INVESTIGATION OF ION CAPTURE IN AN ELECTRON BEAM ION TRAP
CHARGE-BREEDER FOR RARE ISOTOPES
By
Kritsada Kittimanapun

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Physics - Doctor of Philosophy
2014

ABSTRACT
INVESTIGATION OF ION CAPTURE IN AN ELECTRON BEAM ION
TRAP CHARGE-BREEDER FOR RARE ISOTOPES
By
Kritsada Kittimanapun
Charge breeding of rare isotope ions has become an important ingredient for providing
reaccelerated rare isotope beams for science. At the National Superconducting Cyclotron
Laboratory (NSCL), a reaccelerator, ReA, has been built that employs an advanced Electron Beam Ion Trap (EBIT) as a charge breeder. ReA will provide rare-isotope beams with
energies of a few hundred keV/u up to tens of MeV/u to enable the study of properties
of rare isotopes via low energy Coulomb excitation and transfer reactions, and to investigate nuclear reactions important for nuclear astrophysics. ReA consists of an EBIT charge
breeder, a charge-over-mass selector, a room temperature radio-frequency quadrupole accelerator, and a superconducting radio-frequency linear accelerator. The EBIT charge breeder
features a high-current electron gun, a long trap structure, and a hybrid superconducting
magnet to reach both high acceptance for injected low-charge ions as well as high-electron
beam current densities for fast charge breeding.
In this work, continuous ion injection and capture in the EBIT have been investigated
with a dedicated Monte-Carlo simulation code and in experimental studies. The MonteCarlo code NEBIT considers the electron-impact ionization cross sections, space charge due
to the electron beam current, ion dynamics, electric field from electrodes, and magnetic
field from the superconducting magnet. Experiments were performed to study the capture
efficiency as a function of injected ion beam current, electron beam current, trap size, and
trap potential depth. The charge state evolution of trapped ions was studied, providing

information about the effective current density of the electron beam inside the EBIT. An
attempt was made to measure the effective space-charge potential of the electron beam by
studying the dynamics of a beam injected and reflected inside the trap.

For my family.

iv

ACKNOWLEDGMENTS

First of all, I would like to thank my supervisor, Georg Bollen, who kindly accepted me
as one of his student and pushed me hard. In addition, Stefan Schwarz primarily advised
and taught me several things: technical laboratory work, computer programming, attitudes
toward solving problems, etc. He was always available whenever I had questions. Discussion
with Alain Lapierre was very useful. From his experience, he provided me valuable guidance
which is important to my career. I would like to thank Oliver Kester for introducing me
to the EBIT charge breeder and giving suggestions during the early stage of my research.
Daniela Leitner also deserves recognition for her critical comments to my research and
being one of the committee members. I would like to thank Norman Birge and Vladimir
Zelevinsky for serving guidance committee members as well. Thank to Thomas Baumann,
another EBIT group member, for useful suggestion and thesis proofreading.
Good friends are worth being mentioned. I would like to thank Adam Fritsch for proofreading this thesis and sharing many non-physics experiences. Big thank to Kiseok Chang
for encouraging conversation and help once we were in the same research group. I would
like to thank Thai community for a warm welcome since my first day in MSU and giving
me a chance to be a president of the Thai Student Association. Running the organization
is always a great experience.
Last but not least, I would like to thank my parents for supports on what I have been
doing. My wife, Moui, is always beside and encourages me to overcome every problem
I encountered. My daughters, Zoey and Sonia, are such beautiful ones who light me up
and make me completely understand how great being a father. Without my lovely family
members, I cannot imagine my life would be. Thank you.
v

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . .
1.1 NSCL’s Reaccelerator ReA . . . . . . . . . . . . . . . . . . .
1.2 Highly charged ions for reacceleration of rare isotope beams
1.3 History and applications of EBIS/T . . . . . . . . . . . . . .
1.4 Charge breeding requirements for reaccelerated beams . . . .
1.5 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . .

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1
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Chapter 2 Physics
2.1 Electron beam
2.2 Electron beam
2.3 Ion motion . .
2.4 Ion processes

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of an Electron Beam Ion Source/Trap
ion source/trap principle . . . . . . . . . .
and space-charge potential . . . . . . . . .
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Chapter 3 The EBIT as a Charge Breeder
3.1 Injection and extraction . . . . . . . . . .
3.2 Ion capture . . . . . . . . . . . . . . . . .
3.3 Trap capacity . . . . . . . . . . . . . . . .
3.4 Beam dynamics . . . . . . . . . . . . . . .
3.4.1 Beam emittance . . . . . . . . . . .
3.4.2 Effective ellipse transformation . .
3.4.3 Geometrical acceptance . . . . . . .

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22
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31

Chapter 4 The NSCL EBIT Charge Breeder
4.1 NSCL electron beam ion trap characteristics
4.1.1 Electron gun and collector . . . . . .
4.1.2 Trap electrode structure . . . . . . .
4.1.3 Hybrid superconducting magnet . . .
4.2 Test ion source . . . . . . . . . . . . . . . .
4.3 Achromatic Q/A separator . . . . . . . . . .
4.4 Diagnostic devices . . . . . . . . . . . . . . .
4.5 Beamline transport optics . . . . . . . . . .

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33
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Chapter 5 Simulation of Ion Injection and Acceptance
5.1 Calculation of electric and magnetic fields . . . . . . .
5.2 Ion trajectory simulation by SIMION . . . . . . . . . .
5.3 NSCL EBIT simulation code . . . . . . . . . . . . . . .

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44
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vi

5.4

5.5

NSCL EBIT code benchmarking . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Test of energy conservation along the ion trajectory . . . . . . . . . .
5.4.2 Comparison of geometrical acceptance from NEBIT and an analytical
formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Comparison of capture efficiency calculated with NEBIT and an analytical formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.4 Comparison of charge evolution between NEBIT and CBSIM . . . . .
5.4.5 Comparison of capture efficiency between current and earlier versions
Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Capture efficiency with maximum design parameters . . . . . . . . .
5.5.2 Capture efficiency with different transport optics . . . . . . . . . . .
5.5.3 Capture efficiency with parameters used in experiments . . . . . . . .

Chapter 6 Measurements, Results, and Discussion . . . . . . . . . . . . .
6.1 Transverse emittance measurement of K+ beam . . . . . . . . . . . . . . .
6.1.1 Experimental setup and procedure . . . . . . . . . . . . . . . . . .
6.1.2 Emittance of the K+ ion beam . . . . . . . . . . . . . . . . . . . .
6.2 Optimization of ion injection . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Experimental setup for ion injection and capture process . . . . . .
6.2.2 Axial energy spread measurement . . . . . . . . . . . . . . . . . . .
6.2.3 Ion reflection in the EBIT . . . . . . . . . . . . . . . . . . . . . . .
6.3 Dependency of the total efficiency on ion and electron beam currents, trap
size, and trap depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Capture efficiency vs injected ion beam current . . . . . . . . . . .
6.3.2 Capture efficiency vs electron beam current . . . . . . . . . . . . .
6.3.3 Total efficiency vs trap size . . . . . . . . . . . . . . . . . . . . . .
6.3.4 Total efficiency vs trap depth . . . . . . . . . . . . . . . . . . . . .
6.4 Study of the charge breeding process . . . . . . . . . . . . . . . . . . . . .
6.4.1 Charge state evolution and charge breeding time . . . . . . . . . . .
6.4.2 Determination of effective current density . . . . . . . . . . . . . .

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Chapter 7 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . 117
7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
APPENDICES . . . . . . . . . . . . . . . .
Appendix A Transfer matrix for a triplet
Appendix B Voltage distribution . . . .
Appendix C Ion source simulation . . . .

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120
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128

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

vii

LIST OF TABLES

Table 4.1

NSCL EBIT requirements and parameters. The choices for the
design parameters to satisfy the performance requirements are described in more details in the text. . . . . . . . . . . . . . . . . . . . 35

Table 5.1

Comparison of features used in the earlier and the current versions
of NEBIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Table 5.2

EBIT and ion beam parameters used in SIMION and NEBIT unless
otherwise specified. . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Table 5.3

Maximum errors of the total energy. The calculations were performed with the electron beam currents of 1 A and 2.5 A and the
test ion was injected both on- and off-axes. . . . . . . . . . . . . . . 57

Table 5.4

Beam and EBIT parameters for the NEBIT calculations (a) and
sample phase space of 0.1 A and 1 A electron beam currents for
1 T and 6 T regions of the 1T-6T magnetic field configuration and
the 6T-6T configuration (b). The number in the parenthesis indicates the region of the magnetic field used for the evaluation of the
acceptance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Table 5.5

Comparison of geometrical acceptance calculated with the analytical
formula and NEBIT. . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Table 5.6

List of input (top) and output parameters, and geometrical acceptance (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Table B.1

List of voltages used in SIMION and the NEBIT code to test the
conservation of energy along the ion trajectory described in section
5.4.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Table B.2

The voltage setting for a test of geometrical acceptance with the
NSCL EBIT system described in section 5.4.2. For the electron beam
current of 100 mA, the settings for 1T-6T and 6T-6T configurations
are the same. For the electron beam current of 1 A, the TC12
element is set to be 59.2 and 58.5 kV for the 1T-6T and 6T-6T
configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Table B.3

List of voltages used in NEBIT to calculate the charge state evolution.125
viii

LIST OF FIGURES

Figure 1.1

Figure 1.2

The NSCL Coupled Cyclotron Facility. High energy rare isotope
beams produced in flight and separated by the A1900 separator are
delivered to different experimental stations. Low-energy beams are
produced by gas stopping and provided for “stopped beam” experiments or for reacceleration with ReA. . . . . . . . . . . . . . . . . .

2

ReA concept. Fast ions are decelerated by a gas stopper and extracted as a very low-energy beam. This beam is transported to the
EBIT for charge breeding, extracted with multiply higher charge
states, separated by a Q/A selector, and accelerated through an
RFQ and SRF cryomodules. . . . . . . . . . . . . . . . . . . . . . .

4

Figure 2.1

EBIT principle. The major components are an electron beam, a
magnetic field, and trap electrodes. Singly charged ions are injected
and highly charged ions are ejected through a collector. . . . . . . . 11

Figure 2.2

Electron beam energy with correction (a) and space-charge potential
(b) for the first (black), the second (red), the third (blue), and the nth order (green) corrections calculated for the NSCL EBIT geometry
(see text for details). . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Figure 2.3

Schematic showing the atomic processes of an argon gas in the EBIT. 18

Figure 2.4

Electron impact ionization cross section of K+ as a function of
electron beam energy. The electron beam energy is required to be
greater than the binding energy in order to produce the EI process.

20

Figure 3.1

Pulsed injection process. (a) An ion is injected into the trap, (b)
the outer barrier is raised up, and (c) the ion is confined inside the
trapping region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 3.2

Continuous injection process. (a) An ion is injected with the energy
slightly above the outer barrier, (b) the ion experiences the higher
barrier after being charge bred, and (c) the ion is confined inside the
trapping region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 3.3

Three possible methods to extract HCIs from the EBIT: (a) leaky ,
(b) fast, and (c) pulsed extraction. . . . . . . . . . . . . . . . . . . . 25

ix

Figure 3.4

Three possible ion trajectories in the trap. The ion trajectory is (a)
completely inside the electron beam, (b) partially inside the electron
beam, and (c) totally outside the electron beam. . . . . . . . . . . . 26

Figure 3.5

The r.m.s. ellipse in the phase space. . . . . . . . . . . . . . . . . . 29

Figure 3.6

Capture probability calculated from the overlapped area in the phase
space between emittance and acceptance. . . . . . . . . . . . . . . . 32

Figure 4.1

Overview of the NSCL EBIT charge breeder. . . . . . . . . . . . . . 34

Figure 4.2

Side view cross sections of the electron gun (a) and the collector
drawings (c) and the electron gun (b) and the collector assemblies
(d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Figure 4.3

Trap electrode structure for the NSCL EBIT. . . . . . . . . . . . . . 37

Figure 4.4

NSCL EBIT with the test ion source (a) and a side view cross section
showing the combination of a solenoid and Helmholtz coils (b). . . 39

Figure 4.5

A hot cathode ion source (left) and a schematic corresponding to
each component. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Figure 4.6

The Q/A separator consisting of two electrostatic benders and a
bending magnet. The yellow arrow displays the direction of the
beam extracted from the EBIT and transported to the linear accelerator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Figure 4.7

A picture of a microchannel plate installed in the ReA beamline. . . 42

Figure 4.8

Drawing of a quadrupole triplet (a) and a steerer element (b), the
transfer lens (c), and the fully assembled acceleration column consisting of an acceleration/deceleration electrode and an Einzel lens
(d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Figure 5.1

EBIT workbench in SIMION containing a ground electrode, an acceleration/deceleration column, a collector, a transfer lens, and trap
electrodes (a), potential (b) and electric field map (c) solved by
SIMION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figure 5.2

Magnetic field distribution of 1T-6T (black) and 6T-6T (red) used
throughout the calculations. The trap center is at z = 2.12 m. . . . 47
x

Figure 5.3

Comparison of ion trajectories in the 1 T magnetic field without (a)
and with a 2 A electron beam (b) and the 6 T magnetic field without
(c) and with a 2 A electron beam (d). A 60 keV beam of injected
ions and an electron beam energy of 12.5 keV were used. . . . . . . 49

Figure 5.4

Contour plot of radial energy that the ions gain while traveling into
the 1 T (a) and the 6 T (b) magnetic fields. The radial energy is
plotted as a function of the initial phase space. . . . . . . . . . . . . 50

Figure 5.5

Flowchart showing the algorithm of the acceptance calculation. . . . 52

Figure 5.6

Concept of simulated capture efficiency. The ratio of the number
of the trapped to the injected ions in the same phase space area is
interpreted as a capture probability. The ellipse is aligned along the
line from the linear fit (red solid line). . . . . . . . . . . . . . . . . . 53

Figure 5.7

The error of the total energy from on- (black) and off-axis (red)
injections (a) and kinetic, potential, and total energy (b). The ion
is injected with an offset of x = 2.31 mm, y = 0.12 mm, ax =
−31.39 mrad, ay = −2.62 mrad. . . . . . . . . . . . . . . . . . . . 56

Figure 5.8

Acceptance phase space in x direction calculated for 1 A (a) and
2.5 A (b) electron beam currents and a 1T-6T magnetic field configuration. The initial position and angle in x (red) and y (green)
directions are given in circles. . . . . . . . . . . . . . . . . . . . . . . 57

Figure 5.9

The error of total energy calculated from on- (black) and off-axis
(red) ion injections with the electron beam current of 2.5 A. . . . . . 58

Figure 5.10

The acceptance phase space determined in the 1 T region (a, d) and
the 6 T region (b, e) of the 1T-6T magnetic field configuration and
the 6T-6T configuration (c, f) with 0.1 A (a, b, c) and 1 A (d, e, f)
electron beam currents. . . . . . . . . . . . . . . . . . . . . . . . . 61

Figure 5.11

Comparison between the capture efficiency calculated from the analytical formula and NEBIT with the electron beam current of 1 A
and the 6T-6T magnetic field configuration. . . . . . . . . . . . . . 64

xi

Figure 5.12

Charge evolution of iron ions calculated from CBSIM (lines) and
NEBIT (symbols). The highest relative abundances on the leftmost and rightmost curves of the figure represent charge states of
Fe1+ and Fe17+ , respectively. The calculation stopped at a charge
breeding time of 1 ms and the electron beam of 1 A and the 6T-6T
configuration were used. . . . . . . . . . . . . . . . . . . . . . . . . 65

Figure 5.13

Comparison of the the capture efficiency calculated from the current
and the earlier versions of NEBIT. The electron beam of 2.5 A and
12 keV were used with the 1T-6T magnetic field configuration. . . . 67

Figure 5.14

Capture efficiency as a function of injected beam emittance for 1 A
(black) and 2.5 A (red) electron beam current. The calculation were
carried out with the electron beam energy of 12.5 keV and the 1T-6T
magnetic field configuration. . . . . . . . . . . . . . . . . . . . . . . 69

Figure 5.15

Capture efficiency as a function of injected beam emittance for 1T6T (black) and 6T-6T (red) configurations for the 1 A and 12.5 keV
electron beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 5.16

Calculated capture efficiency as a function of voltage applied to the
acceleration/deceleration electrode. . . . . . . . . . . . . . . . . . . 72

Figure 5.17

Calculated capture efficiency as a function of voltage applied to the
Einzel lens: 16.57 (black), 16.32 (red), 16.07 (blue), 15.82 (magenta),
and 15.57 kV (green). . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Figure 5.18

Calculated capture efficiency as a function of electron beam current
for injected ion beams with emittances from 1 - 6 π mm·mrad. . . . 75

Figure 5.19

Calculated capture efficiency as a function of trap size for injected
ion beams with emittances from 1 - 6 π mm·mrad. . . . . . . . . . . 76

Figure 5.20

Calculated capture efficiency as a function of trap depth for injected
ion beams with emittances from 1 - 6 π mm·mrad. . . . . . . . . . . 77

Figure 6.1

Schematic showing the experimental setup for the emittance measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Figure 6.2

Examples of beam images captured by the MCP viewer with different voltages applied to quadrupole A(a), B(b), C(c). . . . . . . . . 81

xii

Figure 6.3

Quadratic fits of beam size squares at different voltages applied to
the quadrupole A(a), B(b), and C(c). . . . . . . . . . . . . . . . . . 83

Figure 6.4

The NSCL EBIT experimental setup: (1) electron gun, (2) electron
gun Faraday cup, (3) trap electrodes and primary components including inner barrier (3a), main trap (3b), and outer barrier (3c),
(4) transfer lens, (5) electron collector, (6) Einzel lens, (7) acceleration/deceleration column, (8) ground electrode, (9) beam observation box 1 (BOB 1), (10) quadrupole triplet lens, (11) LA source
consisting of ion source (11a), deflector (11b), electrostatic bender
(11c), deflector (11d), (12) quadrupole triplet lens, (13) BOB 2,
(14) electrostatic bender, (15) quadrupole lens, (16) BOB 3, (17)
quadrupole doublet, (18) bending magnet, (19) quadrupole doublet,
and (20) BOB 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Figure 6.5

A plot of the ion beam current as a function of the inner potential
barrier (Top) and a Gaussian fit of the first derivative of the ion
beam current with respect to the inner potential barrier (bottom). . 87

Figure 6.6

Time sequences for the injection and the extraction processes for the
deflector (a) and the outer barrier (b). The time sequence for the
outer barrier is used for charge breeding process. . . . . . . . . . . . 90

Figure 6.7

TOF spectra of the ion beam measured after lowering the potential
applied to each electrode: (a) no lowering, (b) after lowering LTE4,
(c) after lowering LTE1, and (d) after lowering LTRAP. . . . . . . . 91

Figure 6.8

TOF spectrum of the ion beam reflected at different locations in
the EBIT and simulated histogram that includes voltage delay, overshoot, and undershoot. The pattern area shows expected signal from
the ion beam reflected off the trap entrance and the inner barrier. . 92

Figure 6.9

Time delay for changing between injection and extraction voltages of
the deflector top (black) and deflector bottom (red) electrodes and
signal from the function generator (blue). The pattern area indicates
a range of voltage that allows the ion beam transport based on the
experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Figure 6.10

TOF spectra of ion reflection and simulated histograms without the
electron beam (a), with the 19.5 keV and 90 mA electron beam for
both simulation and experiment (b), and with the 19.5 keV and
90 mA electron beam for experiment and the 19.5 keV and 25 mA
for the simulation (c). . . . . . . . . . . . . . . . . . . . . . . . . . . 96
xiii

Figure 6.11

Q/A spectra of the ion beam extracted from the EBIT with a 5 Hz
repetition rate, an electron beam current of 126 mA, and a 19.5 keV
electron beam energy. The spectra with and without the external
injection of K+ are shown in black and red dotted curves, respectively. 99

