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PHASE SELECTION AND MEASUREMENT IN A
SUPERCONDUCTING CYCLOTRON

By

James Donald Bailey

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1994

ABSTRACT

PHASE SELECTION AND MEASUREMENT IN A SUPERCONDUCTING
CYCLOTRON

By

James Donald Bailey

Phase selection hardware has been installed in the K1200 superconducting cy-
clotron. These phase slits have successfully selected a beam pulse with a single
peak of F WHM of 2.4° in RF phase, from an initial pulse of FWHM of 14.l° in RF
phase. This reduced pulse transmitted 20% of the unreduced internal beam current.
An internal Si PIN diode detector has been developed to measure the beam time
spectrum. This timing probe was installed and successfully tested in the K1200.
A phase selection simulation was developed using the MSU/NSCL orbit integra-
tion codes MYAXIAL, INFLECTOR, and Z3CYCLON E. The simulation began in
the axial injection line ~3 m below the K1200 median plane. Details of the phase
selection which were measured with the internal timing probe were reproduced by
the simulation. Aspects of injection and acceleration were explored and related to
phase selection, with suggestions made for future improvements in the phase selec-

tion hardware.

To my parents,
Floyd & Sally Bailey,
in gratitude for

their love and moral support.

iii

ACKNOWLEDGEMENTS

I would like to express my gratitude to Jerry Nolen, for his guidance, support,
and friendship, and for taking me on as his student. I am deeply grateful] for Felix
Marti, who trained me in the details of the MSU cyclotron codes, and assisted
me throughout these studies, his friendship and motivation was invaluable. I am
also thankfull for Henry Blosser and Mort Gordon, for their having trained me in

Accelerator Physics.

This project required the assistance of much of the staff of the National Super-
conducting Cyclotron Laboratory, all of whom deserve my thanks. Especially John
Yurkon and Dennis Swan, for their assistance with detectors and electronics, John
Kuchar and Jack Ottarson for their work in designing the phase slits and timing
probe, and the entire Operations staff, who have assisted and trained me in the

operation of the K1200.

This work was supported by the National Science Foundation through the Na-
tional Superconducting Cyclotron Laboratory. They, together with the College of
Natural Sciences and the Physics and Astronomy Department at Michigan State

University, have financially supported my graduate career.

Finally, I would like to give my thanks and appreciation for my wife, Kitty.

Thank you for your support, encouragement, and motivation.

iv

TABLE OF CONTENTS

LIST OF TABLES vii

LIST OF FIGURES viii

1 INTRODUCTION 1

1.1 AN INTRODUCTION TO THE K1200 CYCLOTRON ........ 1

1.2 MOTIVES FOR REDUCING THE PHASE SPREAD ........ 4

1.3 EARLIER PHASE STUDIES ...................... 6

1.4 MOTIVES FOR K1200 PHASE STUDIES ............... 10

1.5 CHAPTER SUMMARIES ........................ 11

2 INITIAL CONDITIONS 13

2.1 INJECTION SETUP, AND APPROXIMATION S ........... 14

2.1.1 Ion Sources ............................ 14

2.1.2 Traversal of the Yoke ....................... '18

2.1.3 Spiral Inflector Injection ..................... 18

2.1.4 Central Region Selection ..................... 20

2.1.5 Injection Matching ........................ 22

2.1.6 A Non-Cylindrically Symmetric B ................ 23

2.1.7 Final Choice of Initial Conditions ................ 24

2.2 PROGRAMS USED/MODIFIED FOR THIS STUDY ........ 26
2.3 ACCEPTANCE OF THE CONTINUOUS (DC) BEAM IN THE

K1200 ................................... 29

2.3.1 2-D Acceptance in Phase Space ................. 31

2.3.2 4—D Transmission Through the Central Region ......... 45

2.4 TRANSMISSION STUDY WITH BUNCHING ............ 60

2.4.1 Debunching in the Yoke ..................... 62

2.4.2 Debunching in the Spiral Inflector ................ 63

2.4.3 Bunching Through the Spiral Inflector ............. 64

V

3 USING A Si PIN DIODE AS A TIMING DETECTOR
3.1 EXPERIMENTAL DESCRIPTION ...................
3.1.1 The Detector ...........................
3.1.2 The Electronics ..........................
3.1.3 A Data Collection and Display Program ............
3.1.4 Results with the External Timing Detectors ..........
3.2 USING THE DETECTORS ON K1200 PROBES ...........
3.2.1 Detector Modifications for Use Inside the Cyclotron ......
3.2.2 Detector Simulation .......................
3.2.3 Signal Variation and RF Pickup .................
3.2.4 Multi—Turn Collection and Beam Centering ..........
3.3 PHASE CURVE MEASUREMENTS ..................

4 PHASE SLITS
4.1 SLIT PLACEMENT AND DESIGN ..................
4.2 CALCULATED SLIT PERFORMANCE ................
4.3 MEASURED SLIT PERFORMANCE .................
4.4 STABILITY ................................
4.5 CONTROLLING PHASE CUTS WITH Em .............

5 EXTRACTION AND PHASE CUTS
5.1 SINGLE TURN EXTRACTION .....................
5.2 EXTRACTION MEASUREMENTS ..................

6 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

LIST OF REFERENCES

vi

66
67
67
68
71
72
73
75
83
86
88
89

92
92
95
103
107
109

114
114
116

119

122

2.1

3.1
3.2

4.1

LIST OF TABLES

K1200 Cyclotron DC Acceptance ..................... 59
Detector Characteristics Prior to Cutting. ............... 79
Detector Characteristics after Cutting and Mounting .......... 80
Phase Cuts and Transmission ....................... 106

vii

1.1
1.2

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
2.23
2.24
2.25
2.26

LIST OF FIGURES

K1200 Median Plane Overview. ..................... 3
B(r) and sin(¢) for the ‘Standard’ Operating Point ........... 8
ECR Switch Yard and K1200 Injection Line ............... 15
K1200 Axial Injection Line. ....................... 19
K1200 Axial Magnetic Field ........................ 20
K1200 Central Region Orbits in the Low Voltage Central Region. . . 21
Injection Beam Envelopes. ........................ 30
2-D Injection Transport. Case 1, x-x’ ................... 32
2-D Injection Transport. Case 1, y-y’ ................... 33
2-D Injection Transport. Case 2, 3-3’ ................... 35
2-D Injection Transport. Case 2, y-y’ ................... 36
2-D Injection Transport. Case 3, x-x’ ................... 37
2-D Injection Transport. Case 3, y-y’ ................... 38
2-D Injection Transport. Case 4, :r-x’ ................... 39
2-D Injection Transport. Case 4, y-y’ ................... 40
2-D Injection Transport. Case 5, m-x’ ................... 41
2-D Injection Transport. Case 5, y-y’ ................... 42
2-D Injection Transport. Case 6, :r-x’ ................... 43
2-D Injection Transport. Case 6, y-y’ ................... 44
23-31 Particle Distribution at the Inflector Entrance. .......... 47
123-1), Particle Distribution at the Inflector Entrance ........... 49
Phase Compression in the K1200 Low Voltage Central Region ..... 50
K1200 Acceptance in Time for the Low Voltage Central Region. . . . 51
E-¢ and r-¢ Correlations Inside the Cyclotron .............. 53
r-z and pr-p, After 11 Turns. ...................... 54
r-p, and r-p, After 11 Turns. ...................... 56
z-p, and z-pz After 11 Turns. ...................... 57
Buncher Test in the Program MYAXIAL ................. 61

viii

2.27 Debunching During Traversal Of the Yoke. ............... 62

2.28 Total Debunching from the Yoke and Inflector .............. 63
2.29 Bunched Beam at the Inflector Exit. ................. 65
3.1 Timing Detector Electronics Schematic .................. 69
3.2 Resolution Of the Hamamatsu External Detectors ........... 73
3.3 Bunched Beam Measured with the Hamamatsu External Detectors. . 74
3.4 The K1200 Timing Probe Head ..................... 75
3.5 The K1200 A5 Probe Drive. ...................... 76
3.6 Time Corrections for the A5 probe. .................. 77
3.7 Detector Modifications Made by SI for Use Inside the K1200 . . . . 78
3.8 Extreme Precessional Effects and Internal Detector Resolution. . . . . 81
3.9 Analog Beam Time Spectra ....................... 82
3.10 Calculated Constant Fraction Output. ................ 85
3.11 Detector RF Pick-Up and Signal Strength. .............. 86
3.12 Shifts in Time from the RF Pick-Up. ................. 87
3.13 Precession Effects on Relative Time Widths. ............. 89
3.14 A K1200 Measured Phase Curve. ................... 90
3.15 Differences in the Measured and Fit Phase Curves. ......... 91
4.1 K1200 Phase Slit Drive Schematic. .................. 94
4.2 Phase Slit Cuts in r-p, Phase Space. ................. 96
4.3 Preliminary Calculation Of the Slit Transmission. .......... 97
4.4 Calculated Slit Performance Using the Bunched 4-D Injection. . . . 99
4.5 r-¢ Density Plot Showing the Overlap Of Turns. ........... 100
4.6 Calculated Phase Slit Cuts After the First Central Region Cut. . 102
4.7 Phase Slit Cuts After the Second Central Region Cut ......... 104
4.8 Comparison of Phase Cuts at Different Frequencies .......... 105
4.9 The Best Stable Phase Cut. ...................... 107
4.10 A Measurement of Phase Slit Stability. ................ 108
4.11 Controlling Phase Cuts with Bz(r). .................. 110
4.12 Calculation Of Cuts Made with the Buncher Tuned to One Edge. . . . 112
5.1 Phase Spectra from the Extraction Measurement. ........... 117

ix

CHAPTER 1

INTRODUCTION

1.1 AN INTRODUCTION TO THE K1200 CYCLOTRON

The K1200 cyclotron, built at the National Superconducting Cyclotron Laboratory
at Michigan State University by H. Blosser, who led the design, construction, and
inauguration[1], has been Operated for Nuclear Physics research since 1988[2]. The
K1200 has proven itself a versatile and reliable accelerator[3]. Beams as light as
a hydrogen molecule, and as heavy as uranium have been extracted with energies
as low as 18 MeV/u (”Ne”), and as high as 200 MeV/u (1608+ on 2/2/94[4, 5].)
This work is a study of the time and energy aspects Of single particle dynamics
in the K1200 cyclotron, with a goal Of providing improved beam quality, and is a
continuation of studies done by Milton at MSU/ N SCL with the K500 cyclotron[6,

7, 8], the world’s first Operating superconducting cyclotron.

Michigan State University’s K1200 cyclotron is a compact, isochronous cyclotron
with superconducting main coils. The use Of two split main coils, together with 21
independent trim coils per hill, allows for the production of isochronous fields over a
range Of 3 — 5 Tesla for many different q/m’s, and final energies. TO be isochronous
w = qB/m must be constant, so B,(r) must be approximately '7 Bo, where 7 is the
relativistic mass increase m = 7 mo. The median plane cross-section is depicted in

Figure 1.1. Three spiral shaped pole tips, or hills, produce an azimuthally varying
l

field, which provides vertical focusing, except in the center. Acceleration is achieved
with three spiral shaped dees located in the valleys between hills, which Operate be-
tween 9 — 27 MHz. The final velocity is a function of charge tO mass, magnetic field
and radius, Often expressed as a bending limit on the final energy, E/ A = Kb(Q/A)2,
with a K, value Of 1200 MeV for the K1200 cyclotron. The extraction radius is ap-
proximately 1 m. A second limit comes from focusing capabilities, and is expressed
as E/ A = K f(Q/A), with K f = 400 MeV. Hence the maximum achievable energy
Of 200 MeV/u is focussing limited with Q / A = 0.5[2].

The cyclotron is currently Operated in first harmonic mode with on-axis injection
through a spiral inflector to fixed central region electrodes which are depicted in
Figure 2.4. Three Electron Cyclotron Resonance Ion Sources (ECR’s) are operated
as external sources, providing the wide range of ion’s and charge states mentioned
above. The injection, inflection, and acceleration voltages are adjusted tO Obtain the
same orbit path through the central region electrodes for every ion[2, 9]. Centering Of
orbits is achieved through a first harmonic magnetic field bump applied with trim coil
1 as the beam initially crosses the radial focussing resonance, V,- = 1 [9]. Precessional
extraction is used, with trim coil 21, producing a first harmonic bump near the
second and final crossing Of the u, = 1 resonance. The beam is then separated
with an electrostatic deflector and guided through the yoke with electrostatic and
magnetic channels[10, 11]. Between injection and extraction, the beam traverses
approximately 750 - 800 turns. The V, — 21!, = 0 difference resonance, coupling
the transverse planes Of motion, must also be crossed, usually before extraction,
but the force is amplitude dependent, so with good beam centering, it is not a
problem. The typical unbunched acceptance Of the cyclotron is 10% of the current
entering the spiral inflector, with the buncher tripling the injected current. Total

transmission from the 90 deg. charge selection magnet, following the ECR’s, through

 

 

 

 

Figure 1.1: K1200 Median Plane Overview.

The K1200 median plane is depicted with extraction elements and probes. The spiral dees
are marked with ‘racetracks’, where the dees are coupled to the dee stems. The A2 (lower
right quadrant) and A5 (upper right quadrant) probes have been drawn fully inserted
above grounded pole—tips, or hills. The central region detail can be seen in Figure 2.4.
The two circles, just to the right, and closest to the central region, are the locations of the
phase slits.

extraction averages 1.4% with a high Of 11.3%. Extracted currents range from highs
Of ~200 pnA (particle nanO-Amps) down to sub ppA, primarily from production

rates Of the particular charge state in the ECR sources[12].

1.2 MOTIV ES FOR REDUCING THE PHASE SPREAD

There has been a constant stream of accelerator improvements over the years. From
Lawrence’s first cyclotron, the world has seen a host Of different types of cyclotrons,
betatrons, synchrotrons, synchrO-cyclotrons, and linacs, with uses from molecular
through elementary particle physics, and applications in medicine, carbon-dating,
wear analysis, and the production Of semiconducting devices and ultra-fine filters.
The use of computers has greatly facilitated many Of these developments, but studies
done on computers, just like experiments done on individual machines, are device
dependent. This makes it difficult to generalize the results, and even when general
results are derived, simulations are Often necessary to implement these results on

new machines.

For cyclotrons, one such development achieved in the 1960’s, was the introduc-
tion Of slits to remove all but a very narrow pulse Of particles in time. The improved
understanding Of particle orbits provided by computer simulations in the central
region demonstrated couplings between radial[13] (and sometimes axial[14, 15]) mo-
tion, and the particles time with respect to the accelerating RF voltage. (Commonly
referred to as RF phase. Unless explicitly denoted otherwise, the word phase will
refer to the RF phase Of particles inside the machine.) One Of the first groups to
use this new technique was MSU, with their K50 cyclotron[13]. A phase dependent
centering effect was exploited, with the computer finding the locations Of maximum

radial spread for both a parallel orbit which was initially displaced in r, and an

initially divergent orbit which was started on the same point. Then with two slits
inserted, one for each Of those locations, the phase width was reduced from a F WHM
of 23° RF to 1.4° RF (3.4 us to 0.2 ns)[13]. It is important to note that maintaining

these cuts requires stable frequency, voltages, and magnetic fields.

By itself, this type Of reduction is highly useful for experimenters using the
Time—Of-Flight (TOF) technique for energy measurement. The reduced duty cycle
provides better intrinsic resolution, in the same manner that a smaller spot provides
better resolution in a spectrograph. But it also permits the achievement Of single-
turn extraction[16]. With the remaining beam centered, the radius Of a particle is
energy dependent, but the energy is phase dependent. The spot size is reduced,
permitting separation Of turns with precessional extraction. 100% Of the beam is
then extracted[13], greatly reducing the activation Of parts inside the machine, and
removing the power dumped on extraction elements. Furthermore, this reduced
energy spread permits precision measurements Of energy levels, such as those found
in nuclear bound states[17]. These precision beam characteristics were then made
Optional, in that the slits could be removed, allowing the experimenter to select the

beam characteristics most suitable for the particular experiment.

It is also important to note that these advances in Accelerator Physics were also
associated with advances in diagnostic instrumentation, particularly the differential
probe to measure precessional effects and turn separation[18, 14]. A common method
to measure phase is the capacitive pickup, a non-intercepting probe that measures
currents associated with image charges produced by the beam. While the first
harmonic of the accelerating frequency is swamped by the RF pickup, the higher
harmonics left by the beam pulse can be used to give the beam phase[19, 20].

These non-intercepting probes need intense beam bunches, but recent advances have

worked with 10 nA currents[21]. Phase spectra are Often measured externally with
such devices as multi-channel plates to see electrons or x-rays produced by the
beam[20, 22], and BaF detectors or fast plastics to see 7-rays or other secondary

beam products[13, 21]. Measuring phase structure internally is more difficult.

1.3 EARLIER PHASE STUDIES

Collins continued the study Of mechanisms producing the phase cuts in the K50 cy-
clotron, finding phase dependent centering and energy gain effects both contributing
to the cuts. He also showed in his simulations that the magnitudes of each Of these
effects varies in machines with different basic characteristics such as the number Of

hills and the electric fields in the central region[23].

At this point it will be appropriate to review a few basic equations pertaining to
acceleration inside a cyclotron. In each gap, an ion will see an accelerating voltage
VD”, sin(wnpt + (1),). TO accelerate an ion, the voltage on a Dee must go from
negative to positive while the particle is traversing that Dee. Thus, with all the Dee

voltages held to the same value, the maximum voltage seen in one revolution is

hD
V0 = 2VD¢¢NDce sin —2—, (1.1)
with N Dee, the number Of Dees, D, the azimuthal width Of the Dees, and h, the
harmonic number of the cyclotron resonant frequency at which the accelerating

voltage is Operated, defined by 7.03;: = hwo. The kinetic energy gain per turn is then

dE
H—n— = qu cos O, (1.2)

where q is the particle’s charge, and (f) is the position, or phase, Of the particle with

respect to the RF accelerating voltage, with d) = (wnpt — ha) averaged over many

gap crossings[24]. This ¢ is designed such that the earlier a particle arrives at a

azimuth, the more negative is its value Of O, while later particles are more positive.

In an isochronous cyclotron then, for particles within the same turn, with small

 

 

A¢,
AE (A4)?
E — — 2 9 (13)
and,
m
AR- qungAE' (1.4)

When B(r) is not perfectly isochronous, the phase of a particle changes according

to

 

3% = 27rh (“iii — 1) = 27rh (Bo; B) = 27th(E). (1-5)

Combining dE/dn and qu/dn, one can solve for It as a function Of E

sin ¢(E) = sin 430 + 3%: f1: fl(E)dE. (1.6)

Now AE has a first order component[23]
AE (A¢) jE ' ¢dE (1 7)
n = — sm . .
E0

This is the cause of the E-q‘) correlation that Collins found. The top graph in
Figure 1.2 shows an azimuthally averaged magnetic field in the median plane Of the
K1200 cyclotron as a function Of radius. This magnetic field is that Of our ‘standard’
operating point, which is used to start the machine after a long shutdown, and is
often used in orbit studies. Overlaid on this field is the isochronous field for the
same Operating point. The deviations from isochronism result in the sin(¢) curve

shown in the lower half Of the graph, which was calculated with Equation 1.6.

 

40 MeV/A Q/A=.249872

I ' I

I

 

111

l l

 

 

 

 

IlIlIlIlI

l I l I l I J I l I l I l I i

o 5 10 15 20 25 so 35 4o 45
R[1n]

 

Figure 1.2: B(r) and sin(¢) for the ‘Standard’ Operating Point.

The median plane magnetic field for the ‘standard’ Operating point, and the isochronous
field for that Operating point. Note the central cone, used to bring down the initially high
values of (I). Also note the roll Off at the edge, where the magnetic field starts to fall to zero,
and the second 11, = 1 crossing occurs. Here, a first harmonic magnetic ‘bump’ forces the
beam to precess, increasing the radial separation at extraction. The sin(¢) curve resulting
from these deviations from isochronism, see Equation 1.6, is shown in the lower graph.
The field is trimmed so that at extraction, f sin(¢)dE = 0, for sin(¢) = 0.

The phase dependent centering correlation is produced by the time dependent
accelerating voltage[25]. When particles enter gaps with different times, they are
accelerated by different amounts, displacing their orbit centers differently. This
effect is more significant when the velocities of the affected particles are lower. As
this effect accumulates, and the particle orbits precess, places can be found with
r-qS correlations. The two r-qS correlations are cumulative, adding to or canceling

each other.

The K500 presented new complications, with higher magnetic fields reducing
the size Of the central region. Also the strong spiral Of the hills, with smaller gaps
between pole faces restricted access to the central region. Vertical holes had been

drilled in the yoke at 7 in. radius, and Milton explored using these locations to

cut the phase. The position Of the holes was determined by machine constraints
such as finding room amongst trim coils, current leads, and dee stems[6]. SOMA,
a second order matrix algorithm, was developed to include non-linear effects in
the computer simulations[26]. And new techniques were explored to measure the

particle phases[7].

What Milton found is that a pin inserted into the beam can simulate a slit by
removing particles with greater radii as the beam pulse is first intercepted by the
pin, then on the following turn removing the particles with lower radii. Essentially
he was using the phase dependent energy gain effects to make his cuts with two slits
placed 120° apart to increase the chance that one will be away from the crossover
region due to centering. In practice, the two slits, each Off-centered on a rotatable
shaft, combined with a coarse central region cut, made it possible to limit the RF
phase width to 4° F WHM[8]. The studies that were made on the K500 were made
difficult by the need to continually correct the machine’s drifting away from a good
tune. (Being the world’s first super-conducting cyclotron, much was learned in

Operating the K500 that was used to improve the design and Operation Of Texas

A&M’s K500 and MSU’s K1200 super-conducting cyclotrons.)

Measuring the internal phase in the more compact and enclosed K500 cyclotron
was a difficult challenge. The spiral Of the hills meant that the internal probes
were only visible through the viewing ports over a small radial range. The higher
energies to which the K500 accelerated heavy ions, together with beam losses at
these energies created a bright 7-ray background which swamped signals from the
beam. TO overcome these difficulties, a PIN diode was inserted immediately behind
the probe head, which intercepted the beam[7, 8]. This detector was radiation and

temperature sensitive, and was sometimes swamped by ions, which stripped Of more

10

charges by the probe, returned to strike the detector itself, but it was useful for
studying the use Of the slits. Ronningen continued the search for a more robust
detector system, exploring avalanche diodes[27], but these studies were interrupted

by the changeover from the K500 to the K1200 cyclotron.

1.4 MOTIVES FOR K1200 PHASE STUDIES

The K1200 is basically a larger version Of the K500. Its extraction radius is
101.2:I:1.7 cm[ll, 28], instead Of 67.5:I:.5 cm[29]. They both have the same range
of central magnetic fields, Bo = 3 T to 5 T, though the pole tip gap is also slightly
larger, 7.62 cm instead Of 6.35 cm[30, 31]. Since the spiral on the hills is approxi-
mately the same as in the K500, the greater radius of the K1200 makes access to the
center of the machine even more difficult. However, the dee stems are also further
out, leaving more room on the cap for drive mechanisms and phase slit installation.
The central region designs are basically the same, with interchangeable spiral inflec-
tors, though the K1200 central region was rebuilt to Operate at lower dee voltages[3].
As mentioned earlier, the design Of the K1200 took advantage of experience with
the K500, with the result being that it is much more stable. Finally, the vertical

access holes in the yoke were machined at the same radius as in the earlier machine.

