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This is to certify that the

dissertation entitled
THE EFFECT OF SPACE CHARGE FORCE (N BEADS
EXTRACIED FRa‘d EIIR ICN SOURCES

presented by
Zu Qi Xie

has been accepted towards fulfillment
of the requirements for

21; D. degree in Bhysms_'

M fr’ WrfiJ—

Major profess?

Date A119 31’ 1989

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

 

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Michigan State
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THE EFFECT OF SPACE CHARGE FORCE ON BEAMS

EXTRACTED FROM ECR ION SOURCES

by
Zu Qi Xie

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
1989

\J

7 .

‘ 2

C) '.

«f7 "‘

(c 05

ABSTRACT

THE EFFECT OF SPACE CHARGE FORCE ON BEAMS

EXTRACTED FROM ECR ION SOURCES

by
Zu Qi Xie

A new 3 dimensional ray tracing code BEAM_3D, with a simple model
to calculate the space charge force of multiple ion species, is under
development and serves as a theoretical tool to study the ECRIS beam
formation. Excellent agreement between the BEAM_BD calculations and
beam profile and emittance measurements of the total extracted helium
1+ beam from the RTECR ion source was obtained when a low degree of
beam neutralization was assumed in the calculations. The experimental
evidence indicates that the positive space charge effects dominate the
early RTECR ion source beam formation and beamline optics matching
process. A review of important beam characteristics is made,
including a conceptual model for the space charge beam blow up.
Better beam transport through the RTECR beamline analysis magnet has
resulted after an extraction geometry modification in which the space
charge force was more correctly matched. This work involved the

development of an online beam characteristic measuring apparatus which

will also be described.

ACKNOWLEDGMENTS

I wish to thank the staff and faculty of the National
Superconducting Cyclotron Laboratory for their support of my education
and the completion of this dissertation. First and foremost, I owe my
deepest gratitude to my thesis advisor Dr. Timothy Antaya for his
guidance, supervision and friendship during the fOur years that I have
worked with him, without his help, this thesis would be all blank
pages. Second, I would like to specially thank Professor Jerry Nolen,
for his guidance in my early graduate career and the freedom he gave
me to work on ECR Ion Source to pursue my academic interests. In
addition, I wish to thank Dr. Thomas Kuo for his encouragement and the
friendship we shared over the past years, and Dr. G. Mank for
performing the 6108 calculations used in Chapter 5 of this thesis.

Finally I am greatly indebted to my wife Li Su, for her love,
patience and encouragement to make it through.

I am also very grateful to Michigan State University and the
National Science Foundation for the financial support during my

graduate study.

ii

LIST OF

LIST OF

Chapter
1.1
1.2
1.3
Chapter
2.1
2.2
2.3
Chapter
3.1
3.2
3.3
Chapter
4.1

4.2

4.3
4.4
Chapter
5.1

5.2

TABLE OF CONTENTS

TABLES.. .................................................
FIGURES ..................................................
1 - Introduction .........................................
Motivation. .............................................

RTECR Source and Its Beam Analysis System ...............

He Beam Technique .......................................

2 - The BEAM_3D Code .....................................
Motivation ..............................................

General Organization ....................................

Special Features ........................................

3 - Emittance Measuring Apparatus ........................
Theoretical Review of Emittance Measurements ............

Online Slit-Wire Scanner ................................

Kapton Camera ...........................................

4 - Extraction Geometry Study ............................
Motivation ..............................................

Theoretical Review ......................................

4.2.1 Equations of Motion ...............................
4.2.2 Effects of Ion Temperature, Magnetic Field and Q/M
Ratio on Beam Emittance ......... . ...............

4.2.3 Extraction Electrode Design..... ..................
BEAM_3D Predictions on the Extraction Electrode Design..

Results .................................................

5 - Space Charge Force and Pre-analysis Beam Transport...

Space Charge Force ......................................

Beam Transit of the Solenoid Magnet .....................

iii

vi

10
13
13
14
22
28
28
4O
42
46
46

50
50

58
64

69
73
77
77
85

5.3 Transit of the Analysis Magnet... ........ . .............. 94

5.4 Matching the 90° Analysis Dipole under the Effect of

Space Charge ................ ... ....................... 98

Chapter 6 - Summary and Conclusions .............................. 102
6.1 Extrapolation to Multiply-Charged Ion Beams ............. 102

6.2 Summary and Conclusions ................................. 103
Appendix - Introduction to ECRIS ................................. 107
[1.1 'Unit' ECR Cell.. ....................................... 107
A.2 ECR Operating Characteristics ........................... 114
LIST OF REFERENCES ............................................... 125

iv

LIST OF TABLES

TABLE PAGE
1.1 RTECR source DC performance for gaseous feed materials.... 6
1.2 RTECR source DC performance for solid feed materials ...... 7
5.1 Beam envelope at the 90° dipole entrance.... .............. 100

LIST OF FIGURES

FIGURE

1.1 A schematic diagram showing the main features of the RTECR
ion source..... ..... . ..................... ...... ...........
1.2 A schematic view of the RTECR analysis system and the
beam analysis systems built for the studies presented in
this thesis ................................................
1.3 A helium spectrum is shown here. 300 euA helium 1+ was
produced by the RTECR source at Vex = 10 kV, Vp = 0 and
80 watts of RF power, while less than 51 helium 2+ was
produced ............... . ...................................
2.1 Flow diagram of the BEAM_3D code.... ........ . ..............
2.2 This figure shows the grid points involved in the
interpolation of field components of an intermediate point
P(r,z) .......... ..... ............ ....... ..... .. ............
2.3 The geometry used in the calculation of the space charge
force ........................................... . ..........
2.4 A schematic view of the extraction geometry and the
initial beam transport line of the RTECR source fer

BEAM_3D calculation ......................... . ...... . .......
2.5 The axial and transverse ion orbits of He1+ and Re?‘+

calculated by the BEAM_3D code .............................

The initial and final ion position distributions...... .....

The initial and final charge state distributions (CSD) .....
2.8 The emittance fittings. A. At the beam defining slit.

B. At the entrance of the 90° dipole ......................
3.1 Schematic cross section of a beam ..........................

3.2 The phase area of a beam with rotational symmetry is
described by an ellipse ............................. . ......
3.3 The particles which lie in the shaded area of the shown
ellipse (z = 0) will evolve to either of the cases in
B (2 = l) or C (2 = L) after a drift distance ..............

vi

PAGE

12

15

18

2O

23
24
25
26

27
29

31

33

A comparison, fer the case Figure 3.33 with drift distance
100 mm, of the line current density and the calculated
current profile if measured with a wire of 0.3 mm wide.
The particles are in the area determine by x, = 9 mm and
x2 = 11 mm for an ellipse with a 45° orientation, a = 5 mm

andb=20 mrad, atz:0 0000000000 ......OOOOOOOOO .........

A comparison, fer the case Figure 3.3C with a drift
distance 500 mm, of the line current density and the
calculated current profile if measured with a wire of
0.3 mm wide. The rest conditions are the same with the

case in Figure 3.4.. ..... ............... ....... ..... .......
The assembly of the wire scanner .......... . ................
10+

A 3 euA Ar beam profile after the analysis magnet is
shown. The large tail is believed due to the high
divergence beam component. An ellipse fit at 901

intensity gives emittance e = 245 mm mrad ....... . ..........
The assembly of the 'Kapton camera' ............ ... .........

A. A schematic view of a three electrode extraction
system. B. Accel-decel voltage distribution. C. Accel-
only voltage distribution. D. Accel-accel voltage

distribution ............ . .................. .... ............

A schematic view of the two extraction electrode systems
utilized in the RTECR. A. The puller has a face angle at
45°. B. The puller has a Pierce spherical face shape

[P154] ................. .. ................... ... ............

The extraction region of an ECRIS with an axial magnetic

field. Ions are extracted from the source at radius r ....

1
Schematic view of a group of identical ions on a circle

travelling along the optical axis.... ......................

The correlation in phase space. Point 1 in the XX' plane

corresponds with point i in the YY' plane ....... . ..........

The effects of ion temperature on the ideal argon beam
emittance as a function of charge-to-mass ratio. Ions
are assumed extracted at 10 kV, extraction aperture
raz 4 nm and with 82: 0.25 T (approximately the same

conditions as fer the RTECR extraction) ......... .... .......

vii

37

38
41

43
45

47

49

53

53

55

61

Argon beam emittances with the ion temperature taken as

T1: t0 eV x q. Other conditions are the same as in

Figure 4.7 ......................... ..... ................... 62
Emittances of cold argon beams with different extraction
voltages and various extraction magnetic fields. The

extraction aperture is r3: 4 mm .......... . ................. 63
Plot of the electrode shapes (heavy lines) and the

equipotential lines external to a planar space-charge-

limited electron beam as determined from Eq. (4.29) [P154]. 66
Electrodes for obtaining axially symmetrical electron

flow of uniform diameter [P154] ............... ....... ...... 68
A comparison the axial and electric field strengths of

45° (denoted by "M2a") and a Pierce spherical pullers.

In both cases the extraction gap is 3.3 cm and the first
electrodes are the same .................................... 70
BEAM_3D calculated beam profiles at a space charge

limited current for the extraction system with a 45°

angle on the puller electrode face and a Pierce

spherical puller. A drum shape in the first gap, and a

fOcus in the puller electrode are seen for the 45°

puller of Figure 4.2A................ ...................... 71
A comparison of the effective emittance after

extraction for the 45° and a Pierce spherical pullers in

the RTECR, for a space charge limited He1+ beam of 1.3

emA at D = 3.3 cm, with Vex = 10 kV. BEAM_3D predicts

the effective emittance of the 45° puller is about three

times that of the Pierce spherical puller .................. 72
Using the He1+ technique, the total extracted current of

the RTECR was measured directly at FCl1 as a function of
extraction voltage, for 3 operating pressures. At low

voltages, the extracted current is space charge limited,
fellowing the Child-Langmuir law (marked Theory). At

higher voltages the extracted current is seen to

saturate.. ................................................. 74
A transmission study on the analysis magnet for

different extraction gaps and helium 1+ currents S 0.5

viii

5.2

5.3

5.4

5.5

5.6

emA. A beam extracted at the space charge limit gives

the best transmission, with decreasing transmission as

the beam intensity falls increasingly below the space

charge limit ...................... . ........................ 76
He1+ beam maximum divergence versus the beam edge radius,

for different beam intensities, after a waist. The

maximum divergence is a constant if the space charge is

zero. But as can be seen, if the space charge force is

taken into account, then the beam maximum divergence will
increase rapidly with the level of the space charge

force ...................................................... 81
A comparison of the beam edge radius with axial drift

distance for various levels of the space charge. The

starting conditions are the same as in Figure 5.1. For

high uncompensated space charge, the beam envelope

rapidly increases with axial drift ........ . ................ 82
A schematic view of the evolution of the emittance

envelope after a waist with and without space charge

ferce. The emittance is the same for both cases, but

with space charge the maximum divergence and beam size
significantly increase .............. ............ ........... 84
A comparison of the divergence versus beam intensity for

space charge limited extraction using the BEAM_3D code.

Even though a parallel beam profile at the first gap is

ensured, the effect of space charge, which increases the
divergence, is clearly seen .......... ... ..... . ............. 86
The effective emittance of He1+ after crossing the

focussing solenoid for various beam intensities . In

each case the extraction is space charge limited, the

beam energy is of 10 keV, and the emittance after

extraction is 69 mm mrad. The 1.0 emA case shows very

large emittance growth due to its large beam profile in

the solenoid, thus the aberrations have become very

severe.. ..... ....... ................... ............. ....... 89
A and B are Kapton foil burns at the divergence box with

He1+ beams of 65 and 550 euA respectively. The beam

ix

5.7

5.8

5.9

5.

11

passes through a defining slit plate 8 cm upstream of the
foil, giving horizontal marks on the foil. BEAM_3D
predicts for 65 euA He1+ with a space charge limited
extraction (vex = 10 kV, Vp = 8.5 kV), beam profile at

the divergence box will be 1.6" and that is experimentally
seen. A 550 euA He1+ extracted at space charge limit
fills the Kapton foil at the divergence box, also

agreeing fairly well with a BEAM_3D calculated profile

of 3" ............... .. ..................... ........... .....

1+ beam in

The measured emittance for the 65 euA He
Figure 5.6A is e = 69 mm mrad, which agrees very well

with the BEAM_3D calculation (see Figure 5.5), in which
the ion thermal energy was taken to be zero................
A 65 euA He1+ beam extracted (Vex = 10 kV, Vp = 0) well
below the space charge limited (Vex = 10 kV, Vp = 8.5 kV)
current results in high divergence and large beam profile.
For this case, BEAM_3D predicts a diameter of 5.5" at the
divergence box... ............................... . ....... ...
BEAM_3D predicts that a 200 euA He1+ extracted at 7, 10,

15 and 20 kV with an extraction gap of 3.3 cm will have
very high divergence and large beam profile at the
divergence box, because the extraction is far below the
space charge limit. Measurements, limited by the
measuring apparatus to a maximum divergence 65 mrad, show
that the actual divergence is higher, in fair agreement
with the calculations ........... ...... .....................
A triangular beam mark is seen on the face of the
collimator of FCl2 assembly for the CPECR. The cause of
this triangle shape is believed to be the space charge
effect on the beam divergence before the magnet

entrance, resulting in filling the magnet aperture and
causing 2nd order aberrations ..............................
A 0105 beam transport calculation for the case in

Figure 5.10. The transit of the analysis magnet with an
unneutralized 1.0 emA helium 1+ beam of starting

emittance 200 mm mrad will result in a triangular shaped

90

91

92

93

96

beam after analysis........ ...... ................. ......... 97
A schematic illustration of better matching of the 90°

dipole for beams with space charge compared to the case

of no space charge ........................ . ........ . ....... 99
A 330 euA He1+ is extracted with space charge limit and
transported through the 90° dipole, this beam has a

waist at the dipole object when the focussing solenoid

is excited with 81 A. However the optimized

transmission occurs at I(sole) = 78 A, for which the

beam waist is about 10 cm closer to the dipole... .......... 101
BEAM_3D code predicts that after crossing the fOcussing

solenoid the effective emittance of Ar8+ (S shaped, due

to the solenoid spherical aberrations) is doubled

compared to its effective emittance before the solenoid.

The CSD and focussing solenoid excitation are based on

actual operating values...............§ .................... 104
A 'Unit' ECR Cell consists of a vacuum vessel, microwave
generator, a minimum-B field and an extraction system ...... 108
A typical axial magnetic field profile produced by a set

of solenoid coils fOr a single stage ECRIS ...... . .......... 109
This figure shows the strength of a hexapole as a

function of radius along one of the poles and in a gap ..... 111
A "minimum-B field" topology as a result of the

superposition of a hexapole and a set of solenoid fields... 112
Single ionization potentials of some atoms and ions ........ 115

Performance comparison between 2-stage and second stage

only RTECR operation for the production of nitrogen ions.

Helium is used as a support gas. Each next higher charge

state shows a large percentage increase in current with

the first stage on ......................................... 116
Ionization rate coefficients S for single ionization of

argon atoms and ions from the ground state by electron-

impact in plasma (Maxwellian distribution, no collision

limit) ......................... ..... ....................... 119
A high temperature oven for producing metal vapor is
equipped with the CPECR Ion Source at NSCL/MSU ............. 122

xi

A.9 The direct dependence of gas mixing effects on mass is

seen in the mixing of lighter gases with argon.. ........... 123

xii

1

Chapter 1

Introduction

1.1 Motivation

The ECRIS (Electron Cyclotron Resonance Ion Source, an
introduction to the ECRIS is presented in the Appendix), is now the
most frequently used new ion source for producing high charge state
positive ions for accelerators and for atomic physics research. ECRIS
originated from plasma fusion developments in the late 1960's and
early 1970's. Observations were made as early as 1969 in during the
use of ECRH (Electron Cyclotron Resonance Heating) in plasma devices
to produce high charge state ions [Ge70,Po70], and the early extracted
beams from these devices were reported in 1972 [8172,Wo72]. Following
the pioneering work of R. Geller and his coworkers at Centre D'etudes
Nucleaires de Grenoble, France, where the ECRIS originated, there are
now about 40 ECRIS in operation or under construction around the
world. The coupling of ECRIS to cyclotrons has resulted in
significant performance gains in energy, intensity, reliability and in
the variety of ion species available. At least five ECRIS have been
dedicated for atomic physics research, and at many facilities atomic
physics programs share ECRIS with nuclear science programs. Although
ECRIS have wide application, it is still a relatively young
technology. The dynamical processes are still not understood in
detail. Important unknowns include the detailed mechanism of
microwave coupling for electron heating, the nature of ion heating in

the plasma and the effect on ion confinement, the systematics of the

2

gas mixing effect [Dr85, Ma86a, An88], and the relationships between
the emittance of the beams extracted from the ECRIS and the magnetic
field, charge state, ion mass, ion thermal energy, space charge force
and electron neutralization and so on. Further development of ECRIS
will require greater understanding of these and other important
issues. For ECRIS coupled to accelerators, the last area mentioned
above, the beam formation process, is critical to the design and
operation of the accelerator coupling line.

