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This is to certify that the
dissertation entitled

PHASE SPACE CHARATERIZATION OF AN INTERNAL ION
SOURCE FOR CYCLOTRONS

presented by

EDWARD RUSSELL FORRINGER

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Physics

 

 

 

 

MSU is an Affirmative Action/Equal Opportunity Institution

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PLACE IN RETURN Box to remove this checkout from your record.
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PHASE SPACE CHARACTERIZATION OF AN INTERNAL
ION SOURCE FOR CYCLOTRONS

By

Edward Russell Forringer

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

2004

ABSTRACT

PHASE SPACE CHARACTERIZATION OF AN INTERNAL ION SOURCE FOR
CYCLOTRONS

By

Edward Russell Forringer

Orbit tracking codes are used to predict the behavior of the beam in a cyclotron
before the cyclotron is constructed by tracking many orbits which collectively are
intended to represent the beam. Cyclotrons with internal ion sources (such as the
series of 250 MeV proton beam cancer therapy cyclotrons being manufactured by
ACCEL Instruments GmbH of Bergisch-Gladbach Germany) present difficulty for
these orbit tracking calculations in that there are several parameters which can be
adjusted in the calculation that have a large effect on the phase space characteristics
of the calculated beam (both the emittance of the beam and the shape of the beam in
phase space). The primary goals of the research presented in this dissertation then are
to experimentally measure the axial and radial emittance and luminosity of the beam
produced by a cold cathode PIG (Penning Ion Gage) internal ion source under dc
extraction and to develop a “recipe” for initial conditions of calculated orbits starting
from the ion source that match the experimentally measured beam.

The experimental results presented in this dissertation, to the best of our knowl-
edge, represent the first published emittance and luminosity measurement of a cold
cathode PIG internal ion source. By taking measurements in several different config-
urations, it was determined that the shape and size of the source aperture has a large
effect on the characteristics of the extracted beam. We were also able to observe that
increasing the plasma arc current in the ion source produces higher current and lumi-

nosity in the extracted beam. The maximum luminosity measured using a Chimney

with a 5.0 mm (0.196”) tall, 0.25 mm (0.010”) wide slit, was 7.1 01—71533. Two other
chimneys with larger apertures were measured at lower arc currents being limited by
the power handling capabilities of the Ion Source Test Stand.

The concepts of ‘plasma boundary’ (section 2.7.2) and ‘plasma temperature’ are
developed as a useful set of parameters for describing the initial conditions used in
orbit tracking. We observe that an approximately flat plasma boundary provides the
best match to the experimental beams emerging from the ‘slit’ style chimneys in our
study, while a concave plasma boundary (curving toward the source axis) provides
a better match for the beam that emerges from the ‘hole’ style chimney. In all
cases, the plasma temperature that provides the best match for experimental beams
is approximately 35,000 K (resulting in a central starting energy of 4.5 eV).

Using the methods presented in this dissertation, the orbit tracking code Z3CYCLONE
is able to predict the beam produced by a cold cathode PIG ion source with adequate

accuracy such that construction of actual cyclotrons can proceed with reasonably

prudent confidence that the cyclotron will perform as predicted.

 

ACKNOWLEDGEMENTS

First, to Dr. Henry Blosser, for suggesting a research topic, for Spending many
hours working on this project, for patiently waiting for me to finish, and for reading
and suggesting changes to many revisions of this dissertation, I owe a humble “thank
you.” Thanks also goes to my guidance committee members Drs. Richard York, Fe—
lix Marti, Terry Grimm, Wayne Repko, and Julius Kovacs. Thanks to the staff at
Harper Hospital (particularly Emanuel Blosser), and ACCEL Instruments who have
shared their expertice and equipment during the construction of the Ion Source Test
Stand and subsequent data collection. My deepest appreciation goes to the incred-
ible NSCL staff including Jim Wagner, Phil Fighter and all the machine shop staff
(particularly Jay Pline for work working with us during the holidays) for getting my
parts made on time so many times, Guenter Stork and Jim Moskalik for designing
many of those parts, Dave Sanderson and Andy Thulin for helping resolve vacuum
issues, Bob Welton for his expert welding, Mark Davis and Kelly Davidson for help
with data collection, and Barbara Pollack and the computer help—room staff for meet-
ing all of my computer related needs. Thanks to the authors and maintainers of the
Z3CY CLONE and associated codes (Dr. Morton Gordon, Dave Johnson, Dr. Marti,
Dr. Steve Snyder, Dr. Dmitry Gorelov and many others over the years). I owe a debt
to Malay Dey, who worked on the NSCL Ion Source Test Stand for a year while I was
away teaching, and while none of the data he collected ended up in this dissertation,
his help during that time is immeasurable. I need to thank my immediate family
(Stephanie, Josiah and Amara) for understanding and patience during this process,
my bosses and colleagues at LeTourneau University, and my parents and extended

family for their support and encouragement.

iv

 

CONTENTS

LIST OF TABLES vii
LIST OF FIGURES viii
1 Introduction 1
1.1 Cyclotron Ion Sources .......................... 1
1.2 Ion Source Figures of Merit: Phase Space, Emittance and Luminosity 5
1.3 Measuring Emittance. .......................... 11
1.4 Orbit Tracking .............................. 13
1.5 Overview of Following Chapters ..................... 15
2 Experimental Setup 17
2.1 The Source ................................ 17
2.2 The Magnet ................................ 20
2.2.1 Modeling the Magnet with TOSCA ............... 22
2.2.2 Modifications to the Magnet and the Final TOSCA Model . . 24
2.3 The Vacuum System .................. ' ......... 29
2.4 DC Extraction and Measurement .................... 29
2.4.1 Relating Radial Emittance Probe Parameters (s and w) to the
Position of the Probes ...................... 30
2.4.2 Relating Axial Emittance Probe Parameters (s and w) to the
Position of the Probes ...................... 35
2.5 Data Collection .............................. 36
2.6 The Orbit Tracking Code ......................... 39
2.7 Initial Conditions ............................. 41
2.7.1 Generating The Ensemble of Rays for Tracking ........ 42
2.7.2 Plasma Boundary Calculations ................. 45
2.7.3 Initial Energy ........................... 48
3 Results 55
3.1 Experimental Methods .......................... 55
3.1.1 Understanding the Graphs .................... 55
3.1.2 Repeatability of the Data .................... 57
3.1.3 Converting Raw Data into Radial Emittance Plots ...... 59
3.1.4 Converting Raw Data into Axial Emittance Plots ....... 64

 

B

3.2 Experimental Results ...........................
3.2.1 Slit Chimney Measurements ...................
3.2.2 Hole Source Measurements ....................
3.2.3 Effect of Arc Current .......................
3.2.4 Atomic Hydrogen Ions ......................
3.2.5 Data Summary ..........................

33 Matching Ensembles of Computed Orbits to the Experimental Beams
3.3.1 Slit Sources ............................
3.3.2 Hole Source ............................

Conclusion

Ion Source Test Stand Operation Manual

A.1 Safety Procedures .............................
A.1.1 High Voltage Operating Procedure ...............
A.1.2 Raising the Cap ..........................
A.1.3 Working on top of the Magnet ..................

A.2 Running a Beam .............................
A.2.1 Pump down the vacuum .....................
A.2.2 Probes, BCM and Software ...................
A.2.3 Steps for taking data once the source is on ............

A.3 Shutting Down ..............................

A.4 Maintenance Procedures .........................
A.4.1 Removing a source without venting the magnet ........
A.4.2 Replacing a cathode. .......................
A.4.3 Retuning the source without breaking vacuum ..........

A.5 Contacts ..................................

66
66
73
77
79
81
91
91
107

111

115
115
115
116
117
117
117
120
120

Approximating a Maxwell—Boltzmann Distribution of Starting En-

ergies

LIST OF REFERENCES

vi

125

127

LIST OF TABLES

3.1
3.2
3.3
3.4
8.1

Effect Of Chimney Slit Size on Emittance ................ 69
Effect Of Arc Current on Luminosity for the 0.010” Slit Chimney . . . 78
Effect of Arc Current on Luminosity for the 0.020” Slit Chimney . . . 78
Data Summary .............................. 81
Discrete Energies (in units of kT) to Represent a Maxwell-Boltzmann

Distribution ................................. 126

vii

LIST OF FIGURES

1.1 Geometry of a Penning Discharge as Used in Internal Ion Sources. . .

1.2 High Intensity Proton Ion Source. ................... 4
1.3 K500 Ion Source. ............................. 5
1.4 Ion Beams With Zero Phase Space Area. ................ 6
1.5 Focusing Ion Beams ............................ 7
1.6 Ion Beam With Non-Zero Phase Space Area .............. 7
1.7 Phase Space Plots of Ion Beams ..................... 8
1.8 Schematic of Slit and Wire Probes for Measuring Axial Emittance. . 12
1.9 Schematic of Slit and Wire Probes for Measuring Radial Emittance . 13
2.1 Ion Source Drawing. ........................... 18
2.2 A Properly Prepared Cathode ...................... 20
2.3 Ion Source Photograph 0 .......................... 21
2.4 Magnetic Field Map ........................... 23
2.5 TOSCA 3—d Model of Magnet ....................... 24
2.6 TOSCA Test Results ............................ 25
2.7 Ion Source Test Stand Magnetic Field. ................. 27
2.8 Magnetic Field Versus Magnet Current .................. 28
2.9 Photograph of High Voltage Dee in Magnet. .............. 31
2.10 Photograph of Open High Voltage Dee ................. 32
2.11 Drawing of High Voltage Dee. ...................... 33

2.12 Geometrical Description of Parameters s and w for Radial Measurements 34

viii

2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
2.23
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15

Geometrical Description of Parameters s and w for Axial Measurements 36
Probe Control Servo. ........................... 37
Inside the High Voltage Cage. ...................... 38
Starting Conditions for Several Rays .................. 43
Dee Voltage Fluctuations ......................... 44
Various Plasma Boundaries ....................... 46
Effect of Plasma Boundary on the Beam as it Leaves the Chimney . . 50
Effect of Plasma Boundary on Radial Slit and Wire Probe Crossing . 51
Effect of Plasma Boundary on Axial Slit and Wire Probe Crossing . . 52
Effect of Initial Energy on Radial Slit and Wire Probe Crossings . . . 53
Effect of Initial Energy on Axial Slit and Wire Probe Crossings . . . 54
Typical Radial and Axial Data Graphs ................. 56
Consecutive Runs in the Ion Source Test Stand ............ 58
Divergence of a Beam ........................... 60
Test Orbits for Calculating Divergence ................. 62
Converting Radial Slit and Wire Probe Position Data to 1' and a, . . 63
Converting Axial Slit and Wire Probe Position Data to z and 01,, . . . 65
Chimney Slits ............................... 67
Proton (50kV) Puller ........................... 68
Effect of Chimney Shape on Extracted Radial Emittance ....... 70
Effect of Chimney Shape on Extracted Axial Emittance ........ 71
Puller Markings .............................. 72
Hole Chimney ............................... 74
Deuteron (25kV) Puller .......................... 75
Emittance Plots with the Hole Chimney ................ 76
Atomic Hydrogen lens and Protons ................... 80

ix

3.16

3.17
3.18
3.19
3.20

3.21
3.22
3.23

3.24
3.25

3.26
3.27
3.28

3.29
3.30
3.31
3.32

3.33
3.34

3.35
B.1

Emittance Plots for 0.010” Slit Chimney with 50 mA Arc Current
(Shown previously in figures 3.9 and 3.10.) ............... 82

Emittance Plots for 0.010” Slit Chimney with 250 mA Arc Current . 83
Emittance Plots for 0.010” Slit Chimney with 350 mA Arc Current . 84
Emittance Plots for 0.010” Slit Chimney with 450 mA Arc Current . 85

Emittance Plots for 0.020” Slit Chimney with 50 mA Arc Current
(Shown previously in figures 3.9 and 3.10.) ............... 86

Emittance Plots for 0.020” Slit Chimney with 100 mA Arc Current . 87
Emittance Plots for 0.020” Slit Chimney with 150 mA Arc Current . 88

Emittance Plots for Hole Chimney with 50 mA Arc Current
(Shown previously in figures 3.14.) ................... 89

Emittance Plots for Hole Chimney with 250 mA Arc Current ..... 90

Plasma Boundary Shape (with an Image Electrode Voltage of 20 kV)
Which Best Matches the Beam Produced by the 0.010” Slit Chimney. 92

'Ifacked Orbits Which Best Match the 0.010” Slit Chimney ...... 93
Different Plasma Boundaries for the 0.010” Slit Chimney Match . . . 97

Plasma Boundary Shape (with an Image Electrode Voltage of 10 kV)
Which Best Matches the Beam Produced by the 0.020” Slit Chimney. 100

Tracked Orbits Which Best Match the 0.020” Slit Chimneys ..... 101
Beam Crossover Points .......................... 102
Different Plasma Temperatures for the 0.020” Slit Chimney Match . . 104

Axial Emittance Plot Comparing Calculations to Experiment for the
0.020” Slit Chimneys ........................... 105

z and pz in the Source-Puller Region .................. 106

Plasma Boundary Shape (with an Image Electrode Voltage of 0.6 kV)
Which Best Matches the Beam Produced by the 0.047” Hole Chimney. 109

Tracked Orbits Which Match the Hole Chimney ............ 110

Maxwell-Boltzmann Distribution of Particle Energies ......... 126

Chapter 1

Introduction

An important overall figure of merit for the ion source of a cyclotron is the phase
space density of the beam it produces. A cyclotron has a restricted phase space
acceptance for acceleration and extraction of an ion beam. Improvements in the
phase space density of the beam leaving the source are directly reflected in improved
phase space density of the extracted beam and higher total extracted beam current.
This dissertation describes measurements of the phase space density of the beam
extracted from a particular cold cathode ion source used in several cyclotrons. The
experimental measurements are also compared to predictions based on computational

ray tracking.

1.1 Cyclotron Ion Sources

The National Superconducting Cyclotron Laboratory (N SCL) has, as a natural part of
its on going research and development of advanced cyclotrons, developed and refined
ion sources for use in its cyclotrons. Modern cyclotrons use several different types
of ion sources. Examples of external ion sources are Electron Cyclotron Resonance

(ECR) ion sources and multicusp ion sources; examples of internal ion sources are

cold cathode sources and hot filament sources.

ECR ion sources are typically used to produce high charge state heavy ions. ECR
ion sources are external to the cyclotron, and the low energy ion beam must be
transported and injected into the center of the cyclotron. The NSCL continues to
develop ECR sources for its K500 ® K1200 coupled cyclotrons [1] [2].

External multicusp ion sources have been used to produce H‘ ions for the CY-
CLONE 30 series of cyclotrons developed by Ion Beam Applications Gmbh of Louvain-
la-nueve, Belgum to produce a beam of negative ions. (Acceleration of negative hy-
drogen ions in these cyclotrons is advantageous in that extraction is straight forword

by means of stripping of the H ions in a thin carbon foil, leading to extraction
efficiencies close to 100% [3].)
Internal ion sources have the advantage of producing the ion at the center of the
cyclotron, thus requiring no low energy beam transport. The class of internal ion
sources studied in this dissertation uses a Penning Ion Gauge (PIG) Discharge [4]
to produce the ion beam. These sources have the basic geometry shown in figure
1.]. Electrons from the cathode are accelerated by the potential difference between
the cathodes and the hollow anode. The axial magnetic field constrains electrons
to move along the magnetic field lines preventing them from readily moving to the
anode. The electrons are then reflected by the opposite cathode and can make many
oscillations through the source raising the probability that they will ionize whatever
gas is present in the ion source. This discharge then produces a plasma from which

positive ions can be extracted by a “puller” electrode through an opening in the

anode. The complicated nature of this discharge is well expressed by Bennett [4]:

“Although a considerable amount of work has been carried out on
Penning discharges the theory is inadequate. In fact relatively little is

known of the mechanism occurring in the ion sources which we will discuss.

 

Hollow Anode

Cathodes /

  

Plasma

B Field

Figure 1.1: Geometry of a Penning Discharge as Used in Internal Ion Sources. (Images
in this dissertation are presented in color.)
The characteristics of the arc can vary widely and depend critically on the
geometry and conditions of operation. Such is the complexity of the many
processes occurring that reproduction of the same conditions even in the

same equipment can sometimes be difficult.”

Internal ion sources have evolved over time. In 1953 Livingston and Jones (LJ)
[5] reported on their experience with a filament source used for high intensity protons
(figure 1.2). Their cathode was a U-shaped tantalum filament, heated with about 400
amps of electric current. The are current (the total current measured between the
anode and cathode of the ion source) was between 2 and 6 amps. As seen in figure
1.2 a 0.2 in2 (129 n1m2) area vertical slit provided the path for ions to exit the source.
With this source Livingston and Jones were able to extract 150 mA using a puller
voltage of 12kV and a source-puller gap of about 0.13” (3.3 mm). [5]

In 1966, Mallory presented the first phase space density studies on an internal ion
source for cyclotrons [6]. The source he used in his studies was also a filament ion

source for proton production. However, Mallory’s source slit was 0.023 in2 (15 mm?)

3

FILAMENT SUPPORT

 

      

Accelerating

Slit: E m

 

0

SECTION A-A

 

 

 

 

J]:

 

Figure 1.2: High Intensity Proton Ion Source (Fig. 2 from Livingston and Jones [5])

i.e. about a factor of 10 smaller than the slit in the LJ source. Using an extraction
voltage of 30kV on the puller and with a source to puller gap varying between 0.2”
(5 mm) and 0.4” (10 mm) for various data sets, Mallory’s source produced proton
beams in the 10 mA range.

In 1983 a team from the NSCL reported on their success in using a Penning
Ion Gauge (PIG) ion source in the newly completed K500 superconducting cyclotron
(figure 1.3) [7]. This source was quite different from the LJ and Mallory sources in
that it used a cold cathode discharge. This K500 source was mainly intended to
produce beams of heavy ions such as Nitrogen, Oxygen, and Argon among others
with protons of only incidental interest. The K500 source, however, employed the
same basic Penning discharge geometry as the LJ and Mallory sources.

More recently, versions of the K500 PIG ion source have been developed for the
K100 neutron beam therapy cyclotron at Harper Hospital in Detroit Michigan [8]
(hereafter referred to as the “Harper Medical Cyclotron”) and for use in a series of 250

MeV cancer therapy cyclotrons being manufactured by ACCEL Instruments GmbH

 

{£3 Copper
E122 Tantalum

{3:3 Boron Nitride

/.
O

Median Plane

lew l ".

 

 

 

 

 

 

 

 

 

 

   

 

  

Anode End Pieces . l
, L High Voltage Rod
“— Cathod and Holder (not shown)

Figure 1.3: K500 Ion Source (Fig. 1 from Antaya [7])

of Bergisch-Gladl.)ach Germany. The first of the ACCEL cyclotrons [9] is now (July
2004) being installed at the Paul Scherrer Institute (PSI) in Villigen, Switzerland (the
PSI PROSCAN project [10]) and two more cyclotrons of this type are under contract.

The ion source used in the 250 MeV ACCEL cyclotrons is modeled very closely
after the source used in the Harper Medical Cyclotron except for the detail of being
optimized for protons rather than deuterons. A primary objective of this dissertation
is to make reliable measurements of the phase space density of the beam produced

by this type of ion source.

1.2 Ion Source Figures of Merit: Phase Space,
Emittance and Luminosity

For readers not familiar with the characteristics of phase space density measurements,
three beams of ions are shown in figure 1.4. The first beam (a) has all the ions moving
in the same direction, but they are spread out. The second beam (b) has all the ions
tightly bunched together, but they are moving in different directions. The last beam

(c) has all the ions moving in the same direction and tightly bunched together. The

 

(a) ‘b’

(c)

Figure 1.4: Ion Beams With Zero Phase Space Area.

last beam is preferred because it is tightly packed and, in the absence of any forces,
will stay that way. However, in some aspects these beams are all equally good. This is
because the first two beams (a and b) can be focused using magnetic or electrostatic
lenses into a tightly packed beam. Figure 1.5 shows a set of lenses for the first two
beams that will transform each into a tightly packed parallel beam.