In summary then, the center of the K1200 has the same basic functionality as the
K500, and slits can be installed which will function in a similar fashion. Even though
the slits won’t function exactly the same way, because Of small differences in B(r),
voltage gain per turn, and the central region, the stability of the K1200 will allow
a more detailed study Of these slits. The greater extraction radius though makes
single-turn extraction more difficult, and limits measurements to long distances from

the slits.

11

The basic improvement that has been made in computers over the years is raw
speed and computing power. There are now programs to calculate 3—D electric and
magnetic fields, and the ray-tracing Of orbits is no longer prohibitively expensive or
time consuming. The following studies use ray-tracing to study the single particle
motion through the inflector to the slits, since injection through a spiral inflector

involves non-linear coupled motion between the transverse planes Of motion[32].

There being no existent timing detectors for the K1200 a new detector was devel—
oped to provide clean internal time spectra for the cyclotron beam. Together with
computer simulations, this detector enables the study Of the time and energy as-
pects Of acceleration in the same way that the internal TV probe has shown detailed

aspects of the 11,. = 2112 Walkinshaw resonance[33, 34].

1.5 CHAPTER SUMMARIES

Chapter 2 develops the initial conditions which will be used in subsequent calcula-
tions. Source conditions, injection line characteristics, and central region geometry
are described so that reasonable starting conditions and necessary approximations
can be developed. Descriptions Of the programs used in simulating K1200 Operation
are presented. Then the chapter finishes with an exploration of the K1200

acceptance.

Chapter 3 presents the use and testing Of a Si PIN diode to directly measure
the time spectra of a beam. Included are descriptions Of the necessary electronics
and the data collection and display routines developed for on-line use. A simulation
of detector response demonstrates understanding of its use. It then describes the
modifications necessary to use such a detector as an internal beam phase probe. The

implications Of overlapping turns inside the machine are followed to their effects on

12

the measured phase spectra, including the deleterious effects of Off-centered beams.
Also described are the effects Of RF pickup as the probe approaches a dee, and the
variation Of signal strength with ion type and energy, and the resulting limits on the
effective use of this detector. The effectiveness Of the timing probe is demonstrated
by measuring the phase curve followed by the beam, with comparisons to curves

calculated from design magnetic fields.

Chapter 4 furthers the understanding and use Of ‘Milton’ type phase slits in
the K1200. Minor improvements incorporated in the slit design and installation
are presented. Then clean spectra measured with the timing probe, the improved
performance Of the K1200 cyclotron, and advances in computing speed are taken
advantage Of in understanding and exploring the use Of these slits. Finally, it explores
the modification Of the magnetic field to control the energy dependent phase - radius

correlation.

Chapter 5 presents extraction measurements using the timing probe and slits,
and simple conditions necessary for single turn extraction. It then summarizes
the results Obtained in this study and suggests possible courses to take for further

improvements in K1200 beam quality.

CHAPTER 2

INITIAL CONDITIONS

In searching for a reasonable simulation Of the K1200 internal beam for use in mod-
eling the phase slits, the realization was made, that an understanding Of the injection
process would be necessary. Simulations starting immediately after inflection into
the central region, while usefu1[8, 35], leave out possible effects from the spiral inflec-
tor’s coupling of the injection phase space coordinates. Also, transmission into and
through the central region proves to be aperture limited by both the inflector, and
the central region electrodes[9, 36]. Central region calculations alone, then, have a
greater uncertainty as to whether the selected phase space is reasonable, or even
physically possible. Starting before injection also allows simulations Of the buncher,

which include the time dependent effects Of traversing the magnetic yoke, and the

spiral inflector[9, 36].

The beginning Of the vertical injection line, ~3 m below the cyclotron midplane
was chosen as a reasonable starting point for these calculations. It is sufficiently
removed to include both the yoke and the buncher, yet not so far as to divert the
cyclotron timing study into an ECR to cyclotron emittance matching study. And

the beam is DC at this point.

13

14

2.1 INJECTION SETUP, AND APPROXIMATIONS

Figure 2.1 shows the layout of the injection lines leading from the ECR’s to the
cyclotrons. Any Of three different ECR’s can be connected to the K1200 or the K500
cyclotrons. Each extracts downward, followed by a 90° analyzing magnet. In two
Of the three extraction lines, before the analyzing magnets, are focussing solenoids
with slits that perform a crude selection on the charge tO mass ratio (q/m). The
analyzing magnets then perform a fine selection on q/ m. All ions with the correct
q/m are then transported through the injection line to a point below the cyclotron
where a second 90° bending magnet guides them up the cyclotron axis to the spiral

inflector.

2.1.1 Ion Sources

Xie’s study on the extraction from the NSCL RT-ECR ion source[37] (room temper-
ature) showed that it is space charge limited with low neutralization. This ECR has
a focussing solenoid before the analyzing magnet, The spread in the beam envelope,
caused by the space charge forces, completely fills the solenoid aperture, sampling
both the spherical and solenoid aberrations Of the solenoid, and causing an effective
growth in the beam emittance[38]. This has been corrected in the N SCL SC-ECR
(superconducting) by moving the solenoid closer to the source. The NSCL CP-ECR
(compact) is closer to its analyzing magnet, and does not have a focussing solenoid
before the analyzing magnet. The analyzing magnets will also distort the beam if
the beam envelope is too large, so the solenoids are used to move the beam waist

closer tO the bending magnets. Xie showed that the emittance, before this growth

15

 

Figure 2.1: ECR Switch Yard and K1200 Injection Line.
The injection line from the ECR sources to the K1200 cyclotron is shown above. The
analyzing magnets are directly below the ECR’s. Solenoids are used to provide focusing.

16
occurs, is

1E
P2

6:

 

 

_ T.“ 1/2 Q 1/2
- ra [(2QVECR) + A9“ (2MVECR) ] (2.1)

where A90 is the azimuthal component of the vector potential at radius ra in the
extraction aperture, VECR is the extraction voltage, and T,-, Q, and M are respec-
tively, the ion temperature (typically a few eV x Q), charge, and mass. Thus the

unnormalized beam emittance can be 50 to 400 7r mm-mrad after analysis[37].

Understanding injection line transmission after the analyzing magnet has been
left to further studies. The analyzing magnet selects all but one charge to mass
ratio of the ions extracted from the ECR, reducing the intensity Of the beam. It
is important to note, that attenuators have been installed in this part of the beam
line[39]. They can be used to reduce the beam intensity by greater than 6 orders Of
magnitude. Their placement ensures that reductions in intensity are not accompa-
nied by changes in the phase space Of the beam, except for any subsequent space
charge effects. The beam intensity drOps even further during injection, reducing the

magnitude Of any space charge effects.

With the greatest extraction current to date being ~200 pnA, the cyclotron
itself is relatively free from space charge effects. Inside a cyclotron, space charge
effects have been separated into two main components. The transverse component
adversely affects the focussing frequencies, with the smaller vertical focussing being
Of prime concern. A formula estimating the limiting current for adverse vertical
focussing was worked out as early as 1961 by Blosser and Gordon[40]

115m = (260 (.420 V: (M) (AEn) (2.2)
27r q

 

with AEn the energy gain per turn, q the charge, wo the orbital frequency, Aqi the

full phase width, b the vertical aperture, and u, the vertical focussing frequency Of

17

the beam. 60 is the permittivity Of free space, and all units are MKS. Note that
the limit is dependent on the square Of 11,, which is smallest in the machine center,
V2 ~ 0.1. More recently, a different estimate was derived by Joho to understand and

increase the high intensity beams at PSI[41].

__ 1 A , bwo 2 A43
IIIm — 4 (Q) Iofll/z( c ) ( 27" (2.3)
Here 10 is moc2/eZo with Z0 = 30 II, and fl = v/c. Note that now there is a
dependance on the beam velocity. It can be shown that,

2
f

[um (Joho) = 21rN (g9) 11,-", (Blosser &. Gordon) (2.4)
where p is the average radius Of curvature Of the beam for one turn, N the total
number Of turns before extraction, and p f the radius at extraction. With both being
approximate estimates of a complex phenomena, the most pessimistic (Joho’s) is
chosen to estimate an upper bound for the K1200. For the high current beam,
25 MeV/u 1603+, ,3 = .0018, and V; 2 .1 at injection, b = 1.4 cm, f = 10.777 MHz,
and A¢ z 18° F WHM with the buncher on. Using these values, In”, = .37 mA,
two orders Of magnitude higher than the highest current injected into the K1200 to
date[12]. (It should be noted that Joho’s estimate was not pessimistic enough. The

V, + 2112 = 4 resonance reduced the maximum possible current by a factor of 4 from

his calculation[41].)

Since this effect is not significant in the K1200 Operation, experiments can be
conducted at extremely low currents with the attenuators, and the resulting mea-
surements (a study of single particle beam dynamics) will not be far from full cur-
rent Operation. There is one regime though where distortions of the beam bunch by
space charge may be Of concern. The effects Of the longitudinal component will be

presented in Chapter 5, where single turn extraction will be discussed.

18

2.1.2 Traversal of the Yoke

Figure 2.2 shows the last leg of the injection line in more detail. The first item
to note is that the horizontal portion Of the line requires magnetic shielding (not
shown.) The magnetic field at 3 m below the midplane is sufficiently strong to
deflect the ions into the pipe walls without this shielding. A 90° iron core bending

magnet is used to deflect the beam upwards.

At various times, there have been different steering and focussing elements de-
signed and/or installed in the axial injection line. Figure 2.2 shows only the naked
solenoid (no iron), which is the only focussing element used in this study. The
solenoid is 2.22 m below the median plane. Following the solenoid is a buncher. De-
signed tO Operate at both first and second harmonics of the RF accelerating wave,
the buncher to date has only been run in the first harmonic with a sine wave driver.
The accelerating gap is 7 mm between two wire grids, and the distance is 1.7 m

below the median plane[9].

The last item to note in the injection line is that there is a sudden reduction
Of the hole radius at z = 0.33 m from the median plane in the iron center plug.
As shown in Figure 2.3, B(z) varies rapidly at this point. This rapid change in
the magnetic field occurs in a distance approximately equal to the forward distance
travelled during one revolution Of the transverse motion. This rules out any adiabatic

approximations such as the one used to describe magnetic mirrors.

2.1.3 Spiral Inflector Injection

The spiral inflector was patterned after the Grenoble spiral inflector, designed by
Belmont and Pabot[42]. It has a 4 mm diameter entrance aperture, a 6 mm diame-

ter exit aperture, and the electrodes have a 1.75 cm radius Of curvature with a gap

19

K BOO CYCLOTRON

 

BUNCHER

lfll
i7] NAKED SOLENO/D
Ilil
was:
*; 90° D/POLE

 

 

Figure 2.2: K1200 Axial Injection Line.

Portion of injection line in the K1200 vault. The axial segment is used in the injection
studies to determine the initial conditions for cyclotron orbit calculations. Depicted are
the buncher, focussing solenoid, and 90° bending magnet. The horizontal section preceding
the last bending magnet has been magnetically shielded.

20

40 MeV/u Q/A=.250 Injection
77,, ,7”. ”.7777

I T

 

T r T

JIAJJJ

11$;AL1111

 

 

 

 

.-
0 FJJllllJllllllllLlll111.111 1

0 500 1000 1500 2000 2500 3000
2 [mm]

Figure 2.3: K1200 Axial Magnetic Field.

The axial magnetic field from a cylindrically symmetric calculation for the
K1200 ‘Standard’ Operating point Q/ A = 0.25 at 40 MeV/u. The yoke begins at 1.46 m
and the center plug narrows at 0.94 m and 0.33 m. The remaining structure is caused
by the reduction Of iron at 0.16 m and and the opening up of the midplane from 0.08 m
to 0.05 m. The rapid changes in B, particularly at 0.33 m, prevent the use Of adiabatic
approximations.

spacing Of 4 mm[9]. Baartman and Kleeven worked out an infinitesimal transfer
matrix for an ideal spiral inflector[32], which unfortunately leaves out edge effects,
which are significant. Also, we fill the aperture of the inflector. This study sur-
mounts these Obstacles by raytracing through an electric field which includes the

fringe field.

2.1.4 Central Region Selection

The central region is depicted in Figure 2.4. The median plane electrodes are shown,
together with equipotential contours for each dee. Overlaid on the potential map are
central rays for starting times Of 185° to 240° relative to the accelerating voltage on
the first dee. A 45° range can be seen to clear the central region. Also visible is the

time dependent spread Of orbit centers, none Of which is correctly centered at this

   

 

 

(a) Sni all Electric Field Map(midplane K1200 first gap)

SYSSTOP: [MARTI.CBIREGS.WV]ELAR624.DAT;1

"9"" ‘7' V'IYIIV" ‘Q‘
746%‘93 R7251?
@fl’ggz‘ ’9‘: A! 4’

     

 

     
 
  
 
 

f %'07$¢’»
Fa»

  

 

 

Figure 2.4: K1200 Central Region Orbits in the Low Voltage Central Region.

Central ray orbits, for starting times 1'0 = 185° — 240° in 5° steps, are overlaid on median
plane cross-sections of K1200 central region equipotential maps which were created using
RELAX3D. Figure 2.4( a) represents the gap between the inflector and the puller, measures
1.0 x 2.0 in2 and is used in the first part of the orbit program Z3CYCLONE. Figure 2.4(b)
is a closeup from the central region map used in the SUPERCYCLONE subroutine Of
Z3CYCLONE, and is 5.0 x 5.0 inz. The dotted electrodes are at ground and the dashed
electrodes are connected to the dees, with equipotential lines marked at 10% intervals.

22

point. The behavior of ions displaced from the central ray has been considered by
Gordon and Marti[24]. They demonstrated that each particle should be associated
with a central ray whose time difference from the particle is,
_ Pr 2
45 — wRFt — W + hgl/r , (2.5)
a correction tO the 45 used in Equation 1.2, so that each with a given 45 will have the
same energy gain per turn later in the machine. Here p; is p, — pm, where p,.o is for

the reference particle or central ray, and 11,. is the horizontal focussing frequency.

Having fixed electrodes in the central region requires that beams for every Oper-
ating point travel the same path in the machine. This is accomplished by selecting
Bo, V303, and VDEE such that the ion in question will have the same bending radius
in every case, 0.795 cm[43]. With Bo and VDEE determined by the orbit charac—
teristics inside the cyclotron, VECR is constrained to provide the requisite energy.
Vsp, the voltage on the spiral inflector, then follows, providing the correct radius
of curvature in the inflector. Note that this means VECR is not a free parameter in

determining the emittance of the injected beam.

2.1.5 Injection Matching

The concept of an eigen-ellipse in phase space, which maps back to itself after one
complete traversal of a repetitive transport system, has been extended tO
cyclotrons[16], in that the particles displacement from the central ray is the co-
ordinate system in which the map is performed. This eigen-ellipse about an accel-
erated equilibrium orbit is then the preferred orientation Of particles in phase space
for transport through the machine. Injection matching is the process of trying to

match this eigen-ellipse with the injected beam. Failure means that the emittance

23

will effectively grow as the beam samples non-linearities in the magnetic and electric
fields. The choice Of injection method, and the design of the central region, as well
as the availability Of injection line focussing elements are the major determinants
of the feasibility as well as the practicality Of injection matching for a particular

machine.

This study extends this concept from the transverse motion Of the beam to
the longitudinal or time and energy coordinates. The non-linearities of transport
through the spiral inflector and central region present an extra challenge towards

achieving good phase selection inside the machine.

2.1.6 A Non-Cylindrically Symmetric B

One further complication must be considered before modelling injection. The iron
in the injection line shielding and bending magnet attract magnetic flux Of the
cyclotron fringe field[2]. This causes the magnetic field immediately following the
bending magnet to be asymmetric. The real magnetic field is difficult to map and
to simulate. The higher the magnetic field, the closer the beam has to be steered to
the inside edge of the bending magnet in order to guide it into the inflector. This
study will ignore this, leaving an understanding of this effect to future injection line
studies, and its removal to future modifications. The solenoid used in this study
cannot be used for focussing until a solution is found where the beam can be steered
through its center. The K500 cyclotron does not have this problem, and its solenoid

can be used to focus the injected beam.

24

2.1.7 Final Choice of Initial Conditions

This study uses ray tracing through a cylindrically symmetric magnetic field, derived

from an axial magnetic field calculation,

B,(z,r) = 8(2) — %B”(z) + C(74) (2.6)
B,(z,r) = ——;— (B'(z) — :8—B"'(z)) + 0(7‘5) (2.7)

starting immediately after the 90° bending magnet, through the solenoid to the

buncher. The buncher, when used, will use a small gap approximation

V 2
5‘0 = u— sin :91 sin(wRFt7 - (Pb) (2.8)
m glvo 2p

to Obtain a delta impulse for the longitudinal velocity Of the beam, where 220 is
the initial velocity Of the particle, p its bending radius in machine center, t,- its
time of arrival at the buncher, and (In, the phase of the buncher with respect to
the RF accelerating voltage. The ray will continue through the inflector, which is
represented by a potential field map from which the electric field can be calculated.
The particle will be transferred into the electric field two grid points away from the
map boundaries to avoid edge inaccuracies in the potential map. This requires an

approximation for the effects Of traversing the first part Of the field,

 

 

(2.9)

vienter = vi 2
U

(x/v2 — v3(Pot(z, y, z) — .5)V’§C’:)

which is repeated upon leaving the electric field,

 

122+v2 Pot :c, ,z —.5 13"-
viexit = vi (f O( ( y ) )VECR) ' (2'10)

02

25

Here Pot(:r,y,z) is the relative potential, on a scale Of 0 for minimum to 1 for
maximum, at the (x,y,z) of the particle as it enters (or exits) the electric field,
Vsp is the voltage across the inflector electrodes, and VECR is the ECR extraction
voltage. (The path through the electric field being unknown, all three velocity
components are scaled the same, which adds a small systematic error in the path
Of the particles.) The final coordinates will then be transferred to a central region
orbit code program which integrates in a magnetic field, derived from a midplane
map, and an electric field, derived first from two successively larger electric potential
maps, see Figures 2.4(a) & 2.4(b), then after 8 turns, the electric field is represented

by an impulse approximation at the gaps between dee and hill.

The initial phase space transmitted through the inflector from the starting point
~3 m below the median plane, will first be mapped. Then the intersection of
100 1r mm-mrad phase spaces in .r-x’ and y-y’ , represented on a uniform grid spaced
every 2 mm and every 2 mrad (approximately 7000 particles), will be used to study
the full 4-D acceptance. (100 1r mm~mrad was the area initially used for the design
Of the inflector[43], with the initial design Of the beam transport system forming
a double waist immediately after the last 90° bending magnet[44].) This will then
be repeated every 5° RF, mapping out the acceptance Of the central region for DC
beams. The buncher studies will have similar pulses spaced every 2° RF. Since the
ion temperature is Of the order Of a few eV x q, see Section 2.1.1, and the extraction
voltage is ~10 kV, the initial energy spread is ignored. Particles passing too close
to electrodes will be removed, and the r and 43 Of the particles at the slit locations

will be saved for simulations Of the slits.

26

2.2 PROGRAMS USED/MODIFIED FOR THIS STUDY ‘

The National Superconducting Cyclotron Laboratory has a number Of programs for
use in designing and simulating various components Of the cyclotron. The following

are those used in this study.

MONSTER[45] is a multi-function program written in house for the creation Of
operational settings to be used when running the K1200 cyclotron. At its root is a
collection Of measured K1200 median plane magnetic field maps. Added to these are
measured fields for the trim coils, bar fields for every magnetic element in the extrac-
tion channel, and a first harmonic bump profile for precessional extraction. Layered
above these are orbit codes and display and analysis routines. The current settings
for both main coils, and all the trim coils are predicted for each Operating point by
interpolating amongst the measured fields and superimposing the trim coils, bump,
and magnetic channels. With satisfactory internal orbit characteristics, settings for
all electric and magnetic extraction elements are determined by first optimizing the
precessional extraction, then tracing extracted orbits through the elements. This
program has proven very successful in predicting Operating set points greatly reduc-
ing tuning time for the Operators. The magnetic fields designed with MONSTER
can be saved and stored for use in other lab orbit codes. All cyclotron midplane
magnetic fields used in this study have been created by MONSTER. MONSTER
has also been used to Obtain some non-standard field settings, such as those used in

the phase curve studies in Section 4.5.

POISSON[46, 47], a code written at Lawrence Berkeley Laboratory to create
2-D magnetic fields, and now maintained at Los Alamos National Lab[48], has been
used to Obtain axial magnetic fields for use in studying injection. Current settings

for the coils are first Obtained by MONSTER, then used in the original geometry

27

used to design the magnet (Obtained from Marti.)

RELAX3D[49], written at TRIUMF, is used to Obtain 3-D electric potential
maps for various electrode geometries. There are separate maps for the spiral in-
flector, the inflector to puller portion Of the central region, and the central region
extending out to 5.0 in. The orbit programs then take derivatives Of the potential

maps to Obtain electric field strengths and directions.

Ray tracing Of orbits is generally done with fourth order Runge—Kutta integration
routines. The axial injection is simulated with two ray tracing programs written by
Marti at MSU[36]. Their function has partly been described in Section 2.1.7. The
first, MYAXIAL, integrates the path Of the particle as it goes up the axis of the
cyclotron, including several possible beam line elements such as electrostatic deflec-
tors, a solenoid, and a quadrupole. The second, IN FLECTOR, integrates through
the magnetic and electric fields in the spiral inflector. The two are merged together,
following the same particles to the exit Of the inflector, with several methods Of dis-
playing and analyzing the resultant ellipses. The author has modified these routines
to include a first harmonic buncher, to stop integrating particles that hit electrodes
or fail to clear apertures, and to create and run large sets Of particles. The output
has also been changed to facilitate the coupling Of these routines to the cyclotron

code.

The particles which have successfully made it through the inflector, and whose
coordinates have been saved in the plane intercepting the starting point Of, and
perpendicular to, the central ray, are then ray traced through the central region
in the program Z3CYCLONE[50]. Also written at MSU, Z3CYCLONE is a com-
posite Of three separate routines. The first integrates in the magnetic and detailed

electric fields Of the inflector to puller part Of the central region, using time as the

28

independent coordinate. The second, named SUPERCYCLONE, integrates in the
magnetic and electric fields of the entire central region, using the azimuth as the
independent coordinate. These two parts are added to the program SPIRALGAP,
which then continues the orbit, integrating in the magnetic field and using an im—
pulse approximation at the gaps for the electric field. The magnetic fields are de-
rived from a map Of the median plane magnetic field, and the electric fields from
3-D potential maps Of the electrodes. This program has been altered in similar
fashion to the MYAXIAL, and INFLECTOR programs, so that orbits intercepting
electrodes are stopped, and so that the orbits which were run through the inflector
can be continued inside the cyclotron. It was necessary to force the transition from
SUPERCYCLON E to SPIRALGAP to take place on the same turn, number 8, at
the same hill center, the zero degree hill on the lower right side Of Figure 2.4(b). The
transfer needs to take place at a position where E’ = 0 (hill and Dee centers), if not,
the energy Of the particle will be incorrect. Centering diflerences between the orbits
on different spirals, shift the center Of the resulting eigenellipse when that spiral is
used to transfer between SUPERCYCLON E and SPIRALGAP. Otherwise the final
phase space ellipse would be a composite Of several different ellipse fragments, with

Offsets along the joints between fragments.