Figure 6.12

Beam current of K16+ detected at BOB 4 with different injected
beam currents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Figure 6.13

Total efficiency of charge breeding into K16+ charge state with different injected beam currents. . . . . . . . . . . . . . . . . . . . . . 101

Figure 6.14

Comparison of total beam currents extracted from EBIT with (red)
and without injection of potassium beam (black) at different electron
beam currents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Figure 6.15

A plot showing particle currents at different charge states from electron beam currents of 135 mA (black), 115 mA (red), 96 mA (blue),
and 76 mA (magenta). The ion beam was extracted from the EBIT
with a 5 Hz repetition rate. . . . . . . . . . . . . . . . . . . . . . . . 103

Figure 6.16

Comparison between the simulated capture efficiency ranges (between red-dash and black-solid line) and the experimental (black)
capture efficiencies as a function of electron beam currents. . . . . . 105

Figure 6.17

Calculated capture efficiency of a beam with an emittance of 3.8 π
mm·mrad at 20 keV as a function of distance between an injected
beam and an electron beam axis. The electron beam current of
135 mA was used. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Figure 6.18

Schematic of the trap with different trap sizes. . . . . . . . . . . . . 107

Figure 6.19

A plot showing particle current of each charge state for different
trap sizes. The ion beam was extracted from the EBIT with a 5 Hz
repetition rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Figure 6.20

Comparison between the simulated capture efficiency ranges (between red-dash and black-solid line) and the experimental capture
efficiencies (black) as a function of trapping size. . . . . . . . . . . . 108

Figure 6.21

Schematic of the trap with different trap potential. . . . . . . . . . . 109

xiv

Figure 6.22

A plot showing particle current at different charge states with trap
potential of -10 V (magenta), -30 V (blue), -50 V (red), -70 V (black)
compared to the outer barrier. The ion beam was extracted from
EBIT with 5 Hz repetition rate. . . . . . . . . . . . . . . . . . . . . 109

Figure 6.23

Comparison between the simulated capture efficiency ranges (between red-dash and black-solid line) and the experimental (black)
capture efficiencies as a function of trap depth. The simulated values are calculated based on the 20 keV ion beam. . . . . . . . . . . 110

Figure 6.24

Mass-over-charge spectra of highly charged potassium obtained by
scanning the bending magnet current for different accumulation times.
The electron beam current and energy were 125 mA and 19.5 keV. . 112

Figure 6.25

Calculated charge state evolution of potassium ions with the continuous injection. The electron beam current density is 500 A/cm2 . . . 113

Figure 6.26

Comparison between calculated (dash line) and experimental (solid
line) charge state evolutions of K12+ (black) and K16+ (light blue).
The electron beam current and energy were 100 mA and 19.5 keV. . 115

Figure 6.27

Electron beam current density as a function of the electron beam
radius simulated by Tricomp. . . . . . . . . . . . . . . . . . . . . . 116

Figure A.1

Transfer matrix elements; A (black), B (red), C (blue), and D (magenta), in horizontal (left) and vertical (right) axes as a function of
applied voltage to the quadrupole A. . . . . . . . . . . . . . . . . . . 123

Figure B.1

Power supply schematic for the EBIT. Except an earthground, all
elements are floating on an EBIT high voltage platform. To control
the electron beam, the electron gun and the collector are biased up
to 20 kV on top of the EBIT high voltage platform. . . . . . . . . . 126

Figure B.2

Schematic of voltages applied to each element. . . . . . . . . . . . . 127

Figure C.1

Simulation of ion production inside the test ion source. . . . . . . . 129

xv

Chapter 1
Introduction
The National Superconducting Cyclotron Laboratory (NSCL) has been successfully providing rare isotope beams produced by the projectile fragmentation method for nuclear science.
Figure 1.1 shows a schematic of the NSCL facility. A high energy stable beam delivered by
two coupled cyclotrons with an energy of > 80 MeV/u impinges on a production target.
Rare isotopes are produced by fragmentation or in-flight fission. The reaction products are
separated by the A1900 fragment separator and delivered to experimental areas.
These fast rare isotope beams have been used for a successful science program, including
nuclear structure studies via intermediate energy Coulomb excitations, finding the limits
of nuclear stability, or investigating the equation of state of nuclear matter. However, in
order to increase scientific knowledge of rare isotopes, it is advantageous to offer those over
a large energy range.
Rare isotope beams at very low energy, “stopped beams” enable precision experiments
with traps and lasers. NSCL was the first facility to stop fast beams in a gas cell [1] and
extract them as low-energy beams for enabling Penning trap mass measurements with the
Low Energy Beam and Ion Trap (LEBIT) facility [2]. Laser spectroscopy has recently been
added with the BEam COoler and LAser spectroscopy (BECOLA) station [3].
In addition to providing fast and stopped beams there is a variety of experiments that
needs beams in the energy range from a couple of hundreds keV/u up to a few tens of
1

Figure 1.1 The NSCL Coupled Cyclotron Facility. High energy rare isotope beams produced
in flight and separated by the A1900 separator are delivered to different experimental
stations. Low-energy beams are produced by gas stopping and provided for “stopped beam”
experiments or for reacceleration with ReA.
MeV/u for nuclear astrophysics and nuclear structure studies. With the realization of ReA,
a reaccelerator of the available stopped beams, NSCL will be the first to provide rare isotope
beams in this energy range that have been produced in-flight.
In order to make best use of the rare isotopes produced it is important that a reaccelerator scheme is chosen that provides high efficiency. The approach taken was to build
a reaccelerator that combines an advanced Electron Beam Ion Trap (EBIT) as a charge
breeder with a modern Superconducting Radio-Frequency (SRF) linac. The NSCL reaccelerator (ReA) is designed to achieve high efficiency for all elements available at the NSCL,
for high beam rate capability and high beam quality, and for providing a variable time
structure of the beam.

2

1.1 NSCL’s Reaccelerator ReA
ReA benefits from using a scheme of reaccelerated highly charged ions (HCIs) instead of
singly charged ions (SCIs) which makes the reaccelerator compact and reduces cost. The
concept of ReA is shown in Figure 1.2.
Cooled SCIs from the gas stopper are selected by a mass separator and transported to a
charge breeder. The EBIT-type charge breeder converts the rare isotope beam from a 1+ to
a Q+ charge state. The EBIT floats on a high voltage platform so that the SCIs delivered
from the gas stopper at an energy of up to 60 keV can be slowed down prior to be captured
in the trap. Once charge-bred, the highly charged ions are extracted toward an achromatic
charge-over-mass (Q/A) separator where the undesired background of HCIs from the EBIT
is suppressed. The beam is then reaccelerated with a linear accelerator consisting of a
Multi-Harmonic Buncher (MHB), a Radio Frequency Quadrupole (RFQ) accelerator and
SRF cavities. The MHB in front of the RFQ is used for acceptance matching. The first
cryomodule after the RFQ houses a rebuncher. The second and third cryomodules have
cavities optimized for a beam with β = v/c = 0.041 and β = 0.085, respectively, where
v is the ion velocity and c is the speed of light. The beam energy is expected to be 0.3 3 MeV/u for 238 U (q/m = 0.25) and 0.3 - 6 MeV/u for light elements (q/m = 0.5).

1.2 Highly charged ions for reacceleration of rare isotope beams
Different methods have been considered for providing higher charge states to ease the
reacceleration of rare isotope beams: using a foil or gas target as a stripper, using an
Electron Cyclotron Resonance (ECR) source as a charge breeder, or using an Electron
3

600 keV/u
MHB

Q/A
selector

80 MHz
RFQ

Rebuncher

80 MHz SRF 80 MHz SRF
β = 0.041
β = 0.085

~ 3 MeV/u
beams

Bending
magnet
Electrostatic
benders

EBIT charge breeder
1+
Q+

12 keV/u, Q+

~100 MeV/u
beams

Gas stopper

60 keV ,1+
Mass
separator

Figure 1.2 ReA concept. Fast ions are decelerated by a gas stopper and extracted as a very
low-energy beam. This beam is transported to the EBIT for charge breeding, extracted
with multiply higher charge states, separated by a Q/A selector, and accelerated through
an RFQ and SRF cryomodules.

4

Beam Ion Source/Trap (EBIS/T) as a charge breeder.
The traditional stripping method is for example employed at ISAC at TRIUMF. Passing
accelerated ions through a gas jet or a foil removes electrons and increases the ion’s charge
state. Such a scheme is costly because pre-acceleration of SCIs to energies of 100 keV/u is
needed before passing through a gas jet or foils. In addition, the longitudinal and transverse
emittance after stripping increases [4] and the stripping efficiency is not very high [5].
ECR Ion Sources (ECRIS) are used or were tested as possible charge state boosters
at many facilities, for example, SPIRAL at GANIL [6], TRIUMF [7], ISOLDE [8], KEKJAERI [9], and CARIBU at ANL [10]. ECRIS employs electron cyclotron resonance heating
to transfer energy into the plasma electrons, that ionize gas into plasma confined by a strong
magnetic field. The SCIs are continuously introduced into the hot plasma with high electron
density.
The ECR-type PHOENIX source has demonstrated using the ECRIS method to charge
breed Pb+ into Pb25+ with an efficiency of up to 7% [11]. A major disadvantage of
operating ECRIS as a charge breeder is a very low beam purity. The working pressure is
around 10−8 − 10−6 mbar and causes the extracted HCIs to contain a significant portion
of residual gas.
The potential of EBIS/T as charge breeders has been recognized after the successful
demonstration at REX-ISOLDE at CERN [12]. EBIS/T charge breeders are under development not only at NSCL [13], but also at ATLAS/ANL and planned for ISAC at
TRIUMF.
The Electron Beam Ion Source (EBIS) and the EBIT use the same principle to create
HCIs. The main differences between them are the trap size and the electron beam current

5

density. A typical EBIS has a large trapping region and is surrounded by a solenoid while
an EBIT has a shorter trap in a strong magnetic field created by Helmholtz coils. Due to
the large trap, the EBIS has large capacity to contain HCIs. On the other hand, the EBIT
can provide short breeding times which result from having a strong magnetic field and high
electron beam current density.
In an EBIS or EBIT, singly charged or neutral particles are bombarded by a nearly
mono-energetic electron beam and become highly charged through electron impact ionization. In EBIS/T devices, one can manipulate the charge state distribution during the charge
breeding process by adjusting the electron beam energy and breeding time. A narrow charge
state distribution is reached by selecting the electron beam energy to be slightly below an
ionizing threshold at atomic shell closures, the so-called closed shell breeding technique, but
the charge breeding time is then longer. The charge capacity of the EBIS/T is determined
by the electron beam current and energy and the trap size. For example, 2×1011 positive
charges can be stored in a trap of 0.8 meter long with a 2.5 A electron beam current and
an electron beam energy of 11 keV. The operation of EBIS/T is very flexible because it
can run in both pulsed and continuous modes with both injection and extraction processes.
Because the device is operated under ultra high vacuum of 10−11 to 10−9 Torr, the beam
contamination is low.
Since the acceptance of an EBIS/T is generally small and determined by the size of the
electron beam, ion beam cooling can be necessary before transporting SCIs into the EBIS/T.
The energy spread of the extracted HCI beam depends on the space-charge potential, charge
states of HCIs, extraction voltage, etc. An achromatic separator may be required to select
a HCI beam with a certain range of energy spread [14]. The closed shell charge breeding

6

technique is successfully utilized to narrow charge state distributions and increase charge
breeding efficiency. A charge breeding efficiency of 23% of 23 Na9+ has been reported with
REX-EBIS at ISOLDE/CERN [12].

1.3 History and applications of EBIS/T
The earliest application of an electron beam compressed by a magnetic field originated
in 1929 by Bleakney when he measured the ionization potential of highly charged mercury
[15]. In 1968, P. A. Redhead investigated the electron impact ionization process by trapping
mercury ions with the electron beam and electrostatic potential [16]. Similar in principle
to an ion trap, the EBIS was invented by E. Donets et al. and results were discussed in
a conference at Saclay in 1969 [17]. In 1989, the Sandia Super-EBIS achieved producing
U82+ at an energy below 1 keV/Q in order to study interactions between low-energy HCIs
[18].
Sharing the same principle of operation with the EBIS, the EBIT developed by M. A.
Levine et al. [19] was built with a short trapping region and used a pair of Helmholtz coils
for generating the magnetic field. Since the EBIT is primarily used for atomic spectroscopy,
an open access at the center of the Helmholtz coils allows to observe X-ray emissions.
The EBIS/T base device has been used in several applications [20]. The EBITs at
LLNL [21], NIST [22], and MPIK in Heidelberg [23] are dedicated to atomic physics and
spectroscopy. The commercial compact Dresden EBIT is used to study the interaction
between HCIs and material surfaces [24, 25]. The RHIC-EBIS at BNL is employed to
produce a highly charged beam for a pre-injector of the accelerator [26, 27]. Rare isotope
beam facilities, such as the REXEBIS at ISOLDE-CERN [28], NSCL EBIT [29, 30], and
7

CARIBU EBIS at Argonne [31, 32] are devoted to post acceleration while the TITAN EBIT
at TRIUMF [33] and the MATS EBIT at FAIR [34] charge breed rare isotopes for mass
measurements.

1.4 Charge breeding requirements for reaccelerated beams
The overall efficiency of the EBIT which is determined by the injection and extraction efficiencies, the transport efficiency, the charge breeding efficiency, and the capture efficiency,
is given by where tot , inj , ext , trans , CB , and cap are total, injection, extraction,
transport, charge breeding, and capture efficiencies, respectively. The injection, extraction,
and transport efficiencies are obtained by optimizing beam transport optics and injecting
a SCI beam with small emittance. The SCI beam has to be well focused while entering
the trapping region. With the limited yield of the rare isotopes, the highest injection and
transport efficiencies are required to ensure that the isotope beam travels into the trap and
is not lost during beam transport.
The charge breeding efficiency determines how efficient the EBIT can charge breed ions
into a single charge state. Due to the distribution of HCIs, the breeding efficiency is normally
limited to between 20% to 40% [12]. However, the closed shell breeding technique has proven
to overcome this limitation. A charge breeding efficiency of 90% was experimentally reached
[35].
The capture efficiency is a crucial parameter for charge breeding rare isotope beams.
The singly charged beam has to overlap well with the electron beam in order that SCIs
are efficiently captured. The maximum efficiency is not easily obtained since the electron
beam size is generally smaller than 100 µm and several parameters are involved for the
8

optimization.

1.5 Thesis overview
To investigate ion capture inside the NSCL EBIT and to maximize the efficiency of the
EBIT through experiments and a dedicated simulation code, the objectives of the work
were
• Optimization of the 60 keV beam transport into the EBIT trap by using SIMION
• Development of a simulation code to investigate ion injection and the capture process
• Observation of the charge state evolution of the externally injected beam from a test
ion source
• Measurements to investigate the capture efficiency of the NSCL EBIT and compare
these experimental data with simulation results.
The thesis is outlined as follows. Physics of an EBIT and its application as a charge
breeder are shown in Chapter and Chapter , respectively. The characteristics of the NSCL
EBIT charge breeder are described in Chapter . Chapter contains information about the
simulation performed to investigate the capture efficiency. The measurements, results, and
discussion of the experiments required for the investigation of the capture efficiency are
presented in Chapter . A conclusion and an outlook are described in Chapter .

9

Chapter 2
Physics of an Electron Beam Ion
Source/Trap
In order to investigate the capture efficiency of an EBIT, it is important to understand how
the EBIT functions and what physical phenomena occur inside. There are several processes
involved and those are discussed in the following sections.

2.1 Electron beam ion source/trap principle
The main components of the EBIS/T are illustrated in Figure 2.1. The EBIS/T primarily
consists of the electron beam, cylindrical trap electrodes, and a magnetic field. The monoenergetic electron beam drives the charge breeding process by successive electron impact
ionization. The electron beam also creates the space-charge potential to radially confine
ions. The electron beam is generated at a cathode, travels through the trap, and is absorbed by an electron collector. The strong magnetic field from a superconducting magnet
compresses the electron beam to high current density for fast charge breeding. While being
exposed to the high density electron beam, ions are axially trapped and charge bred in the
region between two potential barriers: an inner barrier and an outer barrier. The terms of
the inner and the outer barriers used throughout the thesis refer to the barriers close to the

10

Figure 2.1 EBIT principle. The major components are an electron beam, a magnetic field,
and trap electrodes. Singly charged ions are injected and highly charged ions are ejected
through a collector.
electron gun and the collector, respectively. Both barriers are formed by applying different
voltages to trap electrodes. After charge breeding for a certain amount of time, the HCIs
are extracted toward and through the collector by lowering the outer barrier voltage.
Singly charged ions can be externally injected through the collector to the EBIS/T
trapping region. Depending on the application, neutral gas can be introduced into the
EBIS/T via a radial open gap. Unless specified otherwise, from now on, the term “EBIT”
will be used for both the EBIS and the EBIT for simplicity.

2.2 Electron beam and space-charge potential
The maximum compression of the electron beam can be obtained when the conditions of
the ideal Brillouin flow are satisfied. The electrons are generated from the cathode which
11

has zero temperature and situates in the magnetic field free region. The Brillouin radius
rb is,
1
rb =
B

Ie
π 0

1/4
2m3e
,
Ee e2

(2.1)

where Ie is the electron beam current, Ee is the electron beam energy, B is the magnetic
field, me is the electron mass, e is the elementary charge, and 0 is the vacuum permittivity.
Practically, it is impossible to have a zero temperature at the cathode. By including the
finite temperature at the cathode, the electron beam radius is well predicted by the Herrmann theory [36]. The Herrmann radius rh defines a boundary where 80% of the electron
beam passes through and is given by

rh = rb

1 1
+
2 2

1+4

8kTc rc2 me Bc2 rc4
+
,
e2 r 4 B 2
B 2 r4
b
b

(2.2)

where k is the Boltzmann constant, Tc is the cathode temperature, rc is the cathode
radius, and Bc is the magnetic field at the cathode. Maximum electron beam compression
is obtained if Bc = 0. This is the reason why the electron gun is designed to cancel the
field at the cathode as much as possible. For the NSCL EBIT, the electron beam radius
is 80 µm, with Ie = 150 mA, Ee = 19.5 keV, B = 2 T, Bc = 10 G, rc = 3.175 mm, and
Tc = 1400 K. It is obvious from the equation that the magnetic field plays a major role in
determining the electron beam size. By increasing the magnetic field inside the trap, the
electron beam radius becomes smaller and the beam density larger.
The distribution of the electron beam density is studied with two different approaches:
a homogeneous and a Gaussian profile. Both approaches can provide analytical solutions of
space-charge potential and a comparison between the space-charge potential solved by both

12

distributions is discussed in Ref. [37, 38]. However, the former approach is more suitable
to the simulation because it is easier to acquire the analytical solution of the electric field
along the electron beam axis. Due to this advantage, the homogeneous electron density is
employed. The electron beam density is assumed to be uniform up to the Herrmann radius,
beyond which it vanishes.
The space-charge potential φsc is straightforwardly computed by solving the Poisson’s
equation with the homogeneous density and given by




1 1−


2
Qe
φsc (r) =
2π 0 


r

ln rT

r2
r2
h

r
+ ln rT
h

: 0 < r < rh
(2.3)
: rh < r < rT ,

where Qe is the total charge per unit length equivalent to the ratio between the electron
beam current and the electron velocity (I/ve ) and rT is the drift tube radius. The depth
of the radial potential is

φsc (0) =

Qe
2π 0

r
1
+ ln T
2
rh

.