There are some beams which cannot be focused into a tightly packed beam by
using lenses. Figure 1.6 shows such a beam. Any lens that will focus the three rays
that start out at the center will not focus the two rays that start out above and below.
Any lens that focuses the three rays that start out parallel will not focus the two rays
that start at an angle.

To understand the difference between beams that can be perfectly focused and
beams that cannot, it is helpful to graph the beam in canonical coordinates (“phase
space” [12, p335]) as in Fig 1.7. The horizontal axis gives the vertical displacements
of a particular ray at the location where the plot is made, and the vertical axis is
the 2 component of the particles momentum (p2). Figure 1.7 then shows the phase
space diagram of three previously discussed beams. The two beams (a and b) make

a line in phase space, meaning both have a zero phase space area. In contrast, beam

{—fW 3
Vi

(b) o - "——

v 1! 1r

 

 

l

0
1r

 

Figure 1 5 This figure shows how two beams which appear less than ideal can be

focused by electric or magnetic elements (here represented as “thin lenses ) into an
ideal beam.

 

K

L
'-

 

 

Figure 1 6 This beam, unlike the beams shown in figure 1.4 cannot be focused into
an ideal beam by any set of focusing elements.

 

 

 

(a) C p2 __

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9__.
(b) 9—? P2 o—?—-o——--
@_——..
z
9—.
(C) E? 97. i:
9*” I
z

 

 

Figure 1.7: Phase space plot of three “beams” of ions. The top two beams have a
zero phase space area. The third beam has a non-zero phase space area. Phase space
area, is a common measure of the quality of an ion beam.

(c) makes a diamond with a non-zero phase space area. Liouville’s Theorem [12, pp
419-421] requires the density of trajectories in a phase space volume to be constant
so the (a) and (b) distributions in Fig. 1.7 will have zero current and distributions of
type (c) are the ones of practical intrest.

The total volume that a beam covers in phase space (phase space volume), or
more importantly, the phase space density (beam current divided by phase space
volume) is a measure of the quality of a beam. (The basic character of orbits in a
cyclotron leads to cylindrical coordinates to describe the trajectories with the axial
(2,192) phase space describing the vertical area of the beam and the radial (r, p,)
phase space describing the horizontal area of the beam.)

An alternative convenient measure of the compactness of a beam is its “emittance
area” where emittance is defined as the product of beam width (usually expressed in
mm) and beam divergence (usually expressed in milliradians). An axial emittance
plot will then usually have 2 on the horizontal axis and 02 on the vertical axis. For a
beam of particles where p; for each ion is small compared with its total momentum
p, the angle 0; is approximately proportional to the axial momentum i.e:

_ -1 29. N 102
Ozz — tan (5) ~ g. (1.1)
Likewise, a radial emittance plot will have 7‘ on the horizontal axis and a, on the
vertical axis where:

11

p (1.2)

_ Pr
0 =tan 1(—)z
T p

The emittance (e) of a beam(usually expressed as mm-mrad) is the area that the
beam occupies in an emittance plot.

In most situations beams will have vaguely defined edges due to fluctuations in
parameters, non-linear effects, etc. so that the area required to contain 100% of the

beam may be several times larger than the area required to contain 80% or 90% of

9

the beam. To avoid this confusion, emittance is usually reported as the area that
contains 90% of the beam and this convention is adopted in the present study.
While phase Space volume is invariant per Liouville’s Theorem, emittance de-
creases when acceleration occurs, (since the vertical axis of the emittance plot has
been scaled by the momentum of the particle.) Per Gruber [20] emittance can be
normalized by multiplying by the relativistic factors [37. In this dissertation 6 will
represent the experimentally measured 90% emittance whereas 6N will give the nor-

malized value of the experimental 90% emittance i.e.:

6N = ,8’76 (1.3)

Normalized emittance like phase space volume, is invariant with respect to accelera-
tion of the beam.

The best beams will have small axial and radial emittance and a large number of
particles (measured by the electrical current of the beam, I ) This leads to luminosity

(L) as a figure of merit for an ion beam:

I

€r€z

L

 

(1.4)

For an accelerator with a fixed emittance aperture, the luminosity of the ion
source determines the maximum extracted beam current. For this reason, luminosity
is normally the most important figure of merit for an ion source intended for high
intensity cyclotrons. In order to calculate luminosity both radial and axial emittance
data for the same beam are needed. The NSCL ion source test stand however, can only
measure one of these at a time, so that two runs with the same ion source parameters
are required to determine the luminosity. (An apparatus to simultaneously measure

both radial and axial emittance would be much more complicated and costly.)

10

1.3 Measuring Emittance.

The standard method for measuring the emittance of a beam is to use a movable slit
and wire combination. This is the method used in the Mallory dissertation [6] and
the same method is used in the collection of data for this dissertation.

The ion source test stand has a nearly uniform magnetic field pointing in the z
direction (deviations from a flat field are discussed in section 2.2.2). Such a field
causes each ion to travel in a circle in the horizontal plane (7‘, 6) and provides little
focusing in the z direction i.e. the particles will move in a helical path.

Figure 1.8 shows the setup used for measuring 2 emittance. A movable horizontal
slit is placed in the beam path. Since the slit aperture is small (0.010” or 0.25 mm)
with respect to the size of the beam, it blocks the majority of the ions. The slit serves
as a position selector. All of the particles coming through the slit have started at the
vertical position determined by the slit position (2), but they are moving in different
directions ((12) and will diverge from each other.

The wire is placed downstream from the slit. It is scanned across the beam and
measures the current of the beam at each location. The position of the wire indicates
the angle ((12) at which the ions were moving when they went through the slit. To
obtain a complete data set, the slit position is varied and for each slit position the
wire makes one complete scan. By measuring the current hitting the wire at each
combination of slit and wire positions, we then determine the intensity of the beam
at every point on an emittance plot.

Figure 1.9 shows the setup used for measuring 7‘ emittance. Due to the general
radial focusing property of a nearly flat magnetic field, ions passing through the thin
slit converge 180 degrees downstream from the slit. If the wire probe was placed at
this position, it would not be useful in determining the angle the beam had when it

passed through the slit. In contrast, 90 degrees downstream from the slit, the position

11

fsource
a) O

 

 

   
  

beam ./ \.
7 ~wire
slit/
plan view
b) Source Blocked Beam
2
Beam After Slit
Beam Before

side view

Figure 1.8: Simplified schematic of slit and wire probes for measuring axial emittance.
The plan view (a) shows the relative location of the source, slit and wire. The side
view (b) shows the motion of the slit and wire with respect. to the beam. The diagram
does not show the effect of the electric field between the source and the puller on the
bean.

wire

 

l/FF a
after

blocked beam slit

Figure 1.9: Simplified schematic of slit and wire probes for measuring radial emit-
tance. Shown are the relative location of the source, slit and wire. (The diagram does
not include focusing effects of the electric field between the source and the puller.)

of the ions is determined by the angle (or) each had as it passed through the slit. By
placing the wire probe 90 degrees downstream from the slit probe, the radial position
of the beam as it crosses the wire probe is correlated with the angle it had when it

passed through the slit thus determining the divergence (spread in angles or).

1.4 Orbit Tracking

A cyclotron uses electric and magnetic fields to accelerate and direct an ion beam.
The force on a charged particle moving in an electric and magnetic field is given by

the Lorentz force:

F=q(E+axé) (1.5)

If the electric and magnetic fields in the cyclotron are known, the force on a

13

—o

particle and therefore the acceleration (a = f; for non-relativistic speeds) on that
particle can be calculated. For example, if constant acceleration over a small time

interval At is assumed:

an + At) = w:

v

+ c’?(t)At (1.6)

m + At) = m) + {7(t)At + Ei(t)(At)2 (1.7)

[\DIH

At any point in time, if the position and velocity of the ion and the electric and
magnetic field acting on the ion are known, its position and velocity a short time
later can be calculated. This process can be iterated many times to track particle
trajectories from the ion source all the way to extraction. The orbit tracking codes
used at the NSCL use fully relativistic equations of motion and a fourth-order Runge-
Kutta numerical integration method rather than the simple constant acceleration
approximation shown above (equations 1.6 and 1.7). (The numerical errors in fourth
order Runge-Kutta calculations are of the order (At)5 compaired to (At)2 for constant
acceleration.)

Orbit tracking is an important part of the process of designing cyclotrons. With
an internal ion source, it is clear that all the ions that are being accelerated start in
the slit of the ion source. What is not clear is the starting energy the ions have in
the plasma and what direction the ions will move when they leave the source.

As Schubert points out in his doctoral dissertation [11], the direction with which
the ions leave the ion source is strongly dependent on the details of the electric field
near the ion source slit. The shape of the zero volt contour that crosses the slit
(usually called the plasma boundary) is not known a priori and must be determined
experimentally. Also the initial energy of the ions as they leave the source is not
known.

Schubert attempted to determine these initial conditions by comparing computa-

14

tional orbit tracking to orbit paths observed experimentally in the Harper Medical
Cyclotron. (He did these calculations and measurements with a radio frequency (rf)
extraction voltage pulling the ions out of the ion source as happens in a real cy-
clotron versus the dc extraction voltage used in the present study.) Schubert found
combinations of starting energy, starting rf phase, and plasma boundary shape which
allowed his computed orbits to approximately match “foil burns” taken on the first
four orbits in the Harper cyclotron. These solutions were however not unique i.e., it
was possible to compensate for a change in the plasma boundary shape, by choosing
different starting energies or starting rf phase (Schubert dissertation p37).

By using dc extraction in the ion source test stand, starting time is removed as
a relevant variable. By comparing computed orbits to the measurements of the dc
behavior, it is then possible to determine a shape of the plasma boundary and starting
energy which matches the experimentally observed trajectories of the ions leaving the

SOHICB.

1.5 Overview of Following Chapters

Chapter 2 describes the construction and operation of the ion source test stand that
was built for the research described in this dissertation. The magnet, the vacuum sys-
tem, the high voltage system, the probes, and the electronics used for data collection
are described. A description of the cold cathode ion source used in these studies is
given along with a description of the computer codes used for the comparison between
experimentally measured results and orbit tracking results.

Chapter 3 presents results of experimental measurement of the phase space oc-
cupied by the beam from the cold cathode ion source in several configurations in
each case including comparisons with orbit tracking predictions. The results include

different chimney slit shapes and different source are currents. This information then

15

provides a basis for fixing design features of a new cyclotron so that beam trajectories
match the caracteristics of the beam from the ion source.

Chapter 4 summarizes the conclusions reached in this study.

16

Chapter 2

Experimental Setup

2. 1 The Source

The ion source used in the present study is a cold cathode PIG ion source. The source
is nearly identical to the source used in Harper Hospital’s K100 neutron therapy
cyclotron in Detroit, Michigan (Harper Medical Cyclotron). (Specifically, the PIG
source used in taking the data herein presented was designed for use in the 250 MeV
proton medical cyclotron being built by the company ACCEL Gmbh for for use in the
PROSCAN project of the Paul Scherrer Institute (PSI) in Villigen, Switzerland; data
taking took place at the NSCL source testing facility.) Figure 2.1 shows a crossection
view of the cathode—anode region of the source.

Several things are required for the source to operate correctly:

0 There must be a magnetic field that is parallel to the chimney. Sources like the
one used in these studies have been used in magnetic fields as high as 4.5 Tesla
in the Harper Medical Cyclotron (and as low as 0.5 Tesla during low magnetic

field tests in the NSCL ion source test stand).

0 The source requires a steady flow of gas into the anode-cathode area. For

17

 

 

Insulator - Boron Nltrlde

Cooling Water Passage
f

 

 

Anode Base — Copper

 

\ Chimney - Molybdenum

I//Anode - Copper
‘ Cathode-Tantalum

_-Threaded Bod - Molybdenum

 

 

 

 

\ Button - Copper

 

 

Ill/Ill, V/l/I

Gas Inlet

 

 

‘Cethode Rod ~ Copper

 

 

ngh Vacuum Region

 

 

 

 

 

 

 

Cooling Water Inlet

Figure 2.1: CAD (Computer Aided Design) drawing of the cathode-anode region of
the ion source used for this study. (The cathode is off center corresponding to the
position needed in the real cyclotron , whereas the chimney is on-center to match the
position needed in the source teststand.)

18

the present study both hydrogen and deuterium gas were used. The gas was
supplied to the source by a Sierra Instruments Series 810 Mass-Trak Flow Con-
troller. Gas flow rates of 1.5 to 6.0 cubic centimeters (STP) per minute have

been used at various times.

0 There must be sufficient vacuum between the cathode rod and the outer shell
of the source. The boron-nitride insulator, which is a tight fit, separates the
high vacuum region behind the insulator (on the order of 10”5 Torr), from the

lower vacuum region in the chimney and between the anodes and cathodes.

0 There must be a sufficient potential difference between the anode and cathode to
cause the are to strike. For this source a Glassman High Voltage KL series high
voltage supply rated at 3kV and 1A provided the necessary potential. When
the plasma is established, the power supply shifts to current limited operation
and the potential between the anode and cathode drops to the value required
to sustain this current. The cathode anode gap was between 0.075” (1.9 mm)

and 0.150” (3.8 mm) , and is not a critical parameter for the source’s operation.

0 The cathode surface must be prepared to facilitate the striking of the arc. The
first step in preparing the cathodes was to sand them with 100 grit sand paper
until the surface layer was removed and there was a uniformly rough surface.
In the early studies the cathodes were then scratched with the end of a flat
head screwdriver to further facilitate striking of the arc.1 The result is shown

in figure 2.2.

Figure 2.3 is a photograph of the lower half of the ion source. Water cooling for the

cathode rod and the anode base are essential (some copper parts were melted when

 

1In later runs this was found to be unimportant and was omitted.

19

Cathode
. 'r

     
  
     

a

ode Base

 

Figure 2.2: The anode has been removed from the end of the ion source to show
the cathode. This cathode has been prepared by sanding the surface with 100 grit

sandpaper and scratching the cathode with a. screw driver.

the ion source was run without proper cooling). Further instructions on running this

source in the ion source test stand are found in appendix A.

2.2 The Magnet

The magnet which was used for the ion source test stand was originally (circa 1967)
a bending magnet in the beam line at the NSCL. Since being taken out of service as
a bending magnet it has been the starting point for several cyclotron design studies

[11]. The magnet is a room temperature electro—magnet with a pole radius of 13.875”

20

_ Chimne if};

. '~
4" -.

lA'RJd‘é Bas

 

‘ (a.

Vacuum Lock ‘ ~-

r‘
. u

Vacuum Port
Anode Water
Cooling

Gas Su . ol

High Voltage
Input

 

" athode Water
Cooling

Figure 2.3: A photograph of the lower ion source half. (The upper half is a mirror
image of the lower but without a gas inlet.)

21

(.352 m). This magnet was modified (circa 1996) for use as a cyclotron (the “High
Intensity Test Cyclotron”) including installation of a sectored pole tip with four hills,
four valleys, and holes in the valleys for dee stems. A coil current of 100 A producing
a central magnetic field of approximately 10 kilogauss was normally used for the ion

source measurements described in this dissertation.

2.2.1 Modeling the Magnet with TOSCA

During the design of the High Intensity Test Cyclotron, the magnet was mapped in
preparation for modifications suitable for a fixed energy cyclotron. Fieldmaps were
taken at 51 A, 101 A, and 152 A. Figure 2.4 shows a map of the magnetic field at the
101 amp current setting. After these fieldmaps were taken, the magnet was modified
for use as the Ion Source Test Stand; these modifications changed the magnetic field
as will be shown in section 2.2.2.

After the magnet had been mapped, it was modeled with the three dimensional
relaxation code TOSCA [19]. (TOSCA is part of the Opera 3-d software package
produced by Vector Fields Inc.) TOSCA is used for calculating electric and magnetic
fields in non-linear materials. Since the magnet has three symmetry planes, only one
eighth of the magnet needed to be modeled. The shape of the steel (Figure 2.5) and
coils was entered into TOSCA along with a B-H curve for standard steel. Differences
between measured and calculated magnetic fields are shown in figure 2.6 and are gen-
erally smaller than 3%. These differences are believed to be due to the unavailability
of a precise B-H curve for the steel in the magnet and are inconsequential relative to
the goals of this dissertation. The TOSCA results were especially accurate for the

101 amp case.

22

l

 

y (inches)

._ 7%
_1:: y

-15 l I I
— 15 - 10 -5 O 5 10 15
x finches)

 

 

 

Figure 2.4: Shown is a measured magnetic field of the “High Intensity Test Cyclotron”
version of the magnet i.e. before the “Ion Source Test Stand” modifications were
made. The coil current for this measurement was 101 A. Magnetic field contours 3,

5, 7, 9, 11 and 13 kG from the outside working in; the maximum field being 13.6 kG.

 

Figure 2.5: This figure shows a three dimensional model of the magnet steel shape
used in TOSCA to calculate the fields of the ion source test stand magnet. Due to
the symmetry, only % of the magnet needed to be modeled.

2.2.2 Modifications to the Magnet and the Final TOSCA
Model
Since the original field mapping and modeling of the High Intensity Test Cyclotron

version of the magnet, changes have been made to the magnet to match the needs of

using it as an ion source test stand. These changes involved:

0 Removing spacers between the pole tips and the upper and lower yokes so that
the pole tips would be in direct contact with the magnet yoke which increased
the pole tip hill-hill gap from 1.5” (3.8 cm) to 2.25” (5.7 cm) without changing

the exterior dimensions of the poles.

o Enlarging the hole through the center of the magnet to 1.375” (3.49 cm) to fit

the ion source.

0 Drilling and tapping various holes to allow vacuum feed-through fittings to be

24

 

 

 

 

 

 

 

 

 

 

 

 

 

*7- l 1 l 1 1 l 1
‘8 0.$4+~¢++¢¢33+4+++++++++++++++++++++++4++4++++++4+++
16 ~ ~40 + ”
Lao §
14 - . " f
“O
12 q a- ’ ”
a) N ‘0‘ I”; + ’-
m 8 d 1% ++ f
6‘ cfia¢°¢¢°”“&\“*¢6690~&#4‘¢””5”m“"wr f+ _
4 " °”%”1- -
6°“
2 d P
0 l I T l l T
0 2 4 8 1o 12 14 115
R finches)
14 l 1 1 1 1 1 1
"‘3nannn-nggrv+**+****’**"* ‘ *4”*+’”"*§
“c 3'
12 ~ a. + "
10 « f” I 5
ac
b) 8 ‘ L? + h
N “0
a: L39 ”
6‘ “egmkkmaumumwum + b
r
.. ‘ W '-
4 w “0% ”iv
‘34:; J» ’
2 " At”;
0 T I I I I T I
R finches)
8 1 L L l 1 1 1
{Wt-W ‘ gig-0;;;;,“,;;,'. ,‘,~ '-----~_r++4;_
6 fl — b
c) 54_ r
2 a f
L
h
0 1 l l l ' l I

8
'R finches)

Figure 2.6: The measured magnetic field (x) of the High Intensity Test Cyclotron
magnet, and the calculated magnetic field (+) from TOSCA along two azimuths,one
along a hill and another along a valley, for coil currents of (a) 152 amps, (b) 101
amps, and (c) 51 amps.

25

bolted to the pole tips and yoke, etc.

o Modifying the coils by removing the central 4 pancakes of the original 16 double
pancakes, in order to make more room between the coils (leaving 12 x 24 = 228

turns in the upper and lower coils combined).