Most ECRIS have been built for multiply-charged positive ion
injection into accelerators. The sources and injection lines
generally must operate over a broad range of charges and intensities;
the injection rigidity is generally set by accelerator
characteristics. The pressure in the coupling line between ECRIS and
accelerator is low because the ECRIS main stage pressure is low, in

the range of 10'7

T, and it is desirable to avoid the beamline
constitute a source of gas for the main stage operation. IT“:
specifications for the beam transport elements are generally obtained
by assuming (or extrapolating from existing data) a starting emittance
at the source extraction aperture, and tracking that emittance with
transport optics codes up to a match condition near the accelerator.
Generally beams are extracted DC from ECRIS. If the charge
unthin an ion beam is not neutralized, then the charge density in
space is not zero. The consequence of this nonzero charge density is
that it creates an electric field within the extracted beam. For a DC
ion beam with rotational symmetry, this force is predominantly outward

and it will cause the beam to expand in diameter and continuously

change the beam divergence due to the repulsion effects. Such space

3

charge effect can severely alter the beam optics if the space charge
force is very strong. Due to the lack of detailed knowledge of ECRIS
beam formation, the space charge effects have heretofore never been
seriously addressed. Thus the space charge effects on the ECR beam
transport optics have been either ignored or assumed to be non-
important, though space charge effects are often studied during the
design of the ion source extraction electrodes themselves.

A systematic investigation of the characteristics of the ion
beams extracted from ECRIS is a complex study involving many
parameters, most of which are without detailed knowledge as mentioned
previously. Though the importance of studying the ECR ion beam
formation has been realized by many ECR workers, up to now, only a
limited number of emittance measurements of ECR ion beams with very
little systematics [3386, C187, Dr83, Dr85, 0e79, Ma83a, Ma83b, M386b,
Kr86, Tu80, 9086, An88] have been reported since the first high charge
state ion beams were extracted from ECRIS in 1972. None of these
measurements has clearly revealed the characteristics of the ECR
beams, partly because of the lack of systematics, and partly because
good emittance measurements are difficult to make.

In an effort to understand better the requirements for matching
ECRIS beams to the superconducting cyclotrons at NSCL, we have
undertaken an analysis of the beam formation process on the RTECR
[An86a], including the interaction of the initial beams with the first
element of the beam transport system. We have found excellent
agreement between BEAM_3D calculations (presented in Chapter 2) and
helium beam profile and emittance measurements as a function of the

total extracted beam from the RTECR, when a low degree of beam

u
neutralization is assumed in the calculations, as will be presented in
Chapter 5. Space charge effects dominate the early beam formation and
beamline optics matching process.

Initial emittance measurements on analyzed helium and multiply
charged argon beams indicated rather large divergences [An88], and
often triangular shaped beams in real space. To understand these
measurements, we shifted to measurements on the total extracted beam
before analysis, where we could make direct comparisons with the

BEAM_3D code under development at NSCL.

1.2 RTECR Source and Its Beam Analysis System

The RTECR source, shown in Figure 1.1, is built for multiply-
charged ion production and injection into the superconducting
cyclotrons at NSCL. The solenoid coils provide the plasma axial
confinement while the hexapole magnet provides the transverse plasma
confinement. Microwaves can be simultaneously launched.hfix>both
stages or the main stage (second stage) only. A high density lowly
ionized plasma, produced in the first stage, diffuses to the main
stage where highly charged ions are produced at lower pressure. The
plasma chamber is positively biased with 5 - 17 kV (depending on the
beam requirements), and ions leaking out of the bottom magnetic mirror
are formed into a beam by the extraction electrodes located at the
bottom of the source. The performance of RTECR is summarized in Table
1.1 and Table 1.2.

The beam analysis system for the RTECR is shown in Figure 1.2.

The first acceleration gap was designed to be adjustable over the

 
 
   
 
 
  
 
  
 
 
  
  
  
 
 
 
  
  
  
  
 
 
    
  
 
 

MICROWAVE HIGH

2ND STAGE VOLTAGE JOINT (2)

WAVE GUIDE

GAS FEED VACUUM PUMP

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W'NDOW IST STAGE

CHAMBER

INJECTION POSITION
VACUUM 80X ADJUST/ALIGN
PLASMA MECHANISM

CHAMBER

CIRCULAR COIL SAMARIUM/

COBALT

HEXAPOLE
YOKE MACNET
RADIAL PLASMA POLE
CHAMBER PORTS
. IMLZS
(REFJ
PIERCE-TYPE
EXTRACTION \\ _PUMPING
ELECTRODE PORT
EXTRACTION p A MA
PUMP BOX CHAMBER
INSULATOR
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aggr- am...
PUMP ADJUST/ALICN
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Figure 1.1. A schematic diagram showing the main features of the
RTECR ion source.

Table 1.1
RTECR source DC perfbrmance for gaseous feed materials

 

‘ZC ‘“N “0 2°Ne “°Ar “‘Kr '=°Xe ‘271

q

4 25 5 100. 87. 67 19

5 5 6 68. 61 50 5 *

6 * 25.5 52. 41.1 42.

7 * 12.2 16.5 55.

8 * 5.0 94.

9 1.0 44.

10 * * 23

11 7.6 *

12 2.0 23.3 2.3

13 .33 29.0 2.5 1.7
14 15 29.0 2.7 2.3
15 23.2 2.9 3.0
16 * 3.1 *
17 6.8 3.0 2.7
18 3.2 2.7 *
19 1.4 2.3 2.5
20 0.4 1.4 2.3
21 0.8 2 1
22 .45 1 8
23 .20 1 0
24 11 *
25 .035

Conditions: 10 kV extraction voltage; 8 mm extraction aperture;
All currents in unit euA.
* Mixed Q/M.

7

Table 1.2
RTECR source chperfOrmance for solid feed materials

 

7Li ‘9F 2“Mg 2°81 5‘V ‘°‘Ta

Q

1 14.5 5.0 4.5 2.5

2 14.5 5.0 8.4 1.0 6.1

3 1.5 8.0 11.3 0.6 7.8

4 14.0 13.5 1.7 8.7

5 12.0 16. 2.1 11.7

6 * 3.0 12 6

7 0 7 * 15 2

8 0.6 13 5

9 0.2 6 5 0.4
10 0 I
11 1.7 0.5
12 1.0
13 *
14 1 6
15 *
16 3.1
17 3.6
18 3.6
19 3.1
20 2.7
21 2.0
2A 0.6
27 0.11
29 0.08

 

Conditions: 10 kV extraction voltage; 8 mm extraction aperture;
All currents in unit euA.
* Mixed Q/M.

8

range of 0 - 3.3 cm. The source extraction aperture is placed at the
object of a solenoid focussing lens which focuses it, with unit
magnification, to the object of the 90° dipole magnet at Faraday Cup
#1. The solenoid focal length was chosen to put the ion source on the
main floor level and to allow Ar1+ ions to be focussed at a source
bias of 10 W. The double focussing dipole images the beam with unit
magnification at Faraday Cup #2. The beam pipe and solenoid I.D.'s
are 15 cm, while the dipole aperture is 10 cm. An emittance of i 5 an
x t 40 mm mrad at the source extraction aperture was assumed in the
design of the analysis system. Space charge effects were ignored in
these design calculations. The acceptance of the dipole can be
limited by changing adjustable object, divergence and image defining
slits. Emittance measurements are possible on both the object and
image sides of the 90° dipole. In a vacuum box at a position of large
beam size before the 90° entrance, emittance measurements are made by
imaging a defining slit pattern on Kapton film, which darkens on
exposure to the beam, making an image with well defined edges. In the
FC#2 box, we can make emittance measurements in either transverse
plane with an on-line wire scanner, or with Kapton film exposures or
both. These measurement techniques are discussed in Chapter 3. The
two methods are complementary. The wire scanner method allows quick
determination of the emittance for a variety of tuning conditions but
obscures the coherent emittance, while the Kapton film method shows
coherent effects such as relative beam motions and multiple beams.

The initial performance of this analysis system, as described
above, is as follows. With a total extracted current of 0.5 - 1.5 emA

at 10 W (with various source geometries and tuning conditions), the

It. 05......

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   
   

 

9* DIVERGENCE )L”
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RT-ECR q—'i—'K\I<ARTON FOIL
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I I UNIT X :
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o I I
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Focus-1 I I- :90 'DTPOLE 9.113 "T! MEASURING I
SOLENOID . : 1 r 30! :
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more-I T ; —---~-—-- :
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' Jon-I I
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BOX I 2355 FT: IMAGE SLlT HIRE SCNOER KAPTON FOIL '
\Wll I --------- . ......................... I

. I I
1.312 FT .............. '

 

%

I

I

I

I

I
‘rf--_--4oprno—op
Lanes FIE —-I

L ............. I

 

 

 

 

 

DIPOLE

Figure 1.2. A schematic view of the RTECR analysis system and the
beam analysis systems built fer the studies presented in this thesis.

10
first acceleration gap optimized at the maximum possible value of
3.3 cm with zero voltage on the decel electrode. The hard edge
emittance [De83, Ha87] of a helium 1+ beam after extraction should be
expected to be 70 - 100 mm mrad at 10 W for an 8 mm extraction
aperture and B = 2.5 kG, but all early measurements of the emittance
after the solenoid were much higher [An88]. With an analysis
acceptance of about 300 mm mrad, the dipole image was always about
twice the object size, suggesting aberrations, and the overall
transmission, measured as the ratio of FC#2 peak currents to the net
extracted current (source bias current minus the drain current for no
plasma or puller current), or as £FC#2/ZFC#1, was about 40 - 451.
The cause of this overall low transmission, typical for many ECR

sources [An89], was not understood.

1.3 He Beam Technique

We have found that helium plasmas, tuned to maximize the helium
1+, provide good beams for studying the beam formation process in the
RTECR. There is a large enough difference in source conditions for
helium 2+, such that the total extracted current is at least 90-951.
helium 1+, as shown in the spectrum in Figure 1.3. In this regard
hydrogen does not work as well - H: and H+ production are more closely
coupled in ECRIS, and of course any heavier mass species will have a
distribution of extracted charges. The RTECR has a wide dynamic range
of helium 1+ production - from a few microamps to milliamps, even at
fixed low microwave power and essentially constant magnetic field.
The required microwave power is S 100 watts, while we typically use

1.2 kit for high charge argon ion production. We expect low thermal

11
energies at such low input powers [J084], further simplifying the beam
formation process, but the main value of using these helhnn 1+ plasma
is that the extraction gaps and voltages are uniquely specified as a
function of space charge for a single charged species as will be
shown. With this simple He1+ beam extraction over a broad range of
intensities, the effect of space charge on the beam formation and
matching is much clearer than when multiple ion species are extracted,
aids with the analysis, while the results should still be applicable

to the more general case encountered.

12

He Spectrum, Vex: 10 KV, Vp= 0, RF = 80 Watts
400

 

 

 

 

 

 

 

 

P T —T I I F T T I I r T ' I 1 l I l I -‘
I- «I
_ 1+ ~
_ He 1
Q 300 —— _
i I- -I
3 C :
+4 " -I
1:3 200 ~— -—
cu -
5., I-
L. . ‘
:3 - s
U " -I
100 — —
“U r .
cu
N r ‘
. 2+ A
Z? P He
a II ~
c o 1 1 I L 1A1 1 T L 1_ 1 1 i 1 1 1 1
<2 40 so so 100

Analysis Magnet Current (A)

Figure 1.3. A helium spectrum is shown here. 300 euA helium 1+ was
produced by the RTECR source at Vex = 10 kV, Vp = 0 and 80 watts of RF
power, while less than 51 helium 2+ was produced.

13

Chapter 2

The BEAM_3D Code

2.1 Motivation

As mentioned previously, ECRIS for multiply-charged ions can
produce multiple ion species simultaneously. The beam formation
process involves the electric fields produced by the extraction
electrodes, magnetic fields from source solenoid coils, iron yoke and
multipole magnets, the charge state distribution (CSD), space charge
force, the plasma boundary, the ion thermal energy and beam
neutralization. One would like to know what parameters are the most
important for beam quality and accelerator transport matching. To
answer this question, one generally makes simplifying assumptions.
The typical assumptions made are to study only a single ion species
and azimuthal field symmetry, in order to reduce the calculations or
apply an existing code, such as the SLAC Electron Trajectory Code
[He79]. One exception would be KOBRA3, developed at 681, in which
some calculations were done in 3D for ECRIS extraction [Sp85], but
only with extraction of the single species 03+. However, the existing
codes do not include the total magnetic field in an ECRIS extraction
regicni in a 3D calculation of the ion trajectories, while also taking
the other parameters mentioned above into consideration at the same
time. In order to support theoretically the ECRIS beam extraction

experimental measurements of this dissertation, a new code, BEAM_3D

has been developed.

14

2.2 General Organization

Shown in Figure 2.1 is a flow chart of the present BEAM_3D code.
First, primary data input, such as the field data files (which will be
explained in later section), CSD, ion thermal energy, extraction
voltages and the focussing solenoid specifications. Second, ion ray
tracing in the combined fields is performed with an axial step size of
a few tenths mm to 1 mm, and a sequential output data file is
generated. Third, a routine evaluates the emittances at requested
locations and prepares a plot data output file. Fourth, graphic
output, including ion trajectories in actual dimensions, is generated
on a line printer.

Details involved in these calculations are presented below.

1. Assumptions

The present operating code is based on the following
assumptions: (1) the space charge force has only a radial component;
(2) the volume charge density in the region of a very short cylinder

beam of radius r is constant.

2. Starting conditions

The code can handle up to 300 rays (or more if the computer
memory space is available) with different Q/M ion species, each ray is
partitioned, by input, with a portion of the total starting current.
The plasma boundary is not taken into consideration yet due to lack of
detailed knowledge. The ions are emitted from a plane at the chamber
side of the extraction aperture perpendicular to the optical axis.

The initial particle positions can be input or uniformly generated by

15

 

Problem Data Input
Including
E. ‘15. data from POISSON

 

 

 

I

 

Ray Tracing

(Step by Step)
Integral Approximation
RUNGE-KU'I'I‘A Method

 

 

 

I

Emittance Evaluation
at
Requested Locations

I

PLOT

 

 

 

 

 

 

 

 

Figure 2.1. Flow diagram of the BEAM_3D code.

16
the code itself over the extraction aperture. Initial ion thermal
energy can be input or by giving a maximum thermal energy in the unit
of eV x q, then a uniform distribution to this given maximum is

assumed by the code.

3. Integration of the Equation of Motion
The equation of motion of a charged particle in a magnetic and

electric field is described by the Lorentz equation

%E=Q(E+iixfi) (2.1)

where Q is the charge that the particle in question carries. We

change the independent variable from t to 2 through the relation
—: V— (2.2)

to obtain the following equation

'0

(E . 17x8) (2.3)

(1'0.
N "U‘

V
Z

The general analytic solution of Eq. (2.3) is not possible, because of
the coupling terms in the component equations, but a numerical
solution is possible but is sensitive to the calculation step size.
The Runge-Kutta integration technique [R066] is used in BEAM_3D to

solve the integral equations for 9 and F.

17
4. Interpolation of the External Fields
The electric fields of the extraction electrodes and magnetic
fields due to the solenoid coils and iron yoke, which have azimuthal
symmetry, are calculated by the POISSON code [H079] with a small.1nesh
spacing in the r and 2 directions. The fields at a point P(r,z)
between grid points, as shown in Figure 2.2, are linearly interpolated

using the following two dimensional formulae [X187]

 

 

(r-r.)
Fz(r,z) = (p2-p,)(z,-z‘) [(F2.+Fz,-Fz,-Fz,)(z-z,)+(Fz,-
(Fz,-Fz,)
Fz,)(z,-z,)] + —TE::ETT— (z-z,)+Fz, (2.4)
(2’21)
Fr(r,z) = (rz-r,)(z,-z,) [(Fr,+Fr,-Fr,-Fr,)(r-r,)+(Fr,-
(Fr,-Fr,)
FF,)(P2-l‘,)] +W (r-r,)+Fr, (2.5)

where F stands for E or B field.

By using POISSON for the magnetic field generation, BEAM_3D
automatically takes into consideration any iron included in the
problem. The hexapole field is incorporated into the total magnetic
field by calling a subroutine "HEX" [X186]. Our BEAM_3D calculations
have shown, however that the effect of the hexapole field on the beam
formation is on the order of 1%, because the hexapole strength up to
the typical extraction aperture radius is much less than the solenoid
coil strength. So BEAM_3D calculations are usually done without the

hexapole field to speed up the calculation.

18

 

I‘1 r2
‘ 4 *2 r
21 '1 1 ' ’ 2
o P(r,z)
23 "‘ 3 ‘ ‘ 4

 

N¢

Figure 2.2. This figure shows the grid points involved in the
interpolation of field components of an intermediate point P(r,z).