(2.4)

With a 2 T magnetic field, a 0.135 A and 19.5 keV electron beam from a 3.175 mm cathode,
and a trap electrode radius of 5 mm, the central space-charge potential is -115 V.
During the electron beam propagates, the electron beam energy is affected by the potential created by itself and can be corrected in a “self-consistent” way. The correction can
be solved by an iterative or an analytical method. The latter approach will be employed in

13

the simulation. Starting from the iterative method, the correction is

E1 = E0 + φ0,sc (0)
= E0 +
E2 = E0 +
..
.

..
.

C
E0
C
E1

(2.5)

..
.

En = E0 +

C
,
En−1

where C = C(I, rT , rh ) is from Eq. 2.4 in which Qe is replaced by I

me /2E0 and

1/E0

is neglected. Subscripts indicate the order of the correction. If the iteration converges, then
for large n, En = En−1 leading to
C
En = E0 + √ .
En

(2.6)

3 − 2E 2 E + E E 2 = C 2
En
n 0
n 0

(2.7)

The equation is rearranged as

which can be solved analytically. If the electron beam energy satisfies the condition E0 >
3|C|2/3 /22/3 , the real solution is obtained and given by

En = E0 − E0

arccos2 (δ)
arccos(δ)
√
− E0
,
54
3 3

(2.8)

where δ = 1 − 27C 2 /2E03 . For example, results of the electron beam energy with correction

14

and the space-charge potential which are computed based on the NSCL EBIT geometry
are displayed in Figure 2.2. With an electron beam current of 2.4 A, a magnetic field of
6 Tesla, and E0 = 12.5 keV at the trapping region, the difference in potential calculated
with and without correction is 0.75 kV.

2.3 Ion motion
Ion motion in a combined electric and magnetic field is simply described by the Lorentz
equation,
ma = q (E + v × B) .

(2.9)

where m, q, a, v are ion mass, charge, acceleration, and velocity, respectively, and E and B
are the electric and the magnetic field. The effect of the space-charge field and the magnetic
field on ion motion is discussed in the following. Due to the axial symmetry, only the axial
and radial components contributed by space-charge are considered as

E = Er + Ez = −∇r φsc − ∇z φsc .

(2.10)

Assuming the magnetic field inside the trap is along the axis, then B = Bz ez = B. At small
radii, the radial magnetic field component is approximately given by Br = − 12 r dBz . The
dz
equations of motion including the space-charge field are, inside the electron beam r ≤ rh ,
q Qe 1
q
x + B y˙
m 2π 0 r2
m
h
q Qe 1
q
y¨ =
y − B x˙
m 2π 0 r2
m
h

x¨ =

15

(2.11)

Electron energy (keV)

16
14
E0

12
10

E1

E2

8

En

6

Trapping region

4
2
1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

Axial coordinate (m)
(a)

Space charge potential (kV)

3
2
1
0
-1
-2

U0

-3

Un

-4
-5
1.0

1.2

U1
U2

1.4 1.6 1.8 2.0 2.2
Axial coordinate (m)

2.4

(b)
Figure 2.2 Electron beam energy with correction (a) and space-charge potential (b) for
the first (black), the second (red), the third (blue), and the n-th order (green) corrections
calculated for the NSCL EBIT geometry (see text for details).

16

z¨ =

q Qe
m 2π 0

vz

∂vz
∂z

1
2

1−

r2
r2
h

+ ln

rT
rh

−

1 ∂rT
1 ∂rh
+
rT ∂z
rT ∂z

1−

r2
r2
h

and outside the electron beam rh < r < rT ,
q Qe
x
q
+ B y˙
m 2π 0 x2 + y 2 m
q Qe
y
q
y¨ =
− B x˙
m 2π 0 x2 + y 2 m

x¨ =

z¨ =

q Qe
∂vz
vz
ln
m 2π 0
∂z

rT
rh

−

(2.12)

1 ∂rT
.
rT ∂z

We can see that the axial acceleration is determined by the tube radius, the Herrmann
radius, their changes along the axis, and the change of the ion energy along the axis. In the
NEBIT code, which will be discussed in Chapter , these equations are numerically solved
for the ion motion at each time step and the derivatives of rh and rT with respect to the
axial coordinate are calculated by the two-point backward-difference formula [39].

2.4 Ion processes
In the EBIT, ions can undergo many processes. The main processes involving charge state
changes are electron impact ionization (EI), radiative recombination (RR), and charge
exchange (CX). There are also processes contributing to ion dynamics: ion heating by the
electron beam and by ion-ion energy exchange. Details of these processes are described in
Ref. [37]. Figure 2.3 illustrates the charge state evolution of an argon ion. The vertical
axis represents the ionization energy for the different charge states. The inset illustrates
charge state development and an ion escape from the trap.
The total cross section of the RR process, which is obtained from Kim and Pratt [40],
17

Bare
18+

He-like
16+
14+
12+

10+

Ionization Energy

n
tio
a
in
mb e
o
g
c
Re chan
n
e
tio
v
x
i
a
t
E
iz
dia rge
Ion
a
t
Ra
ac
Ch
mp
I
on
ctr
e
l
E

14+
13+

Escape

12+

8+
0

2+

4+

6+

Charge state

Neutral

Figure 2.3 Schematic showing the atomic processes of an argon gas in the EBIT.
scales with Z2eff /K where K is the incident electron kinetic energy and Zeff is the average of
the ion’s atomic number and charge state. The discussion in Ref. [37] shows a comparison
between the RR and the EI cross sections of various krypton charges for a 20 keV electron
beam. At low charge states (< 10+), the RR cross section is smaller than the EI cross
section by a factor of 105 . The RR process starts to dominate at Kr35+ where the RR
and EI cross sections are comparable. The total cross section of the CX process between
ions and residual gas can be calculated by the M¨
uller and Salzborn formula [41]. With a
pressure inside the EBIT of 10−11 Torr and 20 ms of charge breeding time, the probability
for the CX process to occur is < 0.02% and negligible [42].
In Ref. [38], the ion heating by the electron beam and the ion-ion energy exchange are
calculated for Kr34+ and Kr30+ , respectively. The heating requires about 1 ms for the
Kr34+ to reach the maximum confinement energy and causes the ion to escape from the
trap. The momentum exchange of ion-ion collision of Kr30+ also needs approximately 1 ms

18

to be Boltzmann distributed. Given these time scales, it is reasonable to exclude these two
interactions in ion capture simulations.
The EI process is the most important process to produce HCIs. It is simply explained
by removing an electron orbiting an ion with Z+ charge state by a high-energy electron
and the charge state of the ion changing to (Z + 1) +. The reaction can be written as

AZ+ + e → A(Z+1)+ + 2e.

(2.13)

The cross section of the reaction can be parametrized by W. Lotz’s semi-empirical formula
[43],
n
σEI (Ee ) =

aj q j
j=1

ln Ee /Ij
Ee Ij

1 − bi exp −cj Ee /Ij − 1

,

(2.14)

where aj , bj , cj are free parameters specific to each ion and charge state, Ij is the ionization
energy, qj is the number of electrons in the jth subshell, Ee is the electron energy, and n
is the number of subshells in the atom which meets the condition Ee > Ij . The maximum
cross section is approximately 2 - 3 times the ionization threshold energy. As an example,
for an electron beam energy of 1 keV, the cross section of K39 for 2+ to 3+ charge state
change is 3.2 × 10−17 cm2 . Figure 2.4 shows the EI cross section of a potassium ion as
a function of electron beam energy. In order to further ionize an ion, the electron beam
energy must be greater than the threshold energy of each charge state. The ionization
probability of the reaction is given by
t
− t EB
p = 1 − e 1→2 ,

19

(2.15)

2nd ionization

2

(m )

10

3rd ionization

8

EI Cross section x 10

-21

4th ionization
5th ionization

6

4

2

0.1

1

10

Electron beam energy (keV)

Figure 2.4 Electron impact ionization cross section of K+ as a function of electron beam
energy. The electron beam energy is required to be greater than the binding energy in order
to produce the EI process.
with tEB and t1→2 being the time required for an ion to spend inside the electron beam
and to be ionized from a 1+ to a 2+ charge state, respectively. The time t1→2 is related
to the EI cross section by
e
t1→2 =
,
je σEI

(2.16)

2 is the electron beam current density. The time scale of this process
where je = 0.8 Ie /πrh
is in a range of µs for an electron beam current density of 104 A/cm2 . The factor of 0.8
2 encloses 80% of the electron beam.
results from the Herrmann radius where πrh
For a number of ions in a charge state i, the EI process can be described by the rate
equation [37, 44],
dni
EI
EI
= ne νe σi−1→i
ni−1 − σi→i+1
ni
dt

20

(2.17)

where ne , νe are density and velocity of the electrons, ni−1 , ni , ni+1 are ion density in
state i − 1, i, i + 1, and σ EI is the cross section of the EI process for a given charge state.
The equation is valid when assuming the ions are inside the electron beam with a constant
electron beam current density. This rate equation will be used to benchmark the NEBIT
code (see Section 5.4.4) and to calculate the effective current density (see Section 6.4.2).

21

Chapter 3
The EBIT as a Charge Breeder
Optimizing an EBIT as a charge breeder for rare isotope beams requires additional features
than for standard physics applications. The injection process of singly charged ions, the
extraction of highly charged ions (HCIs), and the ion capture process are described in the
following as well as the physics of the ion beams.

3.1 Injection and extraction
A gas jet of neutral atoms or molecules can be injected into the EBIT through a radial
port pointing at the center of the trap electrodes. When the jet passes through the electron
beam, neutral particles are ionized and trapped by the space-charge potential created by
the electron beam. This method to load ions into the trap has been used during the
commissioning phase of the NSCL EBIT. To charge breed a rare isotope beam, the singly
charged ion beam is injected through the collector as mentioned in Section 2.1. There are
two methods in use for external injection: pulsed injection and continuous injection [45].
The pulsed injection concept is shown in Figure 3.1. A pulsed beam is injected into the
EBIT and confined by the outer barrier of the trap which has to be pulsed between the
injection and the extraction processes. In order to maximize the efficiency, the ion beam is
first bunched by a bunching device such as an RFQ buncher before being injected into the

22

1+

Potential

1+

Trapping

Trapping
Potential

Potential

Injection

1+

Outer barrier

(a)

(b)

(c)

Figure 3.1 Pulsed injection process. (a) An ion is injected into the trap, (b) the outer
barrier is raised up, and (c) the ion is confined inside the trapping region.
EBIT. The TITAN EBIT [46] and the REXEBIS [4] have successfully demonstrated the
charge breeding of rare isotope beams using the pulsed injection.
In the continuous injection mode, also known as the accumulation mode, an ion beam is
continuously injected into the trap. Figure 3.2 illustrates this concept. During the injection
process, both potential barriers are fixed. The continuous ion beam with an energy slightly
higher than the outer barrier is injected into the EBIT. Within a round-trip flight from
the outer barrier, the ion is trapped if it loses at least one additional electron. Otherwise,
it will leave the trap. The continuous injection has been demonstrated at REXEBIS and
the total efficiencies of different injected beams are reported in Ref. [42, 47]. The capture
efficiency of continuous injection is very dependent on the emittance of an injected ion
beam. Ions that have large emittance are likely to reflect off the barrier due to the radial
energy pickup because when crossing the magnetic field, the ions partially convert axial into
radial energy. For the NSCL EBIT, the continuous injection is employed to avoid adding a
bunching device which would limit the maximum beam intensity of the singly charged ions.
HCIs can be extracted from the EBIT with three possible methods: leaky, fast, and
pulsed extraction. The concept of each extraction scheme is depicted in Figure 3.3. For
the leaky extraction, also called slow extraction, the ions are continuously extracted from

23

1+

2+

Trapping
Potential

First Breeding
Potential

Potential

Injection

2+

Outer barrier

(a)

(b)

(c)

Figure 3.2 Continuous injection process. (a) An ion is injected with the energy slightly
above the outer barrier, (b) the ion experiences the higher barrier after being charge bred,
and (c) the ion is confined inside the trapping region.
the trap when they have enough axial energy to overcome the confinement barrier. The
HCIs can gain energy from the electron heating process and ion-ion collisions. This method
provides the extracted beam with a small energy spread.
By shaping the trap potential to a slope configuration, similar to Figure 3.3b, the HCIs
are extracted fast as a pulsed beam. This method is valid only if the trap comprises several
electrodes which provide flexibility to create different potential configurations. With a
quick extraction period, the cycle of the charge breeding process can begin in a short time
interval. However, the extracted beam tends to have large energy spread. By lowering the
outer barrier to let the HCIs leave the trap without shaping the trap potential, shown in
Figure 3.3c, the pulsed beam can be extracted with smaller energy spread. This method
has been used in the NSCL EBIT.

3.2 Ion capture
Before being charge bred into HCIs, the singly charged ions have to be captured successfully
by losing at least one addition electron via the electron impact ionization that leads to their
confinement in the EBIT. This ion capture process is directly related to the overlap of the

24

Potential

q+

Leaky extraction

Potential barrier

Potential

(a)

q+

q+

Pulsed extraction

Potential barrier

(c)
Figure 3.3 Three possible methods to extract HCIs from the EBIT: (a) leaky , (b) fast, and
(c) pulsed extraction.

25

Electron
beam

y

x
Ion
trajectory
(a)

(b)

(c)

Figure 3.4 Three possible ion trajectories in the trap. The ion trajectory is (a) completely
inside the electron beam, (b) partially inside the electron beam, and (c) totally outside the
electron beam.
injected ion beam and the electron beam. The overlap can be described by three scenarios:
full, partial overlap, and no overlap as shown in Figure 3.4. The full overlap occurs when
the ion beam trajectories are entirely inside the electron beam. In this case, the possibility
for the ions to lose one electron and then be trapped in the EBIT within a round-trip
flight is large. If the ion beam trajectories partially overlap with the electron beam due to
a high radial velocity or misalignment, the ions have less chance to lose one electron and
become trapped. In the worst case scenario that the ion trajectories are totally outside the
electron beam and the ions never interact with the electrons, the charge breeding process
will never take place. For a beam with small emittance, the best overlap can be achieved
by optimizing the beamline transport optics.
Alternatively, the overlap between the ion beam and the electron beam can be improved
by increasing the electron beam size. However, the better overlap has to be traded with
the lower electron beam current density and consequently longer charge breeding time, see
Eq. 2.16.

26

3.3 Trap capacity
The capacity of the trap is important to determine the number of HCIs stored in the EBIT
charge breeder. Depending on the electron beam current I, the trap size L, and the electron
beam energy Ue in unit of eV, or velocity ve , the trap capacity is given by

Trap capacity =

ρl Ltrap
e

=

I × Ltrap
I × Ltrap
=
eve
e 2 mee Ue

(3.1)

where ρl is linear charge density equivalent to I/ve , and e and me are electronic charge
and mass, respectively. For a 135 mA and 19.5 keV electron beam and 0.6 m trap size, the
trap capacity of singly charged ions is 6.5 × 109 ions.
Not only does a larger trap size provide a greater number of stored ions, but it also
extends the time the singly charged ions spend inside the trap. As shown in Eq. 2.15, the
longer the interaction time, the higher the ionization probability will be.

3.4 Beam dynamics
3.4.1 Beam emittance
The quality of a charged beam can be quantified by “emittance,” an area occupied by the
beam in six-dimensional phase space: two in longitudinal and four in transverse directions.
The longitudinal emittance which well describes the quality of a pulsed beam is defined
by the phase difference ∆φ and the energy spread ∆W . Without an optical element that
couples between the longitudinal and transverse motions, the longitudinal emittance can be

27

considered separately from the transverse emittance. More details about the longitudinal
emittance can be found in Refs. [48, 49].
The transverse emittance of a beam is determined by two transverse coordinates (x, y)
and two angles (x = vx /vz , y = vy /vz ) of the ions. If the beam transport system does
not couple horizontal and vertical motions, the phase spaces of x − x and y − y can be
considered separately and are equivalent for a system with axial symmetry. The emittance
of the beam is constant, if the number of the particles is constant and there are no dissipative
forces involved such as radiation.
From the statistical point of view the r.m.s. emittance ( rms ) can be obtained from
an ellipse in the phase space (x, x ), illustrated in Figure 3.5, which is defined by Twiss
parameters: αrms , βrms , and γrms [50]. The ellipse equation containing ions in phase space
is given by
γrms x2 + 2αrms xx + βrms x = rms ,

(3.2)

2
x2 x 2 − xx . The Twiss parameters are

2
where γrms βrms − αrms
= 1 and rms =

calculated from the second-moment of the particle distribution,

βrms =

x2
rms

,

γrms =

x2
rms

,

αrms = −

xx
rms

.

(3.3)

3.4.2 Effective ellipse transformation
Eq. 3.2 can alternatively be written in a matrix form by

X T σX =

28

(3.4)

x'
x'rms = εrms γrms

Slope = -

αrms
βrms

xrms = εrms βrms

x

Figure 3.5 The r.m.s. ellipse in the phase space.








 x  T
 γ α 
where X = 
 , X = x x , and σ −1 = 
 is an inverse beam matrix.
x
α β
Due to the invariance of the emittance, the transformation of the beam matrix between
two locations is

σ1 = R σ0 RT

(3.5)

where R is a 2×2 transfer matrix that describes how the particle is transported. Considering
an ion with x and x travels through a drift region, the linear transformation of the ion’s

29

position and angle is given by










 x1   1 L   x0 

=

,
x1
0 1
x0

(3.6)

where L is a drift length. The angle remains unchanged, x1 = x0 while the coordinate
is dependent on the drift length by x1 = 1 + x0 L. For a complicated system comprising
several optical elements, the transfer matrix is simply calculated by the multiplication of
transfer matrix of each element, R = R1 R2 ...Rn , and the beam property is transformed by






2
R11

2
R12

−2R11 R12
 β1  

 

 
 α1  =  −R11 R21 1 + 2R12 R21 −R12 R22

 

 
2
2
R21
−2R21 R22
R22
γ1





  β0 




  α0  .




γ0

(3.7)

The above transformation is useful to determine the emittance of the beam. For the
quadrupole emittance scan method, discussed more details in Section 6.1, the r.m.s. beam
size (

rms β1 ) is directly measured. With known transfer matrix elements R11 and R12

that describe the quadrupole strength, the emittance is obtained by fitting the square of
the r.m.s. beam size to the quadrupole strength with the following formula,

2
2
rms β1 = rms β0 R11 − 2α0 R11 R12 + γ0 R12
2 − C R R + C R2
x2 = C1 R11
2 11 12
3 12

30

(3.8)

where C1 , C2 , and C3 are constant and given by

C1 = rms β0
C2 = 2 rms α0
2 +(
2
rms α0 )
C3 = rms
.
rms β0

3.4.3 Geometrical acceptance
Similar to the emittance, the acceptance depicts an area in phase space to represent the
ability to accept the injected beam. The acceptance contains information on the beam size
and orientation for proper focusing. The acceptance which depends on the electron beam
current and energy, the magnetic field, and the extraction voltages, is called a geometrical
acceptance. The geometrical acceptance defines the phase space of the ion beam that fits
inside the electron beam in the EBIT. The geometrical acceptance α, used to test the
NEBIT code in Chapter , is analytically given by [42]

α=π

re
Bre
2Uext

q
+
m


2
2
ρ
qB re
+ l ,
4m
2π 0

(3.9)

where re is the electron beam radius, Uext is the injection potential, q is the ion charge, m is
the ion mass, B is the magnetic field that compresses the electron beam, and ρl = I/ve is the
linear charge density. With NSCL EBIT design parameters of a 2.5 A and 30 keV electron
beam, a 6 T magnetic field, 0.8 m trap size, and for a 60 keV injected potassium beam,
the geometrical acceptance is 6.8 π mm·mrad. In other words, a 100% capture efficiency is
expected for an injected beam of up to 6.8 π mm·mrad if the EBIT can limitlessly accept

31

Figure 3.6 Capture probability calculated from the overlapped area in the phase space
between emittance and acceptance.
the beam.
By considering together the emittance and the acceptance, the overlap of both areas in
the phase space displayed in Figure 3.6 is interpreted as the probability that the ion will
be captured by the electron beam. The probability is maximized if the ion beam emittance
completely overlaps with the acceptance of the EBIT.