In a cyclotron the beam makes many hundreds of turns in the magnet and a very
precise knowledge of the magnetic field is necessary. In contrast, the beam travels
through less than one turn in the Ion Source Test Stand, so a precise map of the
magnetic field is not critical. Because TOSCA had proved reliable for predicting
magnetic fields in our magnet to within a few percent, we decided not to re—map
the magnetic field after the above modifications were made. Instead, the appropriate
changes were made to the TOSCA model, and new calculations were run. The result
was a calculated magnetic field that should accurately reflect the magnetic field in
the ion source test stand to within 1 or 2 %, an accuracy which is quite sufficient for
the goals of this dissertation study.

In his 1966 dissertation Mallory went to considerable lengths (a series of 15 ma-
chining operations on the pole tips of his magnet) to ensure that the magnetic field
in his test stand was uniform. This was done to facilitate radial emittance calcula-
tions. Similar efforts were not taken for the ion source test stand used in the present
study. Calculations showed that radial emittance of the beam could be accurately
calculated even in the presence of small deviations from a flat field. Figure 2.7 is the
magnetic field in the magnet as calculated by TOSCA. The field through which the
beam passes varies by as much as five percent.

Finally, the magnetic field of the magnet was measured with a calibrated Hall
effect probe. This was done to verify the absolute value of the magnetic field in the
magnet. Figure 2.8 shows the location where the magnetic field was measured and a

graph of field versus magnet current.

26

 

&

 

 

g
\L

 

 

/_

 

 

 

-—<

1
(24

l
N

1
04
[\JA
C»!

Figure 2.7: The magnetic field of the ion source test stand. The axes are labeled in
inches. The top figure shows the magnetic field of the whole magnet. The effects of
the hills and valleys are clearly visible. The contours are in 2 kGauss intervals (3,
5, 7, and 9 kG). The bottom figure shows just the central region. The contours are
in 100 Gauss intervals (9.0, 9.1, 9.2, 9.3, 9.4, 9.5, and 9.6 kG),and represent a. 1%
change in the magnetic field. A typical orbit is shown on both graphs. The magnetic
field through which typical orbits travel varies by approximately 5%.

Slit Probe

 

 

Magnetic Field (1(6)
6
l
I

 

 

 

l ‘17 I I
60 80 100 120 140
Current (A)

Figure 2.8: The photo shows the location where the magnetic field was measured.
This location is the same distance from the center of the magnet as much of the
beam’s path. The magnetic field is graphed as a function of coil current in the
magnet. A coil current of 100 amperes was used for the measurements presented in
this dissertation.

28

2.3 The Vacuum System

The limiting factor for the required vacuum in the ion source test stand was the ion
source itself. Experience with similar ion sources in the Harper Medical Cyclotron
showed that for the ion sources to run consistently, there needs to be a base vacuum
(with the ion source gas supply turned off) in the 10"6 Torr range.

The vacuum system for the ion source test stand makes use of the pole tips as
the primary vacuum wall. Six “plugs” were manufactured to seal six of the eight dee
stem holes. Two stainless steel tubes were inserted into the remaining two dee stem
holes which served as the mounts for two turbo pumps. Various turbo pumps ranging
from 600 to 800 liters/ second were used, and these turbo-pumps were backed by a
mechanical roughing pump.

Two thermo-couple gauges and one ion gauge were used to monitor the vacuum.
The thermo—couple gauges were capable of measuring pressures of 1 to 1000 mTorr.
The ion gauge had pressure scales of 10”, 10"”, 10‘s, 10‘7, and 10‘8 Torr.

The best vacuum achieved in the ion source test stand (with source gas supply
turned off) was 8 x 10‘7 Torr. With a gas flow rate of 2.5 cc/ min of hydrogen, the

pressure in the main vacuum chamber is around 4 x 10“5 Torr.

2.4 DC Extraction and Measurement

High voltage is supplied to the dee by a Spellman High Voltage power supply which
is rated at 100 kV and 2 mA. Figures 2.9, 2.10, 2.11 and 2.12 show the high voltage
dee. The puller provides the electric field that extracts the beam from the ion source.
The part of the beam that hits the slit probe or the beam shield is blocked. The
part of the beam that passes through the 0.010” (.25 mm) slit continues in its orbit

around to the wireprobe.

29

Three currents are of interest. The total current drawn from the dee power supply
(as read from the front panel of the power supply) tells us the total beam that is being
extracted from the ion source including beam that is blocked by the puller (plus a
possible “dark current” emitted from the surface of the rice). The second current is
the so called “slit current.” This current is the total current that hits the slit probe
and the beam shield. Except for the small portion of the beam that passes through
the slit, this current represents the total beam that passes through the puller. The
third current is the current hitting the wire. This current is related to the phase space
density of the beam at the location in phase space determined by the location of the
slit and the wire.

The two parameters 3 and w are also recorded. These parameters are related
to the position of the two probes as shown in figure 2.12. Sections 2.4.1 and 2.4.2

describe how 3 and w relate to the actual positions of the slit and wire in the magnet.

2.4.1 Relating Radial Emittance Probe Parameters (s and

w) to the Position of the Probes

In order for the current measured on the wire to be meaningful, the locations of the
slit and wire must be known. The ion source test stand does not simply record the a:
and y coordinates of the slit and the wire. Instead, it records two parameters .9 and
112, which specify the location of the slit and wire probes in their respective tracks
(figure 2.12).

The coordinate system for the ion source test stand is defined such that the center
of the magnet is at (0,0). The center of the chimney is also located at this point (0,
0). The slit probe travels on a line that is parallel to the y-axis such that the slit

stays 0.247” (6.27 mm) to the right of the origin, i.e.

30

High Voltage Rod \
. , m

Probe Drive Rods

“f @N
—\/r \

 

Figure 2.9: The high voltage dee is supported by three aluminum support legs which
each are supported by insulators. The probe drive rods are also insulating. The high
voltage rod contains all the electrical and water cooling lines. It passes through a
feed-through insulator into the high voltage cage on the back of the magnet.

31

 

  

Water Cooled sm Probe

/

'3 .

my .

- .mp1; .r

Figure 2.10: Visible are the slit and wire probes used for radial profile measurements
along with water cooling lines. The beam shield prevents any beam from hitting the
water cooling lines or passing in front of the slit probe and hitting the wire.

32

 

 

 

 

 

 

 

 

 

 

 

Figure 2.11: Drawing of High Voltage Dee.

33

   
 

wire Probe

@
.\

Figure 2.12: A CAD drawing of the central part of the ion source test stand. Visible
are the chimney, puller and the slit and wire probes. Parameters s and w are recorded
along with the current on the slit probe and the current on the wire for each data
point. Parameter s is defined as the distance from the back edge of the puller to the
front tip of the slit probe. Parameter w is defined as the distance from the corner of
the puller to the front edge of the wire probe.

34

22.1.1 = 0.247” (2.1)

gs“, = —1.113” — s (2.2)

The wire probe travels such that the wire stays on the line yum-m = -1:u,,-Te +0650”.
When parameter w is equal to zero the wire is at (.7: =1.196” ,y =—0.626”). For other

values of w:

ywim = —-0.586” — wsin 45° (2.3)

mm". = 1.236” —l— 11) cos 45° (2.4)

2.4.2 Relating Axial Emittance Probe Parameters (s and w)

to the Position of the Probes

For the axial emittance experiments, the slit and wire probes were attached to an axle.
When the probe drive shaft moved in and out, the probe would rotate around the
axle moving the slit or wire up and down in 2 (figure 2.13). Parameters s and 11) were
recorded for each current measurement. These numbers represent the linear position
of the slit and wire probe drive shafts respectively. The probes have a maximum
angular displacement of 3 degrees. Using small angle approximations, the change in

z for the probes is calculated from the change in the probe drive position:

A
A2311: = BAS
Azwire = 22A?!) (2.5)

Where A and B are defined as shown in figure 2.13.

35

 

 

 

 

 

 

Figure 2.13: A CAD drawing of the z slit probe. The slit (not shown) is mounted
on the left side of the probe. As the probe drive shaft moves in and out, the probe
rotates on the axis (marked with an X). The ratio of the lever arms A and B is 65:1
for the slit probe and 5.321 for the wire probe. The recorded value 8 is the linear
position of the probe drive.

2.5 Data Collection

Data collection on the ion source test stand is computer controlled. The positions
of the probes are set with servo motors and read from a potentiometer (figure 2.14).
The current on the slit probe and the current on the wire are read by standard
NSCL beam current monitors “BCMs.” The BCMs have amplifiers and a one-board
computer that makes the current readings available over Ethernet.

The BCM must float at high voltage in order to read the currents on the slit and
wire. Power is provided to the BCM through an isolation transformer, and fiber optic
cables are used to connect the BCM to the labs local area network. All of the high
voltage components that are outside of the magnet are located in a high voltage cage
(figure 2.15). The cage is interlocked such that the high voltage power supply will
not turn on until the high voltage cage door is closed.

A program written by Mark Davis of the N SCL runs the data collection process.

The program (sequencerexe) takes an inputfile like the following.

MIN:2.2 MAX:3.2 SET:N1PRBW SETlePRBE READzN1BCMW READleBCME
NIPRBW:0.1300 N1PRBE:O.64OO MIN:10 MAX:10

N1PRBW:O.1300 NIPRBE:O.6500

36

 

Figure 2.14: Probe Control Servo.

N1PRBW:0.1300 N1PRBE:0.6600

NIPRBW:0.1300 N1PRBE:O.6700

The first line sets some global behavior for the data collection run. MIN and
MAX are the minimum and maximum time the program will wait between data
points. This time is to allow the probes to get to their new positions. SET tells
the program which variables it will be setting and READ tells the program which
variables it will be reading. In this case the position of the two probes NlPRBW
(the slit probe parameter s) and NlPRBE (the wire probe parameter w) are being
set and the two BCM channels NlBCMW (the slit current is) and NlBCME (the
wire current 2}“) are being read. Subsequent lines in the input file are “set” values of
parameters 3 and w for each measurement and (optionally) how long to wait before
moving the probe to the next setting. The output from sequencerexe appears as

follows:

0.131684377789497 0.646714597940445 0.000280803549685515 -3.04795241845568E-6
0.131684377789497 0.656622079014778 0.000280850820126943 -3.21202242048457E-6

0.131684377789497 0.666515201330185 0.000276029750239104 -6.82156206721629E-6

37

1‘?
\

 

 

 

Figure 2.15: A photograph of the high voltage cage. The isolation transformer pro-
vides A / C power to the components on the high voltage platform. The Beam Current
Monitor was custom built by the NSCL staff for our project. It amplifies and reads
the current on the slit and wire probes and makes the values available over the local
area network.

38

0. 131684377789497 0.676966148614883 0.000275840690301266 ~5.80432842980372E-6. . .

The four columns of numbers are the slit probe parameter s, the wire probe
parameter w, the current on the slit probe (is) and the current on the wire (iw)
respectively. The actual position of the probes (as measured by the potentiometer)
rather than the set values are recorded. The slit current is recorded in amps. The
wire current is recorded in hundredths of an amp. The wire current for the points
recorded above are in the noise (10“8 amp range). For a typical beam, peak wire
currents will reach as high as 10 microamps. A typical data run will have 1000 to

3000 data points.

2.6 The Orbit Tracking Code

The NSCL code Z3CYCLONE was designed for tracking orbits from the ion source
slit all the way to extraction in a cyclotron neglecting forces generated by other
particles i.e. a “single particle” calculation. Numerical maps of the electric field (in

a rectangular grid) and of the magnetic field (in a polar grid) are required as input.

From the Z3CYCLONE Instruction Manual Version 4.0:

The Z3CYCLON E program actually consists of three separate parts
which have been woven together so as to make possible the calculation of
an ion orbit starting from the source slit (or [spiral] inflector) all the way

out to the extraction system.

0 Part I tracks the ion from the [ion] source [or from the inflector] to
just beyond the puller, the integration is done in Cartesian coordi-

nates with time as the independent variable.

a Part II [tracking] continues [from Part I to] the edge of the electric

field or until the wanted turn number is reached. This part uses 6

39

as [the] independent variable and the integration is done in polar

coordinates.

0 Part II and Part III differ mainly in the way they treat the rf electric
field.

The default behavior of ZBCYCLON E is to use an electric field on the dees (and
puller electrodes) that alternates with a given rf frequency. Part I (and only Part I)
has an option to use a constant voltage electric field. This feature, along with the
ability to use a small time step make Part I uniquely useful for calculating the path
of the beam in the dc ion source test stand. Part I was modified in two ways for use
in the calculations presented here.

As section 2.7.2 will show, an electric field grid with small node spacing (0.00125”
or 0.032 mm in a: and y and 0.004” or 0.10 mm in z) is required to accurately model
the shape of the chimney slit. If this small spacing was used to calculate the electric
field for the entire ion source test stand (a region 2.5” x 2.5” x .75” or 63mm x 63mm
x 19mm) the electric field grid would have over 750 million nodes. To facilitate faster
relaxation times the electric field grid was therefore divided into a field with small
grid spacing covering the region between the chimney and the puller, and a second
electric field with coarser grid spacing covering the region inside the high voltage dee.
This allowed each field to have less than 20 million nodes resulting in much faster
electric field calculations. (Normally Part I only allows one electric field so the code
was modified to allow the use of the two electric fields.)

The code was also modified to output only the slit and wire crossings of each
calculated orbit (this behavior mirrors the experimental data collected by the ion
source test stand). In its original form, Part I saves the location of the ion at each
time step in the integration (time steps of 22 ns in the small field and 89 us in the

larger field were used) to a file. This file can then be used to plot the orbits. For some

40

calculations, over 500,000 orbits were tracked, each of which had several hundred time
steps. The output files produced by these runs would be too large to be useful (over
15 GB). (A version of Part I with the full orbit output was retained for use when

detailed knowledge of the calculated orbit was needed.)

2.7 Initial Conditions

Given a set of initial conditions (position and velocity), and the magnetic and electric
fields as a function of time, the orbit code Z3CYCLONE will calculate the position
and velocity of a charged particle at each subsequent time. While Z3CYCLONE has
proved to be a reliable orbit tracking program, orbit calculation is only as accurate as
the initial conditions it is given and the selection of accurate initial conditions can be
complicated in a cyclotron with an internal ion source. To obtain the initial conditions
used for the orbit calculations presented in this dissertation we have used a technique
taken from the doctoral dissertation [11] of J. R. Schubert “Extending the Feasibility
Boundary of the Isochronous Cyclotron.” Schubert’s work showed that changes as
small as several thousandths of an inch (hundredths of a mm) in the shape of the
plasma boundary (the surface with electric potential equal to that of the chimney
of the ion source) can have a large effect on beam trajectories under rf extraction.
Accurate ray tracking then requires accurate knowledge of the plasma boundary, the
initial direction of the ions as they exit the ion source, and the initial energy of the
ions.

An ion source is of course a multi—particle system of very large dimensionality
while Z3CYCLON E is a single particle code. “Plasma boundary,” “initial direction,”
and “initial energy” are then approximate concepts which we adjust and compare
with experiment in order to identify rules which will cause the orbit trajectories given

by Z3CYCLONE to concur with observed trajectories to the most accurate degree

41

achievable with single particle computations.

The interior of the ion source houses a hot plasma of high dimensionality whereas
the exterior is a high vacuum region where single particle calculations are known to
be accurate predictors of beam behavior. We therefore guess that the equipotential
surface which goes across the exit slit of the chimney (at the same electric potential as
the chimney) will be a likely place for a single particle calculation to begin. Schubert’s
work then introduced a fictitious central electode in the interior of the ion source
(called the “image electrode”) with an adjustable potential. Changing the potential
of this electrode provides a way of changing the shape of the equipotential surface
across the source exit opening (the assumed “plasma boundary”) from convex to flat
to concave. Searching on this parameter and on the initial energy then allows us to
achieve an optimized match between experimental beam properties and single particle

computations.

2.7 .1 Generating The Ensemble of Rays for Tracking

To approximate a real beam of particles with an orbit code, it is necessary to track
many rays. The tracked rays should represent the full range of reasonable orbits for
ions in the beam. As a starting point, a grid of “primary rays” are evenly spaced in
the source opening. For example, in the chimney with an opening 0.020” (0.50 mm)
wide and 0.196” (5.0 mm) tall we choose to have 403 primary rays with 13 evenly
spaced starting positions across the width of the opening and 31 starting positions
evenly spaced vertically in the opening. All primary rays are started on the plasma
boundary with an initial velocity perpendicular to the plasma boundary (figure 2.16).

For each primary ray, a collection of rays, each of which have a different initial
direction of motion, is tracked.

The starting angles in r and z are centered around the primary ray’s starting

42

 

 

 

//f/' l '/
0.01 -1 //{/’//fl- /
MI / / /
.1 "if; /
0.00 \\\\ ‘ / /
\\\.I\\‘- ________. ._._.——-—

 

—o.o1-i \\~ "
\

.10 .11 .1'2 .13

 

 

 

 

 

 

 

 

 

Figure 2.16: Shown are (left) 13 starting locations in the median plane and (right)
the top 6 out of the 31 vertical starting locations along the center of the slit and each
of these primary ray starts on the plasma boundary as shown. Each primary ray
starts with a velocity vector pointing perpendicular to the plasma boundary. (The
“v” shaped apparent double valued potential just above the highest ray is not allowed
outside of a conductor and is believed to be a plotting artifact - its effect is negligible.)

velocity and are evenly spaced with steps of A0 = fi x 120°, where N is the number
of different starting angles in the r or z direction. If we use a total of 49 starting
directions (N2 = Nr = 7) we are then up to a total of 19,747 tracked orbits.

For each primary ray, and for each starting angle, rays are started with five
different starting energies representing an approximation of the expected Maxwell-
Boltzmann distribution of particle energies in a plasma at a given temperature. (See
appendix B for a full description of how the energies are chosen.) The temperature
of the plasma then is used in calculations is a parameter that is varied in order to
best match experimental results.

Finally, to include the effect of variations in the dee voltage, rays are tracked with
several different accelerating voltages ranging from the nominal accelerating voltage
plus or minus a small variation in Ndee equal steps. (It was observed on an oscilloscope

that the accelerating voltage fluctuated with time as seen in figure 2.17, namely a

steady 60 Hz fluctuation along with apparently random fluctuations.) For a 40 kV

43

nominal accelerating potential, we used a variation of i120 V.

 

(a) The average of 64 traces (A/C cou- (b) In “peak detect” mode at 100 V/div
pling) on a 5 V / div scale shows an approx— the oscilloscope shows several voltage
imately 7 V (about 0.04%) 60 Hz ripple in spikes above 200 V and many voltage
the dee voltage. spikes in the 30 to 40 V range. These

spikes represent about 0.2 % of the nomi-
nal dee voltage.

Figure 2.17: Dee Voltage Fluctuations (17 kV nominal dee voltage.)

If we choose Ndee = 4 then the total number of tracked orbits reaches 394,940. A
computer code was developed to calculate the correct initial conditions for each ray
and produce the input files used with ZSCY CLONE for the calculations presented in

this dissertation.

Positioning the Primary Rays

The plasma boundary is a three dimensional curved surface and we want to test the
hypothesis that each calculated ray starts on this surface. To accomplish this, each
ray is initially placed 0.025” (0.64 mm) outside of the chirrmey opening, well outside of
the plasma boundary. The starting point is moved back toward the chimney opening,
if the potential is still negative (outside the plasma boundary) the point is moved back

again. This repeats until the point is found to be greater than 0 V. An interpolation

44

is done between the last two points to find the exact location of the zero potential
contour. Figure 2.16 shows with + signs the starting positions calculated with this
technique.

