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STUDIES OF LONGITUDINAL BEAM DYNAMICS
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6/01 c:/CiRC/DateDue.p65-p.15

STUDIES OF LONGITUDINAL BEAM DYNAMICS
WITH STRONG SPACE CHARGE EFFECTS
USING A SMALL ISOCHRONOUS RING

by

Jose Alberto Rodriguez

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHYLOSOPHY
Department of Physics and Astronomy

2004

ABSTRACT

STUDIES OF LONGITUDINAL BEAM DYNAMICS
WITH STRONG SPACE CHARGE EFFECTS
USING A SMALL ISOCHRONOUS RING

by

Jose Alberto Rodriguez

In recent years, based on the successful operation of the PSI cyclotron, a
number of authors have proposed to use high power cyclotrons for various
applications. Space charge forces become especially relevant in these machines
due to the large beam currents involved. There is a consensus in the cyclotron
community that a deeper knowledge of these forces is necessary to successfully
build such a cyclotron. This dissertation is part of an effort carried out at the
National Superconducting Cyclotron Laboratory (NSCL) to better understand
these effects. Using a Small lsochronous Ring (SIR) that works in a space
charge dominated regime, we are able to observe and study some of the same
space charge effects that are expected in much larger machines. The focus of
this dissertation is to describe the injection and extraction line of SIR as well as
its control system. We will also discuss the results of simulations performed to
describe the beam dynamics in SIR and how those results compare with the

experiments.

Dedicado a mis padres.
Gracias.

ACKNOWLEDGMENTS

A lot of people at the NSCL have collaborated one way or another in the
SIR project. I am grateful to all of them.

In particular I would like to thank Professor Felix Marti. He has guided me,
as my supervisor, through the past few years. His expertise has been absolutely
critical to build SIR. It has been a pleasure and a great opportunity to work for
him. I will not forget how much he has helped me. Thank you very much.

I also want to say thank you to Eduard Pozdeyev. He came up with the
idea of SIR. We spent many hours together designing and building it. During that
time, we developed a great friendship. Thank you very much.

Richard York has played a very important role in the SIR project. His
interest and support has been essential in getting it built. Thank you very much.

Roger Zink, Renan Fontus and John Bienivagen have worked in the
mechanical design of SIR. Working with them has been a great experience.
Thank you for your critical contribution. I will not forget it.

Dave Sanderson has aligned all the elements of SIR. He also gave us a
lot of advices on vacuum equipment. Don Lawton, AI Zeller, Dallas Cole, Scott
Hitchcock and Dan Pedtke have collaborated in different ways with their
expertise and a lot of ideas. I am grateful to all of them.

David Devereaux has helped us assembling SIR. I wish you the best in
your future.

My first physics teacher, Don Juan Carlos Perez at the “Salesianos de

Atocha” school, played a very important role in my life. Because of him, I started

to be interested in physics and mathematics. He is an excellent teacher. Muchas
gracias.

I am also grateful to the professors of the “Universidad Complutense de
Madrid” where I got my undergraduate degree in physics. They encouraged me
to continue in this field.

The social support has been, at least, as important as the professional
one. I am grateful to all my friends and family. In particular, I want to thank my
parents, Joaquin and Isabel Rodriguez, to whom I dedicate this dissertation. Had
not been for their unconditional love and support, I am convinced I would not
have completed it. I will not forget it. Muchas gracias.

I also want to say thank you to my girlfriend Donatella Canella. She has
always been there for me. Her love, patience and understanding, especially
during the past few months, meant a lot to me. I just hope I will be as good to her
as she has been to me. She is a very special person. Grazie.

Although they may not know, my old friends back in Spain have helped
me during the past few years in a lot of different ways. I know I can always rely
on Javier Barragan, Carlos Lorenzo, Moises Morales and Sergio Gil. I want to
reassure them that they will always be able to count on me as well. Muchas
gracias.

I have also met a lot of friends here. With time, I developed strong links
with them. I Ieamt a lot from their different nationalities and backgrounds. It has

been an incredible experience. Thank you very much.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................. ix
LIST OF FIGURES ............................................................................................... xi
SYMBOLS AND ABBREVIATIONS ..................................................................... xx
1. INTRODUCTION ....................................................................................... 1
1.1. HIGH POWER CYCLOTRONS ................................................................ 3
1.2. DESCRIPTION OF SIR ......................................................................... 6
1.3. SCALING OF SPACE CHARGE FORCES .................................................. 9
1.4. ADVANTAGES OF SIR ....................................................................... 12
1.5. OBJECTIVES OF SIR ........................................................................ 14
1.6. BRIEF DESCRIPTION OF THE CONTENTS OF THE REST OF THE CHAPTERS
16
2. INJECTION LINE OF SIR ........................................................................ 17
2.1. INTRODUCTION ................................................................................ 17
2.2. REQUIREMENTS ............................................................................... 17
2.3. GENERAL DESCRIPTION ................................................................... 19
2.4. ION SOURCE ................................................................................... 22
2.5. EINZEL LENS ................................................................................... 25
2.6. STEERING ....................................................................................... 29
2.7. MASS SEPARATOR ........................................................................... 30
2.8. EMITTANCE MEASUREMENT SYSTEM ................................................. 33
2.9. QUADRUPOLE TRIPLET ..................................................................... 35
2.10. CHOPPER .................................................................................... 37
2.11. INFLECTOR PLATES ...................................................................... 45
2.12. INJECTION LINE FARADAY CUP ...................................................... 46
2.13. BEAM DYNAMICS IN THE INJECTION LINE ........................................ 48
2.14. OTHER INJECTION LINE SCHEMES .................................................. 54
3. EXTRACTION LINE OF SIR .................................................................... 59
3.1 . INTRODUCTION ................................................................................ 59
3.2. DEFLECTOR PLATES ........................................................................ 60
3.3. SECTOR FAST FARADAY CUP ........................................................... 61
3.4. MOVABLE FAST FARADAY CUP ......................................................... 68
3.5. OTHER TYPES OF FAST FARADAY CUPS THAT WERE ALSO CONSIDERED 71
4. ELECTRONICS AND CONTROL SYSTEM OF SIR ................................ 73
4.1 . INTRODUCTION ................................................................................ 73
4.2. SCANNING WIRES ............................................................................ 74
4.3. EMITTANCE MEASUREMENT SYSTEM ................................................. 77
4.4. CHOPPER, INFLECTOR AND DEFLECTOR TIMING ................................. 79
4.5. MOVABLE FAST FARADAY CUP ......................................................... 81
4.6. SECTOR FAST FARADAY CUP ........................................................... 83

vi

4.7. DIPOLES, QUADS, STEERING, EINZEL LENS AND EXTRACTION POWER

SUPPLIES .................................................................................................. 84
4.8. PHOSPHOR SCREENS ...................................................................... 87
4.9. BEAM LIFETIME MEASUREMENTS ...................................................... 88
4.10. OTHER SYSTEMS ......................................................................... 89
4.1 1. A MORE INTEGRATED ALTERNATIVE CONTROL SYSTEM ..................... 90
4.12. CONCLUSION ............................................................................... 91
5. BEAM VARIABILITY ................................................................................ 93
5.1 . INTRODUCTION ................................................................................ 93
5.2. VARIABILITY OF THE MAGNETIC FIELD OF THE DIPOLES ........................ 93
5.3. VARIABILITY OF EXTRACTION AND EINZEL LENS VOLTAGES .................. 95
5.4. ION SOURCE VARIABILITY .................................................................. 97
5.5. OTHER SOURCES OF VARIABILITY ...................................................... 98
5.6. BEAM DRIFT OVER TIME .................................................................... 99
6. ION SOURCE CHARACTERIZATION ................................................... 100
6.1 . INTRODUCTION .............................................................................. 100
6.2. EXTRACTED CURRENT FOR DIFFERENT EXTRACTION VOLTAGES ......... 101
6.3. BEAM TRANSVERSE PHASE SPACE FOR DIFFERENT EXTRACTED CURRENTS
102
6.4. OTHER RELATIONSHIPS BETWEEN CONDITIONS IN THE SOURCE AND
PROPERTIES OF THE EXTRACTED BEAM ....................................................... 106
7. BEAM LIFETIME EXPERIMENTS ......................................................... 108
7.1 . INTRODUCTION .............................................................................. 108
7.2. BEAM LIFETIME DEPENDENCE ON EXTRACTION TURN NUMBER AND
PRESSURE IN THE RING ............................................................................. 109
7.3. BEAM LIFETIME DEPENDENCE ON THE BEAM ENERGY ......................... 111
7. 4. CONCLUSION ................................................................................. 1 12
8. BEAM DYNAMICS SIMULATIONS WITH CYCO: PRELIMINARY
CONSIDERATIONS ......................................................................................... 113
8.1 . INTRODUCTION .............................................................................. 1 13
8.2. DATA REPRESENTATION ................................................................. 1 14
8.3. DESCRIPTION OF THE METHODOLOGY USED IN THE ANALYSIS OF DATA 1 16
8.4. NUMERICAL STABILITY: COMPUTATIONAL PARAMETERS ..................... 120
8.5. NUMERICAL STABILITY: DIFFERENT INITIAL ENSEMBLE ....................... 126
8. 6. CONCLUSION ................................................................................. 130
9. BEAM DYNAMICS SIMULATIONS WITH CYCO: RESULTS OF
SIMULATIONS ................................................................................................. 131
9.1 . INTRODUCTION .............................................................................. 131
9.2. DISPERSION IN THE NUMBER OF CLUSTERS ...................................... 132
9.3. SCALING WITH BUNCH LENGTH ........................................................ 134
9.4. SCALING WITH BUNCH CURRENT ...................................................... 135
9.5. SCALING WITH ENERGY OF THE BUNCH ............................................ 141

vii

9.6. VACUUM CHAMBER SIZE ................................................................. 145

9.7. TRANSVERSE EMITTANCE ............................................................... 147
9.8. MACROSCOPIC PERTURBATION ....................................................... 150
9.9. MICROSCOPIC PERTURBATION ........................................................ 152
9.10. ENERGY SPREAD WITHIN A BUNCH ............................................... 154
9.11. BEAM RADIAL SIZE ...................................................................... 155
9.12. ASYMPTOTIC CLUSTER DENSITY AND MERGING RATE ..................... 157
9.13. CONCLUSION ............................................................................. 159
10. BEAM DYNAMICS EXPERIMENTS WITH SIR ..................................... 161
10.1. INTRODUCTION .......................................................................... 161
10.2. REPEATABILITY OF THE EXPERIMENTAL MEASUREMENTS ................ 162
10.3. JUSTIFICATION OF THE NUMBER OF PROFILES MEASURED .............. 164
10.4. SCALING WITH BUNCH LENGTH .................................................... 166
10.5. SCALING WITH BUNCH CURRENT .................................................. 168
10.6. CORRELATION BETWEEN ENERGY AND RADIAL POSITION OF THE
CLUSTERS ................................................................................................ 170
10.7. DIRECT COMPARISON OF THE RESULTS OF THE EXPERIMENTS AND THE
SIMULATIONS. .......................................................................................... 171
11. CONCLUSION ....................................................................................... 174
APPENDIX A: OPERATING PROCEDURES FOR SIR ................................... 176
A1. — PROCEDURE To TURN ON SIR ......................................................... 176
A2. — PROCEDURE To TURN OFF SIR ........................................................ 190
A3. — PROCEDURE TO REPLACE ION SOURCE FILAMENT .............................. 192
A4. - PROCEDURE To CLEAN THE HYDROGEN LINE ..................................... 194
A5. - PROCEDURE To VENT THE RING ....................................................... 195
A6. -— PROCEDURE To PUMP IN THE RING ................................................... 197
A]. — PROCEDURE To CLEAN COMPONENTS TO BE INSTALLED INSIDE VACUUM
CHAMBER ................................................................................................. 199
APPENDIX B: CONTROL PROGRAMS DESCRIPTIONS ............................... 200
B1. — SCANNING WIRES ........................................................................... 200
BIBLIOGRAPHY ............................................................................................... 202

viii

LIST OF TABLES

Table 1: Main parameters of SIR. ......................................................................... 8

Table 2: Comparison between main parameters of SIR and the PSI Injector II.

Parameters of a bunch in SIR (column 2) are such that the Space
charge forces experienced are equivalent to those felt by a bunch
with the parameters listed in column 1 during its first revolution in the
PSI Injector II cyclotron. In a similar way, the last revolution of the
beam in PSI Injector II (column 3) is compared to SIR in column 4.12

Table 3: Radius of curvature for different mass species in the mass separator of

the injection line of SIR when the H‘, Hf or H3+ species is selected.
........................................................................................................ 32

Table 4: Source conditions used in the measurements Shown in Figure 50. 101

Table 5: Value of main parameters used in the experiment described in this

section. .......................................................................................... 103

Table 6: Estimated beam losses for different working conditions ..................... 112

Table 7: Default parameters used in the simulations performed in this section to

Table

Table

Table

Table

Table

determine the impact that changes in computational parameters
have on the dynamics of the bunch. .............................................. 120

8: Parameters used in the simulations to determine the effect of the

microscopic representation of a bunch in its dynamics compared to
changes in its peak current. .......................................................... 128

9: Bunch characteristics and computational parameters used in the

10:

simulations performed to determine the effect that the choice of the
microscopic realization of the bunch has on the number of clusters
formed. .......................................................................................... 133

Physical and computational parameters used in the simulations
performed to determine how the number of clusters formed scales
with the length of the bunch after it breaks up. .............................. 135

11: Bunch characteristics and computational parameters used in the

simulations performed to determine the effect of the peak current on
the dynamics of the bunch. ........................................................... 138

12: Bunch characteristics and computational parameters used in the

simulations performed to determine the effect of the energy on the
dynamics of the bunch. ................................................................. 142

ix

Table 13: Bunch characteristics and computational parameters used in the
simulations performed to determine the effect of the size of the
vacuum chamber on the dynamics of the bunch. .......................... 145

Table 14: Bunch characteristics and computational parameters used in the
simulations performed to determine the effect of the emittance of the
beam on its dynamics .................................................................... 149

Table 15: Bunch characteristics and computational parameters used in the
simulations performed to determine the effect that local density
fluctuation have on the bunch dynamics. ...................................... 150

Table 16: Bunch characteristics and computational parameters used in the
simulations performed to determine the effect that very small
changes in the choice of the microscopic representation of a bunch
have on its dynamics. .................................................................... 152

Table 17: Bunch characteristics and computational parameters used in the
simulations performed to determine the energy spread induced by
space charge forces. ..................................................................... 154

Table 18: Main parameters of the bunches used in the discussion on repeatability
of measurements ........................................................................... 164

Table 19: Main parameters of the bunches used in the discussion on the
justification of the number of longitudinal profiles measured. ........ 165

Table 20: Main parameters of the bunches used in the discussion of scalability
with length of the number of clusters formed after the initial bunch

break up and during its evolution aftenIvards. ................................ 168
Table 21: Main parameters of the bunches used in the discussion of scalability of
space charge effects with peak current. ........................................ 169
Table 22: Beam parameters when the machine is adjusted to the values listed in
Table 23. ....................................................................................... 186
Table 23: Example of the values of different parameters of SIR to produce
bunches with the characteristics listed in Table 22. ...................... 187
Table 24: Scanning wires initialization parameters ........................................... 200

LIST OF FIGURES

Note: Some of the figures in this document use color.

Figure 1: Picture of the Small lsochronous Ring (SIR). ........................................ 7

Figure 2: The space charge regime, defined by the scaling factor k, in which SIR
can operate is displayed in shaded red. The value of the scaling
factors for other machines described in section 1.1 are represented
by horizontal lines. The tag IN refers to the first revolution in those

machines, while the tag OUT refers to the last revolution. .............. 10
Figure 3: Schematic top and side view of the injection line of SIR ...................... 20
Figure 4: Picture of the injection line of SIR ........................................................ 21
Figure 5: Wiring diagram of the ion source and its associated electronics. ........ 24

Figure 6: Picture of the Einzel lens and puller of the ion source used in the
injection line of SIR .......................................................................... 25

Figure 7: Simion model of the Einzel lens and source extraction region of the
injection line of SIR. Equipotential lines are shown in red. Several
ions were tracked and their trajectories are displayed in black. ...... 27

Figure 8: Focusing distance of the Einzel lens when biased to different voltages
for a 20 keV beam. The picture was expanded for 10 W. The non-
linear effects of the lens can be observed in the dispersion of the
focusing distances for ions entering the source 1, 3, 5 and 7mm
away from the beam axis. ............................................................... 28

Figure 9: Picture of the first two pairs of steering plates in the injection line of
SIR. An old version of the Einzel lens and puller can be seen in top
of the 8" flange that supports the whole structure. .......................... 29

Figure 10: Picture of the mass separator used in the injection line of SIR .......... 31

Figure 11: Selection of ions with different masses in the mass separator of the
injection line of SIR .......................................................................... 32

Figure 12: Picture of the emittance measurement system used to transversely
characterize the beam coming from the ion source ......................... 33

Figure 13: Picture of the quadrupole triplet, chopper and first pair of inflector
plates held by a support frame before being assembled in the
injection line of SIR .......................................................................... 36

xi

Figure 14: Picture of the triplet of electrostatic quadrupoles used in the injection
line of SIR ........................................................................................ 36

Figure 15: Focusing length for a 20 keV beam of the three quadrupoles used in
the injection line of SIR .................................................................... 37

Figure 16: Pictures of the system used to chop the beam in the injection line of
SIR. ................................................................................................. 38

Figure 17: Transverse beam profiles measured with the first horizontal scanning
wire for different voltages in the chopper. When the plates are biased
to more than 1:600V, the beam is deflected and is not injected. ...... 40

Figure 18: The deflection angle of a 20 keV H2+ beam as it goes through the
chopper is plotted in black. The value of the electric field in the
center of the chopper at the time the ions get there is plotted in red.
........................................................................................................ 41

Figure 19: Length of the head and tail of the bunches produced by the chopper
for different ion masses and energies. ............................................ 43

Figure 20: Picture of the second pair of inflector plates located in between two of
the dipole magnets of the ring. ........................................................ 45

Figure 21: Front and side View of the lnflector Plates where main dimensions (in
cm) are specified. ............................................................................ 46

Figure 22: Picture of the Faraday cup at the end of the injection line of SIR. ..... 47

Figure 23: Ions representing different points of the phase space (measured with
the emittance measurement system) were tracked back to the
source and plotted in green and blue. An ellipse representing this
ensemble in red and variations on this ellipse in black can be
accommodated by the injection line and matched to the closed orbit
solution of the ring when injected. ................................................... 49

Figure 24: Envelope of the beam as it moves in the injection line of the SIR. The
curve on top is the vertical beam envelope (perpendicular to the
medium plane of the ring). The bottom curve corresponds to the
beam envelope in the horizontal plane. ........................................... 51

Figure 25: Snap-shots of the phase space of the beam in the injection line.
Ellipses using COSY model in red. (Black in the 30 fields). Inner
(outer) ellipses 10 (50) IT mm mrad. ................................................ 55

Figure 26: Picture of the extraction box of SIR during assembly. ....................... 59

xii

Figure 27: Picture of the sector fast Faraday cup used to measure beam
longitudinal profiles when they are extracted from the ring. ............ 61

Figure 28: Measured rise time of the signal in one of the sectors of the fast
faraday cup when a bunch hits it. .................................................... 65

Figure 29: Measurement of the cross talk between central electrodes of the
sector fast Faraday cup. The amplitude of the induced signal in one
the central electrodes was measured when a signal was sent to the
electrode next to it. .......................................................................... 66

Figure 30: Noise induced in one of the electrodes of the sector Faraday cup
when the chopper, inflector and deflector plates are turned on and
off. ................................................................................................... 67

Figure 31: Picture of the movable fast Faraday cup used to measure longitudinal
beam profiles ................................................................................... 69

Figure 32: Picture of the back of the prototype stripline fast Faraday cup
developed for SIR. .......................................................................... 71

Figure 33: Layout of the scanning wires and their associated control electronics.
........................................................................................................ 75

Figure 34: Front panel of the LabVlEW program used to control de scanning
wires. ............................................................................................... 76

Figure 35: Layout of the emittance measurement system and its associated
control electronics. .......................................................................... 77

Figure 36: Front panel of the LabVlEW program used to control the emittance
measurement system. ..................................................................... 78

Figure 37: Layout of the chopper, inflector and deflector and their associated
control electronics. .......................................................................... 79

Figure 38: Superposition of pictures of extracted beam as seen in the phosphor
screen before matching is performed. ............................................. 81

Figure 39: Layout of the fast faraday cup and its associated control electronics.82
Figure 40: Layout of the sector fast faraday cup and its associated electronics. 83

Figure 41: Front panel of the LabVlEW program used for the data acquisition of
the sector faraday cup. .................................................................... 84

Figure 42: Layout of some of the power supplies used in SIR and their
associated control electronics. ........................................................ 85

xiii

Figure 43: Front panel of the LabVlEW program to control the dipoles, extraction
and Einzel lens power supplies. ...................................................... 86

Figure 44: Layout of the phosphor screens and their associated control
electronics. ...................................................................................... 87

Figure 45: Layout of the beam lifetime measurement electronics and their control
electronics. ...................................................................................... 89

Figure 46: Long term variability of the injection line and ring dipoles power
supply. lo is 109 A that corresponds to a 21 keV Hf beam.
Deviations around this value were monitored over a 10 hour period
of time. ............................................................................................ 94

Figure 47: Long term variability of the extraction and Einzel lens power supplies.
V0 for the Einzel lens power supply is 16.5 kV and for the extraction
power supply is 20 W. The variability of these voltages was
monitored over a period of 10 hours ................................................ 96

Figure 48: Variability of the extracted beam current when the conditions in the ion
source are changed ......................................................................... 97

Figure 49: Y-Y' phase space characteristics over a 6 ‘/2 hours period of time 1
hour after turning on the machine. The injection line was set up to be
able to inject a 20 keV H2+ beam in the ring. ................................... 99

Figure 50: Extraction current versus extraction voltage for different ion masses.
The conditions in the source are enumerated in Table 4 ............... 102

Figure 51: Relationship between arc current and the extraction current of Hi
ions when the filament power is changed as shown in Figure 52. The
value of the arc voltage, extraction voltage and pressure are kept
constant. (Values are listed in Table 5.) ........................................ 103

Figure 52: Relationship between arc current and filament power measured for
constant value of the arc voltage, extraction voltage and gas
pressure. (Values are listed in Table 5.) ........................................ 104

Figure 53: X-Px phase space measurements for different extraction currents.
(We define the x plane as that parallel to the medium plane of the
ring.) The corresponding arc current and extracted beam current are
Shown in the figure. The rest of the source parameters are listed in
Table 5. Growth in the emittance and in the tilt of the beam when the
extracted current is increased (due to stronger transverse space
charge effects in the extraction region) can be observed. ............. 105

xiv

Figure 54: Value of the RMS-emittance and the Courant-Snyder parameters as a
function of the extracted beam current for the source conditions
listed in Table 5. ............................................................................ 106

Figure 55: Normalized beam current versus turn number for different gas
pressures. (21 keV Hf) ................................................................. 109

Figure 56: No as a function of the pressure in the ring for a 21 keV H2+ beam. 110
Figure 57: P100 as a function of the beam energy. ............................................ 111

Figure 58: Example of waterfall diagram for a 300 ns long Hg” bunch with energy
20 keV, peak current 10 uA and emittance 30 TI mm mrad. The
longitudinal bunch profile is plotted after a variable of turns. ......... 115

Figure 59: Top view (in black) and longitudinal profile (in red) of a Hf bunch 60
turns after being injected. The energy when it was injected was 20
keV, the peak current 10 DA, the length 300 ns and the emittance 30
TI mm mrad .................................................................................... 117

Figure 60: Number of clusters counted in longitudinal profile in Figure 59 for
different values of the user defined parameters k and Wm. ......... 119

Figure 61: Evolution of the longitudinal profile of a bunch with characteristics
listed in Table 7 for different values of Ne (Number of times the
space charge electric field is calculated per revolution). ............... 121

Figure 62: Evolution of the longitudinal profile of a bunch with characteristics
listed in Table 7 for different values of Nz (Number of grid points in
the FFT algorithm used to calculate the space Charge electric field in
the 2 direction (perpendicular to the medium plane of the ring)). .. 122

Figure 63: Evolution of the longitudinal profile of a bunch with characteristics
listed in Table 7 for different values of ny (Maximum number of grid
points in the FFT algorithm used to calculate the space charge
electric field in the x-y plane (parallel to the medium plane of the
ring)). The value of dxy is 1 mm in all cases. ................................ 124

Figure 64: Evolution of the longitudinal profile of a bunch with characteristics
listed in Table 7 for different values of dxy (grid size in the FFT
algorithm used to calculate the space charge electric field in the x-y
plane (parallel to the medium plane of the ring)). The value of ny is
216 in all cases. .............................................................................. 125

Figure 65: Evolution of the longitudinal profile of three different microscopic
representations of a bunch with the characteristics listed in Table 8.
Two different peak currents were used to compare characteristics of
the evolution. ................................................................................. 127

XV

Figure 66: Number of clusters versus turn number for three different initial
ensembles representing bunches with two different peak currents.
The rest of the bunch Characteristics are listed in Table 8. ........... 129

Figure 67: Average value and standard deviation of the number of clusters
formed for three different peak currents. The dispersion in values is
due to the choice of the microscopic representation of the bunch. 133

Figure 68: Number of clusters formed after 10, 20 and 30 revolutions for different
initial bunch lengths. The computational and physical parameters
used in the simulations are listed in Table 10 ................................ 134

Figure 69: Waterfall diagrams representing the evolution of the longitudinal
bunch profile for peak currents ranging from 1.43 pA to 11.44 (BA.
The other parameters that characterize the bunch are listed in Table
11. Some events have been labeled with letters A-F. ................... 136

Figure 70: Waterfall diagrams representing the evolution of the longitudinal
bunch profile for peak currents ranging from 12.87 uA to 22.88 LIA.
The other parameters that characterize the bunch are listed in Table
1 1. ................................................................................................. 137

Figure 71: Turn number when the events labeled A thru F in Figure 69 and
Figure 70 occur for different peak currents .................................... 138

Figure 72: Waterfall diagrams representing the evolution of the longitudinal
bunch profile for 1, 2, 5, 10 and 20 uA peak currents. The other
parameters that characterize the bunch are listed in Table 9. The
number of clusters counted is shown in the lower right corner of the
figure. ............................................................................................ 140

Figure 73: Number of clusters as a function of the equivalent tum number (NEQ)
for different peak currents. ............................................................ 141

Figure 74: Number of clusters as a function of the equivalent turn number for
different energies. ......................................................................... 142

Figure 75: Waterfall diagrams representing the evolution of the longitudinal
bunch profile for energies ranging from 12 keV to 22 keV. The other
parameters that characterize the bunch are listed in Table 12. ..... 143

Figure 76: Waterfall diagrams representing the evolution of the longitudinal
bunch profile for energies ranging from 24 keV to 28 keV. The other
parameters that characterize the bunch are listed in Table 12. ..... 144

Figure 77: Waterfall diagrams representing the evolution of the longitudinal
bunch profile for sizes of the vacuum chamber ranging from 2 cm to

15 cm. The parameters that characterize the bunch are listed in
Table 13. ....................................................................................... 146

Figure 78: Turn number when the events labeled A thru G in Figure 77 occur
when the size of the vacuum chamber is changed. ....................... 147

Figure 79: Waterfall diagrams representing the evolution of the longitudinal
bunch profile for beams with emittances ranging from 5 to
40-TT°mm-mrad. The parameters that characterize the bunch are
listed in Table 14. .......................................................................... 148

Figure 80: Number of clusters as a function of the turn number for different beam
emittances. .................................................................................... 149

Figure 81: Waterfall diagrams representing the evolution of the longitudinal
bunch profile for two bunches with different initial longitudinal profile
(top left and right). The initial microscopic representation of the
bunch in the left was generated by displacing macroparticles toward
the center of the bunch. The parameters that characterize the bunch
are listed in Table 15. .................................................................... 151

Figure 82: Effect in the evolution of the position of the macroparticles when one
of them is removed from the initial ensemble. The percentage of
particles that have been displaced Ad at a given turn number is
represented with different colors. The percentage of particles that
have been displaced more than Ad at a given turn number is
represented by contour lines. ........................................................ 153

Figure 83: Energy spread induced by space charge forces as a function of the
turn number for different beam energies (bottom of figure) and
different beam currents (top of figure). The same data is displayed
on the right as a function of the equivalent turn number. The rest of
the parameters of the bunches are specified in Table 17. ............. 155

Figure 84: Top view of three bunches with characteristics listed in Table 9 after a
variable number of turns. The energy spread induced by space
charge forces can be observed in the tilting of the beam. ............. 156

Figure 85: In black circles: number of clusters (averaged over ten initial
representations) formed for a 20 pA peak current (rest of bunch
characteristics are listed in Table 9). The data was fitted to an offset
decaying exponential (solid red line). ............................................ 158

Figure 86: Longitudinal bunch profiles measured with the sector Faraday cup
after the bunch was stored for 29 1/2 turns (on the left) and 98 V2 (on
the right). The characteristics of the bunches, when they were
injected, are listed in Table 18. The number of clusters counted (NC)
is shown next to the corresponding profile. ................................... 163

xvii

Figure 87: Dispersion in the number of clusters counted (Nc) when a bunch with
the characteristics listed in Table 19 was extracted after 55 turns (on
the left). Convergence in the average (Nc’w) and standard deviation
(NcSTD) of the number of clusters counted as the number of profiles
included is increased (on the right). .............................................. 165