32

Chapter 4
The NSCL EBIT Charge Breeder
This chapter describes the experimental setup. Figure 4.1 gives an overview of the EBIT
charge breeder including its test ion source and the Q/A separator. Electrostatic optical
elements are installed at several locations to guide the ion beams along the beamline.
Diagnostic tools, including microchannel plates (MCPs) and Faraday cups, are mounted at
different Beam Observation Boxes (BOBs) to monitor the ion beam currents and shapes.
Section 4.1 describes the main components of the EBIT. A description of the ion source
used for the EBIT commissioning can be found in Section 4.2. Sections 4.3 and 4.4 contain
information on the Q/A separator and diagnostic devices, respectively. Details of the
beamline transport optical elements are presented in Section 4.5.

4.1 NSCL electron beam ion trap characteristics
The NSCL EBIT was built in collaboration with MPIK in Heidelberg and TRIUMF. Starting from the design of the TITAN EBIT [51], a number of changes were implemented
to fulfill the requirements of the rare isotope reaccelerator. The electron gun design was
modified to provide a higher electron beam current. By adding together the EBIT and
EBIS characteristics, the magnet design was changed to a combination of a solenoid and
Helmholtz coils [52]. Table 4.1 lists requirements and design parameters for the NSCL

33

Beam Observation
Box 1 (BOB 1)

Figure 4.1 Overview of the NSCL EBIT charge breeder.
EBIT. The breeding time is estimated to be of the same order as the time used in the gas
stopping process [53]. The total efficiency expected is based on the efficiency REXEBIS
[54] reached at the time that the ReA project was initiated. A large number of stored
charges is required in order to support the high intensity beams needed for the future FRIB
operation. To attain these requirements, the NSCL EBIT was constructed according to the
listed design parameters. For fast charge breeding, the NSCL EBIT aims to reach up to
104 A/cm2 which requires a high magnetic field of 6 T and a high electron beam current
of 2.5 A. An electron beam energy of up to 30 keV is sufficient to charge breed uranium
into the neon-like charge state. The long trap length increases the number of ions that can
be stored and the total efficiency.

34

Requirements
Design parameters
Breeding time
< 50 ms
Electron beam energy
< 30 keV
Total efficiency
20 - 50 %
Electron beam current
< 2.5 A
10
Stored positive charges 10 charges Length of trapping region
0.8 m
Magnetic field
6T
4
Electron beam current density < 10 A/cm2
Table 4.1 NSCL EBIT requirements and parameters. The choices for the design parameters
to satisfy the performance requirements are described in more details in the text.

4.1.1 Electron gun and collector
The electron gun consists of a Pierce-type cathode, an anode, and a focusing electrode.
Using a plug-in design, the electron gun core with a cathode of 6.35 mm in diameter can
be easily replaced by one with a cathode of 12.7 mm in diameter. The small and the
large cathodes were designed to provide up to 1.4 A and 2.5 A of electron beam current,
respectively. The drawing and the picture of the assembled electron gun head is depicted
in Figure 4.2(a, b). Since the compression of the electron beam inside the trap is influenced
by the magnetic field Bc at the cathode (see Eq. 2.2), the compression is maximized if
Bc vanishes. Therefore, the fringe field from the superconducting magnet is reduced by
a soft iron shield with a thickness of 15 mm and canceled by a magnetic field created by
bucking coils inside the iron shield. The coil outside the shield improves the electron beam
transport into the fringe field region. By applying 1 A of current, the set of three coils and
the front coil produce 60 G at the cathode and up to 120 G at the transition region from
the electron gun to the EBIT trapping region.
After passing the trapping electrodes, the electron beam is absorbed by the collector.
Figure 4.2(c, d) shows a drawing and photos of the collector electrode, and its full assembly. The magnetic field inside the collector is reduced by the magnetic field from the coil

35

Front coil

Bucking coils
Focus

Anode
Cathode

Soft iron
Soft
iron

(a)

(b)

Coil
Coil

Extractor
Extractor

e-beam

Suppressor
Suppressor

Ions

(c)

(d)

Figure 4.2 Side view cross sections of the electron gun (a) and the collector drawings (c)
and the electron gun (b) and the collector assemblies (d).

36

Sapphire
insulator

Trap
electrode

Segmented electrode

Segmented
electrode

Slit
Figure 4.3 Trap electrode structure for the NSCL EBIT.
surrounding the collector electrode. Secondary electrons from the collision between the
electron beam and the collector surface are suppressed by the suppressor electrode while
the extractor electrode prevents electrons from traveling into the main beamline.

4.1.2 Trap electrode structure
As shown in Figure 4.3, the trap structure of the NSCL-EBIT consists of 25 electrodes.
The electrodes are made of titanium because it is non-magnetic and has a low thermal
conductivity. The trap size is 0.8 m in length and the overall trap, including support

37

structure, is around 1 m long. The sapphire insulators that are located between trap
electrodes (not seen in the picture) and at both ends are used as 4 K thermal link to the
trap structure. Segmented electrodes at the trap center allow radial access, for example,
injecting a gas jet and x-ray spectroscopy. A small slit attached to the electrodes can be
used for imaging the electron beam with an x-ray CCD camera.

4.1.3 Hybrid superconducting magnet
Figure 4.4 shows the complete assembly of the superconducting magnet, the electron gun,
the collector, and the test ion source (a) and a section view(b). The section view displays
the position of two different types of magnets: the Helmholtz coils and the solenoid. The
Helmholtz coils generate a strong magnetic field in a small trapping region to shorten charge
breeding time due to the high electron beam compression. The solenoid is not only designed
for a large trapping region and storage capacity but also to provide a large acceptance for
the EBIT. Since the magnets can independently produce magnetic fields up to 6 T, the
EBIT can be operated with different magnetic field configurations and electron beam radii.
The study of the capture probability independence of the different field configurations can
be found in Chapter 5.5. Two “bucking” coils at both ends of the magnet support the
electron beam transport from the electron gun to the collector.

4.2 Test ion source
For EBIT commissioning and off-line experiments, a test ion source is available. It is
mounted about 2 m away from the EBIT on an independent beamline. A hot cathode
ion source (Colutron model 100-Q) is used to provide a K+ beam [55]. When a tungsten
38

(a)

(b)
Figure 4.4 NSCL EBIT with the test ion source (a) and a side view cross section showing
the combination of a solenoid and Helmholtz coils (b).

39

Extraction
Electrical
connection

Ceramic
insulator

Filament

Filament

Anode
Quartz glass

Focusing electrode

Figure 4.5 A hot cathode ion source (left) and a schematic corresponding to each component.
filament is heated, it ejects potassium ions through a surface ionization process [56]. Figure
4.5 displays the off-line ion source and its schematic. During the experiment, it was biased
to 20 kV for producing a 20 keV ion beam. The used filament with a 20 mil diameter which
was supplied with a voltage of 10.5 V and a 16 A current provided up to 2 nA during the
tests. The anode was set to zero and the extraction was set at -5 kV.

4.3 Achromatic Q/A separator
The achromatic Q/A separator is designed to analyze and separate HCIs extracted from
the EBIT. The Q/A acceptance of the separator is between 0.2 and 1 for a 12 keV/u ion
beam energy. Within this range, it is enough to cover all isotopes available at the NSCL and
FRIB. The separator mainly consists of two 45◦ electrostatic benders and a bending magnet
as shown in Figure 4.6. Between the second electrostatic bender and the bending magnet,
an adjustable horizontal slit is mounted to be able to cut the energy spread of the beam if
desired. The energy dispersion calculated by first order optics is (x, δE ) = 10 mm/%. The
calculated acceptance for the 12 keV/u ion beam is up to 120 π mm·mrad equivalent to a
normalized emittance of 0.6 π mm·mrad [57].

40

Electrostatic
benders

Bending
magnet

Beam

Figure 4.6 The Q/A separator consisting of two electrostatic benders and a bending magnet. The yellow arrow displays the direction of the beam extracted from the EBIT and
transported to the linear accelerator.

4.4 Diagnostic devices
Based on the requirements to monitor the beam current in the range from 10 fA to 1 nA,
to observe the beam image, and to measure the time-of-flight (TOF) of the ion beam,
microchannel plates (MCPs) and Faraday cups (FCs) were chosen.
The MCP is a device used to detect charged particles and image the beam. It can also
be used to measure a TOF signal when connected to an oscilloscope. Figure 4.7 displays the
MCP mounted along the ReA beamline. The Faraday cup (FC) is a device that measures
the beam current of charged particles in a vacuum system. It contains a measuring cup
and an electron suppressor ring. In order to measure the beam current, the cup is inserted
to obstruct the beam. A negative voltage is supplied to the suppressor electrode to prevent
the escape of secondary electrons from the cup. By connecting the FC to Keithley high
resolution ammeter [58], it is possible to precisely detect the ion beam to a range of 10 fA.
41

Mirror

MCP front
Figure 4.7 A picture of a microchannel plate installed in the ReA beamline.

4.5 Beamline transport optics
Along the beamline, several optical elements are installed to control the ion beams. Several
electrostatic quadrupoles are used for ion transportation. For the NSCL EBIT charge
breeder, two Einzel lenses are used: one next to the extraction electrode inside the ion
source chamber and another inside the acceleration/deceleration column. A transfer lens
is located between the electron collector and the trap entrance in order to focus the ion
beam into the EBIT trapping region and help transport the electron beam to the collector.
To correct the ion beam trajectory along the beamline, electrostatic steerers are employed.
Figure 4.8 illustrates the quadrupole triplet and steerer electrodes, the fully assembled
acceleration/deceleration column, and the transfer lens.

42

Electrical
feedthrough
Electrodes

(a)
Acceleration/
deceleration
electrode

Lens holder

Ceramic

Einzel
lens

Transfer lens

(c)

(d)

Figure 4.8 Drawing of a quadrupole triplet (a) and a steerer element (b), the transfer lens
(c), and the fully assembled acceleration column consisting of an acceleration/deceleration
electrode and an Einzel lens (d).

43

Chapter 5
Simulation of Ion Injection and
Acceptance
Extensive simulations have been performed with the SIMION and “NEBIT” packages. Details of both will be discussed in the following sections. Section 5.1 explains the calculation
of the electric and magnetic fields that are used in the simulations. Section 5.2 reports
ion trajectory simulations that have been studied with SIMION to provide the optimum
voltage settings for ion beam transport. Section 5.3 describes an in-house simulation code
used to study capture efficiencies, called NEBIT. Results of NEBIT comparisons with a) an
analytical formula, b) prediction by the Charge Breeding SIMulation (CBSIM) code, and
c) an earlier version of NEBIT can be found in Section 5.4. Examples of capture efficiency
simulations are discussed in Section 5.5.

5.1 Calculation of electric and magnetic fields
The electric field used in both simulations has been obtained by solving the Laplace equation
for the entire EBIT electrostatic electrode system with SIMION. SIMION is a simulation
package which calculates the electric field and trajectories of charged particles for a given
configuration of electrodes [59]. Based on the design drawing of the EBIT a SIMION

44

electrode system, “workbench,” was created in SIMION that includes a ground electrode,
an acceleration/deceleration column, a collector, a transfer lens, and trap electrodes as
depicted in Figure 5.1a. The instance starts at the location equivalent to the center of the
BOB 1, see Figure 4.1. To avoid a large file size, the SIMION workbench is divided into
two instances: a collector part and a trap part. The collector part starts at the ground
electrode and extends to the center of the transfer lens and the other half includes all trap
electrodes. After assigning voltages to the electrodes, the potential distribution and the
electric field are calculated. Figures 5.1b and 5.1c illustrate the potential and electric field
maps when the electrodes are set for the injection of a 60 keV ion beam. The electric field
is highest at the transition between the ground electrode and the high voltage platform.
For the acceptance simulation, the electric field map files from SIMION are imported into
the NEBIT code.
The NSCL EBIT consists of five groups of magnets: a solenoid, a pair of Helmholtz
coils, two bucking coils, and a collector coil [60]. The magnetic field used in both SIMION
and NEBIT is obtained from an analytical solution for the superposition of the magnetic
fields calculated for each magnet. With the approximation at small radii, the axial magnetic
field component is equivalent to the on-axis one and the radial magnetic field component
is proportional to the derivative of the on-axis magnetic field component. Unless specified
otherwise, the magnetic field configuration used in the simulation are 1T (solenoid) -6T
(Helmholtz coils) and 6T-6T. These magnetic field distributions are illustrated in Figure
5.2. The magnetic field of 1 Tesla is arbitrarily selected to provide a large electron beam size
and 6 Tesla is the highest field strength the NSCL-EBIT can produce. The sketch on top
of the figure indicates the position of each coil. At the center of the collector, the magnetic

45

Ground
electrode

Acceleration
column

Collector Transfer
lens

Trap electrodes

10 mm

10 mm
5kV

45kV 46kV

52kV 54kV

59kV

(a)

60kV 59kV

(b)
50 V/mm
100 V/mm
200 V/mm
300 V/mm
400 V/mm
500 V/mm
600 V/mm

(c)

Figure 5.1 EBIT workbench in SIMION containing a ground electrode, an acceleration/deceleration column, a collector, a transfer lens, and trap electrodes (a), potential
(b) and electric field map (c) solved by SIMION.

46

Collector side
Electron gun side
bucking coil Solenoid Helmholtz
bucking coil
colis
Collector
coil

7

Axial magnetic field (T)

6

1T-6T configuration
6T-6T configuration

5
4
3
2
1
0
0.0

0.5

1.0

1.5

2.0

2.5

Axial coordinate (m)
Figure 5.2 Magnetic field distribution of 1T-6T (black) and 6T-6T (red) used throughout
the calculations. The trap center is at z = 2.12 m.
field is minimized by the field from the collector coil. For the ion trajectory simulations
within SIMION, the magnetic field is separately calculated and saved as a file which can be
imported by SIMION. In NEBIT, the magnetic field is calculated from a routine describing
a superposition of thin coils.

5.2 Ion trajectory simulation by SIMION
SIMION was used to simulate the ion trajectories to understand the ion beam’s behavior.
It provided optimum voltage settings for minimizing the ions’ radial energy pickup. The
larger the radial energy, the less the ions overlap with the electron beam.
47

To simulate the ion trajectories a singly charged ion beam of 60 keV and 10 π mm·mrad
was used. The beam started at the beginning of the ground electrode and traveled toward
the trap. Assuming that the electrons are uniformly distributed over the electron beam
cross section, the space-charge potential, Eq. 2.3, was calculated and added into SIMION
via a user program.
Illustrated in Figure 5.3, the ion beam trajectories in the 1 T and 6 T magnetic fields
are compared without (a, c) and with (b, d) the 2 A and 12.5 keV electron beam. The
location of the outer barrier is indicated in Figure 5.3a. Without the electron beam, the ion
beams are focused by electric and magnetic fields at the trap entrance and a helical motion
is observed which results from existence of the high magnetic field. The ions are retarded
at the outer barrier and pick up radial energy when crossing magnetic field line. Without
proper injection, most of the ions having high radial energy tend to hit the surrounding
electrodes at this location. The ions traveling into the 6 T magnetic field have higher
cyclotron frequency than those of the 1 T magnetic field. When the electron beam is
switched on, the ion beam radius becomes smaller due to the radial space-charge field. The
effect of space-charge to the ion trajectories starts when the ions pass the collector.
Figure 5.4 displays a contour plot for the initial phase space of the radial energy that
the ions gain during the transport into the EBIT. The results were recorded at the location
where the magnetic field is produced mainly by the solenoid. The ions flying into the 1 T
magnetic field gain less energy than those into the 6 T magnetic field. Ions injected with
small transverse velocity or off-axis distance gain less radial energy than those with large
transverse velocity or off-axis distance. The highest radial energy that the ions in a beam
with 15 π mm·mrad emittance can gain are 9 and 90 eV for the 1 T and the 6 T magnetic

48

1 T without electron beam
Ion beam

Outer
barrier

(a)

1 T with 2 A electron beam
Ion beam

(b)
6 T without electron beam
Ion beam

(c)
6 T with 2 A electron beam
Ion beam

(d)
Figure 5.3 Comparison of ion trajectories in the 1 T magnetic field without (a) and with
a 2 A electron beam (b) and the 6 T magnetic field without (c) and with a 2 A electron
beam (d). A 60 keV beam of injected ions and an electron beam energy of 12.5 keV were
used.
49

9 eV

90 eV

0

0

(a)

(b)

Figure 5.4 Contour plot of radial energy that the ions gain while traveling into the 1 T (a)
and the 6 T (b) magnetic fields. The radial energy is plotted as a function of the initial
phase space.
fields, respectively. The contour plot also indicates the proper orientation of the injected
ion beam in the phase space.
It was found from the simulation that the beam focusing is most sensitive to the changes
of voltages at the acceleration/deceleration electrode and the Einzel lens rather than the
transfer lens. The optimization of a voltage setting was achieved by adjusting the voltage
applied to each electrode and tracking the ion beam radius inside the trapping region. The
number of ions lost to the electrode had to be minimized.

5.3 NSCL EBIT simulation code
The NSCL EBIT simulation code (NEBIT) was originally created by E. Gavartin [61], based
on the “IonCool” package [62], to calculate the NSCL EBIT’s acceptance and capture efficiency. The acceptance was evaluated based on an EBIT geometry primarily consisting of
the collector, barriers, and trap electrodes. The magnet structures providing two different
50

Feature
Electric potential
Space charge potential
Electrode structure
Monte-Carlo approach

Earlier NEBIT
Current NEBIT
Linear approximation Solving Laplace equation by SIMION
No energy correction
With energy correction
Simple structure
Real design structure
EI process
EI process, initial sample selection

Table 5.1 Comparison of features used in the earlier and the current versions of NEBIT.
magnetic field configurations were determined based on the EBIT geometry. The potential
was defined by voltages applied to electrodes and linearly interpolated at the drift space.
The radial electric field from electrodes was neglected. The space-charge was simply calculated from Eq. 2.3 and the electric field was calculated by the two-point backward-difference
formula [39].
During this thesis work, NEBIT was developed further by using the detailed NSCL EBIT
geometry which also contains the ground electrode, the acceleration/deceleration electrode,
the Einzel lens, and the transfer lens, see Figure 5.1. The magnetic field distribution is
calculated based on the existing magnet design. The potential and electric field are obtained
by solving the Laplace equation with SIMION and all electric field components are taken
into account. The space-charge potential is calculated using the corrected electron beam
energy by implementing Eq. 2.8. A Monte-Carlo approach is used to determine the EBIT
acceptance and the ionization probability for the EI process. Table 5.1 summarizes main
features used in the earlier and the improved versions of NEBIT. The details of the current
version of NEBIT are described in the following.
The simulation algorithm describing how NEBIT calculates the acceptance of the EBIT
is shown in Figure 5.5. EBIT parameters and configurations containing an electric field, a
magnetic field, and space-charge potential are set at the beginning. Monte-Carlo sampling
is performed within the given phase space at first and the ion beam properties of mass,

51

Define number of samples, Nr,
and the boundary in x, y, x', and y'
Randomly pick the sample (xini, yini, x'ini, y'ini) within the boundary
Convert xini, yini, x'ini, y'ini to rini, phiini, vrini, vphiini
Calculate the ion trajectory with Runge-Kutta integrator
Yes

rion < relectron
No

Generate
rrandom

Calculate cross
section and Pionization
Do ionization

Yes

rrandom < Pionization
No

rion > rdrift tube

Yes

Wall

Stopped

Ionturn++

zion > ztrap
No

No
Ion turns

Yes

No
zion < zbarrier

Yes

Yes

Ionturn = 1

Yes

Pass barrier

Stopped

No

No
Ionturn = 2 and Ne > 1

Yes

Trapped

Record rini, phiini, vrini, vphiini

No
Ne >2

Yes

Trapped

No
Pass barrier

Yes

zion < zbarrier

Lost

Stopped

No
Ionturn = 1

Yes

Stopped

Reflected

No
No

Do ionization
Yes
Ne++

Figure 5.5 Flowchart showing the algorithm of the acceptance calculation.