The slits are simulated in a separate display and analysis program written by
Marti and the author. Every time an orbit intercepts the usable range Of the slits, a
modification to Z3CYCLONE saves the r and 45 coordinates. The slit program then
reads these coordinates, together with final ¢ coordinates of some subsequent turn.
Using these coordinates, the program allows the user to interactively adjust the
position of the slits with the resultant cuts displayed almost instantaneously, even
when 200,000 particles are being searched. It can also display a two dimensional

density plot of 1' vs 45 at the slits. The program runs on VAX workstations, displayed

29

with GKS software on any terminal using X-WINDOWS. The above results were
for a VAXstation - 4000 - 90.

2.3 ACCEPTANCE OF THE CONTINUOUS (DC) BEAM IN THE
K1200

The basic probe which will be used to explore transmission into the cyclotron will
be a pulse Of particles. All components Of the injection line before the buncher are
time independent, so 2 Of the buncher, 1.7 m from the midplane, will be where t = 0
for all particles. The starting position, though, will be immediately after the 90°
bending magnet, 2.972 m below the median plane. Using a pulse Of particles, all
with the same starting time, one can see the spreading in time caused by the yoke
and the spiral inflector. When studying the added time effects Of the buncher and
the central region, pulses with regularly spaced starting times will be used to cover
the total range Of useable times. For the DC portion of the studies, without the
buncher and before the central region, the actual starting time is irrelevant, so one
pulse is sufficient. All calculations will be done with 40 MeV/u, Q / A225 ‘standard’

set point used to start up the cyclotron, and Often used in orbit calculations.

MYAXIAL is used to tune the solenoid for maximum transmission. An initial
ellipse is started, and the solenoid field strength is adjusted to minimize the oscil-
lations in the subsequent beam envelope. Figure 2.5 shows the envelopes for three
field settings near this minimum, and for when the solenoid is Off. Notice the abrupt
change in behavior near .33 m. This is where the field from the yoke, see Figure 2.3,

rapidly changes strength.

30

 

 

 

 

 

 

 

 

 

 

 

        

 

 

 

 

 

 

B |=0.00kG 40 MeV/u Q/A=.250 Injection Bwl=2.50kG 40 MeV/u Q/A=.250 Injection
5 9°...,.Y..,....,..4.,..H,.... 15 ,,,,,
L
10 *- T
E I I
.5. 7 ,
a: * 7
5 *- _
fink» 1
II ,
0 AIJAJAAALIIIIILA‘IAIIIIIIALI o llllllAllll‘LAlll‘llLALAllllL
0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2,000 2500 3000
2 [mm] 2 mm
(a) Injection Envelope 3,0, = 0.00 kG (b) Injection Envelope B”, : 2.50 kG
Bfl=2.65kG 40 MeV/u Q/A=.250 Injection B l=2.80kG 4O MeV/u Q/A=.250 Injection
5 744,....,....,4...,....,H” 15 3°.,,....,....,....,..7-,Yfir
10 r a
E ‘ j
3 t .
m > 4
5 *- _
f 1
o>J_LL1ILLALILLAAIAAILILLAAILLL o AAIAILJ—LAILLALiLALLILLLJJIALL
0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
2 [mm] 2 mm
(c) Injection Envelope B“; = 2.65 kG ((1) Injection Envelope BM = 2.80 kG

Figure 2.5: Injection Beam Envelopes.

Beam envelopes for injection into the K1200 with varying solenoid strengths.
Figure 2.5(c) has minimized the oscillations entering the inflector.
Figures 2.5(b) & 2.5(d) are for nearby solenoid settings which are nearly as good.
Figure 2.5(a) simulates the actual Operating point, see Section 2.1.6. Transmission with
all 4 settings is explored in Section 2.3.1. The inflector entrance aperture has a radius
of 2 mm. The initial ellipse is 8 equally spaced particles simultaneously subscribing
100 1r mm-mrad circles in both z-z’ and y-y’. Abrupt changes in the frequency and am-
plitude of the oscillation occur where B changes rapidly, see Figure 2.3.

31

2.3.1 2-D Acceptance in Phase Space

2-D circular ellipses, with n equally spaced particles on each ellipse, were started in
both z-x’ and y-y’ phase spaces, for each Of the solenoid settings mentioned above.
(Circular when a: is in mm, and :c’ is in mrad. Ellipses will be described in this
phase space with a the length Of the major axis, 5 the length Of the minor axis, and
0 the clockwise rotation Of the ellipse from an upright position.) The transmission
for each setting, complete with coupling effects, is displayed in Figures 2.6-2.13.

The radius Of each circle was gradually increased until one was found where some
particles were lost. Each figure shows z-x’ and y-y’ at the start, and x-vx and y-vy at
the inflector entrance and the inflector exit for all the ellipses which are transmitted
in their entirety. The velocities are expressed as a length by dividing by pr. This
is the same as the cyclotron momentum unit where p is divided by mw, so the units
at the inflector exit are translated to inches for running in Z3CYCLONE, where it

is convenient to use inches for 1', pr, 2, and pz.

The particles in each ellipse are connected by lines with one gap, giving the
appearance Of a spider web. Following the position Of this gap within the web at
different positions along the cyclotron axis, gives a visual sense of changes in the
ellipse orientation. Figures 2.6 & 2.7, case 1, show the transmission Of circular
ellipses for this cyclotron operating point when the naked solenoid is Off. These
ellipses are not well matched, and display strong distortions caused by the non-
linearities in the inflector. Also, the uncut transmission, which is represented by the
area of the largest ellipse drawn in each figure, is relatively small, ~49 7r mm-mrad Of

the initial phase space.

Figures 2.10 & 2.11, case 3, show the transmission with the solenoid tuned

to 2.65 kG, to minimize the oscillations in the beam envelope, as in Figure 2.5.

inflector exit

 

 

 

 

 

32

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.10 . 7 . 0.10 . . 7
0.05 ~ 1 0.05 7 -
"‘ '3'
£- 0.00 7 7 ~"—"7 0.00 7 7
t i:
-0.05 7 7 -0.05 7 7
-o.10 1 . . 70.10 1 ' .
—0.10 -0.05 0.00 0.05 0.10 —0.10 —0.05 0.00 0.05 0.10
x [in] s [in]
inflector entrance
100 I T I 100 I I I
0.5 7 7 0.5 7 7
'E '5‘
.E, 00 7 m 7 .5, 0.0 7 7
E t‘
-0.5 7 7 -o.s 7 7
_1.0 1 1 L .1.0 1 l l
-2 —1 0 1 2 -2 -1 0 1 2
x [m] I [nun]
start
0.016 I T I I T
0.010 7 7
0.000 7 7
'5‘ _
3, 0.000 - @ 77 B301 — 000 kG
3’ 0005
' 49 17 mm-mrad
-0.010 7 7
-0.015 . 1 1 ' l
715 —10 -s 0 0 10 15
x [mm]

Figure 2.6: 27D Injection Transport. Case 1, :r-z’.

27D ellipses, with a = b, in z-z’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit of the inflector. The focusing
solenoid is off, and the largest ellipse which entirely clears the inflector has an area of
49 1r mm-mrad The velocities are expressed in units of if.

33

 

inflector exit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.10 I I T 0.10 I T I
0.05 7 7 0.05 7 7
Ts? CE
7—7 0.00 7 7 7—- 0.00 7 7
fl __.__. N
> >
-0.05 r 1 -0.05 L- 7
70.10 1 1 I —0.10 1 1 .
—0.10 —0.05 0.00 0.05 0.10 —O.10 -0.05 0.00 0.05 0.10
x [in z [in
inflector entrance
1.0 I I I 1-0 I I I
0.5 7 7 0.5 7 7
'3 s
E. 0.0 ~ 7 E, 0.0 7 m 7
H >5
> >
70.5 7 7 —0.5 7 7
-1.0 1 1 1 -10 l I l
-2 -1 0 1 2 —2 -1 0 2
x [mm] Y [mm]
start
0.015 . . . . .
0.010 7 7
0.005 7 -
_ 3‘
13801 _ 0.00 kG 3 0.00, _ @ .
if 0005
49 17 mm-mrad '
-0.010 7 7
_0.015 I 1 I l I
-15 710 75 0 5 10 15

y [mm]

Figure 2.7: 27D Injection Transport. Case 1, y-y’.

27D ellipses, with a = b, in y-y’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit Of the inflector. The focusing
solenoid is Off, and the largest ellipse which entirely clears the inflector has an area Of
49 1r mm-mrad. The velocities are expressed in units of f.

34

Using the solenoid improves the acceptance for these circular starting ellipses, from
49 to 169 1r mm-mrad. The transmission for the two adjacent settings in Figure 2.5
are displayed in Figures 2.8 & 2.9, case 2, where B”; is 2.50 kG, and in Figures 2.12
& 2.13, case 4, where 3,0; is 2.80 kG. Case 2 has the largest acceptance,
196 1r mm7mrad, with the acceptance falling to 121-144 7r mm-mrad for case 4.
Looking at the size and shape Of the ‘ellipses’ at the inflector exit, one sees though
that the matched solenoid setting, case 3, transmits the beam with the least dis-
tortion in the vertical coordinates. In Figures 2.8, 2.10, & 2.12, the :r-x’ starting
ellipses, the distortions in the 271),, phase space get worse as B”; increases. In
Figures 2.9, 2.11, 8:: 2.13, the y-y’ starting ellipses, the distortions in the 271), phase
space get better as B”; increases. For both the :r-x’ and y-y’ starting ellipses, the
2:71), exit phase space gets smaller as B”; increases. Case 3 is an acceptable compro-
mise with some distortions, while still accepting a large initial phase space, though

it is not the full ECR emittance discussed in Section 2.1.1.

An initially-circular phase space ellipse, though, is not necessarily the best ellipse
to use with or without the solenoid. In the 4-D studies, an ellipse was found with
much better transmission when B”; = 0. Figure 2.14 and Figure 2.15, case 5, show
the acceptance to be twice as large, 121 and 100 1r mm-mrad , when the initial ellipse
has a = 3b and 0 = —25°, as that acceptance of the circular ellipses, 49 7r mm-mrad ,
in case 1. Also, the exit phase space in case 5, while distorted, has less distortion
than in case 1. Using these ellipses with 8.01 set at 2.65 kG, case 6, the acceptance
increases to areas equivalent to those of cases 2 & 3, 144 and 196 1r mm-mrad. But
comparing Figures 2.16 & 2.17, where the transmission of case 6 is displayed, to
those Of case 5, the distortion is clearly worse. In fact, it is comparable to that in
Figures 2.6 & 2.7 Of case 1, while the matched circular ellipses, Figures 2.10 & 2.11

Of case 3, have the least distortion of all 6 cases.

35

inflector exit

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

010 . . . 0.10 7 . .
0.05 7 — 0.05 7 —
E E
«— 000 7 7 -—7 000 7 7
I N
D b
—o.05 7 7 70.05 7 7
—0.10 ' ' l -040 1 1 1
—0.10 —0.05 0.00 0.05 0.10 —0.10 -0.05 0.00 0.05 o 10
x [in] I [In]
inflector entrance
I I I 1~0 I I I
0.5 0.5 7 7
'E‘ E
3, 00 .E, 00 7 7
L‘ t‘
70.5 —o.5 — 7
-1.0 —1.0 ' 1 .
—2 -1 o 2
y [mm]

0.015

 

0.010
0.005
B”l = 2.50 kG

0.000

x' [rad]

—o.005
196 1T mm-mrad
70.010

 

 

 

 

-0.015
— 15 - 10 -5

0 5
x [mm]

Figure 2.8: 27D Injection Transport. Case 2, :r-x’.

27D ellipses, with a = b, in 372’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit of the inflector. The focusing
solenoid is at 2.50 kG, and the largest ellipse which entirely clears the inflector has an
area of 196 1r mm-mrad. The velocities are expressed in units Of 5.

 

 

 

 

 

 

 

 

 

0.10 I I I
0.05 1- -1
'3
‘—1' 0.00 - ~
It
>
-0.05 - '1
_°.10 l I L
-0.10 -0.05 0.00 0.05 0.10
x [in
1.0 I I I
0.5 ’- .7
B
.5, 00 7 7
u
>
-0.5 1- '1
—1.0 1 1 L
-2 -1 0 1 2
x [mm]
B = 2.50 kG
sol
196 1r mm-mrad

36

inflector

0.10

0.05

0.00

v: [in]

-0.05

—0 10

' —O.10

1.0

0.5

0.015

0.010

0.005

0.000

y‘ [rad]

-0.005

—0.010

-0.016
- 15

Figure 2.9: 2-D Injection Transport. Case 2, y-y’.

27D ellipses, with a = b, in y-y’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit of the inflector. The focusing
solenoid is at 2.50 kG, and the largest ellipse which entirely clears the inflector has an

exit

 

I I I

I

l I 1

 

 

 

—0.05 0.00 0.05
z in

inflector entrance

0.10

 

I r T

 

 

 

 

 

 

 

 

-5 0

7710
1* [mm]

area of 196 1r mm-mrad. The velocities are expressed in units of f.

15

vx [in]
o
o
o

—0.05

—0 10

' —O.10

0.5

0.0

vx [mm]

0.015

0.010

0.005

0.000

x' [rad]

-0.005
—0.010

—0.0 15

inflector exit

 

 

 

 

 

—0.05 0.00 0.05 0.10

inflector entrance

 

 

 

 

 

 

I l L

 

 

15

-10 -5 0
x [mm]

vz [in]
8

 

 

—0.05 -

 

l l

-O.10

 

 

I
-0.05

—O.10 0.00
z in

I ]

 

vy [mm]
o
c
I

 

 

 

B”, = 2.65 kG

169 1T mm-mrad

Figure 2.10: 27D Injection Transport. Case 3, 272’.
2-D ellipses, with a = b, in :c-z’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit of the inflector. The focusing
solenoid is at 2.65 kG, and the largest ellipse which entirely clears the inflector has an
area of 169 1r mm-mrad. The velocities are expressed in units of g.

38

inflector exit

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.10 I I I 0.10 T I I
0.05 7 7 0.05 7 7
E E
_. 0.00 7 7 7—7 0.00 7 7
g E
—0.05 7 7 -o.05 7 7
-0.10 1 1 1 —0.10 1 1 1
-0.10 —0.05 0.00 0.05 0.10 —0.10 —0.05 0.00 0.05 0.10
x [in] z [in
inflector entrance
1.0 I I I 100 I I I
0.5 7 7 0.5 7 7
E E
E, 00 7 7 E, 00 7 QC» 7
>1 >5
> D
—05 - —< —05 >- -
-10 J ' 1 -10 1 I
-2 -1 0 1 2 -2 -1 0 2
x [mm] y [mm]
start
0.015 I I I I I
0.010 7 7
0.005 7 7
_ '3
Bsol 265 kG 5 0.000 - @ -]
if 0005
169 1n mm-mrad '
—0.010 7 7
_0015 1 l l l 1
715 -10 -5 10 15

0
)1 [mm]

Figure 2.11: 27D Injection Transport. Case 3, y—y’.

27D ellipses, with a = b, in y-y’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit of the inflector. The focusing
solenoid is at 2.65 kG, and the largest ellipse which entirely clears the inflector has an
area of 169 1r mm-mrad. The velocities are expressed in units of g.

inflector exit

 

0.10

0.00 -

v: [in]

 

 

 

 

-0. 10
—0.10

-0.05 0.00
x [in]

inflector entrance

 

1.0

 

 

I I I

 

 

0.015

-1 1 2

start

 

0.010 1-

0.000 '-

x' [rad]

-0.005 1-

-0.010 r-

 

 

 

-0.015
- 15

-5 0 5 10 15
x [mm]

39

 

 

 

 

 

 

 

 

 

 

0.10 . . 7
0.05 7 7
E
7-7 0.00 7 7
II
D
-0.05 7 7
70.10 1 1 1
-0.10 -0.05 0.00 0.05 0.10
s [in]
1.0 . . .
0.5 7 7
E
.E, 00 7 7
:5
770.5 7 7
_1.0 l 1 l
—2 -1 2

B”, = 2.80 kG

121 1r mm-mrad

Figure 2.12: 27D Injection Transport. Case 4, 2273’.
27D ellipses, with a = b, in 372’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit of the inflector. The focusing
solenoid is at 2.65 kG, and the largest ellipse which entirely clears the inflector has an
area of 121 1r mm-mrad. The velocities are expressed in units of f.

 

40

 

   

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

inflector exit
0.10 7 7 7 0.10 7 7 7
0.05 - -1 0.05 - -1
'3‘ TE
._. 0.00 7 7 77 0.00 7 7
N N
> >
—0.05 7 7 -0.05 7 7
-0.10 1 1 1 -040 1 1 I
—O.10 —0.05 0.00 0.05 0.10 -O.10 -0.05 0.00 0.05 0.10
x [in] 2 [in]
inflector entrance
1-0 I I I 1-0 I T I
05 7 7 05 7
'E' s
5, 00 7 7 E 00 -
31 >1
> >
-05 - -] -0.5 '-
-l.0 1 i 1 -10 1 1 1
—2 -1 2 -2 -1 0 1 2
x [mm] Y [mm]
start
0.015 7 7 7 7 7
0.010 7 7
0.005 7 7
_ '3'
Bsol 2'80 kG 5 0.000 7 @ 7
if 0005
144 1T mm-mrad '
770.010 - 7
—0.015 1 l l l l
—15 -10 -5 0 10 15
y {mm}

Figure 2.13: 27D Injection Transport. Case 4, y-y’.

27D ellipses, with a = b, in y-y’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit of the inflector. The focusing
solenoid is at 2.80 kG, and the largest ellipse which entirely clears the inflector has an
area Of 144 w mm-mrad. The velocities are expressed in units of if.

41

inflector exit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.10 7 7 7 0.10 7 7 7
0.05 7 7 0.05 7 7
E" E
77 000 7 7 -—7 0.00 7 7
E '7'
70.05 7 7 -o.05 7 7
—0.10 1 1 1 -0.10 1 1 1
-0.10 -0.05 0.00 0.05 0.10 -O.10 -0.05 0.00 0.05 0.10
x [In] I [in]
inflector entrance
1-6 I I I j I 1-5 I I I I I
1.0 - 7 1.0 7 7
.—. 0.5 7 7 .—. 0.5 7 7
8 El
.5. 0.0 7 7 .E, 0.0 7 ..
E -05 1- 7 ti-OIS r 4
-10 7 7 -1.0 7 7
-15 1 1 1 1 1 '15 1 1 1 1 l
-3 -2 -1 0 2 a 73 -2 -1 0 1 a
x [mm] 1 [mm]
start
0.024 7 7 7 7 7
0.010 7 7
0.005 7 7
'1? _
3, 0.000 7 7 Baal 0'00 kG
if 0005
' 121 1n mm-mrad
—0.010 7 7
4.024 1 1 l 1 1
-24 -16 -6 0 16 24
x [mm]

Figure 2.14: 27D Injection Transport. Case 5, 2710’.

27D ellipses, with a = 3b, in 273’ phase space are started on axis, ~3 m below the me-
dian plane, and followed through the inflector entrance to the exit Of the inflector. The
focusing solenoid is Off, and the largest ellipse which entirely clears the inflector has an
area of 121 1r mm-mrad. The velocities are expressed in units of fj, and the axis scales in
cases 5 8c 6 have been expanded from those in cases 1-4.

42

inflector exit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.10 I I I 0.10 I I T
0.05 - 7 0.05 1- -1
E '27?
-7 0.00 7 7 a 0.00 7 7
1‘ N
> >
70.05 7 7 —o.05 7 7
—0.10 ‘ 1 1 _0_10 1 1 1
-O.10 -0.05 0.00 0.05 0.10 —0.10 -0.05 0.00 0.05 0.10
x [in] z [in]
inflector entrance
1.5 I I I I I 175 I I T I I
1.0 - a 1.0 - -1
H 0.5 7 7 H 0.5 7 7
E E
.5. 00 7 7 .E. 0.0 7 @ 7
’J 5‘
-o.5 7 7 -0.5 7 7
—1.0 +- 7 —1.0 7 7
_15 l l l 1 L _15 1 L 1 1 A
73 -2 71 0 a -a —2 — 0 2 a
x [mm] y [mm]
start
0.024 I I I I I
0.016 - ~
0.005 7 7
_ '3‘
Bsol 0.00 kG 3. 0.000 _ _
P 0005
100 7T mm-mrad '
-0.016 1- -1
70.024 1 1 1 1 1
-24 -16 -8 O 8 16 24

Figure 2.15: 27D Injection Transport. Case 5, y-y’.

27D ellipses, with a = 3b, in y-y’ phase space are started on axis, ~3 m below the me7
dian plane, and followed through the inflector entrance to the exit Of the inflector. The
focusing solenoid is Off, and the largest ellipse which entirely clears the inflector has an
area Of 100 1r mm~mrad. The velocities are expressed in units of %, and the axis scales in
cases 5 8s 6 have been expanded from those in cases 1—4.

0.10

inflector exit

 

 

 

 

 

-0.05

0.00
x [in]

0.05

0.10

inflector entrance

 

1.0 *-

0.0 7

u [mm]

—0.5 r-

 

I

I

I

I

 

I

 

 

Nu—

 

0.024

0.016 7

0.008 *-

0.000 -

x' [rad]

—0.0 16 '-

 

 

 

 

-0.024

24

43

 

 

 

 

 

 

 

 

0.10 I I x
0.05 *- -
'3'
u—a 0.00 '- fl 4
II
b
—o.°6 i- q
_o.lo l l l
-0. 10 -0.05 0.00 0.05 0. 10
z in
175 1 I T I
1.0 '- ‘-
H 0.5 7 7
E, 0.0 '- H 7
p-Ob - 1
-1.0 ,. -1
_1.5 l 1 1 1 l
-3 -2 -1 1 3

B”l = 2.65 RG

144 1r rum-mrad

Figure 2.16: 2-D Injection Transport. Case 6, :r—z’.

27D ellipses, with a = 3b, in 373’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit of the inflector. The focusing
solenoid is at 2.65 kG, and the largest ellipse which entirely clears the inflector has an
area of 144 1r mm-mrad. The velocities are expressed in units of 3, and the axis scales in

cases 5 & 6 have been expanded from those in cases 1—4.

 

0.10

0.05 >-

0.00 -

vx [in]

I

-0.05

 

-0.10 i

 

 

 

-0.10

-0.05

0.00
x [in]

0.05

0.10

 

1.5 r

1.0 _

0.5 r

0.0 *-

vx [mm]

—l.0 h

 

 

 

—3 —2

sol

196 1r

2.65 kG

mm-mrad

44

0.10

0.05

0.00

vz [in]

—0.05

-0.10

-O.10

1.5

1.0

0.5

vy [mm]
o
o

0.024

0.016

0.006

0.000

y‘ [rad]

~0.008

-0.0 16

—0.024

Figure 2.17: 2-D Injection Transport. Case 6, y-y’.

2-D ellipses, with a = 3b, in y-y’ phase space are started on axis, ~3 m below the median
plane, and followed through the inflector entrance to the exit of the inflector. The focusing
solenoid is at 2.65 kG, and the largest ellipse which entirely clears the inflector has an
area of 1961r min-mrad. The velocities are expressed in units of 5, and the axis scales in

inflector

exit

 

I

I

 

1

l

l

 

 

-0.05

0.00
z in

0.05

inflector entrance

0.10

 

 

 

 

 

m_

 

 

 

 

cases 5 & 6 have been expanded from those in cases 1—4.

 

24

45

While these 27D transmission studies where done for only one K1200 operating
set point, they have been sufficient to demonstrate that not only is a focussing ele-
ment similar to the naked solenoid needed to match the injected beam for maximum
transmission into the cyclotron, but a quadrapole type focussing element is also nec-
essary to minimize the distortions in the transverse dimensions of phase space. This
will be true for all the set points, even though the operational settings will vary.
Overcoming the limitations presented by the nonaxial magnetic field during injec-
tion would be a valuable improvement in the injection and control of the cyclotron
beam. A more detailed study of this problem is recommended, with the caveat that
good diagnostics will be needed. The injection conditions which achieved the best
transmission through the inflector, case 3, was not synonymous with the largest ac-
cepted emittance, case 2, so a measurement of the total injected current will not be

sufficient when tuning the injection line for optimum acceptance in the cyclotron.