19
5. Estimation of Space Charge Force
The space charge force for multiple ion species is handled,
based on the assumptions (1) and (2), in the following way, similar to
the model established for the beam of a single ion species [Br67]. The
space charge force due to the charge inside the volume of a cylinder

of radius r, shown in Figure 2.3, is evaluated by Gauss's law
EOIE-d3 = Ipdv = Q = [0, (2.6)

where Qt: 1:01 is the total charge, and Qi is the charge of the i-th
ion enclosed by the volume of 11r21. Integration of the left side of

Eq. (2.6) after some rearrangement gives

Q

 

 

 

1 i
E:r ' 211Eo r X 1 (2'7)
or
1 1 Ii
Er = 21150 r 2 Ai: 2116o r i v (2'8)
21
Q1 Ii
where li=:-jf-:: v is the uniform line charge density of the i-th
21

species, Ii being the corresponding contribution to the total current,
and vzi is the velocity in the z direction of the i-th ion species.
In the initial extracted beam before a dipole magnet, all of the ion
species contribute to the space charge force. Since the charge state
distribution varies rapidly with the charge state q, the trajectories

of individual ion species will be quite different. To properly

omcmno woman on» no coduaaaoamo one ea eon: heuoeomm one

20

.moeou
.m.~ oasmam

 

 

 

 

 

 

 

21
estimate the space charge force on each ray, BEAM_3D recomputes the
space charge force on each ray by counting only the current enclosed

by its orbit.

6. Geometry of Calculation

BEAM_3D will track the beam from the source extraction region
through the first focussing solenoid and a beam collimating slit down
to the entrance of the 1st 90° analysis magnet as shown in Figure 2.4.
The z-axis is taken as the beamline optical axis. In the initial
beamline, after the source extraction electrodes, is an X-Y steering
magnet (which is not taken into consideration in this code, and was
generally set to zero for beam studies), followed by the focussing
solenoid. A beam defining slit is located at the image of the
focussing solenoid and this image is the object of the 1st 90°
analysis magnet. Computing the beam trajectories through the
focussing solenoid to the entrance of the 90° magnet is very
essential, as will be seen, for a proper matching of the ion source

extraction to the beam transport system.

7. Output Form
Figures 2.5 - 2.8 show the graphic outputs of a helium beam
calculation. The orbits of the ions are plotted in the r-z plane,
with the extraction electrodes, shown in Figure 2.5, the focussing
solenoid and the beam defining slit indicated at the proper locations
as well as the ion orbits in the transverse X-Y plane. In this
1+

calculation of both He and He2+ ions, He2+ is over-focused because

the solenoid is set for He1+ transport and hits the beam pipe and the

22
beam defining slit. The initial and final ion position distributions
are shown in Figure 2.6, while Figure 2.7 shows the initial and final

CSD and the emittance fittings are shown in Figure 2.8.

2. 3 Special Features
The special features of the BEAM_3D code are summarized as

follows:

1. The CSD can be artificially specified or based on source
measurements. The focussing solenoid current is set for the focussing
requirements of a selected ion species. In order to have a better
simulation of the beam extraction and transport, the space charge
force is determined by the distribution of multiple ion species. For
a specific solenoid focussing power, some ion species will be over-
focused, possibly hitting the beam pipe at some locations, while other
species will be under—focused, which, depending upon exact conditions,
IMill go through or hit the beam defining slit. Ions that are stopped
by these mechanical structures are removed from consideration, the CSD
is adjusted, and the subsequent space charge calculation is based only

on the remaining ions.

.2. The degree of neutralization of space charge can be studied

by using only a percentage of the full space charge force.

23

lST STAGE

BAFFLE
2ND STAGE

 

 

 

 

, EXTRACTION END PLATE
Z-Z "5' """""""" FULLER

 

r! GROUNDED RING

I/'
III” was!”

—7
X /' ESEERIIIS

 

 

 

 

|I><II

zv

 

 

Figure 2.4. A schematic view of the extraction geometry and the
initial beam transport line of the RTECR source for BEAM_3D
calculation.

24

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28

Chapter 3

Emittance Measuring Apparatus

3.1 Theoretical Review of Emittance Measurements

At each point of any transverse section of the beam, in a region
free of accelerating fields, we have an ensemble of rectilinear
trajectories that form a cone of angular aperture 2da, as shown in
Figure 3.1. The slope of each ray can be simply expressed as a
function of the transverse momentum px and of the longitudinal

momentum p2 of the particle by the relation

x' = px/pz (3.1)

The x-x' phase-diagram of the beam is a plot of the range of values of
x' as a fUnction of x, at constant 2 and integrate over all y values.
The area of this diagram A(x,x'), gives us a measure of the transverse

emittance e,

e = A(x,x')/n (3.2)

where we have followed the definition of Septier [Se67]. For a beam
with no losses in a drift space without an external accelerating
field, say V(z) = constant, this emittance is an invariant of motion
(Liouville's theorem [Be67]).

As mentioned in the previous chapter, ECRIS produce multiple ion

species and these ion species are extracted out of the source

29

 

 

 

 

Figure 3.1. Schematic cross section of a beam.

3O

simultaneously. However, we generally are interested in the emittance
of an ion beam of single species within this ensemble. We will use
the term "beam" to refer to a beam of a single ion species unless
otherwise specified in the text.

The emittance of a beam with rotational symmetry in the phase
plane is described by an ellipse, as shown in Figure 3.2, and this
ellipse is described by the following equation, in generalized x-x'

transverse coordinates

(Ax'-Bx)2 (Ax+Bx')2:

a + b 1 (3.3)

where A : cose, B = sine and a and b are the minor and major axes of
the ellipse as shown in Figure 3.2. Let D(X) denote the distance

between two points (1,2) on the ellipse with the same x coordinate

D(X) = X'(1) - X'(2) (3.“)

Solving Eq. (3.3) yields

1

A2b2+ 82

2 2 2 2
- x

2 [AB(b2- 32)x + ab(A2b + B a 1/2
a

 

X'(1) ) ] (3.5)

1 [AB(b2- a2)x - ab(A2b2+ Bzaz- x2 1/2
2 2 2 2
A b + B a

X'(2) ) ] (3.6)

thus D(x) is given by

2ab

A2b2+ 8282

D(x) = (A2b2+ Beaz- x2)1/2 (3.7)

31

 

 

 

Figure 3.2. The phase area of a beam with rotational symmetry is
described by an ellipse.

32
Eq. (3.7) indicates that D(x) is an even function of x and reaches its
maximum at x = O.
The importance of D(x) is that it can be related directly to
measurable parameters. In order to measure the emittance, one

generally intercepts a beam with narrow slits (to set x i = 1, 2,

1:

.), followed by a scanning system, to measure the beam divergences
(to measure x'(i)). Therefore we first consider what happens when a
beam is intercepted by a slit. For a beam with uniform density 0 in
the phase ellipse as shown in Figure 3.3A (assume at z = O), and the
beam divergences are constants of the motion, then if one traces the
particles that go through a slit (shaded area determined by 4 points
(1,2,3,N) as shown in the ellipse), to a distance of l or L , one will
find these particles evolve to an area still determined by those 14
points (1,2,3,u) as shown in Figures 3.38 and 3.3C. And the

particle's coordinates in X-X' have the relationships to the

coordinates x-x' at z = O

.. ' '
Xi - xi + 1X (1)

X'(i) = X'(i) ' (3.8)

The detailed expression of D(X) for the two cases of Figure 3.38 and
3.3C will be derived below.
For Figure 3.38, the ‘4 points (1,2,3,14) in the X-X' coordinates

are given by

X
I

- x, + lx'(1) X'(1) = x'(1)

X
N
N

x, + lx'(2) X'(2)

X'(2)

33

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34

 

 

X3 = x2 + IX'(3) X'(3) = X'(3)
X. = x2 + lx'(u) X'(u) : x'(h) (3.9)
Graphically one can see that
- X'(J) - x'<2> _ x'(1) - x'gz) _.1
Tan¢ ' X- - X. ‘ ltx'(1) - x'(2)1 ‘ 1 (3'10)

then the divergence of particle p on the line 1-2 would be

x. - x,
X'(p) = x'(2) + (x1- X.)Tan¢- = x'(i) + -l—I——— (3.11)

Thus the vertical distance between point p and point i is given by

x. - x1
- _ - -._L____. < <
D(X)p_i- X'(D) X'(l) - l Xz-Xi-X- (3.12)
likewise, the distance between X'(j) and X'(q) is
x2 - x
D(X)J_q= "'_I__l x.sxjsx, (3.13)

In the interval between X. and X,, the vertical distance between

points n and k is determined by

X,SX SX. (3.14)

k

Although x, and x2 are known, the other xi between region [x,, x,] are

not. In order to have a distribution of D(X) in the X-X' coordinates,

35

D(X) should be expressed as the function of X. Let a : A2b2 + Beaz, B

= ABl(b2 - a2) and Y = abl, we use the relation

X'l + X : X (3.15)

to obtain the following equations,

 

 

 

_ .1. 1 2
D(X)p_l— 1{Y2 + (a + B)2[a(a + B)X + Y(a(Y
(a + 3)2) - a2x2)‘/21 - x,} xzsxsx- (3.16)
1a2x2 1/2
D(X)n_k: 1[Y2 + (a + B)2][(a(Y2 + (a + B)2 ) - X]
x,sxsx. (3.17)
- l. -1 _ 2
D(X)J_q- l{Y2 + (a + B)2[a(a + B)X Y(a(Y
(a + 3)2) - a2X2)1/2] + x2} x.sxsx. (3.18)

Similar analysis gives the D(X) distribution for the case of

 

 

Figure 3.3C
D(X)p_i:-% 2 + Ea + B)2[a(a + B)X + Y(a(Y2
(a + 3) 2) - 02X2)1/2] - x,} xzsxsx. (3.19)
D(X)n_k= Ez—E—il =-—§— x.sxsx1 (3.20)
D(X)J_ _q- {(2 +‘2a + 3)2[a(a + B)X - Y(a(Y2

36

(a + B)2) - a2x2)‘/21 + x2] x,sxsx, (3.21)

where<1==A2b2+ B2a2, B = ABL(b2- a2), Y = abL, and s is the slit
width.

Based on the assumption that the particle density 0 is a
constant, then the product of D(X) and 0 gives the line current

density along the X direction by

A(X) : D(X)o (3.22)
and in arbitrary units

l'(X) = )((X)/o = D(X) (3.23)

Hence D(X) is simply a line current density function. If one uses a
finite width wire to scan the current after a slit and put the current
intensity on the center position of the wire, one would however see a
(rifferent current profile than the profile given by this line current
density function D(X), because of the wire width effect. Comparison
of the D(X) and a wire scanner current profile, if continuously
measured by a finite wire of diameter ¢ = 0.3 mm, are given 111I?igure
3.1% for the case of Figure 3.3B, and in Figure 3.5 for the case of
Figure 3.3C. One can see that due to the finite size of the wire, the
locations of X,, X2, X3 and X. are wiped out by small curvatures. But
X2 and X3 can be determined from the locations where the bean1<m1rrent

goes to zero.

37

Distribution, 6:450, 1:100 mm, ¢(wire)=.3 mm

 

    

 

 

 

 

,_ 1 Y I T I T I I V V f I I r I r T
,0 ’_ Line Current Density _
: 1)0!) :
° _ 1
A b —-:
:3 ° 7 Calculated .
g C Current Profile :
....° 4 :- 10‘) .1
.O . .
2 r .
o T T
l l J L 1 l 1 L l 1 4L 1 L l L l l I. l L4

8 10 12 14
X (mm)

a=5mm,b=20mrad,xl=9mm,x2=11mm

Figure 3.11. A comparison, for the case Figure 3.38, with drift
distance 100 mm, of the line current density and the calculated
current profile as measured with a wire of 0.3 mm wide. The particles
were initially in the area determine by x, = 9 mm and x, = 11 am for
an ellipse with a “5° orientation, a = 5 mm and b = 20 mrad, at z = 0.

38

Distribution, 0:450, L=5OO mm. ¢(wire)=.3 mm

6

 

c0
1UIFII'1ITIIIITIIUIITIITII—J

 

UTlleIIIjVIIIUUIrIUTII

l T
Line Current Density

/* (X)

   
   

llllllLlJ

 

 

3 Calculated :
'8 Current Profile.
:2 2 10C) ‘
lg :
v 1 ...... 4
o _‘
. .
L 1 1 1 1 l 1 1 L 1 l 1 1 J 1 l L 1 1 1 I 1 1 1 1 L4 ‘

7.6 10 12.6 16 17.6 20

X (mm)

a=5mm,b=20mrad,x1=9mm,x2=11mm

Figure 3.5.

A comparison, for the case Figure 3.3C with a drift

distance 500 mm, of the line current density and the calculated

current profile as measured with a wire of 0.3 mm wide.

conditions are the same with the caSe in Figure 3.“.

Other

39

As can be seen above, the line current density function D(X) is
linear in X and the square root of (c,-c,X2), where 01 and c2 are
constants. In general, the interval AX between X, and X, or between
X, and X. is very small, thus l(X) is essentially linear in AX in each
of the three regions except for the region (X., X.) of the case Figure
3.3C where D(X) is a constant. Thus in each of these regions the
distribution of D(X) is approximately a line with a varying slope.
Note that the slopes in the first and the third regions are not the
same. Experimentally, when the current is continuously scanned by a
finite wire, the current collected will be a function of )-(X)¢, where
4) is the width of the finite wire, except at the line vertices, where
the edge is smeared by the change of slope. Away from the vertices,
the slope of the measured current profile is simply equal to d—IQ-Q, or

dX

¢ times the line current density slope (13$ . Hence one can use the

measured current values away from the vertices to determine %fl,

which divided by (1 gives the corresponding slope %fl' Thereafter

dMX)
dX

For each beamlet it will generally be easier to determine X, and X,,

with the help of , one extrapolates the positions of X2 and X, .
since the density 0 may not be a constant inside the ellipse, making
the identifications of X1 and X. in cases 3.38 or 3.3C very difficult.
That is, the current profile may not have a 'flat top' when the
density is not uniform.

Once this line current distribution is correctly determined, the
X2 and X, will be obtained and so are x'(2) and X'(3) by

1 _X’X . _X-x
x(2) 'M’ x(3) 'm (3.214)

140
Determining all such points (x, x') in the phase plane then can yield

the phase area by an ellipse fitting.

3.2 Online Slit-Hire Scanner

we have built an online slit-wire scanner, which is located
about 10" after the image of the analysis magnet as shown in Figure
1.2. This online slit-wire scanner allows quick determination of the
emittance after the analysis magnet for a variety of tuning
conditions, which is very helpful for better matching the beam
transport to the cyclotrons-

This slit-wire scanner consists of a slit plate of many parallel
0.01" x 2.8" slots, ”.9" upstream of the scanning wire. THNeslit
plate is flipped up and down by a rotatory vacuum feedthrough. One
can intercept a beam to make measurements without breaking the vacuum.
The scan wire is a copper wire of diameter 4) = 0.3 mm. Figure 3.6
shows this scanning wire and its support structure assembly. The scan
wire is controlled by a servo motor via a vacuum feedthrough; it takes
about 314 seconds to do one scan. We want to make such slow scans to
have sufficient data for good statistics in the determination of the
beamlet size after the slit plate, but the beam must be very stable.
Of course, if one desires to increase the scanning rate, it is
necessary only to adjust the servo motor drive. The output current
signal from the scanning wire is converted into a voltage signal by a
group of resistors right after the wire feedthrough on the vacuum box

to avoid picking up the AC current noise through the common grounding.

41

 

Figure 3.6. The assembly of the wire scanner.

112

The wire output signal and the wire position information are
recorded by computer and can be analyzed on line to give the beam
profile and the emittance in one transverse phase plane. In this
analysis program, the beamlet edge determinations are based on the
arguments outlined in Section 3.1. The divergences x'(i) versus the
positions x1 are determined, and the emittance is then estimated by an
ellipse fitting routine. One can measure the beam profile and
emittance in the other transverse phase plane by rotating the whole
setup 90°. Figure 3.7 shows an Ar10+ beam emittance measurement made

with this slit-wire scanner.

3.3 Kapton Camera

As mentioned in Chapter 1, we have also made Kapton foil burns,
with a beam defining slit plate (of slot size .010" x 2.8", 3~H"
upstream of the foil), to measure the helium beam profiles and
emittances. This method of course can also be used to measure other
beam profiles and emittances after the analysis magnet where a beam of
single ion species is selected. The advantage of using this technique
is that the device required is simple and gives two dimensional
information (both transverse directions) at the same time, while the
wire scanner moves only in one direction. It also shows coherent
effects such as relative beam motion and multiple beams, which is very
useful for interpreting other beam profile measurements. The
disadvantage of such method is that frequent venting of the beamline
vacuum may be required to remove foils. In order to reduce the
beamline vacuum venting, we have designed a Kapton camera which can do

10 to 12 foil burns.