Figure 88: Experimental verification of the scaling law with the bunch length. The
number of clusters counted for bunches with characteristics listed in
Table 20 scales with the length of the bunches as it can be seen in
the bottom of the figure where the density of clusters is plotted. 167

Figure 89: Experimental verification of the scaling law with the bunch current.
The number Of clusters counted for bunches with characteristics
listed in Table 21 scales with the peak current of the bunches as it
can be seen in the bottom of the figure where the number of clusters
is plotted as a function of the equivalent turn number. .................. 169

Figure 90: Correlation between energy of the ions and radial position. When the
bunch is extracted after ‘/2 a revolution, it hits part of the two central
electrodes of sector Faraday cup (green and red). After 99 ‘/2
revolutions, those clusters in the head of the bunch hit the outer
radius central electrode while those in the tail hit the inner radius
electrode. ...................................................................................... 170

Figure 91: Comparison in the evolution of the average number of clusters
between simulations (characteristics of the bunches listed in Table 9)
and experiments (characteristics listed in Table 21) ...................... 172

Figure 92: Picture of the low conductivity water manifold used to cool down the
ion source, the emittance measurement system and the dipole coils.
...................................................................................................... 177

Figure 93: Picture of the high voltage monitor, grounding rod and lock of the ion
source high voltage cage. ............................................................. 178

Figure 94: Picture of the ion Source and its associated gas handling system. . 179
Figure 95: Picture of the hydrogen tank and regulator ...................................... 180
Figure 96: Picture of the ion source and injection line associated electronics. . 181
Figure 97: Picture of the PCs used for data acquisition and control of SIR. ..... 182
Figure 98: Picture of the ring and extraction line associated electronics. ......... 183

Figure 99: User interface of the video capture and high voltage power supply
control programs. .......................................................................... 183

xviii

Figure 100: Picture of the compressed air control system. The two furthest left
switches are used to position the injection point phosphor screen.
The four furthest right switches open or close the valves in between

turbo pumps and mechanical pumps ............................................. 184
Figure 101: Picture of the fast high voltage switches used to pulse the chopper,
second pair of inflector plates and deflector plates. ...................... 185
Figure 102: Picture of the flange that holds the ion source and the plasma
electrode washer. .......................................................................... 192
Figure 103: Picture of the broken filament in the ion source ............................. 193
Figure 104: Picture of the box in between two of the ring magnets where the
beam injected. ............................................................................... 196
Figure 105: Picture of the vacuum system control area .................................... 197

Figure 106: Picture of the venting valve and one of the thermocouple gauges
used in the injection line of SIR. .................................................... 198

xix

COSY
CYCO

dB

dBm

EPAC
ECRIS
FFT
LabVlEW
LINAC
LCW
MatLab
MHV
MSU
NSCL
OFHC
PAC
PRST-AB
PSI

PXI

RFQ
SCUBEEx
SHv
SIMION

SYMBOLS AND ABBREVIATIONS

Code to perform beam dynamics calculations
Code to perform beam dynamics calculations with strong space
charge forces

 

P .
Gain(dB)alO-logm[ 1‘3”] where Pm and Pour are Input and output

IN
power respectively

Pour (dBm)‘='10'log'°[-Po—Ll/Tm(—mWLV2]

European Particle Accelerator Conference

ECR Ion Source conference

Fast Fourier Transform

LABoratory Virtual Instrument Engineering Workbench
LINear ACcelerator

Low Conductivity Water

MATrices LABoratory

Miniature High Voltage connector

Michigan State University

National Superconducting Cyclotron Laboratory

Oxygen Free High Conductivity

Particle Accelerator Conference

Physical Review Special Topics — Accelerators and Beams
Paul Scherrer Institute

Pci eXtensions for Instrumentation

Radio Frequency Quadrupole

Self Consistent Unbiased Elliptical Exclusion algorithm
Safe High Voltage connector

Code to perform calculations of electrostatic fields and to track ions
in those fields

SIR
SMA
SNS
TcllT k
TDR

Small lsochronous Ring
Sub-Miniature type A connector
Spallation Neutron Source

Tool Command Language I Tool Kit
Time Domain Reflectometer

1. INTRODUCTION

In recent years, a number of authors have proposed USing high power
cyclotrons (typically 1 GeV energy and 10 mA beam current) for different
applications including neutron generators, production of tritium, radioactive waste
transmutation and driving thermonuclear reactors. Some of the details of these
proposals are briefly discussed in the next section of this chapter.

The repulsion among ions in a bunch (i.e. space Charge forces) at these
current levels become very important and must be considered when such a
machine is designed.

While the vertical size of the bunch can be controlled by increasing the
vertical focusing strength, the longitudinal space charge electric field will induce
energy spread within the bunch. Ions in the head (i.e. front portion) of the bunch
will gain energy, while those in the tail will lose it. Since cyclotrons are
lsochronous, the length of the bunch will not change but the radial size of the
bunch will increase. Ions in the head will describe a trajectory with a larger radius
though maintaining a constant revolution frequency despite their higher energy.
In a similar way, the radial position of ions in the tail will be reduced. Refer to [1]
for a complete description of this process.

This effect reduces the turn separation making beam extraction difficult.
Part of the beam is lost in the extraction deflector and these losses induce
activation and heating of the deflector that are not acceptable at this power level.

The operation of the PSI Injector II cyclotron (2 mA average current) has

proven that if the length of the injected bunches is short enough (~ 1-2 cm), the

1

transverse size of the bunch does not grow and adequate turn separation is
maintained.

Even though some understanding about space charge effects in the
isochronous regime exists, this knowledge is not yet complete. Quoting from [2]:

“Available technologies and experience at PSI are a realistic basis for the
design of a cyclotron as a 10 MW proton driver. While scaling laws are seen to
apply in a wide range, further progress In the simulation of space charge
dominated beams is needed to estimate the ultimate performance of this type of
accelerator.”

This dissertation is part of an effort carried out at the National
Superconducting Cyclotron Laboratory (NSCL) at Michigan State University
(MSU) to better understand these effects. Several years ago, Eduard Pozdeyev
and Felix Marti started this effort by developing a computer code for beam
dynamics Simulations in this regime. The results of these preliminary calculations
showed interesting behaviors that were not intuitive. They decided to find a way
to experimentally validate the results of the simulations. The possibility of
requesting beam time at the PSI Injector II was studied.

Since space charge effects are greater at lower beam energies, it is
possible to experimentally study these effects with a much lower energy and
beam current machine. As described in section 1.3, only 12.9 uA of H2+ at 20 keV
is necessary to experience similar space charge forces to those in the PSI
Injector ll cyclotron. A small dedicated machine would also have a number of

advantages. Some of them are explained in section 1.4.

The decision was made to build such a machine. It was called the Small
lsochronous Ring (SIR). At that time, I joined the group and it was decided that I
would mainly work in the injection and extraction lines while another graduate
student, Eduard Pozdeyev, would work on the ring (complete description in [3]).

The focus of this dissertation is to describe the injection and extraction line
of SIR as well as its control system. We will also discuss the results of
simulations performed to describe the beam dynamics in SIR and how some of

those results compare with the experiments.

1.1. High power cyclotrons

The PSI high intensity cyclotron presently has the highest beam power of
any accelerator in the world. It is capable of delivering 2 mA of a 590 MeV proton
beam yielding 1.18 MW of beam power. (Presumably, the Spallation Neutron
Source (SNS) will soon be capable of delivering 1.4 mA of a 1 GeV H‘ beam
surpassing the PSI facility.)

At PSI, a Cockcroft-Walton generator is used as a preinjector accelerating
ions up to 870 keV. This beam is bunched a way such that when the bunches are
accelerated to 72 MeV, their length is approximately equal to their diameter. As
previously mentioned, these “circular” bunches do not deform as they are
accelerated through the machine. Therefore, the turn separation does not vanish
and the extraction losses are kept below 0.02 %.

By the time the bunches are injected into the ring cyclotron, they have

elongated due to longitudinal Space charge forces in the transfer line. Therefore,

3

they experience the radial tilting of the bunch described before although it is not
large enough to completely lose the turn separation (~ 6 mm). This distance is
doubled at the extraction point by injecting the bunches off-center, inducing a
betatron oscillation. The 12 mm separation is enough to keep losses in the
deflector low when the 590 MeV beam is extracted.

P. A. Schmelzbach et al. proposed in [2] a 10 mA 1 GeV machine directly
extrapolating the current PSI cyclotrons scheme. They suggest using an RFQ as
a preinjector into a 120 MeV injector cyclotron as an alternative to the Cockcroft-
Walton generator.

They propose adding two more accelerating cavities in the injector
cyclotron to double the energy gain per revolution. The additional energy gain is
to provide adequate turn separation despite a larger transverse size of the
circular bunches due to the increase in Charge density.

A rebuncher may be used between the injector cyclotron and the main
cyclotron to reduce the bunch elongation produced by the energy spread induced
by space charge forces in the transport line.

A 6.3 MeV energy gain per revolution as opposed to the 2.4 MeV in the
current design is needed to maintain the turn separation in the main cyclotron.
Eight 1 MV accelerating cavities instead of four 730 kV structures would be used
in this scheme.

Other high power cyclotrons have been proposed for a number of

applications. Some of them are listed here.

V. P. Dmitrievsky et al. propose in [4] a three-cyclotron complex to
accelerate a 10 mA H+ beam to 800 MeV. A four-sector cyclotron (Ci-15) would
be used as a preinjector to accelerate the beam from 0.5 MeV to 15 MeV. The
beam is then injected into the second four-sector cyclotron (C-60) to reach 60
MeV energy. The process is repeated with a third ten-sector cyclotron (C-800) to
achieve the desired final energy (800 MeV).

L. Calabretta et al. propose in [5] a superconducting cyclotron to
accelerate 10 mA of Hz” up to 1 GeV per nucleon. The beam would be stripped
in order to extract it. In this case, a good turn separation is not so critical since
protons have a lower magnetic rigidity. Due to the higher rigidity of Hi, a
stronger magnetic field is needed for the size of the machine to be as small as it
would be if protons were used.

T. Kuo et al. propose in [6] a cyclotron to accelerate 10 mA of H‘ to
energies up to 120 MeV as an injector to a larger machine. As in the previous
proposal, extraction by stripping would relax the turn separation requirements. At
the same time, the beam rigidity is similar to that of protons. Although, the low
binding energy of the second electron (0.7 eV) increases the vacuum
requirements and limits the maximum usable magnetic field.

G. Kim et al. propose in [7] a stack of five superconducting cyclotrons.
Each of them delivers 2 mA of 1 GeV protons yielding 10 MW of combined beam
power. The space charge regime in which each cyclotron operates is similar to
that of the current PSI machine which has been proven to work well. On the other

hand, the design of the magnets is far from trivial.

Several options for high power cyclotrons have been discussed. None of
them is free of problems and their feasibility still needs to be demonstrated. The
successful operation of PSI proves that the longitudinal space charge effects can
be managed. Although, a better understanding is needed if the beam current limit

has to be pushed further.

1.2. Description of SIR

The Small lsochronous Ring (Figure 1) consists of four 90° dipole
magnets. Their bending radius is 45 cm and the distance between them is 94 cm
giving a total circumference of 6.58 m. The angle of the pole tips and the
distance between magnets is such that the ring is isochronous. Dipole and
quadrupole corrector coils as well as an electrostatic quadrupole in each straight
section can be used to correct possible deviations from isochronism due to
misalignments or manufacturing errors. They can also be used to change the
tune of the ring or move out of the isochronous condition.

The impact of the earth’s magnetic field and other residual fields on the
beam dynamics was studied to ascertain the lowest beam energy. It was
determined that the impact of these fields on a 20 keV Hf beam was small
enough not to significantly affect the beam dynamics. Therefore, the ring is
typically operated between 20 and 30 keV.

Two turbopumps in the ring and another two in the injection line are
enough to reach a pressure lower than 1043 Torr when there is no gas load from

the source. When the source is used, the pressure raises to ~ 51043 Torr. The

6

half life of the beam for these pressures in the ring is several hundred
revolutions. The break up of the bunch is typically observed after a few tens of

revolutions. A complete description of the ring can be found in reference [3].

 

Figure 1: Picture of the Small lsochronous Ring (SIR).

The chopper in the injection line allows injecting bunches with different
lengths (as short as 100 ns and as long as the ring circumference). The
extraction line is located on the opposite side of the ring. The bunch can be
extracted after a variable number of turns which allows studying turn by turn
evolution. It can be sent to a phosphor screen to study its transverse properties

or to a fast Faraday cup to study its longitudinal profile.

The injection and extraction lines are described in detail in chapters 2 and

3 of this dissertation. The main parameters of SIR are summarized in Table 1.

 

 

 

 

PARAMETER VALUE

Ions H+. H2+. H3+
Beam Energy Up to 30 keV
Beam Current Up to 40 [IA for H2+

 

 

 

 

 

 

Bunch Length From ~ 100 ns to ~ 5 us
ERMS Typically ~ 2-3 Tr-mrn'mrad
for 20 keV, 10 uA H2 beam
Ring Circumference 6.58 m
Dipole typical field ~ 800 Gauss
Dipole Bending Angle (Radius) 90° (45 cm)
Dipoles Pole Face Angle 26°

 

Horizontal Tune: Vx

1.14 (with zero beam current)

 

Vertical Tune: v,

1.11 (with zero beam current)

 

Diagnostics Extraction

Phosphor Screen
Fast Faraday Cup (~ 2 ns time
resolution)

 

Diagnostics Injection

Emittance Measurement System
Faraday Cup
Phosphor Screen

 

Diagnostics Ring

4 Scanning Wires

 

 

 

 

 

Pumping System 4 x 500 Us Turbopumps
Pressure in the Ring with no a
hydrogen load from the source < 10 Torr
Pressure in the Ring with ~ . .8
hydrogen load from the source 5 10 Torr
Beam Half-life 245 Turns for 20 keV H2+

 

 

Table 1: Main parameters of SIR.

 

1.3. Scaling of space charge forces

As described in reference [3], the space charge forces that bunches with
similar sizes experience in the isochronous regime scale with a scaling factor (k)
given by the following expression:

Eq. 1

k 4 ' [AV 1 [PEAK ' h ' LBUNCI!

 

yS-m-h-w3 AV 27r-RAV
where q and m are the charge and mass of the ions, 7 is the relativistic gamma
factor, h is the rf harmonic number, a) is the revolution frequency, 1” is the
average beam current, 1mm is the peak bunch current, R“, is the average
radius of the circumference described by the bunch, and Lam/cu is the length of

the bunch.

Using this expression, we can evaluate the space charge regime in which
some of the machines, mentioned in section 1.1, function. We can, then, find
under what conditions SIR operates in the same space charge regime. It is worth
mentioning here that SIR does not have acceleration capabilities. In this case,
the beam peak current is used, eliminating the dependence of the scaling factor
(k) on the rf harmonic number.

The space charge region that can be explored by SIR is shown as a
shaded red area in Figure 2. The figure shows the values of the Space charge
scaling factor (k) as a function of the bunch peak current. This region has been

defined by four conditions:

o The lower current limit (5 (IA) is defined by the noise to signal ratio in the
measurements of the longitudinal profile using the fast Faraday cup. As
discussed in section 3.3, the noise level in these measurements is equivalent
to a :l: 0.5 pA variation in beam current.

. Even though beam currents higher than 40 [IA could be extracted from the
source, it would require increasing the gas pressure and filament power.
Raising the gas pressure in the source results in higher pressures in the ring
reducing the beam lifetime. Increasing the filament power reduces the

filament lifetime.

 

I

. ”A
m

 

 

 

 

 

 

 

mg C-800 IN
" '0.
E
“O +
"‘ 28keV H2
A:
PSI lnj II IN
PSI lnj II OUT
L I l 1 JL I l l 0800 OUT
0 5 10 15 20 25 30 35 40
'PEAK WA)

Figure 2: The space charge regime, defined by the scaling factor k, in which SIR can operate is
displayed In shaded red. The value of the scaling factors for other machines
described in section 1.1 are represented by horizontal lines. The tag IN refers to
the first revolution in those machines, while the tag OUT refers to the last
revolution.

10

o The voltage rating of the power supply driving the dipoles in the ring limits the
maximum magnetic field achievable, resulting in a maximum H2+ beam
energy of 28 keV.

0 As discussed in chapter 7, the beam lifetime is shorter when the energy is
lower (i.e. higher electron capture cross-section). The beam also becomes

more susceptible to residual magnetic fields for energies below 15 keV.

The horizontal lines in Figure 2 represent the value of the scaling factor
(k) at which some of the machines described in the previous section operate.
The operating parameters of the PSI Injector II when the beam is first injected
and right before extraction are listed in Table 2. These parameters are used to
calculate the scaling factor (k). The peak current necessary in SIR to have the

same scaling factor is then calculated.

 

 

 

 

 

 

 

 

 

 

Parameter (2?; ItnLir '1') SIR Sign?) SIR
lon H+ H2+ H” H2+
q 1 1 1
m 1 2 1 2
E (keV) 870 20 72000 20
13 4.3-10‘2 4.6103 0.37 4.6103
7—1 09-103 1.1-10'5 7.7-10‘2 1.1-10'5
RA, (m) 0.41 1.05 3.5 1.05
h 10 1 10 1
w/c (m“) 0.105 4.4-10‘3 0.105 4.4-10‘3

 

 

 

 

 

 

 

11

 

 

 

 

 

 

 

 

 

 

 

 

 

 

k [_e__3_;_14] 1.72105 172-105 119-105 1.19-105
MPROTON -C m
1,, (pA) 2103 293-102 2103 203-10:2
Lam. (cm) 1.5 1.5 1.5 1.5
[PM (0A) 34104 12.9 2.0105 8.9
73%, (ns) 1.16 10.88 0.14 10.88
BWMIN 602 MHZ 64 MHZ 5.18 GHZ 64 MHZ
me, (e) 025-109 088-106 025-109 060-106
PAV 1.74 kW < 1 mW 144 kW < 1 mW

 

Table 2: Comparison between main parameters of SIR and the PSI Injector ll. Parameters of a
bunch in SIR (column 2) are such that the space charge forces experienced are
equivalent to those felt by a bunch with the parameters listed in column 1 during its
first revolution in the PSI Injector ll cyclotron. In a similar way, the last revolution of
the beam in PSI Injector ll (column 3) is compared to SIR in column 4.

A 20 keV H2+ bunch with peak current equal to 12.9 uA, in SIR, will
experience the same space charge forces as the 870 keV H+ 34 mA peak current
bunch when it is first injected in the PSI Injector ll cyclotron. A lower peak current
in SIR (8.9 pA) is enough to emulate space charge forces before extraction of the

cyclotron (72 MeV).

1.4. Advantages of SIR

When Eduard Pozdeyev and Felix Marti started studying the effect of
space charge forces in the isochronous regime, the possibility of using the PSI

Injector ll cyclotron to validate the computer simulations was considered. It soon

12

became apparent that building a small ring that would work in the same space

charge regime had many advantages. Some of them are enumerated below:

TIME RESOLUTION

The time resolution of the diagnostics necessary to characterize the beam
longitudinally strongly depends on the energy of the beam. For example, to be
able to measure the longitudinal profiles of ~ 1.5 cm long bunches (140
picoseconds) after they are extracted from the PSI Injector II, the bandwidth

(BWMN) of the electronics should not be lower than 5.2 GHZ since:

0.35

MIN =
0:5 ' TBUNCH

Justification of this relationship can be found in [8]. Even though, fast
Faraday cups with 6 GHZ bandwidth have been reported [9], they would not be
appropriate for the required beam power.

On the other hand, 64 MHz bandwidth is enough to have the same
resolution in a low energy and low current machine like SIR operating in the
same space charge regime.

BEAM POWER

The beam power extracted from the PSI Injector II is as high as 144 kW.
The duty cycle could be lowered thus reducing the total beam power either by
pulsing the injected beam or the extracted beam. Fast Faraday cups capable of
handling 4 kW are available [10] but their bandwidth is not large (2 GHZ).

In contrast, the beam power in SIR is so low that cooling is not required.

13

AVAILABILITY

Machines like PSI are routinely overbooked and getting beam time to
perform beam dynamics studies is very difficult.

FLEXIBILITY

As described in the previous section, the space charge regime that can be
studied with SIR cover a large region, even to regimes where no other machine
operates.

Bunches can also be extracted after a variable number of turns providing
a unique opportunity to study the time evolution of the bunches instead of only

obtaining a final picture when the beam is extracted from the PSI Injector II.

1.5. Objectives of SIR

Analytical treatment of the beam dynamics of space charge dominated
beams is a complex problem. The few models available are frequently overly
simplistic and are not able to accurately describe the physics involved. It is often
necessary to use numerical calculations to reproduce the behavior observed in
the beam. These computer codes have to calculate the ions trajectories in
external magnetic and electric fields. They also have to include the electric field
produced by the rest of the charge distribution in the bunch.

The number of ions (N ,0”) in a typical bunch when it is injected into the

PSI Injector ll cyclotron is given by the expression:

1 l

N _—'Q ___I -T _ [AV‘ZII'RAV‘LBUNCH
IONS " e BUNCH — e PEAK BUNCH _

I
e h ' LBUNCH C ' fl

 

14

where QBUNCH is the total charge of the bunch, Team: is the length of the bunch in
time, c is the speed of light and ,6 is the relativistic beta factor. Using the known
values for these parameters listed in Table 2, we can determine that
NW =0.25-109.

Even modern computers are not able to exactly calculate the electric field
produced by such a large number of ions and to track their beam trajectories.
Some assumptions need to be made. Different codes will treat the problem
differently. Macroparticles are used to represent a large number of ions
significantly reducing the computational time. The vacuum chamber geometry is
simplified (i.e. the image charges are not accurately described). The space
charge electric field is not calculated at every macroparticle position; instead it is
calculated in a reduced number of points and then interpolated for every
macroparticle.

In order to determine if these assumptions are reasonable, the results of
the simulations must be validated with experimental measurements. SIR can be
used to confirm that the simplifications used by different codes are reasonable.

As described in section 1.3, the space charge effects approximately scale
with beam current and energy. Therefore, it is also expected that effects that are

observed in SIR can be directly extrapolated to larger machines.

15

1.6. Brief description of the contents of the rest of
the chapters

Chapter 2 is devoted to the injection line of SIR. The requirements and the
general layout of the line are discussed before each of the elements is
individually described. The chapter closes with a discussion on the beam
dynamics in the injection and other injection schemes that were also considered.

The extraction line elements: deflector plates and the two fast Faraday
cups used to measure the longitudinal beam profiles are described in chapter 3.
The electronics and control system of SIR are discussed in chapter 4.

Different sources of beam variability in the injection line and their impact
on the beam matching are analyzed in Chapter 5. A partial characterization of the
ion source is presented in chapter 6. The results of the experiments conducted to
determine the beam lifetime for different gas pressures in the ring and different
beam energies are shown in chapter 7.

The results of the beam dynamics simulations performed with CYCO are
presented in chapter 8 and 9. Some preliminary considerations (such as an
analysis of the stability of the code and methodology used to do the analysis of
data) are included in chapter 8. The dependence on space charge effects of
beam parameters (such as emittance and peak current) are discussed in chapter
9.

Some of the space charge related measurements performed in SIR are
presented in Chapter 10 where they are also compared with the results of the

simulations.

16

2. INJECTION LINE OF SIR

2.1. Introduction

This chapter describes the injection line of the Small lsochronous Ring.
The chapter starts with a section where the requirements of the injection line are
enumerated and discussed, followed by a general description of the line after
which each element is individually described. The chapter closes with a section
where the beam dynamics in the line is described and a discussion about other

injection schemes that were also considered.

2.2. Requirements

IONS vs. ELECTRONS

The decision to use ions was made early in the project. Due to their larger
mass, ions are much less likely to be perturbed by residual magnetic fields than
electrons with the same energy. (Keeping the energy low was important to
accentuate the space charge forces.)

Using ions has some disadvantages. They are more difficult to produce
and the gas flow from the source raises the pressure in the ring reducing the
beam lifetime. A multi-cusp ion source was borrowed from Lawrence Berkeley
National Laboratory. This source was capable of producing the desired H“ and
Hi beam currents. The pressure in the ring due to the gas flow from the source

and its effect in the beam lifetime were estimated (see section 4.7 of [3]). The

17

results showed that the beam lifetime would be long enough to observe the
desired space charge effects. Lifetimes measurements that confirm these

estimates (see chapter 7) have been performed.

ENERGY

It was determined that the optimal beam energy to observe the desired
space charge effects was 20 keV. The injection line and the ring were designed
to handle Up to 30 keV H2+ beams to be able to characterize the beam energy

dependence of space charge effects.

TRANSVERSE BEAM PROPERTIES

The transverse structure of the injected beam had to be matched to the
closed orbit solution of the ring. (I.E. the injection point (x0 and yo) and the (xx, ay,
8,, and B, of the beam were fixed). The injection line had to be able to shape the
beam coming from the source to match the injection parameters. The beam
emittance (< 50 IT mm mrad) is significantly smaller than the dynamic aperture of

the ring. Refer to section 3.2.2 of [3] for a discussion of this issue.

LONGITUDINAL BEAM PROPERTIES
With respect to the longitudinal beam structure, bunches as short as a few
centimeters and as long as the length of the circumference of the ring with no

energy spread had to be injected.

BEAM CURRENT

18

The peak beam current of the bunch had to be accurately determined and
should be able to be as large as 40 [JA to cover the current range in which the

desired space charge effects were expected to appear.

PRESSURE IN THE RING

It was estimated in page 131 of reference [3] that the pressure in the ring
should be below 10‘7 Torr for the lifetime of the beam to be long enough to see
the space charge effects predicted by the simulations. Since the pressure in the
ring is mainly determined by the gas flow from the ion source, the injection line
length, vacuum pipe diameters and distribution of the turbopumps along the line

are critical to determine the final pressure distribution in the machine.

OTHER REQUIREMENTS

There were also other restrictions that were not related to the physics of
the problem to be studied. The whole machine had to fit in the room that was
assigned for the project and the cost of the injection line had to be kept as low as

possible.

2.3. General Description

Figure 3 shows a schematic view of the injection line of SIR where the
different elements and their relative positions are listed. Figure 4 shows a picture
of the injection line.

A multi-cusp ion source is used to produce a beam that includes H“, H2+

and Hi ions. The energy of the beam is defined by the bias voltage of the

19

source. An Einzel lens follows the source and is used to focus the divergent
extracted beam. The puller of the source is used as the first ground electrode of

the lens.

 

 

  
  

   

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

SOURCE I L
In I E o
z '_ n. l—
Ill 0 3 U
..I — m 0 m
“' a s d
E a 5
E 3 no:
. l "- :I: z
I I 53%
m" “ O. In
I ”’3 I ., Sifigte
' §n EMITTANCE h-
i m MEASUREMENT u _
1‘ "’ SYSTEM

Figure 3: Schematic top and side view of the injection line of SIR.

The first two pairs of steering plates are located after the Einzel lens. A set
of identical plates is located in the emittance measurement box. These plates
can be used to steer the beam in both planes to correct for misalignments in the
injection line and perturbations of the beam trajectory due to residual magnetic

fields.

20

A dipole magnet located in between the two sets of steering plates is used
to separate the different ions. The magnet is identical to those used in the ring. A
complete description of the design can be found in page 91 of reference [3].

There is a diagnostic unit right after the dipole magnet. It consists of two
pairs of movable slits. Each pair lays in either the vertical or horizontal plane and
the slits are followed by a shielded Faraday cup to collect the beam current that
passes through. A map of the x-x' or y-y’ phase space can be captured by
moving the slits and measuring the beam current. Fitting the data to an ellipse,
the Courant-Snyder parameters [defined in page 49 of reference 11] at that
position can be determined. These data can also be used to measure the beam

emittance completing the transverse characterization of the beam.

{3’ i ‘
- . 2.-
' V‘J‘

    
  
  

. i .

Einzel Lens

   

1Thar 7 I; T
I -. Steering Plates ' , “
\ '~_ .‘ ~ W ; :3: .
I i W . 7 ,g ‘7 I. I, , . _, _- . ‘
‘ - Quadrupole if“ ‘f ‘
triplet .. “E :
1““— I I . . Mass
7 ‘y‘

«l Chopper ‘11.
i \

Inflector {‘1 )1. _‘ ‘ ' _, 4
Plates ,, K . ' ' ' ' ‘ _
1 ‘ 3 ‘ ~ ‘4 fl’ - Emittance
I \ Q.
1‘ .- Measurement
‘ \ \ System

" “/“T Faraday Cup ,

4""
“1' — " 4 “4|: ,

     
 
  

     
  

     

Figure 4: Picture of the injection line of SIR.

21

A triplet of electrostatic quadrupoles right after the emittance
measurement system is used to match the beam to the closed orbit solution of
the ring. Since four independent parameters must be adjusted (ax, ay, Bx and By),
the Einzel lens is also used.

The quadrupole triplet is followed by a chopper. The chopper consists of
two electrostatic plates that are pulsed to high voltage when the beam is
chopped and grounded when the beam is injected.

The first pair of inflector plates follows the chopper. These plates deflect
the beam 17.5° toward the ring. As an alternative, the inflector can be turned off
to let the beam go straight toward the shielded Faraday cup located at the end of

the injection line where the beam current can be measured.