2.3.2 4—D Transmission Through the Central Region

A full picture of the acceptance into the cyclotron requires the full coupling of the
transverse planes of motion. To this end, a uniformly spaced four dimensional pulse
of particles will be integrated up the axis of the cyclotron and through the spiral
inflector. The same solenoid settings and ellipse shapes used in cases 1, 3, 5, & 6
will be used. The area, though, will be restricted to ~100 7r mm-mrad in each of
the :r-x’ and y-y’ planes, with starting positions centered at (0,0) and spaced every
2 mm and every 2 mrad. The full four dimensional starting conditions will consist

of all coordinates satisfied by the conditions in both planes.

These 4-D pulses will be traced to the inflector, then out through the central

region. Integrating in the central region requires that the dimension of time be

46

fully sampled. To be consistent with calculations using the buncher, time will be
introduced there, with pulses crossing the buncher every 5° RF. This requires that
more pulses be used than if the inflector exit had been used, but gains the advantage
that time at the inflector exit will be fully sampled due to the debunching of particles

in the yoke and the inflector.

Figure 2.18 shows the distribution of these particles in the x-y plane at the
inflector entrance, the radius of the inflector aperture, and the fraction of these
particles which will be successfully transmitted through the inflector. The use of the
solenoid to maximize acceptance into the inflector by minimizing the oscillations in
the beam envelope, is dramatically demonstrated. For the cases where B”; = 0.0 RC,
the primary loss of particles is the entrance aperture, but a small region of particles

with negative :1: can be seen to be lost on the inflector electrodes.

The square patterns, as well as the smaller circles and wedges, most pronounced
in Figure 2.18(b), are byproducts of the starting conditions. The initial grid in x-y
is a square. Each circle is associated with an initial point in z-y. Every point within
one circle or wedge had a specific 2),, and 2),. If it were in an infinitely long uniform
solenoidal field, this particle would travel in a helix, which would return to the same
:c-y, at some later 2. Every particle starting at this point, with the same value of Iv 1 I,
would travel in a similar, though rotated, helix. So all particles with |v 1| = constant
will inscribe a circle, centered at the initial point in :v-y, whose radius oscillates with
a frequency, w, = qB/m, reaching a maximum radius of r, = vl/w” and with a
minimum radius of 0, as it travels down the length of the solenoid. (w, will be called
the gyrofrequency, to distinguish it from wo, the specific cyclotron frequency inside
the cyclotron.) Since v, = «123 — vi and v0 = constant (mono-energetic starting

condition), at any given 2, each set of particles with a given value of vi, would be

47

 

 

 

 

 

 

 

 

 

 

 

   

 

 

Inneeler entrenee B_-l.¢6 e-b transmitted portion inflector entrance B_-2.85 e-Sb lrenunltted portion
3 l l I l
g - ..
—. 1 - _.
1 E
4 E o 7 —
h-I - -'
-g _ a
_a.11 4.1.1.1. _3-
-3 —2 -l 0 l _
x [mm]
(a) Case 3: B”; = 2.65 kG, a=b (b) Case 6: B“; = 2.65 kG, a=3b
“Hector entrenee B_-0.0 e-h trenlmltled portion |nllector entrance B‘-0.0 e=3b Uni-muted portion
V I ' I Y I T ' 3 l . 7 T f

3! 12m;

 

 

 

 

 

 

 

   

-3 —2 —l O 2 3 —3 72 v1 0 l

x [mml

7:: 72 71 o x
x [mm] x [mm]

 

(c) Case 1: B”; = 0.00 kG, a=b ((1) Case 5: B“: = 0.00 kG, a=3b

Figure 2.18: z-y Particle Distribution at the Infiector Entrance.

A 4-D uniform grid of particles, spaced every 2 mm and 2 mrad, were started within the
100 1r mm-mrad x-z’ and y-y’ phase spaces of cases 1, 3, 5, & 6, described in Section 2.3.1,
3 m below the median plane. The position coordinates of each particle at the entrance
of the inflector are represented by a point in each plot. The first plot in each subfigure
is immediately before the entrance aperture, depicted by the solid circle, and the second
plot shows the subset of those particles which successfully clear the electrodes, and the
entrance and exit apertures. The structure is an artifact of the starting conditions.

48

at a different point in their oscillation, and each point in :c-y, will be surrounded by
a disk of particles. With the starting conditions constrained to lie within an ellipse
of area 100 7r mm-mrad in both :r-v, and 3171),, phase spaces, when looking at the
edges of the :c-y distribution, 17; will be limited in size and direction, and a wedge
will be seen. Since 3 is definitely not uniform, we are entering a solenoid, the whole
distribution will be compressed, and there will be distortions, which will be greater

at the edges.

Figure 2.19 shows the distribution of these particles in velocity coordinates at
the same position as Figure 2.18. Once again, clear structure can be seen when the
solenoid is used to focus the particles into the inflector. The distortions in all four
cases demonstrate nonlinearities which result from expanding B to order r2 while
traversing the yoke. Notice that the matched ellipses, case 3 and case 5, matched
to a particular solenoid setting, present a smaller area in velocity coordinates than
do the associated unmatched ellipses. In a field that changes adiabatically, the

magnetic moment would be constant, so

vi, =vi,‘/Bf/B,- =vi,\/363/..7 (2.11)

This is definitely not so, else for cases 1 & 3, max(vj,) would be .81 mm, and in
cases 5 & 6, max(v_|_,) would be 1.3 mm. The solenoid has been used to optimize
the crossing of the nonadiabatic regions described in Figure 2.3 so as to minimize
the growth of U; at these points (see Figure 2.5.) Also noticeable, is the spreading
of 1),, and 12,, with 1:,- and y,-. This is much worse without the focussing solenoid,
removing most of the fine structure in cases 1 & 5 in both Figures 2.18 & 2.19.
These two distinctions, focussing the solenoid in cases 3 & 6, and matching the
ellipses in cases 3 & 5, which prove to be advantageous in increasing the acceptance

of the spiral inflector in Section 2.3.1, can now be followed inside the cyclotron.

49

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

 

inflector entrance 8.32.65 e-b transmitted portion inflector entrance Risa!!!) a-3b tranernitted portion
l I I I I 3 I I I I I I I I I I I I I I
2 7 7 2 7 7 2 7 7 2 7 7
1 7 7 1 7 7 1 7 g 7 1 7 7.. 7
—-. 10— — 3 N31; .," ar— ‘.\::':".‘"'."7
e - e . e 777.21 e as
50 7 7E o 7 7 Eo 7 .227 7E o 7 “7777:. 7
> > > ' “.13 > "-'.'-.':1:::-\.
—1 r- -4 .—.1 ~ —4 —1 >- I‘ .72} -4 —1 P- "- ".- -I
—2 7 7 —2 — 7 72 7 7 —2 7 7
_3 1 1 1 1 1 _3 1 1 1 1 1 _3 L 1 1 1 1 _3 1 1 1 1 1
-3 -2 -1 0 1 2 3 —3 -2 —1 0 1 2 3 -3 -2 -l 0 l 2 3 -3 —2 -1 0 l 2 3
V. [mm] V. [mm] vI [mm] V. [mm]
(a) Case 3: B“; = 2.65 kG, a=b (b) Case 6: B“: = 2.65 kG, a=3b
inflector entrance B_=0.0 aab trenemitted portion inflector entrance B‘=0.0 a-3b tranamitted portion
I I I I I I I I I I T T I I I 3 I I I I I
2 7 7 2 7 7 2 7 7 2 7 7
J I L. 1 I I _.1 I I._ 1 I I
E E E E
E0 I IE. 0 I I E0 I if": 0 I I
-17 .1 7—17 7 —17 7717 7
_2 I- —4 2 -— -1 _2 l— —I -2 >- 4
_3 1 1 1 1 L _3 1 1 1 L 1 _3 1 1 1 1 1 _3 1 1 1 1 1
-3 -2 —l 0 1 2 3 —3 —2 —1 0 1 2 3 -3 —2 -1 0 1 2 3 -3 —2 —1 0 1 2 3
v, [mm] vn [mm] It' [mm] v, [mm]
(c) Case 1: B”; = 0.00 kG, a=b ((1) Case 5: 8,01 = 0.00 kG, a=3b

Figure 2.19: 123712,, Particle Distribution at the Inflector Entrance.

A 4-D uniform grid of particles, spaced every 2 mm and 2 mrad, were started within the
100 1r mm~mrad z-z’ and y-y’ phase spaces of cases 1, 3, 5, & 6, described in Section 2.3.1,
3 m below the median plane. The velocity coordinates of each particle at the entrance of
the inflector are represented by a point in each plot. The first plot in each subfigure is
immediately before the entrance aperture, and the second plot shows the subset of those
particles which successfully clear the electrodes, and the entrance and exit apertures. The
structure is an artifact of the starting conditions.

50

 

Integrated in ZBCYCLONE
I I

 

 

 

 

 

 

 

30 I I I
1
4o MeV/A 4171a1+
20 o- . _‘
0
A O ‘
LL. 0— I I 4
p, 10 , . . ‘
V 0 . e e 1
._ e e 1
o a e e
s 0 , , ‘
1° 0 . ° ° 1
e . e 1
I ’10 1" ° ° ‘1
O 3 .
1 ‘
-20 «1- ___inside puller s
‘___at inflector
_30 L 1 1 1 1

 

O 200 400 600 800 1000 1200
Azimuth (deg)

Figure 2.20: Phase Compression in the K1200 Low Voltage Central Region.

The starting times of 11 central ray orbits started 5° apart in time, and their times of
arrival at an azimuth which includes the inside of the puller, all drawn relative to the time
of the central ray whose starting time is 220°. Note the rapid compression in time during
the first turn.

But first a digression to the central region acceptance, and phase compression
in the first turn within the central region. Figure 2.20 shows the RF times of 11
central rays spaced 5° apart, centered about the starting time of To = 220.°, at the
inflector exit. These times are followed to a position inside the puller and every
360° in azimuth thereafter for 3 turns. (See Figure 2.4(b) for details of the central
ray orbits in the central region.) The first turn compresses the phase spread to half
of its initial width. Calculations carried to the radii of the probes show that the
spread will recover to 5/8ths of its initial width. This is a feature of this central

region design.

The acceptance in time of the central region is displayed in Figure 2.21(a), where
all particles clearing the central region were binned in 1° steps, and the maximum
was normalized to 100%. In all four cases, with small variations, the base is 60°, the

FWHM is 45°, and the transmission is flattopped for 30-40°. Figure 2.21(b) shows

51

   
    

a=b 9= 0' a=3b 9=-—25'

.l1lilililililiJiim
I

7: that clean central region / .RF

   

  

 

 

.l.l.l.l.l.l.lil.l.

I11IIIIIIIIIIIIIIII l I l I

190 200 210 220 ftp 240
T0 RF] at inflector exit

(a) K1200 Acceptance in RF Degrees

 

that clears central region / R

%

 

 

lllllllllf'lllII‘II

—10

—530 -20
I RF]
(b) Beam Phase After 11 Turns

0
¢ after it turn-

Figure 2.21: K1200 Acceptance in Time for the Low Voltage Central Region.

K1200 DC time acceptance is histogrammed for all four 47D transmission studies. The
FWHM is ~ 45° in each case, Figure 2.21(a). The central region compresses this to ~ 29°,
for acceleration inside the cyclotron, Figure 2.21(b). The notation, used here and in the
following graphs, above each graph describes the starting ellipses at the bottom of the
injection line, and on the right side is the strength of the focussing solenoid, in kG.

52

these same particles after integrating 11 turns through the central region. The phase
compression has reduced the FWHM to 29°, but a non-linearity can be seen, in that
it is no longer flattopped, since the trailing phases are compressed slightly more

than the leading phases.

Figure 2.22(a) demonstrates that the phase and energy are very strongly corre-
lated. With a slight broadening, these E7¢ density plots follow Equation 1.2 quite
closely. Figure 2.22(b) shows the r7¢ curves corresponding to these E-d) curves.
Note the broadening of the r745 curves by the physical spot size of the beam in r
and 1),. These graphs demonstrate that the E745 correlations, resulting from having

I sin(¢)dE 76 0, can be used to turn radial cuts in the beam into time cuts.

Figures 2.23, 2.24, & 2.25 are snapshots of the beam density in spatial coordi-
nates after 11 turns of acceleration in the K1200 cyclotron. In Figure 2.23(a), the
density of the beam in r-z is presented. The spot size is significantly larger when the
solenoid is used to focus the beam spot into the inflector. Matching the injection
phase space ellipses reduces the spot size. More importantly, judging from the shape
of the intense core, it makes a more compact ellipse. Note that the behavior of the
spot size here, is exactly opposite of that at the inflector entrance. In Figure 2.18,
the spot size is smaller when the solenoid is being used to focus the beam into the

inflector. The inflector has also left the beam strongly correlated in r and 2.

Figure 2.23(b) has the pr-p, density plots, which correspond to the vx-vy plots
in Figure 2.19. In the same manner as with the spot sizes, the smaller dispersion at
the inflector entrance results in a greater dispersion inside the machine. This is the
cause of the large spot size resulting from focussing the beam into the inflector. Also
important is the correlation induced in the cases with unmatched ellipses. Matching

the ellipse removes this correlation, and results in a smaller core of particles.

53

 

   

 

 

 

 

 

 

 

 

a=3b 6=-25°
I l I I I I I w
-5 ..
.3.
~10 1-
__15 _ II
N
'20 i' I '0)
'__‘ '25 '- 111“" W111!" 0‘
c...
P:
H m
e 2
ll
.0
O
0
mil". . '
"mil J 1 L 1 I 1 I 1 "WI-1 L 1 l l I 1 i 1
.52 .58 .58 .52 .54 .58
E/ A [MeV / A]
(3) E711» Correlations After 11 Turns
a=3b 0=-25'
#1111 w
I.“ I: ~ .8-
II
.N
0':
OI
.—
Ct.
0‘ .
i—' on
s .3.
ll
.0
o
o

 

 

 

 

 

 

4.55 4.85 4.75 4.85 . 4.55 4.85 4.75 4.85
In
(b) r743 Correlations After 11 'I\1rns

Figure 2.22: E7¢ and r7¢ Correlations Inside the Cyclotron.

Figure 2.22(a) shows how the 4-D monoenergetic pulses distribute in E-d) after trans—
mission through the central region. These are density plots where the size of the box
increases as the density in that quadrant increases. Figure 2.22(b) depicts the resultant
r743 distribution. This r743 distribution will be used later to cut the beam in time.

54

    
 

 

00
no”
rITTIIrmrTI

—1

 

O

O
IIIIIIIII'III
.l1l111111111
Ill]!

T‘llllll

 

 

 

 

JIIlIIIlI

 

4.55 4.85 4.75 4.55 _ 4.55 4.55 4.75 4.55
R [1n]

(a) r—z Density Plots After 11 Turns

 

a=b 6: 0'
I l

I

 

 

l l I l l
-o.35-o.3o-o.25—o.2o—o.15 .-0.35-0.30-0.2570.20—0.i5
R
(b) p,-p, Density Plots After 11 'hirns

 

 

 

 

 

Figure 2.23: r-z and p.71)z After 11 Turns.

These graphs correspond directly with those in Figure 2.18, and Figure 2.19. The use of
the solenoid to get improved transmission through the inflector, results in a larger beam
spot and a greater divergence inside the cyclotron, even though these traits were smaller
at the inflector entrance. The matched starting ellipses, cases 3 & 5, also make the these
traits smaller, though not as strongly as the solenoid. Also, the inflector has correlated r
with z.

55

The only clear aperture cuts visible in these phase space plots can be seen in
Figure 2.24(a). Here notches can be seen at the right edge near 1' = 4.9 in. These
notches are from cuts made by the spiral inflector electrodes. These cuts at the
edge are mirrored in the denser core, producing a distorted spot in r-p,, in all but
case 3 where the solenoid has been used with a matched ellipse. It is important to
remember that in any graph with r as one of the axes, that the long spread in r is
due to the E-¢ correlation. Even so, there is still a small reduction in p, when the
injected beam is not focussed into the inflector. Matching, and you may get tired of

hearing this, matches the core of the beam into a smaller spot in r-p, phase space.

The same r-z correlation seen in Figure 2.23(a) can be seen in Figure 2.24(b),
a plot of r—pz. Matching the injection phase space ellipses, gives both a smaller
total spot size (core + halo +tail), and a smaller, more compact core. The solenoid,
having focussed the beam into the inflector, has given a larger spot in this pair of

dimensions as well as in the three previous pairs.

The 27p, graphs, in Figure 2.25(a), are very much like the pr-p, graphs from
Figure 2.23(b). It is fascinating, that in both sets of graphs, that the correlation in
the halo is removed not by matching, as is the correlation in the core, but it is re-
moved by focussing with the solenoid. Otherwise, focussing makes bigger spots than
without focussing, and matching makes the spot size a little bit smaller regardless

of the focussing.

Figure 2.25(b) shows the z-p, motion during a defocussing period within the
cyclotron, depicting part of the incoherent oscillations typical of cyclotron beams.
(Focussing will rotate both the ellipse and the bow tie halo counter—clockwise.) Here,
the response of the beam to injection conditions, remains the same as in the five

previous couplings of the transverse phase spaces of the beam.

56

 

E1

[on

992

 

8

Ion

000 =

 

 

 

 

 

4.55 4.85 4.75 4.85 _ 4.55 4.85 4.75 4.85
R [1n]

(a) r-p, Density Plots After 11 'Ihrns

0=-—25'

l

 

a=3b
'l'l'l

 

 

 

 

 

 

4.55 4.85 4.75 4.85 _ 4.55 4.85 4.75 4.85
R [1n]

(b) r—p, Density Plots After 11 'Dirns

Figure 2.24: r-p, and r-p. After 11 Turns.

The core of the r-p, distribution is crescent shaped without the solenoid. The core becomes
circular when the solenoid is used to maximize transmission through the inflector, and the
injection ellipse has been matched. The notches to the right side of the r-p, graphs are
aperture cuts from the inflector electrodes. In both graphs, matching the starting ellipses
improves the beam characteristics. In r-p,, the beam spot is smaller without the solenoid.

57

 

 

 

     

 

 

 

 

 

 

 

   

 

 

 

 

CH
5
H
.N
o:
01
E
‘ 1111111111].1111111111111
‘—‘ 'I‘II'I'I'I' l'l'l'lll'
ED
__ I13.
7- 7 11
”1.1!:
‘ ‘ .0
o
11111 77 - o
1l1l1l1l1l1111l1|111l111l1
-o.2—0.10.0 0.1 0.2 0.3 _ -o.2-o.10.o 0.1 0.2 0.3
Z [in]
(a) z—p, Density Plots After 11 Turns
a=b 9= 0' 81: 3b 0=—25
.,.,.,.,.,.,..,.,.,.,.,.
I .7, , . U3
0.03 7 _8_
0.01 7 II
. . N
-001 7 '0:
1— - U]
.._..-o.03 1-
;: .
ul-fl ‘
hi ,
N . .. . In
a. 0.03 — -— 72
0.01 — -— 7 "
‘ " .0
—0.01 - 77 — o
-_ .. o
—0.03 — . 77 —
.Jlllililglmn-i—I—LlwgbhnlgL
-0.2—0.10.0 0.1 0.2 0.3 _ —o.2—0.10.0 0.1 0.2 0.3
Z [1n]

(b) z-p, Density Plots After 11 Turns

Figure 2.25: z-p, and z-p, After 11 Turns.

Once again, the spot size is smaller without the solenoid. Matching the starting ellipses
also continues to produce a. smaller beam emittance. In z-p, the unmatched cases produce
a correlation which is reduded with injection emittance matching.

58

In summary, this study of the coupling of the transverse phase spaces resulting
from injecting the beam axially through a spiral inflector has found that r will
be coupled with z and 12,. Matching the injection phase space ellipses into the
inflector will also match the injected beam into the cyclotron’s acceptance, resulting
in smaller transverse beam spots. Matching also removes the coupling of p, with z
and 12,. F ocussing the injected beam into the inflector aperture makes the transverse

beam spot larger.

Finally, with the 4-D injection studies completed, Table 2.1 presents transmis-
sion efficiencies for these four cases. On the left is a description of the injection
parameters for each case, and on the right, the current in each stage is presented as
a percentage of the current of the previous stage. The four stages are at the start,
1mm inside the inflector aperture, Ignfzedor, inside the inflector exit, Im-t, and at the
end of 11 turns of integration through the central region, Ion. [GR is also presented
as a percentage of all the previous stages. At the time of these studies, Lance“, and
Ian could be measured. A Faraday Cup has since been installed to measure 1mm.

as well as its spacial distribution.

The dominant stage is the central region time acceptance. The 45° FWHM cal-
culated in Figure 2.21(a) is 1/8th of the RF period. The one ratio that could be
measured, 103:1,-n flea”, gives 1 / 10th'to l / 9th, which is in good agreement with the.
calculation in all four cases. The use of the solenoid to focus the beam into the
inflector, cases 3 & 4, can eliminate practically all the losses incurred on the inflec-
tor apertures and electrodes. Matching the injection phase space ellipses improves
this slightly. Between cases 1 & 6, without the focussing, is where matching can
be seen to make a significant improvement in the transmission, increasing both the

acceptance in the entrance aperture, and the transmission through the inflector. All

59

Table 2.1: K1200 Cyclotron DC Acceptance.

Injection efficiencies are presented for the four 47D DC acceptance studies. See text for

explanation.

 

 

 

 

 

 

 

 

 

 

 

 

 

Case 1:

Baal = 00 [inflector = 60-5% [start

em: = 1001r mm-mrad

a = b [exit = 89.1% 11.7. flector

5ny = 1007I mmcmrad [CR = 11.9% I...“

a = b = 10.6% [inflector
= 64% Istart

Case 3:

8801 = 265 Iinflcctor = 995% Istart

53,: = 1007r mm-mrad

a = b [exit = 100.0% Iinflector

8ny = 1007r mmomrad Ion = 12.0% [exit

a = b = 12-0% Iinflector
= 11.9% [start

Case 5:

8,01 = 00 Iinflector = 76-0% Istart

5n: = 1007r mm-mrad

a = 30 [exit = 95-4% Iinflector

0 = —25°

5ny = 100w mmomrad I0}; = 12.3% In.“

a = 3b = 117% Iinflcctor

0 = —25° 2 89% Istart

Case 6:

Baal = 265 Llflector = 100.0% Istart

em: = 1001r mm'mrad

a = 3b Iezit = 967% Iinflector

0 = —25°

5W: = 1001r mmmrad I03 2 11.4% [exit

a = 3b = 110% Iinflector

0 = —25° = 110% Istart

 

 

 

60

told, for this one operating point, matching, by itself, can improve the total trans-
mission into the cyclotron by 39%, and with the use of the solenoid, the transmission
can be increased a by a total of 86%. This is 95% transmission during the central
region’s open time aperture, for a 100 7r mm~mrad injection phase space, without

space charge.

It is good to remember, though, that the focussing solenoid in the axial injection
line can not be used since the beam needs to exit the 90° dipole off-axis to be injected
into the K1200 cyclotron. The fact that the transmission into, and the beam inside
the cyclotron, can be improved by matching the injection phase space will still be

true, but the amount that the present injection can be improved is unknown.