H3

as msm u u accesses» mm>am ssamcosca goo um use mundane as
soon coco??? :3: on» 0... one 3533 3 3m... omen: o5.
m“ nocmme mammamcm on» Locum mammona amen

 

.umes

.ucocoasoo

.czosm

as sea m e .e.m oesmse

O¢1
62.5

o x

\

+op
2.5 x
cm Om ON 0. O 0..- ON1 Om.-
. q _ . _ _
.- no..E.EE mvNuw m. H
.1 AXVAVmwnuHH 1
1 050 "Odin. -.
nu

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

>x 0.
+0. 5

O?
0.0

 

 

A“

imais Kapton camera is mounted on an 8" del-seal blank flange as
shown in Figure 3.8. An aluminum frame centered on the beamline axis
holds the two Kapton spools. Two indexing vacuum feedthroughs control
the revolution of the spool, with two revolutions to advance (nus foil
exposure. The burning time depends empirically on the beam intensity.
For example, for a 10 euA/cm2 beam intensity, the burning time is
approximately about 10 minutes. A well defined beam image on the foil
can be obtained. At beam intensities in the range of 100 euA/cm2 or
higher, ion charging effects on the Kapton foil start to blur the
image. At these current densities, we image the beam onto the
metallic side of aluminized Kapton foil and obtain well defined images
on the Kapton side.

The emittance of the beam can be obtained by using a 5 to 10X
magnifying lens to read out the beamlet edges, giving x'(2) and x'(3)
sets for each (x,, x,) pair which can be used to build the phase space

diagram. Results of such measurements are presented in Chapter 5.

45

 

'Ihe assanbly of the 'Kapton camera' .

Figure 3.8.

N6

Chapter 11

Extraction Geometry Study

“.1 Motivation

The ion beam extraction system is usually located near the peak
field of the end mirror. The most common extraction system that has
been used to form beams of ions from ECRIS is shown schematically in
Figure H.1A. It is a three electrode system with applied voltages Va,
Vb and Vc on the relevant electrodes respectively. Positive ions are
expelled from the source and the beam transport line is at ground
potential, which results in the requirements that V0: 0 and Va) 0.
The intermediate electrode with voltage Vb is used to obtain adequate
ion focussing. The beam energy is determined by 113- V0: V3, which is
set by the application, while the voltage difference Va- Vb and the
spacing D between these two electrodes determine the maximum current
that can be extracted from the source for a given plasma. The

variation of the voltage V from negative to positive will enable the

b
extraction system to be one of the 3 cases: 1. accel-decel (Vb< O), as

illustrated in Figure 4.13, the region between Va and Vb is

accelerating and radially focussing while the region between V and V0

b
is with decelerating and defocussing, though the net effect of the
extraction system is focussing if the focussing strength in the
acceleration gap is stronger than the defocussing strength, 2. accel-
only (Vb: V0: 0, electrode b and 0 can be combined as one), as shown
in Figure 11.1C, which produces only a focussing effect in the region

between Va and Vb, 3. accel-accel (Va>V > O), as shown in Figure H.1D,

b

M7

 

 

 

 

 

 

mfg-1°11) ;
/ HH 7

 

 

 

 

Vo>° Vb<0
V630
B
X
Vbj>0 Vb=V°=()
C
Va))Vb>()
Vc=0
D

Figure “.1. A. A schematic view of a three electrode extraction
system. B. Accel-decel voltage distribution. C. Accel-only voltage
distribution. D. Accel-accel voltage distribution.

A8
with focussing strength in both gaps. For historical reasons, only
cases 1. and 2. have been used in ECRIS [J083, 0183, 6e79, An86,
Pa87]. Such accel-decel systems used in ECRIS generally have a
Pierce-type [PiSA] first electrode and various second electrode shapes
(puller electrode), while the third electrode is simply a large bore
ground ring. Figure A.2A shows a schematic view of the original RTECR
extraction electrode system which has a puller of a face angle ”5° tn)
the optics axis, and the first gap was adjustable from O to 3.3 cm by
moving the puller (the second gap is fixed and moves with the puller).
Shown in Figure 11.23 is the current extraction system, which has a
Pierce spherical puller, and the first gap can be adjusted from 3 to 6
(an. A negative high voltage power supply feeds the puller electrode,
thus the source has the ability to extract ion beams under the
conditions of accel-decel or accel-only.

Although ECRIS have been under development for about 12 years,
the best extraction geometry for all ECRIS or whether the best
extraction geometry has a source dependence is still an open question.
During the first operation of the RTECR, we have found the
transmission from FC#1 to FC#2 to be low, as mentioned in Chapter 1 --
only about 110% to 115%, implying a large mismatch between the source
and beam transport system. Thus an extraction geometry study on the
RTECR source has been undertaken in order to ascertain the nature of

this poor transmission.

“9

End Plcie

Puller Ground Ring
£37.55. ‘455‘ .

End PIOTB Pierce
Puller Ground Ring

1 _Z_

Figure “.2. A schematic view of the two extraction electrode systems
utilized in the RTECR. A. The puller has a face angle at “5°. B. The
puller has a Pierce spherical face shape [Pi5H].

50
“.2 Theoretical Review

A.2.1 Equations of Motion

For a magnetic field produced by solenoid coils, Ae(r,z) is the
only nonzero component of the vector potential A. Then a charged
particle of charge Q and mass M moving non-relativistically in a
combinatnn1cfi‘an azimuthally symmetric electric field and a
solenoidal magnetic field, the Hamiltonian (in cylindrical

coordinates) is of the form

 

2
P 2QP
1 2 9 2 2 2 9
.- a—w + .2 ..Z.Q-9-_,._-e,.Q--.,.- <11).

where Pr: pr: Mvr, P9: pe+ QrA9= Mver + QrA9 and P2: p2: Mvz are the
generalized momenta in which pr, p9 and p2 stand for the mechanical
momenta, and vr, v9 and v2 are the linear velocities in the r, O and 2
directions. V(r,z) is the electric potential. Lacking the exact
knowledge of space charge, for simplicity, it is assumed that the
space charge has only the radial component for DC beams, then V(r,z) =
Vex(r,z) + Vsp(r), where Vex(r,z) is due to the applied extraction
potential and Vsp(r) is the potential due to the space charge based on

the above assumption. Therefore the Hamiltonian becomes

P 20?
2 e 2 + 021: _

O
2 + Pz

 

 

r A9) +
r

Q(Vex(r,z) + Vsp(r)) (4.2)

51
The equations of motion are then obtained by differentiating Eq. (4.2)

with respect to the corresponding coordinates

2
f3:_§.}i=_l[_:.e.+Q2A 3:9._Qp(_.A£+lEE_9.)]
r 3r M r3 9 3r 9 r2 r 3r
3V

Q(Eexr+ Espr) where Er' - 3r . (4.3)
F - - Qfl - O that is P - + QrA - constant (4 4)
9‘ ae ‘ ' 9' pa 9‘ ° '
. __3fl ‘1-(Q2A Egg .Q_P_a_A§)+QE
z' 32 M B 32 r z exz

Qp 3A
-—r_9-§z2+QEexz (“5’

Eq. (4.4) shows that P6 is a constant of motion. (ha important
consequence of this result is that if an ion moves from a region with
the above mentioned magnetic field to a magnetic field free region,
the magnetic angular momentum QrAe will be converted into the

mechanical angular momentum

P91: 991* QriAOi ‘ Per: per (Aer: 0) (”'6’

where the subscripts i and f stand for the initial and final regions.
.
In ECRIS the extraction apertures have azimuthal symmetry, with
an ion being extracted at a radius ri with respect to the optical
axis, as shown in Figure 4.3. Such an ion has the generalized angular

momentum

Pei: pei+ QriAei (4.7)

52
The other important consequence of Eq. (4.4) is that since the
magnetic field contributes to the final transverse momentum, it also
then contributes to the emittance, as we will now demonstrate.
Imagine that we have a group of ions with the same mass M and charge
Q, being extracted at the same initial radius r11: 0 and having the

same initial generalized angular and radial momenta P and P

Bi ri’
distributed on a circle of radius ri, and that there are no collisions
among ions during transit. If we trace all these ions from the
extraction aperture to a region of zero magnetic field, as is
schematically shown in Figure 4.4, we will see all these ions
distributed over a circle of radius rf. and having the same mechanical
angular and radial momenta. The phase diagrams enclosed by these ions
can be given by projecting the radial and the angular velocities and
positions of these ions in the cylindrical coordinates into the X-X'
and the Y-Y' Cartesian phase planes. For a convenient derivation, Vrf
and ”er are assumed to be positive, and from the following analysis
one will see the directions of Vrf and "91‘ do not then contribute to

the phase space area. The relations between Vrf’ “er and vx, vy are

given below

vx= vrfcoso - VOfSin¢ (4.8)
vy: vrfsino + vefcos¢ (4.9)
2 2

vx + v = vrf + v9f (4.10)

53

U/Exirqcflon Aperiure

 

 

Figure 4.3. The extraction region of an ECRIS with an axial magnetic

field. Ions are extracted from the source at radius r1.

 

 

 

Figure 4.4. Schematic view of a group identical ions on a circle
travel along the optics axis.

54

It is obvious that v = 0 when v = (v2 + v2 )1/2 at a position X =
y xmax rf Of
rfcosox, while ox is determined by
v
1) = - tan-Wig) (4.11)
x v
rf
Similarly v = 0 when v = (v2 + v2 )1/2 at Y = r sin¢ and (b is
x ymax rf Of f y’ y
given by
v

<1 = tan"(——"f) (11.12)

3’ Var
As Figure 4.5 shows, ion 1 (coincident with X-axis) gives xmax: rf. in

”91‘
the X-X' plane and Yintho) = 7— in the Y-Y' plane. Ion 2
z
(coincident with Y-axis) gives ymax: rf in the Y-Y' plane and
”er
Xint(X:O) = - v_— in the X-X' plane. Ion 3, at a point where the
2

contributions of Vrf and VOf to vy cancel each other, that is, where

vx (or x' = x' ax) is maximum at this point. Similarly ion 4 gives

I - U -
Vymax (Y - Y max)' The total projection of all v”, and v62 (2 - 1,2

...) to the X-X' and Y-Y' planes constructs an ellipse in the

respective phase planes. Noting that xint and Yint are dual value

1 .. 1 .. >
functions of X or Y, namely xint - 1 C1 and Yint - 1 C2 (C1 - O and C2

1 _ 1 -
Z O ), xint - C1 and Yint - C2 are used to determine the areas

enclosed by these ellipses. The areas due to such ellipses in these

two planes are then determined as

55

 

 

1?
v,0 V,
V! 2 V,
4
¢y V.
V.
1°. 1 ' * x
V5
V
\1 1’. 3 .
XI y’

   

p---_._....--

 

\.
5
it

1

 

 

Figure 4.5. The correlation in phase space. Point 1 in the XX' plane
corresponds with point i in the XY' plane.

56

 

Mv p
9f 9f
_ I - - —
AXX" “xmaxxint' 1nflf'Mvz I ' 1'lpz I (“'13)
Mv p
9f 9f
_ I _ _ .. .—
AYY" “ymainnt’ “rflez ' ' 1'lpz I (”'1”)

We then have the following expressions for the beam emittance

due to such group of ions on a circle

per
EX)“: EYY': le—l ((4.15)
. per
Here we see that the Sign of B_— does not affect the phase space
2
areas. EXX'= eyy, is the natural result of such azimuthal symmetry of

the extraction system.

From the above analysis one can further imagine that a beam
consists of many such circular layers; ions have the same momentum
within a layer and various momentum among layers. Each layer of ions
defines an ellipse with a common center in the X-X' and Y-Y' planes.
The total phase area in the X-X' or Y-Y' plane is then normally equal
to the area enclosed by the largest ellipse. In some cases the
emittance could be larger than this when aberrations distort the

ellipse orientations. Thus the beam emittance can be expressed as

E = {A.}/fl (4.16)

57
where {A1} stands for the total phase area due to all the individual
ellipses. If all the remaining ellipses are enclosed by the largest

ellipse of A1 then e reaches its minimum

max’

E . = A. /R (”.17)

And if the largest ellipse of A1 max is defined by the edge-extracted

group of ions, then

E min: Aedge/fl (“'18)

From the above analysis a conclusion could be drawn here; for

any charged particle source with azimuthal symmetry in the extraction
system (fields, electrodes), if the edge-extracted particles have the
largest initial generalized angular momentum, the minimum emittance is

given by

P9 ed e
Emin = |-———JL’( (8-19)
p2

In ECRIS, the edge-extracted ions of the same charge do have the
largest generalized momentum, because of the rA9 term, so that if
ther13.is no lens aberration during the extraction, the beam emittance
should be no smaller than that described by Eq. (4.19). Comparison of
cold ion BEAM_3D calculations with RTECR emittance measurements do

closely follow the emittance given in Eq. (4.19), as will be shown.

58

4.2.2 Effects of Ion Temperature, Magnetic Field and Q/M [htio on
Beam Emittance

Ion-ion collisions are the fastest process in the plasma and
should result in thermalization [He82]. Since the thermalization
should not have any direction preference, the ion velocities should be
isotropic before extraction, and thus the ion thermal velocity will
contmdlnlte to the beam emittance by increasing the mechanical angular
and radial momentum. As indicated by Eq. (4.7), in a field free
regixn1, the maximum mechanical angular momentum of the edge-extracted

ion is of the form

p9,. = ramei + QAea) (1.20)

where ra is the radius of the extraction aperture and A is the

Ga
azimuthal vector component at that location. The linear angular
velocity v91 is the signature of the ion temperature inside the ECRIS.

Then the emittance is

 

| (4.21)

The magnitude of the angular velocity is related to the ion

1/2 1/2

temperature Ti by v91: (Ti/M) and pz: (2MQVex) , hence

T

_ 1 1/2 Q 1/2
Emin' ran—20V“) +11 ) ] (11.22)

(
9a 2MVex

59
Eq. (4.22) shows the contribution of the ion temperature to the beam
emittance. If the extraction voltage vex is constant, one can clearly

see that:

T.
1. if (-é—)1/2>> A9a(_%—)1/2’ the emittance is dominated by the

ion temperature Ti and has the value of

T
E . z 1 1/2

min Pa(§av-) (4.23)
ex

Thus the higher the ion temperature, the larger beam emittance. The
emittance is independent of ion mass M but varies with 0'1/2. If T1 =

t0 eV x q, here tc is constant, then all ion beams will have the same

emittance

 

to 1/2
Eminz ra(2v ) = constant (4.24)
ex
Ti 1/2 0 1/2
2. if (_6_) << A9a(-fi_) , the emittance is dominated by the

magnetic field and the Q/M ratio, and is given by

e (
9a 2MVex

min: Pa (4.25)
Then the higher magnetic field in the source extraction, the larger

the emittance. Also an ion beam with a higher Q/M will have a larger

emittance.

60

T

Otherwise. if (%)1/2 is comparable to A Q )“2

ea( M , then the
ion temperature, magnetic field and Q/M ratio all play important roles
in the ECR ion beam emittance, with the emittance is given by Eq.
(4.22). The conclusions that increasing magnetic field or increasing
ion temperature results in larger emittance still holds, but if the
ion temperature and the magnetic field are kept constant, at the case

1/2/A

where (MTi) ea= Q, the emittance will reach a minimum of cm.

In

. - 1/2 1/4
emigin) - ra(2Aea/Vex) (Ti/M) (4.26)
Finally if the thermal energy scales with charge (T1 = to eV x q), one

would see that

1/2

E + A -—Q-—)1/2] (4.27)

(
9a 2MVex

min: ra[(2V:;)
Again a stronger magnetic field or the higher Q/M ratio would result
in a larger emittance if the other parameters are constant.

The dependence of ion temperature, magnetic field and Q/M on the
theoretical emittance for ideal argon beams, assuming the emittance is
determined by the edge extracted ions and no extraction aberrations,
is numerically calculated and shown in Figures 4.6, 4.7 and 4.8.
Figure 4.6 shows, if all the argon ion species have the same
temperature, one would obtain a minimum emittance for a particular Q/M
if all other parameters are held constant. Figure 4.7 shows this

effect for argon ions with an ion temperature expressed as a constant

61

Ar Beam Emittance of Ideal Beam

 

 

 

 

 

250 ’- I I I I ‘l I I I I l I I I I I f I I I I Ii
3 . Vex = 10 IN I
r ra = 4.0 mm '1
2°° _ 132 = 0.25 '1' '1
A j
1o

a -—-1
E -
e '1
.5. .-
w I I
60 — —
E i
o ’- 1 1 l l I l 1 l 1 l l 1 l l L l l 1 1 I l d

O 5 10 15 20

Figure 4.6. The effects of ion temperature on the ideal argon beam
emittance as a function of charge-to-mass ratio. Ions are assumed
extracted at 10 kV, extraction aperture r3: 4 am and with 82: 0.25 T
(approximately the same conditions as for the RTECR extraction).

Ar Beam Emittance of Ideal Beam

 

  
  

 

 

 

j I II I I I TI l I I IIII I I I I I
200-—
( Ti=tc(erq)T
_ ioxq‘
-. ..J
.. 5XQ‘
150):- 3xq—:
/"\
'U .. -
(U
1.. ~ -
a - -
E 100-_—- 0 ‘j
E ; j
w T' ..
50—— —a
_ Vex=10kV _
: ra=4.0mm -
_ 92:0.25'1' ,
0 l l l l l 11 l l [111 lel l 1 LL
0 5 10 15 20
‘1

Figure 4.7. Argon beam emittances with the ion temperature taken as
T1: tc eV x q. Other conditions are the same as in Figure 4.6.