2.4. Ion Source

A filament driven multi-cusp ion source is used to produce the beam.
Pictures of the source can be seen in Figure 94 and Figure 103. This source
was borrowed from Lawrence Berkeley National Laboratory. More information
about this and similar ion sources can be found in [12] and in page 203 of [13].

Hydrogen is injected into the source from a side port. The flow of
hydrogen is controlled using a needle valve and monitored by a Pirani gauge
installed in the gas line. The typical working pressure inside the source is in the
range of 1 to 10 mTorr depending on the desired extracted current.

Current from the filament power supply (~ from 35 A to 50 A) is passed

through a thoriated molybdenum filament made out of a welding rod. The

22

filament warms up emitting electrons. A voltage difference (~ 100 V) between the
filament and the rest of the source maintained by the arc power supply,
accelerates the electrons toward the walls of the source. In this process, they
collide with hydrogen molecules knocking out electrons and forming the plasma.
Some of the ions in this plasma will eventually move toward the plasma electrode
where the electric field between source and puller will extract some of them
forming the beam. The energy of the beam will be defined by the potential
difference between the source and ground.

Figure 5 shows the schematics of the wiring of the source. The ion source
and the associated instrumentation are all biased to the same high voltage of the
source. An isolation transformer provides the necessary ac power for these
instrumentation. A safety interlock system, designed by D. Pedtke from the
electronics department at the NSCL, turns off the power to the transformer and
the high voltage power supplies if the door of the high voltage cage, where
everything is enclosed, is opened. It also grounds the whole system using a high
voltage relay. The high voltage is monitored using a high voltage probe. The
value of the voltage is displayed next to the door of the cage. A red light also
warns the user when the high voltage is on.

As a redundant safety precaution, every time the door of the cage is
unlocked, the high voltage sections are manually grounded using a grounding
rod. In addition to the safety interlock, there is another interlock to protect the
source from failures in the cooling system that turns off the ac power of the

filament power supply if the temperature of the source rises too much.

23

 

 

 

 

 

 

DC OUT

 

AR
POWER
SUPPLY

ACIN

 

 

 

A

 

 

 

 

 

 

 

 

 

 

 

 

 

AC OUTI ::

ISOLATION

TRANS
FORMER
AC 1N

 

 

 

 

A

 

HV PROBE

A
‘

 

 

 

DC OUT
HNZEL HV
POWER
SUPPLY
AC IN

 

 

 

 

A _+

 

 

& LIGHT

 

 

 

 

- GROUNDED EEIMENTS
- HIGH VOLTAGE EI.ENIENI'S

 

 

I INSULATORS

 

 

 

 

+

Figure 5: Wiring diagram of the ion source and its associated electronics.

24

Refer to chapter 6 for a characterization of the source where extracted
current, emittance of the beam and relative abundance of different mass species

for different conditions in the source are discussed.

2.5. Einzel lens

An Einzel lens (Figure 6) is used to focus the beam coming out of the
source. When the beam is extracted, it has a large angular divergence and, in

absent of strong focusing, it would be lost.

 

Figure 6: Picture of the Einzel lens and puller of the ion source used in the injection line of SIR.
The Einzel lens consists of three different electrodes. The first one is a
stainless steel cylinder that is attached to the modified 8" flange that holds the

25

whole structure. The second one is an aluminum cylinder with three wings that is

biased to high voltage. The third electrode is also made out aluminum. It is

grounded and it is used as a puller of the source. The three electrodes are
positioned and aligned by three macor spacers and clamped together with three
screws.

A polyethylene insulated cable (rated to 40 W) is used to connect the pin
of the high voltage vacuum feedthrough and the high voltage electrode of the
Einzel lens. An alumina tube is used around the pin to increase insulation.

Figure 9 shows a picture of a previous version of the Einzel lens. Some of
the problems that were found with it and later solved in the final version are:

. The distance between puller and the flange that holds the ion source was
increased. The distance between the high voltage Einzel lens electrode and
the puller and ground electrode were also increased. On some occasions,
sparks were produced when the source and/or the Einzel lens were biased to
maximum voltage (30 kV). It was determined, that the distance between
electrodes could be increased, thus decreasing the electric fields in the
surfaces, without compromising the performance.

. The aperture of the puller was increased. It was believed that some of the
sparks could be triggered by electrons emitted from the surface of the puller
when they were hit by the extracted beam. A larger aperture also decreases
the chances of dust from the filament of the source depositing in the surface

of the puller that would likely trigger sparks.

26

o The six macor spacers that were used to separate and align the puller, high
voltage electrode of the lens and ground electrode were perturbing the
electric field of the Einzel lens. This perturbation was generating a three-fold
symmetry in the beam that could clearly be observed in the phosphor screen.
The spacers were electrically hidden from the beam in the new design by
displacing them further away from the beam axis and behind the high voltage

electrode.

Puller (0 V)

Grounded
Flange (0 V)

lon Source Einzel lens HV
(20 kV) electrode (16.5 kV)

 

Figure 7: Simion model of the Einzel lens and source extraction region of the injection line of SIR.
Equipotential lines are shown in red. Several ions were tracked and their
trajectories are displayed in black.

Simulations were performed to minimize the non-linear effects introduced
in the beam by the Einzel lens. Calculations of the electric fields and tracking of

particles were performed using SIMION [14]. Figure 7 shows the equipotential

27

lines (in red) when the source is biased to 20 kV and the high voltage electrode
of the lens to 16.5 kV. We can also see the focusing effect of the Einzel lens in
the ion trajectories (in black).

The focusing distances for different voltages in the lens were calculated
for 20 keV ions entering the lens at different distances from the beam axis. The
results are shown in Figure 8.

It can be observed that the focusing distance depends on the distance to
the beam axis when entering the lens. This dependency denotes the presence of

some non-linear effects despite the effort to minimize them.

 

 

 

 

 

 

 

 

140 Y I I V U T r U
120- '
100- 34 . -
0 1mm
V 3mm
A 80- .
E 32f I 5mm '
U.
60' 0 7mm ‘
30 1.
40- .
20' -
0 l L l l l I l I
4 6 8 10 12 14 16 18 20 22

VON)

Figure 8: Focusing distance of the Einzel lens when biased to different voltages for a 20 keV
beam. The picture was expanded for 10 W. The non-linear effects of the lens can
be observed in the dispersion of the focusing distances for ions entering the
source 1, 3. 5 and 7mm away from the beam axis.

28

2.6. Steering

Two pairs of Oxygen Free High Conductivity (OFHC) copper plates are
used to steer the beam in both planes. They are located right after the Einzel
lens (Figure 9) and before the mass separator. Two more pairs of identical plates
located inside the emittance measurement box in between scanning slits are also
used.

The length of the plates is 9 cm, the width is 8.9 cm and their thickness is
1.3 cm. They are separated by 5 cm and the gap between plates with different

polarities is 6 cm.

  

Macor Spacers

Old Puller

Old Einzel Lens

 

 

Einzel Lens
high voltage First Pair of
feedthrough Steering Plates

 

 

 

Steering Plates

high voltage
feedthroughs

Second Pair of
Steering Plates

 

 

 

Figure 9: Picture of the first two pairs of steering plates in the injection line of SIR. An old version
of the Einzel lens and puller can be seen in top of the 8' flange that supports the
whole structure.

29

Each plate is positioned with respect to the stainless steel frame that
supports them by two alumina washers and held with screws. The head of the
screw is electrically insulated from the frame by alumina washers. Kapton coated
coaxial cables run between the head of the screws and the pins of a Miniature
High Voltage (MHV) vacuum feedthrough.

The purpose of the steering plates is to have the capability to correct the
beam orbit if it is perturbed by residual magnetic fields or misalignments of the
different optical elements. The plates are capable of deflecting a 30 keV beam by
i 65 mrad when biased to :l: 1 kV.

Besides the four pairs of plates mentioned before, the inflector plates and
the bending magnet can also be used for steering purposes. The current of the
injection line magnet can be changed independently from that of the magnets in
the ring. The voltage in the first and second pair of inflector plates can also be

adjusted separately.

2.7. Mass Separator

A dipole magnet, identical to those used in the ring, is used to select one
of the three mass states (H*, H; or H3") produced by the ion source (Figure 10).
Refer to section 4.2 and 4.3 of [3] for a complete description of the magnets.

The magnet is located in between the first set of steering plates and the

emittance measuring system.

30

A non-relativistic ion with mass m , charge q and energy E will describe a
circle with radius R when injected in a magnetic field B perpendicular to its

momentum.

JZ-m-E

q-B

R:

The relationship between the curvature radius of the trajectories of two

ions with the same charge and energy can be written as:

12:120. [ml
0

 

Figure 10: Picture of the mass separator used in the injection line of SIR.

31

In our case, the dipole bending radius is 45 cm for the beam that is
selected. The bending radii for different ions are listed in Table 3.

Figure 11 shows a graphical representation of the trajectories of ions with
different masses and their collision point with the beam vacuum chamber. It can

be seen that every mass species can be clearly separated from the others.

 

Selected mass

H+ H2+ H3+

 

 

H+ 45.0 31.8 26.0

 

H; 63.6 45.0 36.7
Ha+ 77.9 55.1 45.0

Radius of
Curvature
(cm)

 

 

 

 

 

 

 

 

Table 3: Radius of curvature for different mass species in the mass separator of the injection line
of SIR when the H‘, H; or H; species is selected.

 

I H+ when H; is selected I

 

 

I H+ when H; is selected I

 

 

 

\ Vacuum
Chamber

I Hz" when H3+ is selected I

  

 

R I H,“ when H‘ is selected I

-\ e
beam \I H; when H" is selected I

K I H; when H; is selected I

 

 

 

 

 

Figure 11: Selection of ions with different masses in the mass separator of the injection line of
SIR.

32

2.8. Emittance Measurement System

A diagnostic box located between the mass separator and the quadrupole
triplet is used to characterize the beam transversely (Figure 12). It consists of two
pairs of scanning slits that can be moved in the vertical or horizontal plane. The
second slit of each pair is followed by a shielded Faraday cup to collect the

current that makes it through both slits.

 

Figure 12: Picture of the emittance measurement system used to transversely characterize the
beam coming from the ion source.

33

This system can be used to get information about the transverse phase
space of the beam. The first slit lets a fraction of the beam with a well defined
position go through. Of this fraction, just that portion with a well defined angular
range will go through the second slit and be collected in the Faraday cup.

This information is used to readjust the Einzel lens and the quadrupole
triplet to match the beam to the closed orbit solution of the ring when it is
injected.

The system can also be used to measure transverse beam profiles if the
first scanning slit is retracted and just the second one is used.

The scanning drives were already available at the NSCL. Each of them
consists of a copper frame that holds a molybdenum slit. The copper frame is
soldered to a modified 2 ‘74” flange. This flange is attached to a nipple held by an
ISO-160 flange. In between the two flanges, a welded edge stainless steel
bellows is used to allow the linear motion of the copper frame. A shaft, which can
be moved by a stepper motor, is used to push the copper frame in and out.

A shielded Faraday cup is mounted behind the copper frame of two of the
scanning drives. The current collector is attached to a G-1O piece. A copper ring,
that can be negatively biased to act as an electron suppressor, is mounted on
ceramic balls that rest in the current collector.

The diagnostic box that contains the scanning slits was designed to
position them in an optimal way. The typical size of the beam at the first slit
position is ~ 1 cm diameter and its envelope typically goes through a waist at this

point when shaped for ring injection. If the beam emittance is equal to 50 11 mm

34

mrad, and the first slit is positioned in the beam axis, the angle dispersion of the
surviving beam will be 1:10 mrad. Since the distance between slits is 47.5 cm, the
beam diameter in the second slit will be 9.5 mm (approximately the size in the
first slit).

The aperture of the slits is 0.5 mm. For a 10 uA beam with the previous
characteristics, we can expect beam currents of ~ 25 nA to go through both slits.
If the aperture of the slits were reduced, the collected currents would be much
smaller approaching noise level. If the aperture of the slits were enlarged, we

would lose resolution of the measurements.

2.9. Quadrupole triplet

An electrostatic quadrupole triplet is used to shape (together with the
Einzel lens) the beam transversely so that it is matched to the closed orbit
solution of the ring by the time it reaches the injection point (Figure 13 & Figure
14). It is positioned in between the emittance measurement system and the
choppen

The length of the first quadrupole is 10.5 cm, the length of the second is
14 cm and the length of the third is 6 cm. The distance between them is 9 cm
and the distance from beam axis to electrodes is 3.5 cm. The traditional
hyperbolic shape of the electrodes was substituted by a circular shape to simplify
the machining. lts curvature radius is 4.04 cm (= 1.15 x 3.5 cm) to best
approximate the required fields. Simulations where ions were tracked in the

calculated 30 fields showed a negligible effect of this modified geometry.

35

Each electrode is positioned with respect to the stainless steel frame that
supports them by two alumina washers and held with screws. The head of the
screw is electrically insulated from the frame by alumina washers. A Kapton

coated coaxial cable runs between opposite electrodes of the same quadrupole

and from one of them to the pin of a MHV vacuum feedthrough.

First Pair of
Quadrupole 2 Chopper lnflector Plates

    

Quadrupole 1 Quadrupole 3

Figure 13: Picture of the quadrupole triplet, chopper and first pair of inflector plates held by a
support frame before being assembled in the injection line of SIR.

 

Figure 14: Picture of the triplet of electrostatic quadrupoles used in the injection line of SlR.
36

Each pair of opposite electrodes can be individually biased (i.e. the
voltage of the three quadrupoles can be chosen independently from the others).

Ions were tracked in the calculated 30 fields using SIMION to calculate
the focusing distance (in the focusing plane) for different voltages in the
electrodes of each of the quadrupoles when the others were turned off. The
results are shown in Figure 15. The different colors correspond to each of the

quadrupoles.

 

100

 

 

 

 

80

I

60

F (cm)

40

l

 

l l

200 400 600 800 1000
V (V)

 

 

 

Figure 15: Focusing length for a 20 keV beam of the three quadrupoles used in the injection line
of SIR.

2.10. Chopper

37

A pair of OFHC copper deflector plates that are pulsed by fast high
voltage switches are used to chop the dc beam coming from the ion source into
bunches of different lengths (Figure 16). The length of the plates is 5 cm and the
gap between them is 4 cm. When the plates are biased to high voltage, the beam
is deflected in the horizontal plane (parallel to the medium plane of the ring)
hitting the vacuum chamber. When plates are grounded, the beam trajectory is
not perturbed and the beam is injected in the ring.

The chopper is located immediately after the quadrupole triplet and before
the first pair of inflector plates. It was placed as close to the injection point as
possible to minimize the energy spread induced by longitudinal space charge

forces in the drift space between chopper and injection point.

 

Figure 16: Pictures of the system used to chop the beam in the injection line of SIR.

38

Each of the deflecting plates is positioned with respect to the stainless
steel frame that supports it by two alumina tubes and held by two screws inside
the alumina tubes. The head of the screws are electrically isolated from the steel
frame by alumina washers. The high voltage is carried from the pins of MHV
vacuum feedthroughs to the chopper plates by Kapton coated cables surrounded
by alumina beads to add electrical insulation (cable insulation is rated to i: 2 kV).

Originally just two deflecting plates were planned. But, the extension of the
fringe field of the plates makes the length of the head and tail of the bunch fairly
long. lons are perturbed by the electric field of the chopper long before they
reached the plates.

We define the head and tail of the bunch as the parts of the bunch whose
ions have received a transverse kick that is not enough to completely deflect
them and they are still injected in the ring. Part of this effect is due to the rise
time of the high voltage pulse (< 25 ns). Although, even if the rise time were
much smaller, some of the ions, that are already in the chopper when the high
voltage is turned on, will not receive a full transverse kick. They need to enter the
chopper when the full voltage has already been reached to receive a full kick.

To limit the extension of the fringe fields of the deflecting plates, two
frames were added next to the plates. The gap between the plates and the
frames is 0.5 cm. Molybdenum grids with 90 % transparency are attached to the
frames and held by clamping rings pressed by two set screws.

To determine the length of the head and tail of the formed bunches,

several transverse beam profile measurements were made using the horizontal

39

scanning wire located right after the first dipole of the ring. The objective of these
measurements was to determine the value of the kick needed to make the beam
hit the vacuum chamber and not be injected in the ring. In this experiment, the 20

keV Hf beam was not chopped.

 

 

 

 

 

l(pA/mm)

 

 

 

Figure 17: Transverse beam profiles measured with the first horizontal scanning wire for different
voltages in the chopper. When the plates are biased to more than t600V, the
beam is deflected and is not injected.

The transverse profiles resulting from these measurements are shown in
Figure 17. The different profiles correspond to different voltage values in the
chopper. When the voltage is 0 V, the beam profile corresponds to the central
part of a bunch. As the voltage is increased, different parts of the head and tail of

the bunch can be observed. By the time the voltage of the plates reaches 1 600

40

V, the beam has almost completely disappeared. It hits the chamber before being

 

injected.
200 I I f I I I I I
‘ —— Ey (V 1 mm)
175 —s— Def Angle (mrad)
150

.L
N
0'!

 
     

Ey(V/mm)
‘1
0|

Deflection Angle (mrad)
or 8
O o

I-I-n_--—o-I-c—-

.

N
U"

D

o-I-an-u-n—n-u—n-c-n-r

 

O
r

 

 

  

 

 

  

 
     

I-l-I—o-n-t-v-I-o

-o-I—I-I-I-n-u-r-
‘

 

 

100 125 150 175 200
Time (ns)

Figure 18: The deflection angle of a 20 keV H; beam as it goes through the chopper is plotted in
black. The value of the electric field in the center of the chopper at the time the
ions get there is plotted in red.

Simulations were performed using SIMION to calculate the electric field

inside the chopper. It was determined that when the chopper plates were biased

to 1: 3500 V (maximum voltage the fast high voltage switches can generate), a

beam with 20 keV energy was deflected by 185 mrad. So, since the tangent of

the deflection angle is proportional to the deflecting voltage

tan (6“! ) = VL - tan (0:: )

max

41

we can conclude that if ions are deflected by 29 mrad or more when they go
through the chopper, they will not be injected in the ring. This value is also
consistent with the geometry of the vacuum chamber.

For this particular beam (Hi, 20 keV) simulations were performed using
SIMION to calculate the electric field and to track ions in this field. The chopper
plates were biased to a voltage of t 3500 V for 30 ns. Then, the voltage went
down linearly to zero in another 30 ns. It was left equal to zero for another 100 ns
and then the voltage was ramped up to i: 3500 V in another 30 ns. The deflection
angle of ions arriving to the center of the chopper at different times was
calculated. Figure 18 shows, in black, the deflection angle of those ions and, in
red, the value of the transverse electric field when they reach the center of the
choppen

Those ions that reach the center of the chopper early enough (t s 10ns)

will exit the chopper before the voltage starts ramping down receiving a full 168
mrad transverse kick.
Those ions that reach the center of the chopper later in time

(Ions s t 3 30m) will start feeling the ramping down of the voltage before they

leave the chopper, even though the voltage in the plates was still the maximum
voltage when they went through the center of the chopper.

In the same way, some ions will still receive a transverse kick, even if the
voltage in the plates is off by the time they reach the center of the plates, if there
was still some field left when they got in the chopper. These are the ions that will

form the head of the bunch. A similar argument explains how the tail is formed.

42

As determined before, ions that receive a kick larger than 29 mrad will not
be injected into the ring. The horizontal dashed lined in Figure 18 represents this
level. With this information, the length of the head and tail for a 20 keV Hz" can

be determined. We can expect it to be ~ 16 ns long.

 

 

 

 

 

 

 

 

 

 

20
:3: 18
.C
E”
2 16
E
1:3 14
a
8
f 12' —-n— H+ .
-a— H;
1 I- + 4
° _._ H3
10 14 18 22 26 30

Energy (keV)

Figure 19: Length of the head and tail of the bunches produced by the chopper for different ion
masses and energies.

In the hard edge approximation and for small deflecting angles, the
deflection angle 6"" of an ion with mass m, charge q and energy E entering
the chopper at a time t can be written as

Eq. 2

tan (6” ) = q HINT) - d 2'

g-s/Z-m-E,

 

43

where T a Leg - Em—E is the time it takes to go through the chopper, Le], is the

effective length of the plates and g is the gap between chopper plates.

(1.1/Le”

When the voltage is time independent, the traditional tan (674"f )= —
g

 

MI—

is derived from Eq. 2. In our case, the deflecting angle will depend on both the
ion energy and mass. Using Eq. 2 with a maximum deflection angle equal to 29
mrad and effective length of the chopper equal to 4.5 cm (to reproduce the
deflecting angles previously calculated for a 20 keV Hz” beam), we can estimate
the dependence of the length of the head and tail of the bunch for different ion
mass and energy (Figure 19).

From this figure we can conclude that the chopper would be capable of
producing bunches as short as 40 or 50 ns. However, the shortest length is
limited to 100 ns by the width of the pulses generated by the digital delay line that
triggers the high voltage fast switches.

The high voltage fast switches are capable of injecting bunches with a
repetition frequency higher than 30 kHz but the maximum output current of the
high voltage power supplies that feed them (3 mA) limits the maximum frequency

to ~ 1.5 kHz.

44

2.11. lnflector Plates

Two pairs of OFHC copper plates deflect the beam toward the ring. The
first pair is located right after the chopper (Figure 13). The second pair is located
in between two of the dipoles in the ring (Figure 20).

The geometry of both pairs is identical and it is designed to deflect a 30
keV proton beam by 17.5° when they are biased to :t 3.5 W. The lengthwise
wings of the plates are meant to increase the region where the electric field is flat
therefore minimizing nonlinear effects in the beam. Bending one of them
increases the clearance between beam and plate. The most important

dimensions of the plates are specified in Figure 21.

 

 

Figure 20: Picture of the second pair of lnflector plates located in between two of the dipole
magnets of the ring.

45

,3
5.3
/ 11.2 -

OO

 

 

 

 

 

 

 

 

,1
.__1t
‘fil
m (.0

’1
d

 

 

 

 

 

 

N O :
o h' :BEAM AXIS
_ 16.5 .1
It '1
l ------------------------ . r q
I

 

 

 

Figure 21: Front and side view of the lnflector Plates where main dimensions (in cm) are
specified.

2.12. Injection Line Faraday Cup

A shielded Faraday cup located at the end of the injection line is used to
accurately measure the peak beam current injected in the ring. The chopper and
the lnflector that deflect the beam toward the ring are turned off and a
picoammeter is used to determine the dc beam current. Since the beam is not
bunched when it is injected (i.e. very small energy spread), the measured dc
current is identical to the peak beam current of the chopped beam.

The Faraday cup consists of three metallic pieces supported by an 8" CF
flange (Figure 22). The current collector of the Faraday cup is a disc made out of
OFHC copper. A 5 mil thick Kapton foil is used to electrically insulate it from the
flange. The aluminum ring next to it acts as an electron suppressor when biased

negatively. It reflects the low energy (< 100 eV) secondary electrons emitted by

46

the collector when the ion beam hits it. The accuracy of the measurement can be
guaranteed by verifying that no beam hits the second ring that acts as a shield.

The disc and the rings are aligned and electrically isolated from each other
by alumina balls in between them. Four screws are used to clamp everything
together. The screw heads are electrically insulated from the shield by alumina
washers. Kapton coated cables are used to connect the different electrodes to
the BNC vacuum feedthroughs.

The Faraday cup can also be used to verify that the beam is centered in
the beam axis and that its size is reasonable (first step to match the injected

beam to the closed orbit solution of the ring).

Kapton Coated
Cables

   
    

Shield
Electron Suppressor

Figure 22: Picture of the Faraday cup at the end of the injection line of SIR.

47

2.13. Beam Dynamics in the Injection Line

The first component of the injection line that was acquired was the ion
source. The first step before designing the injection line was to determine some
of its basic properties.

In particular, it was important to measure the extracted beam current to
verify that it was able to cover the range of currents necessary to explore the
expected space charge effects. Early measurements showed that the total
extracted current (including H+, Hz“ and Hg”) reached several hundred
microamps. It was determined by simulations that several tens of microamps of a
single mass state would be needed to be able to observe the clustering of the
bunches. The source, therefore, fulfilled the extracted current requirements.

It was also important to measure the emittance of the extracted beam. The
dynamic aperture of the ring and the injection line had to be large enough to
accommodate this emittance.

To design the injection line, it was equally important to have an
approximate idea of the transverse beam properties of the extracted beam (0 and
8 parameters). One of the requirements of the injection line is to be able to inject
beam that is transversely matched to the closed orbit solution of the ring. So, the
injection line should be able to shape the beam coming out of the ion source into
what is accepted by the ring.

In order to get this information, experiments were performed before the
injection line design was finalized. To do this, a preliminary version of the

emittance measurement system was assembled underneath the ion source and

48

the Einzel lens (the distance between the center of the lens and the first slit of the
emittance measurement system was 17 cm).

Different phase-space measurements were made with representative ion
source conditions, extraction voltages and Einzel lens voltages. Ions,
representing different points of the phase-space region where current was
measured, were tracked back through the Einzel lens to a point in between the
puller and the plasma electrode of the source. A snap-shot of the phase-space at
this point was determined and the beam transverse properties were taken as its

initial conditions (independent of the Einzel lens voltage).

150

 

    
   

. \ —--———--j

 

 

 

c I——————————_

Figure 23: Ions representing different points of the phase space (measured with the emittance
measurement system) were tracked back to the source and plotted in green and
blue. An ellipse representing this ensemble in red and variations on this ellipse In
black can be accommodated by the injection line and matched to the closed orbit
solution of the ring when injected.

49

An example of the results of these experiments is given in Figure 23. Two
different initial ensembles (corresponding to two different Einzel lens voltages but
with the same 20 kV extraction voltage and the same source conditions) are
plotted in green and blue. The agreement between both ensembles is reasonably
good. The small discrepancy between them can be explained by possible small
misalignments of the plasma electrode, puller and/or Einzel lens. The red ellipse

(6:50-7r-mm-mrad, a=—4.8, ,6=0.12m) was chosen as a conservative

representation of the extracted beam.

The injection line should not only be able to accommodate a beam with
the previous parameters but also significantly different ones:

0 The parameters determined before, correspond to a beam which is a
combination of H”, Hi and Hi. The beam parameters of the individual
mass states are expected to be different.

0 The conditions in the source (gas pressure, filament current...) and the
extraction voltage have a significant impact in the properties of the
extracted beam.

For these reasons, we could comfortably assert that beams with
significantly different transverse parameters (some of which are shown in black in
Figure 23) could be shaped properly and matched to the closed orbit solution of
the ring.

It was also verified that the size of the beam would never exceed the
acceptance of the hardware installed inside the beam line. To do this, the

injection line was first modeled using COSY Infinity [15]. Next, the voltages of the

50

Einzel lens and the quadrupole triplet necessary to match the chosen initial
ensemble to the closed orbit solution of the ring at the injection point were
calculated. Finally, the beam envelopes along the injection line were calculated

for the chosen initial ensemble and voltage values.

 

l m

 

DPOLE QUAEB INFLECTOR HATES

.7. _ _

 

ENZEL
LENS

 

lcm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 24: Envelope of the beam as it moves in the injection line of the SIR. The curve on top is
the vertical beam envelope (perpendicular to the medium plane of the ring). The
bottom curve corresponds to the beam envelope in the horizontal plane.

An example of the resulting horizontal and vertical beam envelope is
plotted in Figure 24. The envelopes shown are for a 20 keV, Hz",
8:50-7r-mm-mrad beam with initial a=—4.8 and ,6=0.12m. The upper red
curve in the figure corresponds to the vertical envelope (perpendicular to the

medium plane of the ring), while the lower red curve shows the horizontal

51

envelope. The positions of the different elements of the injection line relevant in
the beam dynamics are also specified.

COSY Infinity was used to model the first order beam dynamics in the
injection line of SIR. Even though COSY includes many functions to represent
different optical elements, it was determined that small corrections would have to
be introduced to better represent some of the elements of the injection line. A
description of the COSY model is discussed next.

The Einzel lens was modeled as a thin lens. To determine the relationship
between the Einzel lens voltage and its focusing strength, first the electric field of
the lens was calculated using SIMION. Then, an ion, which was radially
displaced from the beam axis, was tracked in that field and its focusing distance
was determined.

The dipole magnet was modeled as a dipole without edge focusing. A
correction to take into account edge focusing was added after ions were tracked
in the 3-D magnetic field produced by TOSCA [16] and a better matrix to
represent the fringe fields was calculated.

The focusing strength of the quadrupoles for different voltages was
calculated in a similar way as for the Einzel lens. Particles were tracked in the 30
electric fields produced by SIMION. Then, the voltages needed in the COSY
model to have the same focusing strength as in the SIMION model were
determined. (COSY uses a hard edge approximation to determine the focusing

strength. So, it always underestimates it.)

52

The lnflector plates have a focusing effect in the bending plane. The
focusing is due to the different time particles above the medium plane (positive
voltage) spend under the influence of the electric field compare to the time
particles below the medium plane (negative voltage). The longer time in the
electric field, the larger the deflection angle is. There is also a very weak focusing
effect in the transverse plane due to the wings introduced in the geometry of the
lnflector plates. The focusing strength was calculated, as for the other optical
elements, tracking particles in the 30 electric fields produced by SIMION.

These combined focusing effects were modeled in COSY as a thin lens
located in the center of the lnflector plates.