52

x' (mrad)

x (mm)

Figure 5.6 Concept of simulated capture efficiency. The ratio of the number of the trapped
to the injected ions in the same phase space area is interpreted as a capture probability.
The ellipse is aligned along the line from the linear fit (red solid line).
atomic number, and axial energy are initially established. A Runge-Kutta integrator [63] is
used to calculate the ion trajectories since it well solves the ordinary differential equations
of motion. Ionization process is considered if the trajectory is inside the electron beam.
The ions are trapped if they change direction twice and the charge state is greater than
1+ or the charge state turns to 3+ at any location in the trap. The NEBIT output are
the initial positions and angles of the trapped ions and this collection forms the acceptance
phase space of the EBIT. A single ion calculation stops if the trajectory ends up at an
electrode or if the ion leaves the trap.
To acquire the capture efficiency as a function of beam emittance, a separate code is
used. The code initially loads the beam parameters and the acceptance phase space which
is outputted from NEBIT. The acceptance phase space (x − x and y − y ) is fitted with

53

linear and elliptic equations to provide an ellipse orientation and Twiss parameters (α, β, γ).
The capture efficiency is computed from the overlap in phase space of the beam emittance
and the acceptance of the EBIT. The concept of capture efficiency is illustrated in Figure
5.6. With the total number of ions N which are sampled in the defined phase space area,
s = x · x , a number of particles per unit phase space area N/s is calculated. A capture
efficiency cap is given by
cap =

ni
i · N/s

(5.1)

where ni is the number of particles inside the ellipse corresponding to emittance i . By
varying the beam emittance and keep Twiss parameters to be the same, the capture efficiency is obtained as a function of the injected beam emittance. The statistical error of the
√
capture efficiency is calculated from the relative uncertainty, 1/ ni .

5.4 NSCL EBIT code benchmarking
It is crucial to ensure that the simulation code works correctly and provides results consistent with those from other reliable software. In order to benchmark the code, the following
test and comparisons were performed:
1. Test of energy conservation along the ion trajectory
2. Comparison of geometrical acceptance from NEBIT and an analytical formula
3. Comparison of capture efficiency from NEBIT and an analytical formula
4. Comparison of charge evolution from NEBIT and CBSIM
5. Comparison of capture efficiency between current and earlier versions
54

Parameter
Atomic number
Atomic mass (amu)
Electron beam energy (keV)
Electron current (A)
Axial energy (keV)
Cathode radius (mm)
Magnetic field at cathode (G)
Cathode temperature (K)

Value
26
56
12.5
1, 2.5
60
3.175, 6.35
10
1400

Table 5.2 EBIT and ion beam parameters used in SIMION and NEBIT unless otherwise
specified.

5.4.1 Test of energy conservation along the ion trajectory
It is important that the NEBIT code handles forces correctly. Total energy conservation
is calculated to provide a test of numerical issues. The potential energy is obtained from
SIMION and the kinetic energy are numerically calculated. Computed from the spacecharge potential with energy correction, the complex formula for the electric field comprises
several terms which possibly cause mistakes during the code construction. By checking the
conservation of the total energy, it is helpful to find out whether the implementation of
space-charge is correct or not.
The settings for the calculation can be found in Table B.1 of the appendix. The trap
potential is extended up to the TE4 electrode, see Figure B.1. The EBIT and ion beam
parameters are obtained from Table 5.2. The cathode radii for the electron beam current of
1 A and 2.5 A are 3.175 mm and 6.35 mm, respectively. An ion with 60 keV is injected both
on- and off-axes. The off-axis calculation helps investigate how much the radial component
contributes to the total energy.
Figure 5.7 illustrates the error of the total energy for on- and off-axis calculations (a) and
the potential, kinetic, and total energy (b). For the off-axis calculations with 1 A and 2.5 A
55

Error of

total energy (eV)

1.2
1.0
0.8
0.6

Off-axis

0.2

On-axis

0.0

Total energy

60

Energy (keV)

(a)

0.4

Potential energy

50
40
30

(b)

20
10

Kinetic energy

0
0.0

0.5

1.0

1.5

2.0

2.5

z (m)

Figure 5.7 The error of the total energy from on- (black) and off-axis (red) injections (a) and
kinetic, potential, and total energy (b). The ion is injected with an offset of x = 2.31 mm,
y = 0.12 mm, ax = −31.39 mrad, ay = −2.62 mrad.
electron beam currents, the initial positions and angles in the phase space of horizontal and
vertical axes are shown in Figure 5.8. A test ion with extreme initial conditions is chosen
where numerical errors can contribute most. The maximum errors of the calculated from
the initial total energy are shown in Table 5.3. We can see that the error increases with the
electron beam current and the maximum error is independent of the position in the phase
space where the ion is injected. Even though, the error in Figure 5.9 is 25 eV for 2.5 A
electron beam current, the relative error when compared to space-charge potential is less
than 1%.
It is obviously shown that the error starts to appear after ion passes the collector and
results from integrated numerical error during the calculation of axial space-charge electric
field. Within this range of the negligible errors of the total energy, the calculation performed
56

30

20

20

x', y' (mrad)

x', y' (mrad)

30

10
0
-10

10
0
-10

-20

-20

-30

-30
-2

-1

0

1

2

3

-3

-2

x, y (mm)
(a)

-1

0

1

2

3

x, y (mm)
(b)

Figure 5.8 Acceptance phase space in x direction calculated for 1 A (a) and 2.5 A (b)
electron beam currents and a 1T-6T magnetic field configuration. The initial position and
angle in x (red) and y (green) directions are given in circles.
Calculation
on-axis
off-axis

Error (eV)
Ie = 1 A Ie = 2.5 A
1.1
25
1.3
24

Table 5.3 Maximum errors of the total energy. The calculations were performed with the
electron beam currents of 1 A and 2.5 A and the test ion was injected both on- and off-axes.
by NEBIT shows the behavior of conservation of energy. It confirms that the code is good
enough for the acceptance calculation.

5.4.2 Comparison of geometrical acceptance from NEBIT and an analytical
formula
The geometrical acceptance, Eq. 3.9, determines the maximum emittance of an ion beam
that can be filled into the electron beam. With the real NSCL EBIT structure, the geometrical acceptance calculated by NEBIT is compared against the predicted value from

57

Error of total energy (eV)

25

onaxis
offaxis

20

15

10

5

0
0.0

0.5

1.0

1.5

2.0

2.5

Axial coordinate (m)

Figure 5.9 The error of total energy calculated from on- (black) and off-axis (red) ion
injections with the electron beam current of 2.5 A.

58

Parameter
Atomic number
Atomic mass (amu)
Monte-Carlo sample
Kinetic energy (keV)
Electron energy (keV)
Electron current (A)
Cathode radius (mm)
Magnetic field at cathode (G)
Cathode temperature (K)
(a)

0.1 A
1.0 A

Parameters
1T-6T (1T)
xmin , xmax (mm)
-0.35, 0.35
xmin , xmax (mrad)
-8.5, 8.5
xmin , xmax (mm)
-0.7, 0.7
xmin , xmax (mrad)
-20, 20
(b)

Value
26
56
200,000
60
12.5
0.1, 1
3.175
10
1400

1T-6T (6T)
-0.25, 0.25
-5.5, 5.5
-0.4, 0.4
-12, 12

6T-6T
-0.3, 0.3
-6, 6
-0.4, 0.4
-11.5, 11.5

Table 5.4 Beam and EBIT parameters for the NEBIT calculations (a) and sample phase
space of 0.1 A and 1 A electron beam currents for 1 T and 6 T regions of the 1T-6T magnetic
field configuration and the 6T-6T configuration (b). The number in the parenthesis indicates
the region of the magnetic field used for the evaluation of the acceptance.
the analytical formula. The 1T-6T magnetic field configuration is divided into two regions
of constant magnetic field. An injected ion is considered to be trapped if its trajectory
is completely inside the electron beam. On the other hand, the injected ion is lost if the
radius of its trajectory is larger than the drift tube radius, the ion returns, or the axial
coordinate of the ion travels beyond the 1 T or 6 T region.
The voltages applied to each electrode can be found in Table B.2. Once the electron
beam current changes from 0.1 A to 1.0 A, the voltage setting has to be re-optimized to
accommodate the beam into the trap, especially at the trap entrance. The EBIT and the
beam parameters used in these calculations are listed in Table 5.4.
Figure 5.10 shows the acceptance phase space calculated from the NEBIT code using

59

Electron beam
current (A)
0.1

1.0

Magnetic field
configuration
1T-6T
1T-6T
6T-6T
1T-6T
1T-6T
6T-6T

Interested Acceptance ( π mm·mrad) Deviation
region
NEBIT
Geometrical
(%)
1T
1.48
1.57
-5.7
6T
0.66
0.72
-8.3
0.65
0.72
-9.7
1T
5.45
5.33
2.2
6T
2.14
2.21
-3.6
2.20
2.22
-0.9

Table 5.5 Comparison of geometrical acceptance calculated with the analytical formula and
NEBIT.
electron beam currents of 0.1 A (a, b, c) and 1 A (d, e, f), respectively. The red ellipses
represent the calculated acceptance from the NEBIT code. The rotations of the acceptance
phase space show the injected beam characteristics whose trajectories are entirely inside the
electron beam. The acceptance indicated by areas within the red ellipses are compared with
the predicted values and shown in Table 5.5. From the table we can see that the largest
deviation is -9.7 % from the calculation of 0.1 A electron beam current at 6 T region of the
1T-6T configuration. Overall, a good agreement between the two methods is observed.

5.4.3 Comparison of capture efficiency calculated with NEBIT and an analytical formula
Combining the geometrical acceptance α from Eq. 3.9 with the ionization probability from
Eq. 2.15, one can estimate the capture probability of the EBIT. The cross section of going
from a 1+ to a 2+ charge state is obtained from Lotz’s semi-empirical formula with the
given element, see Section 2.4. To acquire the ionization probability, the time the ion spends
inside the electron beam is computed from the ion mean energy in the trap and the trap

60

1T-6T (6T region)
15

10

10

10

5
0
-5

x' (mrad)

15

5
0
-5

5
0
-5

-10

-10

-10

-15
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
x (mm)

-15

-15

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
x (mm)

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
x (mm)

(a)

(b)

(c)

15

15

10

10

10

5

5

5

0
-5

x' (mrad)

15

x' (mrad)

x' (mrad)

6T-6T

15

x' (mrad)

x' (mrad)

1T-6T (1T region)

0
-5

0
-5

-10

-10

-10

-15
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
x (mm)

-15

-15

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
x (mm)

(d)

(e)

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
x (mm)

(f)

Figure 5.10 The acceptance phase space determined in the 1 T region (a, d) and the 6 T
region (b, e) of the 1T-6T magnetic field configuration and the 6T-6T configuration (c, f)
with 0.1 A (a, b, c) and 1 A (d, e, f) electron beam currents.

61

Input parameters
Electron beam current
Magnetic field
Electron beam energy
Trap length
Ion mean energy in trap
Ion extraction energy
Atomic mass

Value
1
6
12.5
0.75
1
60
56

Unit
A
T
keV
m
keV
keV
amu

Output parameters

Value

Unit

Electron beam current density
Time required for 1+ → 2+
EI cross section
Ion mean velocity
Ion-electron overlap time
Ionization probability
Geometrical acceptance

1.46 × 104
1 × 10−6
1 × 1017
8.3 × 104
9 × 10−6
1
2.34

A/cm2
s
cm2
m/s
s
π mm·mrad

Table 5.6 List of input (top) and output parameters, and geometrical acceptance (bottom).

length. The capture efficiency cap is given by




 Emittance
× Ionization probability (%) Emittance > α
α
=
cap



Ionization probability (%)
Emittance < α.

(5.2)

Table 5.6 shows the input and output parameters, and the calculated geometrical acceptance. Depicted in Figure 5.11, the capture efficiency as a function of the beam emittance
are calculated from both the analytical formula and NEBIT where the 6T-6T magnetic
field configuration and the 1 A electron beam current were used. At an emittance >
5 π mm·mrad, the capture efficiencies from both approaches agree. The difference of the
capture efficiency at low emittances can be explained by not having included, in the analytical formula, the possibility that ions are charge bred to higher charge states before
62

they reach the outer barrier. Because of this, ions with small emittance are likely to be
completely inside the electron beam, have large ionization probability, and can be lost. The
capture efficiency from NEBIT is then smaller than what it is predicted by the analytical
formula. By flying the particles on axis, the NEBIT result shows that up to 14 % are
further ionized to the 2+ charge state before the outer barrier. By including this factor
and considering an injected beam with 1 π mm·mrad emittance, the capture efficiency from
NEBIT and the analytical formula are 83% and 86%. At 2 π mm·mrad, the difference of
16% results from radial energy pickup of the ions. The 1+ ions pick up the radial energy
while crossing the magnetic field and insufficiently have energy to overcome the outer barrier. Therefore, those ions that are reflected at the trap entrance cause the efficiency to be
smaller than the value expected from Eq. 5.2.
Concludingly, NEBIT is reliable in calculating capture probabilities. Compared to the
simple formula, it provides necessary details of the ion beam while traveling into the EBIT
which is not available from the analytical formula, for example, the ion trajectory in the
inhomogeneous magnetic field or the effect of the space charge potential to the ion trajectory
as well as the phase space and its orientation of the injected beam which is helpful for setting
up the ion injection optics.

5.4.4 Comparison of charge evolution between NEBIT and CBSIM
CBSIM is a popular code to study charge evolution developed by R. Becker and O. Kester
[44]. The charge evolution in CBSIM is calculated from a rate equation which includes
cross sections for charge exchange, radiative recombination, and a model for ion heating.
However, to compare the charge evolution between NEBIT and CBSIM, the charge exchange

63

100
Capture efficiency (%)

NEBIT

80

Analytical formula

60
40
20
0

0

2

4

6

8

10 12 14 16 18 20

Emittance (

mm·mrad)

Figure 5.11 Comparison between the capture efficiency calculated from the analytical formula and NEBIT with the electron beam current of 1 A and the 6T-6T magnetic field
configuration.

64

100

100

Relative abundance (%)

1+

80

80

NEBIT

60

60

CBSIM

3+

40

5+ 7+

17+
13+
15+
11+

9+

20

20

0
1E-4

40

0

1E-3

0.01

0.1

1

Breeding time (ms)

Figure 5.12 Charge evolution of iron ions calculated from CBSIM (lines) and NEBIT (symbols). The highest relative abundances on the leftmost and rightmost curves of the figure
represent charge states of Fe1+ and Fe17+ , respectively. The calculation stopped at a
charge breeding time of 1 ms and the electron beam of 1 A and the 6T-6T configuration
were used.
and the radiative recombination cross sections are neglected because the pressure in the
EBIT trapping region is very low and the capture process occurs at low charge states.
Therefore, the EI process alone is sufficient. The ionization cross section used in CBSIM is
from Lotz’s formula as well.
Since CBSIM assumes a constant magnetic field, the 6T-6T magnetic field configuration
was used. The NEBIT simulation was performed with the 1 A and 12.5 keV electron beam.
The potential allocations for the trap can be found in Table B.3. To simulate charge
evolution under conditions used in CBSIM, an ion has to start inside the electron beam
and be confined in the trapping region. Both inner and outer barriers are raised high enough

65

to completely confine ions inside the trap. The calculation runs for 1 ms, which is sufficient
to charge breed iron ions up to Fe16+ .
The charge evolutions computed from CBSIM and NEBIT are illustrated in Figure 5.12.
To obtain the charge evolution from CBSIM, we need to know the electron beam current
density because the output of CBSIM is recorded as a product of the electron beam current
density and charge breeding time. For Ie = 1 A, B = 6 T, Bc = 10 G, the electron
beam current density is 1.2 × 104 A/cm2 . At low charge states, the result from NEBIT
agrees with the one from CBSIM while there is a small difference at high charge states.
The optimal charge breeding time for Fe15+ are 0.4 and 0.6 ms calculated from CBSIM
and NEBIT, respectively. Since the magnetic field at the edge of the trapping region is
significantly weaker than that at the trap center by a factor of two, the ions are likely to
experience a lower electron beam current density and require longer breeding time to get
charge bred to a higher charge state. Results from both codes show Fe17+ dominates in
the trap at 1 ms.
In conclusion, only with the electron impact ionization, NEBIT provides the charge
evolution consistent with that from CBSIM.

5.4.5 Comparison of capture efficiency between current and earlier versions
Since different approximations are employed in the original and the improved NEBIT code,
it is important to understand how these differences can influence the capture efficiency.
Figure 5.13 displays a capture efficiency calculated with the earlier and the current versions
of the code. The calculation of the current NEBIT version for the small emittance beam
was carried out with higher statistics than that for the large emittance. At the small

66

110
Current version

Capture efficiency (%)

100

Earlier version

90
80
70
60
50
40

0

2

4

6

8

10 12 14 16 18 20

Emittance (

mm·mrad)

Figure 5.13 Comparison of the the capture efficiency calculated from the current and the
earlier versions of NEBIT. The electron beam of 2.5 A and 12 keV were used with the
1T-6T magnetic field configuration.
emittance range, the capture efficiency from both versions are close to 100% and show an
only small deviation. When the emittance is larger (> 10 π mm·mrad), the difference is
more significant and can be explained by the following: the use of the final EBIT geometry,
the implementation of the electron beam energy correction, and the improvement of the
electric field imported from SIMION.
The geometry of the EBIT used in the current version has a longer distance between
the collector and the entrance of the EBIT, when compared to the earlier version. This
difference causes the ions that form the small emittance beam to be ionized into the 2+
charge state before reaching the trap. The small emittance beam entirely overlaps with the
electron beam, therefore it has a high probability to be ionized into a higher charge state.
This effect is seen in Figure 5.13 where the capture efficiency is computed higher in the
67

earlier version than the current version.
With the electron beam energy correction included (Eq. 2.8), the space-charge potential
created by the electron beam is larger and deeper than that without the correction. Because
of this, ions at larger emittance are well trapped. Furthermore, the electric field from
SIMION also provides the radial component, which is not included in the earlier version of
NEBIT, to help radially confine ions. These two enhancements are particularly important
for the injected ion beam with large emittance.

5.5 Simulation results
We have seen in the previous sections that NEBIT is a reliable tool to study the capture
efficiency. This section will show the simulation results from NEBIT for different operation
parameters.

5.5.1 Capture efficiency with maximum design parameters
The capture efficiencies were simulated for the electron beam currents of 1 A and 2.5 A.
The electron beam currents were chosen according to the value we could obtain from the
previous electron gun commissioning [64] and the maximum designed current.
Figure 5.14 depicts the capture efficiency as a function of the ion beam emittance for
the electron beam currents of 1 A and 2.5 A produced by cathodes with 6.35 and 12.7 mm
diameters, respectively. An electron beam energy of 12.5 keV at the trap center as well as
the 1T-6T magnetic field configuration was used. The 60 keV Fe+ beam was injected into
the EBIT with the 1T-6T magnetic field configuration. The iron beam was chosen because
it is the heaviest element whose database for the EI cross sections are available. The trap
68

Capture efficiency (%)

100
80
60

2.5 A

40
1.0 A

20
0

0

5

10

15

Emittance (

20

25

30

mm·mrad)

Figure 5.14 Capture efficiency as a function of injected beam emittance for 1 A (black) and
2.5 A (red) electron beam current. The calculation were carried out with the electron beam
energy of 12.5 keV and the 1T-6T magnetic field configuration.