The primary rays are started'with initial velocity perpendicular to the plasma
boundary i.e. in the direction of the local electric field. To calculate this direction,
Em, Ey, and EZ were determined from the six grid points closest to each starting
position and the angles ozz = arctan(\/——E%—E—3) and 01,. = arctan(%:1) were determined.
Figure 2.16 shows Z3CYCLONE tracked “orbits” with the electric and magnetic field

turned off so that the initial direction of motion can be seen.

2.7.2 Plasma Boundary Calculations

The calculations of the electric field between the source chimney and the dc “puller”
were made with the three dimensional Laplace equation solver Relax 3d [13]. To
get an accurate representation of the opening in the chimney it is important that the
width of the opening represent “many” gird points. The slit chimneys have slit widths
of 0.010” (0.25 mm) and 0.020” (0.51 mm), and the hole chimney has a 0.047” (1.19
mm) diameter opening. For these calculations, a grid size of 0.00125” (0.032 mm) in
the horizontal (:1: — y) plane and 0.004” (0.10 mm) in the vertical (z) coordinate was
used.

Of interest is the the 0 V equipotential surface in the chimney slit. As stated pre-
viously, for the calculations presented in this dissertation, all particles will be started
on this surface, and since this surface represents the edge of the ion plasma in the

7)

chimney, we refer to it as the “plasma boundary. As also previously discussed (in
section 1.4), Dr. Schubert introduced a cylindrical “image electrode” with an ar-
bitrary positive voltage on the axis of the chimney [11, p29]. This image electrode

does not represent any physical object, but is used to provide a constant electric field

45

 

 

 

 

 

 

 

 

 

 

 

 

o 1 0.1 1
g 0.0 ~ — g 0 0 a -
—0.1 1 —0.1 1
.05 .15 .25 .05 .15 .25
(inches) (inches)
(a) Concave Plasma Boundary. (b) Nearly Flat Plasma Bound-
Image Electrode: 4 kV ary. Image Electrode: 16 kV
0.1
g 0.0 ~ —
-O.1
.05 .15 .25
(inches)

(c) Convex Plasma Boundary.
Image Electrode: 32 kV

Figure 2.18: The graphs show electric equipotentials (-8, -16, and -24 kV) and the
chimney (0 V). Of interest is the shape of the zero volt contour as is crosses the
chimney slit (the assumed plasma boundary).

46

derivative at the plasma boundary. This is important for the electric field interpola-
tion done in Z3CYCLONE. Putting voltages of varying levels on the image electrode
has the additional effect of changing the shape of the plasma boundary thus exploring
the effect of possible different plasma pressures.

Figure 2.18 shows three different plasma boundaries which are the result of differ-
ent voltages for the image electrode. There is no a priori reason to choose one of these
conditions over the others, since all represent valid solutions to Laplace’s equation
with the known boundary conditions (the voltage of the image electrode, chimney
and puller).

The effect of the plasma boundary on the beam as it leaves the chimney is seen
in figure 2.19. Lower image electrode voltages produce a concave plasma boundary
which produces a focusing electric field. Looking carefully at figure 2.19a we see
that ions which start away from the center of the chimney slit cross over the center
of the beam and thereafter diverge in much the same fashion as the convex plasma
boundary (produced by higher image electrode voltages) which produces a defocussing
electric field from the beginning as seen in figure 2.19c. Intermediate image electrode
choices produce a flat plasma boundary as seen in figure 2.19b. Since any of these
beam profiles can reasonably be expected from the chimney-puller geometry, only an
experiment can determine which best corresponds to the actual beam.

Changes in the shape of the plasma boundary of course also change the locations
that the tracked rays cross the slit and wire probes in the ion source test stand for both
radial and axial measurements. We therefore use this to directly compare calculated
orbits with the experimental (3,112) data.

For the orbit tracking calculations presented in figures 2.19 and 2.20, 32,643 rays
were traced for each plasma boundary. As noted previously, the rays started at 13

equally spaced positions horizontally across the opening of the source slit and 31

47

equally spaced positions vertically in the source slit. For each of these 403 starting
positions, 81 rays were traced with nine equally spaced starting angles in the horizon-
tal plane and nine equally spaced starting angles vertically with 3 eV as the starting
energy for each ray. Unlike the final calculations presented in Chapter 3, no spread in
starting energy or acceleration potential is used (since these spreads are not needed
to see the effect of plasma shape).

Figure 2.20 shows graphs of radial wire probe parameter w as a function of the
slit probe parameter s for six sets of rays. The shape of the beam in these radial plots
changes when different image electrode potentials are used in the calculation. Simi-
larly, figure 2.21 shows axial (s, w) graphs for the same sequence of image electrode

potentials used in figure 2.20.

2.7.3 Initial Energy

In section 2.7.2 rays were started with different positions and different starting angles,
but all rays were started with 3 eV of initial kinetic energy. In this section we
investigate what happens to the beam when different starting energies are used in the
calculation. In Chapter 3, when comparing calculations to experimental data, rays
will be tracked with a range of energies with plasma temperature being an adjustable
parameter (as discussed in appendix B). In this section (2.7.3), to emphasize the
effect of starting energy on the calculations, only one starting energy is plotted at a
time.

Figure 2.22 shows radial wire probe crossing versus slit probe crossing (3,10) plots
for several different choices for the initial energy of the ions. Immediately we see
that increasing the starting energy has the effect of increasing the width of the beam
in the w coordinate. Figure 2.23 shows axial wire probe crossing versus slit probe

crossing (3,10) plots for several different choices for the initial energy of the ions. The

48

width of the beam in w and s is affected by the choice of initial energy. Thus when
compairing computed rays with various starting energies to experimental data, the
size of the beam in (3,10) plots will determine which starting energy best represents

the measured beam.

49

 

 

 

.1 .2 .3 . . .1 .2

(a) 4 kV Image Electrode: Concave (b) 16 kV Image Electrode: Nearly Flat
Plasma ' Plasma

 

 

.‘l .2 .3 .4 .5

(c) 32 kV Image Electrode: Convex
Plasma

Figure 2.19: Each orbit is started on the plasma boundary (zero equipotential surface)
with an initial energy of 3 eV. Without knowing the shape of the plasma boundary,
we do not know which of these beams will be produced by the ion source.

50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

s finches) I

(e) 24 kV Image Electrode

 

 

 

 

 

 

 

 

 

 

 

s finches) -

(f) 32 kV Image Electrode

l L L l l l 1 l
1.00 .1 J... a; . b 1.00 .1 '
.. .v“°\ A
a _ ‘1’ ~ 3
.c .c .
.g 0.99~ f” \ ~ g 0.994 r \
3 I“, 3
0.98 -‘ — 0.98 ..
0.97 1 1 1 1 0.97 1 1 1 1
.3 .4 . .6 .7 .3 .4 .5 .6 .7
s finches) s finches)
(a) 4 kV Image Electrode (b) 8 kV Image Electrode
l 1 L l I l 1 l
1.00 " 1.. 100 _,
13 13
0 Q)
.C .C
.LS’ 0.99 — — E 0.99 n
3 3
0.98 -‘ _ 0.98 a
0-97 1 1 M T 0.97 T r 1 1
.3 .4 . .7 .3 .4 . .6 .7
s finches) s finches)
(c) 12 kV Image Electrode (d) 16 kV Image Electrode
l L L l l 1 1 J
1.00 - ~ 1.00 -
1? 1?
O D
.C .C
”E, 0.99 .. _ ”E, 0.99 -‘
z 3
0.98 ‘ - 0.98 -
C197 1 1 1 1 C197 1 1 1 1
.3 .4 .7 .3 .4 6 .7

 

 

 

Figure 2.20: Radial wire probe parameter 1.0 (inches) is plotted versus slit probe pa—
rameter 3 (inches) for calculated orbits started on the plasma boundary (zero equipo-
tential surface).

51

 

 

 

 

 

 

 

 

 

 

 

 

 

().()‘1 l l l
0.03 n _
0.02 d _
1
1; 0,01- Mei} *
2 145%“
.g 0'00 I /,/{/ 1—
; —0.01 ‘ (€12? _
I
-0.02 d _
-0.03 - _
‘0-04 r 1 1
-0.02 -0.01 0.00 0.01 0.02
s finches)
(a) 4 kV Image Electrode
().()‘1 l 1 l
0.03 — _
0.02 a y —
.13”
’0'? 0.01 -1 .12332;’ _
g 0.00~ ”5.3/7 _
-— /v'::"
V N/flE'
3 —0.0I ‘1 "Iii”. .—
g\
—0.02 a ’1 ~
—0.03 d r—
—0.04 1 1 1
-0.02 -0.01 0.00 0.01 0.02
s finches)
(c) 12 kV Image Electrode
0.04 1 1 4
(103— L
(102- c
I; (101- _
0)
‘c ”7’35;
.3 0.00- {(3,-y s
3 -0.01 a “v P
—0.02 ~ _
-0.03 ~ _.
—0.04 r 1 1
-0.02 -0.01 0.00 0.01 0.02
s finches)

(e) 24 kV Image Electrode

 

0.04 1 1 1
0.03 n
0.02 *
0.01-<

0.00 '1

finches)

; -0.01 '1
—0.02 '1

-0.03 ‘

 

 

 

—0.04 r 1
-0.02 -0.01 0.00 0.01
5 (inches)

(1)) 8 kV Image Electrode

 

0.02

 

0.04 A 1 1
0.03 «
0.02 ~ , 1
0.01« .

I
o ,v
:?:'3’

0.00 -* ,',,"*""'b

,4-- ''''

(inches)

3 -0.01 '1
—0.02 -*
~00?) ‘

—0.04

 

 

I I I
-0.02 -0.01 0.00 0.01
5 (inches)

((1) 16 kV Image Electrode

 

0.02

 

0.04 1 1 1
0.03 n
0.02 -1
0.01-1
0.00 ‘

(inches)

3 -0.01—
—0.02 ‘1
—0.03 '1

 

~0.04

 

 

 

If I
-0.02 —0.01 0.00 0.01
s finches)

(f) 32 kV Image Electrode

0.02

Figure 2.21: Axial wire probe parameter (w) is plotted versus slit probe parameter
(s) for calculated orbits started on the plasma boundary (zero equipotential surface).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(e) 10 eV Starting Energy

 

 

 

 

 

 

 

 

 

 

 

 

(f) 20 eV Starting Energy

1 l l J 1 l l 1
1,00 -1 . — 1.00 a . .~ \4 “
U, .. , -.- 1; .-
s 1 : 2 , 5 \
”c: 0.99 d ;- — ”E, 0.99 ‘ i ‘\ '-
3 z
0.98 “ - 0.98 " '-
097 1 T 1 1 097 F i T 1
.3 .4 .5 .6 .7 .3 .4 . .6 .7
5 (inches) 5 (inches)
(a) 0.3 eV Starting Energy (b) 1 eV Starting Energy
1 J. l L l I I l
1.00 r . - ~ 1.00 d *-
1; A ’13
Q) Q)
.C ' .C
E 099— I“ \\ ~ .g 0.99~ -
2 z
0.98 r 1- 0.98 - *-
0-97 I T 1 1 0.97 1 r 1 r
.3 .4 .5 .6 .7 .3 .4 . .6 .7
3 (inches) 5 (inches)
(c) 3 eV Starting Energy ((1) 6 eV Starting Energy
I l l l L I l l
1.00 ‘ h 1.00 n r
’13 ’u?
0 Q)
.C .C
E 0.99 ‘ h ”E, 0.99 4 t-
3 3
0.98 '1 - 0.98 ~ '-
0-97 1 r 1 1 0.97 1 r 1 1
.3 .4 .5 .6 .7 .3 .4 . .6 .7
5 (inches) 5 (inches)

Figure 2.22: Radial Wire probe parameter 1.0 (inches) is plotted versus slit probe pa-

rameter 3 (inches) for calculated orbits started on the plasma boundary (zero equipo-
tential surface).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.04 1 1 1 0.04 1 1 1
0.03 n - 0.03 d h
0.02 ‘ ~ 0.02 a —
I ,If/ I ,//:7'
1;; 0.01- — 7,: 0.01« “I ,- [
m 0 0 '
.C _C .
‘E’ 0.00 ~ _ ”g1 000 _ 1‘
;”001d 5”,,” ' 3-0.01-‘ fill/”l 7
"I" 7’
—0.02 '1 “It - —0.02 '1 1’; —
—0.03 '1 1' -0.03 " 1‘
_0_04 1 1 1 —0.04 1 1 1
—0.02 -0.01 0.00 0.01 0.02 -0.02 -0.01 0.00 0.01 0.02
5 (inches) 5 (inches)
(a) 0.3 eV Starting Energy (b) 1 eV Starting Energy
0.04 1 1 1 0.04 1 1 1
0.03 _ h 0.03 '1 -
0.02 1 ~ 0.02 4 ~
Z? 0.01— — 7,7 001— -
Q) Q)
.C .C
.12) 0.00 - 1— .E 000 .1 _
3-0.01‘ *- g—ODI‘ 1-
-0.02 a L —0.02 — s
—0.03 r - —0.03 -l -
'0.04 I I I —0.04 l 1 1
-0.02 -0.01 0.00 0.01 0.02 -0.02 -0.01 0.00 0.01 0.02
3 (inches) 5 (inches)
(c) 3 eV Starting Energy ((1) 6 eV Starting Energy
0.04 1 1 1 0.04 1 1 1
0.03 -* _ 0.03 - -
0.02 n - 0.02 r -
’0? 0.01“ - ’m‘ 0.01-1 '-
0) 0)
.C .C
E 0.00 r *- .E 0.00 n '-
3-0.01- r 3-0.01n -
--0.02 -1 _ -0.02 ‘ -
-0.03 -‘ '- -0.03 r -
—0.04 1 1 1 —0.04 I I T
-0.02 -0.01 0.00 0.01 0.02 -0.02 -0.01 0.00 0.01 0.02
5 (inches) 5 (inches)

(e) 10 eV Starting Energy

(f) 20 eV Starting Energy

Figure 2.23: Axial Wire probe parameter 11) (inches) is plotted versus slit probe pa-
rameter 3 (inches) for calculated orbits started on the plasma boundary (zero equipo-

tential surface).

54

Chapter 3

Results

In this chapter the methods used to analyze the data from the ion source test stand
are explained (section 3.1). The emittance and luminosity of the beams that were
extracted from the ion source using three different chimneys and two different pullers

are reported (section 3.2), and compared with calculated families of rays (section 3.3).

3.1 Experimental Methods

3.1.1 Understanding the Graphs

Figure 3.1a is a typical graph of radial emittance data from a measurement run in
the ion source test stand. The parameter s which gives the location of the slit probe
is plotted on the horizontal axis and the parameter w which gives the position of
the wire probe is plotted on the vertical axis. (Geometrical descriptions of s and w
were given in figure 2.12.) For radial measurements presented in this dissertation,
the wire thickness is 0.005” (0.13 mm) and the slit width is 0.010” (0.25 mm). Axial
measurements use a 0.015” (0.38 mm) wire and a 0.010” (0.25 mm) slit.

The s and 10 values at which current readings are taken show as a grid of + signs

and the current measured at a point is represented by the size of the + symbol shown

55

Chimney: 0.010”lSlit Arc Curient: 450 (mA) lDee Voltage: 40 (kV)

 

 

 

 

 

 

 

 

1.0
block: 5% max
....................................... “125531713.
1,04 4 ....................................... — 311.2,, 75, m,
“1.02 —
U)
0)
5 1 00 - —
é . 6112:6111: 102827922”
30.98 -
0.96 - - .
0.94 1 1 r
.50 .55 .60 .65 .70
3 (inches)
(31) Radial (3,112) Beam Contours
Chimney: 0.010" Slit Arc Current: 450 (mA) Dee Voltage: 40 (kV)
.75 ' . 1 . L B. .' _ ' . .
. 1 I I 1 1 black: 5% max
.74 ‘ O j j — green: 75:: max
A .73— E —
g) .
a) .
6 72 7 i _
Ex - j 511:” (:urrent: 2225. (a?)
3 : Wire Current: 1157. 01A)
.71- ; ”
.70 - _
.69 1 1 I 1 1 1
.285 .290 .295 .300 .305 .310 .315 .320

 

 

8 (inches)

(b) Axial (s,w) Beam Contours

Figure 3.1: Typical graphs of the s and 111 data. (Parameters s and w give the position
of the slit and wire probes respectively as described in sections 2.4.1 and 2.4.2.)

56

at that point. If the current was very small, the + appears as a dot. Overlaid on
the grid are interpolated contours of constant wire current. They help in visualizing
the size and shape of the beam in (3,112) parameter space. “Imam”, the “slit current”
and the “wire current” are recorded with each radial (5,212) plot. [max refers to
the maximum current read on the wire. The slit current refers to the total current
measured on the slit probe when the probe is moved to a location where no beam is
passing through the slit, thus it is a measure to the total beam current that passes
through the puller.

Figure 3.1b is a typical graph of data from an axial emittance experiment in the
ion source test stand. The parameters .3 and w are again plotted on the x and y axis
respectively. (A geometrical description of s and w for axial measurements is given
in section 2.4.2.) The grid and contours used in the axial data graphs have the same

meaning as they do in the radial data graphs.

3.1.2 Repeatability of the Data

An important indication of the accuracy of a data set is the repeatability of the data.
Figure 3.2 shows two consecutive runs on the ion source test stand. Qualitatively,
the beams cover the same region of the graph. The total integrated current hitting
the wire probe (the sum of the currents at every 3 and w point) differ by 10%. Other

repeated measurement showed similar levels of consistency.

57

Chimney: 0.01)" lSlit

Arc Curient: 450 (mA) lDee Voltage: 40 (kV)

 

 

 

 

 

 

 

 

 

 

1.06
block: 51 mm
1.04 ‘ ' green: 753 max
A1.02 -1 '-
(D
o
5 1 oo -1 s
Lg . merit: ”£7922”
30.923 - —
0.96 - ~
0.94 1 1 l
50 .55 .60 65 70
3 (inches)
(a) Run number 18 from July 2003
Chimney: 0.00“ Slit Arc Current: 450 (mA) Dee Voltage: 40 (W)
1.06 1 i '
block: 5% max
....................................... if. 2301:1116:
1.04 " ....................................... b gredn: 75; max
“1.02 —
(D
Q)
5 1 oo - -
s a“... 1m...
30.98 .
0.96 -
0.94 l l i
.50 .55 .60 .65 .70
5 (inches)

(b) Run number 19 from July 2003

58

Figure 3.2: The two graphs show two runs in the Ion Source Test Stand. The param-
eters for the ion source (are current, puller voltage, gas flow, chimney geometry, etc)
were held constant. The graphs have a qualitatively similar shape showing that the
slit and wire probes measured current at the same locations in each measurement.
The total current measured by the wire probe in the two measurements differ by 10%.

3.1.3 Converting Raw Data into Radial Emittance Plots

The raw data that are measured by the ion source test stand include: the slit probe
parameter (s), the wire probe parameter (w), the current on the slit probe (is)1
and the current on the wire (iw). (See figure 2.12 for geometric descriptions of the
parameters 5 and 10.) To calculate the emittance of the beam we need to know the
(perpendicular) radial width of the beam and the divergence (angular spread) of the
beam.

Figure 3.3 shows a beam which has been mostly blocked by the slit probe. The
origin of the polar coordinate system is chosen to be at the center of the beam i.e. it
is equidistant from the center of the source opening, the central slit position and the
central wire position. Each slit probe position 3 for which some beam passes through
the slit has an associated radius r, the distance from the origin of the polar coordinate
system to the slit. The range of r values then is the radial width of the beam.

For each slit position, current is read on the wire probe at a range of wire probe
positions indicating that the beam diverges after the slit i.e. there is a range of angles
(or) that the beam makes with the unit vector 0. Each wire probe location where a
non-zero wire current, iw, is measured has an associated angle or. The spread of a,
values then is the divergence of the beam.