63

Ar Beam Emittance of Ideal Beam

IIIIIIIIII’TrIIrIIIIll

 

1'
150 —-

6 (mm mad)
8
C)
r 1

 

 

 

 

Figure 4.8. Emittances of cold argon beams with different extraction
voltages and various extraction magnetic fields. The extraction
aperture is ra= 4 11m.

64
times eV x q. A maximum emittance of about 200 mm mrad occurs for
argon 18+ for an ion temperature equal to T1 = 10 eV x q. Figure 4.8
shows the case of zero ion temperature, equivalent to the hard edge
model [De83, Ha87]. In this case the magnetic field determines the
emittances, and further the ions with higher Q/M will have larger
emittances. Argon 18+ has the maximum emittance of about 100 mm mrad
for the specified conditions (extracted at 10 kV) in Figure 4.£3. The
ion temperature in ECRIS is in the order of a few eV x q [Me86, An88],
and based on the above arguments, we could draw a theoretical
conclusion that the maximum emittance should be about 200 mm mrad for

ECR ion beams extracted at 10 kV, for an aperture radius of 4 mm and a

magnetic field of 0.25 T.

4.2.3 Extraction Electrode Design

In ECRIS, the first electrode is generally designed by following
Pierce's design theory [Pi54], which was originally developed for
electron guns. It is based on the following assumptions: (1.) zero
magnetic field; (2.) zero thermal energy; (3.) conservative electric
field; (4.) electrons uniformly emitted from a planar cathode.
Following Pierce, one solves the POISSON equation with the full space
charge taken into consideration, which yields the following solutions
for a rectilinear beam, with a parallel beam profile, in an
accelerating gap.

Inside the beam:
“/3 (4.28)

in”

65
while outside the beam:
2 2/3

V = A (22+ y )

B. -1 2.
out c08(3 tan 2) (4.29)

with

 

9J 2/3
A = [ ] (Ll-30)
4e,(2e/m)1/2

where z is the optic axis, J is the current density, e and m are the
electron charge and mass. Eqs. (4.28) and (4.29) are subject to
boundary conditions V = O at z = O and dV/dz = O at z = O.

The condition voutz O at z = 0 gives the shape of the first
electrode, which requires the electrode has an angle of 67.5° with
respect to the z axis. Voutz Vex at z = D gives the shape of the
second electrode. Such electrode shapes and the equipotential lines
for a rectilinear beam is shown in Figure 4.9. Finally, at z = D we
4/3

have V - V = AD

in - ex , and rearrangement yields the limiting value of

nonrelativistic current density flow

3/2

1/2 V
_ 4e,(2e/m) ex

9D

which is the so called Child-Langmuir Law for the space charge limited
emission [Ch11]. If the current available is less than this maximum
current, then a converging beam profile will result in the transit of
the gap. In the case of a cylindrical beam flow, where %¥-= ()1vithin

the beam in the extraction gap is required, solutions of the POISSON

IA

1.2

[.0

0.!

0.6

0.4

0.2

DISTANCE FROM EDGE OF BEAM (y)

Figure 4.9.

66

 

 

 

-o.osov°

 

 

zoo: 06—95511. —" 3:

  

 

I-I '3 e: "'53 ‘-Z=‘- = 3:22

cameos suancz "1.3"."°".-’,:’I-’:-:':':':':'::.3:=::: ‘

1 1 1 1 °I:’.°}}I1':-'.-131°3-2:231:232'335353'51:-313-1313.:3':Z.

 

- 0.8 - 0.4 O 0.4 0.8 LZ

DISTANCE FROM CATHODE (2)

Plot of the electrode shapes (heavy lines) and the

equipotential lines external to a planar space-charge-limited electron
beam as determined from Eq. (4.29) [P154].

67
equation can only be numerically obtained, but the results are very
similar to the case of a rectilinear beam. According to Pierce, the
first electrode still makes an angle of 67.5° with respect to the
optical axis, while the puller has a spherical face, as Figure 4.10
shows.

For positive ion beams, the above arguments hold except for a
reversal of the extraction electric field direction, and changing e to
Q and m to M. For a beam of multiple ion species, in which it is
assumed that every ion species is uniformly distributed, the Pierce
constant A is then of the form

J1

(Oi/Mi)

2/3

 

A=[
46,2

(4.32)

1/2 X 1/2]

where Ji is the contribution of the i-th ion species of charge Qi and
mass "1' The space charge limit current density is then replaced by
the following expression

1/2 v 3/2
ex

J1 _ 4en2

1/2 '
(Qi/Mi) 90

 

 

This would be the equivalent Child-Langmuir Law for an ion beam of

multiple ion species.

68

 

12

 

 

 

 

 

 

IO 51" /
9

BEAM

N
'\

 

 

 

5‘0

 

 

 

 

 

 

 

 

CATHODE RADIUS
o N
\

_:

 

 

 

 

 

 

 

ommce snow mus or

 

bLUI
\
\
*‘q

J“.
"0

U

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

' ' 00 o .0. ..I o 0'90' 0 a“... "
EDGE 35-33-2923 ::'::.’-’:".3:- -.'-:'-.=:'-:-’-. -" '::’-'-'1 TI“ '.°-°.°.°.'-:-.‘-: .::=: .’-:-’. '
.:::.:..o... Ezia::::£: :.:. 9...... :::.:.:.o.o:. P.}:.:.:.::.1P O (r .::.0..:.: .00 o .0 o o. o o
..... r

 

 

 

 

   

):.-.-.:.°-°--- 3:453:51? :13: 3" :1 35:3:{5-1'::_ i-‘:'.-::.';',‘-,
AXIS o . ’ ’ ' ~::-, .- gm. ”5:: -
O 5 6 7
_z_ DISTANCE FROM CATHODE
Po ’ CATHODE RADIUS

Figure 4.10. Electrodes for obtaining axially symmetrical electron
flow of uniform diameter [P154].

69

4.3 BEAM_3D Predictions on the Extraction Electrode Design

The RTECR source has a three-piece electrode system, as shown in
Figure 4.2. For historical reasons, the original puller electrode in
the RTECR had a 45° angle, while the first electrode following the
Pierce's theory is at a 67.5° angle with respect to the optic axis as
shown in Figure 4.2A. A comparison of the electric field geometry
between the 45° and Pierce spherical pullers is shown in Figure 4.11,
in which the term "112a" denotes the 45° puller. It is seen that,
compared to the Pierce puller, the axial and radial electric fields of
the 45° puller are weaker at the extraction aperture and very strong
at the aperture of the puller. BEAM_3D calculations have suggested
that such an extraction system with a 45° puller does not work
properly when the extracted current is at or below the space charge
limited current. It has less focussing strength at the beginning of
the extraction, and too much at the end, resulting in a drum shape
beam profile in the first gap as shown in Figure 4.12A. A distortion
in the phase area after extraction results in a large initial
emittance, as shown in Figure 4.13. BEAM_3D suggests that an exact
Pierce spherical puller, shown in Figure 4.28, is better than the 45°
puller in ensuring a space charge limited current with a parallel beam
profile in the extraction region, as shown in Figure 4.128, and less
phase area distortion after extraction, see Figure 4.13. Therefore a
better matching of the downstream beamline should result since the
beam brightness is inversely proportional to the square of the
effective beam emittance.

Having demonstrated theoretically that a Pierce geometry is

better (smaller initial emittance), the first of two consequences will

7O

- COMPARISON BETWEEN PIERCE AND MZA ELECTRODE

 

 

 

 

 

 

 

 

 

  

 

 

 
  

 

300000 PI I T fir I r I I I I I I I I I T I 1 I; I I I l’ T4
I
: Pierce: ———- "
. 1 1 .
zooooo — M23; --—---- 11 T
p. I \
r r=O..05..1..15 in ;
E 100000 . --‘
In )- .
[I] L .1
)- .1
0 —“ _____—z ' *1
L. - ::"' __.‘.:‘.-----’,'
1- . ' N ‘ .: _, I .-
L- / .-
’ 1 1 1 8 1 1 1
-100000 L 1 1 1 1 1 1 1 1 L 1 4 ._L_L._ 1 1 m 1 m 1
o 1 z a I.
2 (cm)
COMPARISON BETWEEN PIERCE AND MZA ELECTRODE
1000000 I I I I fir I r I I I I l’ I I 1 I I I j T I T I fl
1 1
800000 L— Pierce: “
. 11211: ---.-~- T
I r-O..05..1..i5 in .' 1, .1
.. oooooo -— I- 1 —J
3 h .541 1‘ 4
9 C I" ‘ ,- 3
U )- ../ ‘ -1
s 400000 :- .’ I -—‘
zooooo - -:
» l
o L L l l m L .l
o 1 z a 4
2 (cm)

Figure 4.11. A comparison the axial and electric field strengths of
45° (denoted by "M2a) and a Pierce spherical pullers. In both cases
the extraction gap is 3.3 cm and the first electrodes are the same.

71

up.”

up... qr...

45° Puller

 

 

     

 

m.» u
l ( n ).

"~00 It.“ to... 70.00 07.00 100.00 “0.00 m.» m."

up... up... 1;

Pierce Spherical
Puuer

3.00 0,... Q.”

r

 

 

 

 

30.00 II.“ 00.0. 70.00 01.00 m... m.“ m.“ ""”zmi”ou.)'.'

Figure ”.12. BEAM_3D calculated beam profiles at a space charge
limited current for the extraction system with a “5° angle on the
puller electrode face and a Pierce spherical puller. A drum shape in
the first gap, and a focus in the puller electrode are seen for the
“5" puller of Figure lLZA.

72

BEAM_3D Cal. He”. Vex=10 kV, I=1.2a4 em‘A

 

   

 

 

 

loo '- I F I I I I I I fi—r I I I I I I I I? r

.. ' .
' /

P ‘ ‘1
L- .1
50 — _
b -1
b 4
T ' 4
a 0 ... _. ........................... _
v I" d
5< : q
-60 t- —- 45° Puller -‘
f / i - - Pierce Puller ‘

1 l l l l L I K 1 l I L l L l l l L l

-100

-40 -30 0 20 4O

X(mm)
¢>=Bmm.Tm=O.D=3.3cm.Z=4-1cm

Figure ”.13. A comparison of the effective emittance after extraction
for the 145° and a Pierce spherical pullers in the RTECR, for a space
charge limited He1+ beam of 1.3 emA at D = 3.3 cm, with Vex = 10 kV.
BEAM_3D predicts the effective emittance of the 115° puller is about

three times that of the Pierce spherical puller.

73
be noted here (the other will be discussed in Chapter 5). It concerns
the adjustment of the Pierce extraction geometry. Figure ”.118 shows
the dependence of total helium 1+ current extracted from the RTECR,
for 3 different main stage operating pressures [An88]. For these
measurements, the source aperture was 8 mm, the extraction gap was 3.3
cm and the puller voltage was zero. The total extracted current is
seen to follow the Child-Langmuir limit (labelled theory) up to a
saturation voltage, and the saturation voltage is seen to increase
with main stage pressure. Along the line labelled D = 3.3 cm, a
parallel beam will be produced in transit of the first gap (as shown
in Figure 14.128). To the right of the theory line, a gap of 3.3 cm
will result in excess focussing in first gap and therefore higher
divergence after extraction. This high divergence will result in a
large beam envelope inside the focussing solenoid, and the solenoid
spherical aberration will become very severe (this will be discussed
in more detail in Chapter 5), and therefore poor beam transport

results.

I.“ Results

In matching ECRIS beams to accelerators, the source tune is set
by the ion production requirements, and the extraction voltage is set
by the injection rigidity. So for example, we might find it necessary
to operate the source on the lower pressure current curve of Figure
4.1” at a net extraction voltage of 10 W. In that case, to minimize
the divergence after extraction, we must decrease the electric field
strength in the first gap, by increasing the gap (D = 5 cm line) or

reducing the voltage (AVp = 5 kV).

7‘4

FC#1 Current vs Extraction Voltage

 

 

 

 

101 p r T— I I I I I Fr d
EU a 3.5x10': '1' E
:X X 1.9210- T 2
_ a 0 1.11110" '1' .
- — Theo -
17 D a I a ' a
100 5' . a x X " x xx ‘1
A Z a a 10 use»: ;
a : D = 3.3 cm . a " . 3
01 .. . ' !
v ‘ | I 1
«It 10"1 _ ‘ . I —.
(D I H ‘AVP=5 kV ; :
:L': E :1
‘ 1
D = 5 cm ‘
10—2 1 L 1 1 1 1 1 1 L
2 3 4 5 6 7 8 910 20
Vs-Vp (kV)

Obj Slit = 30 mm

1+ technique, the total extracted current of

Figure “.1“. Using the He
the RTECR was measured directly at PC“ as a function of extraction
voltage, for 3 operating pressures. At low voltages, the extracted
current is space charge limited, following the Child-Langmuir law
(marked Theory). At higher voltages the extracted current is seen to

saturate .

75

To do this properly, one should know when the extracted current
is space charge limited. This can be achieved operationally by making
the gap and puller voltage tuning parameters. For the RTECR injection
into the cyclotrons at NSCL, we have in fact generally operated to the
right of the D = 3.3 cm line. Since this was the maximum design gap,
the least over-focussing would occur at Vp = O (Vp > O was not a
possibility), which is exactly how the system did operate. Once we
realized this limit, the first gap was modified to work over the range
of 3 to 6 cm. This modified extraction system works better than the
old one in better matching the following beamline and the 90° magnet,
as an increase in transmission of the analysis magnet is observed.
Shown in Figure “.15, are the transmission measurements from PC“ to
FC#2 versus the extraction gap for a helium 1+ beam of intensities (I
.<. 0.5 emA) extracted at 10 W with zero voltage on the puller (below
space charge limited extraction), or a positive voltage on the anller
(D = 3.3 cm, at space charge limited extraction). It can be clearly
seen that, for this current range, space charge limited extraction
gives the best transmission, which we learned theoretically also has
the smallest divergence and emittance after extraction. When the
total extracted current is below that for a space charge limited
extraction, the larger extraction gap gives an extraction closer to
the space charge limit thus has also smaller divergence after

extraction, and better matching to the beamline therefore results.

76

Transmission Study on the lst 90° Dipole

 

 

 

 

400 ’- I I I I I I I I T TIT T I I r T r Ifi I I I I I I I [.1
P D D D=3.3 cm. VP=0 ~
1- K 1‘ D=4.0 cm -
_ x x D=5.0 cm _,
__'1‘ ‘3 D=5.9 cm __
300 _ + + D=3.3 cm. Vp Positive 697° 53% 1
A l" x .
<1 - 78% «
a . - 1
.. I" 4 o "
. (\1 ,. -
2‘): r 0 ‘
r 85% ‘
E; 100— , '- _ ._
1’ Z?) n .1
I /‘ 1 1 1 1 1 "

o 1 L L l 1 1 1 1 l 1 p L I L 1 L L 1 l 1

0 100 200 300 400 500

I (FC#1, e,u.A)
He“, Obj. Slit=15 mm, Ima. smazs mm, Vex=10 kV
Obj. and Image slit Bias: —100 V

Figure 4.15. A transmission study on the analysis magnet for
different extraction gaps and helium 1+ currents S 0.5 emA. A beam
extracted at the space charge limited gives the best transmission,
with decreasing transmission as the beam intensity falls increasingly
below the space charge limit.

77

Chapter 5

Space Charge Force and Pre-analysis Beam Transport

5.1 Space Charge Force

Typical extracted currents from ECRIS are in the range of 1~2
emA for extraction voltages of 5~3O kV, which in turn are set by the
injection requirements of accelerators or research. The energies of
ion beams extracted from ECRIS are then 5~3O keV x q -- ion motion is
nonrelativistic. Low beam energy coupled with high beam intensity
will result in beam growth, if the space charge is not compensated.
The space charge force will exert a relevant influence on the ECRIS
beam transmission, especially when this force is very strong.

For a beam with rotational symmetry, the space charge fOrce does
not have an angular component, thus it has no effect on the ion
angular momentum. As indicated by Eqs. (11.3) and (11.11), the space
charge force affects only the radial velocity, and hence the beam
maximum divergence, as will be demonstrated in the following
discussion.