Snap shots of the beam ellipses (defining Y as the plane perpendicular to
the medium plane of the ring and X as parallel) at different points of the injection
line using the COSY model are shown in red in Figure 25. The two different
ellipses correspond to beams with different emittances (10-n-mm-mrad and 50-rr-
mm-mrad).

Particles were also tracked in the 3D fields produced by SIMION and
TOSCA along the whole injection line. They are shown in the same figure in
black.

It can be observed that the non-linear effects are especially important for
the 50-1r-mm-mrad case. To determine the sources of these effects, each

element was studied separately.

53

Ions, representing perfect ellipses in the phase space, were tracked
through each individual optical element. The results showed a negligible

contribution from all elements except the Einzel lens.

2.14. Other injection line schemes

Different injection line schemes were initially considered:

- Using a Wien filter instead of a dipole magnet to separate the different
mass states. This option was discarded mainly because of lack of space. The
overall length of the injection line would not be much longer than the one that
was finally used, but the 90° bending magnet allows a more efficient use of the
available space.

Using the same design for both the bending magnet and the ring magnets
was also a reason not to choose the Wien filter since the latter would have
required a larger investment in design.

- Using the chopper to deflect the beam toward the ring. The possibility of
using the chopper to deflect the beam toward the ring at the same time was
discarded because of the non-linearities that would have been introduced in the
beam.

As discussed in section 2.10, grids in both sides of the deflecting plates of
the chopper had to be added to limit the extension of the electric field. These
same grids introduce significant non-linearities in the deflected beam but not in
the one injected in the ring. It was, therefore, decided to separate the chopping of

the beam and the deflecting toward the ring.

54

 

1 Between source and puller
2 Between lens and dipole

3 At emittance measurement
4 Before quad 1

5 Between quad1 and quad2
6 Between quad2 and quad3
7 Before chopper

8 Injection point

15 ~15 §§ 15

40
5X

.15 ~40

10 60
W W

~60

1T)

.20

~20

a
O

 

 

25

 

 

. -u
-m -w

60 20
6Y 7Y 8Y
~25 25 ~15 15 -15 15
.60 ~20

Figure 25: Snap-shots of the phase space of the beam in the injection line. Ellipses using COSY
model in red. (Black in the 30 fields). Inner (outer) ellipses 10 (50) TI’ mm mrad.

 

 

 

 

55

 

- Aligning the injection line to the 17.5° injection angle instead of deflecting
the beam by that same angle. Even though this option would have reduced the
number of elements needed In the injection line eliminating the need for the first
pair of lnflector plates, the supports for the different elements of the injection line
would have been much more complicated.

- Injecting the beam radially. The dipole magnets in the ring extend radially
further away than vertically. In order to have enough clearance, a larger
deflection angle would be needed making the design of inflector plates more
challenging.

In addition, the drift between lnflector plates would also need to be longer
making it more difficult to find a good way to match the injected beam.

- Injecting beam from above or from below the ring. The decision to inject
the beam from above was made because the residual magnetic field at floor level
(probably due to magnetization of the reinforcing steel generated by the stray
field of other large magnets in the building) is larger in the region where the
injection line is placed than where the ring is. Raising the injection line reduces
the impact of the residual fields in the beam trajectory. If the injection line had
been lower, the medium plane of the ring would have had to be elevated.
Accessing the center of the ring for assembly or maintenance would have been
more complicated.

- Rotating the dipole magnet by 90° in such a way that the bending plane
would be parallel to the medium plane of the ring. Even though the source would

have been more accessible making the maintenance easier, the weight of the

56

source and gas feeding system would have needed an extra support. In addition,
this option would effectively use more room.

- Using a second Einzel lens as opposed to a quadrupole triplet. The main
advantage of this option is that the mechanical complexity of the quadrupole
triplet is much larger than that of an Einzel lens which would have been easier
and less expensive to build. The length of the injection line would also be
reduced and the alignment of the different elements would have been simplified.
On the other hand, adding a single extra Einzel lens would not give the same
degree of flexibility as a quadrupole triplet to accommodate different initial beam
ensembles. Four different parameters (ex, 0,, [3x and 8,) need to be matched at
the injection point and adjusting just the two knobs of the Einzel lenses do not
guarantee a good match. 80, several Einzel lenses would need to be used,
reducing the advantages of this scheme. While :I: 1 kV power supplies are
needed to bias the quadrupoles effectively, voltages up to 30 kV (depending in
the lens aperture and beam energy) are needed for the Einzel lenses with a
consequent increase in the price of the power supplies. A safety cage (and the
corresponding safety interlocks) would also need to be built around them since
there are not commercially available enclosed vacuum feedthroughs rated for
that voltage.

- Biasing the Einzel lens to a negative voltage. As was previously
discussed, the Einzel lens after the source introduces more non-linear effects in
the beam than any other element of the injection line. To minimize this effect the

aperture of the lens was increased but the improvement was limited. The

57

possibility of biasing the Einzel lens negatively was also studied. In this case, the
first ground to high voltage gap has a focusing effect and the second high voltage
to ground gap a defocusing effect (the net effect is still focusing). Because of this
focus-defocus as oppose to the defocus-focus of the lens when it is biased
positively, the non-linear effects introduced are reduced dramatically. The only
problem with this scheme is that in order to have the same focusing strength, the
magnitude of the negative voltage would need to be much larger that the
magnitude of the positive voltage (even a factor 2 larger). Delivering such a
voltage (-50 to -60 W) to the Einzel lens is technically fairly complicate.
Therefore, this possibility was abandoned.

- Other Einzel lens schemes were also studied to try to reduce the non-
linear effects of the solution finally used. Electric field calculations and particle
tracking was performed with SIMION. Some of the options studied included
breaking the single Einzel lens into several shorter lenses, changing the shape of
the different electrodes, biasing the puller. None of them succeeded in reducing

the problem significantly, so they were not adopted.

58

3. EXTRACTION LINE OF SIR

3.1 . Introduction

This chapter describes different aspects of the extraction line of the Small
lsochronous Ring (Figure 26). The extraction line is very short and it does not
physically extend outside the extraction box of the ring. It is located 180° after the

injection.

mgl Phosphor E‘s
“g Screen ' (r

    
 

Position of the Fast
Faraday Cup when

Electrostatic 1.. ‘ ... .~ . {I z. ‘ - .
Quadrupole . . ' . , ' 4, . Installed
., ‘4 ' g I ,.-» x . .2 _ 1‘7

 

Figure 26: Picture of the extraction box of SIR during assembly.

It consists of a pair of deflector plates, a phosphor screen and a fast
Faraday cup. The deflector plates are pulsed to high voltage to kick the bunch
when extraction is desired. The bunch can be kicked above the medium plane
toward a phosphor screen to study the transverse size of the beam (refer to

section 4.6.1. of [3] for detais). By changing the polarity of the deflector plates,

59

the bunch can also be kicked below the medium plane of the ring toward a fast
Faraday cup to study its longitudinal profile. Two different fast Faraday cups were
developed for this purpose. One of them is a sector faraday cup capable of
capturing the whole bunch at the same time. The second one is smaller and can
be moved radially to capture parts of the beam allowing a better characterization
of the energy spread of the incoming beam. It was designed to maximize its
bandwidth.

The different elements are described in the following sections. The
chapter ends with a brief description of other possible fast Faraday cups

schemes that were also considered.

3.2. Deflector Plates

A pair of OFHC copper plates is used to deflect the beam out of the
medium plane of the ring (Figure 26). The length of the plates is 6.1 cm, the
width is 14 cm and the gap between them is 5.1 cm. As it can be seen in the
picture, the plates are not completely flat. Wings were added in the sides of each
plate to increase the region where the electric field is flat. The dimensions of
these wings are 6.3 mm by 6.3 mm.

Ions, which are above the medium plane of the ring when they are
deflected down toward the fast Faraday cup, will take longer time to reach the
Faraday cup than those that are below the medium plane of the ring. The main

reason for this is that they have to follow a slightly longer path. There is also a

60

small contribution due to the loss of kinetic energy when going through the
plates.

Simulations to quantify this effect were performed using SIMION. It was
determined that the induced blurring of the longitudinal profile could be
significantly reduced by aligning the surface of the fast Faraday cups to be
perpendicular to the median plane of the ring instead of to the incoming beam.
The residual effect in the longitudinal profiles was estimated to be around 1 ns

which is much smaller than the size of the clusters we expected to observe.

 

Figure 27: Picture of the sector fast Faraday cup used to measure beam longitudinal profiles
when they are extracted from the ring.

3.3. Sector Fast Faraday Cup

A sector fast Faraday cup (shown in Figure 27) is used to measure the

longitudinal beam profile of the extracted bunches. Four OFHC copper

61

electrodes are used to collect the beam. Each of the electrodes is directly
attached to the pin of an electrical SMA vacuum feedthrough using a set screw.
50 O RG-316 cables run inside a 1.5” diameter pipe from the SMA connectors to
the exterior of the machine where they are individually connected to broadband
amplifiers. The outputs of the amplifiers are connected to the four input channels
of a digital oscilloscope. Refer to section 4.6 for a complete description of the
electronics used.

The electrodes are positioned and electrically separated from each other
and from the grounded parts of the Faraday cup by macor spacers.

A molybdenum grid is positioned 1.5 mm in front of the electrodes. The
thickness and the line widths of the grid are 2 mils and spacing between lines is
20 mils (i.e. 81 % transparency). The grid is used to shield the electrodes from
the incoming beam and from outside electromagnetic noise. It is clamped
between two 1 mm thick stainless steel frames. The grid and the frames can be
biased down to -100 V to suppress the secondary electrons emitted by the
electrodes when they are hit by the incoming beam.

A Kapton coaxial cable attached to one of the six clamping screws is used
to bias the system. This cable is connected to a BNC vacuum feedthrough
attached to a 1 1/3” nipple welded to the 8” flange that supports the whole
structure.

A Kapton foil electrically insulates the lower frame from the rest of the
Faraday cup. Kapton washers insulate the upper frame from the six clamping

SCI‘BWS .

62

A second 2 3/4” nipple was also added to the 8" flange to be used in the
future if needed.
The radial size of each of the electrodes is approximately 2.5 cm and the

vertical size is 3.5 cm. No gap is left between electrodes since a step-like

structure( ‘1 )is used.

Several factors limit the time resolution of the longitudinal profiles that can

be measured with this Faraday cup:
0 Electronics bandwidth. The 1.5 GHz bandwidth of the oscilloscope used to
capture the profiles is limited by the high frequency limit of the bandwidth

of the amplifiers (1 GHz) that are currently being used. This corresponds
to a rise time 0,.) of 0.35 ns according to the formula below. Justification

of this relationship can be found in [8].

0.35
tR = —
BW

. The gap between current collector of the Faraday cup and shielding grid.
This is especially important for low energy beams. Once the head of the
bunch has gone through the shielding grid, it will start inducing a signal in
the current collector. If the gap is 1.5 mm, a H2+ beam with energy equal to
20 keV will start inducing a signal ~ 1.1 ns before it actually hits the
current collector. There are two main reasons why reducing the gap will
not significantly improve this time. The distance between lines of the grid
should be smaller than the gap to shield effectively. Since the thickness of

the grid lines cannot be reduced below 1 or 2 mils for mechanical reasons,

63

reducing the distance between lines will simply lower the transparency of
the grid. To compensate for this reduction of the transparency, the gain of
the amplifier has to be larger. Typically, larger gain is correlated with
smaller bandwidth for commercially available amplifiers. The other reason
not to reduce the gap is that the capacitance of the Faraday cup would
increase. The effect of this capacitance would perturb the matching of the
impedance of the transmission line, thus perturbing the beam signal.

Matching of the transmission line. Any mismatch of the transmission line
will produce reflections of the high frequency components of the signal
reducing the bandwidth of the system. The geometry of the electrodes of
this Faraday cup was not optimized to match the 50 O of the rest of the

transmission line because of the lack of space.

The best way to determine the time resolution of the Faraday cup is to use

a time domain reflectometer (TDR) to generate a pulse with a very fast rise time

(~ 100 picoseconds). This pulse can be sent toward the collector of the cup and

the reflected pulse can be measured. The rise time of the reflected pulse would

define the time resolution of the Faraday cup.

TDRs are expensive and are not available at the NSCL. So, the next best

thing was done. A bunch was used to generate the pulse and its rise time was

measured. Since the rise time of the bunch itself is not known, this method will

only give an upper limit to the time resolution of the Faraday cup. Actually, based

on how the beam is chopped to generate the bunches, it is very likely that the

time resolution is significantly better than this estimate.

64

Figure 28 shows a typical bunch profile measured with one of the sectors
of the Faraday cup. From the figure, it can be determined that the rise time
(defined as the time to go from 10 % to 90 % of the maximum signal) is 3.2 ns.
Using the relationship between rise time and bandwidth, we can determine that
the bandwidth of the whole system (Faraday cup, amplifier, oscilloscope and

cables) is larger than 110 MHz.

 

    
  

—-—.--—o --~-~—¢-4-1_I—‘—u-I-z-I—I—w-‘-cd

0.7

I

0.5 -

l/lo

.0
or
I

._.-._._._.-._._._._._._._._._._._I._._._._

01_._._._._._._._._._,_._._._._. ._._._._._._.-._.-._._._.-.._._..J

.l

 

 

PI—O—-_t+I-C-I-‘-I—l-O-I-I-I-l-i-'-I—U-U-I

i
!
l
l

 

15 20 25 30 35 40
t (ns)

Figure 28: Measured rise time of the signal in one of the sectors of the fast faraday cup when a
bunch hits it.

The proximity of the different sectors of the Faraday cup has the
undesired effect of cross talk between channels since they are capacitively
coupled.

To try to quantify this effect, the “rf out" channel of a network analyzer was

connected to one of the central electrodes and the “rf in” channel was connected

65

to the other central electrode. A sinusoidal signal with a frequency that was
swept between 300 kHz and 1.5 GHz was produced by the network analyzer (rf
out) in one of the electrodes. The induced signal in the other electrode was
measured (rf in). The relative value of these two signals is displayed in Figure 29.
It can be observed that the maximum induced signal (-18.5 dB) is produced for a
frequency of ~ 75 MHz. That is, a signal will be induced in one of the electrodes
when the beam hits the other electrode. The amplitude of the 75 MHz component

of the induced signal will be 12 % of the amplitude of the same frequency

component of the incoming beam.

 

_‘L
o
I

1

Transmission (dB)

 

 

 

J;

0 250 500 750 1000 1250 1500
Frequency (M Hz)

 

Figure 29: Measurement of the cross talk between central electrodes of the sector fast Faraday
cup. The amplitude of the induced signal in one the central electrodes was
measured when a signal was sent to the electrode next to it.

66

The signals induced in the Faraday cup due to electromagnetic noise were
also studied in an effort to better understand the ratio between signal and noise
levels. Figure 30 shows a measurement of the signal captured by one of the
sectors of the Faraday cup when no beam is being injected in the ring. The noise
induced when the chopper, second lnflector and deflector plates are turned on,

can be clearly identified.

 

 

 

 

 

 

 

 

 

 
 

1 5 I , 1 I ’F l " I r 1
Deflector is -
Deflector rs
. Ltumed on \ K I turned off
Chopper is
turned on

 

 

  

5

 

IOIA)
C)

  
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'5 K lnflector is
i /] turned on

Chopper' rs

turned off ‘

- lnflector is .I

turned off Bunch profile
- when beam is on
‘1 5 I ' ‘ 1 | L 1

t (118)

Figure 30: Noise induced in one of the electrodes of the sector Faraday cup when the chopper,
lnflector and deflector plates are turned on and off.

The amplitude of this noise is typically larger than the beam signal in the
case of the deflector plates since they are closer to the Faraday cup than the
other elements. This is not a problem because if the deflector is turned on 1 us
before the head of the bunch arrives and turned off 1 us after the tail has hit the

Faraday cup, the induced noise does not interfere with the beam signal.

67

Once the large noise sources were eliminated, a residual noise equivalent
to a t 0.5 pA (standard deviation) current remained. This is what defines the
noise to signal ratio. For example, a 10 uA bunch will have a noise to signal ratio

equal to 5 %.

3.4. Movable Fast Faraday Cup

A movable fast Faraday cup can be used to measure the longitudinal
bunch profiles as an alternative to the sector Faraday cup (Figure 31). It consists
of an OFHC copper central electrode where the beam is collected. This electrode
has a conical shape and it is attached to the pin of a 50 0 type N vacuum
feedthrough to which a type N to SMA right angle connector is attached. The
bottom surface of this cone is used to collect the beam. It has a diameter equal to
16.25 mm. An RG-316 coaxial cable, which runs inside the tube, is used to
transmit the beam signal to a broadband amplifier. The output of the amplifier is
connected to a digital oscilloscope. Refer to section 4.5 for a complete
description of the electronics used.

The electrical design of the Faraday cup is a modified version of those
appearing in references [9] and [17]. The conical central electrode is surrounded

by an empty conical stainless steel structure that acts as the shield of a coaxial
transmission line. The impedance (Z0) of a bi-conical transmission line like this

one is equal to

Z0 =2L fip—lnI—Q)
7: 80 d

68

where D is the inner diameter of the outer conductor and d is the outer diameter

of the inner conductor. For the impedance to be equal to the 50 O of the rest of

the transmission line, a ratio 3: 2.303 was chosen.

 

Figure 31: Picture of the movable fast Faraday cup used to measure longitudinal beam profiles.

The previous discussion strictly applies only to infinitely long transmission
lines. In our case, this length had to be limited to 2 cm due to the lack of space,
leading to an 18.7° half angle for the inner cone. This angle is still significantly
smaller than the 25° of reference [10] for which a bandwidth of 2 GHz is claimed.

A molybdenum grid is positioned 1 mm in front of the electrodes. The
thickness and the line widths of the grid are 2 mils and the spacing between lines
is 20 mils (i.e. 81 % transparency). The grid is used to shield the electrodes from
the incoming beam and from outside electromagnetic noise. It is clamped
between a 1.6 mm thick stainless steel ring and a 0.4 mm thick aluminum ring.
The grid and the rings can be biased down to -100 V to suppress the secondary

electrons emitted by the electrodes when they are hit by the incoming beam.

69

A Kapton coaxial cable, attached to one of the four clamping screws, is
used to bias the system. This cable is connected to a BNC vacuum feedthrough
attached to a 1 1/3” nipple welded to the 4%” flange that supports the whole
structure.

A Kapton ring electrically insulates the lower ring from the rest of the
Faraday cup. Kapton washers insulate the upper ring from the six clamping
screws.

The whole system previously described is attached to a commercially
available linear motion feedthrough that can be moved by a stepper motor.

The original intention was to use this Faraday cup to capture a portion of
the beam at a certain radius (i.e. energy). Move it to a different radius to capture
another portion of the longitudinal profile with different energy. These
measurements would then be combined to reproduce the longitudinal profile of
the bunch extracted after a given number of turns. The position of the Faraday
cup when the measurements were made would be used to get information about
the energy spread of the bunch.

The cluster formation process is highly sensitive to small perturbations of
the beam extracted from the ion source what makes it impossible to overlap
longitudinal profiles of different injected bunches. The Faraday cup is still useful
to measure longitudinal profiles for a given radius.

Measurements similar to those performed for the sector Faraday cup to
determine its time resolution were also performed in this fast Faraday cup

yielding very similar results. We were able to determine that the bandwidth of the

70

fast Faraday cup is larger than 110 MHz. (In fact, we believed it is significantly
larger since special care was put in the cup design to be able to maximize its
bandwidth. But, the electronics necessary to performed more precise

measurements are not currently available at the NSCL).

3.5. Other types of fast Faraday cups that were
also considered

A different kind of Faraday cup based on strip-lines was also considered.
An example of such a kind can be found in reference [9]. The back of a prototype

built to verify if it could be used is shown in Figure 32.

Connector 500
Stripline Ground Plane
’ _. . 380 Surface
I.I _ ‘ ' '_ . - Mount Resistor
, ‘ ' ,' Lire“ G: W.
Resistor Matching , ’ -. -.U (I) ’
Network
Collector
Teflon
SMA
Plane

Figure 32: Picture of the back of the prototype stripline fast Faraday cup developed for SIR.

 

3x 67 0 Barrel
Resistors to

 
 
  
  
 
 
 

 

 

 

   
 
      
          

It consists of an OFHC copper current collector. It is soldered to a copper
stripline with the same impedance. The whole line is matched using a network of
matching resistors between this stripline, the 50 Q stripline and the ground plane.

71

The main advantage of this kind of Faraday cup is its size. It can easily fit
in the space available. But, a number of disadvantages make the designs
described in previous sections more attractive:

o The matching resistor network acts as a splitter. Part of the signal is
dissipated in the resistors reducing the output signal. To compensate
for this less an amplifier with larger gain would need to be used.

c The striplines are not shielded and are, therefore, very likely to pick up
electromagnetic noise. Adding the necessary shielding would make the
mechanical design more complicated.

o The most important problem is that it is not possible to make it high
vacuum compatible. First, soldering of different elements is required.
The residual flux in these points is not vacuum compatible. Second,
coaxial cables with SMA connectors need to be used to bring the
signal out of the vacuum chamber. There are no commercially
available SMA connectors that are high vacuum compatible. Several
tests were performed to quantify the effect of these non-high vacuum
rated elements in the pumping time and the results showed that a

system of this type was not acceptable.

72

4. ELECTRONICS AND CONTROL SYSTEM OF SIR

4.1. Introduction

This chapter describes the electronics and the control system used in SIR.
Some possible future upgrades are also discussed. The chapter has been
divided in sections that correspond to different subsystems of the machine. A
brief description of some alternative solutions that were also considered is
included at the end of the chapter. Some of the electronics used appear in Figure
96, Figure 97, Figure 101 and Figure 105.

Some of the requirements of the control system of SIR were:

0 Low cost.

0 Electronics available from previous projects had to be reused if possible to
further lower the cost. (Although, in some cases, using old electronics
increased the development time of the control software.)

0 Independence from the control system of the rest of the NSCL.

. Easy upgradeability. New experiments based on the results of previous
ones have been proposed. The flexibility of the control system allowed
incorporation of new electronics for several tasks without major changes.

0 Automation of the most time consuming tasks (like emittance
measurements and longitudinal profile capture) improves the quality of the
data (beam characteristics drift less over a short period of time), reduces

human error and greatly simplifies the operation of the machine.

73

0 Storage of experimental data for analysis. Even though some data
analysis is performed by the data acquisition programs, all the raw

information is saved for offline data processing.

With these constrains and requirements in mind, a PC-based option was
chosen as the best compromise between low cost and high functionality. Most of
the software was developed in LabVlEW [18] to reduce the development time
since drivers to control most of the instrumentation in this language are typically
provided by manufacturers. When extensive data processing was necessary, the
LabVlEW programs were linked to MatLab [19] that is very well suited for data

processing and visualization.

4.2. Scanning Wires

Two pairs of scanning wires can be used to measure transverse beam
profiles in the ring. They are located in the vertical and horizontal plane of the
ring after ‘A and 1/2 a revolution. Please, refer to [3 page 122] for a complete
description of their design.

They are driven by stepper motors powered by a National Instruments
MID-7604 power drive that is controlled by a National Instruments POI-7334
motion controller.

The beam current, intercepted by the scanning wires, is read by a Keithley
6485 picoammeter after the right signal is selected with a Keithley 7001 equipped

with a Keithley 7158 low current switch card. The analog output of the

74

picoammeter (output voltage is proportional to the measured current for a given
scale) is redirected to one of the analog inputs of a National Instruments PCI-
6036E DAQ for further analysis.

Both the picoammeter and the low current switch are controlled by a PC

using GPIB (IEEE 488) communications. (Figure 33)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

IPC LabVlEW — Motor 1

GPIB —’-—|’ ‘ Scanning Wire 1 ‘
DA AI ' . t '
Q -(—IP1co1mme efl ‘I “

Motion --—-l Motor 2

Controller ___—.-----—--—
Low Cun'ent : Sc aiming Wire 2
Switch

 

 

 

 

 

— Motor 3

 

Scanning Wire 5

 

 

ll

 

 

 

 

 

 

 

Motor 4

——-———d

Scanning Wire 4

 

ll

 

 

 

 

 

Figure 33: Layout of the scanning wires and their associated control electronics.

The control software has been developed using LabVlEW. A picture of the
user interface is shown in Figure 34. The most important functionalities of the
program are:

. It synchronizes the movement of the scanning wires with the data
acquisition displaying it as current density as a function of the position of

the scanning wire.

75

. The most important parameters of the last profile acquired are calculated
and displayed. These parameters include the integrated beam current. the

peak current density, the position and width of this peak.

 

| our IVertical mamhing‘Horizontal mamhi

 

 

 

 

 

- 6
V0“)

 

 

 

Figure 34: Front panel of the LabVlEW program used to control de scanning wires.

The user can save the acquired data for further analysis.

Voltages of the lnflector plates needed to center the beam vertically are
calculated based on information provided by the measured profiles

(position of the peak current) for different voltages in the inflector plates.

76

. An analog functionality for horizontal beam centering using injection line

horizontal steering correctors is included.

4.3. Emittance Measurement System

The Emittance Measurement System consists of a couple of movable slits.
The portion of the beam that goes through both slits is collected by a shielded
Faraday cup. The system is duplicated in the vertical and horizontal plane.

The layout of the control system is very similar to the one used for the

scanning wires of the ring. (Figure 35)

 

 

 

 

 

 

 

PC LabVlEW Motor 1 (x‘)
GPIB —->——1' Faraday cup x-x‘ ‘

 

 

 

 

 

DAQ AI Picoammeter

Controller Low Current
Switch .1 Motor 3 (y‘)

 

 

 

 

 

 

 

Faraday cup y-y'

MM...

 

 

 

 

 

 

 

 

Figure 35: Layout of the emittance measurement system and its associated control electronics.
A LabVlEW program (Figure 36) was written to automatize the data
acquisition. By taking data as the slits move, complete scans (typically 125 x 50

points) can be performed in less than ten minutes.

This same program also fits the measured data to an ellipse and displays

its Courant-Snyder parameters (a, B and y) as well as its rms-emittance (arms).

77

The region of the phase space to be scanned is specified on the left of the
front panel and the information about the beam is displayed on the right of the
front panel once the scan has been completed. This information is later used to
adjust the quadrupole triplet and the Einzel lens to match the injected beam to

the closed orbit solution of the ring.

All the data taken is saved in a file for further analysis if necessary.

 

 

 

Figure 36: Front panel of the LabVlEW program used to control the emittance measurement
system.

A full description of the Self Consistent, Unbiased Elliptical Exclusion
(SCUBEEx) algorithm used to calculate the beam parameters can be found in

references [20], [21] and [22].

78

4.4. Chopper, lnflector and Deflector Timing

A Thorlabs DG100N digital delay line is in charge of triggering the six DEI
PVX-414O high voltage fast switches at the right time. These switches produce
up to :I: 3.5 kV, down to 100 ns short pulses that are used to drive the different
chopper, lnflector and deflector plates.

Using a TclfT k [23] program developed by Felix Marti, running in a PC, that
communicates with the digital delay line though the network and a LanTronix
UDS-1O TCP/IP to Serial Port converter, parameters such as the length of the
bunches that we want to inject as well as for how many turns we want to keep

them in the ring before extraction can be preset.

 

PC tcl/tk ,
Oscrlloscope
Network Trigger

 

 

 

 

 
 
  

 

  
  

 

TCP/IP to

HV Switch Chopper +
Sen al Port .__.__..__.______. _.

 

  
 
 

Digital
Delay Line

    
    

HV Switch Chopper -

 

Vavefomi
Generator

Frequency
Counter

48 Channel HV
Power Supply

    
  

 
 

 

“ HV Switch ->-l lnflector +

__ HV Switch +— lnflector -

 

 

  

 

 

 

_;.. HV Switch Deflector 7'

A
'—j HV Switch Deflector — I

Figure 37: Layout of the chopper, inflector and deflector and their associated control electronics.

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

The voltage monitor of the high voltage switch of either one of the chopper
plates or deflector plates is used to trigger the acquisition of the beam profiles in

the oscilloscope.

79

The dc high voltage is provided by the CAEN SY2527 equipped with two
A1733p and two A1733n power supply modules that is also controlled through
the network with software provided by the manufacturer.

A square wave generated with a Leader LG1311 waveform generator is
used to trigger the digital delay line. A HP-53131A frequency counter is used to
precisely measure this frequency which determines how often bunches are
injected in the ring (Typically ~ 1 kHz).

A National Instruments POI-6602 counter/timer was also considered as a
substitute for the digital delay line, the waveform generator and the frequency
counter. Some of the advantages of this scheme include:

. The number of channels of the currently used digital delay line is 6. This is
enough to trigger the 6 HV switches but not the oscilloscope which is
triggered by the voltage output of the switch driving one of the chopper
plates or one of the deflector plates. In contrast, the POI-6602 card has 8
channels which would allow triggering the oscilloscope at the right time to
simplify the data acquisition process.

. Lower cost.

0 The frequency of the internal oscillator of the POI-6602 is 80 MHz (i.e.
delay time resolution is 12.5 ns) compared to 40 MHz for the DG1OON (i.e.
delay time resolution is 25 ns).