To determine the range of angles or, we need to know the path that each ray
takes from the slit location to the wire locations. Two methods (both approximate)
present themselves. The first method is to use Z3CY CLONE (our orbit tracking
code) to find orbits which start in the chimney opening, pass through the specified

slit location and arrive at the various wire locations. To provide accurate results, these

 

1For data taken after June 10, 2004 the beam current measured on a beam stop downstream of
the wire probe is recorded as i,. After this date the current on the slit probe is measured with an

analog gauge and recorded manually.

59

  
      

 

Range of wire

 

The beam diverges
after the slit

Figure 3.3: r is the distance from the origin to the point where the beam passes
through the slit. a, is the angle that the beam makes with the unit vector 19

60

orbits should have the same accelerating potential (dee voltage) as the experimental
beam thus having the same curvature as the experimental beam. The second method
is to find circular “orbits” which start at the specified slit location and arrive at the
various wire locations. To provide accurate results, these circular orbits should closely
approximate the curvature of the experimental beam. This is accomplished taking
the circle which passes through the center of the chimney opening, the central slit
position, and the central wire position as the reference location (To).

These methods were tested on a sample case to ensure that they give consistant
results. The sample data points have the same slit parameter (s = 0.5353”) and wire
parameters differing by about 0.005” (111 = 0.9677” and 0.9626” respectively). Figure
3.4 shows the tracked rays and the circles that pass through these two data points.
The divergence, as determined by the tracked rays is 4.72 mrad. The circles give a
divergence of 4.44 mrad; a difference of 6%.

Finding a tracked ray that starts in the chimney opening, goes through a specified
slit location and ends at a specified wire location involves a multi-parameter search;
namely finding the correct starting location in the chimney opening, the correct start-
ing angle, the correct starting energy, and the correct puller voltage. In contrast,
fitting a circle of given radius to two points (the slit location and the wire location)
is trivial. Since the methods give very similar results and the difference in computing
efficiency is enormous the circle technique is used to calculate the divergence of the
experimental beam.

Figure 3.5a is a plot of the parameters 3 and w from a typical experimental
radial emittance run. Figure 3.5b shows the same data plotted with a, versus r — To
(deviations from the average radius are plotted to emphasize the width of the beam)
i.e. an emittance plot. The r and a, values at which current readings are taken show

as a grid of (+) signs and dots. Overlaid on top of the data points are contours of

61

 

OO 1 l l l

—0.5 -1 -

 

—1.0- —
—1.5- —
—2.0- -

—2.5 — —

 

 

 

—3.0 1 I I I I
-0.5 0.0 0.5 1.0 1.5 2.0 2.5

(a) Marked with “X’s” are a single slit location and two wire
locations separated by about 0.005” (0.13 mm). Two orbits
were tracked with Z3CYCLONE (red and blue) both of which
pass through the specified slit location and each of which end
at their respective wire locations. Two circles (black) also pass
through the specified slit location and end at the two specified
wire locations.

 

 

 

 

 

—1
—1

0H
k:
oo

1 l l

.3 .4 .5

(b) A closeup of the region after the slit probe. It can be seen
that while the circles (black) and the tracked orbits (blue and
red) do not follow the exact same path from the slit to the
wire, the divergence (angular spread) between the two circles
is very close to the divergence between the two tracked rays.

Figure 3.4: Test Orbits for Calculating Divergence

62

Chimney: 0.010" Slit Arc Current: 450 (mA) Dee Voltage: 40 (kV)
l l l

1.06

 

black: 5% max
red: 25% max
ooooooooooooooooooooooooooooooooooooooo b'm: 50‘ m
1.04- "' ....................................... '— green: 753 max

1.02 -

Tr?
2
0 1.00 ~ — .
LE, ' 3.33m. ”579220
30.98 - —
0.96 - r

 

0.94 1 I
.50 .55 .60 .65 .70
3 (inches)

 

 

 

(a) (s, w) plot showing the slit and wire probe positions along with the current
measured at each grid point.

Chimney: 0.010” Slit Arc Current: 450 (mA) Dee Voltage: 40 (W)
1 - 1

40 .v I .v L .T ..

 

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

. .9 .' .00.
e. .e .e' .-
. I .I .-
... .,. .. ._- ...
e _.. ...- .'. ..,.
.l. -.e ._.- .... ..
-.. ._. ..o ..o .e F—
_4 .
u" ."° "‘ e'.
' e0 ." e.
... . .. .. ‘..
I II. .- 0" O.

 

:6 90.1% emittance:

8 24.3 mm-mrad
E O '7 — normalized emittance:
. 0.224 mm-mrad

6 . - ‘ .u' .'..

 

 

 

—40 TiszI T I I
—3 —2 -1 0 1 2 3
r—r0 (mm)

(b) The same data plotted in (mar) space.

Figure 3.5: Converting Radial Slit and Wire Probe Position Data to r and a,

63

constant wire current, these help to visualize the shape of the beam in emittance space.
The points with the largest current density are plotted with + symbols; adding the
current from each of these points gives approximately 90% of the total beam current.
The rest of the data points are marked with dots. The area represented by the +
symbols is the “90% emittance” of the beam and is recorded with each emittance plot.
(“Normalized emittance,” as discussed in section 1.2, is the emittance multiplied by

the relatavistic factors 3 and 7.)

3.1.4 Converting Raw Data into Axial Emittance Plots

For axial emittance measurements, like radial measurements, the quantities measured
by the equipment are the slit probe parameter (s), the wire probe parameter (w),
the current on the slit probe (is) and the current on the wire (iw). To extract the
traditional axial emittance variables from the data, we make the assumption that the
beam’s z motion is not affected by the magnetic field. This is equivalent to assuming
that the field has constant Bz over the entire orbit. (Tracked orbits in Z3CYCLONE
show that this is a reasonable approximation for the region between the slit and wire
probes.)

Calculating z and (12 is a two step process. First, determine 23m and zwire from
the parameters 3 and w. (see Section 2.4.2). Second, calculate the divergence angle
01,, as the arctangent of the change in z from the slit to the wire divided by the beam

path length from the slit to the wire.

_1 ZWiTC — ZSl‘i-t) (31)

a = tan
z pathlength

The 2 position variable is identified as the height of the beam as it crosses through

the slit (231”). Figure 3.6 shows two graphs. The top graph is a plot of the parameters

64

.75

.72

w (inches)

.71

.70

.69

.285 .29

Chimney: l0.010" Slit Archurrentzl450 (mAl) Dee Volltage: 40 (kV)

 

.74- f
.73— i

_‘ .

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

1

_ imax: 12.5 )
Slit Current: 225. )
Wire Current: 137. M)

 

 

 

l

 

l T l l l
0 .295 .300 .305 .310 .315 .320
5 (inches)

(a) (3.11)) plot showing the slit and wire probe positions along with the current
measured at each grid point.

50

(mrod)

01

Chimney: 0me Slit l Arc Currlent: 450 (mA) Dee Vloltoge: 40 (kV)

 

block: 5% max
red: 25% max
blue: 50

_ green: 75% max

90.2% emittance:
118.1 mm-mrad

_ normalized emittance:
1.091 mm—mrad

 

 

 

 

2 (mm)

(b) The same data plotted in (z,az) space.

Figure 3.6: Converting Axial Slit and Wire Probe Position Data to z and Q;

65

s and w from a typical axial emittance run. The bottom plot shows the same data
plotted versus the emittance variables 2 and oz.

The grid and contours used in the axial emittance graphs have the same meaning
as they do in the radial emittance graphs. The area enclosed by the + symbols is
the 90% emittance of the beam. (The focusing tails observed at the top and bottom
of the axial emittance area are similar to those observed by Mallory [6, p69] and are

produced by the focusing electric field at the ends of the source slit.)

3.2 Experimental Results

3.2.1 Slit Chimney Measurements

One of the key factors determining the performance of an ion source is the shape and
size of the output slit in the chimney. All data for this section (3.2.1) were collected
with two slit chimneys which were made at the MSU physics department machine
shop. (Similar chimneys made by ACCEL Instruments GmbH of Bergisch-Gladbach
Germany for the 250 MeV proton cyclotron were tested later and are not included in
this dissertation.)

Each chimney is made of molybdenum tubing, having outer diameter 0.250” (6.35
mm) and wall thickness 0.020” (0.51 mm). Both chimneys have a 0.196” (5.0 mm)
tall chamfered slit. The difference between the two chimneys is the width of the slit;
one chimney has an 0.010” (0.25 mm) wide slit while the other has an 0.020” (0.51
mm) wide slit. Perspective views of the two slits are shown in figure 3.7.

The puller geometry used in these tests was an original design for the ion source
test stand (figure 3.8) with a 0.195” (5.0 mm) chimney—puller gap intended to hold
50 kV.

To directly compare the two slit chimneys we look at their performance at an are

66

   
  

0.010" Slit

0 .020” Slit

Figure 3.7: The two slit chimneys that were used are shown. One chimney has a.
0.010” (0.254 mm) slit. The other has a 0.020” (0.508 mm) slit. Both have a 10°
chamfer.

\___—.

Chimney i

Puller Center
Puller \ /

      

©

     

 

 

Figure 3.8: This puller was designed for the ion source test stand to hold 50 kV.
The puller has a radius of curvature of 0.500” (12.7 mm) and is centered behind the
chimney. The minimum source to puller gap is 0.196” (5.0 mm).

68

 

 

 

Chimney 90% Current Radial Emittance Axial Emittance Luminosity
(11A) (mm—mrad) (1n m-mrad) (011154—311)

0.010” Slit 44 27 112 1.5

0.020” Slit 203 47 191 2.3

 

 

 

 

Table 3.1: The chimney with the larger slit produces a beam with a larger emittance.
However, the beam is also of higher intensity. The net effect is a higher luminosity for
the chimney with the 0.020” (0.50 mm) slit. (Data sets in the table are taken with
an arc current of 50 mA, gas flow of 3.0 cc/min and puller voltage of approximately
40 kV.)

current of 50 mA. (This low arc current would not typically be used during actual
beam production, but is used here as the only are current common to the data sets of
the two chimneys.) The performance of the ion source with the 0.010” slit chimney
at are current settings ranging from 50 to 450 mA is discussed in section 3.2.3 and a
summary of all data that have been collected is given in section 3.2.5.

Keeping all other source parameters constant emittance measurements were made
with both chimneys. Figures 3.9 and 3.10 show emittance plots for the two chimneys.
Table 3.1 lists the emittance and luminosity for the two chimneys. The chimney with
a 0.020” (0.51 mm) slit has a larger emittance than the chimney with the 0.010”
(.25 mm) slit, but it also produces a higher beam current. As discussed in sec 1.2,
luminosity is defined as accelerated current divided by radial and axial emittance of

the beam. The chimney with the 0.020” (0.51 mm) slit has a higher luminosity at

this are current.

69

 

Chimney: 01.010" Slit 1 Are CurrLent: 50 (nliA) Dee Vloltage: 40 (kV)

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

20- ;11353133jjiijiigjI3iiI?-:;jiii —

90.2% emittance:
26.8 mm-mrad

(mrad)

_ normalized emittance:
0.248 mm—mrad

l’

 

(X

-20- _

 

 

—4o . 1

 

(a) 0.010” Slit Chimney Radial Emittance

4o

 

Chimney: 0.020" Slit Arc Current: 50 (mA) Dee Voltage: 40 (kV)
l l l L 1

black: 5% max
red: 25% max
blue: 50% max
green: 753 max

20—iigjjii.;;j:jii3gjj1::ii.g;j:ZiII3-3":::I::IZiI-:: -

90.0% emittance:
45.9 mm-rnrad

(mrod)

— normalized emittance:
0.424 mm-mrad

f

 

(X

 

 

'1‘

.-' .“ !.'. .‘I‘.'-. _..I.-' .‘
-3 -2 —1 0 1 2 3
r-ro (mm)

 

(b) 0.020” Slit Chimney Radial Emittance

Figure 3.9: The larger chimney slit produces a beam with a larger emittance in r.

70

 

Chimney: 0.010" Slit Arc Current: 50 (mA) Dee Voltage: 40 (kV)
l l l | 1

black: 5% max
. , red: 25% max
I ' ‘ - '_ ' - ~ . , blue: 50% max
50.. . , : ' - ' ~ . _ ,_ green: 75% max

90.1% emittance:
108.1 mm—mrad

(mrad)

— normalized emittance:
0.998 mm—mrad

Z

or

 

—5o— ':§§::§:<§»

 

1 1 l ' I 1

 

 

2 (mm)

(a) 0.010” Chimney Axial Emittance

100

 

Chimney: 0|.020" Slit 1 Arc Curient: 50 (nliA) Dee Voltage: 40 (W)
A

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

50*

90.2% emittance:
185.9 mm-mrad

(mrad)

— normalized emittance:
1.717 mm—mrad

1

(X

_50_

 

 

 

—100 1 1 ' ' *1 ‘ '
—3 —2 -1 0 1 2 3
2 (mm)

 

(b) 0.020” Chimney Axial Emittance

Figure 3.10: The larger chimney slit produces a beam with a larger emittance in z.

71

 

Figure 3.11: Puller Markings

Puller Markings

In Spring of 2004 the ion source was run in the test stand continuously for several
months in order to test the lifetime of the cathodes (which did not quit working
during that test). The ion beam which was aimed slightly to the right in the puller
opening cut away at the tungsten insert in the puller (figure 3.11). The cut tells
us a couple of things about the beam. First, the height of the cut is about 0.15”
(3.7 mm) which is consistant with the height of the beam measured at the slit probe
inside the dee and noticeably smaller than the 0.196” (5.0 mm) height of the source
opening. Second, the notches at the top and bottom of the cut indicate that the top
and bottom of the beam are wider than the center of the beam. This is likely the

result of the interaction of the beam with the non-linear electric fields near the top

72

and bottom of the source opening.

3.2.2 Hole Source Measurements

A second set of experiments was performed with a chimney and puller region modeled
after the central region of the Harper Medical Cyclotron in Detroit MI. Because the
K100 uses a deuteron beam the emittance measurements for the “hole” chimney were
taken with deuterons accelerated to a nominal dee voltage of 20 kV (as opposed to
protons at a nominal dee voltage of 40 kV for the slit chimneys).

As seen in figure 3.12, the opening in the chimney has a 0.047” (1.19 mm) hole
with a chamfer that is machined by using a center hole drill to create a sharp edge
at the base of the hole. The puller is shown in figure 3.13.

The beam extracted from the hole chimney is significantly different from the beams
extracted from the slit chimneys. The radial emittance shows significant curvature
(figure 3.14a) and the axial emittance (figure 3.14b) shows that the beam is diverging
by the time it reaches the slit probe (in contrast with the beam from the slit chimneys
which is converging when it reaches the slit probe) with particles above the center
of the beam moving up, and particles below the center of the beam moving down.
(Our probes were not able to measure the full height of the beam.) The emittance of
the beam from the hole chimney was larger than the emittance from either of the slit
chimneys. Because, the ions extracted from the hole chimney were only accelerated
to 20 keV (as compared to 40 keV for the ions from the slit sources) it is appropriate
to compare the normalized emittances. The radial normalized emittance (0.66 mm-
mrad) was about 50% larger than that of the slit chimney (.44 mm—mrad) and the
axial emittance was larger than could be measured. More than half of the beam which
came through the puller was not measured by the wire probe. It is likely that the

beam grew in 2 until part of the beam was blocked by the top and bottom of the dee.

73

60’Chamfcr

0.047" hole

 

Figure 3.12: The hole in the chimney is 0.047” (1.19 mm) with a sixty degree chamfer.

At 50 mA of arc current, the normalized luminosity of the beam which made it

 

to the wire probe was 129 fi, about half of that for the slit chimney with the
same are current (264 mmfisr). It is relevant to note that with its internal target the

Harper Medical Cyclotron’s performance is not presently limited by beam quality or
beam current, so there is no pressing need to improve the luminosity in the cyclotron’s
ion source. Also, with a 250 mA are current, the hole chimney has higher luminosity
than the 0.010” slit chimney at the same are current (the 0.020” slit chimney was not

run at are currents above 150 mA).

74

l\ i
\

Chimney I

Puller \ Puller Center

  

 

 

 

 

 

 

 

Figure 3.13: This puller was designed for the ion source test stand and has the same
geometry as the puller in the K100 medical cyclotron. The chimney is not centered
in the puller. (The chimney is centered at (0.000,0.000) and the puller is centered
at (0.021,0.000).) The minimum gap between the chimney and the puller is 2.9 mm
while the gap at the source opening is 3.0 mm, meaning that the beam does not see
the peak electric field. This is not optimal for extracting the maximum beam current,
but the layout has worked well in the K100 cyclotron. This puller will hold about 25
kV in the ion source test stand.

75

 

 

 

 

 

 

Chimney: 0.047" Hole Arc Current: 50 (mA) Dee Voltage: 20 (kV)
100 l l l 1
black: 5% max
red: 25% max
blue: 50% max
green: 75% max
50 a
G 90.0% emittance:
8 138.4 mm-mrad
E O - — normalized emittance:
L 0.639 mm—mrad
(S
_50 _
—100
(a) Radial Emittance
Chimney: 0.047" Hole Arc Current: 50 (mA) Dee Voltage: 20 (kV)
100 l l . l l I
' ‘ ' black: 5:: max
red 25% max
blue 50% max
green: 75% max
50 4
8 90.1% emittance:
8 185.1 mm—mrod
E O - _ normalized emittance:
N 0.855 mm—mrad
ES
__50 _
—1OO

 

 

4H

 

(b) Axial Emittance

 

Figure 3.14: Emittance Plots with the Hole Chimney

76

3.2.3 Effect of Arc Current

Experience with PIG ion sources has shown that a larger are current can produce a
more intense beam. This was verified using the slit chimneys. lV’leasurements were
taken with are currents ranging from 50 mA to 450 mA for the 0.010” slit and from 50
mA to 150 mA for the 0.020” slit. (Higher arc currents were not used for the 0.020”
slit chimney due to concerns about damaging the slit probe with higher beam currents
i.e. above 600 ,uA.) The hydrogen gas flow was 3.0 cc/ min for all runs. Table 3.2 and
3.3 show the general trend of increasing arc current producing increased beam current
as expected. For the 0.010” slit, there was no noticeable change in the emittance of
the beam for different currents, and it does not appear that space charge (the mutual
repulsion experienced by the positive ions in the beam) was a significant factor at
beam currents below 230 11A. For the 0.020” slit, both the radial and axial emittance
grow with increasing current. The growth in emittance could be an indication that
the shape of the plasma boundary changes with are current or that increasing space

charge forces are causing emittance growth.

77

 

 

 

 

 

 

 

 

 

Arc Beam Beam Current / Radial Emitt. Axial Emitt. Luminosity
Current Current Arc Current (mm-mrad) (mm-mrad) (61,151”)
(mA) ()1A) (X1073)
50 52 1.0 27.2 112 1.7
250 165 0.66 25.5 141 4.6
350 195 0.56 23.5 121 6.9
450 227 0.50 25.0 127 7.1

 

Table 3.2: Results from four measurements of radial and axial emittance with the
0.010 inch slit chimney. The puller voltage was 40kV. All parameters were kept
constant except the arc current.

 

 

 

 

 

 

 

 

 

Arc Beam Beam Current / Radial Emitt. Axial Emitt. Luminosity
Current Current Arc Current (mm-mrad) (mm-mrad) (mfisr)
(mA) (11A) (X10‘3)
50 230 4.6 47.1 191 2.6
100 401 4.0 57.9 206 3.4
150 590 3.9 64.9 239 3.8

 

Table 3.3: Results from three measurements of radial and axial emittance with the
0.020 inch slit chimney. The puller voltage was 40kV. All parameters were kept
constant except the are current.

