surface mount resistors mounted on an rf carpet with a centimeter
scale for reference.

45

3.4

Applying rf & dc voltages on the rf carpet

Rf carpets require a combination of rf and dc voltages to operate. This section will ﬁrst
cover the methods used in this study to generate and apply the appropriate rf voltages for
the rf carpet, and then the dc voltages for the rf carpet. Lastly, the unique method used to
combine the rf and dc voltages and apply them to the rf carpets is presented.

3.4.1

Rf voltages for the rf carpet

The rf voltage for the rf carpet was generated using resonant LC circuits [20]. In this approach, L, the inductor, and C, the capacitor are connected in series to an AC power supply.
Depending on the applied signal frequency, the inductive reactance XL and the capacitive
reactance XC cancel at the resonant frequency, fr , in units of Hz given by the expression:

fr =

1
√
2π LC

(3.1)

where L is given in henries and C is given in farads. At the resonant frequency, the only
resistance to current ﬂow comes from the resistive losses encountered with the wires in the
circuit. These minimal resistive losses allow for minimal power consumption while providing
a maximum rf amplitude. This is the major advantage of using resonant LC circuits to
provide the rf voltage for the rf carpets.
An Agilent 33120A arbitrary waveform generator (AFG) and a T&C Power Inc. AG
series ampliﬁer were used to supply the sinusoidal waveform up to 10 MHz. The AG series
ampliﬁer also indicates the reﬂected power in the circuit and was useful for tuning the
circuit to the resonant frequency (taken to be the point at which the ampliﬁer indicated
there was no reﬂected power in the circuit). A ferrite core transformer was used to match
the 50Ω output impedance of the ampliﬁer to the impedance of the load. The capacitance
of the circuit is dominated by that of the rf carpet. Since the carpet electrodes consists
of very many Cu strips sandwiching a dielectric, the carpet electrodes provide a very large
capacitive load depending on the size and pitch of the electrode setup. Air-core coil inductors
46

provided the inductance and were changed as necessary to obtain the desired rf operating
frequency. Variable capacitors (15 - 150 pF) were added to the LC circuit in order to match
the amplitude of the separate rf phases. A schematic design of the rf circuit is shown in Fig.
3.13.

CL

Figure 3.13: Schematic diagram of the LC circuit used to generate the rf voltages for the
rf carpet. CL is the capacitive load determined by the rf carpet. Typical ranges for the
components: Variable Capacitors = 15 - 150 pF, Air-core inductors = 3 - 10 µH, CL = 700
pF - 10 nF.
The disadvantage of using a resonant LC circuit is that the resonant driving frequency
depends on the capacitance and the inductance of the individual circuit. Over all of the rf
carpet prototypes, the total capacitive load of the system was found to lie in the range of
30 pF to 11 nF. For a desired rf operating frequency in the range of 1 to 3 MHz with a
capacitive load of 5 nF requires an inductance of 5 µH to 0.5 µH respectively. At the 5 µH
level, the inductance can be introduced in the circuit by using the air core coil inductors
47

mentioned in the previous paragraph. However, at the 0.5 µH level, the stray inductances
of all components begin to be important and keeping the inductance at or below this value
becomes diﬃcult.
A method to reduce the capacitive load for the carpets with greater than 4 nF capacitive
load (typically carpets with a 20 cm to 50 cm transport distance, a = 0.38 mm) was to
segregate the carpet electrodes and drive each segment with a separate LC circuit. In order
to limit the minimum amount of required electronics, the restriction of using only 1 AFG and
1 ampliﬁer was imposed. Diﬃculties encountered with this method included segmenting the
carpet electrodes in evenly matched capacitive loads and matching the rf phase and amplitude
at the segment boundaries. Since the electrodes were part of a pcb, the segmentation had to
be designed beforehand and was permanent so that the capacitive load could not be changed
unless the design was changed and a new ﬂex pcb was manufactured.
The matching of the rf phase and amplitude at segment boundaries was achieved by using
variable capacitors to tune each phase and a 4-channel oscilloscope was used to observe the
two rf phases for the adjacent segments. A tune was determined to be satisfactory when there
was < 15% diﬀerence in rf amplitudes and 180◦ diﬀerence between each adjacent phase. The
rf phase and amplitude were measured at the carpet surface and also at a diagnostic point
outside the chamber as a function of input voltage from the AFG because, once the chamber
was closed, there would be no easy way to measure the characteristics of the rf inside the
vacuum chamber. All of the values reported in the results represent the rf voltages on the
surface of the rf carpet.
The Q-value is a measurement of quality for a resonant circuit deﬁned by:

Q=

fr
∆f

(3.2)

where fr is the resonant frequency as deﬁned above, and ∆f = fH − fL , where fH and fL
are equal to the high half-power frequency and the low half-power frequency respectively.
The resonant circuits for these studies did not require a very large Q-value because the rf

48

discharge limit in He gas was reached long before the maximum rf voltage could be applied
to the rf carpet electrodes. Therefore, the Q-value of the circuit was not maximized. The ∆f
for the resonant circuits used in the ion transport measurements was measured to be 0.08
MHz for a fr of 2 MHz, resulting in a Q-value of approximately 25. The limiting factor to
ion transport was not the Q-value of the resonant circuit, but rather the ability to apply
the desired resonant frequency over rf carpets with diﬀerent capacitive loads with minimal
adjustments to the resonant circuit.

3.4.2

DC voltages for the rf carpet

The individual dc voltages for the rf carpet were established using a resistive voltage divider
chain. Since the ions are positively charged and transported from an outer radius to an
inner radius, a positive voltage, VCarpHi, was applied to the carpet electrodes at the outer
radius. Then, for each successive inner electrode, the applied voltage was connected to the
next voltage step down from VCarpHi. For the innermost electrode, the applied voltage
is one resistive division above electrical ground. This was necessary because the collection
electrode, located a carpet gap distance g away from the innermost carpet electrode, was
held at electrical ground. Originally, the resistor chain was located outside of the chamber
and the individual dc voltages for each rf carpet electrode was brought into the chamber by
individual pins in two 9-pin subminiature-D (D-sub) feedthroughs.
This method with, for example, 18 traces of carpet pitch on the order of 1.5 mm and
the electrode grouping method in Chapter 2, only results in a transport distance of 5 cm.
Increasing the transport distance (20 - 50 cm) and decreasing pitch (sub-mm) would require a
multi-pin feedthrough with over 1,000 pins. Fabrication of a 1,000 pin feedthrough is possible,
but this still has the problem of attaching 1,000 cables to the rf carpet. In order to avoid
having a 1,000-pin feedthrough, the resistor chain was moved to the inside of the chamber
and included on the same ﬂex board as the carpet electrode itself by using surface mount
technology and designing resistor pads and a routing scheme for each individual carpet trace.
This signiﬁcantly reduced the required feedthroughs for the dc voltages for the rf carpet but
49

Test Chamber
ecollect

einner

eouter
g
VCarpHi

Figure 3.14: Schematic diagram of the initial resistive voltage division used to apply the
individual dc voltages to the rf carpet electrodes with the resistor chain located outside
the chamber. eouter and einner refer to the electrodes at the outer radius and inner radius
respectively. ecollect refers to the collection electrode. g refers to the gap between the rf carpet
electrodes. The items encompassed by the dashed line were in the rf carpet test chamber.
increased the complexity of the pcb.
The value of VCarpHi can be converted into the electric drag ﬁeld strengths, Edrag , in
(V/cm) by the expression:

Edrag =

V CarpHi
M axDist

(3.3)

where MaxDist is the maximum transport distance in cm of the rf carpet (the distance
between the outermost radius and the collection electrode).

3.4.3

Combining the rf and dc voltages

Operation of the rf carpet requires a combination of rf and dc voltages. A common method
for combining a rf voltage with a dc gradient is to use a resistive voltage divider for the dc
gradient and use individual capacitors to transmit the rf signal to each electrode. Originally,
like the resistor chain, the capacitors were also located on the outside of the chamber and the
50

Test Chamber
ecollect

einner

eouter

g
VCarpHi

Figure 3.15: Schematic diagram of the resistive voltage division used to apply the individual
dc voltages to the rf carpet electrodes with the resistor chain located on the inside of the
chamber.

VCarpHi
Test Chamber

ɸ1

ɸ2

Figure 3.16: Schematic diagram of the method used for early rf carpet prototypes to apply
the dc voltages and rf voltages to the individual traces. The resistor chain and capacitors
were located on the outside of the test chamber.
51

combined rf and dc voltage was brought into the chamber with the 9-pin D-sub connectors.
A schematic diagram of this method to combine the rf and dc voltages for the rf carpets
is shown in Fig. 3.16, where the two phases from the rf circuit are indicated by φ1 and
φ2 . The same problem was encountered for the capacitors as was for the resistor chains
outside of the chamber as discussed in section 3.4.2. It was necessary to devise a way to
bring the capacitors into the chamber and to reduce the number of required feedthroughs.
Using surface mount capacitors was an option, but this would require mounting of a large

Test Chamber

VCarpHi

ɸ1

ɸ2

Figure 3.17: Schematic of the method used to apply the dc voltages and rf voltages to the
individual traces. The resistor chain and capacitors are located on the inside of the test
chamber. The Kapton dielectric is shown in orange. The capacitors are formed from the two
Cu traces.
number of additional components on the pcb. A new method was devised to take advantage
of the material properties of the diﬀerent Cu-clad laminates used in ﬂex pcb manufacturing.
By using a double-clad Cu laminate (Cu sandwiching a Kapton dielectric) as the material
used for the ﬂex circuit, the capacitors for each trace can be created by mirror images of
the carpet electrodes on the bottom side of the Kapton substrate. The rf is applied to the
underside of the ﬂex circuit which is capacitively coupled to the topside (transport side) of
52

the ﬂex circuit. The dc voltages were generated with surface mount resistors as in section
3.4.2 and applied directly to the topside of the carpet. This is equivalent to the schematic in
Fig. 3.16, but avoids the installation of individual capacitors.
A study was conducted of the amount of rf voltage that was transmitted to the top Cu
layer as a function of the amount of overlap between the bottom Cu layer and top Cu layer.
The results are shown in Fig. 3.18. From the results, a full mirror image on the bottom side
of the Kapton substrate was found to maximize the amount of transmitted rf.