69

of 0.75 m was defined between LTC11 and LTE4 electrodes, see Figure B.1. At small
emittance, the capture efficiency is high since the ions travel close to the electron beam axis
and have high probability to be trapped during the round-trip flight. On the other hand,
the beam with large emittance has a small chance to be charge bred and trapped since the
overlap between the ion beam and the electron beam is small. The decrease of the total
efficiency for the injected beam having large emittance was also observed at REXEBIS [12].
At 10 π mm·mrad of ion beam emittance, the capture efficiencies of 80 % and 51 % for the
electron beam current of 2.5 A and 1 A, respectively, could be reached in the simulations.
As expected, the higher the electron beam current, the higher the efficiency will be.
Assuming Bc = 10 G, the electron beam current of 1 A produces 1.5 kV of space-charge
potential and the electron beam current density of 1.2 × 104 A/cm2 can be reached at the
trap center. The 2.5 A electron beam current creates 3.7 kV space-charge potential with
electron beam current density of 8.8 × 103 A/cm2 . The fact that the higher electron beam
current gives the lower electron beam current density is due to the increased cathode size
for the higher current.
The capture efficiency was also investigated for different magnetic field configurations
as shown in Figure 5.15. The same ion beam parameters and trap size as the previous
calculation were used for this study. The 12.5 keV and 1 A electron beam was used and
yielded the electron beam current density of 1.6 × 103 A/cm2 and 1.2 × 104 A/cm2 at 1 T
and 6 T regions, respectively. At 10 π mm·mrad of ion beam emittance, the efficiencies
of 51 % and 21 % were predicted. For the 1T-6T configuration, the electron beam radius
at the extended trap section is larger than that of the 6T-6T. Since the bigger electron
beam radius provides a better overlap between the ion and the electron beam, the capture

70

1.0

1T-6T magnetic field
6T-6T magnetic field

Capture probability

0.8

0.6

0.4

0.2

0.0
0

5

10

15

Emittance (

20

25

30

mm·mrad)

Figure 5.15 Capture efficiency as a function of injected beam emittance for 1T-6T (black)
and 6T-6T (red) configurations for the 1 A and 12.5 keV electron beam.

71

Capture efficiency (%)

50

15.70 kV
15.45 kV

40

15.20 kV
14.95 kV

30

14.70 kV

20
10
0

0

2

4

6

Emittance (

8

10

mm·mrad)

Figure 5.16 Calculated capture efficiency as a function of voltage applied to the acceleration/deceleration electrode.
efficiency becomes larger.

5.5.2 Capture efficiency with different transport optics
The optimization of the setting was performed for every electrode but only three of them,
the acceleration/deceleration electrode, the Einzel lens, and the transfer lens, were chosen
as examples. The calculation in this section used the EBIT and the beam parameters from
the experiment. The 2T-2T magnetic field configuration as well as the 19.5 keV and 135 mA
electron beam was used and the 20 keV K+ beam was injected into the EBIT. Figure 5.16
illustrates the capture efficiency as a function of emittance for different voltages applied to
the acceleration/deceleration electrode. The variation of the voltages causes the efficiency
to be different by 17 % and 4 % at 1 and 4 π mm·mrad. Within this range of voltage, the

72

Capture efficiency (%)

50
16.57 kV

40

16.32 kV
16.07 kV

30

15.82 kV
15.57 kV

20
10
0

0

2

4

6

Emittance (

8

10

mm·mrad)

Figure 5.17 Calculated capture efficiency as a function of voltage applied to the Einzel lens:
16.57 (black), 16.32 (red), 16.07 (blue), 15.82 (magenta), and 15.57 kV (green).
capture efficiency is less influenced by the acceleration/deceleration voltage at a large than
a small emittance beam. For the 1 π mm·mrad beam, 14.95 kV applied to the electrode
provides the highest efficiency. If the emittance is larger than 1 π mm·mrad, the highest
efficiency is obtained when the voltage is adjusted to 14.70 kV.
Figure 5.17 depicts the calculated capture efficiency as a function of voltage applied to
the Einzel lens. Within a range of 1 kV applied to the Einzel lens, the capture efficiencies
are different by 10 % and 3 % for 1 π mm·mrad and 4 π mm·mrad beams, respectively. The
highest capture efficiency is received by adjusting the voltage of the Einzel lens electrode
to 15.57 kV. The effect on the Einzel lens is small at a large emittance beam as well.
Simulations were also performed to optimize the voltage applied to the transfer lens,
Figure 6.4 item 4. It is found that within 1 kV range, the capture efficiency for 2 π mm·mrad

73

and larger are almost equivalent. By using NEBIT to optimize the voltage setting for the
beam transport into the EBIT, we do not only obtain the optimal value but also are able
to indicate that the acceleration/deceleration electrode and the Einzel lens are the most
sensitive to the ion beam.

5.5.3 Capture efficiency with parameters used in experiments
Different EBIT parameters, electron beam currents, trap sizes, and trap potential were
systematically studied using NEBIT. An electron beam of 19.5 keV and the 2T-2T magnetic
field configuration were used throughout the following calculations. Figure 5.18 displays
the simulated capture efficiency as a function of electron beam current for the injected
beam emittance ranging between 1 - 6 π mm·mrad. The maximum trap size of 0.64 m,
defined by the distance between LTC10 and LTE4 electrodes (see Figure B.1), was set. At
this range of the electron beam current, the capture efficiency is apparently different even
when the emittance of the injected beam is small. The trend of the capture efficiency for
different electron beam currents is in the same direction that the higher the electron beam,
the larger the simulated capture efficiency. The relation between the electron beam current
and the ionization probability can be found in Eq. 2.15 and 2.16.
Figure 5.19 illustrates the simulated capture efficiency as a function of trap size for the
injected beam emittance ranging between 1 - 6 π mm·mrad. The electron beam current
of 100 mA were used. The capture efficiency for the beam with smaller emittance is more
influenced by the trap size than that with larger emittance. Because of the short distance
in the trapping region, ions do not spend enough time to interact with the electron beam
and are not further ionized to the 2+ charge state. Therefore, a small amount of ions are

74

Capture efficiency (%)

70
60

1

mm·mrad

4

mm·mrad

2

mm·mrad

5

mm·mrad

50

3

mm·mrad

6

mm·mrad

40
30
20
10
0

75

90

105

120

135

Electron beam current (mA)

Figure 5.18 Calculated capture efficiency as a function of electron beam current for injected
ion beams with emittances from 1 - 6 π mm·mrad.

75

Capture efficiency (%)

60

50

1

mm·mrad

4

mm·mrad

2

mm·mrad

5

mm·mrad

3

mm·mrad

6

mm·mrad

40

30

20

10

0
0.40

0.45

0.50

0.55

0.60

0.65

Trap size (m)

Figure 5.19 Calculated capture efficiency as a function of trap size for injected ion beams
with emittances from 1 - 6 π mm·mrad.
trapped and the capture efficiency is low.
Figure 5.20 depicts simulated capture efficiency as a function of trap depth for the
injected beam emittance ranging between 1 - 6 π mm·mrad. The electron beam current of
122 mA was used. The negative value indicates that the trap potential is lower than the
outer barrier. The trap potential has to be optimized since the trap depth, corresponding to
the ion energy in the trap, can influence the capture efficiency. The optimal value is -30 V
for a beam of 1 π mm·mrad and changes to -10 V for a beam of 2 π mm·mrad or higher.
The optimal value expresses the balance of the ion energy and the trapping potential. If
either of these values is too large or small, the capture will become small. The relation
between the capture efficiency and the trap depth are described in details in Section 6.3.4.

76

Capture efficiency (%)

60
50

1

mm·mrad

4

mm·mrad

2

mm·mrad

5

mm·mrad

3

mm·mrad

6

mm·mrad

40
30
20
10
0
-60

-40

-20

Trap depth (V)

Figure 5.20 Calculated capture efficiency as a function of trap depth for injected ion beams
with emittances from 1 - 6 π mm·mrad.

77

Chapter 6
Measurements, Results, and
Discussion
In order to investigate the efficiency of the NSCL EBIT, several studies were performed.
The emittance of the ion beam generated from the test ion source was determined. The
voltage settings to efficiently transport the ion beam into the EBIT were optimized by
employing a radial energy pickup technique and observing the location of the ion reflection.
With optimal tuning, capture efficiencies were systematically studied through the variation
of injected ion beam currents, electron beam currents, trap sizes, and trap potential depths.
From the charge state evolution, the effective electron beam current density was estimated.
Details of each measurement are contained in the following sections. In Section 6.1, the
transverse emittance measurement of the beam from the test ion source is discussed. The
optimization of the ion injection into the EBIT is described in Section 6.2. The relation
between capture efficiency and the EBIT parameters is investigated in Section 6.3. Section
6.4 reports on the charge state evolution of potassium ions and a measurement of the
effective current density of the electron beam.

78

6.1 Transverse emittance measurement of K+ beam
We have seen in Section 5.5 that the capture efficiency changes as a function of the injected
beam emittance. If the emittance of the beam from the test ion source is well measured,
it allows us to calculate the capture efficiency of the EBIT correctly. With the current
experimental setup, the emittance measurement was performed by using a well known
quadrupole scan method [65]. The method requires, at a minimum, a quadrupole lens and
a screen for imaging the beam. The emittance is obtained by fitting the beam profiles using
the quadrupole transfer matrix elements.

6.1.1 Experimental setup and procedure
Figure 6.1 schematically illustrates the devices used for the emittance measurement. A
20 keV beam of K+ was generated from the test ion source and transported to an MCP at
BOB 1. Along the beamline, the beam was directed by an Einzel lens, a quadrupole triplet,
steerer electrodes, an electrostatic bender, and an electrostatic deflector. Inside BOB 1, the
MCP was mounted to provide an image of the beam , which was captured by a camera.
The horizontal and vertical beam profiles were extracted from the beam images with
different voltages applied to each of the three quadrupoles of the triplet as depicted in Figure
6.2. The voltages were varied independently for one quadrupole during the measurement
while keeping the voltages of the others constant. Once the applied voltage was off the
optimal value, the beam was out of focus leading to a wider beam diameter on the viewing
screen in one direction. A Gaussian function was used to fit the beam profile and the beam
size was described by one standard deviation (1σ) which is equivalent to the r.m.s radius.

79

Ion source
20 kV

Steerer

Electrostatic
bender
Deflector

C

B

A

BOB1
MCP screen

Figure 6.1 Schematic showing the experimental setup for the emittance measurement.
The transfer matrix of the triplet is needed for the quadrupole scan method and the details
in Appendix shows how to extract the transfer matrix of the triplet. Fitting the square
of the r.m.s. beam size as a function of applied voltage with Eq. 3.8 provides the beam
emittance. By repeating the same steps with all three quadrupoles, three values of the
emittance are given.

6.1.2 Emittance of the K+ ion beam
Figure 6.3 illustrates the fitting results from quadrupole A(a), B(b), and C(c). The emittance extracted from quadrupole A and C are x = 1.41±0.02, y = 4.53±0.35 π mm·mrad
and x = 5.54 ± 0.13, y = 3.71 ± 0.38 π mm·mrad, respectively. The error bars are calculated from the fitting process.

80

VA = 1300V
VB = 2850V
VC = 1850V

VA = 1725V
VB = 2850V
VC = 1850V

VA = 2100V
VB = 2850V
VC = 1850V

(a)
VA = 1725V
VB = 2850V
VC = 1850V

VA = 1725V
VB = 2600V
VC = 1850V

VA = 1725V
VB = 3050V
VC = 1850V

(b)
VA = 1725V
VB = 2850V
VC = 1850V

VA = 1725V
VB = 2850V
VC = 1450V

VA = 1725V
VB = 2850V
VC = 2250V

(c)
Figure 6.2 Examples of beam images captured by the MCP viewer with different voltages
applied to quadrupole A(a), B(b), C(c).

81

The data set of the beam size from varying the voltages applied to the quadrupole B
cannot reasonably be fitted with the quadratic function to provide the emittance. The
plot in Figure 6.3b shows a small peak at the center of the curve. Even though there
is not a solid conclusion for this small peak, a possible reason is the beam size may be
so large that the ions experience higher order effects of the electric field generated by
the quadrupole B. An independent emittance measurement was performed with the same
triplet and the result from the quadrupole B also showed a small peak. From two unrelated
emittance measurements, the triplet was similarly applied with positive, negative, and
positive voltages. For this voltage pattern, the horizontal beam size is always large at the
quadrupole B location. This may confirm that the small peak resulted from the large beam
size.
A SIMION simulation was performed to calculate the expected emittance of the ion
beam from the test ion source. The filament coil was constructed with toroidal electrodes.
Potassium ions were generated at the surface of the electrode with 0.01 eV of kinetic energy.
The ions were driven to the anode pinhole by the potential difference between the filament
and the anode. Other ion optics, such as the Einzel lens, an electrostatic bender, etc.,
were added along the beamlime. The K+ beam was transported toward BOB 1 where its
properties were recorded. The simulated r.m.s. emittance is 0.77 π mm·mrad for a 20 keV
ion beam.
After the measurement was finished, the test ion source was disassembled and it was
found that the anode was not firmly installed in the quartz chamber. The center of the
anode was off-center of the filament by 1 - 2 mm. This confirmed that the source was
not properly aligned to the beamline axis. Since the anode was also deformed from a flat

82

Horizontal axis (x)

2

x , y

2

2

(mm )

8

Vertical axis (y)

6
4
2
0
600

900

1200 1500 1800 2100 2400
Voltage (V)

(a)
1.4

Horizontal axis (x)

16

Vertical axis (y)

1.0

x

y

2

8

2

2

(mm )

12

2

(mm )

1.2

0.8

4
0.6

2600

2800

3000

3200

Voltage (V)

(b)
25
Horizontal axis (x)

2

x ,y

2

2

(mm )

20

Vertical axis (y)

15
10
5
0
1250

1500

1750

2000

2250

Voltage (V)

(c)
Figure 6.3 Quadratic fits of beam size squares at different voltages applied to the quadrupole
A(a), B(b), and C(c).
83

to a convex shape, this could distort the electric field at the pinhole area and cause the
difference between the calculated and measured emittance. In addition, the K+ beam was
possibly generated from the anode as the pinhole on the anode was slightly covered by
substances produced from the filament. During the past commissioning of the EBIT, there
was evidence that the K+ beam was not only generated from the filament but also partly
from the anode. This was confirmed by applying a high enough voltage to the anode to
block the K+ beam from the filament yet still detecting the K+ beam. These reasons may
explain why the measured emittance is larger than the expected value.
By taking into account that the beam is large inside the triplet and the data from the
quadrupole B cannot be fitted with the quadratic function, the emittance of the ion beam
are x = 1.4 − 5.5 π mm·mrad and y = 3.7 − 4.5 π mm·mrad. The average emittance is
3.8 π mm·mrad.

6.2 Optimization of ion injection
The NSCL EBIT charge breeder aims to achieve a high total efficiency taking into account
injection, extraction, capture, and charge breeding efficiencies. The voltage settings of the
beam transport optics have to be optimized in order to ensure maximum overlap of the ion
and the electron beams in the trapping region.

6.2.1 Experimental setup for ion injection and capture process
Figure 6.4 depicts the schematic of the experimental setup of the ion injection. A 20 keV
K+ beam from the test ion source was injected into the EBIT. The beam alignment was
adjusted by using the same optical elements as in the emittance measurement, described
84

in Section 6.1. While entering the high voltage region, the beam was first retarded by an
acceleration/deceleration column consisting of an acceleration/deceleration electrode and
an Einzel lens. The column and the EBIT were biased to 17 kV, and the potential in the
trapping region was set to be 15 V lower than the ion beam energy.
During the extraction process, the ions were ejected through the collector. The acceleration/deceleration electrode, the deflector, and the triplet between the test ion source and
BOB 1 were switched from the optimal injection to the optimal extraction voltage. Along
the beamline toward detectors at BOB 4 , the quadrupole triplet, a quadrupole singlet,
and two quadrupole doublets were used to focus the beam before entering the Q/A separator, between the electrostatic magnet, before entering the dipole magnet, and before the
detectors, respectively.
For the alignment of the ion beam and the energy spread measurement, another MCP
and Faraday cup were installed next to the last trap electrode where the electrode gun head
was inserted. These diagnostic devices were used to capture images and currents of the ion
beam that passed through the trapping region. The transport efficiency was obtained and
used to identify the alignment between the trap and the injected beam. After finishing the
transport efficiency measurement, the detectors were retracted and the electron gun head
was moved to the detector location.
The electrostatic benders at the Q/A section were utilized to select ions with a certain
energy. Located between the dipole magnet and the electrostatic benders, a Faraday cup
monitored the current of all the HCIs having the same range of axial energy. After the
bending magnet, the MCP in combination with an oscilloscope was used to observe the
TOF signal, and the current of the selected ions was recorded by a Faraday cup.

85

19

20

18

17
16

11a
15

11b
90

o

3b 3a

3c

11c

14
13

11
12

11d
10

9

8 7 6

5

4

2
3

1

Figure 6.4 The NSCL EBIT experimental setup: (1) electron gun, (2) electron gun Faraday cup, (3) trap electrodes and primary
components including inner barrier (3a), main trap (3b), and outer barrier (3c), (4) transfer lens, (5) electron collector, (6)
Einzel lens, (7) acceleration/deceleration column, (8) ground electrode, (9) beam observation box 1 (BOB 1), (10) quadrupole
triplet lens, (11) LA source consisting of ion source (11a), deflector (11b), electrostatic bender (11c), deflector (11d), (12)
quadrupole triplet lens, (13) BOB 2, (14) electrostatic bender, (15) quadrupole lens, (16) BOB 3, (17) quadrupole doublet,
(18) bending magnet, (19) quadrupole doublet, and (20) BOB 4.

86

Current (pA)

500
400
300
200
100
0

current (pA/V)

1st derivative of

19980

19985

19990

19995

19990

19995

V = 19990.3 ± 1.7 V
c
FWHM = 2.0 V

19980

19985

Inner potential barrier (V)

Figure 6.5 A plot of the ion beam current as a function of the inner potential barrier (Top)
and a Gaussian fit of the first derivative of the ion beam current with respect to the inner
potential barrier (bottom).

6.2.2 Axial energy spread measurement
To minimize beam losses during the beam transport, a technique of radial energy pickup
minimization was employed. While crossing the magnetic field, an ion converts a part of
its axial to radial kinetic energy. Due to the large overlap between the electron and the ion
beam, ions with small radial energy are more likely to be captured in the EBIT than those
having large radial energy. The ions with large radial energy can also be reflected at the
trap entrance or hit an electrode while returning at the inner barrier location. The optimal
voltage setting provides the maximum reduction in the radial energy pickup.
While injecting the ion beam into the EBIT, the inner potential barrier was scanned
between 2,980 and 3,000 V on top of 17 kV high voltage. The current of the ion beam
passing through the trapping region was measured by the electron gun Faraday cup. The
87

optimized setting was obtained by varying the voltages applied to the acceleration column
lens, the transfer lens, the first few trap electrodes at the trap entrance, and other transport
optics. Figure 6.5 shows the ion currents measured by the electron gun Faraday cup, a fitted
curve, and the first derivative as a function of the inner potential barrier. The data are fitted
with a sigmoid function and its first derivative is fitted with a Gaussian function. A FWHM
of 2.0 V from the fit having a χ2ν = 1.56 is obtained. To investigate the energy spread, a
simulation was performed to study the ion production in the ion source. It was found that
ions created from the filament, where the potential is 6 - 9 eV higher than the potential
platform, were extracted. The simulation results in Appendix show the trajectories of
ions that can be transported to the beam line. These ions are created from the filament
at location 4, 5, and 6 which are applied with 6, 7.5, and 9 V higher than the ion source
platform, respectively.
In conclusion, the axial energy spread of the ion beam was measured by transporting
the ion beam into the trap and the optimal voltage setting was obtained by minimizing the
ion radial energy. Having a small axial energy spread of 2 eV is important to provide a
good measurement of capture efficiency.