78

 

 

3.2.4 Atomic Hydrogen Ions

Livingston and Jones report [5, Fig 9] that for a filament ion source, production of
the atomic ions H; and H; was dependant on ion source are current with atomic
ion production decreasing with increasing arc current. A possible error in the results
reported in this dissertation then arises from the possibility that atomic ions might
contribute to the currents measured in the NSCL test system. Figure 3.15, for exam-
ple, shows calculated orbits in the ion source test stand for protons and H; ions along
with the setup used to observe protons and H3“ ions simultaneously. The slit probe
did not have the range to cover the whole proton beam and H; beam at the same
time, so we were unable to make quantitative measurement of the ratio of protons to
H2+ ions.

Under normal ion source opperating conditions, (arc currents ranging from 50 to
350 mA, arc voltages less than 3 kV i.e. the power supply was current limited, and
hydrogen gas flow rates greater than 2.0 cc / min) no H; ions were observed. We were
able to observe H; ions by lowering the gas supply to 0.5 cc/ min. At this setting, the
are shifted to the 3.5 kV limited mode of the are power supply and the arc current
dropped to 90 mA in a fast step. Since none of the results reported here used such a
low gas flow, we conclude that the proton beam results given in this dissertation do

not include atomic ion effects.

79

 

 

Slit Probe Range

 

Beam Stop

 

 

 

—3.0 1 1 1 1 1
—O.5 0.0 0.5 1.0 1.5 2.0 2.5

Figure 3.15: Plot shows calculated trajectories for protons and atomic hydrogen ions.
Parts of each of these beams pass through the range of slit positions selectable in
the Ion Source Test Stand. Using this setup, we were able to determine that atomic
hydrogen ions were not produced from the cold cathode PIG ion source under normal
operating conditions.

80

3.2.5 Data Summary

The following runs were made with results as listed. (See figures 3.16, 3.17, 3.24.)

 

 

 

 

 

 

 

 

 

 

 

 

 

Chimney Dee Arc Gas Beam Rad. Emit. Axial Emit. Luminosity
Voltage Current Flow Current (Normalized) (Normalized) (Normalized)
(kV) (mA) (cc/min) (14A) (mm~mrad) (mm-mrad) (“"51“,~ )/( mmgfir)
Slit 0.010” 40 50 3.0 52 27.2 (0.252) 112 (1.03) 1.7 (170)
(MSU) 40 250 3.0 165 25.5 (0.235) 141 (1.30) 4.6 (380)
40 350 3.0 195 23.5 (0.217) 121 (1.12) 6.9 (518)
40 450 3.0 227 25.0 (0.231) 127 (1.17) 7.1 (525)
Slit 0.020” 40 50 3.0 230 47.1 (.435) 191 (1.77) 2.6 (230)
(MSU) 40 100 3.0 401 57.9 (.535) 206 (1.90) 3.4 (325)
40 150 3.0 590 64.9 (.599) 239 (2.21) 3.8 (323)
Hole 0047” 20 50 1.5 200 > 143 (.602) > 195 (0.000) n/a
20 250 2.5 720 > 115 (.534) > 213 (0.983) n/a

 

Table 3.4: Data Summary

81

 

Chimney: 01.010" Slit Arc Curqent: 50 (111A) Dee \(oltoge: 40 (kV)
l

 

 

 

 

 

 

 

 

 

 

40
black: 5% max
red: 25% max
blue: 50% max
green: 75% max
20 - *-
8 90.2% emittance:
E 26.8 mm-mrad
E O - _ normalized emittance:
_ . . . 0.248 mm-mrad
6 .
_20 _ .—
—4O 1 l r l l
—3 -2 —1 0 1 2 3
r-ro (mm)
(a) Radial Emittance
Chimney: 0.010" Slit Arc Current: 50 (mA) Dee Voltage: 40 (kV)
4. 1 . 1 1 1
black: 5% max
red: 25% max
blue: 50% max
50 a ,. green: 75% max
8 90.1% emittance:
8 , 108.1 mm-mrad
E O _ :— normalized emittance:
N ‘ 0.998 mm-mrad
t5 1
-50 r ' I 1 - . I j : ‘P . I : 1 . :—
. d . ' q
7 I T I I
—3 — —1 O 1 3
2 (mm)

(b) Axial Emittance

Figure 3.16: Emittance Plots for 0.010” Slit Chimney with 50 mA Arc Current
(Shown previously in figures 3.9 and 3.10.)

82

Chimney: 01.010“ Slit 1 Are Cunient: 250 (mA) Dee Vloltage: 40 (kV)

 

 

 

 

 

 

 

 

 

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

90.4% emittance:
25.6 mm-mrad

normalized emittance:
0.237 mm—mrad

black: 5% max
red: 25% max
blue: 50% max

_. green: 75% max

90.0% emittance:
134.2 mm-mrad

normalized emittance:
1.239 mm—mrad

40
20-
{6‘
E
s 01
6L
_2() _
"'40 n l I I
-3 -2 —1 0 1 2 3
r—ro (mm)
(3) Radial Emittance
Chimney: 01.010" Slit Arc Curient: 250 (mA) Dee lialtage: 40 (kV)
. r .45: ' ' - - ° :
50 —f I
’6 : f
2 » -
E 0 '3 l , 1
.. 1 : ‘
(S I ' 1
_50_ I l
r I
-3 —2 2 3

Figure 3.17: Emittance Plots for 0.010” Slit Chimney with 250 mA Arc Current

 

2 (mm)

(b) Axial Emittance

83

 

Chimney: 0.0'0” Slit Arc Current: 350 (mA) Dee Voltage: 40 (kV)

40 1 . 1 . L fi 1 1

. .. """" black: 5% max
. - - - ° red: 25% max

blue: 50% max
green: 75% max

a. .' .' no.
I. '.. ..- ..- ..
' .. -,e ..e'- .e'
I. ‘ e '9.
.I .n- ..0 ..e .
' no “ ..c e-
—1 . e .O .0 e. h
.' 9' .' el.
0 . e e
'o- ..e ...e ‘.e ..e
' e. e‘ ..0‘ .e
.' . .n .e
.c It. a. .I.

90.3% emittance:
23.0 mm-mrad

(mrod)

normalized emittance:
0.212 mm-mrad

 

r

a

-20— 33-11333-:::Ii?3~:::12;§2======”“' -

 

 

 

—4O 1 l l l l
-3 -2 -1 0 1 2 3
r—r0 (mm)

(a) Radial Emittance

 

Chimney: 01.010" Slit I Are Curient: 350 (mA) Dee \ioltage: 40 (kV)

black: 5% max
red: 25% max
blue: 50% max
r green: 75% max

50-

90.0% emittance:
113.0 mm-mrad

(mrod)

normalized emittance:
1.043 mm-mrad

a

_50 _.

 

 

 

 

2 (mm)

(b) Axial Emittance

Figure 3.18: Emittance Plots for 0.010” Slit Chimney with 350 mA Arc Current

84

a

 

(mrad)

a

 

 

 

 

 

(mrad)

Z

 

 

 

 

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

90.1% emittance:
24.3 mm—mrad

’— normalized emittance:

0.224 mm—mrad

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

90.2% emittance:
118.1 mm-mrad

_ normalized emittance:

1.091 mm—mrad

Chimney: 01.010" Slit 1 Are Curqent: 450 (mA) Dee Vloltoge: 40 (kV)
20 -
O ..
_20 — _
‘40 T. l : I. T T 1 _
—3 -2 —1 2 o
r—ro (mm)
(a) Radial Emittance
Chimney: 01.010" Slit I Are Curqent: 450 (mA) Dee Vloltage: 40 (kV)
50 - ~
0 — i : 1
—50- : i : -
I I I i _
-3 -2 -—1 0 2
2 (mm)

(b) Axial Emittance

85

Figure 3.19: Emittance Plots for 0.010” Slit Chimney with 450 mA Arc Current

2049""

(mrad)

01

Chimney: 0.020" Slit Arc Current: 50 (mA) Dee Voltage: 40 (kV)
l l l l l

 

 

 

100

 

' i

—1

'I '1

N — -- . :- .I . Z. 2. '1 Z. I

r—ro (mm)

(a) Radial Emittance

Chimney: 3.020" Slit I Arc Curgent: 50 (nliA) Dee Vloltage: 40 (kV)

 

 

50~

(mrad)

2

or

_50 _

 

—100

 

 

2 (mm)

(b) Axial Emittance

 

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

90.0% emittance:
45.9 mm—mrad

1— . .
normalized emittance:

0.424 mm-mrad

black: 5% max
red: 25% max

blue: 50% max
green: 75% max

90.2% emittance:
185.9 mm—mrad

_ normalized emittance:

1.717 mm—mrad

Figure 3.20: Emittance Plots for 0.020” Slit Chimney with 50 mA Arc Current
(Shown previously in figures 3.9 and 3.10.)

86

 

 

 

 

 

 

 

 

 

 

Chimney: 0.020" Slit Arc Current: 100 (mA) Dee Voltage: 40 (kV)
40 ,. I _. I .. 1 1 ' .

I block: 5% max
red: 25% max
blue: 50% max

green: 75% max
20 - " ‘-
9 90.1% emittance:
E 57.7 mm-mrad
E _ normalized emittance:
b 0.533 mm-mrad
6 . ..
_20_.-':__...-" —
‘40 ‘ ' I I. "I. "I ‘i _
——3 —2 -1 O 1 2 .J
r—r0 (mm)
(3) Radial Emittance
Chimney: 0.020" Slit Arc Current: 100 (mA) Dee Voltage: 40 (kV)
J l l l J
. . . _ . . . ~ - . , block: 5% max
; . . . j I . . _ I - . . j '_ - - red: 25% max
. I j - . , j j - ’ ~ . . ' ~ blue: 50% max
: . . ‘ ‘ green: 75% max
50 - : ‘
:6 90.1% emittance:
8 195.6 mm—mrod
E O — _ normalized emittance:
N 1.806 mm-mrod
(S
—50 - _
-100 I I I r I _
-3 -2 —1 1
2 (mm)

(b) Axial Emittance

Figure 3.21: Emittance Plots for 0.020” Slit Chimney with 100 mA Arc Current

87

 

Chimney: 0.020" Slit Arc Current: 150 (mA) Dee Voitage: 40 (kV)
40 . 1 . Q. 4.. 1 . . 1 .

' ' ' H black: 5: max
red: 25% max
blue: 50% max

green:75%max
2o —

90.0% emittance:
64.4 mm—mrad

(mrad)

_ normalized emittance:
0.595 mm—mrod

a

 

 

-—3 —2 —1 O 1 -'
r—ro (mm)

 

 

N— I: '2 '1

(:1) Radial Emittance

 

 

 

 

 

Chimney: 0.020" Slit Arc Current: 150 (mA) Dee Voltage: 40 (kV)
100 ~ 1 ' l . l .l ' l .

. . block: 5% max
red: 25% max
blue: 50% max
green: 75% max

50 - -

:6 90.0% emittance:
8 226.2 mm-mrod
E O _ _ normalized emittance:

N 2.089 mm—mrad
d

_50 — _.
- 100 F I I ‘I I _

—3 — —1 1
2 (mm)

(b) Axial Emittance

Figure 3.22: Emittance Plots for 0.020” Slit Chimney with 150 mA Arc Current

88

Chimney: 0.047" Hole Arc Current: 50 (mA) Dee Voltage: 20 (kV)
l l l l

 

 

 

 

 

Chimney: 0.047" Hole Arc Current: 50 (mA) Dee Voltage: 20 (kV)
I l l l I

 

100
50 -
’6‘
E
.E, 0 -
6.
_5O _.
—100
100
50 -
6‘
E
e 0 -
6N
_50 _

 

 

 

 

block: 5% max
red: 25% max
blue: 50% max
green: 75% max

90.0% emittance:
138.4 mm—mrod

— normalized emittance:

0.639 mm—mrad

black: 5! max
red: 25% max
blue: 50% max

green: 75% max

90.1% emittance:
185.1 mm-mrad

— normalized emittance:

0.855 mm—mrod

Figure 3.23: Emittance Plots for Hole Chimney with 50 mA Arc Current

(Shown previously in figures 3.14.)

Chimney: 0|.047" Holel Arc Current: 250 (mA) Dee \(oltoge: 20 (kV)

 

 

 

 

 

 

 

 

 

100
black: 5% max
red: 25% max
blue: 50! max
green: 75% max
50 -
:6‘ 90.0% emittance:
8 114.9 mm—mrad
E O _ _ normalized emittance:
__ 0.530 mm—mrad
6
_50 —1
—100
(3) Radial Emittance
Chimney: 0.047" Hole Arc Current: 250 (mA) Dee Voltage: 20 (W)
100 1. . . .1. 1 . 1 . 1
' - ' ' ' block: 5: max
red: 25% max
blue: 50% max
L green: 75% max
50 ~
3 90.0% emittance:
8 204.0 mm-mrod
\E/ O — h normalized emittance:
N 0.942 mm—mrad
6
_50 _ _
—100 l
— 4

 

2 (mm)

(b) Axial Emittance

Figure 3.24: Emittance Plots for Hole Chimney with 250 mA Arc Current

90

3.3 Matching Ensembles of Computed Orbits to
the Experimental Beams

For all comparisons between computed orbits and experimental data, graphs will show
the experimental data as contours on top of a grid of black + signs and computed

data as a collection of blue dots.

3.3.1 Slit Sources

Trajectories of 394,940 rays were computed for each calculation presented in this
section (3.3.1). There are, first of all, 403 different starting positions for the ions
on the zero potential surface across the chimney opening (13 across the width of the
opening and 31 vertically). 49 different starting angles were tracked from each starting
position 7 angles in the median plane (covering 103 degrees), 7 different starting
angles vertically (covering 103 degrees). For each combination of starting position and
starting angle 20 different rays were tracked, namely: five different starting energies
representing a plasma temperature of 35000 K (resulting in a maximum starting
energy of 11.7 eV) and 4 different accelerating potentials (36.5i0.060 kV for the
0.020” slit and 37.25zt0.060 kV for the 0.010” slit) 2. Orbits which came into contact
with the chimney before exiting the chimney opening were dropped as were orbits
which hit the puller.

Figure 3.25 show the plasma boundary that produced the best match between
calculations and experimental data for the 0.010” (0.25 mm) slit chimney with figure

3.26 showing the relevant (5,112) plots. The fit was produced with a flat plasma (image

 

2Experimentally, the accelerating potential is read with an analog gauge which is accurate to i
0.5 kV. The accelerating potential used in the calculations, which are sensitive to changes as small
as 0.02 kV, is the one which produces the best fit to the experimental data and is always within the

uncertainty in the experimental accelerating potential.

91

 

0.06 a —
0.04 . —
0.02 - -
o.oo - —

—o.02 - -

 

—0.o4 — —

 

 

—0.06 — L

 

f

I I I I I I
.06 .08 .10 .12 .14 .16 .18

Figure 3.25: Plasma Boundary Shape (with an Image Electrode Voltage of 20 kV)
Which Best Matches the Beam Produced by the 0.010” Slit Chimney.

electrode voltage of 20.0 kV). The computed orbits give an excellent fit to the radial
(5,10) plot of the experimental beam (figure 3.26a), namely they produce a plot with
the same size in s and w, the same curvature, and the same orientation.

The computed orbits match the axial (3,10) plot of the experimental beam to a
lesser extent in that they produce a plot with the same area in (3,112) space (and
therefore also with the same emittance), however, the shape of the beam in axial
(3,212) space does not match. Immediately obvious is the fact that the computed
beam has approximately two times the range of values of s and w meaning that the
computed beam is twice as tall in 2 at the slit and wire probe positions. Also, the
focusing “tails” at the ends of the beam are suppressed and the slope of the computed
beam is steeper than the experimental beam.

Figure 327 shows the effect of changing the image electrode voltage. A more
concave plasma boundary (image electrode of 8 kV) produces a beam that is too

large in the radial s parameter and has little effect on the z plot (improving the fit

92

Chimney: 0.010" lSlit

Arc Curient: 250 (mA) Dee Voltage: 40 (kV)
l

 

 

 

 

 

 

 

 

 

 

1.0
black: 5% max
, . . . iii-253; m
104 - . . .................... - green: 75% max
“102-iii] iiiiii, —
m ......
a) ...............................
.C ..................
8 1-00 ' Imox: 3.9 04A)
3 _ Slit Current: 162. g
3 ' " WIre Current: 129.
0.98 a 4.. ~
0.96 — i . Z .................... —
0.94 I I I
.50 .55 .60 .65 .70
5 (inches)
(a) Radial (s,w) Match
Chimney: 0.010" Slit Arc Current: 250 (mA) Dee Voltage: 40 (kV)
.78.....‘.....‘.....'...,.‘..,
31 block:5xImx
. red: 25% max
, blue: 50% max
7 6 _ _ green: 75% max
E .74 43 -
-C :
E I Imax: 8.8 Out)
v : Slit Current: 165.
g .72 *3 — Wire Current: 102. 8:2;
.70 - -
.68 I I I I
.28 .29 .30 .31 .32 .33

8 (inches)

(b) Axial (5,10) Match

Figure 3.26: Tracked Orbits Which Best Match the 0.010” Slit Chimney

93

 

0.06 -:
0.04 d
0.02 -
0.00 - ,
-0.02 a 1

 

—0.04 -
-0.05 -

 

I

 

 

I I I I I I
.06 .08 .10 .12 .14 .16 .18

(a) More Concave Plasma Boundary: Image Electrode 8 kV

94

Chimney: 0.010" Slit
l

Arc Current: 250 (mA) Dee Voltage: 40 (kV)
l l

 

106
blackzsxmax
red:25%max
blue:50%max
_ - ...... ‘reen: max
104 g 75::
102- ---------- ‘
A
(I)
Q) ......
.8 ............
C1.00—
LI/

  

W

 

 

 

 

 

 

 

 

_ lmax: 8.9 OLA)
Slit Current: 162. ;

Wire Current: 129.

0.94 I I I
.50 .55 .60 .65 .70
s finches)
(b) More Concave Radial Plot: Image Electrode 8 kV
Chimney: 0.010" Slit Arc Current: 250 (mA) Dee Voltage: 40 (kV)
.78. 1111
block: 5% max
_ red: 25% max
- blue: 50% max
76 _ _ green: 75% max
,0? i
q, .74 -. _
I .
8 I lmax: 8.8 (M)
C} I Slit Current: 165.
.72 “I - Wire Current: 102. 1
3 :
.70 - -
.68 I I I I
.28 .29 30 31 .32 .33

Is finches)

(c) More Concave Axial Plot: Image Electrode 8 kV

95

 

0.05 -
0.04 ~
0.02 -
0.00 - ,

—0.02 -

 

-0.o4 - ,5

-0.05 - [.1
I

 

 

 

r I I I I I
.06 .08 .10 .12 .14 .16 .18

((1) More Convex Plasma Boundary: Image Electrode 36 kV

96

Chimney: 0.010" Slit
l

Arc Current: 250 (mA) Dee Voltage: 40 (kV)
l l

 

 

 

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

lmax: 8.9 (uA)
Slit Current: 162. 1
Wire Current: 129.

 

 

 

 

 

 

 

black: 5% max
red: 25% max
blue:

50% max
_ green: 75% max

lmax: 88 05A)
Slit Current: 165. 3
Wire Current: 102.