0 Probably the most important difference is that the POI-6602 is capable of
generating trains of pulses as opposed to the single pulses of the

DG100N. This would allow extracting consecutive bunches after a variable

80

number of turns which could be used to improve the matching procedure.
Figure 38 shows how a typical beam looks like before matching is
achieved. As the matching improves, the amplitude of the betatron
oscillations is reduced. Eventually all the beam spots would collapse into a

single spot when the beam is optimally matched.

 

Figure 38: Superposition of pictures of extracted beam as seen in the phosphor screen before
matching is performed.

Despite these advantages, the DG100N scheme was chosen because it is

a stand alone instrument (i.e. independent of the PC operating system).

4.5. Movable Fast Faraday Cup

A movable Fast Faraday Cup (FCC) is used to measure the longitudinal

profile of the extracted bunches. The FFC is moved by a stepper motor powered

81

and controlled with the same type of power drives and motion controller as the
scanning wires (Figure 39).

The beam current as a function of time is measured by a LeCroy LC-
6840XL digital oscilloscope (1.5 GHz bandwidth, up to 8 GS/s, up to 16 MPoints
memory) after the signal is amplified by a Miteq AM-1309 or a Miteq AM-1607-
1000 broadband amplifiers (50 or 40 dB gain, 8 or 12 dBm maximum output
power, 10 kHz - 1 GHz Bandwidth). Based on the specifications of the
oscilloscope and amplifiers, beam current changes happening in time intervals as
short as 1 ns can be accurately measured.

The voltage monitor of one of the high voltage switches is used to trigger
the oscilloscope. The data can be downloaded from the oscilloscope using GPIB
communications.

The electron suppressor system can be biased to measure real beam
current or it can also be used to further amplify the signal adding to the incoming

proton beam current the outgoing secondary e- current.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PC LabVlEW
Motion
Controller ‘—-—>—'Powc1‘ Drivel-+4 Motor
GPIB qoscilloscope ‘-lAiiij)lifiei‘]<-' Fast Faraday CUP
I Trigger 6' Suppressor

 

 

 

 

 

 

 

Chopper 7 e~ Suppressor |
HV Switch

Power Supply

 

 

 

 

Figure 39: Layout of the fast faraday cup and its associated control electronics.

82

4.6. Sector Fast Faraday Cup

A sector fast Faraday cup can be used as an alternative to the movable
fast Faraday cup. In this case, the four channels of the oscilloscope are used to
measure the individually amplified signals of each sector. The rest of the system
is analogous to the one described in the previous section for the movable fast

Faraday cup. (Figure 40)

 
    
 

   

GPIB
Network

Sector FFC
Sector 1

          
        
    
 
    
    
 

  

Channel 1
Channel 2
Channel 3
Channel 4
T

 

   

  

Sector 3

  
 

    

TCP/IP to

 

Sector 3

    

Sector 4

    
  

Digital

e‘ Suppressor
Power

Figure 40: Layout of the sector fast faraday cup and its associated electronics.

A LabVlEW program (Figure 41) was developed to automate the data
acquisition of the longitudinal profiles of the extracted bunches after a variable
number of turns. The number of profiles to be acquired for a given turn number
(typically ~ 100) and the range of turn number to be covered (typically 1 to 100)
are specified on the left of the front panel. As the measurements are done the

profiles are displayed and the data is saved for further analysis.

83

mom Profile 1: Turn # [377“

an; code 05'

 

 

5;?50
Remnants)
(H.683:
Charles
111

Figure 41: Front panel of the LabVlEW program used for the data acquisition of the sector

faraday cup.

   

. , l i .l

| I I I I I I l I I .

5E-8 1E-7 LEE-7 2E-7 2.5E-7 3-7 ELSE-7 16-7 4.5-7 SE7
Tine

 

4.7. Dipoles, Quads, Steering, Einzel lens and

Extraction Power Supplies

Since the energy of the beam is lower than 30 keV, we were able to
effectively use a number of electrostatic elements (a quadrupole triplet in the

injection line, four quadrupoles in between dipole magnets in the ring, six pairs of

steering plates, chopper, inflectors and deflector).

A modular CAEN SY2527 crate with two A1733p (12 Channels positive 4
kV / 2 mA) and two A1733n (12 Channels negative 4 kV / 2 mA) cards was

chosen because of the need to minimize the cost relatively high number of high

voltage power supplies needed. (Figure 42)

Control software with basic functionality was provided by the

manufacturer. A LabVlEW program to store and recover the status of all the

channels was also developed.

84

Two 30 kV / 5 mA Spellman power supplies are used to bias the Ion
Source and the Einzel lens. These units have analog outputs proportional to the
voltage and current that were connected to the analog input channels of a
National Instruments POI-6036E data acquisition card installed in a PC. They
also include an analog input that can be used to set the voltage of the supply that
could be used in the future to automate changing the energy of the beam. New
analog voltage output channels should be added since all the available ones are

currently being used for other tasks.

LabVlEW Extraction PS
A0 Voltage Monitor
DAQ AI Current Monitor

DAQ DO Einzel PS

Voltage Monitor

Channels H V Line PS

10V t .1
Power Supply 0 Zero-Flux Current T

Quads Ring PS
Steering '

 

Zero-Flux Current T

Figure 42: Layout of some of the power supplies used in SIR and their associated control
electronics

Two 135 A / 20 V TCR Electronic Measurement power supplies are used
to drive the four ring dipole magnets connected in series and the injection line
dipole magnet respectively. Two Holech Zero-flux current transformers are used

to precisely measure the output current produced by the supplies. The output of

85

the controllers of the current transformers is connected to analog input channels
of the DAQ card.

The ac power used by the these power supplies is automatically turned off
if the temperature of the magnet coils reaches 80°C protecting the magnets if

there is a failure of the cooling system.

 

 

 

 

 

.9 SNIEIWIIIEIII I‘uwvl Surpriljrfsliy DAQ rariir
9100 I 99129 lrrtLheDholeCurent (A)
9 100 I 96.859 Ring oracle Curant (A)
Mode ‘ ’ ' " Extr v
a: m 9999 m M
QUIT PWSE 6.3%8 Ptoarrneber (xA)

 

 

 

 

  

I I I
rioléois'oalozr'ummziomah
Thus)

I Reset Mini. L'rle opera Oxrait~ 3:?“ng {in

 

 

 

 

 

 

Figure 43: Front panel of the LabVlEW program to control the dipoles. extraction and Einzel lens
power supplies.

A LabVlEW program was written to set and monitor the Einzel lens and
extraction voltages as well as the dipole currents. Figure 43 shows its front panel.
The main functionalities of the program are:

0 Set and monitor the current in the coils of the dipoles as read by the Zero-

Flux current transformers.

86

. Monitor the extraction voltage and the Einzel lens voltage.

. Plot any of these voltages or currents as a function of time to monitor long

term variability of the power supplies.

4.8. Phosphor Screens

Two phosphor screens provide visual information about the position and
transverse profile of the beam. The first one is movable and is located in the
injection section of the ring. It can be used to observe the beam either as it

comes from the injection line or in the medium plane after a single turn.

 

PC LabVlEW

GPIB —""—l
DAQ AI n-{Picoammeterj

l

Low Current .
PC Smtch l—H Faraday Cup ]
:44 Phos hor Screen

Card 7 ' ~, , , * i
SWMh CCD 1 Phosphor Screen I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 44: Layout of the phosphor screens and their associated control electronics.

The second one is permanently located above the medium plane of the
ring, above the fast Faraday cup. The deflector plates can be used to kick the
beam off the medium plane and direct it to the screen that can also be used as a
non-shielded Faraday cup. Please, refer to [3 page 122] for a complete

descnpfion.

87

Two CCD cameras, connected to a generic video capture card through a
video switch, allow us to take digital pictures or movies using software developed
at the NSCL by John Priller.

The fixed phosphor screen is connected to one of the channels of the
same low current switch used for the scanning wires and the emittance
measurement system to be used as a non-shielded Faraday cup.

Using a National Instruments POI-1409 image acquisition board together
with the LabVlEW and IMAQ [24] software packages was also considered. This
option was discarded clue to its higher cost. The main advantage of such a
system is the specificity of the software that could be developed. It could allow,
for example, calculating and displaying numeric values for the beam position and
sizes in real time. It could also communicate these values to other control
programs further automatizing the matching process. Upgrading to such a

system is possible if these capabilities are needed in the future.

4.9. Beam Lifetime Measurements

The sector Faraday cup can also be used to measure the average beam
current when all the sectors are connected to a picoammeter (Figure 45).

The length of the injected bunch and the injection repetition frequency can
be used to calculate the duty cycle. The reading of the picoammeter can then be

corrected to calculate the average current of the injected bunch.

88

Measuring how the average bunch current decreases as the bunch is
stored in the ring for a longer time, the beam losses can be quantified and the

beam lifetime can be calculated.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PC LabVlEW Sector FFC
GPIB ‘Pi co llneter‘ ‘ . Sector 1
Network Sector 2
Sector 3
TCP/IP to Sector 4
Serial Port
I Digital flector W e' Suppressor
Delay Lme Swrtches Power Suppl

 

 

 

 

Wavefo u
Generator

 

Figure 45: Layout of the beam lifetime measurement electronics and their control electronics.

A LabVlEW program was written to automatize this process. The program
will automatically change the number of turns the bunch is stored in the ring and
measure the beam current as read by the picoammeter. All the data is then

saved in a file for further analysis.

4.10. Other Systems

There are other systems that are not currently computer controlled. Some

of them are:
. Magnetic Quadrupole Correctors in the ring.

. Magnetic Dipole Correctors in the ring.

89

. lon Source instrumentation.
0 Pressure Gauges.

Two bipolar 12 Al 36 V Electronic Measurement power supplies are used
to power the magnetic quadrupole corrector coils. They could be computer
controlled in the future if necessary. Four 3 A / 15 V Agilent E3610A power
supplies are used to power the magnetic dipole corrector coils. They do not have
any kind of remote control capabilities.

The lon Source instrumentation includes a filament power supply, an are
power supply and a Pirani gauge. They are all biased to the extraction voltage (5
30 kV). They are currently operated manually using insulating rods attached to
the different knobs. A fiber optic transition between high voltage and ground could
be used to operate them remotely if necessary in the future since all of these
devices have remote control capabilities.

Up to five ion gauges are used to monitor the pressure in different parts of
the accelerator. The ion gauge controllers (Varian Ratiomatic 843) have analog
outputs that could be used, for example, to record the pressure as a function of

time.

4.11. A more integrated alternative control system

Alternative control systems based on VME, VXI and PXI technology were
considered but these options were finally discarded due to their higher cost.

Nevertheless, some considerations about the PXI (Pci eXtension for

90

Instrumentation) [25] option are enumerated here since future upgrades may
require new capabilities.

A PXI system is, simplifying, a regular PC with a higher number of PCI
slots and added synchronization capabilities. The number of PCI cards (GPIB
communications, DAQ, Motor Controllers, Video Capture...) that a regular PC
can host is limited to 3 or 4. On the other hand, a PXI system can host 18 or
more of these cards.

Several PCs had to be used to perform all needed functions relying on the
network connection to communicate among them. In some applications where
the timing is critical (ex. beam profiles taken with scanning wires: beam current is
read as stepper motors move), synchronization using the network is not possible
since timing is not guaranteed.

A PXI system can host many more modules increasing the possible
functionalities and providing a more integrated solution, simplifying

communication and synchronization among the modules at the same time.

4.12. Conclusion

An inexpensive PC-based control system for SIR has been completed. A
good number of electronic components previously available in the lab have been
reused further lowering the overall cost of the project.

The performance is considered satisfactory and able to cover all present
needs. Future upgrades are possible if considered necessary. Some of them

have been discussed.

91

Please, refer to page 200 for a detailed description in how to use some of

the most important control programs to perform different experiments.

92

5. BEAM VARIABILITY

5.1. Introduction

Different sources of variability have been identified and their impact on the
beam has been studied. Three different time scales were defined. The
expression “short term variability” is used when changes in the beam
characteristics can take place within a single bunch (hundreds of nanoseconds to
a few microseconds). We refer to “long term variability” when changes in the
beam can arise over a period of time longer than seconds. Finally, we refer to
“bunch-to-bunch variability” when changes between consecutive bunches may
be induced by the variability (part of a millisecond to several milliseconds).

The main source of beam variability is the ripple of power supplies.
Particularly important are the power supplies that drive the dipole magnets and
the one that defines the extraction energy (i.e. ion source bias voltage). Their
impact on the beam is discussed in the next two sections of the chapter. The
variability of the ion source is described section 5.4. A brief description of other
sources of beam variability and a series of long term measurement of the y-y’

beam phase space characteristics are also included in this chapter.

5.2. Variability of the magnetic field of the dipoles

The long term variability of the magnetic field produced by the dipoles in

the ring and in the injection line mass separator was measured by monitoring the

93

current needed to drive them over a period of 10 hours (using zero-flux current
transformers). The nominal current (lo) was set to 109 A that corresponds to a
magnetic field of ~ 610 Gauss [3 page 173] and a beam energy of ~ 21 keV for

Hz” ions. The results of this test are shown in Figure 46.

 

1.0001

 

 

 

 

 

 

 

Injection Line Magnet Power Supply ' I
1 l-
3 0.9999 -
0.9998
0.9997 + ‘ ‘ h ‘
0 2 4 6 8 10
1'0003 ' Ring Magnets Pow'er Supply '
1.0002
3 1.0001
1 .-
09999 ‘ ‘ ‘ ‘ ‘
0 2 4 6 8 10
Time (hours)

Figure 46: Long term variability of the injection line and ring dipoles power supply. lo is 109 A that
corresponds to a 21 keV Hz’ beam. Deviations around this value were monitored
over a 10 hour period of time.

It can be observed that the current is stable within t 10" of the nominal
value after an initial transition period of 1 hour in the ring magnets power supply
and 2 to 3 hours in the injection line magnet power supply.

There will be no fast changes in the magnetic field that could have an

impact on the short term variability of the beam. Since the dipoles behave as a

94

RL low band filter, signals with a frequency higher than its cut-off frequency ( fC)

are damped.

R

fC:2-Ir-L

 

The inductance (L) and resistance (R) of the coils of the dipoles were
measured (L = 120 pH, R = 40 m0) yielding a frequency cut-off equal to 53 Hz.

There may still be differences in the magnetic field felt by consecutive
bunches since oscillations in the :t: 10“ level were measured in the millisecond
time range.

The impact of these variabilities on the beam at the injection point was
calculated using the COSY Infinity model described in section 2.13. It was
determined that a :l: 10“ relative change in the nominal value of the current of the
injection dipole yields less than t 1 mm error in the vertical position of the beam
at the injection point. This error is considered acceptable since it is just a small

fraction of the beam size at that point (~ 1 cm).

5.3. Variability of extraction and Einzel lens
voflages

In a similar way as described in the previous section, the variability of the
extraction power supply and the Einzel lens power supply was monitored. The
results of these tests are shown in Figure 47.

The extraction voltage is stable within :l: 10“ of the nominal value (20 kV)

after an initial transition period of 1 hour. On the other hand, the Einzel lens

95

power supply requires 2 hours to be stable within 1 10‘3 of its nominal value (16.5
kV). Both power supplies are supposed to be identical (same manufacturer and
model number) and this difference between them can not be explained by the
load they drive since they were interchanged with similar results.

The Einzel lens voltage has been readjusted before experiments to
maintain its focusing strength constant over time. The effect in the vertical
position of the beam at the injection point due to a fluctuation in the beam energy
is approximately half of that of a similar fluctuation in the magnetic field of the
dipole. Therefore the drift in voltage is also considered acceptable after a couple

of hours of warm-up time.

 

 

 

 

 

 

 

 

 

 

Einzel Lens Power Supply
1.004 -
3
- 1.002 - i
>
1 _ AvtA
0 2 4 6 8 10
Extraction Power Supply
1.0004 -
o
>
> 1.0002
1 l-
0 2 4 6 8 10

Time (hours)

Figure 47: Long term variability of the extraction and Einzel lens power supplies. V0 for the Einzel
lens power supply is 16.5 kV and for the extraction power supply is 20 IN. The
variability of these voltages was monitored over a period of 10 hours.

96

5.4. lon source variability

The extracted beam current was monitored for different source conditions
(gas pressure and filament current) over periods of ten minutes. It was
determined that the extracted current fluctuated around its nominal value with a

standard deviation approximately equal to i: 0.4 %.

 

14

13

 

12

 

11

 

3. —— Arc voltage changed
8 _ — Filament current changed
.- -------- Gas pressure changed

 

 

 

 

 

0 10 20 30 40 50 60 70 80 90
Time (s)

 

Figure 48: Variability of the extracted beam current when the conditions in the ion source are
changed.

With respect to the short term variability, the fast Faraday cup was used to
measure fast changes in the beam current after half a revolution. This method is
limited by the noise picked up by the cup. This noise level is equivalent to a i 0.5
pA beam current as discussed in section 3.3. Therefore, extracted beam current

fluctuations below this level could not be measured properly. Larger fluctuations

97

than that where observed when the gas pressure in the source was too low
(corresponding to < 310‘8 Torr pressure in the ring).

The extracted current was measured while different source conditions
were changed in order to determine the time necessary for the source to
stabilize. Some of the results are shown in Figure 48. It can be observed that it
takes less than a minute for the extracted beam current to stabilize when the arc
voltage or the gas pressure is changed. Some oscillations in the extracted beam
current can be observed when the filament current is changed. They typically last
for two to three minutes and are believed to be related to ripple of the filament

power supply.

5.5. Other sources of variability

The isolation transformer, used to power the ion source instrumentation,
was found to produce a time dependent magnetic field that perturbed the beam.
The transformer was moved further away and its magnetic field was shielded
with sheets of mu-metal (nickel-iron alloy with very high magnetic permeability).

The perturbation in the beam introduced by the rest of the power supplies
used to bias the quadrupole triplet, steering plates and lnflector and deflector

plates is negligible compared to the ones previously discussed.

98

5.6. Beam drift over time

To evaluate the combined effect that the previously described voltage and
current drifts have on the beam, the emittance measurement system was used to
characterize the beam over time.

The injection line was set up to inject a 20 keV Hz" beam in the ring. An
hour after it was turned on, the first y-y’ (perpendicular to the medium plane of
the ring) phase space scan was performed. Measurements were repeated over
the next 6 1/2 hours. An ellipse was fitted to each data set. The RMS-emittance (8

ms), the Courant-Snyder parameters (a, B and y) and the center of the ellipses

(X0, P0) are shown in Figure 49.

 

 

 

 

 

 

 

 

 

2.5 r . , j I U I
G ..
E 2" , .5 1:: - E‘s? “3.52, 9 .
E x»-
Ea WNVQ/vwh
5,2 1.5- If/ g
to: , ' .,
Ea -
w. A 1" #9 [W a
F." E
5 .5
>7 >8 05" / + a 1
E —t— p
E —n— Y
“ 0” -a— ERMS ..
“ _._ X.
-_ _. P0
'0.5 l l ‘ l L I
0 1 2 3 4 5 6 7

Time (hours)

Figure 49: Y-Y' phase space characteristics over a 6 ‘/2 hours period of time 1 hour after turning
on the machine. The injection line was set up to be able to inject a 20 keV H2
beam in the ring.

99

6. ION SOURCE CHARACTERIZATION

6.1. Introduction

As discussed in section 2.4, a filament driven multi-cusp ion source is
used to produce the beam. The source was borrowed from Lawrence Berkeley
National Laboratory. Some of its characteristics can be found in [12].

A complete characterization of the source requires measuring the beam
current and emittance of the three different mass states (H+, Hi and Hi) for
different source conditions. These conditions are defined by the gas pressure in
the source, the extraction voltage, the filament current (and filament resistance)
and the arc current (and voltage). It is easy to realize that the large number of
possible combinations makes a complete characterization unfeasible. The picture
gets more complicated since, on some occasions, the previous history of the
source has an impact on the properties of the extracted beam. For these
reasons, we will limit this discussion to some general trends that have been
consistently observed when a single source parameter was changed.

In the next section, an example of the relationship between extracted
current and extraction voltage for the three mass states is discussed. The impact
that changes in the extracted beam current have on the phase space of the
beam is analyzed in section 6.3. The chapter is closed with a brief review of other
relationships between conditions in the source and properties of the extracted

beam that have been observed.

100

6.2. Extracted current for different extraction
voflages

The extracted beam current for different extraction voltages was
measured for the three mass states. The source conditions are enumerated in

Table 4 and the results of the measurements are shown in Figure 50.

 

 

 

 

 

 

 

 

 

IFILAMENT (A) VFILAMENT (V) IARC (A) VARC (A) PRING (TOW)
38.6 5.4 0.63 100 9-10‘8
Table 4: Source conditions used in the measurements shown in Figure 50.

The extracted current 1m (i.e. charge per unit time) can be expressed as

a function of the energy (E), ion mass (m ) and charge per unit length

dQ

—— as
d!

[EXT

_12. E
d] m

Fitting the experimental values to this equation, it can be estimated with

95 % confidence level that the charges per unit length for the different masses
are (with these source conditions):

11*: “$523110"?9 (:3%)
dl m

H;: d—Q=2.07-10‘“£ (320.5%)
d] m

H;: d—Q=3.97-10"'2£ (:2%)
d1 m

We can also conclude that, for these conditions in the source, around 3A of

the extracted current corresponds to H; and the rest is equally divided between

101

the other two mass states. It is worth noting here that the relative abundance of
the differences masses depends strongly on the gas pressure in the source. It
has been observed that the most abundant mass state is H3+ for higher

pressures .

35

 

 

 

 

 

 

A
O
U

l

 

I.

l
.1
1r

 

 

 

5 1 O 1 5 20 25 30
Vexr (W)

Figure 50: Extraction current versus extraction voltage for different ion masses. The conditions in
the source are enumerated in Table 4.

6.3. Beam transverse phase space for different
extracted currents

The emittance measurement system was used to characterize the x-x’
(parallel to the medium plane of the ring) phase space of the extracted beam for

different extraction currents.

102

A 20 keV H2+ beam was selected with the mass separator after being
focused with the Einzel lens (16.5 W). The pressure in the ring was 6.510” Torr
(due to gas flow from the source) and the arc voltage was 100 V throughout the
experiment. The filament power was first set to 243 W yielding 2.12 A of arc
current. The Hz” extracted current amounted to 29.2 pA for these conditions. At

this time, the first phase space scan was performed.

 

Vexr (kV) VEINZEL (kV) '00 IEXT (IJA) IARC (A) VARC (V) PRING (Torr)

 

20 16.5 H; 3.5-21.2 0.1-2.1 100 6.5103

 

 

 

 

 

 

 

 

 

Table 5: Value of main parameters used in the experiment described in this section.

30

 

I

25

20

15.

IE.T (uA)

10

 

 

 

0 l l l
0 0.5 1 1.5 2
I ARC (A)

 

Figure 51: Relationship between arc current and the extraction current of Hz" ions when the
filament power is changed as shown in Figure 52. The value of the arc voltage,
extraction voltage and pressure are kept constant. (Values are listed in Table 5.)

103

The filament power was lowered yielding lower arc currents and extracted
beam currents. The beam phase space was scanned at different points during
this process. The relationship between the arc current and the filament power is
shown in Figure 52. The relationship between arc current and extracted current is

plotted in Figure 51. Some of the phase space maps measured, are shown in

 

 

 

 

Figure 53.
2.5 I I l j I I

2 ~ .

A 1.5 I. III
S,
0
I!
4;

_ 1 l- _,

0.5 ~ .

1 40 1 60 180 200 220 240
PFILAMENT

Figure 52: Relationship between arc current and filament power measured for constant value of
the arc voltage, extraction voltage and gas pressure. (Values are listed in Table 5.)

It can be observed that, as expected, the emittance of the beam grows as
the extracted current increases due to the larger transverse space charge effects
in the extraction region. It can also be seen that the beam tilts more when the
extracted current is higher. Said in a different way, the waist of the envelope of
the beam is reached further down the injection line when the extracted current is

higher. Since the strength of the Einzel lens was not changed throughout the

104

experiment, we can conclude that the angle divergence of the beam in the puller
is larger when the extracted current increases. This larger divergence is also due
to the higher transverse space charge forces in the extraction region.

To quantify these effects, an ellipse was fitted to the measured data using
the Self Consistent Unbiased Elliptical Exclusion (SCUBEEx) algorithm described
in references [20], [21] and [22]. The rms-emittance and the values of the

Courant-Snyder parameters of these ellipses are shown in Figure 54.

 

4 IARC=1.13A;IEXT=21.2pA IARC=1.42A;IEXT=25.3pA IARC=1.84A;IEXT=29.1pA

    
 

  
 

 

4 IARC=0.1A; IEXT=3.5pA lmc=o.39m IEXT=9.5pA IARC=0.74A; lm=149gA

 

 

 

 

 

 

-5 0 5 -5 0 5 -5 0 5
X (mm)

Figure 53: X-Px phase space measurements for different extraction currents. (We define the x
plane as that parallel to the medium plane of the ring.) The corresponding arc
current and extracted beam current are shown in the figure. The rest of the source
parameters are listed in Table 5. Growth in the emittance and in the tilt of the beam
when the extracted current is increased (due to stronger transverse space charge
effects in the extraction region) can be observed.

105

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2D
A 4.
1.5»
a E.
. n
1 2'
0.5
o 9 9 o 9 9
o 10 20 30 o 10 20 30
2’ - -
:15» 2' ‘
E 1 .
>- 1»
0.59
o 9 9 o 9 9
0 1o 20 30 o 10 20 30
IEXTIIIA) IsnIIIA)

Figure 54: Value of the RMS-emittance and the Courant-Snyder parameters as a function of the
extracted beam current for the source conditions listed in Table 5.

6.4. Other relationships between conditions in the
source and properties of the extracted beam

Two sets of experiments were conducted to measure the extracted beam
current as a function of the gas pressure. In the first set, the extraction voltage
(20 W), the arc voltage (100 V) and the filament power (290 W) were fixed. As
the gas pressure was increased, so did the arc current and the extracted beam
current. In the second set of experiments, the extraction voltage, the filament
power and the arc current were fixed. As the gas pressure was increased, the arc

voltage was free to self adjust keeping the arc current constant. The extracted

106

beam current did not significantly change for a given are power when the
pressure was changed.

The results of these experiments seem to confirm that the arc power is the
most important parameter to determine the extracted beam current once the
filament power and gas pressure reach a threshold value. Reasonable
conclusion since the electrons emitted from the filament (i.e. arc current) ionize
the gas in the source forming the plasma.

The mission of the filament power is to facilitate the electron emission
from the filament. (Le. a lower arc voltage is necessary to produce a given are
current). Just a fraction of the gas in the source is ionized. Increasing the

pressure by itself does not significantly increase the extracted current.

107

7. BEAM LIFETIME EXPERIMENTS

7.1. Introduction

The injected beam peak current plays a critical role in most of the
experiments performed using SIR since it is the most important single parameter
to characterize space charge effects. Special attention was paid to make sure it
could be measured accurately using a Faraday cup at the end of the injection
line. The same attention has to be paid to minimize and quantify the beam losses
in the ring:

. The acceptance of the ring is large enough to accommodate the large
energy spread induced by the space charge effects. Refer to chapter 3 of
[3] for a complete discussion of the beam dynamics in the ring.

. Collisions with residual gas in the ring produce beam losses (mostly by
electron capture and scattering in the 10‘7 to 10'8 Torr range of pressures
and in the 10 to 30 keV range of energies). The strict cleaning procedure
described in page 199 was used for the elements inside the vacuum
chamber to limit the component of the residual pressure due to outgassing
to less than 10‘8 Torr. Differential pumping in the injection line reduces the
component of the residual pressure due to gas flowing from the ion source
to 10'7-10‘8 Torr depending on the source working pressure. Refer to page

126 and page 174 of [3] for a complete discussion on this issue.

The lifetime measurements of Hz" and its dependence on turn number,

residual gas pressure and beam energy will be discussed in this chapter.

108

7.2. Beam lifetime dependence on extraction turn
number and pressure in the ring
The normalized bunch average current (1/10) as the number of turns the
bunch is stored in the ring (N ) behaves as:
Eq. 3
L _ ex Pl)
[0 p No
The constant N0 depends on the gas pressure and the energy of the
beam. Figure 55 shows the decay of the normalized average beam current as N

increases for a 21 keV H2+ beam. Different curves correspond to different gas

pressures in the ring.

 

  

Illo

 

   

- — 2.5e-8 Torr
—°— 4.8e-8 Torr
-—e— 8.0e-8 Torr
—— 1.2e-7 Torr
0'2 i _._ 2.2e-7 Torr

4.4e-7 Torr
—9-— 8.2e-7 Torr

 

 

 

 

 

1 l I

0 20 40 60 80 1 00
# Tu rns

 

Figure 55: Normalized beam current versus turn number for different gas pressures. (21 keV Hz’)

109

The values of N0 were calculated for the different pressures by fitting the

experimental data to Eq. 3. The results are shown in Figure 56.

800 r r l r

 

700 - a

600 - -

500 - .

No

400

I
1

300 - -

200 ~ 9

100

I
I

A

 

 

 

0 0.2 0.4 0.6 0.8 1
Pressure (Torr) x 10‘3

Figure 56: No as a function of the pressure in the ring for a 21 keV H2+ beam.
The dependence of N0 with the pressure can be described as:

Eq. 4

N0=10095£
P

where the constant Ploo only depends on the beam energy. This result was

expected since the probability of collision with the residual gas is proportional to
the distance traveled, measured in mean free path units (i.e. increasing the
pressure by a factor two is equivalent to decreasing the traveled distance by the

same factor).