#,94'4:9'3





















 ;07,541-49942:,079945:,07
Figure 3.18: Results from the study of capacitive coupling of the voltages to the individual
traces. The voltage ratio on the top trace to that on the bottom is shown as a function of
fractional overlap of the layers.

53

3.5

Push electrodes

The push electrodes directed the ions towards the surface of the carpet electrodes by providing a constant electric ﬁeld perpendicular to the repelling force of the carpet electrodes
which then ”pushes” the ions near the surface. Aside from the practical aspect of guiding the
ions towards the rf carpet, the push ﬁeld also acted as an artiﬁcial space charge ﬁeld. The
reader may recall from Ch. 1 that the space charge ﬁeld is produced during the thermalization of energetic beams and is primarily responsible for the loss of extraction eﬃciency with
increasing beam rate. Thus, it was important to determine when the repelling force provided
by the carpet electrodes was overcome by the space charge ﬁeld. By measuring the transport
eﬃciency as a function of push ﬁeld and equivalently, the space charge ﬁeld, the maximum
incoming beam rate that the cyclotron gas stopper could withstand before incurring losses in
the extraction eﬃciency could be calculated. Though the maximum push ﬁelds/space charge
ﬁelds that the rf carpet could operate at were determined, the corresponding beam rates
for the push ﬁeld/space charge ﬁelds were beyond the scope of this work. In order to keep

VPushLo

VPushHi = VCarpHi + PushOffset
VPushLo = GND + PushOffset

VPushHi

VCarpHi

Figure 3.19: Schematic of the voltage designation for the push electrodes using the voltages
on the carpet electrodes as a reference.
the push ﬁeld constant over the full length of the carpet electrodes, exactly the same dc
54

gradient on the carpet was applied on the push ﬁeld electrodes as on the transport carpet
plus a constant dc oﬀset. The high voltage on the push electrode resistor chain (VPushHi)
and the low voltage on the push electrode resistor chain (VPushLo) established the dc gradient. Oftentimes, a copy of the carpet pcb was used to make the push electrodes to match
the appropriate shape and dc gradient. The push electrodes were located 13 cm away from
the carpet electrodes. The ion source housing was located in between the push and carpet
electrodes, and the face was 4 cm away from the carpet electrodes. For instance, if VCarpHi
was set to 40 V and the desired push ﬁeld was 5 V/cm, then VPushHi was set to 85 V and
VPushLo was set to 45 V. A photograph of the ion source positioned inbetween the carpet
electrodes and push electrodes is shown in Fig. 3.20.

Figure 3.20: A photograph of the ion source located in between a 50 cm rf carpet (right) and
the push electrodes (left).

55

3.6

Calibration of the ion source current

The measurements to calibrate the ion source current were important to establish the size of
the ion current leaving the ion source and impinging on the carpet electrodes since that value
was used to determine the transport eﬃciency. With the deﬁnitions introduced in section 3.2
to measure the ion current leaving the ion source [I(IS)] and the ion current hitting the ion
source housing [I(Lens)], the ion current leaving the ion source housing [I(Carp)] is given
by:

 0,,0
30,79


 0,,0 3(


 











' '498




Figure 3.21: Calibration of the ion source output used for transport eﬃciency measurements.

[I(Carp)] = [I(IS)] − [I(Lens)].

(3.4)

[I(Carp)] diﬀers from [I(Coll)], the ion current measured on a collection electrode, and
[I(CP )], the ion current measured on the collection plate, because [I(Carp)] is not a directly
56

measured quantity. For transport measurements, [I(Carp)] was typically in the range of 1
- 2.5 nA. With the ion source housing and ion source biased in the range of 50 - 150 V,
the current measurements would be sensitive to any leakage current due to stray resistances
on the order of GΩ between any ion source component and electrical ground. Due to the
humidity of the environment and the cleanliness of the insulating break separating the ion
source feedthroughs on the outside from the test chamber at ground potential, a resistance
on the GΩ level often did exist and the leakage currents had to be accounted for when
calculating the true ion source current output. For calibration purposes, only the voltage on
the ion source (V1) and the voltage on the ion source housing (V2) had to be monitored.
Calibrations were conducted prior to and following transport measurements. The calibration
procedure went as follows: (1) V1 and V2 were kept at the same voltage level and scanned
from -40 V to 80 V in steps of 40 V while recording the current measurement for the ion
source and ion source housing. The current measurement would vary linearly for the ion
source and stay at a constant value for the ion source housing. This would provide enough
points for a linear calibration (from Ohm’s law). A sample measurement is shown in Fig.
3.21 which indicates the resistance was 667 GΩ.
A check of any resistance between the ion source and ion source housing was made next.
(2) V2 was set to 10 V below V1 and the same voltages were stepped through. The current
measurements were recorded for both the ion source and ion source housing. A 10 V potential
diﬀerence was used because this value was typically used for transport measurements. Over
the course of the entire study, no noticeable resistance was found between the ion source and
the ion source housing down to the level that could be observed with a Keithley picoammeter.
Once the calibration was taken and the ion source temperature reached equilibrium, the
calibration could be applied for the determination of the ion source current leaving the ion
source housing. A check of this calibration was done by positioning the ion source directly
above the collection plate and conﬁrming that:

[I(Carp)]corr = [I(CP )]
57

(3.5)

where [I(Carp)]corr is the corrected value from the calibration. This allowed a direct check
of the calibration without having to disentangle the transport along the rf carpet.
The transport eﬃciency of the rf carpet, trans , was then given by the expression:

trans

3.7

=

[I(Coll)]
.
[I(Carp)]corr

(3.6)

Linear carpet transport

Ion Source

Collection
Plate
Collection
Electrodes

Figure 3.22: A photograph of the setup used in the transport measurements with the linear
rf carpet. With this setup, the ion source could be moved to the collection plate to verify
the transport eﬃciency.
A variety of rf carpet designs were studied throughout the measurements, but the general
operating principles described in the previous section remained the same. For the most part,
the push electrodes were changed to match the shape of the current rf carpet design. The
58

linear rf carpet transport setup was the ﬁrst rf carpet setup used for transport measurements. The transport distance was 5.4 cm and the ion source housing acted primarily as the
push electrodes because it extended across 80% of the transport length. Since a dc gradient
could not be applied to the ion source housing, the push ﬁelds were not constant across
the transport distance. This setup demonstrated the ﬁrst ion transport with rf carpets at
the NSCL, but more reliable measurements were found in later setups. A photograph of the
linear rf carpet setup is shown in Fig. 3.22.

3.8

Semi-circle transport and extended semi-circle transport

The electrode conﬁgurations were modiﬁed to be larger semi-circular patterns for better ion
conﬁnement with transport distances up to 18 cm. The ﬁnal design consisted of a semicircular pattern with a radius of 17 cm with a series of arcs that extended the transport
distance to 48 cm all within the 40 x 50 cm2 area. The pitch was 0.38 mm and the gap
spacing was 0.19 mm. The setup is shown in 3.23.

Figure 3.23: Test setup for a large 50 cm rf carpet (a = 0.38 mm, γ = 0.5. Push electrodes
are shown on the chamber door.

59

3.9

Discharge tests

Before transport measurements were conducted, measurements to determine the maximum
rf voltage that could be applied to the carpet electrodes before causing dielectric breakdown
of the He gas were conducted. Using the same ﬂex pcb material used to fabricate the rf
carpets, a small series of test pads were constructed with varying electrode and gap widths
ranging from 0.2 mm to 0.7 mm. A small mounting support coupled to a 6” conﬂat ﬂange

Figure 3.24: A photograph of the support structure and test pad used in the discharge tests
on a 6” conﬂat ﬂange.
was constructed to keep the ﬂex PCB surface uniform with insulated standoﬀs to apply the
voltage to the test pad as shown in Fig. 3.24. Additional insulation in the form of ceramics
and Kapton were used to ensure that the discharge occurred between the parallel small
electrodes on the pad and not between the structure and the chamber walls. The chamber
pressure was set to the desired value and the applied RF voltage increased till a discharge
60

was observed between the adjacent electrodes.
A set of measurements with one test pad at two diﬀerent rf frequencies is shown in Fig.
3.25.



