Development of a multi-element x-ray excitation probe for the measurement of spatial distributions of energetic ions, at...

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Title:
Development of a multi-element x-ray excitation probe for the measurement of spatial distributions of energetic ions, atoms, and molecules
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xviii, 268 leaves : ill. ; 28 cm.
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English
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Ferrari, Angelo M., 1934-
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bibliography   ( marcgt )
theses   ( marcgt )
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Thesis:
Thesis (Ph. D.)--University of Florida, 1991.
Bibliography:
Includes bibliographical references (leaves 258-264).
Statement of Responsibility:
by Angelo M. Ferrari.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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oclc - 25540961
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Full Text















DEVELOPMENT OF A MULTI-ELEMENT X-RAY EXCITATION PROBE
FOR THE MEASUREMENT OF SPATIAL DISTRIBUTIONS OF
ENERGETIC IONS, ATOMS, AND MOLECULES














BY
ANGELO M. FERRARI














A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1991































Copyright 1991

By

Angelo M. Ferrari


































To Raquel















ACKNOWLEDGMENTS


Many people have helped me with their wisdom, their

encouragement, or their love to reach this stage in my

academic and professional career. Among them are my

teachers, my friends, and my dear family. It would be

impossible for me to thank all of them individually without

fear of leaving out someone that justly deserves to be

included in the list. Therefore, I will limit myself to

mentioning those who most recently and most directly have

given me their support in the work related to this

dissertation.

First, I acknowledge the interest that the members of

my committee have shown in my work, in particular that of

its chairman, Dr. Samim Anghaie. His constant support and

almost unlimited availability for enlightening discussions

have been key factors in my successful completion of this

dissertation.

I have learned much from informal conversations with my

fellow students. Two of them deserve special mention since

they also helped me in the performance of many of the

measurements required for this work: Robert Williams and Leo

Bitteker. My sincere thanks go to them.









I am in debt to my old friends and colleagues Edward

Fairstein, Peter Thieberger, and Sergio Pissanetzky for more

reasons that I can possibly mention.

The love and patience of my wife Raquel and of my

children, Lucia, Mario, and Pablo, kept me going at times

when my energy seemed to evaporate.

I appreciate the financial support of the Electric

Power Research Institute (EPRI) through a grant to the

University of Florida. In particular, I thank Dr. David H.

Worledge of the EPRI Nuclear Power Division for his vision

in facilitating the support of the project of which this

work is a part.

Finally, I also acknowledge the financial support of

Drs. Donald Price and Thomas Walsh of the University of

Florida Research Foundation and of the Division of Sponsored

Research.
















TABLE OF CONTENTS


ACKNOWLEDGEMENTS . ..

LIST OF TABLES . .

LIST OF FIGURES . .

ABSTRACT . . .

CHAPTERS


1 INTRODUCTION . .

2 MOTIVATION AND BACKGROUND . .

2.1 Motivation .. . .
2.1.1 The Self-Collider Fusion Reactor .
2.1.2 Diagnostic Instrumentation
Requirements of the SCFR .
2.2 Background: Existing Methods of Particle
Density Distribution Measurement .
2.2.1 Beam-current Measurements .
2.2.2 Secondary Emission Measurements .
2.2.3 Other Methods of Particle Beam
Characterization .
2.2.4 Applicability of Existing Methods
to the SCFR Diagnostic Requirements


. 1

. 5

. 6
. .. 6


3 THE MULTI-ELEMENT X-RAY EXCITATION PROBE METHOD

3.1 Operation of the Multi-Element X-ray
Excitation Probe System. . .
3.2 Targets for Use with the Multi-Element
Probes . . .
3.3 Applicability of the Method to the SCFR
Diagnostic Needs . .
3.4 Other Applications for X-ray Excitation
Probes . . .

4 PRODUCTION AND DETECTION OF X-RAYS FROM TARGETS
BOMBARDED BY ENERGETIC PARTICLES .

4.1 Introduction . .
4.2 Stopping of Energetic Ions by Matter .
4.3 Production of Characteristic X-rays .


Page

iv

ix

xii

xvi


* *







* .