110

7.3. Beam lifetime dependence on the beam energy

Similar experiments were conducted to determine the influence that the
energy of the beam has in determining its lifetime. The results are summarized in

Figure 57.

 

2.5

I
I

P1 00 (Torr)

I
l

0.5

 

 

l l l

0 l l l l I l
10 12 14 16 18 20 22 24 26 28

Energy (keV)

 

Figure 57: P100 as a function of the beam energy.

In the range of energies of our interest (20 to 30 keV), these relationship

0‘9 Torr

can be approximated linearly as IDloo = k-E where k ; 8.8-1 keV

(:I: 8 % with

95 % confidence level). Combining these last results with Eq. 3 and Eq. 4, the

following semi-phenomenological relationship for H; ions can be derived:

111

Eq. 5

 

—I—=exp(—l.13-10° keV WP)
10 Torr E

Eq. 5 will later be used to estimate the beam losses in different
experimental conditions. As a representative example, some of these values

appear in Table 6.

 

 

 

 

 

 

 

 

I — I

10" P (Torr) E (keV) NTURNS
0.1 3-10“3 20 62
0.1 3-10“3 25 78
0.05 3-10‘8 20 30
0.05 3-10‘8 25 38

 

 

 

 

 

 

Table 6: Estimated beam losses for different working conditions

7.4. Conclusion

The lifetime of H2+ bunches for different residual gas pressures, different
extraction turn number and different beam energies has been measured and a
semi-phenomenological relationship among them has been determined.

The results of these experiments indicate that in order to minimize the
beam losses, the hydrogen pressure in the ion source should be kept as low as
possible (the pressure in the ring is proportional to the pressure in the source).

In these conditions, the beam losses will be limited to less than 5 % in the

tens of turns necessary to observe the space charge effects.

112

8. BEAM DYNAMICS SIMULATIONS WITH CYCO:
PRELIMINARY CONSIDERATIONS

8.1. Introduction

CYCO was developed by Eduard Pozdeyev to simulate the beam
dynamics of intense beams in isochronous cyclotrons. Refer to chapter 2 of
reference [3] for a complete description of the code. CYCO has also been used
to study different aspects of the beam dynamics in SIR.

A large number of simulations have been performed to characterize the
impact that parameters such as the peak current, energy or emittance have on
the longitudinal beam dynamics of SIR. The results of these simulations are
presented in chapter 9. This chapter is meant to be an introduction to those
results.

Different methods used to represent the information product of these
simulations are described in the next section of the chapter. This section is
followed by a discussion of the methodology used to analyze the data. The
stability of the results produced by CYCO when different computational
parameters are changed (such as the number of times the space charge electric
field is calculated per revolution), is studied in section 8.4. This section is
followed by a discussion of the impact that the choice of the microscopic
representation of the bunch to be studied has in its dynamics. The chapter closes

with a conclusion where the results are summarized.

113

8.2. Data representation

CYCO outputs the value of the six coordinates of every macroparticle
(typically ~ 300000) with a frequency that can be defined by the user (typically
once per revolution in the ring). Since bunches are tracked for ~ 75 turns, it is
easy to realize that the amount of data generated for every simulation performed
is large.

Representing all this information in a way in which the relevant features
are enhanced and become apparent was the first problem that we faced when
analyzing the data. Some of the ways data will be presented include:

- Particles are projected on a plane where each of them is represented as
a dot. Information in the other four coordinates is not used. In these projections,
we have defined the z axis as that perpendicular to the medium plane of the ring,
the y axis is parallel to the injection line and the x axis is perpendicular.
Clustering of the injected bunches due to the space charge forces can clearly be
observed when represented this way.

The main problem with this representation is that in some regions, where
the concentration of macroparticles is large, the picture saturates. In some cases,
a randomly selected subset of macroparticles is plotted to avoid this problem.

- Another way to prevent saturation is to use contour lines to represent
particle densities in a plane.

- Both of the above methods clearly show details in the structure of

bunches for a given turn number. In order to better understand how this structure

114

evolves in time, movies were created where consecutive frames showed the
bunch after a variable number of turns.

- As discussed in chapter 10, the measurements performed with the fast
Faraday cups are restricted to beam current as a function of time. This
information has to be compared with the simulations. In some cases, the results
of the simulations are shown that way, to facilitate direct comparison (red curve

in Figure 59).

Vlcm)
| (uA)

 

   

1

0 10 20 30 40 50 0

70
Turn #
Rotation of clusters

Figure 58: Example of waterfall diagram for a 300 ns long H2’ bunch with energy 20 keV, peak
current 10 pA and emittance 30 ‘IT mm mrad. The longitudinal bunch profile is
plotted after a variable of turns.

- Waterfall diagrams have proven to be a very convenient way to visualize
relevant information as an alternative to the movies previously discussed (Figure
58). Longitudinal profiles for consecutive turn numbers are shown next to each

115

other in a color map where the color represents the local beam current. Several
important questions can be answered by comparing these diagrams:

Turn number at which bunch breaks up into clusters.

How the size and density of clusters evolve with turn number.

How fast clusters merge together. In some cases, the clusters rotate
around each other. These two events are difficult to distinguish when individual
longitudinal profiles are studied. It becomes apparent when a top view of the
beam is observed. As an alternative, the behavior of the longitudinal profiles for

later turn numbers can be used to distinguish between both possibilities.

8.3. Description of the methodology used in the
analysis of data

Counting clusters in longitudinal profiles

As discussed in the following chapters, the beam current, emittance and
energy have a big impact in the evolution of the number of clusters formed when
the breakup occurs. Counting the number of clusters of the longitudinal bunch
profiles requires establishing criteria to define what we consider a cluster.

These criteria are described with the help of the following example. Figure
59 shows the top view (in black) and the longitudinal profile (in red) of a H2+
bunch, sixty turns after being injected according to simulations. The energy,
when it was injected, was 20 keV, the peak current 10 pA, the length 300 ns and

the emittance 30 11 mm mrad.

116

First, the peak current of the injected bunch is calculated (IPEAK). In the
simulations, this is a known parameter (10pA plotted as a solid blue line).

In the experiments, the peak current is calculated for every longitudinal
profile measured after half a turn (typically ~ 100 profiles). The average of these
values is used as the reference peak current. (Frequently, there is dispersion in
these values due to small fast fluctuations in the extracted current from the

source).

 

98 l I \l I I I I I I 35

, -‘ 30
96 _ r.
r r 25
E ‘ “' " ~ ‘- 5 <5
8 7 I 9...“. 1 '93.: ‘3
>< \ I , . i ." _ —
92 -.i ' ‘ 15

Ill llil 1 9:22;”

”UV M WWW

2.0 -10

-5 -\l5m

Figure 59: Top view (in black) and longitudinal profile (in red) of a H2+ bunch 60 turns after being
injected. The energy when it was injected was 20 keV, the peak current 10 pA, the
length 300 ns and the emittance 30 11 mm mrad.

 

r...—

 

 

 

 

UI

 

 

 

O

 

88

A threshold current is defined by the user. This value is typically a fraction

of the average current calculated before (I.< = k IpEAK). Two values where chosen

117

in this example: k1 = 0.5 and k2 = 0.75 yielding to In = 5 pA and IQ = 7.5 uA
(plotted as dashed blue lines).

The intersection points between these lines and the longitudinal profile are
calculated and grouped in pairs. Each pair represents a candidate to cluster.

Out of all these candidates, just some of them will qualify depending on
their width (Wmin) that is also defined by the user (typically 2 mm to 5 mm or the
equivalent time in the case of experimental profiles). This process is necessary to
prevent counting peaks produced by electromagnetic noise picked up by the fast
Faraday cup. It also prevents wings of clusters from being counted (like the ones
shown in note 3 and 4 in Figure 59).

Those clusters that qualify are counted.

In this example, the number of clusters counted is ten (when k = 0.75 and
Wm... = 5 mm). Two peaks that are barely distinguished are labeled note 1. Two
more possible clusters (see note 2 and 3) are not counted here. In some cases,
clusters rotate around each other. When this happens, sometimes it is not
possible to distinguish them in the longitudinal profiles since they appear
combined as one.

When k = 0.5 and Wm," = 5 mm, the number of clusters counted is 9 since
clusters partially hidden behind each other (see note 1, 2 and 3) are not counted
and the width of the other two candidates (note 4 and 5) is not enough to qualify
them as clusters.

Figure 60 shows the number of clusters, counted with the method just

described, for other values of k and Wm. There is not unique way to count

118

clusters. In most of the cases, k was chosen equal to 0.5 and wmln equal to 5 mm
or the equivalent time for measured longitudinal profiles.

In any case, the values of k and Wm," were identical every time the
“number of clusters counted” were compared (between simulations, between
experiments or between simulations and experiments).

Even though this does not guarantee that all the clusters were counted, it
does guarantee that results can be compared among them and dependencies
can be established.

For example, the values of k and Wm used to count clusters in Figure 66

were the same for all the curves and equal to 0.5 and 5 mm respectively.

 

 

 

 

 

 

 

 

 

12 I I I I l I
10 " ‘ - "
.8 8' ‘
C
8
O
2 6 - .
° l
'6
2
0 4}
u u
+ Wm“: 2.5 mm
2 . -e— wmln= 5 mm .
—+— Wmm= 7.5 mm
_ mm: 10 mm
0 L l I
0 0.5 1 1 5

Figure 60: Number of clusters counted in longitudinal profile in Figure 59 for different values of
the user defined parameters k and Wm".

119

8.4. Numerical stability: Computational parameters

In order to determine the reliability of the code CYCO, a number of
simulations were performed where different computational parameters (such as
how often the space charge electric field is calculated or grid size of the FFT
algorithm) were changed. For the code to be trusted, it is expected that changes
in these parameters will not have a significant impact on the beam dynamics
compared to changes in physical parameters of the beam such as the peak
current, energy or emittance.

The calculations will also allow us to determine reasonable values for
these parameters. After certain level, the improvement of the accuracy of the
results due to, for example, further decreasing the grid size of the FFT algorithm

does not compensate for the increase in computation time.

 

 

Physical Computational
Value Value
Parameters Parameters
Ion H; Ne 180
Energy 20 keV Nz 26
Emittance 10 TI mm mrad ny 215
Length 70 ns dxy 1 mm
lnj. Peak Current 20 pA
Number Turns 30
Vac. Chamber Size 5 cm

 

 

 

 

 

 

Table 7: Default parameters used in the simulations performed in this section to determine the
impact that changes in computational parameters have on the dynamics of the
bunch.

120

All the calculations on this section where performed on a bunch with the
characteristics and computational parameters listed in Table 7 unless specified

othenlvise.

Parameter changed: “Ne”
“Ne” is the number of times the space charge electric field is calculated
per revolution. The electric field is assumed to change slowly and does not need

to be recalculated every integration step.

 

1" -

 

Ne=45
15 25
Turn #

 

 

Figure 61: Evolution of the longitudinal profile of a bunch with characteristics listed in Table 7 for
different values of N9 (Number of times the space charge electric field is calculated
per revolution).

121

Figure 61 shows the evolution of the longitudinal bunch profile as turn
number is increased for different values of "Ne”.

It can be observed that increasing its value above 90 or 120 does not
introduce significant qualitative changes in the bunch evolution. It will become
more apparent that these changes are very small compared to the ones
produced by increasing or decreasing beam current or emittance later on in the

chapter.

 

 

 

 

Turn #

Figure 62: Evolution of the longitudinal profile of a bunch with characteristics listed in Table 7 for
different values of N2 (Number of grid points in the FFT algorithm used to calculate
the space charge electric field in the z direction (perpendicular to the medium
plane of the ring)).

122

Parameter changed: “N2”

N2 is the number of vertical (perpendicular to the medium plane of the
ring) grid points of the mesh used in the FFT algorithm used to calculate the
space charge electric field. The dimensions of the mesh size in this direction can
be calculated dividing the full height of the vacuum chamber (5 cm) by Nz.

Figure 62 shows the evolution of the longitudinal bunch profile as turn
number is increased for different values of “N2”. The impact in the bunch
evolution of increasing the value of this parameter seems to be very small.

Almost no difference can be observed between N2 = 32 and N2 = 256.

Parameter changed: “ny” and “dxy”

“ny” is maximum value for the product of the number of grid points of the
mesh in the x axis and the number in the y axis used in the FFT algorithm used
to calculate the space charge electric field. The x and y axis form a plane parallel
to the medium plane of the ring. “dxy” is the default transverse mesh size in this
plane.

As mentioned before, the vertical size of the box, in which the space
charge electric field is calculated, is fixed throughout the problem and is equal to
the vertical size of the vacuum chamber. On the other hand, the transverse sizes
of the box increase as the transverse size of the beam grows due to the energy
spread induced by the space charge forces. CYCO uses “dxy” as the mesh size
in this plane until the number of points needed to continue with that size reaches
“ny”. At which point, the mesh size will be equal to the product of the transverse

sizes of the box divided by “ny”.

123

Figure 63 shows the evolution of the longitudinal bunch profile as turn
number is increased for different values of "ny". The value of “dxy” is equal to 1
mm. Although, this value is not used throughout the calculations because the

total number of points needed would be larger than “ny”.

 

 

 

 

Figure 63: Evolution of the longitudinal profile of a bunch with characteristics listed in Table 7 for
different values of ny (Maximum number of grid points in the FFT algorithm used to calculate the
space charge electric field in the x-y plane (parallel to the medium plane of the ring)). The value
of dxy is 1 mm in all cases.

Significantly different evolution can be observed when ny is not large
enough. On the other hand, the cases where ny=215 and ny=216 are

qualitatively very similar.

124

Figure 64 shows the evolution of the longitudinal bunch profile as turn
number is increased for different values of “dxy” when the ny=216 is high
enough not to have an impact in the dynamics.

Small qualitative changes are observed especially among the cases
where dxy = 1 mm, dxy = 0.5 mm and dxy = 0.2 mm implying that the simulations

are stable as long the size of the grid is a fraction of the beam diameter.

 

80

 

 

 

25 5
Turn #

Figure 64: Evolution of the longitudinal profile of a bunch with characteristics listed in Table 7 for
different values of dxy (grid size in the FFT algorithm used to calculate the space
charge electric field in the x-y plane (parallel to the medium plane of the ring)). The
value of ny is 216 in all cases.

125

8.5. Numerical stability: Different initial ensemble

Besides the intrinsically computational parameters described in the
previous section, the choice of the microscopic representation of the bunch
should also have a limited impact on the bunch evolution compared to its
macroscopic characteristics.

In addition to CYCO, Eduard Pozdeyev also developed a support program
to generate a microscopic representation of the bunch to be studied.
Macroscopic characteristics of the bunch such as length, emittance, energy,
radial position and beta functions at the injection point are specified in an input
file. The charge and mass of the ions, the number of macroparticles representing
the bunch and a seed number used to randomly generate the position of these
particles, are also included in the input file. .

When the program is executed, it generates a file with a microscopic
realization of the desired bunch that is later used as an input to CYCO. Different
realizations of the bunch will be produced when the seed number is changed.
Several simulations were performed to determine the impact that changing the
microscopic representation of a bunch has on its dynamics. Three different
ensembles with the characteristics listed in Table 8 were generated by changing
the seed number used to create them.

The evolution of the three different ensembles is shown in Figure 65 for
two different values of the charge that each macroparticle represents. On the left
column, the bunch peak current (lo) is equal to 10uA (i.e. Qmaaopame = 62.4 e).

On the right column, lo is equal to 5pA (i.e. Qmacmpamcie = 31.2 e).

126

lo=10pA lo=5pA

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I
-20 -
w 3
-10 -, _ .
p- , .
c"
-T— .
o ~—____--J—- i (2
.. Les-E H,
~ ' -- ._> . I ‘
20
0
-2. . 'I
.’ l > ‘ I I 3
-10
A 2
5 o _ I2:
> ' . ‘ .
1o -.7 h 7 V I‘ * 1
20 ' '
Ensemble2 0
-2. j
3
-10
0 :.. . L 2
10 - ~ I l
1
20 “
. ‘ ‘ _ Ensemge1 0
0 20 40 60 0 20 40 60

Turn #

Figure 65: Evolution of the longitudinal profile of three different microscopic representations of a
bunch with the characteristics listed in Table 8. Two different peak currents were
used to compare characteristics of the evolution.

127

 

 

Physical Computational
Value Value
Parameters Parameters

Ion H2+ Ne 180

Energy 20 keV Nz 2°

Emittance 30 rr mm mrad ny 215
Length 300 ns dxy 1 mm

In]. Peak Current 5 or 10 pA
Number Turns 75
Vac. Chamber Size 5 cm

 

 

 

 

 

 

Table 8: Parameters used in the simulations to determine the effect of the microscopic
representation of a bunch in its dynamics compared to changes in its peak current.

There are significant qualitative differences in the evolution of the
longitudinal profiles depending in the microscopic realization of the bunch. The
position of the formed clusters and the neighbors they merge with, change
depending on the initial ensemble chosen.

This behavior denotes a strong dependence of the clustering process on
the initial conditions. Small changes in the initial distribution have a noticeable
effect on the macroscopic evolution.

On the other hand, some other macroscopic characteristics such as when
the break up of the bunch occurs or how fast clusters merge, follow a trend that
is relatively insensitive to the initial ensemble chosen. It is clear that the bunch
break up occurs sooner when the current is 10 pA than when the current is 5 pA.

To quantify these similarities, the number of clusters was counted as a
function of the turn number for the six different problems studied in Figure 65.
The results are shown in Figure 66.

128

 

+ Ensemble 1: 5uA
+ Ensemble 2: 5pA
+ Ensemble 3: 5pA

 

   
 
  

 

 

 

20 - _._ Ensemble1z10uA
_._ Ensemble 2: 10pA
Ensemble 3: 100A
15~ ‘M i
2 n ‘9
3
6 ’ . A‘ k...”— ,.\l.
a 10L :- ' A «has?

 

 

 

 

 

o l l l l
0 10 20 30 40 50 60 70

Turn#

Figure 66: Number of clusters versus turn number for three different initial ensembles
representing bunches with two different peak currents. The rest of the bunch
characteristics are listed in Table 8.

A significant dispersion in the number of clusters at a fixed turn number
exists among different initial ensembles. However, these differences are still
significantly smaller than those due to changes in the bunch peak current.

Other simulations were performed in which different macroscopic
characteristics of the bunch were changed for different microscopic realizations.
The results were similar to the ones just discussed.

These strong dependences of the macroscopic evolution of the bunch on
the initial conditions have also been observed experimentally as is discussed in

chapter 10.

129

8.6. Conclusion

The procedure used to count the clusters in longitudinal profiles from
simulations and experiments was described in detail. Even though two
parameters are defined by the user, comparisons of the number of clusters for
different longitudinal profiles can be carried out as long as these values are held
constant.

It was established that the results of the simulations of CYCO did not
significantly depend on computational parameters when reasonable values were
chosen. The code was, therefore, stable in the respect to changes in those
parameters.

It was established that the choice of the microscopic representation of the
injected bunch had a significant impact in the evolution of the bunch. However, it
was also shown that these changes are small compared to the ones introduced

by changes in the beam properties (such as beam current, emittance or energy).

130

9. BEAM DYNAMICS SIMULATIONS WITH CYCO:
RESULTS OF SIMULATIONS

9.1. Introduction

As mentioned in the previous chapter, the program CYCO, developed by
Eduard Pozdeyev, has been used to perform the simulations of the beam
dynamics in SIR. The main results of these simulations are described in this
chapter.

The chapter starts with a discussion of the differences in the results that
can be expected from the choice of the microscopic representation of a bunch. It
is an effort to show that the differences found when the characteristics of the
bunch are changed, later in the chapter, can not be explained just by the choice
of the representation of the bunch.

The impact of the length of the bunches on their dynamics is analyzed in
section 9.3. It will be shown that the number of clusters formed scales with bunch
length. In a similar way, the differences in evolution due to changes in peak
current and beam energy are studied in sections 9.4 and 9.5. Increasing the peak
current accelerates the cluster formation while increasing the energy, decelerates
the process.

In section 9.6, it will be shown under what conditions the vertical size of
the vacuum chamber does not have a significant effect on the dynamics. The
impact of the emittance of the beam will be studied in section 9.7 and in sections

9.8 and 9.9 we will analyze how different perturbations of the initial bunch affect

131

its evolution. The energy spread induced by space charge forces will be covered
in section 9.10 and growth of the radial size of the beam in 9.11.
The chapter will be closed stating some questions that will have to be

addressed by future research.

9.2. Dispersion in the number of clusters

As discussed in section 8.5, the choice of the microscopic representation
of a bunch has a significant impact on the formation of the clusters. It is important
to quantify the impact of this choice relative to more fundamental parameters like
the beam peak current or energy.

Fourteen different microscopic realizations of bunches with characteristics
listed in Table 9 and peak currents equal to 5, 10 and 20 pA were generated (ten
realizations for the 20 pA case). Their evolutions were calculated for 75 turns and
the number of clusters at a given turn number was counted in each case. Then,
their average value and standard deviation were calculated.

The results are shown in Figure 67. The solid lines represent the average
value and the shaded areas around them are limited by :l: one standard deviation
around the average. The value of the standard deviation after the initial break-up
is around 1.1 clusters and does not depend on the value of the average number
of clusters. Therefore, if the difference between the number of clusters counted in
two different situations is several times the standard deviation, we will be able to

affirm that is not due to the choice of the microscopic representation.

132

 

 

Physical Computational

Parameters Value Parameters Value

Ion H; Ne 180

Energy 20 keV Nz 26

Emittance 30 TI mm mrad My 215
Length 300 ns dxy 1 mm

lnj. Peak Current 5, 10 & 20 pA k 0.5
Number Turns 75 Wm," 5 mm

Vac. Chamber Size 5 cm

 

 

 

 

 

 

Table 9: Bunch characteristics and computational parameters used in the simulations performed
to determine the effect that the choice of the microscopic realization of the bunch
has on the number of clusters formed.

 

    
   
  

20. IpEAK=5|JAi1Sd
Ipw=1o uAtlsd

15-

e

0

u

2

o .

u 10
5. l lpEAK=20pAt1sd

  

 

 

 

 

0 10 20 30 40 50 60 70
Turn #

Figure 67: Average value and standard deviation of the number of clusters formed for three
different peak currents. The dispersion in values is due to the choice of the
microscopic representation of the bunch.

133

9.3. Scaling with bunch length

In order to determine the impact of the length of the injected bunch on its
evolution, simulations using bunches with lengths ranging from 40 ns to 200 ns
were performed. The other characteristics of the bunches and the computational
parameters used in the simulations are listed in Table 10.

The number of clusters formed were counted after 10, 20 and 30
revolutions. The results are shown in Figure 68. The number of clusters any time
after the initial break-up is proportional to the length of the original bunch.
Therefore, a cluster density can be properly defined and the results obtained for

a given bunch length can be scaled to describe bunches with different lengths.

 

20

 

I Turn 10 I
. Turn 20
are Turn 30

 

 

 

Number of clusters

 

 

 

l l

0 1 1 1 1 L
40 60 80 100 1 20 1 40 1 60 1 80 200
Bunch Length (ns)

 

Figure 68: Number of clusters formed after 10, 20 and 30 revolutions for different initial bunch
lengths. The computational and physical parameters used in the simulations are
listed in Table 10.

134

 

 

 

 

 

 

Physical Computational

Parameters Value Parameters Value

Ion Hf Ne 180

Energy 20 keV Nz 26

Emittance 10 11 mm mrad ny 215
Length 40 - 200 ns dxy 1 mm

In]. Peak Current 7.14 uA k 0.5
Number Turns 30 Wmm 5 mm

Vac. Chamber Size 5 cm

 

Table 10: Physical and computational parameters used in the simulations performed to determine
how the number of clusters formed scales with the length of the bunch after it

breaks up.

9.4. Scaling with bunch current

To determine the effect that the bunch peak current has on its dynamic, a
number of simulations were performed where the current was increased from lo
(= 1.43 pA) to 16-lo in lo current steps. The rest of the bunch characteristics
including its microscopic representation (i.e. number, position and momentum of
all the macroparticles) and computational parameters used (Table 11), were

identical in the sixteen cases. The number of ions that each macroparticle

represents is the only difference between them.

The evolution of the longitudinal beam profiles of the bunches in the first
eight cases (lower current) are shown in Figure 69 and the rest in Figure 70.

Several events (merging of clusters or rotations around each other) were labeled

with letters A thru F.

135

 

Tum #

 

 

 

 

Figure 69: Waterfall diagrams representing the evolution of the longitudinal bunch profile for peak
currents ranging from 1.43 uA to 11.44 pA. The other parameters that characterize
the bunch are listed in Table 11. Some events have been labeled with letters A-F.

136

Turn#

 

 

 

 

Figure 70: Waterfall diagrams representing the evolution of the longitudinal bunch profile for peak
currents ranging from 12.87 pA to 22.88 pA. The other parameters that
characterize the bunch are listed in Table 11.

137

 

 

Physical Computational
Value Value
Parameters Parameters

lon Hz“ Ne 180

Energy 20 keV N2 26

Emittance 10 rr mm mrad ny 215
Length 70 ns dxy 1 mm

lnj. Peak Current 1.43 — 23 pA
Number Turns 30
Vac. Chamber Size 5 cm

 

 

 

 

 

 

Table 11: Bunch characteristics and computational parameters used in the simulations performed
to determine the effect of the peak current on the dynamics of the bunch.

 

 

 

 

 

 

 

 

0.6 . . -
0.2 0.4 0.6 0.8 1 1.2

log1o(I/l°)

 

Figure 71: Turn number when the events labeled A thru F in Figure 69 and Figure 70 occur for
different peak currents.

138

Since the microscopic realization of the bunch is the same and the
differences in the dynamics due to changes in the peak current are not large, the
same event can be identified in the different cases studied.

Figure 71 shows, on a logarithmic scale, how the turn number changes
with the peak current when these events occur. The data is reasonably well
represented by straight lines with slope equal to -1. Therefore, we can conclude
that the time (i.e turn number) it takes for a specific event to happen is
approximately inversely proportional to the peak current of the bunch.

Similar simulations were conducted in bunches with the characteristics
listed in Table 10. Two different microscopic realizations of 1 and 2 pA peak
current bunches, fourteen of 5 and 10 pA and ten of 20 pA were used. The
results of the calculations for one of these realizations are shown in Figure 72. In
addition to the evolution of the longitudinal profiles, the number of clusters
counted for the five different currents are shown in the lower right corner.

The different values obtained for the different microscopic realizations
were averaged and their standard deviation was calculated. The results are
shown in section 9.2 (Figure 68).

If the time it takes for a specific event to happen is inversely proportional

to the peak current, the turn number at which the total number of clusters is NC

should also be inversely proportional to the current (I ).

We can define an equivalent turn number as TEQ a T.I(;1A). The number

of clusters as a function of this “equivalent turn number” should be, consequently,

independent of the beam current.

139

 

 

..—
——-
——

- —‘~_
—~———-
.;_
~—

ll

 

 

 

 

 

# Clusters

 

 

 

 

Turn #

Figure 72: Waterfall diagrams representing the evolution of the longitudinal bunch profile for 1. 2.
5, 10 and 20 pA peak currents. The other parameters that characterize the bunch
are listed in Table 9. The number of clusters counted is shown in the lower right
corner of the figure.

140

Figure 73 shows the same information as Figure 67 represented as a
function of the equivalent turn number. It can be clearly seen that the scaling

described before works very well.

 

 

 

 

 

 

 

 

 

 

20 -
15 ~
:2
0
77.
2
g 1or
5 » ,
0| 1 l I. l 1
o 250 500 750 1000 1250 1500

Equivalent Turn it

Figure 73: Number of clusters as a function of the equivalent turn number (NEG) for different peak
currents.

9.5. Scaling with energy of the bunch

In order to determine the effect that the energy of the bunch has on its
dynamics, a number of simulations were performed where the energy was
increased from 12 keV to 28 keV in 2 keV energy steps. The rest of the bunch
characteristics including its microscopic representation and computational

parameters used are listed in Table 12.

141

It is worth noting here that the linear charge density was not changed.

Therefore, since the energy changes, the peak current will also change.

 

 

Physical Computational
Value Value
Parameters Parameters
Ion Hz“ Ne 180
Energy 12 - 28 keV Nz 26
Emittance 30 11 mm mrad ny 215
Length 41.52 cm dxy 1 mm
Total Charge 1.5-10'12 c k 0.5
Number Turns 75 Wmin 5 mm
Vac. Chamber Size 5 cm

 

 

 

 

 

 

Table 12: Bunch characteristics and computational parameters used in the simulations performed
to determine the effect of the energy on the dynamics of the bunch.

 

 

 
  
 
 
 
 
  
  

 

 

 

 

 

 

25 I I I I l I
—E=12keV
—E=14keV
—E=16keV
20- —E=18keV -
E=20keV
—E=22keV
—E=24keV
215- ——E=26keV *
.3 -——E=28keV
3
E3
*10- .
5r .
0o 3 4 5 6 7
Equivalenttumil

Figure 74: Number of clusters as a function of the equivalent turn number for different energies.

142

‘20

E=12keV

UI

 

 

 

'15

10

 

 

 

0 20 40 60 0 20 40 60
Turn # Turn #

Figure 75: Waterfall diagrams representing the evolution of the longitudinal bunch profile for
energies ranging from 12 keV to 22 keV. The other parameters that characterize
the bunch are listed in Table 12.