70,/43'# 5
5 '














5 9477

Figure 3.25: Measured rf voltage breakdown voltage (frequency shown in plot) for an electrode gap spacing of 0.7 mm and an electrode width of 1 mm.
These two rf frequencies spanned the initial rf frequency operating range for the rf carpets.
This measurement showed that the breakdown voltage had almost no variation over this
frequency range. A more instructive method of displaying the breakdown curves was to show
them as a function of pressure times distance (pd). This function collapses all of the data
(See Fig. 3.26), which then allowed predictions of the rf breakdown voltage at the relevant
operating pressures and electrode gaps. This is shown in Fig. 3.26. Unfortunately, the rf
breakdown curves indicate that the desired operating pressure and rf carpet electrode gap
correspond to the minimum of the breakdown curve!
A strong dependence on the gas purity as evidenced by the number of purge cycles (Sec.
61

00.974/0,5
22
00.974/0,5
22
00.974/0,5
22

70,/43'# 5
5 '















5/ 9477
22

Figure 3.26: Measured rf breakdown voltage as a function of pd constructed from the rf
breakdown curves taken at three diﬀerent electrode gaps.
3.1) was found in the variation of the measured breakdown voltages (see Fig. 3.27.). The
variability of the breakdown is due to the diﬀerent contaminants in the system that can drive
the breakdown voltage higher or lower as seen in [21]. Care was then taken to prepare the
system and verify that a reference point on the breakdown curve could be reproduced after
each time the chamber was opened, pumped down, and purged.

3.10

Setting voltages for transport measurements

The voltages on the rf carpet electrodes and push electrodes were set before the beginning
of every transport measurement. Voltage settings were chosen that would lead to stable ion
motion over the rf carpet and not incur discharge. An rf frequency of 2 MHz at 160 VRF,pk−pk
and a push ﬁeld and drag ﬁeld of 3 V/cm at 80 torr was simulated to have stable ion motion
over the rf carpet. The Epr and Ed /κ stability parameters for these rf carpet settings are
1.78×10−2 and 1.11×101 respectively, and correspond to the region of ion motion stability
62

70,/43'# 5
5 '

















:2-0741!:708

Figure 3.27: Range of the measured rf (1.5 MHz) breakdown voltage as a function of the
number of purges at an electrode gap of 0.525 mm and a pressure of 60 torr.
introduced in Sec. 2.6.
The voltages for V CarpHi, V P ushHi, and V P ushLo were calculated from the desired
electric ﬁeld strengths for the drag ﬁeld and the push ﬁeld. For example, a drag ﬁeld of 3
V/cm with the collection electrode at ground potential and a transport distance of 48 cm
would correspond to V CarpHi being biased to 144 V. The push electrodes were located 13
cm above the carpet electrodes, and a desired push ﬁeld of 3 V/cm for a rf carpet with a 3
V/cm drag ﬁeld would correspond to V P ushHi and V P ushLo being biased to 183 V and 39
V respectively. The voltages that were applied to the ion source housing were calculated in
a similar manner. The ion source was located 4 cm away from the carpet electrodes and sat
at a variable radial position on the rf carpet. The ion source housing was biased in a manner
to have the same electric ﬁeld strength as the push ﬁeld. For example, in the scenario of a 3
V/cm drag ﬁeld and push ﬁeld, the ion source sitting at a 10 cm radial distance away from
the collection electrode would be biased to 69 V.

63

3.11

Uncertainty in the transport measurements

The error bars for the transport measurements are given by the standard error of the mean
(SE) for repeated measurements given by:
σ
SE = √
n

(3.7)

where σ is the sample standard deviation and n is the number of measurements.

3.12

Transport measurements

The transport measurements mainly consisted of three parts: 1) determining if the rf carpet
could operate and transport ions at the operating pressures of the cyclotron gas stopper, 2) if
ions could be transported over distances corresponding to the average radius of stopped ions
predicted by simulations, and 3) if ions could be extracted from the rf carpet. In addition to
these three main studies, many measurements were conducted that gave further insight into
the operation of rf carpets and these will also be presented in the following sections.

3.12.1

The eﬀect of the applied rf voltage

This section will initiate the discussion of the transport of ions and reveal the limitations on
the transport of ions using rf carpets imposed by the eﬀective potential and the rf discharge
limit. These limitations will naturally lead into the discussion of the pressure limits on the
operation of rf carpets.
The applied rf voltage to the electrodes plays the most important role in the transport
of ions because the strength of the eﬀective potential was proportional to the square of the
applied rf voltage. Conceptually, the greater the applied rf voltage, the farther the ions can
be transported above the rf carpet surface, and the less likely for a collision between the ions
and the electrodes to occur. From the rf discharge limits measured in Ch. 4, the applied rf
voltage cannot be increased indeﬁnitely, rather electrical discharge creates a hard constraint
64

on the ion transport. By measuring the transport eﬃciency as a function of the applied rf

%7,38547911.03.












'# 5
5 ' 5 9477

Figure 3.28: Results from simulations of rf carpet ion transport indicating a pressure scaling
relationship by the collapse of the transport eﬃciency curves in VRF,pk−pk (V )/p(torr) space.
Rf carpet parameters: Rf = 2 MHz, Drag Field = 3 V/ cm, Push Field = 30 V/cm, Transport
Distance = 5 cm, Pitch = 0.38 mm, γ=0.5. Black diamonds: 30 torr, Red stars: 60 torr.
voltage, the transmission eﬃciency curves can be used to predict the required rf voltages
to reach the same transport eﬃciencies at diﬀerent pressures. This is possible because the
eﬀective potential scales with the ratio VRF,pk−pk (V )/p(torr). This general pressure scaling
trend was also conﬁrmed through simulations shown, for example, in Fig. 3.28 using the
hard-sphere collision model introduced in Section 2.7.3.
The measurements to determine the eﬀect of the applied rf voltage were conducted with
all other experimental parameters held at constant values. The reported rf voltages are the
VRF,pk−pk values measured at the surface of the rf carpet electrodes. Since the rf discharge
limit was determined before the transport measurements, the maximum applied rf voltage
for transport measurements was limited to be 10 - 15 VRF,pk−pk below the discharge limit,
65

with typical values of 160 - 170 VRF,pk−pk depending on the gas pressure and electrode
pitch. The transport eﬃciency was then determined for diﬀerent applied rf voltages up to
this maximum limit and the data were then used to construct a transport eﬃciency response
curve for those particular settings. A simple example is shown in Fig. 3.29. This process
was repeated a minimum of three times in both the direction of increasing and decreasing
applied rf voltages for each set of parameters.

%7,38547911.03.










'# 5
5 '



Figure 3.29: Measured transport eﬃciency as a response to the applied rf voltage on the
carpet electrodes. Experimental parameters: Chamber pressure=20 torr, Rf = 3.47 MHz,
Drag Field=3 V/cm, Push Field=3 V/cm, Transport Distance=16 cm, Pitch = 0.38 mm,
γ=0.5, I(Carp) = 700 pA.
With certain experimental parameters, it was possible that the ions could travel to the
collection electrode without any transport along the rf carpet electrodes. With the typical
experimental parameters mentioned in the text, this always occurred when the ion source
was located less than 3 cm away from the collection electrode. In order to ensure that
66

the transported current was completely due to transport over the rf carpet, a check was
made that there was no current measured on the collection electrode when the rf voltage
was reduced to 0 VRF,pk−pk . A second check to conﬁrm that the current measured at the
collection electrode was all due to transported ions, was that no measured current should be
on the collection electrode when the ion current leaving the source was reduced to zero with
all the electrodes biased.

%7,38547911.03.










'# 5
5 '



Figure 3.30: Example of the predicted transport eﬃciency curves scaled from the data in Fig.
3.29 as a function of the applied rf voltage on the carpet electrodes. Rf carpet parameters: Rf
= 3.47 MHz, Drag Field=3 V/cm, Push Field=3 V/cm, Transport Distance=16 cm, Pitch
= 0.38 mm, γ=0.5. Red circles: 40 torr, Blue triangles: 60 torr.
Veriﬁcation of the pressure scaling ﬁrst required a measurement at a gas pressure that
could provide the complete shape proﬁle for the eﬃciency curve and had a transport eﬃciency
near 100% for at least one applied rf voltage value. The complete curve removed the problem
of the extrapolation to calculate the applied rf voltage for transport eﬃciencies approaching
67

100%. Chamber pressures of 20 - 30 torr typically provided the appropriate gas pressure to
obtain a complete transport eﬃciency proﬁle such as that shown in Fig. 3.29.

%7,38547911.03.