2.4 TRANSMISSION STUDY WITH BUNCHING

The buncher was depicted in the axial injection line in Figure 2.2. It was designed
after the Argonne Low Energy Buncher[5l] It is capable of being driven at both lst
and 2nd harmonics of the RF accelerating voltage. The gap, which is 1.7 m from
the median plane, consists of two wire meshes, spaced 7 mm apart, each of which
can be driven independently. At the edge of the meshes, the electrodes extend out
in a cone, with the entrance cone extending vertically for ~5 cm, and the exit cone
extending vertically for ~10 cm. The radius of curvature of ions when entering
the central region is always 7.95 mm. Thus the cones extend over the distance a
particle travels in two RF periods for 2nd and lst harmonics, respectively. This
should average out the effect of the electric fields while approaching and leaving the

buncher, so these portions will be left out of the buncher approximation.

The buncher gap is short enough, 7 mm, compared with the distance traveled in

one RF period, 50 mm, that it can be treated as an instantaneous impulse on the

61

Buncher in MYAXIAL

 

 

 

 

 

 

6 T l 7 l
4 - _
V buncher = .01 V ECR
2 _ particles on axis a
:1
x
°’ 0
:3
(U
a.)
_2 p s
_4 _ _
-6 1 1 1 1
—60 —4O —20 O 20 4O 6O
tau start

Figure 2.26: Buncher Test in the Program MYAXIAL.

A test of the small gap buncher approximation added to MYAXIAL. Particles traveling
on axis should respond as if a drift followed the buncher, except for chromatic terms in
the inflector. The approximation works correctly.

beam. Equation 2.8 in Section 2.1.7 gave the small gap approximation which was
added to MYAXIAL to represent the buncher. A buncher voltage of 1% of the ECR
extraction voltage, gives the optimum tuning of this buncher formula for a gap of
7 mm and a drift of 1.7 m. Particles traveling on axis in the injection line should
respond to the buncher like they were drifting, until they reach the inflector, where
they will take different paths due to the energy spread imparted by the buncher.
Figure 2.26 shows the time distribution of particles at the exit of the inflector, which
were started on axis at the buncher, with the buncher voltage set at 1% of the ECR
extraction voltage. There is little difference in the final result for these particles
from those in an equivalent drift section, so the straight section optimization will
be used to select the initial buncher voltages. Typically, the buncher is tuned to
a value greater than this, overbunched, to maximize the current injected into the

cyclotron, with the total current being increased by a factor of three[9].

62

a=b 6: O.’ a=3b 9=—25.'

YITTYTTT'III'II'UI pilil'lYITIII'IYI'I'I"

 

        
 
             

 

   
 
  
  

 

  
 

9 99.5% transmission '1;- 96.7% transmission 1 CD
5 a it “.3.
7 i=1; 1— —
e E .7". .. II
E 5 1:- 1.” 1 N
' 4 E 1.— — ‘0,
3 :E— —— — or
\ 2 E 1.— _
m :— -o- ..
m 1 f—-:—-‘:—:_ ~-
H ‘1'- d
.2 9 53.9% transmission 1: 72.5% transmission .m
a) a __ 0
Ln -- "'
as 7 1: ll
‘3‘ 6 1:
o 5 "‘ O
B\ 4 1- O
3 1: o
2 ‘23:. j:-
1 :——__ r

 

 

0 10 20304050607080 90 0 10 2930405080708090

inflector entrance

Figure 2.27: Debunching During Traversal of the Yoke.

The debunching of the four 4-D pulses as they travel from the buncher to the inflector
entrance. The shaded portion is the fraction which is transmitted through the inflector.
Matching the injection phase space, upper left and lower right, minimizes the debunching

in the yoke. Using the solenoid to improve transmission also helps reduce the debunching
in the yoke.

2.4.1 Debunching in the Yoke

It is well known that particles travelling in a magnetic mirror towards increasing
B, with Iv ii 74 0, transfer kinetic energy from v” to 12 .L [52]. This is true even when
the field is not adiabatic, and the particles are not reflected by the mirror. This is
the situation for the injected beam as it enters the solenoidal field of the cyclotron.
The rate of travel of the particles will decrease if Iv 1| 7’: O, with the rate of decrease

being greater for greater initial values of v 1- These particles will take longer times

to reach the inflector.

This behavior is shown in Figure 2.27, where the 4-D pulses used in cases 1, 3,
5, 86 6 were assigned the time t = 0 as they crossed the plane of the buncher, which
was turned off. This Figure demonstrates that both the solenoidal focussing, and the

phase space matching are necessary when minimizing the debunching of the beam

63

Space Matching

T l

 

Phase

‘ Y 3;“ ='2.65 '
E i001! nun-mrad a-b O- O.’ 99.5% —
100w nun-mrad a-Sb O--25.' 96.7%

  
  
 
   

 

_1.._

1001! nun-mrad a-b O- 0.' 63.9% —
1001! nun-mrad «an 0--26.' 72.5%

75 accepted / 'RF
(0 4s 03 o N 4=~ o: oo

 

 

Figure 2.28: Total Debunching from the Yoke and Inflector.

The pulses displayed in Figure 2.27 have been followed to the inflector exit, with the phase
of the buncher adjusted to put the axial ray with sin(¢) = 0 at T = 220°RF. The inflector
has rounded off the peaks, significantly reducing the most focussed peak, and greatly
extending all of the bases, leaving the FWHM approximately the same in each case.

in the yoke. Using a smaller initial phase space would be the only way to further
reduce this debunching, but that can only occur by throwing away a significant

portion of the beam extracted from the ECRs.

2.4.2 Debunching in the Spiral Inflector

Marti showed that the spiral inflector used in the NSCL cyclotrons will debunch
particles on the edge of a 100 7r mm-mrad ellipse, an amount comparable to the
debunching due to the yoke[36]. Figure 2.28 presents the total debunching that has
occurred in the pulses shown in Figure 2.27, as they exit the inflector. The inflector
has greatly expanded the tails, and significantly rounded off the tallest peak. The
FWHM though, has not been significantly changed for any of the starting conditions.
This is because the debunching in these beams is dominated by the large initial phase

space. Case 3, with the matched solenoid, where the debunching in the yoke has

64

been minimized, is the case that is most significantly affected by the inflector.

This debunching presents an intrinsic limit on how tight the buncher can bunch
the beam. Obtaining beam phase cuts narrower than these peaks will require that
the peaks themselves be cut, with significant reductions in the intensity of the beam.
Also, the buncher should not be tuned on the central ray, since the peak lags behind

the central ray, and the center of the FWHM lags behind the peak.

2.4.3 Bunching Through the Spiral Inflector

To study the time properties of the buncher, a finer grid was used in time than in
the DC studies. The grid in time, was reduced from a uniform spacing of every 5°
RF, to a uniform spacing of every 2° RF. To fully accommodate the buncher, this
grid was extended to 135 grid points, representing a range of 270° RF. With the
need to raytrace over 1 million particles for each case studied, the bunching study
was limited to the two extreme cases. Case 1, with the poorest transmission, and
not matched, is used to represent the real conditions for this operating point, and
case 3 is used to represent a best case. It is possible for other operating points to

be as good as case 3, or worse than case 1.

Figure 2.29 shows the the bunching of these beams at the exit of the inflector,
using the same buncher voltage as above, 1% of VECR. The difference in these peaks

is due solely to the debunching in the yoke and the inflector.

There is one minor modification to the phase space of the beam as it exits
the inflector. Using Vbun = 0.01VEoR, adds a time dependent energy spread to
the beam. The more energetic particles are deflected by a slightly smaller amount
when they travel through the spiral inflector. The beam then paints the exit phase

space, adding a very small, starting time dependent, coherent oscillation inside the

65

Bunched Beam at the Inflector Exit V =0.0l V

bun

 

   
  
 
   
   

 

 

 

 

   

r Y T l T 7 Y T I I I I 7 I I I 7 f1 ‘ I I U I T V T:
2400 ._ Case 3 E
E 8.01:2.65 RG 5
1800 E— M h d 1
au:e I
h. L J
p: 1200 a
g. 600 — *3
h 1 1 1 % 1 1 1 l 1 1 1 1 1 1 l 1 1 1 l 1 1 1 l 1 1 1
-E _ Case 1 3
:3 900 r B =o.oo kG i
o : sol -<
O ,.
600 T Unmatched
300 L 1
h 1 1 1 l 1 1 1 l 1 L 1 l 1 1 1 l 1 1 1 L 1 1 1 l 1 1 1

 

 

 

160 180 200 220 . 240 260 280 300
T: [ RF]

Figure 2.29: Bunched Beam at the Inflector Exit.

Intensity vs time at the exit of the inflector, for bunching cases 1 & 3 with
V5,". = 0.01VECR. The peak width in both cases is due to the debunching demonstrated
in Figure 2. 28. Case 1 is for the normal injection settings used with the ‘standard’ oper-
ating point. Case 3 was focused with the solenoid, and matched the injection phase space,
minimizing the debunching.

cyclotron.

Finally, the phase of the buncher, with respect to the accelerating RF, needs to
be adjusted for transmission through the central region. This will be left for later,

in the phase slit simulations.

CHAPTER 3

USING A Si PIN DIODE AS A TIMING DETECTOR

It was necessary to develop a new timing detector for the K1200 cyclotron. A
considerable amount of effort had been put into detector development for the earlier
MSU cyclotrons[7, 8, 27]. An interesting aspect of the PIN diode used by Milton
to detect gammas, was that it sometimes was struck by heavier particles which
left stronger signals[53]. If a detector could be made which would directly detect
the beam, which consists, after all, of heavy ions, it would have the best chance
of overcoming the noise from inside the cyclotron. (There are many gamma, x-
ray, and neutron sources inside, as well as the RF itself.) There is also a lot of
experience in nuclear physics in using solid state detectors for measuring E, AE,
and sometimes t, in nuclear reaction by-products. A drawback is that these solid
state detectors have a low count rate capability, though the K1200 injection line can
accommodate this by attenuating the injected beam current, using a grid system, by
as much as 6 orders of magnitude. Solid state detectors are damaged by heavy ions,
Knoll estimates that Si detectors fail after ~ 108 incident heavy ions per square
centimeter[54]. Si PIN diodes, being relatively inexpensive, were chosen to study
the ‘test of principle’, and having succeeded as an external beam time detector,
a specially designed Si detector was manufactured for testing and use inside the

cyclotron.

66

67

3.1 EXPERINIENTAL DESCRIPTION

Three different types of Si detectors were used in external beam studies. The first,
5 mm x 5 mm x 300 mm, was used simply to show that a Si detector could be used
to measure beam time spectra immediately outside of the cyclotron. The second
type, two Hamamatsu 18 mm x 18 mm, 300 pm thick Si PIN photodiodes, was used
to measure detector resolution, and to make measurements covering the entire beam
cross sectional area. The last type, two transmission mounted, Micron Semiconduc-
tor, 3 cm x 3 cm x 300 pm, totally depleted ion implanted structure, Si detectors,
was used in a TOF measurement as part of an atomics physics experiment[55].
The electronics and data taking programs developed from an ad-hoc adaptation of
pre—existing equipment, to a dedicated setup with a specially written program to
control data taking and display. The following descriptions of the electronics and

data taking program will only cover the final configuration.

3.1.1 The Detector

The detectors were all operated in reverse bias, at full depletion. When an ion
passes through the silicon, it excites electrons, taking 3.6 eV to create each electron-
hole pair[54]. These pairs are then collected on opposite sides of the detector, the
total charge collected being proportional to the energy deposited in the detector.
(Heavy ions leave such intense tracks of electron-hole pairs, that the resulting plasma
partially shields itself from the electric field, allowing some of the pairs to recombine,
and lengthening the collection time[54].) The rapid rise in current during collection
is then used as a reference for when the ion struck the detector. This fast signal has

a rise time of 5 ns.

This reference signal is then compared to a second signal generated by the

68

cyclotron’s RF system. In this way, the position of each particle striking the detec-
tor is determined in time in such a way that it can be converted to a relative RF

phase for use in cyclotron studies.

While possible, it would have been difficult to turn this measurement into an
absolute measurement of RF phase. The RF signal is taken from a pickup loop which
is inside the resonator of dee C. Before an electronic measurement of the absolute
RF phase could be made, the phase of the signal in the pickup loop, relative to
the voltage on the dee, would have to be calculated at each frequency for which
data is taken. Then after measuring the propagation time of every cable, which
is temperature dependent, and the processing time of each piece of electronics, an

absolute measurement of the RF phase could be made.

Instead, when an absolute measurement was needed, a technique developed by
Smith & Garren was used to get a reference point[56]. This technique, which will
be explained in Section 3.3, consists of detuning the frequency, a somewhat lengthy
process, until sin(¢) = +1 at some radius, and also to sin(¢) = —1 at the same
radius. The relative position of the operating frequency to the two measured fre-

quencies directly determines the operating value of sin(¢(r)).

3.1.2 The Electronics

A schematic of the detector electronics is shown in Figure 3.1. The bias on the detec-
tor, and its guard ring, is provided by a Tennelec Dual High Voltage Power Supply,
Model TC953A, which is mounted in an Ortec 401A NIM bin in the operator’s
control room. The charge on the detector, is collected with a charge-sensitive Ten-
nelec TC178 Quad Preamplifier, which is in the vault near the detector. Mounted

immediately before the input into the charge-sensitive preamplifier is a LBL Time-

69

 

 

 

 

 

 

   

= ' i F‘.‘*
' i Vax '
DETECTOR l 'l 8:2:
1 111
L1 j 1 L_
PROBE . A
TIME
1'ch OFFI
[ 1 :
>Display
or". 1 . ITerminal,
m. ‘ PC's
FILTE _" _ '
NIM CAMAC
ELECTRONICS ELECTRONICS

 

 

IN CONTROL ROOM

Figure 3.1: Timing Detector Electronics Schematic.

The general schematic of the electronics used to collect and process time and energy signals
from the K1200 timing probe. The signal collection is controlled from a VAX computer,
and the final spectra are displayed on a terminal, usually a PC. See text for a detailed
explanation.

Pickoff fast amplifier. It uses a transformer to read the high frequency part of the
signal coming from the detector, and amplifies it so that it can be sent to a remote
location. Also in the cyclotron vault is a low pass filter, built in house for the guard
ring power line. To accommodate the length of the probe on which the detector is
mounted, and to allow for its travel, 25 feet of a thin coaxial Lemo cable is needed
to connect the detector to the time pickoff, and the guard ring to its filter. This
adds to the detector capacitance when estimating the detector noise. The exter-
nal measurements did not have this problem. Homemade amplifiers mounted in
the probe head immediately after the detector would be a better solution, provided

that they are well shielded from the accelerating RF, and can survive in the harsh

70

conditions inside the cyclotron (high radiation and a strong magnetic field.) As it
is, the electronics in the cyclotron vault are in a sizable magnetic fringe field. The
signals from the two amplifiers, one proportional to the energy deposited, the other

for the time, are then fed to the control room for processing.

In the NIM bin in the control room, the time signal is amplified again in a
Phillips Scientific Model 778 fast preamplifier. A Tennelec Model TC455 Quad
Constant Fraction Discriminator (CF D) is then used to uniformly determine the
time of arrival of each pulse. (This is true for pulses of different amplitude, but not
necessarily so for those of different shape. The CF D is set with a constant fraction
of .2 and a delay of 3.3 ns.) Several output signals are then taken from the CFD,
both of which are sent to a LBL designed quad gate and delay generator (QGDG).
The leading edge of the first turns on a Latch which is turned off after all the signals
have been processed. The output of the latch is used, in another portion of the
QGDG, to create a gate signal whose leading edge represents, in a Time to Digital
Converter (TDC), the time of arrival of the particle in the detector. The second
output signal of the CFD is also used to create a gate which is delayed to coincide
with the processed energy signal when it arrives in an Analog to Digital Converter
(ADC). Also in the NIM bin is a Tennelec TC241 amplifier which is used to amplify
and shape the energy signal before it is sent to the ADC. The final CFD output,
when not being used to tune the CFD, is sent to a Tennelec TC526 rate meter,

which is monitored for detector safety, and sometimes for intensity information.

The TDC, a Lecroy Model 2228A, and the ADC, a Lecroy Model 22593, are
mounted in a Kinetic Systems Model 1502 CAMAC crate (Computer Automated
Measurement And Control.) (Both converters have ~2000 channels. The TDC is
set at 100 ns full scale, and the ADC has a full scale of -2 V.) Also in the CAMAC

71

crate are a BiRa Model 3251 NIM Out and a Lecroy Model 2323A Programmable
Dual Gate Generator (PDGG). The RF signal, which has been converted to a NIM
pulse in an ORTEC Model 436 100 MHz Discriminator, is delayed in the PDGG
and then sent to the TDC (necessary to prevent an overlap of signals in the TDC.)
The TDC then uses the time signal as its start, and the RF signal as the stop, and
digitizes the quantity (tRp — tdetector)- Both this value and the value of the energy,
from the ADC, are transferred to a VAX Workstation by a Kinetic Systems Model
3929 SCSI Crate Controller. Having processed the data, the CAMAC program sends
a signal to clear the Latch via the NIM Out module. In this manner, overlapping

time signals will be ignored, but they can still pile up in the energy measurement.

3.1.3 A Data Collection and Display Program

The data taking program was written in a collaborative effort by Au, Marti, and the
author. The data collection portion is actually a separate program which controls
the CAMAC modules from the VAX. A portion of its memory is shared in common
with the data display program. Through this ‘mailbox’ the data display program
instructs the data collection program to start, stop, and clear, as well as reading the
histogrammed output for data analysis. The graphics output of the data display
program is written in GKS and needs X-Windows to run. It has two graphics
windows, displaying the current spectra in the top window, and comparing it with
up to 10, differently colored, stored spectra in the bottom window. These stored
spectra can be current spectra which have previously been stored, or saved spectra
which have been read in from the disk. Any of the stored spectra and the current
spectra can be written to disk, saving them for subsequent analysis. Interesting

portions of the spectra can be expanded to fill the whole window. The data collection

72

can be switched from an accumulative mode, which can accrue sufficient counts to
obtain good statistics, to a tuning mode, which speeds up tuning by automatically
erasing the old spectra each time the data collection side completes a new histogram

(1024 counts.)

The ease of use of the graphical interface, together with spectra comparisons and
the tuning mode, make the data taking and display program a rapid and efficient way
of measuring and tuning the time spectra inside the cyclotron. The only drawback
is the lengthy set up time required to install the probe containing the detector, and
tune the detector electronics. Once this is done, everything else works quickly. A
1 nA °°Ar1°+ beam can be attenuated in the grid system to as low as 206 counts/ sec.
At this rate a new spectra is accumulated every 5 seconds in tuning mode. (Usually
the attenuation is set to obtain several thousand counts/ sec. The data collection
program is limited to 1 histogram/see, but it is not slowed down by excess counts,

so this allows the beam to be cut by slits without impeding data taking.)

3.1.4 Results with the External Timing Detectors

Measurements taken with the external beam were very promising. Figure 3.2 is
from alpha particles that passed through both of the Hamamatsu detectors. The
resolution of each detector, including the electronics, was 310 ps FWHM, after
correcting the two detector measurement by 1/\/2. This is the equivalent of 15°
RF for the 13.5 MHz frequency used to accelerate the 40 MeV/ u beam.

Figure 3.3 was also taken with these detectors and 40 MeV/ u alpha particles. It
was taken using the buncher set at several different phases, (In, with respect to the
accelerating voltage. They are clean sharp spectra showing distinct structure. With

allowances made for the cuts in the beam made by the central region, and the cuts

73

40 MeV/A ‘He” 13.4648 MHZ
1200 I T I I 1 l n I l i

1100 r '4
1000 - —
900 ' «— + 10 ns delay -’ I
800 _ 4
700 ~ ~
600 P -
500 r —
400 — -
300 E —
200 - -
100 - —

O L L. L I .1 _1__

—1012 3 4 5
tlstart-t

 

counts

 

 

 

2 stop (us)

Figure 3.2: Resolution of the Hamamatsu External Detectors.

The resolution of the Hamamatsu detectors was measured to be .31 ns FWHM. The
measurement was taken using the signals from a’s which pass through both detectors.
The signal from the first detector was used as a start, and the signal from the second
detector was used as a stop.

and possible spreading made by the extraction system, they reproduce the bunched

beam calculations of Figure 2.29, for the exit of the inflector, very nicely.

These results were sufficiently promising, that the design of an internal timing

probe, using a detector similar to the external detectors, was embarked upon.

3.2 USING THE DETECTORS ON K1200 PROBES

As was depicted in Figure 1.1, the K1200 cyclotron has two radial probe drives,
labeled A2 and A5. These were designed such that the probes themselves are in-
terchangeable. There are several current probes, and a TV probe that views a
scintillator inserted into the beam[33, 57, 58]. The timing probe complements the

existing probes, allowing different aspects of the beam to be tuned and studied.

Figure 3.4 shows the timing probe head. The middle picture is fully assembled,

74

4o MeV/A ‘He“ 13.4648 MHz
100 I I T fi
= 10.’
50 _ g + W _
100 “ ‘1‘ l ‘ i
= o.“
w W‘ W I
too "‘ ‘r‘ : ‘ 1

 

 

 

 

 

Counts/.25 RF deg. (73. of max.)

 

 

 

0
RF deg.

Figure 3.3: Bunched Beam Measured with the Hamamatsu External Detectors.

Beam spectra measured with the external beam using the Hamamatsu detectors. The
various spectra have the buncher set at different phases which were calibrated with respect
to the accelerating voltage. The RF phase (x-axis) is relative not absolute. Compare these
spectra to the calculation in Figure 2.29.

looking at the detector through a hole in the copper shield. The shield was an
attempt to hide the detector from the internal RF fields. The hole allows the beam
to strike the detector first. The top picture depicts the detector mount, and the
bottom picture is a cut away, which shows vacuum seals, signal feed throughs, and
the maximum angle of incidence of the beam on the detector (necessary for the A2
drive.) Since the beam spot is typically only a few millimeters high, the detector

has an active area of 1 cm2.

While it too can work in either drive, for convenience, all the measurements
made with the timing probe were done on the A5 drive, depicted in Figure 3.5. The
angle of incidence of the beam on this drive is typically 28° to 30° over the whole

of its range, which is shorter than the range of the A2 probe.

The path of the A5 probe, instead of being truly radial, would, if extended, pass

tangential to a circle of 16.351 inch radius. The center of the dees spiral out at a

75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

culh/hllq.t M. 1:. 1994 1413312)

Figure 3.4: The K1200 Timing Probe Head.

Details of the timing probe head assembly are shown. Also included in the picture, are the
detector mount, the copper RF shield, the vacuum seals, and the vacuum feed throughs
for the detector signals. The angles depicted on the lower cut away show that the beam
will clear the shield for the range of incident angles incurred when used in drive A2. In
drive A5 it is typically, 28° to 30°.

rate of -4.40737° / in, to 39.2 in, where they curve outwards to maintain a constant
azimuth. The time measurements taken with the timing probe need to be corrected
from the position of the probe head, to the dee center, which is the phase reference
point. To do this, equilibrium orbits are run in the design magnetic fields to get
the time of travel from the center of the dee, assumed always to be a spiral, to the
probe. The result is displayed in Figure 3.6. Note that this correction, though used
for all measurements, is no longer valid past 39.2 in, where the dees no longer spiral

and this correction is over. The result will be that the corrected of is too small.