6.2.3 Ion reflection in the EBIT
The behavior of the injected beam in the EBIT was studied by measuring the TOF signal
of reflected ions. While traveling into the trap, incoming ions could reflect at any position
where the ion axial energy was insufficient to overcome the potential. By setting the inner
potential barrier to be significantly higher than the ion beam energy, the beam will not be
able to traverse the inner barrier. In order to reach the highest capture efficiency, the TOF

88

signal must be dominated by ions reflected off the inner barrier. This guarantees that the
ions enter the trapping region where the capture and the charge breeding process occur.
The ion beam from the test ion source was injected into the EBIT. Since there was not
a trapping process, the outer potential barrier was set to be equal to the trap potential.
The voltage applied to the deflector electrode was varied between the optimal values for
injection and extraction. The ion beam from the reflection was transported to the Q/A
separator, where the electrostatic benders and the bending magnet were set for the 20 keV
ion beam and K+ ions (Q/A = 1/39), respectively. An oscilloscope was connected to the
MCP at BOB 4 to record the TOF signal and a trigger to the TOF signal was generated
by a function generator. Figure 6.6 depicts the time sequence for varying voltages applied
to the deflector and the outer barrier between injection and extraction. For the study of
ion reflection, only the time sequence of the deflector is applied while both sequences of
deflector and the outer barrier are used when charge breeding process exists. The data
acquisition of ion TOF starts when the deflector voltage is switched from the injection to
the extraction voltage. The extraction time is always kept at 5 ms while the injection and
the breeding time varies according to the cycle period. The breeding process begins and
stops at 0.4 ms after the deflector voltage changes between the extraction and the injection
voltage. The outer barrier is also lowered for 5 ms to eject HCIs out of the trap.
The TOF spectra in Figure 6.7 displays peaks of TOF signals for different locations
where the ion beam returns. By individually adjusting the potential on each electrode, we
could identify which electrode reflected the beam. Figure 6.7a shows the spectrum which
was formed by ions reflected inside the EBIT when the LTE4 electrode (see Figure B.1)
was set as the inner barrier. In Figure 6.7b, after decreasing the LTE4 potential, the ion

89

textraction
tcycle

Deflector

Extraction voltage
tinjection

(a)
Injection voltage

Outer barrier

tbreeding

No potential barrier
(b)
With potential barrier

Time (ms)
0 tinj,start tbreeding,start tinj, stop tbreeding, stop
Figure 6.6 Time sequences for the injection and the extraction processes for the deflector
(a) and the outer barrier (b). The time sequence for the outer barrier is used for charge
breeding process.
beam passed through the trapping region toward the electron gun and the part of the TOF
signal corresponding to the ion reflection at the LTE4 disappeared. By lowering LTE1, its
contribution to the TOF signal was measured. The peaks of the TOF signal in Figure 6.7c
and Figure 6.7d are almost identical. The peak in Figure 6.7d disappeared after lowering
the voltage applied the LTC11 electrode. From a sequence of lowering the voltages applied
to LTE4, LTE1, LTRAP, and LTC11, we can conclude that most of the injected ions reflect
off the potential created by LTE4 and a small number of ions reflect at the location of LTE1
and LTC11, while there is no ion reflection at LTRAP.
Ions reflected at the LTC11 location cannot enter the trapping region and get charge
bred to higher charge states. If this number of ions is large, it will reduce the injection
efficiency. Optimization was performed to increase the fraction of the beam entering the
trapping region and to diminish the portion reflected from the outer barrier. In addition to

90

-100

-50

0

50

100

150

200

250

300

350

0

-10

Time-of-flight signal (mV)

-20

beam reflected at LTE4

(a)

With inner potential barrier

0

-10

beam reflected at LTE1

-20

(b)

Lower inner potential barrier

0

-10

-20

(c)
Lower LTE1 potential

0

-10
beam reflected at LTC11

-20

-100

(d)

-50

Lower LTRAP potential

0

50

100

150

200

Time-of-flight (

250

300

350

s)

Figure 6.7 TOF spectra of the ion beam measured after lowering the potential applied to
each electrode: (a) no lowering, (b) after lowering LTE4, (c) after lowering LTE1, and (d)
after lowering LTRAP.

91

-22
-20

Voltage (mV)

-18
-16
-14
-12
-10
-8
-6
-4
0

50

100

150

Time (

200

250

300

s)

Figure 6.8 TOF spectrum of the ion beam reflected at different locations in the EBIT and
simulated histogram that includes voltage delay, overshoot, and undershoot. The pattern
area shows expected signal from the ion beam reflected off the trap entrance and the inner
barrier.
measuring the TOF signal of ion reflection with the MCP, the Faraday cup at BOB 4 was
also used to measure currents of ions reflected at different locations. The total current of
ion reflection in Figure 6.7a was 5.8 pA for 50 Hz repetition rate and 5.6 pA reached the
center of the trap. With this voltage setting, 95% of the ion beam detected at BOB4 was
transported to the trap center.
To better understand the reflection process, a simulation with SIMION was carried out
to reproduce the experimental result. The simulation started with the voltage setting that
was used to obtain results in Figure 6.7a. Based on the axial energy spread measurement, an
ion beam with an energy of 19990 ± 2 eV at BOB 1 was used. The ion beam was Gaussian
distributed with a standard deviation of 0.6 mm corresponding to a beam with FWHM of
1.4 mm. The voltage setting was adjusted to match to the experimental TOF signal, Figure
92

6.7a. The first TOF signal is expected around 24 µs, equivalent to the time K + needed
to travel from the deflector electrode to the MCP at BOB 4. The last ion reflected off
the trap entrance takes approximately 100 µs to reach BOB 4 and most ions that reflected
off the inner barrier should spend less than 200 µs to reach BOB 4. If the injected beam
mainly comprises ions reflected off the trap entrance and the inner barrier, the TOF signal
is expected to be large at the beginning and then small. The large contribution of the TOF
signal is from ions reflected off both the trap entrance and the inner barrier, while the small
contribution is only from the ions reflected from the inner barrier (green pattern in Figure
6.8). However, the experimental results show that the first signal reached the MCP later
than that in the simulation and the TOF signal disappears between 75 - 112 µs.
The lost signal can be explained by the performance of a power supply for the deflector.
A high voltage probe was directly connected to measure the output voltage from the power
supply. During switching between the injection and extraction voltages, there was a time
delay caused by the power supply and an overshoot and an undershoot of the high voltages,
as depicted in Figure 6.9. Changing between two set voltages takes approximately 36 µs.
The time delay caused the first signal to arrive at the detector about 62 µs after the trigger
signal. The overshoot and the undershoot at around 49 µs blocked the extracted beam and
caused the discontinuity of the TOF signal. By taking the time delay into account, the
histogram in Figure 6.8 illustrates the simulated result that matches the TOF spectrum
from the experiment.
Furthermore, matching the simulation result with the TOF signal of the ion reflection
provides information of the beam emittance and potential distribution. The calculated
r.m.s. emittance of 5.7 π mm·mrad where xrms = 0.8 mm and xrms = 7.7 mrad is close

93

6
Deflector top electrode

Voltage (kV)

Deflector bottom electrode

4

Function generator

2

0

-2
0

50

100

150

Time (

200

250

300

s)

Figure 6.9 Time delay for changing between injection and extraction voltages of the deflector
top (black) and deflector bottom (red) electrodes and signal from the function generator
(blue). The pattern area indicates a range of voltage that allows the ion beam transport
based on the experiment.

94

to the upper bound of the emittance measured in Section 6.1 where the r.m.s. of the beam
size is 1.6 mm wide.
To determine the effective space-charge potential created by the electron beam, the
experiment was setup similar to the study of the ion reflection. The TOF signals of K+
were recorded both when the electron beam was off and on.
Figure 6.10a shows the TOF signal of K+ when the electron beam was off and the
simulation results that match to the TOF signal. The TOF signal starts around 57 µs and
the shape of the signal may result from the combination of the inhomogeneous magnetic
field and the potential distribution in the trap. In this measurement, an effect from the undershoot and the overshoot after switching high voltage for the extraction and the injection
was not observed. The possible reason was that, with this setting, the beam spot detected
by the MCP at BOB 4 moved on the MCP screen when the voltage changed from the
undershoot and the overshoot. Therefore the MCP could still detect the ions even though
the voltages were in the undershoot and overshoot ranges.
In Figure 6.10b, the TOF signal was experimentally recorded when the 19.5 keV and
90 mA electron beam was on and the histogram showed the result simulated with the same
electron beam current and energy. It is obvious that the histogram does not match to the
experiment. The ions in the simulation travel faster than the real ions in the trapping
region.
To obtain consistent results between the experiment and the simulation, displayed in
Figure 6.10c, the electron beam current used in the simulation was reduced to 25 mA
providing approximately 25 V on the electron beam axis. Since the ions that mostly travel
inside the electron beam are further ionized to 2+ charge state, the TOF signal of K+

95

Figure 6.10 TOF spectra of ion reflection and simulated histograms without the electron
beam (a), with the 19.5 keV and 90 mA electron beam for both simulation and experiment
(b), and with the 19.5 keV and 90 mA electron beam for experiment and the 19.5 keV and
25 mA for the simulation (c).

96

detected at BOB 4 is mainly from K+ that travel around the electron beam. The effective
space-charge potential that these ions see from the 90 mA electron beam is equivalent to
the space-charge potential created by a uniformly distributed electron beam of 25 mA.

6.3 Dependency of the total efficiency on ion and electron beam
currents, trap size, and trap depth
As mentioned in Chapter , the capture efficiency contributes to the total efficiency. There
are several parameters involved in the capture efficiency, for example, electron beam current,
electron beam energy, trap size, trap potential depth, magnetic field configuration, barrier
location, etc. However, only three dominant parameters: electron beam current, trap size,
and trap potential depth, were investigated.
The capture efficiency can be obtained from the total efficiency using Eq. ??. The
results from the ion reflection study support that the injection and transport efficiencies
of K+ are almost 100%. For ions with higher charge states which are more confined to
the electron beam axis, 100% of the extraction efficiency can be expected. The breeding
efficiency is also 100% since the total current is calculated from currents of all charge states.
Therefore, the capture efficiency is equal to the total efficiency.
The EBIT total efficiency is computed from the current of HCIs recorded after the Q/A
separator and divided by the injected beam current from the test ion source recorded at
BOB 1 (see Figure 6.4);
Ii /i
i
,
tot = I
inj

(6.1)

where Ii is the electric current of a charge state i and Iinj is the injected current. The
97

measurement to determine the capture efficiency has been performed by following steps:
1. Inject the K+ beam from the test ion source and measure the beam current at BOB
1 (see Figure 6.4).
2. Remove the Faraday cup, let the beam travel to the EBIT and be charge bred for a
desired period of time, normally between 20 - 500 ms.
3. Extract the HCIs through the collector by lowering the outer potential barrier and
adjust the Q/A separator to accept highly charged potassium.
4. Start a Q/A scan to record a current of HCIs ejected from the EBIT.
5. Repeat the same process but vary the following parameters:
(a) Injected ion beam current.
(b) Electron beam current.
(c) Trap size defined by the length between LTC11 or the outer barrier and the inner
barrier which varies from LTRAP, LTE1, and LTE4, see Appendix B.1.
(d) Ion energy in trapping region defined by the total trap depth.
For the study of the efficiency on the electron beam current, re-optimization of voltage
setting for each measurement was required since the total potential changed with electron
beam current. The focusing of the injected ion beam changed as well. For mapping out
other interested parameters, the optimizations were not necessary for each step.

98

120

N

7+

6+

O
7+

O

Current @ BOB 4 (pA)

100

17+

K

W ith K+ injection

16+

N

K

W ithout K+ injection

6+

N

80

5+

15+

K

60
N

13+

40

Ar

K

16+

Ar

14+

4+

He

1+

N

4+

5+

O

O

3+

12+

K

20

Ar
18+

30

11+

Ar

K

0

13+

12+

K

Ar

35

3+

O

10+

K
11+

9+

K

8+

K

40

45

Magnet current (A)

Figure 6.11 Q/A spectra of the ion beam extracted from the EBIT with a 5 Hz repetition rate, an electron beam current of
126 mA, and a 19.5 keV electron beam energy. The spectra with and without the external injection of K+ are shown in black
and red dotted curves, respectively.

99

Figure 6.11 displays typical Q/A spectra recorded at the BOB 4 Faraday cup. Not only
do the spectra contain elements from the injected beam, but they also provide information
about beam contamination from residual gases inside the trapping region, mainly C, N, O,
Ar, and Ne. Ba ions from the electron cathode sometimes were seen in the Q/A spectrum.
By comparing the spectra with and without external injection, we can distinguish the peaks
of highly charged potassium ions.

6.3.1 Capture efficiency vs injected ion beam current
The capture efficiency was investigated for different injected beam currents. Since the peak
of K16+ in Figure 6.11 is well isolated from peaks of highly charged background ions, K16+
is a good choice for studying the capture efficiency. Figure 6.12 displays the particle current
of K16+ as a function of injected beam current. By using an attenuator, the injected beam
current was reduced by factors of 10 and 100. The detected beam current rose linearly at
small injected beam current. The efficiency to charge breed into K16+ , illustrated in Fig
6.13, is calculated from the ratio of the particle current of K16+ to the injected current.
We see that the efficiency is constant at small incoming beam current and drops at high
incoming current. The reason is that the trap was saturated by highly charged ions of the
injected beam.
For an electron beam of 135 mA and 19.5 keV and the 0.64 m trap, the charge capacity
is about 1 nC, equivalent to an extracted beam current of 1 nA at 1 Hz repetition rate. Due
to the injected beam of 1.4 nA, a large portion of the beam was not captured and charge
bred, so the capture efficiency was reduced.
The trap capacity was investigated through the extracted beam currents. The total

100

Beam current of K

16+

(ppA)

5
4
3
2
1
0

10

100

1000

Injected beam current (pA)

Figure 6.12 Beam current of K16+ detected at BOB 4 with different injected beam currents.

Total efficiency of K

16+

(x10

-3

)

5.0

4.5

4.0

3.5

3.0

2.5

2.0
10

100

1000

Injected beam current (pA)

Figure 6.13 Total efficiency of charge breeding into K16+ charge state with different injected
beam currents.

101

Total current @ BOB 3 (nA)

+

Without K
1.6

+

With K

injection

injection

1.4

1.2

1.0

0.8

0.6

70

80

90

100

110

120

130

140

Electron beam current (mA)

Figure 6.14 Comparison of total beam currents extracted from EBIT with (red) and without
injection of potassium beam (black) at different electron beam currents.
beam current was measured at BOB 3 (see Figure 6.4) before the bending magnet. Figure
6.14 illustrates the total ion beam current as a function of electron beam current with
and without external beam injection from the test ion source. The extracted ion current
measured with external injection is smaller than that without external injection. Since a
potassium ion is heavier than the background ions, the lighter ions gain momentum from
ion-ion collisions and, at a certain point, have high enough energy to escape the trap. This
explanation is supported by the spectra shown in Figure 6.11 where the peaks of highly
charged residual ions are smaller than those without external injection. Therefore, less
beam current is extracted after external injection than that without external injection.

102

Particle current (ppA)

6

135 mA

5

115 mA

4

96 mA

3
76 mA

2
1
0

6

8

10

12

14

16

18

Charge state

Figure 6.15 A plot showing particle currents at different charge states from electron beam
currents of 135 mA (black), 115 mA (red), 96 mA (blue), and 76 mA (magenta). The ion
beam was extracted from the EBIT with a 5 Hz repetition rate.

6.3.2 Capture efficiency vs electron beam current
As seen in Chapter 2.4, the ionization time strongly depends on the electron beam current:
the higher the electron beam current, the larger the electron beam current density and
the shorter the breeding time. With the short breeding time, injected ions have a higher
probability of being charge bred to 2+ or 3+ charge states within a round-trip flight and
trapped in the trapping region. The trap capacity is also dependent on the electron beam
current, see Eq. 3.1. Figure 6.15 shows particle currents of each charge state at electron
beam currents of 135 mA, 115 mA, 96 mA, and 78 mA. For an accumulation time of
200 ms, K15+ dominated in the trap and the ejected currents increased with electron beam
currents.
A comparison between simulation and experimental capture efficiencies is depicted in
103

Figure 6.16. The simulated capture efficiencies are taken from Section 5.5.3 with emittance ranging between 1.4 - 5.5 πmm·mrad. The maximum total experimental efficiency
of 2.3 ± 0.1 % was obtained at the electron beam current of 135 mA. The error bar was
mainly from the fluctuation of the read current. However, considering the range of the injected beam emittance, the error bar can be larger than 0.1%. At 76 mA, the experimental
efficiency is smaller than the trend of capture efficiency of higher electron beam currents
because the voltage setting was not well optimized while recording currents of HCIs. From
the simulation, the highest efficiency was reached for a 135 mA electron beam current. The
comparison between simulated and experimental efficiencies shows an overprediction by a
factor of seven even though they illustrate the same trend. The difference between the
experimental and the simulated values can possibly be explained by following reasons; the
large range of the measured emittance, the saturation of the trap, the ion beam alignment,
and incorrect assumption for the electron beam density. Assuming the beam emittance
of 5.5 πmm·mrad, the capture efficiency is still different by a factor of three. Because of
injecting too much ion beam, the trap was saturated with highly charged potassium ions as
shown in Figure 6.11 and this limitation was not implemented in the simulation. Including
this factor to the capture efficiency, the overprediction decreases by a factor of 1.5.
A further simulation was performed to study the effect of misalignment of the injected
ion beam to the electron beam axis, as illustrated in Figure 6.17. An electron beam current
of 135 mA was used. For an ion beam with an emittance of 3.8 π mm·mrad, the capture
efficiency drops by factors of 1.2 and 2.0 if the ion beam is misaligned by 0.5 and 1.0 mm,
respectively. Due to the setup of beamline alignment, the misalignment can be at most 0.5
mm. By combining all three reasons, it is not enough to explain the overprediction factor

104

6
Capture efficiency (%)

Upper bound simulated efficiency / 7

5

Lower bound simulated efficiency / 7
Efficiency

4
3
2
1
0

70

80

90

100

110

120

130

140

Electron beam current (mA)

Figure 6.16 Comparison between the simulated capture efficiency ranges (between reddash and black-solid line) and the experimental (black) capture efficiencies as a function of
electron beam currents.
of seven. Therefore the investigation of the electron beam current density is required to
reveal the missing overprediction factor and this will be more clarified in Section 6.4.2.

6.3.3 Total efficiency vs trap size
Not only does trap size contribute to the trapping capacity, but it also influences the time
ions spend inside the trap. If the ion trajectory overlaps with the electron beam, the ion
spends a longer time inside the trapping region and therefore the probability for ionization
to K2+ or K3+ is higher. The schematic of three trap sizes is shown in Figure 6.18. The
full trap size (0.64 m) started from the outer barrier (LTC11, see Figure B.1) to the inner
barrier (LTE4). The potentials produced by LTE1 and LTRAP were raised to be equal to
the potential from LTE4 in order to have 0.51 m and 0.43 m trap sizes, respectively. Figure

105

Capture efficiency (%)

14

12

10

8

6

0.0

0.2

0.4

0.6

0.8

1.0

Off-axis distance (mm)

Figure 6.17 Calculated capture efficiency of a beam with an emittance of 3.8 π mm·mrad
at 20 keV as a function of distance between an injected beam and an electron beam axis.
The electron beam current of 135 mA was used.
6.19 shows experimental particle currents for each charge state for different trap sizes. The
total current of highly charged potassium ions rises as the trap size increases.
Figure 6.20 illustrates the comparison between the simulation and experimental capture efficiencies. The simulated capture efficiencies are taken from Section 5.5.3 with the
emittance range between 1.4 - 5.5 πmm·mrad. A maximum efficiency of 2.1 ± 0.1% was
obtained from the largest trapping size where an electron beam current of 100 mA was set.
Again, the error can be larger based on the range of the measured emittance. Although the
simulation and the experimental results evolve in a similar trend, they are still different by
a factor of seven. The low capture efficiency can be explained by reasons similar to those
mentioned in Section 6.3.2.