'# 5
5 '



Figure 3.31: Comparison of measured (open symbols) and predicted (closed symbols) transport eﬃciency curves as a function of the applied rf voltage on the carpet electrodes. Rf
carpet parameters: Rf = 3.47 MHz, Drag Field=3 V/cm, Push Field=3 V/ cm, Transport
Distance=16 cm, Pitch = 0.38 mm, γ=0.5. I(Carp) = 700 pA Red circles: 40 torr, Blue
triangles: 60 torr. Black dot-dash line: discharge limit.
Once the complete transport eﬃciency curve was obtained, it could be used to predict the
applied rf voltage needed at diﬀerent pressures to achieve the same transport eﬃciency by
scaling the applied pressure with VRF,pk−pk (V )/p(torr). Using this scaling and the results
from Fig. 3.29, predictions of the transport eﬃciency at higher pressures as a function of
the applied rf voltage were made. Two example predictions are shown in Fig. 3.30. This
pressure scaling technique suggests that a 100% transport eﬃciency across the rf carpet
could be achieved if the applied rf voltage could be increased accordingly. Unfortunately, the
68

measured transport eﬃciencies are limited by rf discharge and is shown as the dashed line
in Fig. 3.31.
The measured transport eﬃciencies and the predicted transport eﬃciencies were in good
agreement with each other and provided a useful tool to verify if transport eﬃciency measurements were consistent amongst each other at diﬀerent pressures for identical rf carpet
parameters over time.
Though scanning the applied rf voltage was instructive, the actual operating mode of
the rf carpet would be to apply the maximum rf voltage on the rf carpet electrodes without
incurring discharge. The maximum transport eﬃciency that could be achieved (dictated
by the maximum rf voltage that could be applied) at a buﬀer gas pressure was the truly
signiﬁcant measure of how eﬃcient rf carpets would be in the pressure regime of the cyclotron
gas stopper.

3.12.2

Operating pressures of the rf carpet

One of the main requirements for the rf carpet was that it had to transport ions in the
pressure regime of the cyclotron gas stopper. The impact of the buﬀer gas on the conﬁning
force of the rf carpet was discussed in Section 2.2.1. From the simulations of the cyclotron
gas stopper that included solid degraders arranged azimuthally in the stopping chamber, the
pressure range was found to be 40 - 110 torr. This section will present the results obtained
for the transport eﬃciency of the rf carpet in this pressure regime.
Measurements for determining the transport eﬃciency at diﬀerent pressures was straight
forward once appropriate voltages were determined for the rf carpet electrodes and push
electrodes. The applied rf voltage was set to the maximum voltage before discharge occurred.
According to the rf discharge curve, the broad minimum sits in the desired pressure range
and the rf voltage did not vary by more than 10% over the studied pressure range. The
ion source was positioned over the rf carpet and a certain distance away from the collection
electrode. The ion current on the rf carpet, I(Carp), was held constant during the pressure
scan. The transport eﬃciency was determined initially at 20 torr and then the pressure of
69

the test chamber was increased. At each new pressure for which a measurement would be
taken, the gas inlet was closed and the ion current on the rf carpet was allowed to stabilize
before the transport eﬃciency was determined. The results from a single measured pressure
scan for the rf carpet with one set of rf carpet parameters and the predictions from pressure
scaling from the previous section are shown in Fig. 3.32. The predictions of the transport
eﬃciency at diﬀerent pressures are in good agreement with the measured values, but show a
trend of decreasing transport eﬃciency at the higher pressures needed for the cyclotron gas
stopper.

%7,38547911.03.

















5 9477
Figure 3.32: Measured (black squares) and predicted (red circles) transport eﬃciency of
the rf carpet over the operating pressure regime of the cyclotron gas stopper. Rf carpet
parameters: Rf = 3.47 MHz at discharge limit, Drag Field=3 V/cm, Push Field=3 V/cm,
Transport Distance=16 cm, Pitch = 0.38 mm, γ=0.5, I(Carp) = 700 pA. Black squares:
Measured, Red Circles: Predictions.
From these measurements, we gained insight into the performance of rf carpets at higher
70

pressures which would be more suitable for a linear gas stopper. Since the scaled values of
the transport eﬃciency over the pressure range are in very good agreement with the results,
the predictions can be extended further to predict the pressure limit of the rf carpets. The
predictions were made by using the scaling technique described in the previous section on a
transport eﬃciency proﬁle at 60 torr to arrive at the predicted transport eﬃciency proﬁles at
the higher pressures. The data points for the predictions shown in Fig. 3.33 were obtained by
ﬁnding the intersection of the separate transport eﬃciency curves and an applied rf voltage
of 170 VRF,pk−pk corresponding to 10 VRF,pk−pk below the rf discharge limit.

%7,38547911.03.





















5 9477
Figure 3.33: Predicted transport eﬃciency as a function of pressure for the rf carpets. Rf
carpet parameters: Rf = 3.47 MHz at discharge limit, Drag Field=3 V/cm, Push Field=3
V/cm, Transport Distance=16 cm, Pitch = 0.38 mm, γ=0.5, I(Carp) = 700 pA.
From the predicted transport eﬃciencies, the performance of the rf carpet is expected to
drop steadily to 150 torr where the transport eﬃciency is <10%. To put this in perspective,
71

the NSCL linear gas cell, was operated without rf electrodes at pressures up to 760 torr.
The rf carpet parameters that impact the transport eﬃciency at higher pressures that can
be varied are the rf driving frequency and the pitch. Increasing the rf amplitude would also
increase the transport eﬃciency, of course, but the rf amplitude would always be discharge
limited in this pressure and electrode gap regime. Increasing the rf driving frequency, an
increase in the transport eﬃciency was observed. This variation is shown in Fig. 3.34. This

%7,38547911.03.

















5 9477
Figure 3.34: Comparison of transport eﬃciency over the operating pressure regime of the
cyclotron gas stopper for a rf driving frequency of 2 MHz (blue triangles) and 3.47 MHz
(black squares). Rf carpet parameters: Rf voltage at discharge limit, Drag Field = 3 V/cm,
Push Field = 3 V/cm, Transport Distance = 16 cm, Pitch = 0.38 mm, γ = 0.5, I(Carp) =
700 pA.
increase in transport eﬃciency is not directly apparent in the eﬀective potential equations,
but is revealed when considering the micromotion (oscillations) of the ion due to the applied
rf. At lower frequencies, the ion travels a longer distance than it does at higher frequencies
72

before it undergoes a change in direction due to the change in the phase of the rf. This leads
to an ion moving closer to the rf carpet for lower rf frequencies than higher rf frequencies.
This can be seen in the example trajectories of ions from simulations of ion transport along
an rf carpet shown in Fig. 3.35. This eﬀect becomes exacerbated in more realistic microscopic
simulations that include collisions with the neutral buﬀer gas. Due to the fact that resonant
circuits are used to apply the rf voltage, increasing the rf frequency is a challenging task
because of the large capacitive load of the rf carpet. The challenges of large capacitive loads
in resonant circuits and a method to approach this problem is discussed in detail in Section
3.4.1.







 22





 22














 22






 22



Figure 3.35: Typical simulated trajectories of ions at 2 MHz (black line) and 3.47 MHz (red
line) showing that increasing the rf driving frequency increases the ion’s minimum distance
from the rf carpet surface (blue line) and therefore increases the ion’s survivability.

Another rf carpet parameter that has an important eﬀect on the transport eﬃciency
73

at higher pressures is the electrode pitch. By decreasing the electrode pitch, an increase
in transport eﬃciency was observed, as is shown in Fig. 3.36. It should be noted that the
measurements conducted with the rf carpet with the larger pitch were performed much earlier
than those with the smaller pitch and therefore had a I(Carp) ≥2.5 nA. Thus, for a proper
comparison, the results of a smaller pitch carpet will also be presented for the relatively large
values of I(Carp) ≥ 2.5 nA. It was subsequently observed that localized losses under the
ion source were highly dependent on I(Carp) and that the transport eﬃciencies were not
representative of the true performance of the rf carpet for I(Carp) > 1 nA. With that said,
the results presented for the pitch comparison are suﬃcient for comparison purposes.

%7,38547911.03.

















5 9477
Figure 3.36: Comparison of the transport eﬃciency for a pitch of 1.5 mm, γ = 0.7 (red
circles) and a pitch of 0.38 mm, γ = 0.5 (blue triangles). Rf carpet parameters: Rf voltage
at discharge limit, Drag Field = 3 V/cm, Push Field = 3 V/cm, Transport Distance = 16
cm, I(Carp) ≥ 2.5 nA.
This gain in transport eﬃciency from reducing the pitch arises from an increase in the
74

eﬀective potential. Pitches of 1.5 mm and 0.38 mm were studied in these measurements.
Reducing the pitch much below 0.38 mm is limited by the manufacturing capabilities of
pcb companies where a typical 5 mil. gap and trace width are possible corresponding to
a minimum pitch of 0.25 mm. The diﬀerence in the calculated eﬀective potential provided
by a rf carpet with a pitch of 1.5 mm and 0.38 mm is presented in Fig. 3.37 along with
the calculated eﬀective potential for a rf carpet with a pitch at the manufacturing limit of
0.25 mm. Note that such a reduction in pitch leads to an increase in the capacitive load
and a resultant decrease in the resonant frequency, which goes in the opposite direction of
the desired trend. A solution to the increased load would be to use even more additional
segmentation along the carpet as discussed in Section 3.4.1 which requires additional rf
circuits.

110.9;0!49039, '














89,3.0,,1742.,7509 59.