143

 

E = 24 keV ' ' E'= 26'kev'

a;
A

 

—-—--' - -——- k
M \I
_ _; N
«A

-‘——“‘"" H
__,_‘______‘__..—-—

,’ ~

0

 

1'0 20 313455550 io
Tum#

 

 

o 20 4‘0 60
Turn #

Figure 76: Waterfall diagrams representing the evolution of the longitudinal bunch profile for
energies ranging from 24 keV to 28 keV. The other parameters that characterize
the bunch are listed in Table 12.

The results of these simulations are shown in Figure 75 and Figure 76. In
a similar way as done for different peak currents, an equivalent turn number

T
T
59 E(keV)

 

can be defined. If the evolution of the bunch scales with the energy

in such way, the number of clusters counted as a function of the equivalent turn
number should be independent of the energy. The results shown in Figure 74

confirm the validity of this scaling.
144

9.6. Vacuum chamber size

To determine the effect that the size of the vacuum chamber has on the
bunch dynamic, a number of simulations were performed where its vertical size
(9) was increased from 2 cm to 15 cm. The rest of the bunch characteristics
including its microscopic representation and computational parameters used
(Table 13), were not changed.

The results of the simulations are shown in Figure 77. Several events
were identified and labeled with letters A thru G. The turn number when they
occur as a function of size of the vacuum chamber is shown in Figure 78. We can
conclude that while the size of the chamber has a significant impact on the
dynamics of the beam when the size is close to 2 cm, it quickly decreases when

the size is increased.

 

 

Physical Computational
Value Value
Parameters Parameters

Ion Hz“ Ne 180

Energy 20 keV Nz 26

Emittance 30 ‘lT mm mrad ny 215
Length 300 ns dxy 1 mm

Inj. Peak Current 10 (A
Number Turns 75
Vac. Chamber Size 2 - 15 cm

 

 

 

 

 

 

Table 13: Bunch characteristics and computational parameters used in the simulations performed
to determine the effect of the size of the vacuum chamber on the dynamics of the
bunch.

145

 

 

 

 

 

 

Tum#

Figure 77: Waterfall diagrams representing the evolution of the longitudinal bunch profile for sizes
of the vacuum chamber ranging from 2 cm to 15 cm. The parameters that
characterize the bunch are listed in Table 13.

146

75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+ EventA
70' N : EventE -
65- “a -v- EventC ‘
-B- EventD
60- + EventE ,
+ EventF
55'- \ *- EventG ‘
at 50- ' = T -
IE) 8 a
r— 45- 4
40- ~
35- 4
30- ~
25- -
20 l J l
0 5 10 15 20

9 (cm)

Figure 78: Turn number when the events labeled A thru G in Figure 77 occur when the size of the
vacuum chamber is changed.

9.7. Transverse emittance

To determine the effect that the emittance of the beam has on the bunch
dynamic, a number of simulations were performed where the emittance was
increased from 5 to 40-Tr-mm-mrad. The remaining bunch characteristics and
computational parameters (Table 14) used were not changed.

The results of the simulations are shown in Figure 79. The evolution of the

number of clusters was determined and it is shown in Figure 80.

147

 

 

 

 

 

10 20 30 40 50 60 70
Tum#

 

 

0 20 40 60

Figure 79: Waterfall diagrams representing the evolution of the longitudinal bunch profile for
beams with emittances ranging from 5 to 40-n-mm-mrad. The parameters that
characterize the bunch are listed in Table 14.

148

 

 

Physical Computational
Value Value
Parameters Parameters
Ion Hf Ne 1 80
Energy 20 keV Nz 26
Emittance 5 - 40 11 mm mrad ny 215
Length 300 ns dxy 1 mm
Inj. Peak Current 5 pA k 0.5
Number Turns 75 Wm," 5 mm
Vac. Chamber Size 5 cm

 

 

 

 

 

 

Table 14: Bunch characteristics and computational parameters used in the simulations performed
to determine the effect of the emittance of the beam on its dynamics.

 

 

    
  

 

 

 

 

 

 

35 V T T l I l l
+ a=57cmm mrad
30_ +a=10nmmmrad -
—~— s=201cmmmrad
—-— a=30nmmmrad
25- —a=40nmmmrad -
g 20 -
til
2
O
u 15 .
10 -
5 ..
0I I I l I I I I
0 10 20 30 40 50 60 70

Turn #

Figure 80: Number of clusters as a function of the turn number for different beam emittances.

149

We can conclude that while the emittance of the beam plays an important
role in initiating the bunch break up (turn number at which it occurs), its influence
in the dynamics afterwards (rate at which clusters merge and final cluster
density) is not important. The information about the transverse properties of the

beam is lost after the break up.

9.8. Macroscopic perturbation

To understand the effect that perturbations of the local current density
have on the beam dynamics of the bunch, the evolution of two different bunches
with the characteristics listed in Table 15 was calculated. Although the average
current density in both cases was the same (5 pA), in one case the local charge

density was perturbed.

 

 

Physical Computational
Value Value
Parameters Parameters
lon Hz" Ne 180
Energy 20 keV N2 26
Emittance 30 11 mm mrad ny 215
Length 300 ns dxy 1 mm
lnj. Current 5 pA (Average)
Number Turns 75
Vac. Chamber Size 5 cm

 

 

 

 

 

 

Table 15: Bunch characteristics and computational parameters used in the simulations performed
to determine the effect that local density fluctuation have on the bunch dynamics.

150

The longitudinal beam profiles of the bunches, when they are injected as
well as their evolution in the ring, can be seen in Figure 81.

It can be observed that the break up of the bunch occurs earlier in the
region of the bunch where the local density is higher. Moreover, the break up
starts at the same time it would have started if the average current of the bunch
was equal to the local density at that point. Said in a different way, it is the local

current density the one that determines when the break up occurs.

 

 

 

 

 

 

 

 

 

 

 

 

y(cm)

Figure 81: Waterfall diagrams representing the evolution of the longitudinal bunch profile for two
bunches with different initial longitudinal profile (top left and right). The initial
microscopic representation of the bunch in the left was generated by displacing
macroparticles toward the center of the bunch. The parameters that characterize
the bunch are listed in Table 15.

151

9.9. Microscopic perturbation

As discussed in sections 8.5 and 9.2, the choice of the microscopic
representation of a bunch has a significant impact on its macroscopic dynamics.
To better understand this process, the dynamics of two different microscopic
realizations of a bunch with characteristics listed in Table 16 was studied. The
only difference between the two realizations is that one macroparticle out of the
0.3106 was removed in one of them. Therefore, the charge per macroparticle

also changed slightly.

 

 

Physical Computational
Value Value
Parameters Parameters

Ion H2+ Ne 180

Energy 20 keV Nz 26

Emittance 30 11 mm mrad ny 215
Length 300 ns dxy 1 mm

lnj. Peak Current 20 uA # macroparticles (NT) 0.3106 (-1)
Number Turns 75
Vac. Chamber Size 5 cm

 

 

 

 

 

 

Table 16: Bunch characteristics and computational parameters used in the simulations performed
to determine the effect that very small changes in the choice of the microscopic
representation of a bunch have on its dynamics.

The distance between the positions of a given macroparticle in both
realizations was calculated for every particle and turn number. The results are
shown in Figure 82 where the vertical axis is the turn number (TN) and the

horizontal axis is the distance between positions (Ad). The color scale represents

152

the percentage of particles that have been displaced Ad by turn TN from the
position they would have if that single macroparticle had not been removed. The
contour lines represent the percentage of particles that have been displaced
more than Ad by turn TN.

It can be observed that more than 10 % of the macroparticles have been
displaced more than 2.5 cm by turn number 75 due to the very small perturbation

in the initial representation of the bunch.

 

 

log1o(N/NT)

I I I
Is 5.) u
u:

 

 

 

 

0 1 2 3 4 5
Ad (cm)

Figure 82: Effect in the evolution of the position of the macroparticles when one of them is
removed from the initial ensemble. The percentage of particles that have been
displaced Ad at a given turn number is represented with different colors. The
percentage of particles that have been displaced more than Ad at a given turn
number is represented by contour lines.

153

9.10. Energy spread within a bunch

The energy spread induced by space charge forces has been studied for
different beam currents and energies. The dynamics of different bunches with the
characteristics listed in Table 17 has been studied.

As expected, the energy spread grows faster when the peak current is
larger or the energy is lower as is shown on the left of Figure 83. At first, the
energy spread grows linearly but after some time the growth slows down
probably reaching an asymptotic value at the end although this has not been
venfied.

It can be observed that the scaling laws, used in previous sections, also
work very well to describe the energy spread differences. See plots on the right
of the figure where the energy spread is shown as a function of the equivalent

turn number.

 

 

 

Physical Computational
Value Value
Parameters Parameters
Ion H2+ Ne 180
Energy 22 - 28 keV N2 26
Emittance 30 11 mm mrad ny 215
Length 41.52 cm dxy 1 mm
Total Charge (0.6 — 6)-10‘12 C
Number Turns 75
Vac. Chamber Size 5 cm

 

 

 

 

 

Table 17: Bunch characteristics and computational parameters used in the simulations performed
to determine the energy spread induced by space charge forces.

154

 

(d

N
or

N

 

llll

 

 

 

AE/E(%)
"u:

—L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.5
0 . A A . 4; A. A
0 20 40 60 250 500 750 1000 1250 1500
2'5 —E=22keV —E=22keV
+E=24keV +E=24keV
2 +E=26keV +E=26keV
+E=28keV +E=28keV
$1.5 - 1
Lu
Lu
<1 1 '
0.5
0 . - . ‘ ._ . .
0 20 40 60 0 1 2 3 4
Turn # Equivalent Turn #

Figure 83: Energy spread induced by space charge forces as a function of the turn number for
different beam energies (bottom of figure) and different beam currents (top of
figure). The same data is displayed on the right as a function of the equivalent tum
number. The rest of the parameters of the bunches are specified in Table 17.

9.11. Beam radial size

As described in section 1.1, the longitudinal space charge electric field

induces energy spread within the bunch. Ions in the head of the bunch gain

energy as they are pushed by the rest, while those in the tail lose it.

155

 

 

 

 

 

 

 

 

 

 

I -
.I 52
H ‘0
r ‘—
-- o:
’— S
.‘ I-
-'
-
I I‘ll
* '
M
‘-—- 2
T‘-
g: N
‘—
‘M OE
- 3
-— '—
‘
-
fl" 53
H .E
8
.. >4
% 2
t. co
-_-. CE
=— 3
_ l.—
1
_
"‘5: 9
~.—- '
L9.
V'
oE
3
'—
9
V N
0') O)

 

$93
0
N

Figure 84: Top view of three bunches with characteristics listed in Table 9 after a variable number
of turns. The energy spread induced by space charge forces can be observed in
the tilting of the beam.

156

Since the ring is isochronous, the length of the bunch does not increase
but the radial size of the bunch does. Ions in the head describe a trajectory with a
larger radius maintaining the revolution frequency constant despite of their higher
energy. In a similar way, the radial position of those in the tail is reduced.

This behavior is reproduced by the simulations. Figure 84 shows the top
view of bunches with characteristics listed in Table 9 several turns after being
injected. It can be observed that after four turns the head of the bunch has
shifted toward a larger radius while the tail shifted toward a smaller radius. This

effect is more accentuated when the beam current is higher.

9.12. Asymptotic cluster density and merging rate

As discussed in previous sections, the number of clusters formed after the
initial break up for ten different microscopic representations of bunches with the
characteristics listed in Table 9. The average number of clusters is shown as

circles in Figure 85. These data can be fitted to a curve (solid line) like:
T
N = N00 + (NO —Nw)oexp(——)
t
From which, the following values for N00, No and 2' can be calculated

with a 95 % confidence level:

N00 =7.52:3% N0 =23.79:5% t=l6.61i9%

As discussed in previous sections, N,o does not depend either on the

size of the vacuum chamber nor on the beam energy, current or emittance. It

157

was determined that it is proportional to the length of the bunch which allows

N00
defining a final cluster density ".0 =——- that will be independent of the
LBUNCH

length of the bunch. Questions on the nature of 1100 are opened. What defines its
value is not clear and needs to be studied.

In a similar way, the rate at which clusters merge (r ) is independent of the
beam energy, current or emittance when the number of turns is expressed as

equivalent turn numbers.

 

25 I T r I I Y I

20

# Clusters
at

_L
O

 

 

 

 

5 ~ .
0
00000
0 l l l l 1 L l
0 10 20 30 40 50 60 70
Turn #

Figure 85: In black circles: number of clusters (averaged over ten initial representations) formed
for a 20 uA peak current (rest of bunch characteristics are listed in Table 9). The
data was fitted to an offset decaying exponential (solid red line).

158

9.13. Conclusion

Extensive simulations have been performed to evaluate the impact that
different changes in beam parameters have on the bunch dynamics. The main
results are summarized next:

- Some dispersion in the number of clusters counted (:l: 1.1) should be
expected because of the slightly different dynamics due to the choice of
microscopic representation of the bunch.

- The number of clusters after the break up occurs is proportional to the
length of the bunch.

- Increasing the beam current accelerates the break up process of the

bunch. Events that occur at turn number N when the beam current is I, will

occur at turn % when the current is k-l .

- Increasing the beam energy decelerates the break up process of the

bunch. Events that occur at turn number N when the beam energy is E and

Q

BUNCH

 

linear charge density is , will occur at turn k.N when the energy is koE

with the same linear charge density.

If what is kept constant is the beam current I , from the relationship

[2Q Q.2-E

av: _

LBUNCH LBUNCH m

 

 

where v is the velocity of the ions, events that take place at turn number N

when the beam energy is E, will happen at turn k.N when the energy is k-E’”.

159

Therefore, the results of the simulations confirm the validity of the scaling
law discussed in 1.3 in the range of beam energies and currents studied.

- The effect of the vertical size of the vacuum chamber is very small if the
size is larger than 4 cm.

- The emittance of the beam plays an important role in determining when
the bunch break up occurs. It is not very important in defining the dynamics
afterwards.

- The evolution of the bunch is highly sensitive to the initial conditions of
the bunch. Very small perturbations in the initial conditions have a significant

effect in dynamics of the bunch.

160

10. BEAM DYNAMICS EXPERIMENTS WITH SIR

10.1. Introduction

Bunches with different characteristics have been injected into the ring and
their longitudinal profiles have been measured after a variable number of turns
using the Faraday cup described in section 3.3.

In section 10.2, the repeatability of these measurements will be discussed.
It will be shown that the details of the longitudinal profiles of bunches with similar
characteristics (energy, peak current and emittance) are not identical when they
are extracted after the same number of turns. It is believed that these differences
are due to the impact that small perturbations of the initial conditions have on the
bunch evolution. It will also be shown that more general characteristics (such as
when the bunch break up occurs, the number of clusters formed at that point or
the rate at which they merge afterwards) have less variation. We will use those
general characteristics to study differences in dynamics due to changes of the
bunch length (section 10.4) and current (10.5). The number of longitudinal
profiles needed to determine the value of those general characteristics with a
high confidence level will be discussed in section 10.3.

The correlation between energy of the ions and their radial position will be
briefly mentioned in section 10.6. The chapter will close with a direct comparison
between simulations and experiments of the evolution of the number of clusters

with turn number for four different bunch currents.

161

10.2. Repeatability of the experimental
measurements

As shown in sections 8.5 and 9.2, the choice of the microscopic
representation of a bunch has a significant impact on its computed dynamics. It
was also shown that the effect of changes in more fundamental beam
parameters, such as its peak current or energy, is larger than that due to the
choice of microscopic representation.

The same sensitivity to initial conditions is also observed experimentally.
Three longitudinal beam profiles, measured after the bunch was stored for 29 ‘/2
turns, are shown on the left of Figure 86. The profiles on the right were measured
after 98 ‘/2 turns. The characteristics of the bunch are listed in Table 18. It can be
observed that, although the details of the profiles differ from measurement to
measurement for bunches with the same extraction turn number, these
differences are small compared to those when extraction turn number changes.
In particular, the number of clusters is significantly different.

The method used to count the number of peaks is identical to that
described in section 8.3 for the results of the simulations. In this example and in
the rest of the experimental results discussed in this chapter, the value chosen
for the parameter k is 0.5 and 5 mm for Wmin.

The dashed blue line shown in Figure 86 represents the value of the
current at which the number of clusters is evaluated. In this case, IK = k - lpEAK =

0.5 - 14 pA = 7 pA. The red solid line represents the clusters that are counted.

162

Note that one of the clusters in the lowest right profile does not qualify since it is

not wide (i.e. long) enough.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

40

NT=29'/2 I R I NT=98'/2 I n
30~ I I .
20'
1018511 . _. e. ..... 1.567.- _ _ _.
WW ll Ill ILNWM
40 l l l H 1 I
30'

20-

NM)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10-

40 . . . r . . . . . . . I .

Z
I II
I .3
. .3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

30 r
20 ' ‘ u
‘0 $161.2 I ,r.__:_"_c_=5.__w_U_ , K}

 

0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350
T(ns) T(ns)

Figure 86: Longitudinal bunch profiles measured with the sector Faraday cup after the bunch was
stored for 29 ‘/-.~ turns (on the left) and 98 ‘/2 (on the right). The characteristics of the
bunches, when they were injected, are listed in Table 18. The number of clusters
counted (NC) is shown next to the corresponding profile.

The number of clusters counted (NC) is not the same for all the profiles

measured at a given extraction turn number. There is some dispersion in their

163

values. Note that a similar dispersion was also observed in the results of the
simulations when the microscopic representation of the bunch was changed
(Figure 66). In any case, it is clear that the average number of clusters in turn
number 29 ‘/2 and 98 1/2 are different.

In a similar way, it will be shown, in the rest of the chapter, that the
average number of clusters formed at a given turn number is different when the

bunch length or peak current are changed.

 

 

Beam Beam
Value Value
Parameters Parameters
Ion Hz“ Length 300 ns

Energy 20.8 keV Emittance ~ 30 rr mm mrad
Current 14 uA

 

 

 

 

 

 

Table 18: Main parameters of the bunches used in the discussion on repeatability of
measurements.

10.3. Justification of the number of profiles
measured

In order to determine the number of profiles needed to calculate the
average number of clusters with a high confidence level, the profiles of 250
bunches were measured 55 1/2 turns after injection. (The main characteristics of
the injected bunches are listed in Table 19.) The number of clusters in each
profile were counted (NC). The results are shown on the left of Figure 87. It can

be observed that the number of clusters ranged between five and twelve.

164

The average number of clusters (NCAV) and its standard deviation (NcSTD)

as a function of the number of profiles included to calculate them are shown on

 

 

the figure on the right.
Beam Beam
Value Value
Parameters Parameters
Ion H; Length 300 ns
Energy 20 keV Emittance ~ 30 11 mm mrad
Current 10 pA Number Turns 55

 

 

 

 

 

 

Table 19: Main parameters of the bunches used in the discussion on the justification of the
number of longitudinal profiles measured.

 

 

 

 

 

 

 

 

 

 

 

2 4 6N8 101214 0 50 100 150 200 250
c #Profiles

Figure 87: Dispersion in the number of clusters counted (Nc) when a bunch with the
characteristics listed in Table 19 was extracted after 55 turns (on the left).
Convergence in the average (New) and standard deviation (Ncsm) of the number
of clusters counted as the number of profiles included is increased (on the right).

165

Based on this information, it was decided to use 100 profiles to determine
the average number of clusters and its standard deviation. The experiment
showed that no significant changes are seen measuring beyond that number of
profiles.

In the rest of this chapter, we will refer to the average number of clusters
obtained from the 100 measured profiles simply as “number of clusters”. In some
occasions, the number of clusters will be represented as a colored region limited
by the average number of clusters :l: one standard deviation. See, for example

Figure 88.

10.4. Scaling with bunch length

Several scaling laws were discussed in chapter 9. In particular, it was
determined that, according to the simulations, the number of clusters formed
when the bunch first breaks up and during its evolution afterwards is proportional
to its length.

In order to verify this scaling law experimentally, bunches with lengths
ranging from 150 ns to 600 ns and characteristics listed in Table 20 were injected
in the ring and their longitudinal profiles were measured. The number of clusters
counted for every extraction turn number and bunch length are shown in the top
of Figure 88. The corresponding densities of clusters are shown in the bottom of

the figure.

166

It can be observed that the scaling law works very well especially for the
longer bunches. The turn number at which the break up occurs and the rate at

which the clusters merge afterwards do not depend on their original length.

 

 
      
 

 

4o
TBUNCH = 600 ns
30 ' ‘
TBUNCH = 300 ns
2” 20 ’ TBUNCH = 150 DS

 

NC /T3(ps)

 

 

 

o l I_ I l l l I l I
0 10 20 30 40 50 60 70 80 90 100
Turn #

Figure 88: Experimental verification of the scaling law with the bunch length. The number of
clusters counted for bunches with characteristics listed in Table 20 scales with the
length of the bunches as it can be seen in the bottom of the figure where the
density of clusters is plotted.

Note that the beam was not perfectly matched to the close orbit solution of
the ring when it was injected as it can be inferred from the small oscillations in
the average number of clusters. The frequency of these oscillations is the same

as the betatron frequency.

167

 

 

Beam Beam
Value Value
Parameters Parameters
Ion H2+ Length 150, 300 & 600 ns
Energy 20.8 keV Emittance ~ 30 ‘IT mm mrad
Current 19.9 pA Number Turns 100

 

 

 

 

 

 

Table 20: Main parameters of the bunches used in the discussion of scalability with length of the
number of clusters formed after the initial bunch break up and during its evolution
afterwards.

10.5. Scaling with bunch current

In order to verify the scaling law described in section 9.4 experimentally,
bunches with different peak currents (5.0, 9.9 and 19.9 pA) were injected into the
ring and the evolution of their longitudinal profiles was measured. The rest of the
characteristics of the bunches are listed in Table 21.

The evolutions of the number of clusters with turn number for the three
different peak currents are shown in the top of Figure 89. The evolutions as a

function of the equivalent turn number (defined in section 9.4: TE 2 T-I(pA)) are

shown in the bottom figure.

The experimental results clearly corroborate the validity of the scaling of
space charge effects with peak current that was discussed in section 1.3 and that
had already been verified by the simulations in the previous chapter.

These experiments were repeated for bunches of different energies (24.92

and 16.75 keV) obtaining similar results.

168

 

NCLUSTERS

 

 

Turn number

 

20 . . E

NCLUSTERS

 

 

 

1 000 1 500 2000

Equivalent tum number

0 500

Figure 89: Experimental verification of the scaling law with the bunch current. The number of
clusters counted for bunches with characteristics listed in Table 21 scales with the
peak current of the bunches as it can be seen in the bottom of the figure where the
number of clusters is plotted as a function of the equivalent turn number.

 

 

 

 

 

Beam Beam
Value Value
Parameters Parameters
Ion H; Length 300 ns
Energy 20.8 keV Emittance ~ 30 11 mm mrad
Current 5.0, 9.9 & 19.9 pA

 

 

 

Table 21: Main parameters of the bunches used in the discussion of scalability of space charge
effects with peak current.

169

10.6. Correlation between energy and radial position
of the clusters

When the sector Faraday cup is used to measure the longitudinal profiles,
the beam is typically divided among sectors. As it can be seen in Figure 90, the
beam hits the two central current collectors when it is extracted after half a turn.
About two thirds of it hit the outer radius one versus one third hitting the inner

radius one.

Turn 1 Turn 99
Head
' Outer
/ Radius
‘ Inner

Radius

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I’m-III) II” , , .

0 100 200 300 400 0 100 200 300 400 500
Time (ns)

 

Figure 90: Correlation between energy of the ions and radial position. When the bunch is
extracted after ‘/2 a revolution, it hits part of the two central electrodes of sector
Faraday cup (green and red). After 99 V2 revolutions, those clusters in the head of
the bunch hit the outer radius central electrode while those in the tail hit the inner
radius electrode.

As previously described, the head of the bunch gains energy while the tail

loses it due to longitudinal space charge forces. Since the ring is isochronous,

170

ions in the head will describe a circumference with a larger radius than those in
the tail. This effect can be observed in the longitudinal profile after 99 ‘/2 turns.
Clusters in the head of the bunch hit the outer radius collector while those in the

tail hit the inner radius one.

10.7. Direct comparison of the results of the
experiments and the simulations.

Up to this point, we have discussed the experimental verification of some
scaling laws that had already been studied in the simulations performed in
chapter 9. At the beginning of this chapter, it was shown that due to the high
sensitivity of the break up process to the initial conditions direct comparison of
the longitudinal profiles was not possible. Although, it was still possible to study
the evolution of the average number of clusters.

At this point, we would like to compare directly the results of these
measurements with some of the simulations in the previous chapter. In particular,
we will compare the simulations performed with bunches with characteristics
listed in Table 9 with the measurements of bunches with the characteristics listed
in Table 21.

Simulations are shown in grey in Figure 91 while experiments are shown
in red. It can be observed that the agreement is remarkably good. The
simulations describe when the break up of the bunch occurs as well as the

merging rate of the clusters for the three higher peak currents.

171

 

20 pA

    

 

| ' . |
I Experiments f

 

 

# Clusters

 

 

 

 

 

Turn #

Figure 91: Comparison in the evolution of the average number of clusters between simulations
(characteristics of the bunches listed in Table 9) and experiments (characteristics

listed in Table 21 ).

172

The 2 pA case is not very interesting. The noise to signal ratio in the
measurements for such low currents is very high. In some cases, this noise is
misread as clusters. This explains why the standard deviation is much larger than
in other cases as well as why the average number of clusters counted is larger
than one before the break up occurs.

Just two different microscopic representations of the bunch were used in
the simulations in this case. For this reason, only the evolution of average

number of clusters is shown. The standard deviation is not significant.

173

11. CONCLUSION

Partial conclusions were included at the end of several chapters of this
dissertation. We will summarize here the most important ones:

The Small lsochronous Ring (SIR) has been completed and it is working
well. In particular, all the requirements of the injection and extraction lines
described in this dissertation have been achieved.

The control and data acquisition systems of SIR have been finalized.

Extensive simulations have been performed using CYCO to study the
longitudinal beam dynamics in the ring. The impact of beam emittance, peak
current and energy have been studied and the scaling law described in section
1.3 has been numerically validated.

The evolution of the longitudinal profiles of bunches with different
characteristics have been measured. Although the details of these profiles are
not repeatable and therefore not exactly described by the simulations, general
features such as when the break up occurs, into how many clusters it breaks and
how fast the clusters merge afterwards are accurately described by the
simulations.

The simulations have also shown that the beam variability observed
experimentally is compatible with the small perturbations of the initial conditions

likely to happen when the beam is extracted from the ion source.

174

The good agreement between simulations and experiments give us
confidence that CYCO can be used to describe the longitudinal beam dynamics
in other isochronous machines where space charge forces are strong.

Some questions remain open and more research will be necessary to
answer them in the future. Especially intriguing is the nature of the final cluster

density (nm) or the rate at which clusters merge (2') that were briefly mentioned

in section 9.12. It would also be very interesting to find a simple explanation to
justify why the bunch as a whole is not as stable as the cluster distribution into

which it evolves.

175

APPENDIX A: OPERATING PROCEDURES FOR SIR

The Small lsochronous Ring (SIR) has a variety of subsystems that must
be operated in a safe manner both for machine protection and personal safety.
Different procedures have been developed to perform some of the most common
tasks on the machine and included in this appendix to be used as a reference by
future users. There is not a unique way to operate the machine. Some of the
steps may be performed in different order and some of them can be skipped in
certain conditions. Although, it is not recommended until full familiarity with the
machine has been achieved.

It is worth mentioning here that:

The sections that have been biased to high voltage must be
grounded with the grounding rod immediately after the ion source cage is
unlocked.

There is not exception to this rule.

A.1. — Procedure to turn on SIR

COOLING OF THE MACHINE (See Figure 92)

. Open the main low conductivity water (LCW) return valve. The pressure
reading should be around 30 psi.

0 Open the main LCW supply valve. The pressure reading should be around
135 psi. A differential of pressure between the supply and the return line

of around 100 psi is necessary to guarantee that the flow of water in the

176

system is sufficient to dissipate the heat fast enough to avoid a
temperature rise that could damage different components of the machine.
a Open the secondary LCW supply valves for the ion source, injection line
magnet, emittance measurement system and magnets in the ring.
0 Open the secondary LCW return valves for the ion source, injection line
magnet, emittance measurement system and magnets in the ring.
Note: Opening the return valves before opening the supply valves
guarantees that the pressure in the water circuits is not too high thus preventing

leaks.

Main Return Valve

Supply Line

Main Supply Valve
é—— Supply Pressure

     
 

Secondary
Return Valves

Secondary
Supply Valves

Figure 92: Picture of the low conductivity water manifold used to cool down the ion source, the
emittance measurement system and the dipole coils.

HIGH VOLTAGE PROTECTION
0 Verify Einzel lens power supply is off. (Figure 96)
0 Verify extraction power supply is off.

0 Verify high voltage monitor reads zero kV and high voltage light is off.

177

0 Unlock and open the door of the high voltage cage. (Figure 93)
0 Ground high voltage parts with grounding rod.

Note: Even though all the high voltage parts of the system are grounded
automatically when the door is unlocked, they must be manually grounded to
guarantee personal safety if automatic system fails.

Note: The ion source hardware and its power supplies must be grounded
with the grounding rod independently. A short in the cable connecting them could

leave one of them floating at high voltage.