1.06
1.04 — . . . 1 ................ —
“1.02-Vi'fi'Tfl'w'”""""" ..... —
a) ........................
.c
1:: 1.00 — -
g0.98 — i i . :, _
0.96 — . i I _
0.94 I I I
.50 .55 .60 .65 .70
5 (inches)
(e) More Convex Radial Plot: Image Electrode 36 kV
Chimney: 0.010" Slit Arc Current: 250 (mA) Dee Voltage: 40 (kV)
.78.....',,...'.....'.....'...
.76 -§
§ .74 - —
I .
o
.E 3
g .72 -: _
.70 - -
.68 I I I I
.28 .29 .30 .31 .32 .33
8 (inches)

(f) More Convex Axial Plot: Image Electrode 36 kV

Figure 3.27: Different Plasma Boundaries for the 0.010” Slit Chimney Match

97

Figure 3.25 show the plasma boundary that produced the best match between
calculations and experimental data for the 0.010” (0.25 mm) slit chimney with figure
3.26 showing the relevant (s, 0)) plots. The fit was produced with a flat plasma (image
electrode voltage of 20.0 kV). The computed orbits give an excellent fit to the radial
(3,212) plot of the experimental beam (figure 3.26a), namely they produce a plot with
the same size in s and w, the same curvature, and the same orientation.

The computed orbits match the axial (8,10) plot of the experimental beam to a
lesser extent in that they produce a plot with the same area in (8,7.U) space (and
therefore also with the same emittance), however, the shape of the beam in axial
(5,10) space does not match. Immediately obvious is the fact that the computed
beam has approximately two times the range of values of s and w meaning that the
computed beam is twice as tall in .2 at the slit and wire probe positions. Also, the
focusing “tails” at the ends of the beam are suppressed and the slope of the computed
beam is steeper than the experimental beam.

Figure 3.27 shows the effect of changing the image electrode voltage. A more
concave plasma boundary (image electrode of 8 kV) produces a beam that is too
large in the radial s parameter and has little effect on the z plot (improving the fit
only slightly). A more convex plasma boundary (image electrode 36 kV) produces a
beam that is too small in the radial s parameter and increases the size of the z plot
slightly so that it is less of a match for the experimental beam.

Figure 3.28 shows the plasma boundary that produced the best match between
calculations and experimental data for the 0.020” (0.50 mm) slit chimney with figure
3.29 showing the relevant (3,10) plots. Again, this fit was produced with a flat plasma
(image electrode voltage of 10.0 kV).

The computed orbits match the radial (5,10) plot of the experimental beam in

that they produce a plot with the same size in s and w, and the same curvature.

98

However, the calculated orbits are rotated with respect to the experimental beam.
This rotation has to do with the location of the “crossover” of the beam (see figure
3.30). If the crossover is after the wire probe, parts of the beam with larger 3 values
will also have larger m values producing a positive slope in the (3,211) plots. If the
crossover is before the wire probe, parts of the beam with larger 5 values will have
smaller w values producing a negative slope in the (s, w) plots. If the crossover is
right at the wire, the (3,212) plot will be symmetric. The experimental data shows
evidence that the beam has crossed over before reaching the wire probe. The location
of the crossover of the calculated trajectories can be adjusted by changing the plasma
boundary, but no change in the plasma boundary moved the crossover enough to
match the experimental beam.

Similar to the 0.010” slit case, the computed orbits for the 0.020” slit do not match
the axial (5,211) plots as well as they do the radial (3,112) plots.

Figure 3.31 shows the effect of choosing different plasma temperatures. 10,000 K
(3.35 eV maximum starting energy) appears to be too low a temperature to provide
a reasonable match for the experimental beam while 55,000 K (18.4 eV maximum

starting energy) appears to be too large.

99

 

Fri

 

 

0.05 — -
0.04 " ..
0.02 - 1 ..

0.00 - —

 

—0.02 — -

—0.04 - , _
I
i

—0.05 - —

 

 

 

l

I I I I I I
.06 .08 .10 .12 .14 .16 .18

Figure 3.28: Plasma Boundary Shape (with an Image Electrode Voltage of 10 kV)
Which Best Matches the Beam Produced by the 0.020” Slit Chimney.

100

Chimney: 0.020" Slit Archurrent: 50 (mA)l Dee Voltage: 40 (W)
I I I I

1.06

 

black: 5% max
.............. ._ ..... ......... red: 25% max
104— . .. ... blue: 50; max
green: 75% max

I

1-02‘If1173133151351:SITTEIEEEEC33'§.ff1§§f§:::.3 ”
73100—1.” .11]. 1.18,:1 1::.8882::thfl'ifljlifl —
Q) i.'.:.:;I':Hiiljiiiiii:.':'::I:IZ.:..I:':':1'” ..
8098-131: _ lmax: 11.0 (pA)
C Slit Current: 228. I
3096‘ 21.1 _ WIre Current: 226.
0-94‘Ef'fifffffif. $331213}?

0_92_ :t:: :k::':.

 

 

.35 .40 .45 .50 .55 .60 .65 .70
s(inches)

 

 

(a) Radial (5,111) Match

 

Chimney: 0.020" Slit Arc Current: 50 (mA) Dee Voltage: 40 (kV)
78 _ J l l 1

black: 5% max

:353533333135333155:E:3 "gnaw,
,76-E::::::::::;::::-:::::t -9

.74 {I

lmax: 9.2
Slit Current: 260.
- Wire Current: 132. GM)

w (inches)

.72 —§

.70 -

 

 

 

.68

 

T I I I
.28 .29 .30 .31 .32 .33
5 (inches)

(b) Axial (s,w) Match

Figure 3.29: Tracked Orbits Which Best Match the 0.020” Slit Chimneys

101

 

f e
e. .-
.. _ -
'e 'e
‘ _.I
.8. ‘ .e
._ - '.
- I ' L.
8. .
o
e
o
e
o
.
e

 

 

\

CIOSSOVGI‘

 

Figure 3.30: The beam crosses over itself twice, once just after exiting the chimney
and again approximately 180 degrees downstream.

102

Chimney: 0.020" Slit Arc Current: 50 (mA) Dee Voltage: 40 (kV)
I I I I l l

106

 

black: 5% max

.. .. . red:25%max

1.04 .. ., Mumsox max
,, green:75%max

l

1.02—-;a:$232,229;213135.32:22;a?:21::::3:25:§:2:?3§‘-§ifa;; —
73100-:7: ”[11,.'i'Tiii’TIZliiEiIIL'iiLZIl."":ZII:IIiEZEE.Ii:l —

lmax: 11.0 04A)
Slit Current: 228.
_ Wire Current: 226.

E098-2;:222122352:2122,z;;: 332;:zi322i1:;-;:;;:~ 4411441

:0_95_i:131;:..;::1 ._
0.94—222%;:zéiéfzzxézzlzzzf93:21:i.e::ziis‘évvtr'
0.924)....” , ,

 

 

 

 

(190 .i.,Hg.xhgu-hwiuflnuiimrh{i.mir
.35 .40 .45 .50 .55 .60 .65 .70
s finches)

(3.) Radial (s,w) plot with 10,000 K

Chimney: 0.020" Slit Age Current: 5'0 (mA) Deel Voltage: 40 (kV)

.78

 

black:5%max
red:25%max
If.::::':::::::'::::::: bbezsoxmax
.76—fii::::::;:::'::::"" —9'

.74 —§

lmax: 9.2
Slit Current: 260.
— Wire Current: 132. OLA)

w finches)

.72 -§

.70-

 

 

 

.68

 

I I I I
.28 .29 .30 .31 .32 .33
s finches)

(b) Axial (s,w) plot with 10,000 K

103

1.06

Chimney: 0.020" Slit
I I

Arc Current: 50 (mA) Dee Voltage: 40 (kV)
I I I I

 

104—;.““

1_02_: :': :5; .1. :.":. ::':::...: 11.1:

731.00—I::i.i':lii,'l..f'l':"CLI.iIiIfif: T’

5 .
20.98--

3095s;jfu~'

0.94—91 1

092 "

 

 

black: 5% max
red: 25% max
blue: 50% max
green: 75% max

lmax: 11.0 (ILA)
Slit Current: 228.
_ Wire Current: 225.

 

0.90
.3

I I I
5 .40 .45 .50

55

5 (inches)

(c) Radial (s, w) plot with 55,000 K

I“ I
.60

.65

Chimney: 0.0l20" Slit Age Current: 50 (mA) Deel Voltage: 40 (kV)
I

.70

 

 

w (inches)

.70 -

.76 —§
.74 —§

.72 -§

 

.68

 

black: 5% max

_ green: 75% max

knax: 9.2
Slit Current: 260.
1- Wire Current: 132. 0M)

 

 

.2

I I
8 .29 .30

I
.31

l

.32

.33

5 (inches)

(d) Axial (3,111) plot with 55,000 K

Figure 3.31: Different Plasma Temperatures for the 0.020” Slit Chimney Match

104

Chimney: 0.020" Slit Arc Current: 50 (mA) Dee Voltage: 40 (W)
l I I

 

 

 

 

 

100
black: 5% max
red: 25% max
blue: 50% max
green: 75% max
50 - -
:6 90.2% emittance:
8 182.2 mm-mrod
O - — . . .
\E/ normallzed emIttance.
N 1.190 mm—mrad
8
_50 ._ _
—4 —2 O 2 41
2 (mm)

Figure 3.32: Axial Emittance Plot Comparing Calculations to Experiment for the
0.020” Slit Chimneys

Axial Focusing in the Source-Puller Region

For a better understanding of the mismatch in 2 between the calculated orbits and the
experimental beam, it is helpful to look at a z emittance plot. Figure 3.32 shows the
same data as figure 3.29b but now plotted with a, versus .2 (as explained in section
3.1.4). We see that the experimental data (contours) have a general negative slope
such that rays that cross the slit with positive 2. tend to have a negative angle 0; and
rays that cross the slit with negative 2 tend to have positive angles. This represents a
converging, or focused beam. The computational data (blue dots) have the opposite
behavior showing a general defocusing trend. Also, the “tails” at the ends of the
beam which are a result of the focusing electric field at the top and bottom of the
source slit are less pronounced in the computed data. Overall, the experimental beam
is more strongly focused than the computed trajectories.

Figure 3.33 shows tracked orbits starting on the plasma boundary with z and pz

105

 

chimney

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l puller top

 

 

 

 

 

 

:4.- ............ » ..
c. ..... e- nd'.'b“'_"F.-.C-~e ...... ........
"' 'l' ' '-'- -- ...................... In": ''''''''''' .‘s'e.e.-.
""""""" '1""""" 1 .eeeopeoe..........
‘II 8‘ ..... bee I n IIIIIII
""" CII" FOO-O-QO-ee eleee-eeeeeeeeeeeel
O eeeee 1 ..... .....I. q Iiee eeeeeeeeeeeeeeeeeee
cg eeeee I. ....... .1.. ...................
..... (nelson-econ. IO‘IO eeeee-eeeeeeeeeeeee
O IIIII 4 OOOOO Fl 0 IIIIII .l.‘.. e) eeeeeeeeeeeeeeeeeee
..... (eeeeeh ..p- ...(.. ne-e-e-o-eee-eoe-I-
.1 lllll be cube e . e+eo ) eeeeeeeeeeeeeeeeeee
e ed eeeee b e-Ieo o e at e e)e eeeeeeeeeeeeeee
..... {en-eehoeewe eeele )eeoeeIe-eeeeeeeeeee-
eeeee de-eeepeeebe noel. leeoeealoeeeeeeeeeel
0‘!
p
z e ‘. I, ...
. 3|.I" .
111:2..aI--=31
A-1181---aa. IL.’
EI'I..""""'IIIIIIII"IIIll000' """ 1'?‘ - o
..l,-.... «- ' e . . .
.:5;:._|:|";;l.l| g:::::::=:g; 2 :;‘:l o. . .
'.'-. '. I: 0.. . .u : ' .
I..- .'..'- ...... 'e. 1“ ' ‘ . ' . I
ate. I. .- ‘e. .. . e .
n.. e e. O ' '
’u o. . .
O'e .. .
. .....
- . """""""
I I .
. e
I o
O ...
"""""""
e
.... eee' e
e e
O

 

 

Figure 3.33: z and 192 in the Source-Puller Region

106

 

graphed with respect to r 3. (15 orbits, each above the median plane, are shown.)
The z vs. r plot show the overall behavior, the top few rays are initially focused
before returning to a roughly horizontal trajectory. The central rays appear to travel
horizontally through the source to puller region with little focusing or defocusing.
The pz vs. 7‘ plot is more sensitive to small deviations from a horizontal path showing
that all the rays, even those close to the median plane, move toward negative pz values
while exiting the chimney. Since the rays are above the median plane, negative pz
denotes a focused beam, and in the region close to the chimney, the beam is becoming
increasingly focused. About half way between the chimney and the puller, the focusing
effect of the electric field reverses and the pz values move back toward zero i.e. the
trajectories are returning toward horizontal. By the time the beam enters the puller,
most of the rays have reached positive 19,, indicating that they are now diverging or
defocused. For the majority of the beam (11 out of 15 rays shown) the defocusing
effect from the puller is stronger than the focusing from the chimney resulting in a
positive p3.

The above analysis holds for the computed orbits, but we know from the exper-
imental data that the real beam is converging (focused) by the time it reaches the
slit probe. The computational model either underestimates the focusing of the beam
near the chimney or overestimates the defocusing of the beam as it enters the puller.

It is not clear at this point why this discrepancy exists.

3.3.2 Hole Source

For the hole chimney calculations a total of 528,220 rays were tracked. There are 961

possible different starting positions for the ions inside the chimney opening (31x31 in

 

3Here 1' refers to the distance from the center of the chimney, not the center of the orbit as in

section 3.1.3.

107

a 0.047” square grid) of which 539 lie within the 0.047” (1.19 mm) diameter source
opening. 49 different starting angles were tracked from each starting position 7 an-
gles in the median plane (covering 103 degrees), 7 different starting angles vertically
(covering 103 degrees). 20 different rays were tracked for each combination of start-
ing position and starting angle; five different starting energies representing a plasma
temperature of 35,000 K and 4 different accelerating voltages (17.3:I:0.03 kV in equal
steps). Orbits which came into contact with the chimney before exiting the chimney
opening were dropped as were orbits which hit the puller.

Figure 3.34 shows the plasma boundary which produced the best fit between
computed orbits and experimental measurement for the Harper style chimney with
figure 3.35 showing the relevant (3,212) plots. The best match between computed orbits
and experimental data was achieved by using a highly concave plasma boundary; an
image electrode voltage of 600 V was used. This plasma boundary produced strong
over focusing between the chimney and the puller.

The computed rays match the experimental data well for the radial plots. The
shape of the beam when plotted in (3,211) space is the same for experimental and
computed data. Similar to the case with the 0.020” slit chimney, the experimental
and calculated plots differ by a rotation indicating the the crossover point is for the
calculated rays is not the same as the experimental beam.

The experimental and calculated axial plots are both a straight line with wire
parameter w increasing linearly with slit parameter s. The slope of the beam in
(s, w) space is not identical indicating that the calculated orbits are diverging faster

than the experimental beam.

108

 

0.06 ..

0.04 -

0.02 -

...—”M.“

0.00 - 1 -
—0.02 a —

—0.04 - -

 

 

—0.06 - —
/

 

r

I I I I I I
.06 .08 .10 .12 .14 .16 .18

Figure 3.34: Plasma Boundary Shape (with an Image Electrode Voltage of 0.6 kV)
Which Best Matches the Beam Produced by the 0.047” Hole Chimney.

109

w (inches)

w (inches)

.82

Chimney: 0.047" Hole Arc Current: 50 (mA)
I I I I

 

.94_ .1.;34'3-913'5-3 .. _. . ._
.92.‘ If:
.90- 1
.88- ;

 
  
  

 

 

'\I
00

I I

—I

 

.4 .
5 (inches)

(a) Radial (5,112) Data

 

.80 -

.78 —

.76 -

.74 -

 

 

 

.—

 

     

 

l

1 1 VI2 1 I
.29 .30 .31

5 (inches)

(b) Axial (s,w) Data

.32

Dee Voltage: 20 (kV)
I

block: 5% max
red: 25% max
blue: 50% max
green: 75% max

knax: 1.4 )
Slit Current: 268.
Wire Current: 86.

Chimney: 0.0147" Hole Arlc Current: 5'0 (mA) Deel Voltage: 201(kV)

black: 5% max
red: 25% max
blue: 50% max

green: 75% max

' lmax: 5.4
Slit Current: 243.

Wire erent: 116. OLA)

Figure 3.35: Tracked Orbits Which Match the Hole Chimney

110

Chapter 4

Conclusion

Characterizing the Cold Cathode PIG Ion Source

The construction of the Ion Source Test Stand at the NSCL has allowed us to measure
the radial and axial emittance and luminosity of a cold cathode PIG internal ion
source under dc extraction. To the best of our knowledge, these are the first such
measurements made on a cold cathode ion source. (Measurements for filament style
internal ion sources were reported by Mallory in 1966.)

The slit chimneys produced a beam that was nearly horizontal (in z) and was,
on average 70% as tall as the chimney opening after passing through the puller. The
hole chimney produced a beam that (in the absence of strong focusing) diverged in
z.

A general trend of increasing accelerated current (and luminosity) with increasing

A

c1712 —-sr

 

arc current was observed. The maximum measured luminosity of 7.1 was
obtained with the 0.010” (0.25 mm) slit chimney running at an arc current of 450
mA and a gas flow rate of 3.0 cc/min (at STP). Higher luminosities would likely

have been possible with the 0.020” slit chimney had we been able to run it at similar

arc currents, but the accelerated current of 590 LA with a 40 kV puller voltage

111

and 150 mA arc current were considered to be near the cooling limit of the test
stand apparatus. The 0.047” “hole” chimney (the style used in the Harper Medical
Cyclotron) produced a deuteron beam of over 700 [.LA with a puller voltage of 20 kV
and arc current of 250 mA.

For the 0.010” slit chimney producing currents ranging from 52 to 227 “A, the
emittance of the beam did not change significantly as the arc current (and hence
the beam current) was increased. For the 0.020” slit chimney producing currents
ranging from 230 to 590 MA increasing the beam current by 160% increased the
radial emittance by 38% and the axial emittance by 25%. The emittance growth
is evidence that either the shape of the plasma boundary changes with increasing
current, or that increased space charge forces are causing the emittance of the beam

to grow,

Matching Experimental Beams With “Single Particle” Orbit Tracking

With appropriate initial conditions, the orbit tracking code Z3CYCLONE is able to
predict to good accuracy the beam produced by the cold cathode PIG ion source.
Starting orbit tracking on the so called “plasma boundary,” (the zero volt equipo-
tential that crosses the opening in the chimney) we were able to produce sets of
calculated orbits which matched the radial emittance of the experimental beam very
well, while somewhat underestimating the axial focusing of the beam between the
source and the puller. Designing a cyclotron with an aperture adequate to accept the
calculated beam therefore represents a conservative approach.

In each case presented in this study, a plasma temperature of approximately 35,000
K (resulting in a maximum energies for calculated trajectories of about 12 eV) pro-
vided the best agreement with experimental beams.

No general rule was found for choosing an image electrode voltage (i.e. plasma

112

boundary shape) which would best match the experimental beam for all chimneys.
For the slit chimneys, an approximately fiat plasma provided the best match for the
radial emittance of the experimental beam while somewhat over estimating the size
of the beam in z, and for the chimney with a 0.047” diameter hole a highly concave
plasma was found to provide the best match. (The beam produced by an internal
ion source clearly depends strongly on the shape of the opening in the chimney;
and the appropriate starting conditions for each new chimney design will need to be

determined experimentally.)