Figure 3.37: Comparison of the calculated eﬀective potential a A=85 ion experiences from a
rf carpet with a pitch of 1.5 mm (red circles), 0.38 mm (blue triangles), and 0.25 mm (black
squares) in 80 torr of He gas with a driving frequency of 2 MHz, Rf voltage at discharge
limit and a push ﬁeld of 10 V/cm.
75

Thus, the two rf carpet parameters that can be changed to increase the operating pressure
of the rf carpets of reducing the pitch and increasing the rf driving frequency naturally
counteract each other. Reducing the pitch to the manufacturing limit of 0.25 mm can easily
be accomplished by changing the design sent to the pcb manufacturers. As stated before, this
will increase the capacitive load of the rf carpet and bring the resonant frequency down or
require the use of multiple circuits or higher rf power. A rf carpet with a 0.25 mm pitch that
is 50 cm long will have a capacitive load of approximately 15 nF. Taking a minimum value of
3 µH for the inductance from the secondary winding, wires, etc. for the combined circuit, the
rf carpet would have to be broken into approximately 15 segments with a capacitive load of
1 nF each to reach a resonant frequency of only 3 MHz. From the results already described
in this section, the rf carpet would have to be driven at a frequency higher than 3.47 MHz to
operate with near 100% transport eﬃciency for the higher pressure regime of the cyclotron
gas stopper. For example, to achieve a driving frequency of 6 MHz with a 50 cm rf carpet
with a pitch of 0.25 mm would require 64 individual segments and rf circuits!

3.12.3

Transporting ions over long distances

A main requirement for the development of an rf carpet for a cyclotron gas stopper was that
it should transport ions over a distance approaching 50 cm, corresponding to the maximum
average radius of stopped ions from the cyclotron gas stopper simulations. The stopping radii
from simulations for a sample of diﬀerent ion species at 60 torr in the cyclotron gas stopper
is shown in Fig. 3.38. Since Rb ions were primarily studied in this oﬄine characterization,
the simulation results for 79 Br are most relevant and correspond to a stopping radius and
therefore transport distance of approximately 30 cm. Transportation of Rb ions at this
distance and greater was achieved at high transport eﬃciencies and will be presented in
this section. Transporting ions over this long distance would also be applicable to the axial
transport of ions along a linear gas cell.
The majority of the rf carpets studied had a maximum transport distance of up to 20
cm, and the bulk of the studies and comparisons were for a transport distance of 16 cm.
76




#,/:8 .2































Figure 3.38: Simulated stopping radii for 16 O, 79 Br, and 127 I ions stopped in the cyclotron
gas stopper at 60 torr. The stopping radii correspond to the distances the ions would need
to be transported along the rf carpet.
Only the ﬁnal rf carpet design had a large enough electrode structure to transport ions over
distances approaching 50 cm. This carpet demonstrated that ions could be transported over
that distance and that the electronics to apply the rf and dc components had advanced to
the state that one could drive a rf carpet of that size. As discussed in Ch. 3, the maximum
panel area for the ﬂex pcb is 45 cm x 60 cm. With a portion of the ﬂex circuit reserved for
surface mount components and a physical clamping area, the resultant electrode structure
had a maximum transport length of 48 cm.
The technical challenges of transporting ions over long distances using the rf techniques
described in Section 3.4, was that the rf carpet had to be segmented into manageable capacitive loads to increase the resonant frequency. At the time of the design, the frequency
relationship was not well established determined and the original design had a resonant fre77

quency of 2 MHz. Within the given tolerances, air core coil inductors could be modiﬁed
and variable capacitors could be used to operate all segments of the rf carpet at a resonant
frequency of 2 MHz. The resonant frequency is dictated by the capacitive load of the rf
carpet and the tolerances for the 2 MHz system were not suﬃcient to signiﬁcantly increase
the frequency because of diﬀerences in the individual capacitive loads and the entire system
could only be driven at a resonant frequency of 2 MHz or less. It is clear from the discussion
in section 3.12.2 that increasing the driving frequency would result in a higher transport
eﬃciency regardless of the transport distance. To apply a higher driving frequency than 2
MHz over the entire 48 cm rf carpet requires a redesign.
Another challenge to transporting over longer distances is the maximum dc voltage that
could be applied before a discharge occurred across the feed-throughs to the chamber held
at electrical ground. This discharge limited the maximum drag and push ﬁelds that could
be established on the rf carpet. In linear cells, the dc voltages are typically used to establish
the drag ﬁeld at approximately 10 V/cm, but the experimental setup required for testing
rf carpets is diﬀerent. In addition to the dc voltages on the rf carpet needed to establish
the drag ﬁeld, the push electrodes have to be held at an even higher potential to establish
the push ﬁeld. To put things in perspective, a 10 V/cm drag ﬁeld over 50 cm referenced to
electrical ground would require VCarpHi to be 500 V. With the push electrodes 13 cm above
the rf carpet, and a desired push ﬁeld of 10 V/cm, VPushHi would have to be 630 V. These
voltages would undergo discharge in the pressure regime for the reference measurements (20
- 30 torr), and so the push and drag ﬁelds had to be limited to 3 V/cm at these pressures.
In order to compare the data with that for higher pressures, the push and drag ﬁelds were
maintained at 3 V/cm for the long distance measurements.
Measurements for determining the transport eﬃciency at diﬀerent distances were straightforward once the rf carpet electrodes and push electrodes could sustain the appropriate voltages. As with the pressure studies, the applied rf voltage was held at the maximum voltage
before rf discharge occurred. The ion source was positioned over the rf carpet and moved
to diﬀerent positions over the rf carpet corresponding to diﬀerent transport lengths. The
78

transport eﬃciency was determined and the ion source was moved to a new position. At
every new position, the center of the ion source body was biased at a voltage so that the
corresponding electric ﬁeld between the ion source and the rf carpet matched the push ﬁeld.

%7,38547911.03.
























%7,38547989,3.0 .2
Figure 3.39: Measured transport eﬃciency at 20 torr (black squares), 40 torr (red circles),
and 60 torr (blue triangles) over diﬀerent transport distances across the rf carpet. Rf carpet
parameters: Rf voltage at discharge limit at 2 MHz, Drag Field = 3 V/cm, Push Field = 3
V/cm, I(Carp) = 500 pA.

The results of the measurements are shown in Fig. 3.39 and indicate that the rf carpet
could be used to transport ions over distances of approximately 40 cm at high transport
eﬃciencies (>90%) depending on the pressure. This distance corresponds to the maximum
average stopped radius of ions from the cyclotron gas stopper simulations. It is clear that if
the ion motion is stable and well above the rf carpet surface, as in the case of low pressures
and low push ﬁelds, the ion survives long transport distances at nearly 100% eﬃciency as
79

shown in Fig. 3.39. In the case of high pressures and high push ﬁelds where ion losses occur
on the rf carpet, it is expected that more ion losses would occur as the transport distance is
increased, as shown in Fig. 3.40.

%7,38547911.03.
























%7,38547989,3.0 .2
Figure 3.40: Measured transport eﬃciency at 80 torr over diﬀerent transport distances across
the rf carpet. Rf carpet parameters: Rf voltage at discharge limit at 2 MHz, Drag Field = 3
V/cm, Push Field = 3 V/cm, I(Carp) = 1 nA.
On the other hand, the transport eﬃciency was found to be low but constant for a series
of distances which indicated that the losses were localized. This phenomenon is shown in
Fig. 3.41, where the data for the 60 torr measurements with an I(Carp)=2.5 nA resulted in
a relatively constant transport eﬃciency of approximately 50%. The suggestion is that the
ion losses were mainly occurring near the ion source or within 8 cm of the ion source. The
constant value of the eﬃciency at transport distances of 8 cm and 40 cm, suggested that
there were no ion losses once past the localized eﬀect of the ion source. Further investigation
80

showed that I(Carp) also had a large eﬀect on the measured transport eﬃciency and this is
presented in the following section.

%7,38547911.03.
























%7,38547989,3.0 .2
Figure 3.41: Measured transport eﬃciency at 60 torr with I(Carp) = 2.0 nA over diﬀerent
transport distances across the rf carpet. Rf carpet parameters: Rf voltage at discharge limit
at 2 MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm.

3.12.4

Eﬀect of ion current and the push ﬁeld on ion transport

The sensitivity of the transport eﬃciency to the ion current, I(Carp) was not apparent until
long distance transport was possible. Very signiﬁcant ion losses were observed directly under
the ion source. The absolute values of I(Carp) was largely ignored up until that point, as
long as ions were impinging on the rf carpet and the transport eﬃciency could be calculated
reliably. The eﬀect of the push ﬁeld is also part of this section because it was studied at the
same time as the variation with I(Carp) because they were the two parameters (aside from
81

increasing the pressure) that would challenge the operation of the rf carpet. By varying the
push ﬁeld, the eﬀect on the transport eﬃciency of an opposing electric ﬁeld on the rf carpet
could be determined. Originally, before it was determined that the ion source resulted in
localized losses, varying I(Carp) was thought to mainly determine the eﬀect on transport
eﬃciency of the total electric charge moving on the rf carpet.

%7,38547911.03.




 
 (  
 



 
 (  


 
 (  













43:77039 3
Figure 3.42: Measured transport eﬃciency at 30 torr with varying I(Carp) for a push ﬁeld
of 10 V/ cm (black squares), 15 V/cm (red circles), and 20 V/cm (blue triangles). Rf carpet
parameters: Rf voltage at discharge limit at 2 MHz, Drag Field = 3 V/cm, Transport Distance
= 8 cm.
These measurements were conducted by ﬁrst establishing the appropriate voltages on
the rf carpet, the push electrodes, and the ion source. The test chamber was at a static
pressure and the rf voltage was 10 VRF,pk−pk under the rf discharge limit. I(Carp) was
varied and the transport eﬃciency was determined for a given distance. Then, the push ﬁeld
was increased and the transport eﬃciency was determined for a new value of I(Carp) again.
82

The results of these measurements at 30 torr are shown in Fig. 3.42. The results indicate
that, the transport eﬃciencies decrease linearly with I(Carp). The transport eﬃciency for the
diﬀerent push ﬁelds in the limit of zero ion current (no space charge limit) can be estimated
by taking the y-intercept of the linear trends (e.g.