3.2.1 Detector Modifications for Use Inside the Cyclotron

Any probe operating in the outer radius of the cyclotron requires an active area
which extends nearly to its outermost edge. This is because the beam’s radius gain

per turn can be as small as .5 mm before crossing V,- = 1. To overcome this defect,

76

 

16155127

1994

 

 

 

 

captains/shrubs.“ Jun. 13.

 

Figure 3.5: The K1200 A5 Probe Drive.

The A5 probe drive is shown with the probe fully extended. It is inserted into the gap
between the grounded pole tips. The point in the lower left corner is the machine center,
with the two spirals approximating the centers of the dee and hill. Note how the probe
approaches the accelerating gap.

two specially built detectors were purchased from the Senter for Industriforskning
in Norway (Center for Industrial Research.) These detectors were built with normal
guard rings, and then they were cut, one just outside the innermost guard ring,
the other just inside this same guard ring. These cuts are depicted in Figure 3.7.
Table 3.1 lists the detector characteristics before cutting, and Table 3.2 lists these
same characteristics after cutting and mounting. Compared to an uncut reference
detector, the cuts have raised the leakage current in the guard rings of both detectors
by three orders of magnitude. Without the innermost guard ring, the leakage current
in the active area has a similar increase. These cuts leave a dead area that is at

most 190 pm, sufficiently small enough to detect the beam at any radius.

The detector with the outside cut was tested first. It had the same response as

77

 

 

   
  

85 I I I I I I I I I
- — + — — 130-43.:171116 E/A-4O Q/A-.202
80 _ __..__ 130—39131sz E/A-25 Q/A—.176 .‘b 4
----+---- 80-35.136kG E/A—so Q/A-.3OO
0

0‘
I

------- o----- B —31.934kG E/A-80 Q/A-.375_ 9

—T Dee enter
0: \‘i \2
O" O

I I

Detzstor
O
I

 

 

45 1 1 1 1 1 1 1 1 1
31 32 33 34 35 36 (3'7) 38 39 40 41
1n

 

R A5 probe

Figure 3.6: Time Corrections for the A5 probe.

The calculated time of travel in RF degrees is presented as a function of the A5 probe
radius. The variation of a couple of degrees from different operating points is primarily
a function of Ba. With the iron fully saturated, the contribution of the pole tips remains
constant. Thus the flutter decreases with increasing Bo, reducing the scalloping of orbits
for these settings.

the detectors discussed previously. The fast signal had the same shape, complete
with the same 5 ns rise time. A resolution test was not conducted on this detector,
but Figure 3.8 is a spectrum that was taken with this detector. It is from an analog,
63Cum“, of the intended beam, 28Si”. With a slightly different charge to mass
ratio, .286079 as opposed to .285995, the copper ions have slipped ~80° away from
the silicon ions. After one more inch, it will no longer gain sufficient energy to clear
the detector’s dead area. It is believed that the multiple peaks in Figure 3.8 are a
consequence of the beam precessing in radial phase space due to an off centering of
the beam. (Only one time can be truly centered at any given radius.) With only a
couple of turns of each precessional cycle having sufficient radial separation to clear
the dead area, and the turn number at which the ions strike the detector being a
function of phase, see Equation 1.2, the result is a multi-peak structure in phase.

d¢/dn at this radius is not large enough to cause this separation, but may be causing

78

 

 

 

 

 

 

 

 

Figure 3.7: Detector Modifications Made by SI for Use Inside the K1200 .

The position of the two different cuts in the detector guard rings are depicted above.
These cuts were necessary for use inside the K1200 cyclotron, where the radius gain per
turn can be as low as 0.5 mm. Pictures are courtesy of Lars Evenson of the Senter for
IndustriForskning, Norway.

79

Table 3.1: Detector Characteristics Prior to Cutting.

Measurements made prior to the detector modifications for the two specially manufactured
detectors and a reference detector. This table courtesy of Lars Evenson of Senter for
Industriforskning, Norway

Device Bias Voltage Active Current Guard Current
Uncut 40 V 65 pA 650 pA

Cut outside inner 50 V 35 pA 509 pA

guard ring

Cut inside inner 50 V 65 pA 560 pA

guard ring

an apparent change of the total phase width measured by the detector. Note that
many of these peaks have a FWHM of 200 ps, an indication of the detector resolution
achievable with this detector. Figure 3.9 shows the full spectra from which these
peaks were taken. Using both the phase separation at these radii, and the amplitudes

of the energy deposited in the detector, the three peaks were identified as 63Cult”,

\

35C11”, and 28Si8+ (left to right.)

The detector cut inside the inner most guard ring also proved to be useable. Like
the other detector, its fast signal has a rapid rise time, 6 ns. As the peak decayed,
though, it had an extended shoulder. It is as if there is a second rapid change in
the current occurring shortly after the current begins to be collected at the detector
sides. The purpose of the guard ring is to maintain the electric field uniformly
throughout the active area, and to reduce the leakage current from the detector
active area. The propagation velocity of the electrons and holes are each dependent
on the strength of the local electric field, so the collection times will be affected by
this change. The CFD works with the leading edge of the signal, so this substructure

on the tail does not adversely affect the time measurements. Measurements from

80

Table 3.2: Detector Characteristics after Cutting and Mounting.

Measurements made after the detector modifications for the two specially manufactured
detectors and a reference detector. This table courtesy of Lars Evenson of Senter for
Industriforskning, Norway

Device Depletion Active Current Guard Current
Voltage

Uncut 40 V 1.3 nA 2.4 nA

Cut outside inner 35 V 38 pA 18 11A

guard ring

Cut inside inner 40 V 4.0 [1A 4.3 11A

guard ring

both detectors will be used hereafter without distinguishing their source.

The multiple peaks in Figure 3.8 show that under extreme conditions, that the
detector can measure an altered spectrum. This particular case was for extremely
low energy gain, coupled with precessional effects. The dead area will function like
one of our phase slits, except it is much thinner, and the turn overlap is signifi-
cantly larger at the radii of the detector. Separating the description of the beam
at the position of the detector into four classifications is useful in considering other

ramifications. These are spot size, energy gain, phase width, and the r-gb correlation.

If the radius spread of the beam, for one particular a5, is smaller than the dead
area of the detector, then the dead area can completely remove this particular time,
and partially remove adjacent times. A especially large Ar would itself be collected
over several turns. The dead area will slice out small segments of the r—pr, and
z-p, phase spaces, with each slice made at different orientations, depending on the
rotation of the particles in those planes, described by 27ru,, and 27m” after one

complete orbit. In this case, the percentage lost from each phase will vary some

81

Beam at 36.5 in.
50 I I I I I I I I I

I

 

 

 

 

 

 

 

 

 

 

0.1L .11....

—5 -4 -3 -2 -1 O 1
t (ns)

Figure 3.8: Extreme Precessional Effects and Internal Detector Resolution.

A measurement made with the timing probe illustrating that the resolution is at most
200 ps FWHM. This beam is an analog close enough in q/m to the design beam that it
survives past 36 in. It is far enough out of phase, giving it a low energy gain per turn,
that it needs the betatron precession to clear the dead area at the edge of the detector.
This provides thin cuts in time.

small amount.

We have seen some of the effects of small energy gain, the percentage lost for all
phases will be large. This will make small variations appear large. The larger the
energy gain, the fewer cuts per ° RF. Large spots sizes will only be cut once if at

all, if the energy gain is large enough.

The r-¢ correlation is a measure of how the cuts vary with phase. Large phase
widths will always have partial correlation, even if they are centered about the
phase with maximum energy gain. Small phase widths may all be near that of
maximum energy gain, in which case there is no correlation, or they may all be
strongly correlated. The energy gain and spot size effects then vary with the phase
of the particles, according to the portion of the r-¢ diagram occupied by the beam.

How rapidly it varies depends on the energy gain, and how much it varies on the

82

 

 

 

 

 

 

 

 

 

 

I I I I I
N
28 ~8+ 35 10+ 63 18+ 0'8 :1:
70 MeV/A s1 C1 Cu 0., 2
01
0.4 51’.
C”.
0.2 l‘
I I I I I I I I
N
0.8 — _ __ m
m 2
E 0.8 — — — N
m
,_, 0.4 — p _ g
3 0'3.
0.2 1... r— — [x
ALJIIL 1 111IIIIL1 1 1 1 1 1 '7
~100 -1‘0 ~120 -100 -00 -00 -160 -140 ~120 -100 -ao -00 N
deg RF (12:35.5) deg RF (R=36.5) g
cu
I I I I I | I I I I v
m
m 0.8 — — — c0
4.) l‘
-~ 0.8 — — — ”IL H
7,; l L l .1
O 0'4 _ — — -1oo -1w -120 -100 -a0 -00
‘7' 0,2 _ _ _1 deg RF (R=37.5)
W4 1 1 1

 

 

 

Figure 3.9: Analog Beam Time Spectra.

The full time spectra for 70 MeV/u 28Si8+ and two analog beams, measured with the
internal timing probe. The relative spacing in time, together with relative energy signals
enabled the identification of the three peaks, which are from right to left, 283?”, 35C110",
and °3Cu18+. Figure 3.8 is a close up of the lower left corner of the bottom middle spectra.

spot size.

It is conceivable that the leading and trailing edges of the r-¢ diagram will be
cut more than the central portion. AE/ E, which is always proportional to 2AR/ R,
is proportional to A43, when the beam is strongly correlated. Thus A¢ o< 2AR/ R.
From Figure 4.5, at 7 in, AR, was calculated to be 0.25 in over the last 5° of the
strongly correlated tail at slit B. Using this as a possible case, and extrapolating to
40 in, the correlation could be as large as .14 in per ° RF. The dead area can be
as large as .008 in, so if the spot size is smaller than .008 in, counting both leading

and training edges, 1 / 10th of a degree could be lost. Oddly enough, the smaller the

83

correlation, the greater the possible loss. The extrapolation also ignores the change
in the phase curve. If the phase spread returned to .05 in per ° RF at the detector,

the lost time would be approximately three times as great.

But remember, that this reduction in the full width requires small spot sizes.
For large spot sizes, the last time would only be less intense, and would present
much smaller reductions in the measured half width. Also, none of the above in-
cluded precession of an off centered beam, see Section 3.2.4, which can add its own
variations in intensities and widths of measured times. It is best, and was generally
practiced, to measure the same spectrum at different radial positions, to check for

variations from these extreme cases.

3.2.2 Detector Simulation

A constant fraction discriminator works by inverting and delaying the signal, then
adding it to the original signal which has been reduced to a fraction of its original
amplitude. The zero crossing then occurs at a constant fraction of the maximum
amplitude of the signal. This reduces a significant portion of the walk in the signal
caused by differing amplitudes. Indeed, for signals of the same shape, this walk is

nearly eliminated.

The internal probe can take measurements of the beam over the range of
.625 Ema; to Em“, and the beam passes through the detector at an angle. So
for various ions and energies, the beam may always punch through the detector,
with the deposited energy decreasing as a function of radius. Or, the beam may
always stop in the detector, in which case the deposited energy and the depth of
penetration will both increase as a function of radius. In this case, the signal shape

itself could vary, causing some walk in the CFD. Or, it may be a combination of

84

the two previous cases. For any of the above, some ions will cross through the front

corner of the active area, while others can traverse the entire detector thickness.

To simulate these effects, the program ELOSSI59], written by Winger at MSU,
was used to obtain the energy loss profile for several different ions incident on the
detector with different initial energies. (100 MeV/u 3A1“, 40 MeV/u 33ml“,
30 MeV/u §§9Xe23+, and 25 MeV/u ‘l’gAr'H'. Each was run from .6 Emu/u, just
below a radius of 32 in, to Emu/u.) A simple model of the detector, developed by

Spieler[60], was then used to simulate the collection of charge from the detector.

Approximate the electric field across the fully biased detector as a linearly de-

creasing field with

Vb - V1)
‘9an — D a (3'1)

 

where V1, is the bias voltage, VD is the depletion voltage, and D the thickness of the

detector. The maximum field is then

2V1)
£77163 _ D + gmzn- (3.2)

The velocity is then 17(23) 2 p - 8(3), where at low fields, 5 S 2.5 - 103 V/cm, in
room temperature silicon, and p- is 1350 cmZ/Vs, and 0+ is 480 cmz/Vs[60]. (All

of these detectors were operated under these conditions.)

This detector model was then used as a current source in a simple integration
circuit to simulate the signal from the detector. These signals, which reproduced the
detector fast signal, complete with 5 ns rise time, were input into a CFD simulation
with a fraction of .2 and a delay of 3.3 ns. Figure 3.10 shows the calculated time
delay between the constant fraction input and output signals from this simulation.

The solid lines are for the 100 MeV/u, the large dashes for the 40 MeV/u, and

Exit Detector After

 

 

 

3.93 1 ’,L-———-\ 1 1___ I
’<’-‘ \ ."-‘.,.....~ .‘l'._
I \ _." o
‘\,..-""\\‘-..F“1.1Th1‘3kness
_.7"”~~1‘\ ..........
3.92 _ ...... .." T__ ‘‘‘‘‘‘‘ '2: fl
.————- \____f‘ A
\l
' 2/3 Thickness
.91 — ‘
3 _ 100 MeV/u 2:18
40
...... 25
3.90 *- ----- _ _ _ so MeV/u 2:54 ‘

‘

.._
.........
~--
‘ s...
................
—-— -..
~-----—JP
—_—
~———_h—

3.89 — W" . "
1/3Th1ckness

 

 

 

delay till constant fraction output (us)
I
I

388 l l l l l
30 32 34 36 38 4O 42

A5 probe (in)

Figure 3.10: Calculated Constant Fraction Output.

The time to reach a .2 constant fraction, including the 3.3 ns delay, for particles leaving
the detector after travelling through 1 / 3rd (lower set), 2/3rds, and 3/3rds (upper two
sets) of the detector thickness. Each set uses the internal energies of 100 MeV/ u 133111“
(solid), 40 MeV/u ‘f‘s’Arlo+ (large dash), 30 MeV/u gi9Xe23+ (small dash), and 25 MeV/u
ngr“ (dotted) extracted beams. The 2/3rds and 3/3rds cases are practically identical

except when the Bragg peak exits the detector. The 1/3rds case will add slightly to the
FWHM of a measurement.

the dotted lines for the 25 Mev/ u calculations, each of which was for Z = 18.
The small dashes are for the 30 MeV/u, Z = 54 calculation. The lower grouping
is for. those particles leaving the active area after traversing 1 / 3rd of the detector
thickness, while the upper groupings are for those particle's exiting after 2/3rds
of, and the full detector thickness. The upper four curves demonstrate the mixed
condition, where the particle gains enough energy to punch through the detector.
This calculation shows that electronic response will be relatively the same for both
energetic medium sized particles, and slow heavy particles. There will also be a

slight broadening caused by the small fraction of particles which pass through the

86

RF pickup compared with Signal strength

 

300 I 1 I 1 I I I I 1
—O—— 100 MeV/A a'Ar’” £V=389.0 IN
250 _ ——-——— 100 MeV/A "Ar“: 13v=815.5 kV q
—.—"— 40 MeV/A “Aid“ XIV-227.9 RV
— — 0- — - 100 MeV/A aArm Signal (est)
A _ __ _ _ 40 10+ -
> 200 ._ '- 40 MeV/A Ar Signal d

 

 

 

 

O 1 , %% + re 1 e 1

 

30 31 32 33 34 35 36 3'7 38 39 4O

RA5 probe (in)

Figure 3.11: Detector RF Pick-Up and Signal Strength.

Measurements of the timing signal and RF pick-up are compared as a function of the A5
probe radius for two beam energies. Inside of 32 in, the RF pick-up increases rapidly,
rendering the timing detector useless. Outside of 32 in, the detector works best for low
energy heavy ions, but still works over a large fraction of the K1200 operating diagram.

tip of the leading corner.

3.2.3 Signal Variation and RF Pickup

As was previously discussed, the signal strength will vary with radius. A close
look at Figure 3.5 shows that the A5 probe approaches an accelerating gap as it
travels towards smaller radii. The detector, which is essentially a parallel plate
capacitor is open to the electric field which penetrates the vertical gap in the hill.
With the accelerating voltage in the range of 50 to 200 kV, even an exponentially
attenuated field can be strong enough to mask the signal. Figure 3.11 shows the
relative strengths of the RF pick-up signal and the time signal of the detector as
a function of the A5 probe radius, measured, after the LBL time pick-off, in the
control room. In all cases, inside of 32 in, the amplitude of the RF pick-up increases

exponentially. This makes the region of innermost travel of the A5 probe, 28 in to

87

 

3,0 1 1 Calculated at 18 MHz

  
 
    

Shift in time when:

2.5

VRF = 0.30‘fgignal

2.0 -
/\0.18V..,..1
1.5 r”/—\o.12V.m-a
\o.osv..-..a \/‘

 
     
  

I18

 

 

 

 

 

 

RA5 probe (in)

Figure 3.12: Shifts in Time from the RF Pick-Up.

Calculated shifts in time from adding a small sine wave to the detector signal. Calculated
at 18 MHz with VRp = .06 — .30 V..-9M1. The solid curves are the net shift, and the lower
curves are the relative expansion when A45 = 40° (dotted line), and A¢ = 10° (dashed
line). The radial differences in the net shift from the RF pick-up may need correcting in
phase curve measurements. The relative expansion at worst adds 10% to the measured
widths.

32 in, unusable for the timing detector. For the 40 MeV / u measurement, the signal is
so much stronger than the pick-up, that the RF has no effect on the measurements.
With the signal decreasing and the accelerating voltage increasing as the beam
energy goes up, the 100 Mev / u measurement is no longer unaffected. This effect
can be calculated, and resolves itself into two components, which are shown in
Figure 3.12. The first is a shift in the measured time of the spectra, which because of
the path 0f the probe, together with the radially changing phase curve, is dependent
on the probe radius. The change of this shift as a function of radius can distort phase

curve measurements. These signals should always be measured, and when necessary,

88

the correction should be calculated. The second part is a result of different phases
in one bunch having different net shifts. This will cause a small expansion of the

measured phase widths.

3.2.4 Multi—Turn Collection and Beam Centering

Multi-turn collection on the detector was introduced in an extreme case in Figure 3.8.
In that picture, with the number of turns in a precession cycle being 1/|1/r — 1|, and
with V, m 1.1, it took ~150 turns to collect the entire beam bunch. Normally,
multi-turn collection is not so drastic. It will still have an effect on the timing mea-
surement, though not so pronounced. Calculations made with central rays spaced
every 5° in To, from 185° to 235°, show that at 32 in, it takes ~20 turns for the A5
probe to collect a beam bunch. As the probe is withdrawn, this increases to ~35
turns. (These calculations were made with the ‘standard’ beam, and were done to

get a sense of how the probe works. The results for other operating points will vary.)

To see how precession will change measurements made under normal conditions,
the time of arrival on the probe was calculated for these central rays. The central
ray with To = 220° was centered in these calculations. Figure 3.13 shows the sepa-
ration in the times at which a few of these starting times strike the detector. The
phase width, which was compressed in the central region, shown in Figure 2.20, has
remained constant inside the rest of the cyclotron. The sawtooth structure seen in
the time spread of the particles is from the precession of the off centered ions. Note
that this occurs even for small phase spreads, if the orbits are off centered. At 32 in,
the normal sin(¢) curve is rising, and at 36 in, it is falling. Comparing the time
spreads at these two places, one sees that the measurements will be, respectively,

expanded and compressed under these conditions.

89

40 MeV/A ‘He” calculation
I

 

18 I I I

 

 

 

 

I I I I
15 F _. “‘r\~‘~/~\‘\v/\\\\J/\\\\J/\\\_
T 70:220' T 70:195.
7152207775195
12 ” ‘"' ‘
E
L, 9 — —L —
(.
<3 7' ’“T
6 _ 10:197' 10:193' “E ‘
7' ’"T
\ 10:197' 10:193'
/ \ /\ /
3 :’ / \ " \_'-—' ‘*__. __ _. _ -
\ / / \/ \Jr’ \//‘ \// ‘1
0 1 l l I J 1 l I
32.2 32.4 32.6 32.3 36.2 36.4 36.6 36.6
R (in)

A5 probe

Figure 3.13: Precession Effects on Relative Time Widths.

The betatron precession of off centered times in the beam cause a periodic variation in
the measured time separation of ions in the beam. Depending on the location along the
phase curve of the measurement, this effect can be compressive or expansive.

These multi-turn and precessional effects will cause a small uncertainty in the
width and location of phases measured inside the machine. The precession is a
byproduct of the betatron motion, and multi-turn collection is machine dependent.

Therefore these effects can occur in measurements made in any cyclotron.

3.3 PHASE CURVE MEASUREMENTS

One of the uses of the timing probe is the measurement of ¢(r). Figure 3.14 is one
such measurement. A technique developed by Smith and Garren[56] was employed
to turn the relative phase measurements of the timing probe into an absolute phase
measurement. Let wRF = (1 + e)wo, then

(1 + €)wo

(.12

0(3) = — 1 = (1 + e)Q(E) + c. (3.3)

90

100 MeV/A 36Ar12+ 20.1333 MHz
0.4 1 l I I T l I
0 Smith-Gerren

0 timing probe
c--3.67e—5 sum-.053

 

    
    

0.3 F
0.2 1
0.1

design freq. 20.1376 MHz

sin(¢)

0.0

—O.1 —

-O.2 —

 

 

_03 l l l l 1
32 33 34 35 36 3'7 38 39 4O

RA5 probe (in)

 

Figure 3.14: A K1200 Measured Phase Curve.

The relative phase curve was measured with the timing probe, and set in absolute coor-
dinates with a Smith—Garren RF detuning measurement. The measured curve was then
fit with the output from the design settings in MONSTER, using the frequency error, e,
and sin(¢o) as parameters in the fit.

Making sure that the beam is not lost at an interior radius, adjust the frequency,
way, until half of the initial intensity is lost. Repeat in the opposite direction. Then
from using 9(E) and 45 = i90° in Equation 1.6,
h
l = sin(d>o)+ (1 + €+)%%/Q(E)JE + 6+2—7r 0v/dE (3.4)

, 27rh 21rh
—1 _ sm(¢o) + (1 + e_)q—V: / Q(E)dE + 6.— v0] dE (3.5)
sin(¢(r)) can now be calculated. It is :

(6+(r) + 6-(7'))
(6+(r) - 6-(7‘))

This was done for three of the points at which data was taken, and all the data

sin(950)) = - (3.6)

points, which are the spectra centroids, were then shifted accordingly. The solid
line through the data points is a fit of 9(E) from the magnetic field output by

MONSTER, the program used to design the operating settings for this beam. The

91

100 MeV/A 36Ar12+ 20.1333 MHZ
0.06 I I I I I I I

0.05
0.04
0.03
0.02
0.01
0.00
—0.01
—0.02
—0.03

 

Asingb

 

 

 

 

32 33 34 35 36 .37 38 39 40
RA!) probe (ID)

Figure 3.15: Differences in the Measured and Fit Phase Curves.

The difference in the measured and fit sin(¢) curves of Figure 3.14. The difference is
invalid past 39 in, since the fit curve did not extend to the last measured point (40 in.)
The variation in the rest of the curve is :l:1°, so it is unknown if the structure is real, or
just random measurement error. The sin(¢) measurements are a close fit to the design

field.

exact voltage used inside the cyclotron is unknown, but it is approximately the
design voltage. Using this voltage, the frequency was slightly lower than optimum,
~700 Hz. The optimum frequency is 3.6 kHz lower than the design frequency,

implying that the magnetic field is 0.018% low.