As mentioned in Chapter 2, the space charge force for a
rotationally symmetric beam of multiple ion species uniformly

distributed is of the form

 

1 1
x v. 15.11

78
In a drift region after extraction, an ion on the outmost
surface of a beam consisting of multiple ion species, experiences a

radial force of (in cylindrical coordinates),

 

2
. p I.
p =—3 -—°——£ 1 (5.2)

where pe is the mechanical angular momentum, a constant of motion, and
r is the radius of the beam. As indicated by Eq. (11.3), the first
term originates from the initial canonical angular momentum after
extraction from the source, while the second term is the radial space

charge force in Eq. (5.1). Rearrangement of Eq. (5.2) yields

2

" pe Q Ii
r : M2r3 + ZuMeor X vzi (5'3)

 

 

Integrating Eq. (5.3) once with respect to the time t gives the radial

velocity vr equation

 

2
pa 1 1 Q r 1 1/2
vr : [_§( 2 - 2) I uMe,ln( r ) Z v 1 (5.“)
M r m zi
m
where rm is the radius of the beam where VF: 0.
p9
Recalling the angular velocity is v9 = i?“ one finds the maximum
. . . . 2 2 1/2 .
transverse divergence at by d1v1d1ng Vt: (vr + v9) tw'the axial

velocity vz of the ion in question

79

 

2
V P
,_t _ 9 Q Ii 1/2
at ’ v " [ 2 2 2 + 21“(p r) X —] (5.5)
2 M vzrm nMeovz m vzi

Eq. (5.5) clearly indicates that particles on the beam surface will
have a constant maximum transverse velocity, and a constant maximum
divergence, if the space charge force is zero since Pe after
extraction is constant. This is precisely the condition that is
assumed in beam transport calculations when one omits the space charge
force. Otherwise a is a function of r, which we will show is a

t
function of the axial drift distance 2. Thus at will be a function of
2, that is, the maximum divergence of the beam changes along the optic
axis if the space charge is not fully compensated.
The beam profile is obtained by integrating Eq. (5.11) once more

with respect to the time t

 

- 71-11111—1): 1 ——]"/2c1 = 1: (5.6)
I"

0M6, v21

'1 H '3
KICDUN
A

'1
a 10]..

here t = €_z_ is simply the time that it takes the i-th ions to travel
zi

from rm to r, assuming t = O at r = rm. There exists no analytical
solution for the left side of Eq. (5.6), but numerical integration
techniques can be used to give a reasonable result.

To get a feel for the nature of Eq. (5.6) we can formulate an
approximate solution. Let r : rm + X and assume X is small (i.e. a

short drift). Then we have

 

 

 

 

 

 

 

02 I
.9. _l_. _l_. ...Q. ..2. 1
M2 ( 2 ‘ 2) * uMe,ln( r 1 X v .
r m 21
m
2
2p 1.
9 94, 1
~[ + X ]X (5.7)
M2r3 «Mcorm vzi
and Eq. (5.6) becomes
2
2p I X
t = [ 293 + “M2 r X v1 1‘”2 I cur/w“2 (5.8)
M r ° m 21 0
m
Performing the integration and re-arranging terms yields
2 2
r-r‘=l[2pe Q X11 Z_ (59)
m H 2 3 “Hear v 2 ' ’
M r m 21 v .
m 21

The beam envelope is seen to have a quadratic dependence on 2, with
two terms, one due to the initial momentum of the edge particle and
the other arising from the space charge force.

For unneutralized ECRIS beams, we will now show that the second
term dominates. We have solved equations (5.5) and (5.6) numerically
for a helium 1+ beams of 10 keV energy and of various intensities
after a waist, and plot these results in Figures 5.1 and 5.2. At zero
intensity, Figure 5.1 shows that the maximum divergence is independent
of the drift distance, and Figure 5.2 shows that a slow increase in
the beam radius with the drift distance will be observed. As the
intensity increases both the maximum divergence and beam radius

sharply increase with the drift distance. An unneutralized 1.0 emA

81

Vex=10 I(V. Vp=0 KV. Rm=4. mm. Ra=4. mm. Bz= .251 T. He1+
100

 

 

 

 

 

 

 

 

 

ijI IIIfiIIIIIIIIIII'IIII II

: ‘15 \no DBB' q
A 80'— -—1
'3 " 1505“» 1
H " fl
E L' ‘506mh '1
f; 60:— I=O.4mA ‘
O - -1
‘5 P I-OZinA ‘
E I -' . -1
4°1— ' -'
C3 P 1 q

t ..
g ' 4
E 201" I=0.0mA _j
0" r
g _ .

or-PI ILLLLLLlllLlllllllllLlfi

O 20 40 60 80 100

R(mm)

Figure 5.1. He1+ beam maximum divergence versus the beam edge radius,
for different beam intensities, after a waist. The maximum divergence
is a constant if the space charge is zero. But as can be seen, if the
space charge force is taken into account, the beam maximum divergence
will increase rapidly with the level of the space charge force.

82

Vex=lD KV. Vp=0 KV. Rm=4. mm, Ra=4. mm. Bz=.251 T. He1+
100

 

 

 

 

- I I I I rfI I I I I I I I I I 1 I I I I I I I I I I
80 L _
_ 60 r— °&. ....
A P .1
E: b / ..,. 66$.
1- ’ . .1
V - \ ¢° %& .
I" 40 — X ’0' &. -—1
I \ o?‘ 3
I ‘I 0?, 19" I
20 r- \ ‘ .—
E i 5 00 “1" .
.- _’-/ 1
o I L I L I I L I J L I I ILL l I J L L1 I I IL I l L L I I q
0 25 50 75 ‘ 100 125 150
Z (cm)

Figure 5.2. A comparison of the beam edge radius with axial drift
distance for various levels of the space charge. The starting
conditions are the same as in Figure 5.1. For high uncompensated
space charge, the beam envelope rapidly increases with axial drift.

83
helium 1+ beam will have an envelope radius 11 times the zero space
charge radius after a drift of only 1 M. That is an enormous effect.
In the RTECR analysis system, the distance from the extraction
electrode to the solenoid center, and the distance from FC#1 to the
90° magnet entrance are both of the order of 1 M.

In the case of no space charge force, the beam maximum

divergence is a constant and so is xint= rm, that is
. . ‘19

£(no sp) = xmaxxint: xintxmaxz lsgl = constant. (5.10)

In the case of nonzero space charge force, both the X' and X are
max int

in) lon er constants and notin that X - r and X' - 'Xfifil .E§_

g 1 3 max' int- vz ‘ pzr ’
the product of X and X!

max int
‘19
e(sp) = X' X X' X l-—1 = e(no sp) (5.11)

int max= max int: pz
is also a constant and equal to the emittance with no space charge
force. That means the space charge force does not contribute to the
beam emittance. A rigorous proof that the space charge force does not
contribute to the beam emittance is given by L. Mills and A. M.
Sessler for more general cases [M158]. Although the space charge
force does not contribute to the beam emittance, compared to the case
of no space charge force, it increases both the maximum beam
divergence and the beam envelope along the beam optical axis, and this

effect is illustrated in Figure 5.3 (the effective emittance can be

811

XI

WITH SPACE CHARGE

 

  

NO SPACE CHARGE

 

Figure 5.3. A schematic view of the evolution of the emittance
envelope after a waist with and without space charge force. The
emittance is the same for both cases, but with space charge the
tllaxilmm divergence and beam size significantly increase.

85
increased by the indirect effect of space charge causing aberration
distortions).

We note here another important consequence for the emittance
after extraction from a Pierce geometry for high, but still space
charge limited currents. Even if'a parallel beam is obtained in a
Pierce - 1st extraction gap, the divergence after transit of the
extraction electrodes will increase with increasing intensity. In
Figure 5.11, BEAM_3D emittance calculations for helium 1+ beams are
compared for these different intensities; in all 3 cases the first gap
was D = 5 cm; Vex(end plate) = 10 kV, and the voltage on the puller is
varied to ensure a space charge limited current. The starting thermal
energy is taken to be zero. In each case the emittance after
extraction is 77 mm mrad, but the divergence increases with increasing
intensity as a result of the radial space charge force. This is a
pure space charge effect -- mitigated only if there is some degree of
neutralization in the initial beam. The 1 emA case in Figure 5.11 is
typical fOr the total extracted current from ECR sources including the
RTECR, and we will show that a significant emittance growth may occur
in the transit of the focussing solenoid from such high initial

divergences.

5.2 Rm Transit of the Solenoid lhgnet

As mentioned earlier, the RTECR beamline had been designed under
the assumption of a nominal beam emittance (5 x 110 mm mrad), without
taking the space charge force into consideration. But the space
charge force is not negligible, at least before the analysis magnet,

because we have found indirectly that the level of neutralization may

86

BEAM_3D Cal. He”, Vex=1o kV, SCL Currents

 

  
   

 

 

 

I III I I I I I I r Ij' I III I I I fr I I I I I I I I I
1- ' 1
r e = 77 mm mrd i 3 ‘
50 F- ° -‘
1- -1
L. -1
A I" ..
1..
E o r— ............... .-
v 1' 4
5< r ~
’ -' I (emA) _ ‘
r. - a
1 1 0.2
-50- . -
_ . | 2 0J5 -
__ | 3 1.0
L I I I L I I L L I. I I Li LI LLLLL I I I L I L L4
-30 -20 -10 0 10 20 30

X(mm)
-¢=8mm,Tw=O.D=5cm.Z=4lcm

Figure 5.“. A comparison of the divergence versus beam intensity for
space charge limited extraction using the BEAM_BD code. Even though a
parallel beam profile at the first gap is ensured, the effect of space
charge, which increases the divergence, is clearly seen.

87

be quite low, less than ten percent approximately, because BEAM_3D
calculations without any neutralization agree quite well with
measurements. Thus this space charge force increases the maximum beam
divergence well beyond the nominal design beam divergence at the
entrance of both the solenoid and the analysis magnets, resulting in
an emittance growth due to the lens aberrations. The observed low
transmission from PC“ to FC#2, and the high divergence after
analysis, are a consequence of this space charge force. The main
point is -- since the divergence grows with drift distance due to this
space charge force, the beam transport magnets are not in the right
locations to correctly image the beam, that is, space charge alters
the beam transport system.

A beam crossing the solenoid with a large envelope will undergo
an effective emittance growth due to the spherical aberration. This
can occur for high intensity ECRIS beams because of low
neutralization. Figure 5.5 shows emittances predicted by BEAM_3D,
after crossing the solenoid for .065, 0.5 and 1.0 emA He1+ extracted
from the RTECR. In these calculations Tl. is set to be zero, so the
initial emittances of 69 mm mrad are determined by the other source
conditions. In all three cases the puller voltage is chosen to
achieve a space charge limited extraction in the first gap, and zero
space charge neutralization is assumed. The emittances after crossing
the solenoid, plotted at the position of FC#1, are seen to
significantly increase with intensity. This is simply due to the
increase in the beam envelope due to space charge (as shown in Figure

5.3) before the entrance of the solenoid.

88

The effective emittance growth due to the solenoid aberration,
originating from a large beam envelope in the solenoid due to the
space charge force, will also increase the beam envelope after the
solenoid. BEAM_3D predicts that for a 65 euA He1+ extracted at 10 W
at the space charge limit, the solenoid should be excited with 81 A to
focus the helium beam with a waist at the object of the analysis
magnet (FC#1), and will have a beam envelope of 1.6" at the divergence
box, and is experimentally seen as shown in Figure 5.6A. Figure 5.68

1+ beam, also extracted at 10 kV at the space

shows that a 550 euA He
charge limit, has doubled the beam size at the divergence box due to
space charge agreeing fairly well with a BEAM_3D calculated width of
3".

The corresponding measured emittance at the divergence box for
the 65 euA case is shown in Figure 5.7. As can been, the measured
emittance of 69 mm mrad agrees with the calculated starting emittance.
In the calculation, with T_,_o = O, the emittance is determined by the
magnetic field. Good agreement with measurement does suggest that the
initial emittance of this 65 euA case is dominated by the magnetic
field.

BEAM_3D predicts that if an extracted beam is far below the
space charge limit in the extraction gap (voltage much greater than
space charge limit voltage), the situation is much worse. It will
result in very high divergence and large beam profile after extraction
due to the excessive focussing strength in the extraction gap. Again
such beam will have a very large beam profile at the divergence box
due to severe solenoid aberrations and measurements support BEAM_3D's

predictions. Shown in Figure 5.8 is a Kapton foil burn for a 65 euA

89

BEAM_3D Cal. He”. Vex=10 kV, SCL Currents

 

I I I I l I I

.

~ Initial
—: 69 mm mrd

D

 

  
 

 

 

A
1: " i
E 0 _ _ ....................... _
v L After Solenoid ‘
- _ 1
N +- I ‘ .
_ (emA) (mm turd),
40,. 1 0.065 as _
P 2 0.50 92 y
r , 3 1.0 340 .

L L I L L I I I L L L I I L I _L I J I

-20 -1o 0 10 20

X (mm)

¢=8mm,T,o=O,D=3.3crn,Z=190cm

Figure 5.5.

focussing solenoid for various beam intensities.

The effective emittance of He

1+

after crossing the
In each case the

extraction is space charge limited, the beam energy is of 10 keV, and

the emittance after extraction is 69 mm mrad.

The 1.0 emA case shows

very large emittance growth due to its large beam profile in the

solenoid, thus the aberrations have become very severe.

9O

\

 

 

 

 

 

 

 

 

 

 

mmmu'
"11111111”

:11

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-...W M \ ..
B

Figure 5.6. A and B are Kapton foil burns at the divergence box with
1+

He beams of 65 and 550 euA respectively. The beam passes through a

defining slit plate 8 cm upstream of the foil, giving horizontal marks
on the £011. BEAM_3D predicts for 65 euA He“

with space charge
limited extraction (Vex =

10 kV, Vp = 8.5 kV), beam profile at the
divergence box will be 1.6" and that is experimentally seen. A 550

1+

euA He extracted at space charge limit fills the Kapton foil at the

divergence box, also agreeing fairly well with a BEAM_3D calculated
profile of 3".

91

He“, 65 epA at. FC#1. Obj. 10 mm. L=7.87 cm

 

 

 

 

 

40 I I I I I T I I I r I T r I I I r I III
I l T l l .J
P d
20 — _.
P d
A ~ 1
s _ «
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-301'- -1
1: e = 69 mm mrd‘
t 1
_w I I I L L I I I L L I I LI L I I I I I I I I I

-20 -1o 0 10 20

X (mm)

Vex = 10 kV, Vp = 8.5 kV, [sol = 82 A

Figure 5.7. The measured emittance for the 65 euA I-Ie1+ beam in Figure

5-6A is e = 69 mm mrad, which agrees very well with the BEAM_3D
calculation (see Figure 5.5), in which the ion thermal energy was
tzaken to be zero.

92

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Figure 5.8. A 65 euA He1+ beam extracted (Vex = 10 kV, Vp = 0) well

below the space charge limited (Vex = 10 kV, Vp = 8.5 kV) current
results in high divergence and large beam profile. For this case,
BEAM_3D predicts a diameter of 5.5" at the divergence box.

93

BEAM_3D Cal. He”. 200 epA. z = 2565 mm

 

 

 

 

I I I I I I I I I T I I I I I I I I I T I I f I
. - x . ..
00 - x x _
_ 6 o a o :
A
E ' i
E ‘0 r— —
v ,. 1
N - -4
g . .
X P Tto = 0 1
20 — , _.
_ Calculation: x x ‘
- Measured (at least): 0 o ‘
o L I I I I I I L I I I I L I I I I I I I L L I L
0 10 16 20 26

 

100

 

 

 

- I I f I r I IiT I I 1’ I I I fI I I I I I I I I ‘
r- d
P x x
. x 1
00 — ..
r- x 4
C 0 D U U :1
A
LE- 60 — —
V P' .4
>4 I .
3 4° ’ “
5< ; I
’ Tt0 = 0 ‘
2° :— Calculation: x x g
- Measured (at least): :1 o 1
o I I _I I I L L I I I l I I I I I I I I I I ,I d
0 5 10 is 20 25
Vex (kV)

Figure 5.9. BEAM_3D predicts that a 200 euA He1+ extracted at 7, 10,
15 and 20 W with an extraction gap of 3.3 cm will have very high
divergence and large beam profile at the divergence box, because the
extraction is far below the space charge limit. Measurements,
limited by the measuring apparatus to a maximum divergence 65 mrad,
show that the actual divergence is higher, in fair agreement with the
calculations.

911
He1+ beam extracted well below the space charge limited current. As
can be seen, this 65 euA He1+ beam profile fills the whole measuring
frame, and as BEAM_3D predicts, has a diameter lager than the 550 euA
space charge limited case. Figure 5.9 shows the BEAM_3D predictions
and measurements (the measurements are limited by the apparatus) of
the maximum divergences and beam profiles for a 200 euA He1+ beam
extracted at 7, 10, 15 and 18 W with a gap of 3.3 cm. All of these
extraction conditions were well below the space charge limit

extraction, and result in high divergence in the beamline due to over

focussing in the first gap.

5.3 Transit of the Analysis Magnet

Because of the unneutralized space charge force, the divergence
at the entrance of the analysis magnet can be significantly higher
than that assumed in the beam transport design calculations. The
transit of the analysis magnet may then result in substantial beam
aberrations. We have graphic evidence of this effect for the other
operating ECRIS at NSCL, the CPECR [An86b]. The analysis system for
the CPECR differs from that for the RTECR, in that there is no
focussing magnet -— the source extraction electrode is placed directly
at the object of the 90° magnet (FCH in the RTECR system). During
the first year of operation of the CPECR, primarily lithium beams were
produced for injection into the [(500 cyclotron. For lithium
production the source is operated at high pressure on helium support
gas with lithium vapor coming from an oven. The total extracted
current is about 1 emA with about 50% helium 1+. After about 1 year

of operation in this manner the source was moved to a different

95
beamline, and the image Faraday cup assembly (equivalent to FC#2 in
Figure 1.2) happened to be removed as a part of this operation. We
found a large triangular beam mark on the face of the A Jaw collimator
mounted just before this Faraday cup, as shown in Figure 5.10.