= 0.937 for 10 V/cm).

In order to determine the eﬀect of the push ﬁeld on the transport eﬃciency, I(Carp) can
be held constant and the push ﬁeld can be scanned. The measurements at 30 and 60 torr
are shown in Fig. 3.43. This can also be inferred, of course, from a slice in constant I(Carp)

%7,38547911.03.
















!:80/ '.2
Figure 3.43: Measured transport eﬃciency at 30 torr (black squares) and 60 torr (red circles)
for varying push ﬁeld strengths. Rf carpet parameters: Rf voltage at discharge limit at 2
MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm, Transport Distance = 8 cm, I(Carp) =
2 nA.
for the 30 torr measurements of the results shown in Fig. 3.42. Since it was impossible to
measure the transport eﬃciency without ion current, simulations using HS-collisions discussed in Sec. 2.6.3 (which don’t take into account any space charge eﬀects) were conducted
83

to determine if the simulated transport eﬃciencies matched up with the ’no space charge’
limit taken from the y-intercepts of the I(Carp) studies. This was done as an attempt to
decouple the push ﬁeld eﬀects from the localized space charge eﬀects produced from the ion
source. The comparison between the HS-collision simulations, the ’no space charge’ limit,
and experimental measurements taken at I(Carp) = 2 nA for a case of 30 torr is shown in
Fig. 3.44. The comparison shows a stark disagreement between the HS-collision simulations
and the experimental measurements. The large discrepancy between the HS-collision simulations and the experiment could possibly be due to the fact that the eﬀects of the I(Carp)
and the push ﬁeld could not be properly disentangled. Thus, independent simulations that

%7,38547911.03.





















!:80/ '.2
Figure 3.44: Transport eﬃciency at 30 torr for a varying push ﬁeld for experiment (black
squares), the ’no space charge limit’ inferred from experiment (red circles), and HS-collision
simulations (blue triangles). Rf carpet parameters: Rf voltage at discharge limit at 2 MHz,
Drag Field = 3 V/cm, Push Field = 3 V/cm, Experimental transport distance = 8 cm,
Simulated transport distance = 5 cm, I(Carp) = 2 nA.

84

incorporated detailed space charge eﬀects [22] were conducted in an attempt to include all
the known processes in the transport of ions with rf carpets: the eﬀects of the buﬀer gas,
the push ﬁeld, and the space charge. Taking the more interesting gas pressure of 60 torr,
a comparison between the HS-collisions simulations, the space charge simulations, and the
experimental results is shown in Fig. 3.45. The space charge eﬀects bring the simulation
results closer to the data but they still do not match the experimental measurements.

%7,38547911.03.




























!:80/ '.2
Figure 3.45: Transport eﬃciency at 60 torr for a varying push ﬁeld for experiment (blue triangles), space charge simulations (red circles), and HS-collision simulations (black squares).
Rf carpet parameters: Rf voltage at discharge limit at 2 MHz, Drag Field = 3 V/cm, Push
Field = 3 V/cm, Experimental transport distance = 8 cm, Simulated transport distance =
5 cm, I(Carp) = 2 nA.

85

3.12.5

Ion Extraction from the rf carpet

The last main requirement for the rf carpet studies was to demonstrate that ions could be
extracted from the rf carpet. Since the main purpose of the rf carpet was to guide thermalized
ions towards the center of the cyclotron gas stopper and bring them to an extraction oriﬁce,
it was important to demonstrate that ions could also be extracted eﬃciently from the rf
carpet. Extraction of ions from an rf carpet has already been demonstrated by M. Wada [3],
and he contributed a small rf carpet with an aperture in the center. This small rf carpet,
called here the extraction rf carpet, was excellently suited for the transition between the high
gas pressure in the stopping chamber and the diﬀerentially pumped region. A photograph of
the circuit board is shown in Fig. 3.46.

Aperture

Transport Area
O-ring electrode

Figure 3.46: Photograph of the extraction rf carpet from Wada [3] with an aperture used for
ion extraction measurements. The outer o-ring electrode was used to conﬁne the ions on the
rf carpet.

86

Table 3.3: Parameters for the extraction rf carpet
Parameter
Outer radius of rf electrodes
Pitch
Electrode width
Extraction hole diameter
VRF,pk−pk
Rf frequency

used in extraction measurements.
Value
2.5 cm
0.3 mm
0.15 mm
0.5 mm
< 70 V
5 - 8 MHz

Extraction oriﬁce

Main rf carpet

Extraction
rf carpet

Figure 3.47: Photograph of the setup used for ion extraction. The extraction rf carpet is
mounted below the main (large) rf carpet and a collection electrode is mounted below the
extraction rf carpet (not shown).

87

The exact parameters of the extraction rf carpet are listed in Table 3.3. The center
aperture diameter was in the sub-mm region which was typical for apertures in gas stopping
stations. A small transport area and a small pitch allowed for a high resonant frequency
and an increased eﬀective potential, in which the advantages of both parameters have been
discussed in previous sections. In fact, the use of the extraction rf carpet was planned during
the design phase of the last large rf carpet. Thus, after the suite of transport measurements
were completed with the large rf carpet, a hole was cut into the pcb to remove the collection
electrode so that the extraction rf carpet could be mounted below the carpet. A photograph
of this arrangement is shown in Fig. 3.47. To determine the extraction eﬃciency from the
extraction rf carpet, another collection electrode was mounted below the extraction rf carpet.

Large rf carpet

push electrodes

push electrodes
for small rf carpet

1

2

O-ring electrode

small rf carpet
3

collection electrode

Figure 3.48: Schematic diagram of the setup used for ion extraction. The red and blue
hatched marks represent the electrodes in which rf was applied. The dotted electrodes represent the electrodes in which dc voltages were applied. The diﬀerent collection electrodes
for the diﬀerent transport modes are labeled with their appropriate number designation.
Transport mode 1 collected on the extraction rf carpet electrodes encompassed by the dash
line. Transport mode 2 collected on the o-ring electrode and is encompassed by the dot-dash
line. Transport mode 3 collected on the collection electrode mounted below the extraction
rf carpet encompassed by the dot-dot-dash line.
88

The extraction rf carpet was operated in an identical manner as the main rf carpet as
described in Sec. 3.4. The only diﬀerence in general operation was the method of applying
the rf voltages to each electrode. The device used surface mount capacitors rather than the
new technique used to apply the rf underneath the main rf carpet. The smaller transport
area and the capacitive load allowed for a resonant frequency in the 5 - 8 MHz range.
It was important to diﬀerentiate the ion losses at diﬀerent parts of the transport process
in order to determine which transport stage might need improvement. Thus, the transport
eﬃciency had to be determined for three diﬀerent transport modes: 1) Transport from the
top rf carpet to the extraction rf carpet, 2) Transport to the extraction rf carpet and along
the extraction rf carpet, and 3) Transport to the extraction rf carpet and through the central
aperture to the collection electrode. The extraction rf carpet electrodes could be used as a
collection electrode for transport mode 1 and the o-ring surrounding the extraction rf carpet
could be used as a collection electrode for transport mode 2 with reversed drag ﬁeld on the
extraction rf carpet. A schematic of the setup showing the three transport modes is shown
in Fig. 3.48.
Transport mode 1 was achieved by establishing the voltages on the large rf carpet electrodes, push electrodes, and the ion source as mentioned in the previous sections. In addition
to this, the underside of the main rf carpet was biased with a dc voltage to act as a set of
push electrodes in the region between the two rf carpets. The extraction rf carpet was then
separately biased and used as the collection electrode. The transport eﬃciency for transport
mode 1 matched the results for pure surface transport. Thus, there were no ion losses during
the transport between the large rf carpet and the extraction rf carpet.
Transport mode 2 was achieved by operating the large rf carpet and push electrodes for
the extraction rf carpet as in transport mode 1 and also applying a rf voltage and a drag ﬁeld
on the small rf carpet. However, the dc gradient on the extraction rf carpet directed the ions
towards the outer radius (rather than towards the inner radius) to be collected on the o-ring
that was biased separately. The set of push electrodes for the extraction rf carpet did not
have a dc gradient, so the push ﬁelds will be presented as a range. The transport eﬃciency
89

%7,38547911.03.














97,.94371.,7509'# 5
5 '


Figure 3.49: Measured transport eﬃciency for transport mode 2 (collection on the o-ring
electrode) as a function of the rf voltage applied to the extraction rf carpet at a gas pressure
of 40 torr. Main rf carpet parameters: Rf voltage at discharge limit at 2 MHz, Drag Field
= 3 V/cm, Push Field = 3 V/cm, Transport distance before large hole = 8 cm. Extraction
rf carpet parameters: Frequency = 5.28 MHz, Drag Field = 8 V/cm, Push Field = 20 - 27
V/cm.
as a function of applied rf voltage on the extraction rf carpet for transport mode 2 is shown
in Fig. 3.49 and suggest that none of the ions were lost once they reach the extraction rf
carpet. Also, pure transport with the dc ﬁelds did not occur because no transported ions
were observed when the rf voltages were reduced on the extraction rf carpet.
Transport mode 3 had the same operation as transport mode 2, except for the dc gradient
on the extraction rf carpet directed the ions towards the inner radius and the ions were
collected on an electrode mounted directly below the aperture of the extraction rf carpet.
The o-ring electrode used to collect ions in transport mode 2 was biased to conﬁne the ions
on the extraction rf carpet. The electric ﬁeld between the innermost ring of the extraction

90

%7,38547911.03.