The fit of the calculated curve to the data is very good. Figure 3.15 shows the
differences in these curves. The variation here is from +.3° to -1.5° , except for
r > 39 in. The calculated and measured magnetic fields are very close in shape. If

more data points had been taken, the shape could be derived from the data by,

AB qu
7=9(E)= 2 -—hc 08¢((E))d: (37)

which is from Section 1.3.

The use of this detector is well understood, and it performs satisfactorily, pro-

vided that the ion being studied has sufficient large Z to leave a large signal.

CHAPTER 4

PHASE SLITS

Phase slits, following the design of those used by Milton in MSU’s K500 cyclotron
were installed in the K1200 cyclotron. The use of these slits in the more stable
K1200 , with measurements using the new timing detectors, together with com-
parisons to the multi-dimensional ray-tracing simulations begun in Chapter 2, has
resulted in a confirmation of the manner in which the slits function, and a better

understanding of their limitations.

4.1 SLIT PLACEMENT AND DESIGN

The K1200 yoke was machined with 6 vertical access holes in the center of the hills.
There is one hole through each upper and lower pole tip, to maintain both the 120°
rotational symmetry, as well as the vertical symmetry about the median plane of
the magnetic field. The location of these holes, at ~7.00 in radius, was constrained
by the spacing between the trim coils. The copper RF liner currently has apertures
for only 2 of the vertical hole pairs. The lower hole in one hill is used for a current
probe, which is often referred to as the ‘phase slit probe’, because of its location. To
avoid confusion, the radial probe built to measure the phase spectra, see previous
chapter, has been labeled as the ‘timing probe’. Of the remaining three holes, access

to the other lower hole is restricted by a gate valve in the injection line (visible above

92

93

the buncher in Figure 2.2.)

Opening the holes in the remaining hill would require the removal and machining
of parts of the center plug, which during construction were only machined for the
first two hole pairs. (These iron pieces are sufficiently removed from the median
plane that they do not significantly impact the 3—fold symmetry in the median
plane.) Their use would also require machining new holes in the liner, which also
serves as a vacuum liner. These changes could cause hard to trace and hard to
fix vacuum leaks, they are time consuming, and would require shutting down the

cyclotron. This is considered undesirable, and would be done only if necessary.

This leaves only two holes which could be used to deploy the phase slits. Fortu-
nately, they are on separate hills. Their location above the cyclotron median plane
requires that no oils or fluids be used in the drives, since a leak would contaminate

the accelerating cavity.

The ‘slits’ used in the K1200, are Milton’s off-centered pins mounted on rotatable
shafts, see Section 1.3. The pins are made of tungsten and are soldered onto a
removable copper head, allowing pins with different thicknesses to be used on the
same shaft. The copper heads are designed such that the outermost edge of the pin is
3 / 8ths of an inch from the shaft center. The pins used in the present measurements
of this study have a diameter of 0.094 in. The radius gain per turn at the position

of the phase slits is ~0.16 in.

The shafts, with a 0.50 inch O.D., are hollow stainless steel, with a smaller inter-
nal tube that provides cooling water to the shaft head. The water leaves through the

outer shaft, which is soldered vacuum tight to protect the K1200 vacuum integrity.

The shaft drive, depicted in Figure 4.1, a slight modification of Milton’s design,

is mounted on the K1200 cap. On the top is an air cylinder which through the flow

94

AW CyHnder
Potentiometer\\

  
   
    
 

Vocuum Bellows

Boll Volve

\
Shoft\

Figure 4.1: K1200 Phase Slit Drive Schematic.

The slit drives have five basic functions. They are to 1) seal this exit of the K1200 vacuum
chamber, 2) enable the rapid changing of phase slits while still under vacuum, 3) insert
and retract the phase slits, 4) rotate the phase slits, and 5) provide rotational feedback
to the control electronics. See the text for a description on how this design accomplishes
these goals.

of high pressured air inserts and retracts the shaft. When retracted, the drive can
be locked in place, and the air cylinder removed, allowing the removal of the shaft.
The drive also provides a vacuum seal for the accelerating cavity. With the shaft
installed, an O-ring immediately above the bellows provides the vacuum seal. When
removing the shaft, a special fixture is used to stop the shaft before the head clears
the O-ring. In this position, the pin is within the bellows, allowing a ball valve to be
closed, which maintains the seal on the vacuum. The shaft can then be completely

removed. This procedure enables a rapid changing of the pins.

The rotation of the shaft is driven by an external motor, which coupled to a
worm gear, simultaneously rotates both the shaft, and a 5—turn potentiometer. The
potentiometer provides the location feedback necessary to accurately control and

report the angular rotation of the pin. The motor is an electronic stepping motor

95

which is mounted 8 ft above the cap, inside iron shielding. The horizontal section
of the drive shaft uses two coupling bellows to allow for the vertical motion of the

slits.

4.2 CALCULATED SLIT PERFORMANCE

The initial studies of the K1200 phase slits, done with Rifuggiatto[35], showed that
each individual slit would function in the manner described by Milton[8], cutting
the beam on two consecutive turns. Figure 4.2 shows simulations of cuts made on
one starting time, To = 216°, assuming slits on all three hills. The positions and
diameters of the pins were selected to completely fill the gap between the r-p, phase
spaces on two consecutive turns of starting time To = 220°. The ellipses are ac-
celerated equilibrium orbit eigenellipses, with an initial area of 100w mm-mrad , as
they appear on successive turns at each hill center. The orbits were calculated by
SOMA[26]. The initial conditions of the ellipse were calculated with Equation 2.5,
in order to minimize the differences in energy gain within the ellipse. The different
shapes and positions of the eigenellipses on each hill are a measure of the nonuni—

formity of the magnetic field and of the orbit’s off centering at this radius.

At the slit radius,

/;O=2163in(¢)dE < ,/ Sin(¢)dE < 0, (4-1)

10:220

so the time shown, To = 216°, has a smaller total energy than that of To = 220°, and
its radial cut is made on the outside edge of the pin. Figure 4.2 also demonstrates
a less obvious function of the slit’s azimuthal spacing. Orbits bound by focussing
forces revolve around a fixed point in phase space. In the case of acceleration,

the orbits circulate around the accelerated equilibrium orbits (A.E.O.) The angle

96

To=216° 9=-30.526
004 If fi— / I I

0.02 l- ‘

 

0.00 - "

l

m

“-0.02

l
L

 

I”

o.
-0.04

1

-0.06

 

 

 

'008 1 1 1 1 r 1 1
6.6 6.7 6.6 6.9 7.0 7.1 7.2 7.3
r (in)

1
l 1

:- =216° 62-270 526

0

OOO

 

—002 1—

-0.04 '-

(In)

-006 *-

 

 

1.-0 06 '-
Q.

 

-0.l0 -

-0.12 *-

 

11Ҥ\\\\ \

 

 

-014 * . ' ' -
6.6 67 66 69 7.0 71 72 73 7.4
r (m)

n-zw 9--150.528
0.08

0.00 -
0.04 r
0.02 L

 

I l

 

Pr (in)

0.00 l"

\\\\\\\

-0.02 r a

 

 

 

.—

l l

 

-0.04 ‘ 1 ‘
6.6 6.7 6.6 6.9 7.0 7.1 7.2 7.3 7.4
r (in)

Figure 4.2: Phase Slit Cuts in r-p, .Phase Space.

Calculated cuts in an initially 100 1r mm-mrad eigenellipse in r-p, phase space about the
accelerated equilibrium orbit with To = 216°. A slit was used on each hill, with the position
and width of each slit adjusted to barely pass all of the eigenellipse about the To = 220°
central ray. Notice how the slits each cut a different portion of the ellipse. The angle of
rotation of the particles in r-p, phase space is V,A0. Here A0 = 120°, and v, is near to 1.
(Calculation by D. Rifuggiatto)

97

1400 r I I I I I I I I I I

 

 

12004. _

1000 *- ’ ~

 

 

800 - -*
600 — - _

400 L - —

 

200 — _ a

 

 

 

 

 

 

 

 

 

0 l L l l l l l l l 1 l

208 210 212 214 216 218 220 222224 226 228 230 232

1'0 (RF deg.)

 

Figure 4.3: Preliminary Calculation of the Slit Transmission.

Total transmission for a range of starting times,“ 1'0 = 210 to 236, calculated as in
Figure 4.2. The slits make a nearly triangular cut in time, with a FWHM of 6° in To.
Any further reductions in the phase width will reduce the transmission of the peak. Af-
ter the central region compression, A45 is ~ 4° in this calculation. (Calculation by D.
Rifuggiatto)

subtended by this revolution about the A.E.O as the particle advances an amount

A0, is 14%;". Near the phase slits, 11, ~ 1, thus between every hill, the particles
rotate ~ 120°, and the next slit cuts a different area of the r-p, phase space. This
means that successive cuts on the same turn can make a cut in time that is sharper

than any one slit could make by itself.

The total time cut made by this simulation, ranged over starting times To = 210
to 236, is shown in Figure 4.3. It shows that this procedure will cut the beam into
a nearly triangular distribution with a FWHM of 6° in To. After the central region

phase compression, this is 4° in Ad).

To further study, and more accurately simulate the cuts that the slits make

98

in the phase spread of the beam, orbits from the 4—D bunched injection studies of
Section 2.4 were continued past the slits. Only the unmatched case was used, since
this approximates the actual conditions currently used in everyday operation of the
cyclotron. The radii and phase of the particles were saved at each hill, if the radius
was within the range of the phase slits. These were then used in the slit simulation
program described in Section 2.2. The program displays the cuts in the phase of

some subsequent turn, well clear of the phase slits.

Figure 4.4 is a printout of the graphical display from the slit simulation pro-
gram. In the upper left corner is the uncut phase spectra, histogrammed in 0.25°
bins. Ninit is the number of particles in the calculation, with Ntotal the number
of particles surviving in each frame. Nmax from the uncut spectrum is used to
scale the histogram in each window. On the right side are the cuts made by each
individual slit, including the hypothetical slit C (bottom). On the left side, below
the uncut spectrum, are the spectra from the cumulative cuts made by slits A & B

(middle), and slits A, B, 86 C.

Each individual pin makes many cuts in the beam, not just two! In this calcu-
lation, the beam takes as many as 6 turns to clear the phase slits. This is made
clear in the r-¢ density plots of Figure 4.5, which are used in the slit program to
aid in tuning. The top graph is the distribution at slit A, and the bottom is at slit
B. The vertical lines mark the outside edges of the pin settings which were used in
Figure 4.4. These density plots should be compared with that in the lower left cor-
ner of Figure 2.22(b), which has the same injection settings except that the buncher
was off. Note that the bunched beam has a more strongly localized center than the

unbunched beam.

Several things can be learned from these two graphs. First, the injected current

99

 

 

  
   
    
 

 

 

 

 

 

 

 

 

    
  
 

 

 

 

 

 

 

 

 

 

 

1. 1.0
No] Slits' ' Sl’it I1 I I ‘ I I
a 0.3,_Ninit= 29574 3 0.8 total- 125560 _
Z Ntotal= 2957 1 r I 6.9120
\0.5_Nmax= 446 \0.6- _.
m m
u u
§(L4—- §(L4r- —
o 0
U 0.2— U 0.2— —
0 0 l l l l l J 0 0 IA l L I l l I
'-410-35-30-25-20-15-10 -5 0 '-40-3s-3o-25-20-15—10 -s 0
phi [deg. RF] phi [deg. RF]
1.0 1.0
SlEtsTA I 3‘ ' ' ' s11: I3 ' ' ' ' '
a 0.8,_Ntoca1= 48303 _ a 0.8 total= 102842 _
0311:: 0.0940 rB= 7.0784
2 z
\~0.6— — \40.6— —
m m
g 0 4 g 0 4
o 0
U 0.2r- -< U 0.21- -1
o c [A AAA I 0 0 HA I I I I
'—410-3s-30-2s-20-15-10 -5 0 °-<10-35-30-2s-20-15—10 -s 0
phi [deg. RF] phi [deg. RF]
1.0 1.0
sin-3'11, '9, 's. d I ‘ s11: 15 l T I ‘ '
fi 0.8 total: 20023 _ fi 0.8,_Ntotal= 123917 _
E g rC= 7.0470
\ 0.61- -1 \ 0.6— —
m m
u u
g 0.41- — g 0.4—- a
o o
O 0.2— — U 0.2— —
0 G [A A 1 4m 0 C l l l l l
'-410-35-30-25-20-15-10 -s 0 '-410-3s-3o-2s-20-15-10 -s 0

 

 

 

 

phi [deg. RF] phi [deg. RF]
BEAM TIMING SPECTRA

$8$DKAO: [BAILEY . AXIAL . ALPHA . CENTREG] CRSOBlT2108L4 . DAT; 1
$8$DKAO: [BAILEY . AXIAL .ALPHA. CENTREGJCRSOBlT21OC . DAT; 1

Figure 4.4: Calculated Slit Performance Using the Bunched 4-D Injection.

The phase slit cuts are simulated using the orbits continued from the bunched 4-D injection
study. The cuts made by the individual slits (right column) produce multiple peaks,
implying multiple turn overlap at 7 in. the phase slits are wide, cutting the peak of the
transmitted beam. But, in this simulation, the resulting satellites could not be removed,

even with all three slits (left column.) The buncher has increased the uncut transmission
from 6.4% to 20.7%.

100

 

 

—40 — ' ' ~—

 

 

m 1 I I l I I 1
6Y80 8.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20

 

 

1v I I I I I I I

O

 

I —__l

 

 

-30

I J 1 I I I n
6180 8.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20
PHI VS R AT THE SLITS

 

 

 

 

Figure 4.5: r-¢ Density Plot Showing the Overlap of Turns.

Calculated r-d) density plots at the two phase slits. The tight conditions in the supercon-
ducting cyclotron have resulted in 6 overlapping turns, in radius, at the location of the
phase slit. The vertical lines denote the position of the phase slits used in Figure 4.4.

with the buncher is 20.7%, as opposed to 6.4% without the buncher. Second, this
slit thickness, Dslit = 0.094 in, is too large to transmit all the beam of one phase.
Third, the multiple peak transmission makes it difficult to obtain just 1 nice peak in
time. Essentially, the small peaks of one slit need to be aligned with the valleys from
the other slit, while still preserving a significant fraction of the overlap in the main
peaks. These small peaks are mostly from the tail of the bunched distribution.
And fourth, a slit on the third hill could not make cuts as distinctly as the two
present slits. The differences are the byproduct of the beam centering. Operational
conditions such as nonuniform dee voltages may put this difficulty at one of the
other hills. The third slit helps narrow the cuts made with the other two slits, but

can not remove the smaller satellites. Finally, narrower slits, while transmitting

101

more of the main peak, transmit more of the satellites. Thicker slits reduce both

the satellites, and the main peak transmission.

The great overlap in turns indicates that the central region transmission should
be restricted to a smaller phase width. To be properly done, such a change would
require a redesign of the central region. For instance, in Figure 2.4(b) the best place
to cut the beam, with nearly uniform separation in time and space for posts, is in
the third turn on the hill in the lower left quadrant of the graph. But posts here
would change the electric field by more distinctly separating the accelerating gaps
on either side of the hill. This would slightly deflect the beam on the previous two
orbits, with changes in the orbit centering, and a possible adverse effect of deflecting
the beam into the back of the puller. A good slit should also be controllable, or at
least capable of rapid insertion and removal for runs where the beam intensity has
a higher priority than the phase width. This will be difficult to achieve in the tight

confinement and limited access of the K1200 central region.

Slits could be put between the posts on the hill in the upper left quadrant, with
smaller changes in the electric field. The beam is separated in time and radius as
it passes through this window, but nonuniformly. To observe the general results of
central region slits, the radius of the orbits were saved at this position and filtered
as if a slit were installed. Figure 4.6 and Figure 4.7 were phase slit studies done
with the same buncher settings as Figure 4.4, but with two different central region

slit filters.

In the first, Figure 4.6, the filter was set to pass the main peak (everything
between 1.35 in and 1.45 in.) The phase slits were then able to make sharp cuts in
time, with a resultant two slit peak of 2.3° F WHM. The satellites are still present,

but at a reduced intensity. This is because the earlier starting times do not separate

102

 

 

        

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0 1.0
No‘ 511:3' ' I Lillit I ‘ ‘ ' ' '
0.8441161: 29574 2 a 0.8 total: 7279 n
Ntotal: Z rA= 6.8990
\ 0.6m)“ -— \ 0.6— —
In 01
g 0 4 g 0 4
. -- —1 . -- fl
0 0
U 0.2— — U 0.2~ —
0 0 l l l l l l 0 0 IA 1 l l
2410-35—30—25-20-15-10 -5 o '-<Io-35-30-25-20-15-10 —5 0
phi [deg. RF] phi [deg. RF]
1.0 1.0
$113.19“! 311.1." ' "
mammal: 36076 _. g 0.8_Ntotal= 752 _
Dslit: 0.0940 2 rB= 6.8806
\ 0.6— - \ 0.6- -
In m
g 0 4 g 0 4
. I- — . — —
o 0
U 0.2— —« U 0.2— —
0 c 1 ALA 1 M1. 0 0 LA I
'-40—35-30—25-20-15-10 -5 0 °-410-35-30-25-2o-15-10 -5 0
phi [deg. RF] phi [deg. RF]
1.0 1.0 j
$1691.67}. 6 ‘ ' SlTit & ' ' ' '
fi 0.8_Ntota1= 15066 _ o_8j_Ntota1= 79297 2
E rC= 7.0062
\ o 6— - \ 0.6— .1
In m
u u
5 0.4-— — 5 0.41— A
o 0
U 0.2— — U 0.2— —
o G I AI AMI. I J‘ I o G I I I I
'-4lO-35-30-25-20—15-10 -5 0 "-410-35-30-25-20-15-10 -5 o
phi [deg. RF] phi [deg. RF]

BEAM TIMING SPECTRA

CR Slit 1.35 to 1.45 in

$8$DKAOz [BAILEY.AXIAL .ALPHA. CENTREG]CRSOBIT21OSL4 . DAT; 1
$8$DKAO: [BAILEY .AXIAL .ALPHA. CENTREG]CRSOBlT21OC . DAT; 1

Figure 4.6: Calculated Phase Slit Cuts After the First Central Region Cut.

A central region cut has been used to pass the main peak of Figure 4.4. The resultant
phase slit cuts transmit a narrower peak with reduced satellites, at a cost of an additional
25% in intensity overall.

103

much at this central region slit. So, including part of one earlier time includes part

of all the earlier times. The later starting times do separate.

In the second, Figure 4.7, the filter has been moved to 1.30 in through 1.40 in.
Here, we have cut the earlier times, so the central region cut is sharper, further
reducing the size of the tail. This makes for fewer satellites in the phase slit cuts,
allowing the slits to be positioned to remove most of these particles. This particular
set up has another drawback, however, in that the beam remaining after the central
region cuts is the portion with smaller values of I f sin(¢)dE I (smaller values of (I)
in Figure 4.5.) Under this condition, the phase slits can not make cuts as sharp as

those in Figure 4.6.

A good design for the phase selection system would include the best of both
simulations. A central region cut would be made at times which are spread out
in radius to produce a well defined beam in time. This cut should also be narrow
enough to result in separated turns at the phase slits. 10° should be sufficient.
Then the phase slits could be used solely in cutting the main peak. The beam at
the phase slit should also be spread out in time, allowing the slits to make sharp
cuts in time to refine the phase selection. As will be demonstrated below, this is
achievable through changes in the trim coil magnetic field profiles, but note that
this makes turn separation at the phase slits more difficult to achieve. Estimating
from Figure 4.5, for large values of | f sin(¢)dE I, a central region cut to 5° might be

necessary to preserve separated turns at the phase slits.

4.3 MEASURED SLIT PERFORMANCE

The features which dominated the phase slit calculations were also found in the

measurements, but to a lesser degree. Figure 4.8 has spectra which were measured

104

 

 

   
  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. 1.0
NoISLILtsI I I I SlIit. I1 I I I I I
0.8 init= 295741 _ g 0.8 tota1= 55989 _
Iguana: 155609 2 WA: 6.9528
\ 0.6—me: 3554 — \ 0.6— —
m 01
g 0 4 g 0 4
. r- — . 7 fl
0 0
U 0.2- — U 0.2— ~
0 G l I I I I I O O l I [L I I
°-40-35-30-25-20-15-10 -5 0 '-40-35-30-25-20-15-10 -5 0
phi [deg. RF] phi [deg. RF]
1.0 1.0
SlIitsIA I. BI I I I SlIit I3 I I I I I
g 0.3,_Ntot:81= 25020 _ a 0.8,_N1;01;61= 49626 ..
Dslit= 0.0940 rB= 6.9073
25 23
\ 0.6— — \ 0.6— —«
01 m
o o
0 0.2— — U 0.2— ~—
0 G I l I [‘1 I 4* 0 G I [AJ 1 l
'-410-35-30-25-20-15-10 —5 0 '-40-35-3o-25-20-15-10 -s 0
phi [deg. RF] phi [deg. RF]
1.0 1.0
SlirtsIA,IB, Is. 6 I I 816:6 I I I I I
O‘BFNtota1: 10349 a go'spNtote1= 72304 _
z rc= 6.8634
\ 0.6— -— \ 0.6— —
m m
u u
5 0.4— — § 0.4— —
o o
O 0.2— — U 0.2? —
0 G I I I Al 41,41 0 G I I I I I
'—40-35-30-25—20-15-10 -5 0 '-410-35-30-25-20-15-10 -5 0

 

 

 

phi [deg.

RF]
BEAM TIMING

CR Slit 1.30 to 1.40 in

 

 

 

phi [deg. RF]
SPECTRA

$8$DKAO: [BAILEY . AXIAL . ALPHA . CENTREG]CRSOB1T21 OSL4 . DAT; 1
$8 $DKAO: [BAILEY . AXIAL .ALPI-IA . CENTREG] CRSOBlTZlOC . DAT; 1

Figure 4.7: Phase Slit Cuts After the Second Central Region Cut.

A central region cut has been used to make a narrower cut than that of Figure 4.6. This
results in fewer satellites in the phase slit cuts. The final peak is fatter here than that of
the first central region cut. This is because the final position of the transmitted beam in
the r-p, diagram is closer to that of maximum energy gain.

105

Comparison of Phase Cuts at Different Frequencies
2000 I" I I I T I V Y I ..

1500 L80 MeV/A “0“
L1 = 18.3596 MHz

 

  
  
  
   
  
  

1000
500 —

 

250 ~
1 66
200 _50 MeV/A '0

150 ._f = 14.9313 “Hz

100 *-
50 I-

Counts/channel

I.
1,

 

300 P25 MeV/A "0’;
200 ._.f = 10.7931 “H2

100 P

 

 

-25 —20 -15 —10 —5 o 5 10 15 20 25
RF deg.

Figure 4.8: Comparison of Phase Cuts at Different Frequencies.

External measurements of the extracted beam phase width, at three different frequencies,
with and without phasecuts, expressed as a function of the RF period. The areas of the
cut spectra are scaled to those of the uncut spectra, using their relative extracted currents.
Each is ~30% of the uncut spectra. The final RF width of the time spectra, as expected,
seems to be approximately independent of the operating frequency. Theoretically, one
should be able to make identical cuts at every frequency, but the initial conditions vary
too widely to prove this.

with the extracted beam at different frequencies. Even after extraction, satellite
remnants remain in the beam. The calculation, however, has overestimated the
difficulty in minimizing and removing these satellites. This is not conclusive, the
extraction channel could be making additional cuts. The final spectra tend to be

more like those of the central region cuts in Figures 4.6 8:: 4.7.