     

Vlllilb‘r
'

High Voltage
Cage Lock
High Voltage

Monitor

Figure 93: Picture of the high voltage monitor, grounding rod and lock of the ion source high
voltage cage.

FEEDING GAS TO THE ION SOURCE
o If the source has not been used in several weeks or if the injection line has
been vented since last time the source was used, refer to the procedure to

clean the hydrogen line.

178

0 Close the needle valve in the cage using isolation rod. A needle valve is
used to control the flow of hydrogen into the ion source. This flow and the
conductances of the different portions of the vacuum chamber determine
the pressure distribution in the whole machine. (Figure 94)

. Open the right angle valve in the cage. A right angle valve is used to
guarantee that there is not continuous flow of hydrogen into the source
when the machine is not being operated. The needle valve by itself does

not work as an open/close valve.

Right Angle Valve I
-

   
 

Source Water

C m Lines

Temperature 00 9
Sensor

Ion Source

Ceramic HV f ' ’ Clamping
Break " ' _ Screws

Figure 94: Picture of the ion Source and its associated gas handling system.

Einzel Lens HV
Feedthrough

. Open the valve in the hydrogen tank. (Figure 95)
. Verify gas pressure after regulator is around 20 psi. A regulator is used to

reduce the pressure from the gas tank to a pressure a little bit higher than

179

atmospheric. No air will penetrate in the line if a leak develops thus

preventing contamination of the hydrogen.

Oil Filter
Power Off
Safety Valve

\

H2 Line Valve
H2 Tank Valve

Tank Pressure
Pressure regulator

   

Hydrogen Tank

Figure 95: Picture of the hydrogen tank and regulator.

TURNING ON THE ELECTRONICS

. Turn on digital multimeter in the cage. A digital multimeter is used to
measure the arc current. The analog dial of the power supply is not
accurate enough. (Figure 96)

0 Verify that the distance between high voltage elements and ground
elements in the high voltage cage is at least 8 to 10 cm to prevent sparks.

0 Close and lock the door of the high voltage cage. (Figure 93)

. Set the current of the filament power supply to zero. If the machine is
turned on with a non-zero filament current, the thermal shock in the

filament may break it. The filament current has to be ramped up slowly.

180

Set voltage in the Einzel lens and extraction power supply to zero. If the
machine is turned on with the high voltage on, sparks may be produced
and the polished surfaces of the puller or Einzel lens may be damaged.

The extraction voltage and the voltage of the Einzel lens have to be

ramped up slowly.

  

7

     
   

l .
,‘fik
3:

Magnetic 8 I ' , .
Shield : _ . I"
. 1'. Arc Power Supply
r ' 1
Isolation , 1 , -. I Filament Power
Transformer ,. I, ’ . ,. r I Supply

      
 

Digital " ” i - .
Multimeter ‘ ‘ ‘ ’ '
Cr ‘ § _

Pirani Gauge I

  
 
  
  
 
 
 
 
 
   
 
   
  

'W‘éfl

CAEN Power
Supply
Einzel Lens
Power Supply

C Motor *- ,\ {. Safety Box
ontrollers - o, Start/Stop Button

H' hV It I A“ “iv I 4
.rg 0 age 2 - ' - ,2 Extraction
Eight & Alarm Power Supply
Digital Delay Quad Corrector Coil
Lrne ,

Power Supply
Zero-Flux Transformer i
Controller

   

 

‘0

 

Controller

 

 

i
‘\
V;
. ‘.

 

err

Inj. Line Magnet
Power Supply

9
’»

Figure 96: Picture of the ion source and injection line associated electronics.

. Turn on injection line magnet and ring magnets power supplies.

Start program to control the magnet power supplies. Execute ‘Computer 1’

> ’Drive C’ > ‘Folder SIR' > ‘Folder Applications’ > ‘PowerSupplies

Controls”. (Figure 43).

181

 

 

 

Data Acquisition Card
Motor Controller Card

 

Power Supplies Control
Scanning Slits
Scanning Wires
Emittance Measurement
Oscilloscope Data Acq.
Beam Lifetime Meas.

 
       
     
    

1i ’ Video Capture
I‘M-“V Delay Line Control

: . ' I":"| , “MLHHIII‘H
I 1' {/7 1‘ “Lilli“ iiltiiil.-.ll..i CAEN PS Control
'l

  
   
 
    
 
    

Video Switch
PU 2:

C
Video Capture Card r:

t.
r
“I.
. r a

CPU 1:

   

GPIB Card ._._

 
 

Figure 97: Picture of the PCs used for data acquisition and control of SIR.

Retract emittance measurement system slits. Execute ‘Computer 1’ >
’Drive C’ > “Folder SIR’ > ‘Folder Applications’ > ‘ScanningSlits’ after
verifying that the motor drive (Figure 98) is connected to control them.
This program will automatically retract the slits every time it is restarted.
Turn on the CAEN power supply.

Start program to control the CAEN power supplies (quads, lnflector,
deflector, chopper, steering...) Execute ‘Computer 2' > ’Drive 0’ > ‘Folder
SIR' > ‘Folder Applications’ > ‘HVPS Controller’. (Figure 99)

Verify that all the elements inside the vacuum chamber are grounded or
connected to the corresponding instrumentation. If any of these elements
are left floating and the beam hits it, it will charge up and spark.

Start program to monitor phosphor screens. Execute ‘Computer 2’ > ’Drive

C’ > ‘Folder SIR’ > ‘Folder Applications’ > ‘VMonitor’. (Figure 99).

182

 
 
  

   

FFC Grid
voltage control

Picoammeters

Digital Multimeter
Dipoles Current

   
    
    
 
  
    
 
  

Frequency

  

Counter

 

Waveform
Generator

 

  

Digital
Oscilloscope

  
   
 
 

Quad Corrector
Coil Power Supply

I

  
   

Ring Magnets
Power Supply

Phosphor
Screen

. . . CAEN Control
Injection Line

 

 

 

g . I” __ -‘ : Pro ram
PositivePS , " ,’ ‘1; :‘ " : ’,.., I " g

 

 

 

 

 

 

 

 

 

 

 

 

 

{2"

. . ' b} V‘ I
17"“ “7 nr-rwrr; F: 1.91 fifirmm‘
ns.-J nae 399: ram...“ ilm »...— il-m ....... 15.—r- “: 12:.»— J ‘ “M ""

 

Figure 99: User interface of the video capture and high voltage power supply control programs.

183

Select video channel corresponding to the injection point CCD camera.
(Figure 97)

Retract the phosphor screen at the injection point (Figure 100). The beam
power dissipated in the phosphor screen should be as low as possible in
order to maximize the lifetime of the phosphor. This can be achieved by
lowering the duty cycle of the chopper if it is important not to change the

transverse beam properties.

Air Regulator

 

 

Screen Controls

Injection Point
Phosphor

 

Turbo Pumps
Valve Controls

 

 

Figure 100: Picture of the compressed air control system. The two furthest left switches are used

to position the injection point phosphor screen. The four furthest right switches
open or close the valves in between turbo pumps and mechanical pumps.

Retract scanning wires in the ring (Figure 34). Execute ‘Computer 1' >
’Drive C’ > ‘Folder SIR’ > ‘Folder Applications’ > ‘ScanningWires’ after
verifying that the motor drive (Figure 98) is connected to control them.
This program will automatically retract the wires every time it is restarted.

Turn on and enable the six fast high voltage switches (Figure 101). They
were placed next to their load to minimize the raising time since most of

the capacitance of the load is due to the length of the coaxial cables. (The

184

rise time of the generated pulses is longer when the capacitance of the

load is larger.)

  
    
 

High Voltage Switches:
Positive Chopper
Negative Chopper

 
 

 

Compressed
Air Controller

High Voltage Switches:
Positive lnflector
Negative lnflector
Positive Deflector

Negative Deflector

  
   
 
 

Injection Point
CCD Camera

 
 
 
 

 

Figure 101: Picture of the fast high voltage switches used to pulse the chopper, second pair of
lnflector plates and deflector plates.

. Push the START button located underneath the safety electric box in
between Ion source cage and LCW manifold wall. (Figure 96)

- Verify the sound alarm is on. The purpose of the alarm is to warn the user
if the high voltage is still on when the cage is opened. This event should
only happen if the high voltage relay, used to ground the whole system
automatically, fails. The alarm will also sound every time the system is
turned on and the high voltage is set below a hundred volts. The purpose
of the alarm in this mode is to let the user know that the alarm is working.
If the alarm does not sound, the machine should be turned off and the

electronics department should be contacted.

185

Turn on the extraction power supply. (Figure 96)

Turn the extraction voltage up to ~ 1 kV.

Verify the sound alarm went off. If this is not the case, the safety system is
not working properly. The machine should be turned off and the
electronics department should be contacted.

Turn on the Einzel lens power supply.

Use program ‘PowerSuppliesControls’ in PC 1 to cycle the magnets in
injection line and ring. Three cycles (0 to 130 A and back to 0 in 10 A
steps) are typically performed before the current is again ramped in 10 A
steps to the working current for the desired ion mass and beam energy.
(Figure 43). Even with the maximum current (130 A), the steel in the
magnets is far from saturation. Refer to page 172 in reference [3] for the
measured hysteresis curve of one of the magnets.

Start program to control the digital delay line that triggers the high voltage
switches that drive the chopper, lnflector and deflector. Execute ‘Computer

2’ > ’Drive C’ > ‘Folder SIR’ > ‘Folder Applications’ > ‘Delay’.

 

 

 

 

 

 

Ion Hz‘”
Energy 20.9 keV
Beam Current 20 pA
Bunch length 300 ns
Repetition Rate 1 kHz

 

 

 

Table 22: Beam parameters when the machine is adjusted to the values listed in Table 23.

186

0 Adjust different devices to the desired working values. An example of
those working values that can be used as a starting point are specified in
Table 23. They correspond to a beam with approximately the
characteristics listed in Table 22.
Note: Special care must be taken when adjusting the filament current. The
knob is very sensitive and too much current will burn the filament.
Note: The extraction voltage, Einzel lens voltage and filament current

should be ramped up slowly over a period of 5 to 10 minutes.

Table 23: Example of the values of different parameters of SIR to produce bunches with the
characteristics listed in Table 22.

 

 

 

Parameter Value Comment
Extraction Voltage 20 kV As read by ‘PowerSuppliesControls’
Einzel Lens Voltage 16.5 kV program.

 

There is not direct way to measure the gas
Gas Pressure in the ~ 1-10 pressure in the source. The pressure in the
Source mTorr injection line, ring and in the source inlet are

monitored instead.

 

As read from ion gauge controllers (Figure
Gas Pressure in the ~ 610‘8
105). This pressure in the ring corresponds
ring Torr
to the right source working pressure.

 

Gas Pressure in the __ 0 01-0 1
' ' As read from Pirani gauge controller.
Source inlet Torr

 

 

 

 

 

187

 

Injection Line Dipole

 

As read by digital multimeter connected to

 

 

 

 

 

 

109.1 A
Current the controller of the Zero-flux transformer.
Ring Dipoles Current 108.6 A (Figure 93)
Ring Dipole correctors: .
As read by the dipole correctors power
Magnets 18 2 + 0.3 A .
supplies.
Magnets 3 & 4 - 0.3 A
Repetition Frequency 1 kHz As read by frequency counter.
Arc Voltage 100 V As read by analog indicator of arc P.S.
As read by digital multimeter next to power
supply. The arc current is adjusted by
Arc Current 0.4 A
slowly increasing the filament current
keeping the arc voltage to 100 V.
The filament voltage is not really adjusted.
The knob should be set in such a way that
Filament Voltage ~ 5 V
the filament current is not limited by the
maximum voltage drop.
The filament current should be increased
until the arc current reaches 0.4 A. The
Filament Current ~ 35 A resistance of the source filament will

increase over time as it deteriorates thus

decreasing the needed filament current.

 

 

 

 

 

188

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m lL_ST_1 X21:
a
g; lL_ST_1Yi
5 0 V
0:9 lL_ST_2X1:
3
E lL_ST_2Yi
35 lL_QUAD_1j: 0 V As read by the control program of the
it
i': l f l 1.
2 lL_QUAD_21: 1: 400 V CAEN power supp y or S ots 0 and
'3! (Figure 99)
E lL_QUAD_3:i: i 800 V
Chopper Plates :1: 3500 V
lnflector Plates 1 12400 V
lnflector Plates 2 12280 V
Deflector Plates 12000 V
RG_ST_1Y1
9
-: RG_ST_2Y1
8 0v
5 RG ST 3y: As read by the control program of the CAEN
a, _ _
C
if RG_ST_4Y:|: power supply for slots 2 and 3.
Electron Shields - 150 V
Ring Quad 0 V
Beam Energy 20.9 keV
Bunch Length 475 mm As read by digital delay line control
Tail Length 1 us program.
lon Hf

 

 

 

189

 

A.2. — Procedure to turn off SIR

. Slowly turn down to zero the filament current. (Figure 96)

. Turn down to zero the arc voltage.

0 Turn down to zero (in 10 A steps) the current in the ring and injection line
magnets using the program ‘PowerSuppliesControls’. (Figure 43)

. Turn off all the CAEN high voltage power supply channels using program
‘HVPS Controller’ (Figure 99). Close the program.

0 Turn off the CAEN power supply.

. Retract the phosphor screen at the injection point (Figure 100).

o Retract emittance measurement system slits using program
‘ScanningSlits’ if necessary.

. Retract scanning wires using program ‘ScanningWires’ if necessary.

. Close needle valve using extension rod. (Figure 94)

. Close hydrogen tank valve. (Figure 95)

. Turn down to zero the Einzel lens voltage. Then, turn off the power supply.
(Figure 96)

. Turn down to zero the extraction voltage. Then, turn off the power supply.

. Verify sound alarm is on. The purpose of the alarm is to warn the user if
the high voltage is still on when the cage is opened. This event should
only happen if the high voltage relay, used to ground the whole system
automatically, fails. The alarm will also sound every time the system is

turned off or the high voltage is set below a hundred volts. The purpose of

190

the alarm in this mode is to let the user know that the alarm is working. If
the alarm does not sound, the electronics department should be
contacted.

Turn off the extraction power supply. The sound alarm should still be on.
Push the STOP button located underneath the safety electric box in
between Ion source cage and LCW manifold wall. (Figure 96)

Verify the sound alarm went off.

Verify high voltage monitor reads zero kV and high voltage light is off.
Unlock and open the door of the high voltage cage. (Figure 93)

Ground high voltage parts with grounding rod.

Note: Even though all the high voltage parts of the system are grounded

automatically when the door is unlocked or the STOP button is pressed, they

must be manually grounded to guarantee personal safety if automatic system

fails.

Note: The ion source hardware and its power supplies must be grounded

with the grounding rod independently. A short in the cable connecting them

would leave one of them floating at high voltage.

Close the right angle valve in the cage. (Figure 94)

Turn off digital multimeter in the cage. (Figure 96)

Close door of the high voltage cage.

Close the main low conductivity water (LCW) supply valve.

Close the main LCW return valve.

191

Note: Closing the supply valve before closing the return valve guarantees

that the pressure in the water circuits is not too high thus preventing leaks.

A.3. - Procedure to replace ion source filament

0 Close valve separating injection line from ring.

0 Follow procedure to vent the injection line.

0 Follow the procedure to clean the hydrogen line. Skip the last step. Do not
let hydrogen back into the line.

. Disconnect all the cables from the source including the filament and arc
cables, Pirani gauge. temperature sensors...

. Disconnect gas line. (Figure 94)

0 Disconnect water cooling lines.

. Disconnect isolation rod from needle valve.

0 Unscrew the four clamping screws. (Figure 102)

 
 
    
 
     

" ’93,
. . -

N Ceramic
Spacers Holes

Ion Source
Clamping Holes

  

  

Plasma

. : ' . ; Electrode Hole
0ng Grove » .1 _ . ,. ..

Figure 102: Picture of the flange that holds the ion source and the plasma electrode washer.

192

0 Carefully remove ion source and gas handling system.

0 Cover plasma electrode hole while plasma electrode washer and the o-
ring grove are cleaned. Any residue falling through this hole may deposit
in top of the puller producing a spark when high voltage is turned back on.
This could damage the polished surface of the puller.

0 Remove broken filament. (Figure 103)

0 Remove the o-ring and carefully clean it. Inspect it for scratches and if it is
in good condition, cover it with vacuum compatible grease. If it is
damaged, replace it with a new Viton o-ring. (Viton is rated to resist higher

temperatures.)

Filament Residue

 

Figure 103: Picture of the broken filament in the ion source

0 Clean the filament residue deposited in the ion source internal walls and

elsewhere.

193

. Install new filament. The filaments are made out of a modified thoriated
molybdenum welding rod.

0 Install the Viton o-ring.

0 Install the ion source. Attach the four clamping screws.

. Connect all the cables, water cooling lines and gas line as they were
before. The ion source wiring is described in Figure 5.

0 Follow procedure to pump the injection line.

. Follow procedure to clean hydrogen line.

A.4. — Procedure to clean the hydrogen line

. Close right angle valve inside the cage. (Figure 94)

. Slowly open needle valve to release the hydrogen trapped between it and
right angle valve. The pressure in between the two valves is ~ 20 psi. If
the valve is not opened slowly, the hydrogen would be released too
quickly and the ion gauges and turbo pumps would automatically turn off.

. Close valve of hydrogen tank. (Figure 95)

. Close compressed air driven valves of the two injection line turbo pumps
(Figure 100). The pressure in the injection line will go up since turbo
pumps are not working in this mode. The pressure will quickly go down
again when the valves are opened again.

. Open hydrogen line valve. (Figure 95)

194

. Wait until pressure in hydrogen line is below 500 mTorr as measured by
thermocouple gauge in the line. (Figure 105)

. Close hydrogen line valve.

0 Wait until pressure in hydrogen line is below 200 mTorr as measured by
thermocouple gauge in the line.

. Open compressed air driven valves of the two injection line turbo pumps.

. If the injection line is not going to be vented, open the hydrogen tank valve

and verify that the pressure after the regulator is ~ 20 psi.

A.5. - Procedure to vent the ring

0 Close the right angle valve in the ion source cage. (Figure 94)

. Slowly open the needle valve to release the hydrogen trapped in between
right angle valve and needle valve. The pressure in between the two
valves is ~ 20 psi. If the valve is not opened slowly, the hydrogen would be
released too quickly and the ion gauges and turbo pumps would
automatically turn off.

. Close the gate valve that separates the injection line and the ring if just the
injection line or the ring needs to be vented. (Figure 104)

0 Turn off the ion gauges. (Figure 105)

0 Close the compressed air controlled valves in between the turbo pumps
and the mechanical pumps. (See Figure 100 and Figure 104)

. Turn off the turbo pumps (Figure 105).

195

Injection Line
Faraday Cup

Gate Valve

Compressed Air
Controlled Valve

Turbo Pump

 

Figure 104: Picture of the box in between two of the ring magnets where the beam injected.

Wait until turbo pumps have stopped rotating (Typically ~ 30 minutes). To
verify that they have stopped, they can be briefly turned on and the speed
indicator can be checked.

NOTE: The rotating blades of the turbo pumps will be damaged if air flows

into the chamber through them before they have fully stopped.

Shut down the cooling water for the turbo pumps.

Unplug the power of the power-off safety valve in between turbo pumps
and mechanical pumps. (Figure 95)

Turn off the mechanical pumps.

If the gate valve in between injection line and ring is closed, the machine
can be left in this mode for weeks or months if necessary. Not much water

will be trapped in the walls since the pressure inside will stay in the

196

hundreds of millitorr range for a long time thus reducing the pumping time
to go back to the high vacuum conditions afterwards.

. Slowly open venting valve (Figure 106). The system can be vented either
with air or with dry nitrogen to minimize the amount of water trapped in the

walls (i.e. the pumping time will be reduced).

 

Turbo Pump Controllers:
Next to lon Source
Emittance Measurement Box
Injection Box in the Ring
Extraction Box in the Ring

  
 
   
  

 

 

 

Ion Gauge Controllers:
Next to lon Source
Emittance Measurement Box
In the ring as beam finds them

 

 

Compressed
Air Line

City Water Line
Turbo Pump Cooling

Figure 105: Picture of the vacuum system control area.
A.6. — Procedure to pump in the ring

. Close venting valve. (Figure 106)

0 Turn on the mechanical pumps.

. Plug the power of the power-off safety valve in between turbo pumps and
mechanical pumps. (Figure 95)

0 Open the compressed air controlled valves in between the turbo pumps

and the mechanical pumps. (Figure 100 and Figure 104)
197

Steering Plates
Feedthrough
Thermocouple
Gauge

  

Einzel Lens
Feedthrough

Venting Valve

  

Mass
/ Separator

Figure 106: Picture of the venting valve and one of the thermocouple gauges used in the injection

line of SlR.

Wait until the pressure inside the vacuum chamber is around 100 mTorr
as read by the thermocouple controllers (Figure 106). It should take ~ 30
minutes to reach this pressure.

Open the cooling water for the turbo pumps.

Turn on the turbo pumps (Figure 105). Wait until they reach full speed.
Turn on the ion gauges.

Wait until the pressure in the ring goes below 10'7 Torr before restarting

experiments.

198

A.7. — Procedure to clean components to be installed
inside vacuum chamber

Wear powder free latex gloves during the whole cleaning and installation
procedure. Use q-tips to reach inside the tapped holes or difficult areas in
every step that follows.

If the material of the piece is copper, scrub thoroughly with a Scotch Brite
sponge damped in lemon juice. Lemon juice is very effective to remove
the oxide layer formed in copper when in contact with air.

Rinse with abundant water.

If the material of the piece is aluminum, stainless steel, copper, alumina or
macor, scrub thoroughly with a Scoth Brite sponge damped in a solution of
Alconox detergent. Most of the oil used when the pieces are machined will
be removed in this step.

Rinse with abundant water.

Use acetone to clean the detergent and water residue.

Use ethanol to clean the acetone residue.

Dry the ethanol spraying with compressed air.

Install the piece in the vacuum chamber as soon as possible after it has

been cleaned.

199

APPENDIX B: CONTROL PROGRAMS DESCRIPTIONS

B.1. — Scanning Wires

Every time the program is started, the user will be asked to choose an

initialization file. This file contains the information listed in Table 24 about each of

 

 

the drives.
Parameter Comment
Name = "Box2 X" Name of the Scanning Wire.
Use = TRUE Is this drive going to be used?
Reset = TRUE Does this drive need to be reset when the program

Steps/mm = 1575

SwToAxis = -58.62
RestPosition = -49
NegativeLimit = -56

PositiveLimit = 38

Speed = 4000

Acc = 10000
Channel # = 7

 

 

is restarted?

Relationship between stepper motor steps and linear
distance moved.

Distance between limit switch and beam axis (mm).
Distance between beam axis and rest position (mm).
Maximum distance from beam axis where movement
is allowed (mm) in negative direction.

Maximum distance from beam axis where movement
is allowed (mm) in positive direction.

Maximum movement speed (steps/second).
Maximum movement acceleration (steps/secondz).
Low current multiplexer channel where wire is
connected.

 

Table 24: Scanning wires initialization parameters

The program will reset the drives and move them to the rest position if

specified in the init file before the user can operate the program. (Figure 34)

200

 

 

The yellow vertical cursor specifies the current position of the wire. The
red vertical cursor specifies the position where the wire is going to move when
the “Move” button is pressed. Change the number in the control “To” or move
directly the cursor to change this value. Press the “Continuous” button instead of
the “Move” button to continuously move the wire between its starting and final
position until the button “Continuous” is pressed again.

Change the vertical scale (Current density) to change the scale in which
the picoammeter acquires the data.

All the profiles, that are taken, will be displayed in the graph until the
corresponding “Delete” button is pressed. The last profile taken will be displayed
as number 1, displacing the previous ones down in the list.

Press the button “Save” to save the data currently displayed in the
corresponding graph. A new window with the information to be saved will be
opened at which point, the user will be able to modify it if needed. Press the
“Save” button in this window to save the modified data.

Acquire three different profiles with different voltages in the inflector plates
before pressing the “Vertical matching” button to center the beam vertically. A
new window will open where the used voltage values can be specified. The
correct values to center the beam will appear afterwards. Proceed in a similar
way to center the beam radially.

A very similar program was developed to use the scanning slits of the
emittance measurement system. Please, use these instructions as a reference to

use that program.

201

BIBLIOGRAPHY

List of papers published about the SIR project:

J. Rodriguez, E. Pozdeyev, F. Marti. “Control System of the Small
lsochronous Ring”. EPAC 2004. Page 830.

J. Rodriguez, E. Pozdeyev, F. Marti, R. York. “Experimental Results of the
Small lsochronous Ring”. EPAC 2004. Page 2191.

J. Rodriguez, E. Pozdeyev, F. Marti. “Beam Diagnostics of the Small
lsochronous Ring”. EPAC 2004. Page 2795.

F. Marti, E. Pozdeyev, J. Rodriguez. “Study of Space Charge Effects using
a Small Storage Ring that works in the lsochronous Regime”. Cyclotrons
2004.

J. Rodriguez, E. Pozdeyev, F. Marti, R. York. “Initial experimental Results
of the Small lsochronous Ring”. PAC 2003. Page 2649.

E. Pozdeyev et aI. “Progress Report on the Small lsochronous Ring
Project at NSCL”. PAC 2003. Page 138.

E. Pozdeyev, J. Rodriguez. “Computer Simulations of the Beam Dynamics
in the Small lsochronous Ring Project at NSCL”. EPAC 2002. Page 1398.

E. Pozdeyev, F. Marti, J. Rodriguez. “Small lsochronous Ring Project at
NSCL”. EPAC 2002. Page 1395.

J. Rodriguez, E. Pozdeyev, F. Marti. “Injection Line of the Small
lsochronous Ring”. EPAC 2002. Page 1401.

E. Pozdeyev. “A Small lsochronous Ring for experimental study of the
Longitudinal Space Charge Effect in lsochronous Cyclotrons”. PAC 2001.
Page 3549.

E. Pozdeyev. “A fast Code for simulation of the Longitudinal Space
Charge Effect in lsochronous Cyclotrons”. Cyclotrons 2001. Page 411.

General bibliography:

A. Chao. “Handbook of Accelerator Physics and Engineering”. World
Scientific.

202

 

D. Carey. “The optics of charged particle beams”. Harwood academic
publishers.

J. Livingood. “Principles of cyclic particle accelerators”. D. Van Nostrand
Company.

 

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[2]

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[6]

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[11]

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M. M. Gordon. “The longitudinal space charge effect and energy
resolution”. Cyclotrons 1969. Page 305.

P. A. Schmelzbach, et al. “The PSI high intensity cyclotron and its
extrapolation to a 10 MW driver”. High Intensity and High Brightness
Hadrons Beams. 2002. Page 197.

E. Pozdeyev. “CYCO and SIR: New Tools for Numerical and Experimental
Studies of Space Charge Effects in the lsochronous Regime”.
Dissertation. Michigan State University, 2003.

V. P. Dmitrievsky, et al. “The high current cyclotron complex for an
electronuclear way of production of energy“. Cyclotrons 2001. Page 434.

L. Calabretta, et al. “A superconducting ring cyclotron to deliver high
intensity proton beams”. EPAC 2000. Page 918.

T. Kuo, et al. “A possible high current H- injector for cyclotron-based
energy amplifier accelerator”.

G. Kim, et al. “A superconducting isochronous cyclotron stack as a driver
for a thorium-cycle power reactor”. Cyclotrons 2001. Page 437.

Application Notes Tektronix. “Understanding Oscilloscope Bandwidth,
Rise Time and Signal Fidelity”.

M. Bellato, A. Dainelli, M. Poggi. “Design and test for the fast Faraday Cup
of the ALPI post-accelerator”. Nuclear Instruments and Methods in
Physics Research A 382. 1996. Page 118.

Princeton Scientific Corporation. “Coaxial Faraday Cup Type DF040”.
www.princesci.com

A. Chao. “Handbook of Accelerator Physics and Engineering”. World
Scientific.

Y. Lee et al. “A Compact filament-driven Multicusp Ion Source”. Nuclear
Instruments and Methods in Physics Research B 119. 1996. Page 543.

203

 

 

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[16]

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[13]
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[2 5]

Huashun Zhang. “Ion Sources”. Springer. 1999

David A. Dahl. “SIMION 3D v.7.0. User’s manual”. 2000.

M. Berz. “COSY Infinity”. www.bt.pa.msu.edu/index_files/cosy.htm.
“TOSCA”. Vector Fields. www.vectorfields.com

M. S. Zucker, J. W. Bittner. “A Faraday Cup with High Frequency
Response for a 200 MeV LINAC Proton Beam”. 0-7803-0135-8/91 IEEE.
Page 1270.

“LabVlEW 7.0”, National Instruments, www.ni.com.

“MatLab 6.5”. The MathWorks. www.mathworks.com.

M. P. Stockli et al. “Self-Consistent, Unbiased Exclusion Methods of
Emittance Analysis”. PAC 2003. Page 527.

M. P. Stockli et al. “Variable Exclusion Method for Self-consistent,
Unbiased Emittance Analysis”. EPAC 2004.

M. P. Stockli, R. Welton, M. Leitner. “Emittance Measurements and
Analysis”. ECRIS 2004.

“TcllTk”. www.tcl.tk.
“IMAQ”. National Instrument. www.ni.com.

“PXI Techonology Review”. www.pxionline.com.

204

 

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