97,.94371.,7509'# 5
5 ' 



Figure 3.50: Measured transport eﬃciency for transport mode 3 (collection through the
aperture) as a function of the rf voltage applied to the extraction rf carpet at a gas pressure
of 40 torr at an extraction rf carpet frequency of 5.28 MHz (red circles) and 8.56 MHz (black
squares). Main rf carpet parameters: Rf voltage at discharge limit at 2 MHz, Drag Field =
3 V/cm, Push Field = 3 V/cm, Transport distance before large hole = 8 cm. Extraction rf
carpet parameters: Drag Field = 8 V/cm, Push Field = 20 - 27 V/cm, Collect Pull Field =
25 V/cm.
carpet and the collection electrode is referred to as the collect pull ﬁeld. The results for
transport mode 3 for two diﬀerent extraction rf carpet frequencies are shown in Fig. 3.50.
In this transport mode, ion losses were observed through the aperture of the extraction rf
carpet. The proﬁle of the transport eﬃciency curves show that increasing the rf voltage would
not substantially improve the ion survival for either rf frequency. In addition to investigating
the transport eﬃciency through the aperture, this transport mode provided further evidence
for the advantage of using a higher rf frequency on the rf carpets, as can be seen by the much
steeper response curve to the applied rf voltage for the rf frequency of 8.56 MHz compared
91

to 5.28 MHz. Since transport mode 2 had nearly 100% eﬃciency, these losses are attributed
to the region close to the aperture. It should be noted that gas ﬂow was not present in this
experimental setup, and would reduce these losses in an operational device setup. However,
ion losses could be expected due to space charge losses near the oriﬁce. Further conﬁrmation
that ion losses occurred near the aperture region and that the presence of gas ﬂow would
reduce these losses, is shown in the sensitivity of the transport eﬃciency to the strength of
the collect pull ﬁeld in Fig. 3.51. The stronger the collect pull ﬁeld, the deeper the electric
ﬁeld penetration through the aperture which pulls the ions through the aperture when the
ions are at the innermost radius.

%7,38547911.03.












97,.94371.,7509'# 5
5 ' 



Figure 3.51: Measured transport eﬃciency for transport mode 3 (collection through the
aperture) at Collect Pull Fields of 25 V/cm (black squares), 40 V/cm (red circles), and 70
V/cm (blue triangles) as a function of the rf voltage applied to the extraction rf carpet at a
gas pressure of 40 torr. Main rf carpet parameters: Rf voltage at discharge limit at 2 MHz,
Drag Field = 3 V/cm, Push Field = 3 V/cm, Transport distance before large hole = 8 cm.
Extraction rf carpet parameters: Drag Field = 8 V/cm, Push Field = 20 - 27 V/cm.
92

The ion extraction measurements also revealed a high transport eﬃciency in the presence
of a strong push ﬁeld on the extraction rf carpet. The push ﬁeld that the extraction rf
carpet was able to sustain was (20 - 27 V/cm) while still transporting ions. Recall that such
high ﬁelds resulted in all the ions being lost in the push studies for the main rf carpet.
This increased survivability can be directly attributed to the reduced pitch, the increased rf
frequency, and the shorter transport distance of this device.

3.12.6

Ion drift time measurements

For rare isotope studies, it is important for the rf carpet to transport ions fast enough to
minimize decay losses. The ion drift times for these rf carpets are dictated by the drag ﬁeld.
The drift times predicted by ion mobilities were compared with measurements and generally
conﬁrmed the expected ion transport times along the rf carpet.

AFG

Pulse
Generator

Ion Source

Collection
Electrode

Keithley
Analog Out

Rf Carpet
O-Scope

Figure 3.52: Schematic used for the timing measurements.
These measurements were conducted by using an Agilent 33120A arbitrary waveform
generator (AFG) to provide a 5 Hz square waveform as an external trigger for a pulse generator that pulsed the ion source (On/Oﬀ). The ion current was then measured on the
collection electrode by observing the analog output of the Keithley picoammeter on a dig93

ital oscilloscope. In this setup, transport eﬃciencies were not obtained. A schematic of the
experimental setup is shown in Fig. 3.52.

3,4 :95:9 '













%20 8
Figure 3.53: Measured pulse train (black) and ﬁt curve (red) at 40 torr for rf carpet parameters: Frequency = 3.47 MHz, Drag Field = 3 V/cm, Push Field = 3 V/cm, Transport
Distance = 14.4 cm.
A sample of one of the pulse trains along with a Chi-square minimized curve ﬁt from
Igor Pro 9 [23] using a sawtooth function modiﬁed by two exponential functions for the
rise and fall times is shown in Fig. 3.53. The drift time can be extracted from these ﬁt
coeﬃcients and the comparison between a set of sample measurements and the predicted ion
mobilities is shown in Fig. 3.54. There is excellent agreement between the predictions and
the measurements that conﬁrms the ion transport times follow the expected ion mobilities.
From these measurements, ion transport times will be directly given by the drag ﬁeld which
is itself limited by the maximum dc voltage that can be applied without incurring discharge.
Ion transport speeds were the same regardless of the rf frequency studied (2 MHz and 3.47
94

MHz). This problem was discussed in Sec. 3.10.3. We can predict the transport times of an
ion with a K0 = 20 cm2 /(V·s) over a 50 cm rf carpet with a typical drag ﬁeld of 10 V/cm
at 80 torr will have a transport time of approximately 24 ms. The maximum drag ﬁelds
are indeed a known limitation in current gas stopping stations and designs to apply a drag
ﬁeld greater than 30 V/cm (Savard) and 100 V/cm (KVI) at 100 mbar are currently being
investigated.

%7,385479$500/ .28
















7,0/ '.2
Figure 3.54: Comparison of the measured ion transport speed (open red circles) and the
predicted ion transport speeds (black squares) from ion mobility calculations. Rf carpet
parameters: Pressure = 20 torr, Frequency = 2 MHz, 3.47 MHz, Push Field = 3 V/cm,
Transport Distance = 24 cm.

95

Chapter 4
Summary and Outlook
In this work, a feasible extraction scheme for a cyclotron gas stopper using rf carpets was
developed and characterized. The main requirements of eﬃcient transport of thermal ions in
the pressure range of a prospective cyclotron gas stopper, for the required distances of the
cyclotron gas stopper, and extraction of the ions from the rf carpet were satisﬁed.
The rf carpet was demonstrated to transport ions at ≥80% eﬃciency at gas pressures up
to 80 torr, which is within the operating pressure range of the cyclotron gas stopper. Ion
transport over a distance of 40 cm at pressures up to 60 torr was also achieved at near 100%
eﬃciency. This long distance corresponded to the average distance the ions would have to be
transported to the extraction oriﬁce located in the central region of the proposed cyclotron
gas stopper. The extraction of ions from the rf carpet was also successfully demonstrated
with an eﬃciency of approximately 75% eﬃciency without gas ﬂow.
In comparison to the rf carpet from RIKEN with a diameter of 3 cm and a subsequent
transport distance of 1.5 cm, this work has demonstrated the transport of ions over an order
of magnitude larger distance. Attempts at RIKEN to operate larger rf carpets were hindered
due to heating issues [4]. The use of resonant circuits, allowed the successful operation of rf
carpets with much larger sizes with less than 1 W of power consumption. The drawbacks
of using such techniques are also described in this text. The other experimental systems
developed for gas catchers at GSI [24] and Argonne [25], are constructed using discrete
96

electrodes with a typical electrode pitch on the order of 1 mm, rather than the sub-mm
pitch that can be achieved with rf carpets. The rf frequency used in these devices was ≤
1 MHz. In this work, the smallest pitch size studied was 0.38 mm, which showed a clear
advantage over a pitch size of 1.5 mm in experiment. The advantages of increasing the rf
frequency were also shown in the present measurements. The rf carpet studied in this work
has a smaller pitch and increased rf frequency over the ion-guiding devices in the GSI and
Argonne gas catchers. From these two parameters that were shown to have the largest impact
on transport eﬃciency, it can be inferred that the rf carpet studied in this work would have
a superior transport eﬃciency than existing systems.

RF Carpet
Segments

Insulation
and
shielding

Figure 4.1: Design and arrangement of a series of rf carpets that would allow for a rf carpet
coverage of 1 meter in diameter.
Though the results in this work have demonstrated transport distances of 40 cm, the
proposed cyclotron gas stopper will require a rf carpet covering an area with a 1 meter
diameter. Given the present manufacturing limits of 45 x 60 cm, it would be impossible
to cover this area with only one rf carpet. Thus, a method to arrange a series of carpets
97

azimuthally to cover the full area was developed but not yet fabricated. The technique
requires a 4 Cu-layer ﬂex pcb material (Cu-Kapton-Cu-Kapton-Cu-Kapton-Cu) instead of
the 2 Cu-layer (Cu-Kapton-Cu) ﬂex pcb material used in this work. These additional Cu
layers allow the routing lines for the dc and rf voltages to all be located on one edge of a
rf carpet segment while allowing room for a set of dc electrodes arranged on the other edge
of the rf carpet segment. These dc electrodes will be responsible for establishing the electric
ﬁelds in the transition region between two rf carpets pieces. The concept and the orientation
of four sectors that would cover the area is shown in Fig. 4.1.