4.4 Absorption of X-rays in the Target Material 61
4.5 Detection of X-rays .. 62
4.6 The Specific Detected Photon Yield 64

5 IMPLEMENTATION OF THE MULTI-ELEMENT
PROBE METHOD . ... 68

5.1 Construction and Assembly of Probes 70
5.1.1 Laminiform Probes . ... 70
5.1.2 Filiform Probes . ... 70
5.1.3 Selection of Materials for Probe
Construction . ... 77
5.2 The X-ray Detector . ... 77
5.2.1 Non-Continuous Use . ... 79
5.2.2 Sufficient Resolution ... 80
5.2.3 Reasonable Efficiency ... 82
5.2.4 Physical Configuration ... 83
5.3 The Very Low Noise Preamplifier ... 85
5.4 The Linear Amplifier . ... 97
5.4.1 Amplification . ... 98
5.4.2 Pulse Shaping and Noise Filtering .. 101
5.4.3 Pole-Zero Cancellation .. .. 111
5.4.4 Baseline Restoration . .. .112
5.5 The Multi-Channel Pulse-Height Analyzer 114
5.5.1 Determination of the Required MCA
Specifications . .... 117
5.5.2 Specifications of the Selected
Analyzer . ... 121
5.6 System Integration . ... .121

6 MEASUREMENT OF SPATIAL PARTICLE DISTRIBUTIONS
USING THE MULTI-ELEMENT X-RAY EXCITATION PROBE 124

6.1 Calibration Facility . ... .126
6.1.1 The Van de Graaff Accelerator and the
Beam Line Used in the Measurements 126
6.1.2 Energy and Current Calibration of
the Van de Graaff Accelerator 131
6.2 Calibration of the X-ray Spectrometer 162
6.3 Calibration of X-ray Excitation Probes 164
6.3.1 General Method of Probe Calibration 166
6.3.2 Calibration of Probes with Laminiform
Targets . ... 174
6.3.3 Calibration of Probes with Filiform
Targets . . 175
6.3.4 Calibration of Probes Using Partially
Ionized Beams . .... 194
6.4 Measurements of Beam Profiles and Position
Using Multi-Element X-ray Excitation Probes 195
6.5 Measurement of Beams Neutralized with
Carbon Foils . ... 196


vii









7 CALCULATION OF SPECIFIC DETECTED PHOTON YIELDS .207

7.1 Calculation of the Specific Detected
Photon Yield for Targets Bombarded with
Protons in the Energy Range from 0.5
to 2.5 MeV ....... 208
7.1.1 Calculation of Ysd for Thick Laminiform
Targets .. . 208
7.1.2 Calculation of YS for Filiform Targets 215
7.2 Calculation of Specific Detected
Photon Yields for Thin Gold Wires Excited
by High-Energy Protons . ... .223

8 CONCLUSIONS . . ... .225

APPENDICES

A FABRICATION OF THIN SEAMLESS ALUMINUM WINDOWS 230

B SPECIFICATIONS AND CALIBRATION CERTIFICATE OF
THE K485 CURRENT METER . ... .249

C DATALOG FORM . . .. 252

D APPLICATION OF X-RAY PROBES TO SCFR
MEASUREMENTS . . ... .254

REFERENCES . . ... .258

BIOGRAPHICAL SKETCH . ... .265


viii

















LIST OF TABLES

4-1 X-ray production cross sections for protons in
tungsten, calculated with Equation 4-4 .

5-1 Target materials used in the laminiform probes

5-2 Reduced list of metals suitable as targets


in x-ray excitation probes .

6-1 Resonances in the 27Al(p,y)28Si Reaction
(between 800 and 1200 keV) .

6-2 Energy levels of 2Si . .

6-3 Data for the determination of k at the
922.6 keV resonance . .

6-4 Data for the determination of k at the
937.2 keV resonance . .

6-5 Data for the determination of k at the
991.88 kev resonance . .

6-6 Data for the determination of k at the
1025.0 keV resonance . .

6-7 Data for the determination of k at the
1118.4 keV resonance . .

6-8 Summary of the determinations of k and
calculation of the average value .

6-9 Calibration of the K261 current source .


6-10 Main energy peaks of the calibration sources

6-11 Switching magnet settings for north line .

6-12 Charge-to-protons conversion factors .

6-13 Measurements of Ysd for laminiform Nb targets
(K-series) . . .

6-14 Measurements of Yd for laminiform Mo targets
(K-series) . . .


S 78


137

139


143


144


145


145


146


152

159

161

169

173


176


177


. .


. .


. .

















6-15 Measurements of Ysd for
(K-series) .