106

Inner
barrier
Outer
barrier

0.64 m
0.51 m
0.46 m

Figure 6.18 Schematic of the trap with different trap sizes.

Particle current (ppA)

7

Trap size 0.64 m

6

Trap size 0.51 m
Trap size 0.43 m

5
4
3
2
1
0

6

8

10

12

14

16

18

Charge state

Figure 6.19 A plot showing particle current of each charge state for different trap sizes. The
ion beam was extracted from the EBIT with a 5 Hz repetition rate.

107

6

Capture efficiency (%)

Upper bound simulated efficiency / 7
5

Lower bound simulated efficiency / 7
Experiment

4

3

2

1

0
0.40

0.45

0.50

0.55

0.60

0.65

Trap size (m)

Figure 6.20 Comparison between the simulated capture efficiency ranges (between reddash and black-solid line) and the experimental capture efficiencies (black) as a function of
trapping size.

6.3.4 Total efficiency vs trap depth
The trap depth determines the ion beam’s axial energy inside the trap and a deeper potential
well leads to higher ion energies. Since high energy ions spend less time in the trap, the
probability to be charge bred into K2+ or K3+ charge state becomes smaller. On the
other hand, if the potential is too shallow, K2+ ions may be able to leave the trap within
a round-trip. In addition, trapped ions may be heated through electron-ion collisions and
gain enough momentum to escape the trap [66, 19]. Therefore, the trap potential needs to
be optimized. A schematic of different trap depth is shown in Figure 6.21. The negative
sign indicates that the trap potential is smaller than the outer barrier.
In this measurement, the electron beam current was set to 120 mA. Figure 6.22 depicts
particle currents for several charge states. The experimental results provided the highest
108

Inner
barrier
Outer
barrier
-10 V
-30 V
-50 V
-70 V

Figure 6.21 Schematic of the trap with different trap potential.

7
Trap potential -10 V

Particle current (ppa)

6

Trap potential -30 V
Trap potential -50 V
Trap potential -70 V

5

4

3

2

1

0
8

10

12

14

16

18

Charge state

Figure 6.22 A plot showing particle current at different charge states with trap potential of
-10 V (magenta), -30 V (blue), -50 V (red), -70 V (black) compared to the outer barrier.
The ion beam was extracted from EBIT with 5 Hz repetition rate.

109

7
Upper bound simulated efficiency / 7

Capture efficiency (%)

6

Lower bound simulated efficiency / 7
experiment

5

4
3

2

1

0
-70

-60

-50

-40

-30

-20

-10

Trap depth (V)

Figure 6.23 Comparison between the simulated capture efficiency ranges (between red-dash
and black-solid line) and the experimental (black) capture efficiencies as a function of trap
depth. The simulated values are calculated based on the 20 keV ion beam.
and the lowest ion yields when the trap depth was set to -30 V and -70 V, respectively.
Figure 6.23 displays a comparison between simulation and experimental capture efficiencies.
The simulated capture efficiencies are taken from Section 5.5.3 with the emittance range
between 1.4 - 5.5 πmm·mrad. The experimental efficiency increased when the trap depth
changed from -70 V to -30 V and dropped down when the trap depth was -10 V. The
maximum efficiency of 2.1 ± 0.1 % was acquired when the trap depth was -30 V. At -10 V,
the experimental efficiency was lower than that of -30 V while the calculated efficiency at
-10 V was larger than that of -30 V. The reason is, in the experiment, the trapped ions may
be heated up by the electron-ion collisions and have enough kinetic energy to escape the
shallow trap while this collision is excluded in the simulation. Therefore, the trap depth
has to be optimized to avoid losing ions via this process.

110

6.4 Study of the charge breeding process
Understanding the charge breeding process is very important for the operation of the EBIT.
The highest abundance of the specific charge state can be obtained by charge breeding ions
within a proper time interval. The comparison between the calculated and the experimental
charge breeding times also provides information about the effective electron beam current
density, which indirectly helps determine how well the ion beam overlaps with the electron
beam.

6.4.1 Charge state evolution and charge breeding time
Figure 6.24 depicts mass-over-charge spectra for different accumulation times of highly
charged potassium. By scanning the dipole magnet current, ions with different A/Q ratios
extracted from the EBIT were detected. The abundance of each ion and charge state is
dependent on the accumulation time. For several accumulation times, the evolution of the
abundances can be observed. As the accumulation time increases, the highest abundance
of a certain A/Q ratio changes from the higher to the lower ratio.
Without considering the radiative recombination and charge exchange processes, the
calculated charge state evolution of potassium based only on the EI process is plotted in
Figure 6.25. The rate equation, see Eq. 2.17, is numerically solved with the following
initial conditions: an electron beam current density of 500 A/cm2 and the EI cross section
calculated for the 19.5 keV electron beam energy. The calculation assumes that the ion beam
trajectory entirely overlaps with the electron beam. When compared between experimental
and calculated results, the optimum time giving the highest abundance is significantly

111

17+

26.4

Beam current of highly charged ions at BOB 4 FC(pA)

17.6

K

18+

K

16+

K

14+

K

13+

K

12+

K

11+

K

10+

K

9+

K

8+

K

667 ms

15+

K

8.8
0.0
90

200 ms

60
30
0
228

100 ms

152
76
0
420

67 ms

280
140
0
540

50 ms

360
180
0
570

40 ms

380
190
0
2

3

4

5

Mass-over-charge ratio

Figure 6.24 Mass-over-charge spectra of highly charged potassium obtained by scanning the
bending magnet current for different accumulation times. The electron beam current and
energy were 125 mA and 19.5 keV.

112

100

Abundance (%)

80

60

1+

19+

40

9+

20

0
1E-6

1E-4

0.01

1

Accumulation time (s)

Figure 6.25 Calculated charge state evolution of potassium ions with the continuous injection. The electron beam current density is 500 A/cm2 .
different. The reason is that the ion beam trajectory in the experiment partially overlaps
with the electron beam and the ions then need to be charge bred over a longer time into
higher charge states. The helium-like potassium, K17+ , abundance dominates over the
nearby charge states as a result of closed-shell charge breeding where the 17th and 18th
ionization energies of potassium are 1.03 and 4.61 keV.

6.4.2 Determination of effective current density
An effective electron current density is used to analyze how well the injected ion beam
overlaps with the electron beam in the EBIT. If the ion beam completely overlaps with
the electron beam, the effective current density is expected to be maximum and identical
to the current density of the electron beam. The effective current density is obtained
from a comparison between calculated and experimental charge state evolutions. Figure
113

6.26 illustrates the evolutions of K12+ and K16+ acquired from the experiment and the
calculation mentioned in section 6.4.1. K12+ and K16+ were selected for the study of
effective current density because they show clear peaks in the range of 0.01 to 0.5 ms of
accumulation times. The evolution of K12+ and K16+ were obtained by changing the
accumulation time from 16 - 500 ms and setting the magnet currents to allow only K12+
and K16+ to the detector. The experimental abundances are normalized by the number
of particles per pulse. At 16 ms, K12+ started to be produced in the trap while there
was not significant amount of K16+ . K16+ appeared when the accumulation time was
approximately 40 ms. The optimum accumulation times for charge breeding K12+ and
K16+ are 83 and 251 ms, respectively.
From the rate equation (Eq. 2.17) for an electron beam current density of 500 A/cm2 ,
the optimum accumulation times providing the maximum abundance of K12+ and K16+
are 26 and 122 ms, respectively. Since the charge breeding time is inversely proportional
to the electron beam current density, the effective electron beam current densities of K12+
and K16+ are 157 and 243 mA/cm2 . The effective current density is not close to the
calculated value of 500 mA/cm2 where Ie = 125 mA, B = 2 T, and the electron beam
density is uniform. The difference can be explained by two possible reasons. Firstly, the ion
trajectory does not well overlap with the electron beam. In this situation, K16+ ion is more
confined and its trajectory better overlaps with the electron beam than that of K12+ ion.
Secondly, the electron beam may not be uniformly distributed over the its cross section.
Due to these arguments, the electron beam at the trap center was further investigated via a
simulation by Tricomp [67]. The result of the simulation in Figure 6.27 supports the second
argument that the electron beam is not uniformly distributed over its cross section.

114

Abundance (%)

40

30

Experiment
Calculation with 500 mA/cm2

K16+
20

K12+

10

0
0.01

0.1

Accumulation time (s)
Figure 6.26 Comparison between calculated (dash line) and experimental (solid line) charge
state evolutions of K12+ (black) and K16+ (light blue). The electron beam current and
energy were 100 mA and 19.5 keV.
Using this information the small capture efficiency in Section 6.3 can be explained if the
K+ ions travel in the region of low electron beam current density. Assuming that the K+
ions are mostly in the region where the electron beam current density is about 100 A/cm2
or less, the value from the NEBIT calculation for this assumption can be significantly
decreased and the overprediction may be reduced by a factor of up to five.

115

250

Electron beam

2

current density (A/cm )

300

200

150

100

50

0
0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Electron beam radius (mm)

Figure 6.27 Electron beam current density as a function of the electron beam radius simulated by Tricomp.

116

Chapter 7
Conclusion and Outlook

7.1 Conclusion
The ion capture process inside the EBIT charge breeder was investigated via simulations and
experiments in order to understand how the EBIT functions and to maximize the capture
efficiency. The NEBIT code was used to calculate the EBIT acceptance and predict the
capture efficiency. The current version of NEBIT was upgraded from an earlier version
[61] by using the real design of the NSCL EBIT, improving the space charge potential
with the electron beam energy correction, using the Monte-Carlo method for ion selection,
and importing more realistic electric fields from SIMION. The NEBIT code was validated
to provide the reasonable results after being tested with the concept of conservation of
energy and compared to the analytical formula, CBSIM program, and the previous version
of NEBIT. With the design parameters of the 2.5 A electron beam current and the 1T6T magnetic field configuration, NEBIT demonstrated that it is possible to attain capture
efficiency of more than 80% for an injected ion beam with an emittance of less than 10 π
mm·mrad. NEBIT was also used and will help optimizing the voltage setting. It can predict
the capture efficiency based on the setup used in the experiment.
The EBIT was experimentally setup with the 2T-2T magnetic field configuration and
an electron beam of 19.5 keV. A K+ beam of 20 keV from the test ion source was used to

117

study the EBIT capture efficiency. The emittance of the K+ beam was measured by the
quadrupole scan method. The voltage setting to efficiently transport the ion beam into the
trap was optimized by minimizing the radial energy pickup and observing the TOF signal
of ion reflection. The behavior of the electron beam in the trap was deduced from the TOF
signal of ion reflection when the electron beam existed. The capture efficiency was studied
through variations of the injected ion beam current, electron beam current, trap size, and
trap potential depth. From the evolution of highly charged potassium, the effective current
density of the electron beam was experimentally extracted for K12+ and K16+ .
From the comparison of simulations and experiments, the capture efficiencies were found
to be overpredicted by a factor of seven. The overprediction is mostly due to the electron
beam current density which is assumed to be uniformly distributed in the simulation while
it is actually not in the real experiment.

7.2 Outlook
As the NEBIT code can be used to calculate the capture efficiency for the EBIT, there
is still room for improvement, for example, importing the self-electric field generated by
the charged particles from a separate code. This modification will make the calculation
much faster. Besides the EI process, the other processes such as radiative recombination,
charge exchange, electron heating, etc. can be added. For a simple calculation of the
capture efficiency, it is enough to include only the EI process but in the experiment, the
cycle period is in the scale of tens to hundreds of milliseconds in which the HCIs can be
influenced by other processes. With the addition of these processes, the NEBIT code will
be able to provide more realistic prediction of the capture efficiency.
118

The experiment can also be improved by running the EBIT with a higher electron beam
current than 135 mA. During the time these measurements were performed, the electron
gun could only provide the electron beam current of up to 150 mA. After being modified,
the electron gun could produce up to 800 mA electron beam current. At this electron beam
current, the EBIT acceptance was significantly larger than the emittance of the injected ion
beam. The capture efficiency, which was not limited by the emittance of the injected ion
beam, achieved 30% closed to the predicted value. With this capture efficiency, it strongly
confirms that the NSCL EBIT is a good charge breeder for rare isotope beams. In addition
to high electron beam current, the electron beam current density must be maximized and
made uniform within the a certain radius in order to succeed in fast charge breeding.
Finally, this thesis provides useful information from both simulation and experimental
aspects for the EBIT and EBIS charge breeder community. The NEBIT code can be used
to predict the capture efficiency and understand the detailed behavior of ions in the EBIT.
The experimental results can help guide and be a good lesson for the EBIT charge breeder
operation to reach the highest total efficiency.

119

APPENDICES

120

Appendix A
Transfer matrix for a triplet
The transfer matrices as a function of the quadrupole voltage can be extracted from SIMION
by the following steps;
1. Create an instance in SIMION containing a quadrupole triplet and an MCP screen
and fly two particles in vertical and horizontal axis with a small radius and angle.
2. Record initial and final positions and velocities then calculate the transfer matrix
components.
3. Plot the transfer matrix entries as a function of voltage applied to quadrupole A, B,
or C and linearly fit to extract the transfer matrix as a function of voltage.
To simplify the calculation, only the first order transfer matrix is considered. Therefore,
trajectories of test ions are chosen to be close to the axis in order to avoid an effect of
higher order terms. Furthermore, the determinant of the transfer matrix has to be unity.
Two 20 keV test ions were injected into the quadrupole triplet with the following initial
conditions: x1 , y1 = 0 mm, x1 , y1 = 3.3 mrad, x2 , y2 = 1.8 mm, and x2 , y2 = 0. The
example of the transfer matrix elements, see Eq. A.2, of the quadrupole triplet and the drift
space to the MCP screen in vertical and horizontal axes are displayed in Figure A.1. The
transfer matrices were linearly fitted as a function of voltages applied to the quadrupole
A. The transfer matrix elements were also calculated when altering voltages applied to the
121

quadrupole B and C. The emittance can finally be extracted from the quadratic equation,
containing the transfer matrix elements,

σ11 = (V A1 + A2 )((V A1 + A2 ) · σ11 + (V B1 + B2 ) · σ12)
+ (V B1 + B2 )((V A1 + A2 ) · σ12 + (V B1 + B2 ) ·

2 + π2σ2
12 )
2
π σ11

(A.1)

with A1 , A2 , B1 , and B2 being constants in the following transfer matrix,




 V A1 + A2 V B1 + B2 
M=
.
V C1 + C2 V D1 + D2

122

(A.2)

Transfer matrix element

1
B

0

D
-1

A
-2

-3

-4

C

-5
1400

1600

1800

2000

2200

2400

2200

2400

Voltage (V)

1.0

Transfer matrix element

B

0.5

0.0

D

-0.5

-1.0

A

-1.5

C

1400

1600

1800

2000

Voltage (V)

Figure A.1 Transfer matrix elements; A (black), B (red), C (blue), and D (magenta), in
horizontal (left) and vertical (right) axes as a function of applied voltage to the quadrupole
A.

123

Appendix B
Voltage distribution
Electrode
Injection tube
Acceleration electrode
Outer lens
Inner lens
Extraction endcap
Collector
Suppressor
Trap endcap
Transfer lens
Trumpet
TC13
TC12
Outer barrier (TC11)
TC10-TC1
Main trap
TE1
TE2-TE4
Inner barrier (TE5)
TE6-TE7

Voltage (kV)
0
45.8
45.8
45.8
50
52
51.5
53
53.8
56.2
57.5
59.5
59.9
59.9
59.9
59.9
59.9
0
0

Table B.1 List of voltages used in SIMION and the NEBIT code to test the conservation
of energy along the ion trajectory described in section 5.4.1.

124

Electrode
Injection tube
Acceleration electrode
Outer lens
Inner lens
Extraction end cap
Collector
Suppressor
Trap endcap
Transfer lens
Trumpet
TC13
TC12
1st barrier (TC11)
TC10-TC1
Main trap
TE1-TE4
2nd barrier (TE5)
TE6-TE7

Voltage (kV)
100 mA 6T6T-1A
0
0
45.8
45.8
45.8
45.8
45.8
45.8
50
50
52
52
50.5
51.5
53
53
54
54
56
56.5
58
58
58.5
59.2, 58.5
59.8
60
59.5
59.5
59.5
59.5
59.5
59.5
65.4
65.4
65.4
65.4

Table B.2 The voltage setting for a test of geometrical acceptance with the NSCL EBIT
system described in section 5.4.2. For the electron beam current of 100 mA, the settings
for 1T-6T and 6T-6T configurations are the same. For the electron beam current of 1 A,
the TC12 element is set to be 59.2 and 58.5 kV for the 1T-6T and 6T-6T configurations.

Electrode
Outer barrier (TC11)
TC10-TC1
Main trap
TE1-TE4
Inner barrier (TE5)

Voltage (kV)
62.5
60.5
60.5
60.5
62.5

Table B.3 List of voltages used in NEBIT to calculate the charge state evolution.

125

Relative to
pulsed HV

Relative to
e-gun HV

Cathode

(E-gun HV)
Anode

TC14
TC13
TC12
TC11
TC10
TC9
TC8
TC7
TC6
TC5
TC4
TC3
TC2
TC1
Trap
TE1
TE2
TE3
TE4
TE5
TE6
TE7

Transfer electrode

Collector
Coll2
Coll1

Coll3=Coll4

Coll-EL
Outer electrode

Coll-Acc

Earth ground

Relative to
pulsed HV

10 cm

Relative to
e-gun HV

Figure B.1 Power supply schematic for the EBIT. Except an earthground, all elements are floating on an EBIT high voltage
platform. To control the electron beam, the electron gun and the collector are biased up to 20 kV on top of the EBIT high
voltage platform.

126

Ion source

Quadrupole
triplet

Bender
Deflector

Acceleration/
deceleration
Collecter
electrode
Einzel Lens

Ground
electrode

Electron
gun

Transfer
lens

20 kV
15 kV

Trap electrode

16.4 kV 16.5 kV

19.6 kV
17 kV
2 kV 15 kV 18.5 kV

Ground

Figure B.2 Schematic of voltages applied to each element.

127

19.99 kV

21 kV
2 kV

Appendix C
Ion source simulation
The simulation of the test ion source was performed to investigate the production of K+ in
the ion source chamber. Figure C.1 shows a series of locations where the K+ are produced
from the filament. The top figure illustrates the geometry of the filament and six figures
at the bottom display the trajectories of ions created at different locations of the filament.
The filament is modeled with small rings and ions are generated around the ring with initial
energy of 0.01 eV. The ions are driven by the electric field between the filament and the
anode. Voltages applied to the filaments varies from 2 - 9 V based on the valued read from
the power supply during the experiment. The anode voltage was set to zero compared to
the filament. The extraction electrode and the focusing lens were set to -1.57 kV and -4.80
kV, respectively.
From the simulation, K+ ions extracted from the ion source were generated from the
filaments at location 4 - 6 where they were supplied by 6, 7.5, and 9 V, respectively.

128

Ion source
Filament
Filament location 6
.
.
.
Filament location 1

Focusing
lens

Extraction
electrode

Filament Location 1

Filament Location 2

Filament Location 3

Filament Location 4

Filament Location 5

Filament Location 6

Figure C.1 Simulation of ion production inside the test ion source.

129

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