98

Bibliography

Bibliography
[1] D.J. Morrissey. Extraction of thermalized projectile fragments from gas. European
Physical Journal - Special Topics, 150(1):365 – 366, 2007.
[2] G. Bollen, D.J. Morrissey, and S. Schwarz. A study of gas-stopping of intense energetic
rare isotope beams. Nuclear Instruments and Methods in Physics Research Section
A: Accelerators, Spectrometers, Detectors and Associated Equipment, 550(1-2):27 – 38,
2005.
[3] Michiharu Wada, Yoshihisa Ishida, Takashi Nakamura, Yasunori Yamazaki, Tadashi
Kambara, Hitoshi Ohyama, Yasushi Kanai, Takao M. Kojima, Youichi Nakai, Nagayasu
Ohshima, Atsushi Yoshida, Toshiyuki Kubo, Yukari Matsuo, Yoshimitsu Fukuyama,
Kunihiro Okada, Tetsu Sonoda, Shunsuke Ohtani, Koji Noda, Hirokane Kawakami, and
Ichiro Katayama. Slow ri-beams from projectile fragment separators. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials
and Atoms, 204:570 – 581, 2003. 14th International Conference on Electromagnetic
Isotope Separators and Techniques Related to their Applications.
[4] A. Takamine, M. Wada, Y. Ishida, T. Nakamura, K. Okada, Y. Yamazaki, T. Kambara,
Y. Kanai, T.M. Kojima, Y. Nakai, N. Oshima, A. Yoshida, T. Kubo, S. Ohtani, K. Noda,
I. Katayama, P. Hostain, V. Varentsov, and H. Wollnik. Space-charge eﬀects in the
catcher gas cell of a rf ion guide. Review of Scientiﬁc Instruments, 76:103503–1–103503–
6, 2005.
[5] L. Weissman, D. A. Davies, P. A. Lofy, and D. J. Morrissey. Stopping energetic heavyions in one-bar helium: broad incident momentum distributions. Nuclear Instruments
and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment, 531(3):416 – 427, 2004.
[6] L. Weissman, D.J. Morrissey, G. Bollen, D.A. Davies, E. Kwan, P.A. Lofy, P. Schury,
S. Schwarz, C. Sumithrarachchi, T. Sun, and R. Ringle. Conversion of 38ca/37k projectile fragments into thermalized ion beams. Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment,
540(2-3):245 – 258, 2005.
[7] L. Weissman, D. A. Davieas, P. A. Lofy, and D. J. Morrissey. Stopping energetic heavy
ions in one-bar helium: narrow incident momentum distributions. Nuclear Instruments
and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment, 522(3):212 – 222, 2004.
100

[8] G. Bollen, D. Davies, M. Facina, J. Huikari, E. Kwan, P. A. Lofy, D. J. Morrissey,
A. Prinke, R. Ringle, J. Savory, P. Schury, S. Schwarz, C. Sumithrarachchi, T. Sun,
and L. Weissman. Experiments with thermalized rare isotope beams from projectile
fragmentation: A precision mass measurement of the superallowed β emitter 38 ca. Phys.
Rev. Lett., 96(15):152501, Apr 2006.
[9] G. Sikler, D. Ackermann, F. Attallah, D. Beck, J. Dilling, S. A. Elisseev, H. Geissel,
D. Habs, S. Heinz, F. Herfurth, F. Heberger, S. Hofmann, H. J. Kluge, C. Kozhuharov,
G. Marx, M. Mukherjee, J. Neumayr, W. R. Pla, W. Quint, S. Rahaman, D. Rodrguez,
C. Scheidenberger, M. Tarisien, P. Thirolf, V. Varentsov, C. Weber, and Z. Zhou. First
on-line test of shiptrap. Nuclear Instruments and Methods in Physics Research Section
B: Beam Interactions with Materials and Atoms, 204:482 – 486, 2003. 14th International
Conference on Electromagnetic Isotope Separators and Techniques Related to their
Applications.
[10] G. Savard, J. Clark, C. Boudreau, F. Buchinger, J. E. Crawford, H. Geissel, J. P. Greene,
S. Gulick, A. Heinz, J. K. P. Lee, A. Levand, M. Maier, G. Mnzenberg, C. Scheidenberger, D. Seweryniak, K. S. Sharma, G. Sprouse, J. Vaz, J. C. Wang, B. J. Zabransky, and Z. Zhou. Development and operation of gas catchers to thermalize fusionevaporation and fragmentation products. Nuclear Instruments and Methods in Physics
Research Section B: Beam Interactions with Materials and Atoms, 204:582 – 586, 2003.
14th International Conference on Electromagnetic Isotope Separators and Techniques
Related to their Applications.
[11] G. Bollen, C. Campbell, S. Chouhan, C. Gunaut, D. Lawton, F. Marti, D.J. Morrissey,
J. Ottarson, G. Pang, S. Schwarz, A.F. Zeller, and P. Zavodszky. Manipulation of rare
isotope beams - from high to low energies. Nuclear Instruments and Methods in Physics
Research Section B: Beam Interactions with Materials and Atoms, 266(19-20):4442 –
4448, 2008. Proceedings of the XVth International Conference on Electromagnetic
Isotope Separators and Techniques Related to their Applications.
[12] M. Sternberg and G. Savard. A study of the cyclotron gas-stopping concept for the
production of rare isotope beams. Nuclear Instruments and Methods in Physics Research
Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 596(3):257
– 268, 2008.
[13] Mark Huyse, Marius Facina, Yuri Kudryavtsev, Piet Van Duppen, and ISOLDE collaboration. Intensity limitations of a gas cell for stopping, storing and guiding of radioactive
ions. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 187(4):535 – 547, 2002.
[14] H.G. Dehmelt. Radiofrequency spectroscopy of stored ions - i: Storage. Adv. At. Mol.
Phys., 3:53–72, 1967.
[15] Raymond E. March and Richard J. Hughes. Quadrupole Storage Mass Spectrometry.
John Wiley and Sons, 1989.
[16] Taeman Kim, Aleksey V. Tolmachev, Richard Harkewicz, David C. Prior, Gordon Anderson, Harold R. Udseth, Richard D. Smith, Thomas H. Bailey, Sergey Rakov, and
101

Jean H. Futrell. Design and implementation of a new electrodynamic ion funnel. Analytical Chemistry, 72(10):2247–2255, 2000.
[17] S. Schwarz. Rf ion carpets: The electric ﬁeld, the eﬀective potential, operational parameters and an analysis of stability. International Journal of Mass Spectrometry, 299(2-3):71
– 77, 2011.
[18] T. Hasegawa and K. Uehara. Dynamics of a single particle in a paul trap in the presence
of the damping force. Applied Physics B, 61:159 – 163, 1995.
[19] http://www.simion.com.
[20] A. James Diefendefer. Principles of Electronic Instrumentation. Brooks/Cole, 1994.
[21] J. Park, I. Henins, H.W. Herrmann, and G.S. Selwyn. Gas breakdown in an atmospheric
pressure radio-frequency capacitive plasma source. Journal of Applied Physics, 89:15 –
19, 2001.
[22] R. Ringle. 3dcylpic–a 3d particle-in-cell code in cylindrical coordinates for space charge
simulations of ion trap and ion transport devices. International Journal of Mass Spectrometry, 303(1):42 – 50, 2011.
[23] http://www.wavemetrics.com.
[24] J.B. Neumayr, L. Beck, D. Habs, S. Heinz, J. Szerypo, P.G. Thirolf, V. Varentsov,
F. Voit, D. Ackermann, D. Beck, M. Block, Z. Di, S.A. Eliseev, H. Geissel, F. Herfurth,
F.P. Heberger, S. Hofmann, H.-J. Kluge, M. Mukherjee, G. Mnzenberg, M. Petrick,
W. Quint, S. Rahaman, C. Rauth, D. Rodrguez, C. Scheidenberger, G. Sikler, Z. Wang,
C. Weber, W.R. Pla, M. Breitenfeldt, A. Chaudhuri, G. Marx, L. Schweikhard, A.F.
Dodonov, Y. Novikov, and M. Suhonen. The ion-catcher device for shiptrap. Nuclear
Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 244(2):489 – 500, 2006.
[25] W. Trimble, G. Savard, B. Blank, J.A. Clark, F. Buchinger, T. Cocolios, J.E. Crawford,
A. Frankel, J.P. Greene, S. Gulick, J.K.P. Lee, A. Levand, M. Portillo, K.S. Sharma,
J.C. Wang, B.J. Zabransky, and Z. Zhou. Development and ﬁrst on-line tests of the
ria gas catcher prototype. Nuclear Physics A, 746:415 – 418, 2004. Proceedings of the
Sixth International Conference on Radioactive Nuclear Beams (RNB6).

102