The bulk of our object side foil burns on the RTECR do not show
triangular beams, for example as those shown in Figures 5.6 and 5.8,
so this mark on the CPECR FC#2 assembly is more likely related tn) the
transit of the analysis magnet than to beam effects at the source.
Beam transport calculations at the design emittance (5 x 140 mm mrad)
for this dipole design do not show evidence for triangular beams after
transit of the analysis magnet [N087]. In addition, extensive magnet
studies do not show magnetic field errors that might result in
triangular beams [N089]. If however we consider the transit of the
analysis magnet with an unneutralized 1.0 emA beam having the design
starting emittance at the object point, we are able to generate the
triangular beam marks observed. Figure 5.11 shows an intensity
contour plot and transverse coordinate beam profiles at the image of
our dipole magnet with a 1.0 emA He+ beam having a starting emittance
of 200 mm mrad. The intensity is uniformly distributed across the
initial beam profile. This calculation was made with the 6105 beam
transport code [H087]. The calculated profile has the same shape as
the observed slit plate mark in Figure 5.10, and would be due to the
second order aberrations that result from excessive divergence at the
magnet entrance. The excessive divergence is due to the space charge
growth. Furthermore, the y-profile in this calculation is strikingly
like the scanner profile for an Ar10+ beam made after the RTECR

analysis magnet that was shown in Figure 3.8.

96

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97

 

PLOT 0F 1x VS a)

x - RANGE -O.200E'
a - RANGE -O.100E°(

 

 

 

 

 

 

 

 

 

 

 

PLOT 0F 0( VS Y)

X - RANGE -O.3OOE°
Y - RANGE -O.3OOE-

 

 

I I j I I If I I I I I

 

 

 

 

 

 

 

90 DEGREE MAGNET :

Figure 5.11. A 6108 beam transport calculation for the case in Figure
5.10. The transit of the analysis magnet with an unneutralized 1.0
emA helium 1+ beam of starting emittance 200 mm mrad will result in a
triangular shaped beam after analysis.

98
5.11 Matching the 90° Analysis Dipole under the Effect of Space Charge

As mentioned above, the space charge force alters the effect of
the beam transport system. So even if the beam is extracted at the
space charge limit and properly focussed by the solenoid, with little
emittance growth crossing the solenoid, the space charge force still
can increase the beam divergence and beam envelope beyond the analysis
magnet design limit, and a poor transmission of the analysis magnet
will result. The lens will treat the beam, regardless of the prior
history of the beam, if it has the right divergence and beam profile
at the dipole entrance, as if it comes from the design object
location, and image the beam at the design image point. If the space
force is zero after the dipole entrance, it will not affect the beam
imaging process. If the space charge force after the dipole entrance
is not negligible, then this force will still affect the beam
transport after the transit of the dipole, and the beam may not be
imaged at desired location with the right size. In addition, an
emittance growth may occur in the dipole transit because of
aberrations.

Based on the above arguments, one may improve the transmission
of the 90° dipole by deceiving the magnet. The deception is to move
the beam waist closer to the magnet entrance than in the design, as
schematically illustrated in Figure 5.12. Because of the shorter
drift distance to the dipole when the waist is moved closer, the
increase in the beam divergence and the beam envelope due to the
effect of space charge will be less than if the beam waist was at the
design object. If this results in beam characteristics that are

closer to matching the design optics at the dipole entrance, then the

99

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100
ions will be imaged closer to the design image location. We tried
this technique, it works, and further confirms the transport limiting
effects of space charge on the drifting beam. As shown in Figure
5.13, a 330 euA He1+ was extracted from the RTECR at the space charge
limit, has a waist at the dipole magnet object when the focussing
solenoid was excited with 81 Amps, and the maximum transmission for
this setting is about 791. If the solenoid excitation decreases to 78
Amps, the beam waist moves about 10 cm closer to the magnet entrance,
a maximum transmission of about 871 is obtained. BEAM_BD calculations
show that the solenoid spherical aberration is minimum for this beam
after the transit of the focussing solenoid either for the solenoid
excitation of 81 or 78 Amps, but the second case (78 Amps) gives a
beam with much closer divergence and beam profile to the optics
design, as shown in Table 5.1. Therefore at 81 Amps, the beam is both
bigger and has higher divergence -- both are bad, and the transmission
decreases as a result. Thus the dipole magnet matching with a closer

beam waist is simply due to the beam space charge.

Table 5.1

Beam envelope at the 90° dipole entrance

 

Design at BEAM_3D (He1+ 330 euA)
90° entrance Solenoid: 78 (A) 81 (A)
xmax (am) no 37 All
Xéax (mrad) MO “3 52

 

Note: A beam of 5 x 110 um mrad is assumed at the object in the

optics design. The drift distance is 1 meter to the 90° entrance.

101

He“, 330 epA (FC#1), Vex = 10 kV, Vp = 2.6 kV

 

   

 

 

 

10° ’- Ifi T I I l I I T I r I T I l’ I I I I I I I I I l I I I I
I 1
- 4
0.0 :- 28 x 28 slit -:
7: I 1
2;: (L6 P- -:
rat. I 17 X 17 slit .
\ _ . ..
0*2 "' -4
o 0.4 I . .
E; ; 20 x 10 snt 3
0:: 0.2 L 1
i .
00 r. l 1 l I I I I I l I I 1L1 I I l I LI I L I l J I I I I I d
' 70 72.5 75 77.5 00 82.5 as

1301 (A)

¢ex = 8 mm, ‘I’pul = 12 mm. D = 5 cm

Figure 5.13. A 330 euA He1+ is extracted with space charge limit and

transported through the 90° dipole, this beam has a waist at the
dipole object when the focussing solenoid is excited with 81 A.
However the optimized transmission occurs at I(sole) = 78 A, for which
the beam waist is about 10 cm closer to the dipole.

102

Chapter 6

Summary and Conclusions

6.1 Extrapolation to mltiply-Cl'arged Ion Deals

The original motivation for the development of BEAM_3D, and the
beam measurements on the RTECR, was to study the emittance and beam
transport matching of multiply-charged ions. This has led to the He1+
technique, simplifying both the calculations and the experimental
studies. We have found indirect evidence for low neutralization of
the initial beams, with several important consequences. It is
necessary for the extraction to be space charge limited in the first
gap, leading to the use of a complete spherical Pierce lens system, to
minimize the initial divergence for any total extracted current. The
space charge force is proportional to the square root of M/Q, which

1

means the space charge force from 100 euA Ar + is equivalent to 316

euA He1+ at the same extraction voltage. Thus for heavier ion beam
transport, the space charge force before the analysis, if not
neutralized, will become much stronger than for a helium ion beam at
the same extraction voltage and with about the same total extracted
current. Although the space charge force does not increase the beam
phase area, there may be lens aberrations due to substantially larger
than design divergence at the magnet entrances. The high divergence
tails and triangular shapes of ECRIS beams after transit of the
analysis magnet are likely due to this effect.

The RTECR tunes for multiply-charged ions require much higher

1

microwave power than for the He + beams, and gas mixing, and we have

103
measured thermal energies of about 6.5 eV x q for higher charged argon
ions [An88]. As a consequence the starting conditions are likely to

be some what different for multiply-charged ions than for the He1+

studies reported here. Preliminary BEAM_3D calculations for an Ar8+
beam extracted from the RTECR have been made, using T4,, 5 5 eV x q,
and an actual charge state distribution of intensities among argon
ions and oxygen support gas ions. These calculations showed that the
Ar8+ ions are sensitive to the full unneutralized beam current before
the solenoid entrance. A spherical aberration occurs in the solenoid
crossing, increasing the emittance about a factor of two, as shown in
Figure 6.1. The solenoid does some pre-analysis, but the lost ions
are mostly of higher charge than 8+ and do not constitute a
significant percentage of the total extracted current. Therefore for
such Ar8+ beams, we have then essentially the same problem as for the
He1+ beams -- the divergence growth before lenses would be expected to
be a critical limiting phenomenon. We have already seen in Figure 3.7
that high divergence tails are observed on highly charge argon ions
measured after the analysis magnet, and there is an expectation that
this will prove to be due to aberrations as a consequence of high

divergence at the analysis magnet entrance, when further measurements

are made.

6.2 Sumary and Conclusions

In this thesis, some aspects of the RTECR ion beams have been
studied both theoretically and experimentally. The new 3 dimensional
code BEAM_3D, with a straightforward space charge model for beams of

multiple ion species, has proved to be a successful analysis tool at

1011

BEALBD Cal. Ar“. 15 em (FCflZ). Vex=13.44/—2.15 xv
60 I I I

 

20

 

 

X'(rnr)

O
r'filT'ITIUUUIII'IT]'IIU[IIII
I
I
I

 

 

¢=8/ 12 mm, '1‘,°<5 qu, D=5 cm, I(sol)=94.3 A

Figure 6.1. BEAM_3D code predicts that after crossing the focussing
solenoid the effective emittance of’Ar8+ (S shaped, due to the
solenoid spherical aberrations) is doubled compared to its effective
emittance before the solenoid. The CSD.and focussing solenoid
excitation are based on actual operating values.

105
least for the helium beams. A better extraction geometry to ensure a
parallel beam with minimum divergence at the extraction gap has been
introduced. The aberration of the focussing magnet lens due to a
large beam envelope has been demonstrated, and subsequently a better
transmission through the analysis magnet resulted from the realization
that the space charge force was driving the focussing lens aberration.

The good agreement between BEAM_3D calculations and equivalent
measurements suggests additionally that the plasma boundary and
starting thermal energies do not play a significant role in
determining the emittances when the source is tuned for these He1+
beams.

Based on the studies presented above, it seems not too
unreasonable that an emittance upper limit of 200 mm mrad is
achievable, if no aberration occurs during source extraction, for an
aperture of 8 mm, an extraction voltage of 10 kV, and a magnetic field
of 0.25 T, since there no evidence that the ion temperature is higher
than 10 eV x q. For cool ion beams, the transverse emittance is
simply dominated by the magnetic field which converts a small amount
of momentum into the angular direction. While if the ions are warm,
at a few eV per charge state, both the ion temperature and magnetic
field are comparable in contributing to the beam emittance.

Space charge neutralization is very low in the RTECR beam line
and therefore the space charge dominates the pre-analysis beam
transport. The RTECR beamline is capable of transmitting a beam of 5
x 140 mm mrad emittance, but space charge alters the beam transport by
increasing the beam divergence, so the main task is to compensate the

space charge force to avoid lens aberrations.

106

Shortening the beam drift distance is onecaf the means to
compensate for this space charge effect. Since the beam envelope is
quadratically proportional to the drift distance, reducing half of the
drift distance can reduce a factor of u of the beam envelope, and the
aberration will become very small. Other alternatives would be to
(1). generate a parallel electron beam within the ion beam to fully
neutralize the space charge [Kr87], and one could then return to the
designed beam transport system based on zero intensity transport
calculations, or (2). assume a maximum space charge in the design of
the beamline, and weaker beams would be properly transported by
retuning the beamline.

All of these techniques can be subjects for future study on
ECRIS ion beam characteristics to fully understand this young

technology for future development of ECRIS.

107

Appendix

Introduction to ECRIS

An ECRIS is a confined plasma device from which it is possible
to extract useful beams of highly-charged ions. Microwaves are
launched into the plasma, resonantly accelerating confined electrons.
These hot electrons ionize atoms in a process loosely described as
electron impact ionization. Ions lost from the magnetic confinement
zone fall into the extraction zone where beams are formed. The key
components of this kind of positive ion source and the main operation

characteristics will now be briefly discussed.

A.1 'Unit' ECR Cell

All ECRIS have at least one unit ECR cell, which will now be
defined. A unit ECR cell consists of a vacuum vessel, a minimum-B
magnetic bottle [N183], a microwave generator and an extraction
system, as illustrated schematically in Figure A.1. The vacuum vessel

6 to 10"7 T), and serves as a

is maintained at low pressure (~10-
microwave resonance cavity. The minimum-B field provides the plasma
confinement and nested closed magnetic surfaces for resonant electron
heating. This minimum-B field is fOrmed by superposition of a pair of
solenoid coils and a multipole magnet. The solenoid coils (room
temperature or superconducting coils) produce a tandem magnetic mirror
field, as shown for the NSCL CPECR [An86b] in Figure A.2. Tandem

mirrors would provide the well known axial confinement for a

collisionless plasma, but do not contribute to good radial confinement

108

GAS

 
   
  

WE VACUUM VESSEL

(PLASMA CHAMBER)

 
   
   
   

MINIMUM B
MAGNET/C FIELD

 

 

HEXAPOLE

/

RF

/ \\
———-—-7————-—-——

- -___<::~—--

  
 

COILS

.\

\ EXT RACT ION

Figure A.1. A 'Unit' ECR Cell consists Of a vacuum vessel, microwave
generator, a minimum-B field and an extraction system.

109

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110

due to ion - ion collisions and bad field curvature in between the
mirror coils. The addition of a multipole magnet, which produces a
magnetic field that increases with radius (quadrupole or higher
multipole), provides improved radial confinement. For historical
reasons, most ECRIS have used a hexapole magnet for this purpose. Ir)
ECRIS, most hexapole magnets are made of Rare Earth Cobalt permanent
magnets (for example, SmCo, or Sm2Co,,) because equivalent strength
coils would have very high power consumption, we choose permanent
magnets at the price of a loss of field adjustability. As can be seen
in Figure A.3, the field strength of a typical ECRIS hexapole magnet
varies approximately with the square of the radius over most of the
magnet bore [An83]. The superposition of a tandem mirror (solenoid
field) with a hexapole field is then one way to produce a minimum—B
field, In such a superposition, the magnetic field will increase in
all directions away from the center. It has been established
experimentally that a minimum-B field provides better plasma
confinement compared to the case of only a tandem mirror field [1062],
the resulting minimum-B field topology produce by a.set of mirror
solenoid coils and a hexapole magnet is schematically shown ixll?igure
A.“ [An87b].

The longer ion and electron confinement times in a minimum-B
field has significant consequences for high charge state ion
production. First, the step-by-step ionization dominates the
ionization process [Ge85], so the longer the ions stay in the plasma,
the more probable higher charge states become. Second, electrons will

have higher energy in the plasma if their confinement time increases.

111

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71 I
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AVIS

 

 

 

 

 

 

 

 

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164‘;

Figure A.“. A "minimum-B field" topology as a result of the
superposition of a hexapole and a set of solenoid fields.

113
Charged particles moving at a magnetic field will experience a

Lorentz force

§=QGX§ (A.1)

where Q is the charge that the particle carries, 3 is the particle
velocity and 8 is the local magnetic field. For historical reasons,
we call the frequency of such particle rotation the "cyclotron
frequency", which is related to the local magnetic strength B, the
charge Q and the mass M of the charged particle by the following

expression

:I‘B

(A.2)

If the charged particle is an electron, the above cyclotron frequency

is called the "electron cyclotron frequency".

- 93 (A.3)

w -
co m
e
where e and me are the charge and mass of the electron respectively.
When a plane wave of frequency w is launched into a plasma having
electrons confined by a magnetic field, acceleration is possible where
w 2: wec' Energy can then be transferred into the electrons from the
incoming electromagnetic wave. This energy transfer process is called

"Electron Cyclotron Resonance Heating". As a consequence of the

heating, the energetic electrons then can bombard the atoms and ions

11A

to a certain degree of ionization. In ECRIS the electron energy
gained by ECRH heating can be up to hundreds keV, but the peak of the
distribution is at tens of keV [Be8li], which improves the probability
for ionizing a variety of atoms and ions as can be seen from the
ionization potentials, taken from Carlson et a1 [Ca70], of various
atoms and ions shown in Figure A.5.

Some ECRIS make use of two ECR cells, for example, the RTECR is
a two stage room temperature ECRIS [An86a]. In two stage ECRIS, the
first stage produces a predominantly 1+ dense plasma which diffuses
into the second stage (main ionization stage). The advantage of two
stage operation is the coupling of two stages greatly enhances the
high charge state ion production, because the main stage operating
pressure is substantially reduced while maintaining a high plasma
density. Comparison of one stage versus two stage operation for

nitrogen ion production in the RTECR is shown in Figure A.6.

A.2 ECR Operating Characteristics
Here we briefly summarize important operating characteristics of
DC mode ECRIS. The reader is referred to the literature, especially

[6e79, Jo8fl], for additional information on this subject.