Future Work

Because the beam extracted from the ion source is strongly dependant on the shape
and size of the opening in the chimney, it may be possible to observe significant gains
in luminosity by optimizing this shape. In particular, gains in luminosity were seen
when moving from a 0.010” (0.25 mm) slit to a 0.020” (0.50 mm) slit, a natural
choice would be to try even wider slits. The depth and angle of the chamfer can also
be further optimized. The chamfer in both of the slit chimneys tested was 10° (a
value which was used based on the results of the 0°, 10° and 20° used in Mallory’s
studies with a filament source), however further optimization of this angle for cold
cathode ion sources may be possible and should be explored. Finally, the chamfer for
both chimneys was 0.010” deep (out of a 0.020” thick chimney wall) leaving a 0.010”
deep “tunnel” which may not be optimal, especially for the more narrow 0.010” slit.
Increasing the depth of the chamfer may allow higher beam currents from the source.

When a plasma is confined in a magnetic field it may be appropriate to model
the plasma as having two different temperatures T" and Ti representing two different
Maxwellian distributions for the components of velocity parallel and perpendicular

to the magnetic field.[22]. This dual temperature modeling of the plasma may allow

113

for a better match between the experimental beam and calculated orbits.

The fact that increasing the beam current resulted in an increase in emittance of
the beam produced by the 0.020” (0.50 mm) wide slit chimney indicates that space
charge may Ilc ve an effect on the beam in the region between the chimney and the
puller. While the results presented in this dissertation indicate that single particle
codes are sufficient for cyclotron design studies, higher quality matches between cal-
culated and experimental beams may be possible with an orbit tracking code which
takes space charge into effect. Development of such a code or adaptation of existing
space charge codes to orbit tracking in the central region of a cyclotron would test

this hypothesis.

114

Appendix A

Ion Source Test Stand Operation
hflanual

Updated July 2004

A. 1 Safety Procedures

A.1.1 High Voltage Operating Procedure

1. Introduction
This document describes a procedure to be followed by personnel accessing
exposed high voltage equipment inside the safety cage in the N1 vault.

2. Authorized Personnel

No one should access the inside of a high voltage cage who is not authorized to
work on the system. Authorized personnel include Ted Forringer Henry Blosser
and Malay Dey. Please contact one of these if you need access to this high
voltage cage.

3. Steps to Activate High Voltage System:

(a) Close the cage door, and insert the key into the interlock device.
(b) Check that the cage is secure.

(c) 'Ihrn on the high voltage supply.

(d) Set high voltage as needed.

115

4. Steps to Turn OFF the High Voltage System:

(a) ”Dial down” high voltage supply so that the set point is O K V.
(b) Turn off high voltage supply.
(c) Open cage, tripping safety interlock switch.

(d) Before contacting any surface, use the shorting hook to discharge any
possible high voltages, noting the result as follows: Touch the tip of the
grounded hook to all major metal surfaces, including the high voltage feed
connection. If a spark is noticed while doing this, there is a safety problem
that must be repaired. If a spark is noticed each time the hook touches a
surface beyond the first time, the high voltage may still be on!

MAKE SURE OTHER MEANS ARE USED TO REMOVE HIGH VOLT-
AGE FROM THE APPARATUS BEFORE CONTACTING ANY SUR-
FACE!

Leave the shorting hook connected to the apparatus if possible.

(e) The system is now safe.

A.1.2 Raising the Cap

Authorized personnel only may raise this magnet cap or work inside this magnet. If
access to inside of magnet is needed, contact Ted Forringer, Henry Blosser, Malay
Dey or Gunter Stork.

1. Open the high voltage cage.

(a) Follow the procedure for opening cage.

(b) Maintain visual control of cage to ensure HV will remain off while working
inside the magnet.

2. Vent the magnet (follow the procedure in section A3).

3. Ensure magnet power supply is off.

2‘3

Undo magnet current and interlock connectors (between top and bottom).
Disconnect water and are supply from top half of the source.
Disconnect arc supply from the bottom half of the source.

Remove upper source tray.

poses”

Crank first three turns by hand.

116

A.1.3 Working on top of the Magnet

Authorized personnel only may work on top of this magnet. If access to top of magnet
is needed, contact Ted Forringer, Henry Blosser, Malay Dey. or Gunter Stork.

1. Open the high voltage cage.

(a) Follow procedure for opening cage.

(b) Maintain visual control of cage to ensure HV will remain off while working
on top of magnet.

2. Remove all loose items (tools etc.) from top of magnet when work is finished.

A.2 Running a Beam

u

   
 
  
 

Ion Gauge

'1 Thermocouple Gauges
Roughing Line
Main Vacuum

Turbo Controllers

Upper
Lower

A.2.1 Pump down the vacuum

1. Close the magnet and all valves.

[0

. Open the hydrogen/ deuterium gas supply valve on the lower source.

. Turn on the flow meter and set to less than 0.1 cc/ min.

39-03

Start rough pumping, by plugging in the roughing pump.

9"

Turn on the thermocouple gauges. Wait until both TC gauges read between
100 and 300 mTorr before turning on turbo-pumps.

03

. Turn on both turbo pumps.

.‘1

When both TC gauges read ”zero” pressure (pegged to left of scale) turn on
the Ion Gauge. Vacuum should reach better than 2:1:10‘5 with 1.0 cc/min gas
flow, or 8:510‘6 with gas valve closed. Expect 4 to 6 hours of pumping for a
good vacuum.

117

 

Turn on the magnet

1.

2.

Check that the orange cable and the interlock cable connecting the upper and
lower magnet coils are attached.

The magnet power supply is the approximately 3 x 3 x 2 foot black and tan
crate in the North East corner of the vault. Ensure that the circuit breaker is
in the “on” position.

The power supply is named SRCTSTMAG and can be accessed from the PLCApp
or ArcNet MDI 32.

Turn on the high voltage

1.
2.

Follow the procedure listed in the safety section.

The dee voltage power supply is the Spellman 100KV supply on the electronics
rack on the north side of the vault.

. The voltage is controlled with a hand held “battery box.” The switch on the

box should be set to ( - ) “negative.”

. If the deuteron puller is being used, set the puller voltage to 20 KV.
. If the proton puller is being used, set the puller voltage to 40 KV.

. Wait for sparking to stop before turning on source. This should take less than

one minute if the test stand has been run recently.

Turn on the source

1.
2.

3.

The power supply is the tan Glassman 3KV supply in the electronics rack.
Follow this checklist before turning on the source.

(a) Double check vacuum is below 7X 10‘6 Torr.

(b) Double check that all five water lines are connected; two sets for each
source, plus one going into the high voltage cage.

(c) Double check that the magnet is on.

(d) Double check that the gas (hydrogen or deuterium) is flowing at 0.5 to 6.0
cc / min.

(8) Double check that the dee voltage is on and has stopped sparking.
Set the current limit for the are before turning the supply on.

(a) 50 mA - gives a very stable ”low current” beam.

(b) 250 mA - the standard testing mode - higher current.

118

I

 

(c) 450 mA - maximum current mode (may overheat dee if run for long periods
of time).

4. Press the green “on” button.

5. The dee will start sparking again. Wait until these sparks are less frequent than
about 10per minute. Less sparks will result in better data.

6. The source is working correctly, and the beam is being accelerated if:

(a) The current read on the arc power supply is equal to the set point.
(
(c) The red light above the current set knob is on.
(d) The red light above the voltage set knob is off.

b) The voltage read on the arc power supply is between 1.0 and 2.7 KV.

(e) There is a purple/ red glow coming from the chimney.
7. Common problems:

(a) Voltage reads 3KV and current reads zero. “Open Circuit.” Check that
both arc supply leads are plugged into the sources.

(b) Voltage reads 3KV and current reads below set point. “Arc not struck.”

i. Increase gas flow.
ii. Decrease cathode/ anode gap.
iii. Replace cathode.

(c) Current reads at set point, voltage is unusually low, no glow from chimney.
Short circuit: clean anode, possibly replace cathode.

(d) The red light above the voltage knob is on and the red light above the
current knob is off. “Bad arc.” Current is probably being “pulsed.” This
is not desirable, but it is still possible to take data. Try increasing gas
supply or decreasing cathode/ puller gap.

119

A.2.2 Probes, BCM and Software

There are five devices associated with this experiment that can be accessed from the
computers.

1.
2.

SRCTSTMAG - the airport magnet power supply. Read only.

NlPRBE and NlPRBW the motor controls for the probes. E (east) is the wire
probe. W (west) is the slit probe. These can be set and read.

NlBCME and NIBCMW the beam current monitors. E is the wire and W is
the slit. Read only.

Programs for accessing these devices:

1.

ArcNet MDI 32 (anetmd32.exe): This program can read and set devices. It is
useful for moving the probes or reading the magnet current.

Chart Recorded 32 (bcmchart.chr): This program plots the output of any device
as a function of time. This is useful for monitoring the progress of a run.

BCM program (NlBCM.mt2). This program is used to talk to the beam current
monitor. At the very least it must be used to turn on (init) each channel. If the
beam current suddenly goes to zero during a run, you will need to INIT both
channels again.

Sequencer: This program is the main control program for taking data. It reads
an input file and sets the desired position for the probes. It then writes an
output file with the probe position and current readings.

A.2.3 Steps for taking data once the source is on.

1.

Check that BCM is turned on. A green flashing light on the back of the box
tells you that it is working. Also, the Ethernet to fiber (small box) should be
on.

. Go back to you computer. Open the BCM program and initialize both channels.

Channel one is the wire; channel two is the slit.
Open the chart recorder and set the ranges to appropriate values.
Open the Sequencer program

(a) Choose an input file this file will have a list of commands telling the se-
quencer where to place the probes.

(b) Choose an output file Sequencer will write the data to this file.
(c) Press start.

(d) Watch the chart recorder to make sure everything is going correctly. You
should be able to monitor the motion of the probes, the total current
hitting the slit, and the current hitting the wire. Slit current should be
relatively constant, while the wire current will show intermittent peeks.

120

A.3 Shutting Down

1. If you are going to stop taking measurements for several hours, but will be back
the same day:

(a) Turn off the arc supply. The cathodes have a limited lifetime. Turning off
the arc current will prevent the cathode from being wasted.

(b) Turn off the dee voltage battery box (the box that sets the voltage level).
There is no need to waste the battery, and there it is safer to turn off the
high voltage when not in use.

2. If you are leaving for the day, but expect to continue taking data tomorrow: Do
everything above plus:

(a) Turn down the gas flow until the flow meter reads negative. This will stop
the gas from flowing.

(b) If you do not need the magnetic field to remain constant, it is a good idea
to turn off the magnet. If you are going to use the same magnetic field
in your data tomorrow, it is OK to leave the magnet power supply on
overnight.

3. If you are done taking data for several days: Do everything above plus:

(a) Disconnect the power from the gas flow meter.
(b) Close the valve on the gas bottle.
(c) Turn off both turbo pumps. There is no need to turn off the roughing
pump unless you are venting the magnet.
4. If you need to do maintenance inside the magnet or are shutting down for an
extended period of time:
Do everything above plus:
Vent the magnet.

The important thing here is not to damage the turbo pumps. Venting too
quickly or causing a high pressure on the back of the turbo can damage the
pump. Do not open any valves quickly or stop the roughing pump until both
turbos have stopped spinning.

(a) Turn off the turbo pumps.

(b) There is a valve on each half of the ion source.

(c) Open the valve slowly until you see the pressure on the TC gauge start to
rise, and then close the valve again.

((1) Wait 3 to 5 minutes for the turbos to pump out all the air you just allowed
into the vacuum chamber. This pumping will slow the turbos down.

121

(6) Repeat steps 2, 3 and 4 several times until the turbo pumps have stopped
spinning. You can tell they have stopped by placing you hand on the pump,
if you do not feel any vibration the turbo pump has stopped spinning.

(f) You can now close the valve for the roughng pump and open the vent
valve to let air back into the magnet.

A.4 Maintenance Procedures

Track

Latches

Stop Latch

Clamp Out Latch

Clamp in Latch

Two vacuum lock latches

Valves:

Turbo pumping valve

Main ball valve (red Handle)
Vent valve (black handle)

 

A.4.1 Removing a source without venting the magnet

The most important thing to keep in mind when removing a source is that we need
to protect the turbo pumps from any sudden rush of air. A quick increase in pressure
in the vacuum chamber can break the turbo pumps. Therefore, it is important to
keep in mind whether or not there is air in the source. and whether or not the source
is completely isolated from the rest of the vacuum chamber.

1. Turn off arc and puller voltages.
2. If the track has been removed, reinstall it before removing the source.

3. Disconnect the water and power from the source.

122

 

10.
11.
12.

. Close the turbo pumping valve.
. Release the clamp in latch.

. Slide the source out of the magnet until it reaches the stop latch.

Clamp the source into the out position with the clamp out latch.

. Close the main ball valve Now the source is completely isolated from the rest

of the vacuum, and, importantly, the turbo pumps.

. Open the vent valve to allow air to come into the source.

Disconnect the turbo pumping valve from the source.
Release the two vacuum lock latches.

Slide the vacuum lock away from the magnet and release the source.

A.4.2 Replacing a cathode.

1.

Remove the source, if you do not want to break vacuum, be sure to correctly
follow the preceding procedure.

Unscrew the four screws that hold the anode to the end of the source.

. Use needle nose pliers to unscrew the cathode from the source.

. If the cathode can be reused at a different angle, add or remove .005 inch copper

washers so that the cathode will be realigned with a clean spot below the hole
in the anode. If the cathode cannot be reused, get a new one.

. Screw the cathode back on as tightly as possible. If the cathode is not rotated

to the position you want when it is tight, add or remove washers, do not settle
for a loose cathode.

. The cathode anode gap should be between .5 and 2 mm

A.4.3 Retuning the source Without breaking vacuum.

1.
2.

Place the source on the track, and latch it in the out position.

Slide the vacuum lock against the main ball valve and latch it in place.

. Attach the turbo pump valve to the source, but DO NOT OPEN IT.

. There is air in the source, we do not want this air to get into the main vacuum,

so we must pump it out. Attach a small pump to the vent valve and pump all
the air out of ion source. If you are replacing the lower source, the gas flow
should be ON at this point. The flow should be 0.1 cc/ min or less.

123

 

5. Using one of the thermal couple gauges, wait until the pressure in the source is
less than 20 mTorr.

6. Close the vent valve (removing the small pump from the system) and then open
the main ball valve (opening the source to the main magnet).

7. Open the turbo pump valve.
8. Slide the source into the in position.
9. Clamp the source in.

10. Connect water and power.

11. You may have to wait 30 minutes or so for the vacuum to recover before running
the source.

A.5 Contacts

0 For any problems you can contact Ted Forringer.

TedForringer©letuedu
(903) 233-3959 work
(903) 553-9641 home

0 For problems with the beam current monitor and the probe drive motors or
controllers, contact Kelly Davidson or John Priller

e For problems with the Sequencer program (or other software) contact Mark
Davis.

0 For problems with the magnet power supply contact Dan Scott or John Brandon
0 For mechanical problems with dee, water cooling etc, contact Gunter Stork.

o For questions about using the vacuum systems, contact Dave Sanderson or Andy
Thulin

o For problems with the source (maintenance etc.) contact Emmanuel Blosser at
Harper Hospital

(313) 745-2313 work
1—888—442-1334 voice pager

124

Appendix B

Approximating a
Maxwell-Boltzmann Distribution
of Starting Energies

The fraction of particles (F) whose kinetic energy falls in the range E1 to E2 is given
by the l\-’Iaxwell-Boltzmann distribution [21, p 707]:

52
F = A Ee‘E/deE (3.1)
E1
where A is a normalization constant, k is the Boltzmann constant (8.617x10‘5 eV/ K),
and T is the temperature in kelvin. Expressing kinetic energy in units of kT, c =
E / kT, the equation can be re—written:

F = /62 e 6—6 dc (B2)

which is normalized such that [6” 6 6“3 dc = 1. To approximate this distribution
with discrete energy levels, each energy level should represent an equal number of
particles. Figure 8.1 shows the energy density function divided into five equal areas
(equal fractions of particles) with the value of e that best represents each area marked
with an ‘X.’

For the general case, with N energy levels 6,, (n = 1, 2, ...N):

6n 2n—1
“d = B.
[0 cc 6 2N ( 3)

 

Integration by parts leads to

2n — 1
2N

which is a transcendental equation that does not have an obvious general solution for
en, however, solutions for various values of N and n are given in table 8.1. For the
comparisons between calculated trajectories and experimental data in section 3.3 we
use five energy levels to represent the energy distribution.

(€n+1)€—E" =1—

 

(3.4)

125

 

 

  
  
    

 

L l l l
m.4- ~
.9
U
...:
0.3- _
O.
“—
O
>‘2- l—
J‘:
In
C
I)

 

4 6
E/kT (unitless)

Figure 8.1: Maxwell—Boltzmann Distribution of Particle Energies

 

 

1 2 3 4 5
0.73 1.68 3.24 x x
0.61 1.31 2.12 3.61 x

0.53 1.10 1.68 2.44 3.89 x
0.48 0.96 1.42 1.96 2.69 4.12
0.44 0.86 1.25 1.68 2.19 2.90 4.31

ll
><><ou

7
x
x
x
x

 

 

ZZZZZ”
ll
Nomads

 

 

Table B.1: Discrete Energies (in units of kT) to Represent a Maxwell-Boltzmann
Distribution.

126

 

LIST OF REFERENCES

[1] Gammino, S. et al.. ‘Effects of Frequency and Magnetic Field Scaling on the
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[2] Zavodszky, P et al. ‘Emittance Studies of the ARTEMIS ERC Ion Source’ Proc.
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[3] Jongen, Y. ‘The Cyclone 30, a 30 MeV, High Intensity H ' Cyclotron for Ra-
dioisotope production.’ 7th Conference on Applied Accelerators, St. Petersburg,
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[4] Bennett, J. R. J. ‘Review of PIG Sources for Multiply Charged Heavy Ions.’
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[5] Livingston, Robert S. and Royce J. Jones. ‘High Intensity Ion Source for Cy-
clotrons.’ Rev. Sci. Inst. 25, 6, (1953)

[6] Mallory, Merrit Lee Phase Space Density Studies on Cyclotron Ion Sources,
Ph.D. Thesis, Michigan State University, 1966.

[7] Antaya, T. A. et al. . ‘Operating Experience with an Ion Source in a Supercon-
ducting Cyclotron.’ IEEE Nuc. Sci. NS-30. #4, (1983) 2716

[8] Blosser, H. G. et al. . Compact Superconduction Cyclotron for Neutron Therapy,
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[9] Schillo, M. et al. Compact Superconducting 250 MeV Proton Cyclotron for the
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[10] http : //p-therapie . web . psi. ch/proscan.htm1

[11] Schubert, Jeffery R. Extending the Feasibility Boundary of the Isochronous Cy-
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[12] Goldstein, Poole and Safko Classical Mechanics 3rd ed. Addison Wesley, San
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127

 

 

[13] http : //www . triumf . ca/compserv/relax3d . html
[14] Lynn, Y. Ernest Lawrence’s Cyclotron: Invention for the Ages.
[15] Blosser, H. G. Physics 961 Lecture Notes, (1971).

[16] Stockli, Martin P. et al. ‘Accurate Estimation of the RMS Emittance from Single
Current Amplifier Data’ Spallation Neutron Source Conf. AP 80, (2002)

[17] Pozdeyev, Eduard. ‘A New Code for Simulation of Space Charge Effects
in Isochrounous Cyclotrons’, National Superconducting Cyclotron Laboratory.
1999.

[18] Edwards, D. A. and M. J. Syphers An Introduction to the Physics of High
Energy Accelerators John Wiley & Sons, Inc. 1993. pp 78-83

[19] TOSCA, Vector FIelds Inc., England.

[20] Gruber, Peter ‘Normalized Emittance in the Case of Large Momentum Spreads’
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[21] Young, H. and R. Freedman University Physics 11th ed. Addison Wesley, San
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[22] Chen, Francis F. Plasma Physics and Controlled Fusion, 2nd ed. Planum Press,
New York, NY. 1985.

128

 

   

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