This comparison of extracted beams also shows that the process of phase selection
with the slits is relatively independent of the frequency at which the cyclotron is
operated. This was an expected result, since the orbit path through the central
region is the same for all ions, and the accelerating RF voltage defines most of the
time processes in the cyclotron, but it was important to verify. The sin(¢) curve

in Equation 1.6 depends on the inverse of the voltage gain per turn, as well as the

106

Table 4.1: Phase cuts and transmission.

The fractional transmission is presented for several different extracted beams using the
phase slits to cut the phase width of the beam. 5° FWHM cuts are easily obtainable with
25% to 30% transmission. These are also relatively easy to maintain.

 

 

 

 

 

 

 

 

1011 Energy ¢FWHM ¢FWHM 1 cut / 10
(MeV/ A) uncut cut

”03+ 25 l5.°RF 5.7°RF .33
I°O5+ 50 12.7° RF 7.8° RF .24
6.6°RF —
“Mg"+ 60 11.°RF 2.6°RF .25
18‘06+ 80 14.5° RF 4.7°RF .30
"$319+ 80 12.°RF 4.6°RF .23
3.6°RF —

 

 

 

 

 

frequency, and the deviations of the magnetic field from isochronism. The magnetic
field shape for an isochronous cyclotron does vary with final energy, since it should
follow the 7(1‘) curve. Also the operating points are interpolated from a mesh of
premeasured fields. These things may make reproducing the sin(¢) curve at each
operating point difficult. These effects will show up in the timing cuts. There are
other parameters which can also affect the cuts, such as bad centering caused by

unbalanced dee voltages.

5° FWHM tends to be an easily reproducible, and easily maintainable phase cut
at all frequencies. Table 4.1 shows the transmission for these as well as a few other
external measurements. 25% to 30% transmission is easily obtainable with these

phase cuts.

The best cut to date is shown in Figure 4.9. This is 2.4° FWHM, and it had a
20% transmission when measured just before extraction, (at 39.5 in.) Presumably
extracted transmission would be as good, if not better for this beam. One satellite

forms a shoulder on the main peak, the rest are practically gone. Cuts like this have

107

#:76184871 MHz .49ns or 2.4'RF FWHM at 34.0 in.

I I I I I I I F I

 

650
600 P
550 ~
500

m 450
IE." 400
g 350
o 300
250
200
150
100
50

O I - __ ' -
—2.0-1.5 -1.0 —0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
t (ns)

 

 

 

Figure 4.9: The Best Stable Phase Cut.

Internal time spectrum of a cut made to 2.4° FWHM, compared to an uncut spectrum at
the same radius. The long flat tail in the cut spectrum consists of real particle signals.
The vertical scale, ‘counts’, has not been scaled to reflect actual currents. The transmitted
current with the cuts is 20% of that without cuts. Smaller cuts have been achieved, but
as yet none have been found to be stable over time.

been possible on other measurements, but each has required significantly more effort
to achieve and maintain than the cuts to 5° FWHM. Smaller cuts, when achieved,
have proven to be highly unstable and unreproducable. They also come at a price

of low intensities, transmissions are typically _<_ 1%.

4.4 STABILITY

To test the stability of the cuts made with the phase slits, a test was made in a
period immediately following a shut down. The cyclotron and the phase slits were
tuned. Then the cuts made with the phase slits were followed over a 7 hr period,
by taking periodic measurements of the extracted beam time spectra. The result
is displayed in Figure 4.10. Figure 4.10(a) tracks the first and second moments of

the time spectra, as well as the FWHM of the main peak. No control settings were

108

 

 

 

 

 

 

 

60 MeV/A "’Si'I 16.3682 MHz 700 60 MeV/A “SI“ 16.3682 MHZ
I I I T I I
600 '- .-
500 ’— -1
3600 ’- ‘1
fl
.‘5
8000 ~ 3
200 ’- _.
[00 I— —4
o I I
-26 -20 ~16 -10 -? 0 IO 16
0 1 7 46 (RF)

 

 

 

 

3 4
Time (hours)
(a) Changes in the First and Second Mo- (b) Phase Structure After 5 Hours.
ments of the Beam Time Spectra.

Figure 4.10: A Measurement of Phase Slit Stability.

The structure in time of the extracted cyclotron beam was followed for 7 hours. The
centroid experienced a net drift of 1.2 ns. The second moment was relatively stable, but
the actual structure drifted, as attested by the rapid fluctuations in the peak width. The
peak in Figure 4.10(b) is 3.6° FWHM.

adjusted in this time period. And at the conclusion of the measurement, no control
read outs had changed. The iron yoke is heated by the RF, and is known to warm
up after a shutdown. This changes its permeabilty, requiring a fine tuning of the
cyclotron by the operators, but the external yoke temperature did not change. (The

yoke is cooled externally and the internal temperature can not be measured.)

The drift in the first moment was matched by a drift in the uncut spectra, and
probably occurred after the phase cuts. This drift is equivalent to a change of 2
parts in 105 per turn times the ~800 turns inside the cyclotron. If this drift was
caused by heating of the iron yoke, this could be confirmed with N MR measurements
at the cyclotron center. Drifts in the centroid can be monitored and corrected for
in TOF experiments. The electronics to do this require a time signal from some
external detector, were built by Meier, and are currently available for use by the

experimenters.

109

The second moment had small fluctuations, averaging 0.69 :I: .07 us, but at the
same time, the width of the main peak had much greater variations, averaging
0.57 :t .16 ns. These variations are either changes in the phase slit cuts, or the cuts
made at extraction. Either way, this implies that the time cuts need to be monitored

in the extracted beam.

Experience has shown that the periodic adjustments, needed to retune the cy-
clotron, tend to drift the operating conditions away from the optimum tune. It may
sometimes be necessary to search for the optimum, including the extraction system,
when maintaining the tune of the phase slits. Changes in the injection line have
been known to change the phase cuts, as well as the extraction. The fluctuations
had apparently begun to settle down at the end of the stability measurement. If this
is true, the amount of retuning should decrease as the temperature stabilizes, and
the cyclotron settles in to new operating conditions. External phase measurements
could be used by the operators as feedback when making adjustments in the RF

frequency and voltage, as well as the magnetic field.

4.5 CONTROLLING PHASE CUTS WITH B(r)

Equation 1.7, together with Equation 1.6, implies that the magnetic field can be
used to improve the phase cuts. It is difficult though to change the phase curve
without adversely affecting the orbits. The equation depends on the integral of the

phase curve, so it takes a significant change to make a difference at the phase slits.

Figure 4.11(a) shows three phase curves which were developed with the program
MONSTER. The solid curve is from the normal operation of the K1200 cyclotron.
The location of the phase slits is ~0.03 E/Emaz. At this location, the dashed curves

accumulate lower and higher values of | f sin(¢)dE|. These curves were tested in the

sin(¢)

0.6

0.4

0.2

0.0

-0.2

~04

—O.6

—0.8

0.0

 

 

 

I I I

 

 

 

0.2

40 MeV/A “’Arw’
I I I I

0.4 0.
E/Emex

6 0.8

(a) 3 sin(¢) Curves Normal is Solid.

low rsin¢dE

 

buncher on

 

| I

—4»—

 

I— —d
dpfl ‘
M

.4

77 J1 I

>—

 

J A‘L

-4

d

_4

 

 

300 860 400 450 600 350 400 450 600 350 400 450

slit A only

slit 8 only

both slits

500

(c) Phase Cuts with Lower |fsin(¢)dE|.

110

buncher on

no buncher

40 MeV/A ‘°Ar’°
I I I 1

° norma f5in¢dE
I

 

T

—1»—

-0-

I

T

I"

—<

.4

l

 

 

 

 

 

 

260 300 360
slit A only

260 300 360
slit 8 only

260

both sli

300 360
ts

(b) Phase Cuts with Normal sin(¢) Curve.

buncher on

no buncher

Figure 4.11: Controlling Phase Cuts with Bz(r).
Phase cuts were made with the magnetic field set to produce three different phase
curves. The width of the phase cuts should be proportional to | f sin(¢)dE I, Equation 1.7.
Figure 4.11(a) show the three phase curves.
The smaller dashes are for the low case, and the larger dashes for the high case.
Figures 4.11(b) 81. Figure 4.11(d) show that this equation is true. Figure 4.11(c) straddles
f sin(¢) = 0, so it is over twice as large as the normal case. The x-axis is channel number
measuring t — tap, so smaller channel numbers have a more positive phase.

40 MeV/A “Arm
1 I I I

high IsinquE
T JI I

 

T I

4

.1

4-1

.—

_

p—

—1

d

.1

 

 

III/III

 

5

 

 

 

300 350 400
slit A only

300 360 400
slit B only

300 360 400
both slits

(d) Phase Cuts with Higher | f sin(¢)dE|.

The phase slits are at 0.03 E/Emaz.

111

cyclotron. Each beam was successfully extracted without changing the extraction
settings from the normal case. The remaining graphs in Figure 4.11 present cuts
using the phase slits for each case. Both slits in the normal case, Figure 4.11(b),
leave four peaks in the beam. The phase slits can be adjusted to emphasize one of
these peaks, which can be further enhanced over the others by using the buncher.
The high case, Figure 4.11(d), works in a similar fashion, except each pin makes
five peaks, each of which is narrower than those in the normal case. (This is a
confirmation of Equation 1.7.) This produces a narrower main peak, but makes it
more difficult to eliminate the satellites. The low case, Figure 4.11(c), makes three
fatter peaks. The main peak encompasses the particles with maximum energy gain,
as well as particles on both sides of the peak energy gain, so it is much wider than

the other two cases.

This demonstrates one of the easier methods of obtaining relatively clean phase
cuts, so Figure 4.11(b) was recreated in the calculation shown in Figure 4.12. Here
the buncher was phased to one side of the acceptance window, then the phase slits
were tuned to remove the tail. Comparing the results to those of Figure 4.4, the
peak is wider, but the satellites are greatly reduced, making this a cleaner phase

cut.

The other easy method of tuning the phase slits is as follows. First, bunch the
beam for maximum current. This will place the bunched peak near the center of the
acceptance window, like in Figure 4.4. Then scan the transmitted current for each
pin individually. Place the pins for maximum transmission, then use the timing
detector to fine tune the cuts. This procedure works well for external detectors, and

produced the ~5° cuts in Figure 4.8.

The discrepancies between the phase slit calculations and measurements could

112

 

 

H
H
O

 
 
   
  

 

 

 

 

 

 

 

 

 
  
      

 

 

 

 

 

 

 

 

92311.; I I 1 311.1 ' ' I ' .
0.8,.Ninit= 209660 _ 0_8 tota1= 93937 _
Ntota1= 209660 If» 6.8806
\ 0.6—Nmax: 4370 \ 0.6— ._
01 m
I; 0 4 g 0 4
o 0
U 0.2— U 0.2»— -1
0 C I l l l l l 0 G In I l
°—40-35-30-25-20-15-10 -5 0 '-40-35-30-25-20-15-10 -5 0
phi [deg. RF] phi [deg. RF]
1.0 1.0
311.211.31'“ 311.1' ' ' 1'
0.8,.Ntotal= 62957 _ Ema total: 126668 _
Dslit: 0.0940 2 r = 6.9779
x 0.6— — \ 0.6—
m m
u u
g 0-4— — g 0.4—
o 0
U 0.2— — U 0.2~
0 0 l A; l l 0 0 1A 1 l I l
“-410-35-30-25-20-15-10 -5 0 '-410-35-30-25-20-15-10 -5 0
phi [deg. RF] phi [deg. RF]
1.0 1.0
SlIitsIA,IB, Is. 6 I I s11: E F I ' ' I
§ 0.3 total: 30554 _. 35 0.3,.Ntota1= 94460 _
E F" E rC= 7.0141
\~0.6— — \~0.6~ a
m 01
u u
5 0.4— — 5 0.4— —
o 0
U 0,2— - U 0.2—
0 0 l I .1; 0 C l l l l l
--40-35-30-25-20-15-10 -5 0 °-40-35-30-25—20-15-10 -5 0

 

 

 

 

 

 

phi [deg. RF] phi [deg. RF]
BEAM TIMING SPECTRA

$8$DKAO: [BAILEY . AXIAL .ALPHA. CENTREG] CRSOBlT2258L4 . DAT; 1
$8$DKAO: [BAILEY . AXIAL . ALPHA . CENTREG] CRSOBlT22 5C . DAT; 1

Figure 4.12: Calculation of Cuts Made with the Buncher Tuned to One Edge.

The normal case depicted in Figure 4.11(b) is reproduced by the calculation. This shows
that the calculations, while still pessimistic, successfully reproduce the beam conditions
at the slits.

113

have several simple causes. One would be that the sin(¢) curve in the calculation
achieves a greater | f sin(¢)dE| than inside the K1200 . This would give fewer, and
fatter, peaks in the measurements than in the calculations. At present, these mea-
surements are the closest we can come to measuring sin(¢) at this radius. (The
Smith—Garren technique, using the ‘phase slit probe’, which is also at 7.00 in, would
require very large frequency changes. Another possibility could be the small dif-
ferences in the measured and calculated central region acceptance. The calculation
has a 45° acceptance window, with small phase space losses, accepting 12% of the
injected beam. The measured acceptance is 10%, which means that the acceptance
window could be as narrow as 36°. This would also result in fewer peaks in the
measurements. It should also be remembered that the calculation used a uniform
100 7r mm-mrad initial ellipse. This is an assumption which affects beam spot size
and density. A smaller spot, or a spot whose center is denser will make sharper cuts

(thinner peaks) which are easier to remove.

CHAPTER 5

EXTRACTION AND PHASE CUTS

One of the purposes of using the phase slits was to achieve single turn extraction,
and if not, to improve extraction efficiency. There are many benefits of single turn
extraction, clean extraction, narrow spreads in time and energy, etc. Improving the
extraction efficiency would still have some benefits: it would reduce the radioactive
activation of cyclotron parts, and would increase the total extracted current for
beams which are limited by beam current on the electrostatic deflector. This chapter
presents the progress made towards these goals, and suggests methods of achieving

them.

5.1 SINGLE TURN EXTRACTION

A simple method of estimating if single turn extraction is possible, is to esti-
mate the spread in 03 which will fill the useable portion of the extraction aperture.
With the accelerating frequency and voltage, and the magnetic field tuned so that
f sin(¢)dE = 0, the energy of the particles follows a cosine curve in 03. If the turns
are seperated in energy, then it is possible to seperate them in radius. Allow for the
thickness of the septum, and the physical spot size of the beam by assuming that

1303, the spread in (,0 for one turn, occupies no more than 1/ 4th the energy spacing

114

115

between turns. Then,

|¢| < (%); ~1.4° (5.1)

would be the maximum allowable value of (b. This back of the envelope calculation
restricts the total spread in phase to 3° , at the base, before single turn extraction

is possible. The best cut to date, Figure 4.9, is 6° at the base.

One major restriction remains to be discussed. When Welton first talked about
longitudinal space charge[61], he remarked that the leading particles would be ac-
celerated, and the trailing particles decelerated by the electrical repulsion between
them. He also suggested that this could be corrected by detuning the RF. Formulas
for working with longitudinal space charge within a cyclotron, were first derived and
experimentally demonstrated by Gordon at MSU[62]. It does increase the energy
spread of the beam but in a non-linear fashion. The particles rotate in a ‘vortex’
motion. Gordon demonstrated on the K50, that this energy spread can be partially
cancelled out by shifting the RF frequency. Adam showed that with sufficient current
that the vortex motion will develop into a spiral instability[63]. Joho demonstrated
that accelerating cavities operated at high multiples of the accelerating frequency
can correct part of the nonlinear spreading[4l]. The K1200 is not equipped to do
the latter, but can correct the linear portion. This will still leave a spreading in the
energy, and thereby the radius, of the beam at extraction. The net effect of this

spreading will be an upper limit on the single turn extracted current, at which the

phase cut will need to be narrower than those above.

Further progress towards single turn extraction will be aided by extraction orbit
studies which will refine the estimates above. These studies should include space
charge calculations. Central region cuts, and magnetic field profiles could then be

designed so that the phase slits produce the necessary clean phase cuts. It may also

116

be necessary to restrict the initial emittance. This should also be learned in the

extraction studies.

5.2 EXTRACTION MEASUREMENTS

Clearly we have not yet achieved a phase cut where single turn extraction is possible.
The best cut, in Figure 4.9, has a base of 6° and a few particles are even further from
the peak. If the extraction were tuned properly, it should be possible to improve

the extraction efficiency by using this peak.

The first extraction measurement using the slits seemed to confirm this, with
the extraction efficiency improving from 45% to 65%, when comparing the current
measured on the 1 finger probe in the A2 drive at 39.5 in with that measured
by the same probe in the extraction channel. Outside the cyclotron, on the A-
012 Faraday cup, the efficiency improved from 35% to 55%. For a beam that is
limited by losses on the deflector[64], an improvement in the extraction efficiency
can increase the total current extracted. In the case of this extraction measurement,
assuming a 20% transmission through the phase slits, the extracted beam could
be increased by 240%, provided that the injected current could be increased by
780%. For experiments where high intensities are not needed, (most of the 47r
nuclear physics detectors,) using the slits will reduce the activation of the extraction

elements, (often the ‘hottest’ parts when the cyclotron is opened.)

This initial success was confused by the second extraction measurement. After
examining how various controls affected extraction, a very careful search found set-
tings where the uncut bunched beam had a 65% extraction comparing 39.5 in to
the extraction channel. Using the phase slits could not improve this efficiency. The

external efficiency, though, was only 35% in both cases. (The magnetic channels

117

80 MeV/u “Arm Extraction

 

l ' VT I 1 I . r ' I 1 I T I
Extraction Channel ¢-351n I—39.5in
_ uncut — 1.05 nA — 1.65 nA T

cut - 0.50 nA 0.80 nA

      
 

 

 

ounts scaled s.t. area oc current

A

0—70 —60 -5O -4O :30 —20 -10 O 10 20 30
90 [RF] (arb. zero)

Figure 5.1: Phase Spectra from the Extraction Measurement.

An extraction measurement was made where both the cut and uncut beams had ~65%
extraction efficiencies. The phase spectra of this measurement are displayed above, mea-
sured in the extraction channel, and at 35 in. The shaded peaks are with the phase slit
cuts. Amazingly, the uncut beam was bunched to 64° FWHM, thus it could be extracted
at an efficiency comparable to that of cut beams. The cut beam is 3.6° FWHM.

were left alone, and may not have been optimized.) The first measurement was with
40 MeV/u 4I’Arl‘”, and used the cut and uncut beams in Figure 4.9. The second
was on 80 MeV/u 40Arlzl', and is shown in Figure 5.1. This result contradicts the
idea that phase cuts can always improve the extraction efficiency. A closer look
though shows that the uncut beam was bunched to 64° FWHM. It was extracted
at a 65% efficiency because it was already very narrow in phase. 65% seems to be
the present limit. This could possibly be from transverse spot size. As with the
single turn extraction, improvements should come with smaller beam emittances,

and narrower phase cuts.

For practical purposes, when a beam is limited by losses on the deflectors, a
measurement of the extraction efficiency should be made. If the efficiency measured

with the A2 probe is significantly less than 65%, and the source can provide currents

118

that are an order of magnitude, or more, higher, then the phase slits should be used
to increase the total extracted current. Caution is advised when using the A5 probe
for the current measurements. It intercepts the extraction channel at a greater
radius, and the beam passes several extraction elements between the two probes.
Presuming that there is no calibration problem between the 1 finger probe, and the
A-012 Faraday cup, the beam will suffer losses after the A2 probe, some of which
may occur between the two probes. So the maximum extraction efficiency may be

lower on the A5 drive than on the A2 drive.

CHAPTER 6

SUMMARY, CONCLUSIONS, AND
RECOMMENDATIONS

Phase slits have been introduced into the K1200 cyclotron which are capable of pro-
ducing narrow peaks in time, F WHM of 3° to 5° RF, with a few particles from times
outside the peak which can always get past the slits. The processes by which these
phase slits cut the beam are clearly understood, with calculations that are capa-
ble of reproducing the details found in the measurements. These cuts are capable
of improving the extraction efficiency, and while not yet sufficient for single turn

extraction, the improvements outlined below should make this possible.

A detector has also been designed and deployed in the K1200 which is capable of
measuring the time spectra inside the cyclotron. It has a resolution of 200-300 ps.
200 ps is 2° RF at 27 MHz, our maximum operating frequency, and 300 ps is
2° RF at 18 MHz. This resolution will aid in obtaining the :tl° cuts necessary
for single turn extraction. While this detector measures only at extremely low
intensities, these measurements can still be used to measure the time cuts which
will be necessary for single turn extraction in preparation for when space charge is
introduced. This detector can also be used to measure time processes in the beam
as it is accelerated to different radii, as well as the sin(¢) curve inside the cyclotron.

It is limited, though, to the outer 8 in, and use with heavier ions.

119

120

Even though a cyclotron’s acceptance is defined mostly by apertures, and not
stability regions, the stability regions still define the shape of the optimum injected
ellipse. This study has found that matching the injected ellipse reduces the size
of the beam core as well as that of the beam halo. Furthermore, it reduces the
debunching of the beam, in time, incurred when traversing the yoke and the spiral
inflector, which increases the amount of current which can be bunched into the peak
selected by the phase slits. It will also minimize distortions produced in the vertical
phase space of the beam at injection, as well as minimize the correlations induced

by the inflector.

The focussing solenoid in the axial injection line is also of great importance
in injecting the beam. Its main function is to maximize the initial acceptance
of the spiral inflector. Without it, the calculations showed a possible reduction of
almost 50% in the injected current. Like matching the injected ellipses, the focussing
solenoid can be used to minimize the debunching in the yoke and the spiral inflector,
and the distortions in the injected vertical phase space. Also, it reduces the blow up
in the beam incurred as the injected beam crosses the non-adiabatic regions in the

yoke. Using the solenoid, though, exacts the price of a larger internal beam spot.

Together, focussing with the solenoid, and matching the injected beam will
greatly improve the cyclotron beam, improving the performance of the buncher
and the phase slits, as well as aiding in traversing resonances and extracting the
beam. Our present inability to do these things is a handicap which when overcome

will enhance the performance of the K1200 cyclotron.

The present work has shown that the most important improvement needed to
produce clean cuts, as well as narrower cuts, is a central region slit. The effectiveness

of the slits is presently hampered by the large number of turns needed for the

121

beam to clear the slits. Using a central region slit to introduce an initial out which
will produce separated turns at the phase slits will free the slits from the task of
minimizing the satellites, allowing them to be used in optimizing the phase cut. It
will also allow the use of the specially designed magnetic fields which enhance the

effectiveness of the phase slits.

Some effort should also be directed towards finding and producing an optimum
initial emittance for injection into the cyclotron. This study started with the beam
at the ECR, where it is extracted with a large emittance, 50-400 7r mm-mrad . It
next looked at the inflector which may accept as much as 170 r mm-mrad , but which
clearly accepts most of 100 7r mm-mrad . It followed the beam from the inflector,
through the central region, to the slits, which make cleaner cuts in time when cutting
smaller emittances. It then looked at the deflector, where the maximum radius gain
is .15 in. A 170 7r mm-mrad initial emittance will produce a .14 in diameter beam
spot. The reduction in size achieved by using superconducting magnets is also
reducing the optimum beam size at these critical points. Depending upon ones
needs, i.e. single turn extraction, much of the beam from the source may need to be
discarded. But this reduces the beam current. A reduced beam size during injection
will also eliminate the particles which suffered greater debunching in the yoke and
spiral inflector, effectively enhancing the performance of the buncher. All of this will
need to be quantified in order to optimize transmission when single turn extraction

is achieved.

[1]
[2]

[3]
[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]
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