1. ECRIS reach charge equilibrium.
In equilibrium, net charge gain in the ECRIS plasma should be

zero. Thus we require that,

5e = {1q(¢;+¢:+....) (A.u)

Q

115

Ionization Potential

 

‘0‘ IIIIlfirrII,TIIfIIIITIITIII

 

103 ,
9 103 _
s I
/’
E
a" , He H
Ar H
)03 Obi!
100 1 L LJ I l l 1 l l l I L I L l l L l L i L 1
O 5 10 16 30

Figure A.5. Single ionization potentials of some atoms and ions.

116

STRONG 2 STAGE OPERATION VS. 2ND ONLY

 

 

 

 

 

 

 

 

 

 

 

 

BO .- I I I I I I I l I I I I I I I I I I I I f I I I I T I fi
: He“ N3 + He Feed j
.. ....-- 2 STAGE -
60 L— __ 2ND ONLY ""‘
i : N‘+ N1+ I;
f " N5+ N3+ 51 -
g _ N2+ ;: .1
12‘ - fl 1
D '- q
0
Q ” ..
a — —
5 .
g ' -1
'- 1 1 I I I 1 I L I I I I I I 1 1 1 1 I I I I I I L 1 I 1 J

 

 

 

50 75 100 125 150 175
ANALYSIS MAGNET CURRENT

Figure A.6. Performance comparison between 2-stage and second stage
only RTECR operation for the production of nitrogen ions. Helium is
used as a support gas. Each next higher charge state shows a large
percentage increase in current with the first stage on.

117
where Qe is the electron flux density, 5; stands for the flux density
of ions with q electrons removed, and there may be as many as i of
ions of different elements with the same charge state q in the plasma.
Since the net gain of electrons and ions in the plasma should be

zero, we must also have

dNe dNi
a;— = Adi: = 0 (A5)

where Ne is the electron density and N is the ion density of charge

iq
state q.

2. The probability of producing multiply-charged ions in a
single electron impact collision falls off rapidly with increasing ion
charge Q.

The production of highly-charged ions in ECRIS is dominated by
step-by-step ionizations [Ge85]. The single step ionization rate, for
an ion going from state q to q+1, is a function of the electron energy

E and is given by

R (E)

ion q,Q+, (2)-ve(E)~ue(E) (A.61

: oion q+q+1

where o is the electron impact single ionization cross
ion qoq+1

section which falls off rapidly with increasing charge state q for a

given electron temperature [Mu80], ve is the electron velocity and Ne

is the electron density. The ionizing electrons in an ECRIS are not

monoenergetic, but have an energy distribution. An integration must

118
be performed on all possible energies to calculate the ionization rate
R [JoBM]. The exact form of the electron distribution in ECRIS is not
yet clearly known. For simplicity, a Maxwell distribution is
generally used in order to estimate the ionization rate. Shown in
Figure A.7 are calculations of ionization rate coefficients S =
(Rion q+q+1/ Ne) for stepwise ionization of argon atoms and ions,
using electron-impact cross section due to Muller et al [111180], and

the atomic subshell binding energies from Carlson et al [Ca70].

3. Charge exchange between ions and neutrals occurs in plasma
and this is an important limiting process.

Single charge capture from neutrals dominates the charge
exchange process. The cross section for single charge capture,

proposed by Muller and Salzborn [Mu77], is

= 1.u3 10-12-q1'170P6’;76 cm2 (A.7)

oexch q+q-1
where P, in eV, is the first ionization potential of the atom. Muller

and Salzborn also give formulae 0 through 0

exch q+q-2 exch Q¢q-u°

However, as q increases, the double and higher order charge exchange
processes can be ignored when compared to the single charge exchange
process. Typically, these single charge capture cross sections are
three to four orders of magnitude larger than ionization cross
sections. The corresponding rate of single charge capture between

ions and neutrals is

119

Ioniztion Rate Coefficients

 

 

 

 

10-6 :- I I IIIIIII I I IIIIII] I I IIIIIII I IIIIII‘
E
" q
1.0-7 §_ 1
E
7 2
..8 h /
10 .E. 3
E
5‘ _. 45
“in - 67
B 1.0—9 r-
3 E
"’ E
o h 1213/
...1 .1
10 E— 14 g
E 15 j
" 16 -
10"11 4 IIIIIIII 1 UIIIIII 1 I4IJILII J 1 IJIJIJ

...

102 103 104 105
Te (eV)

10

Figure A.7. Ionization rate coefficients S for single ionization of
argon atoms and ions from the ground state by electron-impact in
plasma (Maxwellian distribution, no collision limit).

120

Rexch q+q-1= oexch q+q-1.vin.N° (A'B)
where vin is the relative velocity between ions and neutrals and No is
the neutral density. The ions in ECRIS plasma are rather cold
compared to the electrons, at most a few tens to a hundred eV for ions
of charge state q S. 20 [K086, Me86, An88], and the ion velocities are
much slower than the electrons. Thus there is a competition between
ionization and charge exchange in ECRIS plasma. Since we do not have
much control over the charge exchange cross sections and the relative
velocity Vin, the most effective way to reduce such charge exchange is
to reduce the neutral density N., and ECRIS generally do operate at
low pressure, to ensure the best performance of the source. Typical
operation pressures in the ECRIS ionization (main) stage is 10.6%7 T,

for two stage ECRIS, the operation pressure in the first stage is
10‘3~'“ T.

4. The electron density is limited.
The maximum electron density in plasma is tied to the microwave

frequency by the following relation

N = 1.2ux10’8r2 (A.9)
ec
which is a consequence of a limit for electromagnetic wave injection
for a given plasma density. Here Nec is the critical electron density
and f is the microwave frequency. According to Eq. (A.6), increasing

the electron density will increase the ionization rate, therefore to

121
improve the high charge state ion production we should raise the
density, but Eq. (A.9) sets an upper limit on how high we can raise
electron density in ECRIS plasma for a given microwave frequency f.
Thus one wants to increase the electron density further in ECRIS, the
microwave frequency and the magnetic field should be increased

accordingly.

5. Low gas consumption.

The source of plasma in an ECRIS is neutral gas. The gas
consumption is in the order of one standard cc/hr, due to the low
operating pressure and good ionization efficiency. For example, the
gas consumption of the RTECR has been measured to be $1 standard cc/hr
[An87a]. A 1 standard cc/hr consumption of helium is equivalent to

~7.5x1o15

particle/sec, while the total extraction current from the
RTECR (mainly He1+ beam) is 0.5 emA, or 3x1015 particle/sec. The

ionization efficiency is then IE z N /N,, = 110%. Metallic ions can be

1
produced by the use of an oven that makes metal vapor, as shown for
the NSCL CPECR in Figure A.8, or by direct feed of the material into

the main stage plasma [Sa87].

6. A mixture of a lighter gas as support gas usually boosts the
yields of the intermediate and high charge state ions of a heavy gas.

Figure A.9 shows a comparison of pure Argon feed to the effect
of mixture of Argon with lighter gases obtained from the RTECR, and
similar results were also been observed in other ECRIS [Br811, Ly811].
This effect has been observed in most ECRIS, readers are referred to

the literature of ECRIS for the details. The effect of gas mixing

 

122

   
 

WINDOH
jfi

 
  

TURBO PUMP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

xsruxs
{You
“c": d_. arcsowsvs
xzxuots 1—. ._..- use
. —Ill _'
:L

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure A.8. A high temperature oven for producing metal vapor is
equipped with the CPECR Ion Source at NSCL/MSU.

123

.comnm no“: mommm Loanmda no mcfixfia on» a“ zoom
3 mama :0 33.36 mats... new no mucoucoqoo noon: of. .o.< 6.33m

Qw>ozma wzomhumqm O

 

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s . E o. m s . e s . s
. . . q . 4 Ts.“
n a,
n 9 .z
m xa komuum oszHz men as
. . 7
n M? , ...; \ch zoom... zoomc mumnE
I . I II ./
... /.,. .1.
m x”. ..®1\\\\0I + . s."
. .. «I I
r Hz.» .4. /
I ./;1 I". I
W ,1“! 1.1/,/. D
n NO+\ «Bur/DI ./.H.: 7.06 .(fx
I .1”! .1.
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m ~2+\ . ”Hz” . 3.33.358! In
la n. .lonoloto-0151510lvlanal-lé Os.“

 

12“
could be explained by an ion cooling model proposed by Antaya --energy
transfer from the heavy ion species to the light ones [An88]. Such
thermalization results in longer confinement time of the heavy ion
species. A preliminary energy spread measurement of'argon versus
argon mixed with oxygen as coolant on the RTECR, strongly supports the

above explanation for the gas mixing [An88].

125

LIST OF REFERENCES

An83

An86a

An86b

An87a

An87b

An88

An89
Ba86

Be67

Be84

8172

T.A. Antaya, J. Moskalik and D. Lawton, NSCL Annual Report
1983-8“, p. 267.

T.A. Antaya, Z.Q. Xie, Proc. 7th Workshop on ECR Ion Sources,
Julich, w. Germany, 1986, p. 72.

T.A. Antaya, Z.Q. Xie and D.P. Sanderson, NSCL 1986 Annual
Report, p. 17“.

T.A. Antaya, L. Gneiting, W. Nurnberger, D.P. Sanderson and
2.0. Xie, Proc. of Int. Conf. on ECR Ion Sources and their
Appl., East Lansing, NSCL Report #MSUCP-U7, 1987, p. 86.

T.A. Antaya, H.G. Blosser, J.M. Moskalik, J.A. Nolen and A.F.
Zeller, Proc. of Int. Conf. on ECR Ion Sources and their Appl.,
East Lansing, NSCL Report #MSUCP-fl7, 1987, p. 312.

T.A. Antaya, Proc. Int. Workshop on ECR Ion Sources, Grenoble,
France, 1988.

T.A. Antaya, private discussion.

E. Baron, L. Rex and M.P. Bourgarel, Proc. 7th Workshop on ECR
Ion Sources,Julich, W. Germany, May 1986, p. 25.

M.Y. Bernard, Focusing of Charged Particles, Academic Press INC.
(edited by A. Septier), New York, NY, 1967, Vol. I, p. 3“.

V. Bechtold, L. Friedrich and F. Schulz, Proc. of Tenth Int.
Conf. on Cyc. and their Appl. East Lansing, 1984, p. 118.

S. Bliman, R. Geller, W. Hess, B. Jacquot, IEEE Trans. N§;19,

No. g, 1972, p. 200.

Br67

Br8“

Ca70

Ch11

C183

C187

De83

Dr83

Dr85

6870
6879

6685

Ha87

He79

H079
1062

126
George R. Brewer, Focusing of Charged Particles (edited by A.
Septier), Academic Press Inc., 1967, p. 7“.
v. Brautigam, H. Beuscher, H.G. Mathews, J. Reich, P. Wucherer,

Proc. 10th Int. Conf\ on Cyclotrons, IEEE 84CH1996-3, 1984, p.

 

122.

T.A. Carlson, C.W. Nestor Jr., N. Wasserman and J.D. McDowell,
Atomic Data g, 1970, p. 63.

C.D. Child, Phys. Rev. 32, 1911, p. 492.

DHL.Clark, J.G. Kalnins and C.M. Lyneis, IEEE Trans. Nucl.
Sci. N§;3Q, 1983, p. 2719.

D.J. Clark, Proc. Int. Conf. on ECR Ion Sources and their
Appl., E. Lansing, Nov 1987, p. H33.

O.C. Dermois, Particle Accelerators, Vol. 15, 1983, p. 63.

A.6. DrentJe, Physica Scripta, 13, (1983) HS.

AWG. Drentje, Proc. 6th Int. Workshop on ECR Ion Sources,
Berkeley, 1985, p. 73.

R. Geller, Appl. Phys. Lett. 16, No 19, 1970, p. ”01.

R. Geller, IEEE Trans. Nucl. Scien. N§;26, No. g, 1979, p.
2120.

R. Geller et al, Proc. 6th Int. Workshop on ECR Ion Sources,
Berkeley, 1985, p. 1.

H.L. Hagedoorn et al, Proc. of Int. Conf. on ECR Ion Sources and
their Appl., East Lansing, NSCL Report #MSUCP-u7, 1987, p. 389.
William B. Herrmansfelt, ELECTRON TRAJECTORY PROGRAM, 1979.

R.F. Holsinger, New England Nuclear, 1979.

Yu.V. Gott, M.S. Ioffe, V.G. Telkovskii, Nucl. Fusion, 1962

Suppl., part 3, p. 10145.

J083

J088

K686

Kr86

Kr87

LyBH

Ma83a

Ma83b

Ma86a

M886b

M886

M158

hh77

M680

N183

127
Y. Jongen and G. Ryckewaert, IEEE Trans. Nucl. Sci. N§;3Q, 1983,
p. 2685.
Y. Jongen, Proc. 10th Int. Conf. on Cyclotrons and their Appl.,
IEEE 89CH1996-3, 198“, p. 322.
H. K8hler, M. Frank, B.A. Huber and K. Wiesemann, Proc. 7th
Workshop on ECR Ion Sources, Julich, W. Germany, 1986, p. 215.
W. Krauss-Vogt, Proc. 7th Workshop on ECR Ion Sources, Julich,
W. Germany, 1986, p. 27”.
(EVA. Krafft, Ph.D. Thesis, Accelerator & Fusion Research
Division, LBL, Univ. of Berkeley, 1987.
C.M. Lyneis, private communication.
H.-G. Mathews, H. Beuscher, W. Krauss-Vogt, Proc. Int. Ion

Engineering Congress - ISIAT'83 &IPAT'83, Kyoto, Japan, 1983.

H.-G. Mathews, H. Beuscher, W. Krauss-Vogt, IKP Ann. Report 83,
p. 125.
M. Mack, J. Haveman, R. Hoekstra and A.G.- Drentje, Proc. 7th

Workshop on ECR Ion Sources, Julich, W. Germany, 1986, p. 152.
G. Mank, M. Liehr and E. Salzborn, Proc. 7th Workshop on ECR
Ion Sources, Julich, W. Germany, 1986, p. 103.

F.W. Meyer, Proc. 7th Workshop on ECR Ion Sources, Julich, W.
Germany, (1986) 11.

R. L. Mills and A. M. Sessler, MURA Rept. No. 53;, Midwestern
Universities Research Association, Stoughton, Wisconsin, 1958.
A. Muller and E. Salzborn, Phys. Lett. 62A, No Q, 1977, p. 391.
A. Muller et a1, Atom. Molec. Phys., 1;, 1980, p. 1877.

D.R. Nicholson, Introduction to Plasma Theory, John Wiley &

Sons, 1983, p. 206.

N087

N089

Pa87

P154

P070

R066

$887

$867

Sp85

Tu80

W882

W072

W086

128

J.A. Nolen, S. Tanaka, A. Zeller and N. Bhattacharya, Proc.

Int. Conf. on ECR Ion Sources, NSCL Report #MSUCP-“7, E.

 

Lansing, Nov 1987, p. “5“.

J.A. Nolen, private communication.

R.C. Pardo and P.J. Billquist, Proc. of Int. Conf. on ECR Ion
Sources and Their Appl., East Lansing, NSCL Report #MSUCP-“7,
1987, p. 279.

J. R. Pierce, Theory and Design of Electron Beams, D. VAN
NOSTRAND INC., 1954, p. 173.

H. Postma, Phys. Lett. 31A, No. 4, Feb 1970, p. 196.

Michael J. Romanelli, Mathematical Methods for Digital
Computers (edited by A. Ralston and H.S. Wilf), John Wiley 8:
Sons, Inc., 1966, p. 110.

D.P. Sanderson, T.A. Antaya and 2.0. Xie, Proc. of Int. Conf.

on ECR Ion Sources and Their Appl. , East Lansing, NSCL Report

#MSUCP-47, 1987, p. 300.

A. Septier, Focusing of Charged Particles, Academic Press INC.
New York, NY, 1967, Vol. II, p. 151.

P. Spadtke, KOBRA3 - THREE DIMENSIONAL RAYTRACING INCLUDING
SPACE-CHARGE EFFECTS, IEEE Trans. Nucl. Sci. N832, 1985, p.
2465.

N.Chan Tung, S. Dousson, R. Geller, B. Jacquot and M. Lieuvin,
Nucl. Instr & Meth, 11“ (1980), 151.

11.1. West, Jr., Calculation of Ion Charge-State Distribution in
ECR Ion Source, UCRL-53391, LLNL, 1982.

A. van der Woude, IEEE Trans. N§;19, No. g, 1972, p. 187.

B.H. Wolf, K. Leible, P.Spadtke, N. Angert, J. Klabunde and

W087
X186
X187

2885

129
B. Langenbeck, Proc. 7th Workshop on ECR Ion Sources, Julich,
W. Germany, 1986, p. 103.
H. Wollnik et al, Nucl. Instrum. nad Meth. 5258, 1987, p. 402.
2.0. Xie and T.A. Antaya, NSCL 1986 Annual Report, p. 166.
2.0. Xie and T.A. Antaya, Proc. Int. Conf. on ECR Ion sources,
NSCL Report #MSUCP-47, E. Lansing, 1987, p. “20.
A.F. Zeller, J.A. Nolen Jr. and L.H. Harwood, NSCL 1985 Annual

Report, p. 165.