6-16 Measurements of Yd for
(L-series) .


laminiform Pd targets


laminiform Ta targets


S 178


S 179


6-17 Measurements of Yd for laminiform W targets
(L-series) . . 180

6-18 Interpolated values of Ysd for laminiform
targets (K-series) . .. 181

6-19 Interpolated values of Ysd for laminiform
targets (L-series) . .. 182

6-20 Materials and sizes of wires used in filiform
probes . .... 184

6-21 Correction factors for current-integrator
readings for 2.5 MeV protons striking Mo
and Pt wire targets at 450 . .. 187

6-22 Measurements of Ysd for filiform (d = 127 Am)
Mo targets (K-series) . .. 188

6-23 Measurements of Ysd for filiform (d = 127 m)
Pd targets (K-series) . .. 189

6-24 Measurements of Y for filiform (d = 127 Am)
W targets (L-serles) . .. 189

6-25 Measurements of Ysd for filiform (d = 127 Mm)
Au targets (L-series) . .. 189

6-26 Interpolated values of Ysd for filiform
(d = 127 Mm) targets (K-series) ... .190

6-27 Interpolated values of Ysd for filiform
(d = 127 Mm) targets (L-series) ... .191


6-28 Measurements of Y for filiform Mo targets at
Eo = 2.5 MeV (K-series) . .

6-29 Measurements of Yd for filiform Pt targets at
Eo = 2.5 MeV (L-series) . .

6-30 Principal x-ray lines of the target materials
used in the measurement of beam profiles .

7-1 Normalized target penetration (t/R) vs.
normalized proton energy (E/Eo) .


193


193


195


212









7-2 Depth intervals and proton energies used in
Equation 7-2 . . .214

7-3 Interpolation multipliers . .. 215

A-1 Percent transmission of photons by beryllium 232

A-2 Percent transmission of photons by aluminum 233

A-3 Percent transmission of photons by Mylar 237















LIST OF FIGURES
Page

2-1 Examples of exoergic nuclear reactions which
could be produced with colliding beams 7

2-2 Approximate diagram of the field lines of the
superconducting magnets used in the SCFR 9

2-3 Complete array of the superconducting magnets
used in the SCFR and approximate diagram of
the field lines . .. 10

2-4 Representation of the trajectories of the
particles in the SCFR showing the focusing
effects of the axial and radial field
components . . 11

2-5 Particle density as a function of the radial
distance . .... 12

2-6 SCFR concept with direct energy conversion
system . . ... .. 13

2-7 Methods of particle injection in the SCFR 17

3-1 Illustration of the principle of operation
of the multi-element x-ray excitation method 29

4-1 Stopping and range of protons in tungsten 42

4-2 Energy loss of a proton beam with initial energy
E = 1 MeV as it penetrates a thick tungsten
target, graphed from data of Andersen and
Ziegler. Curve is a fifth order polynomial
fit. Vertical segments are standard
deviations calculated with Bohr's formula 44

4-3 Characteristic x-ray nomenclature ... 49

4-4 Examples of characteristic x-ray spectra ... 50

4-5 K-series x-ray production cross sections computed
with Reuter's formula and Reid's program 53


xii










4-6 L-series x-ray cross sections plotted from
published data . .

4-7 Energy distribution of protons of initial energy
Eo = 1 MeV vs. average energy , as they
penetrate a thick tungsten target. The areas


under the curves are equal


4-8

5-1


Geometry for Equation 4-13 .

Longitudinal section of test chamber show
target holder . .


5-2 Aperture-type holder . .

5-3 Fork-type holder . .

5-4 Jig for assembling filiform probes .

5-5 Definition of resolution .

5-6 High-purity germanium detector .

5-7 Charge-sensitive preamplifier .

5-8 Pulsed optical feedback charge-sensitive
preamplifier . .

5-9 Differentiating network .

5-10 Integrating network . .

5-11 System block diagram . .

6-1 Simplified diagram of the experimental
beam line . .

6-2 Diagram of the target-detector geometry


. 66

ring
71

. 72

. 74

. 75

. 81

. 86

. 90


. 95

S. 106

107

. 122


S 128

S .. 132


6-3 Experimental arrangement for energy calibration
of the Van de Graaff accelerator .

6-4 Gamma-ray spectrum of 28Si acquired with a 5-inch
x 5-inch NaI(Tl) detector. The horizontal scale
(energy) ranges from 0 to approximately 14 MeV.
The vertical scale (counts) is logarithmic

6-5 Correspondence between steps in the gamma-count
graph with resonances in the 27Al(p,y)28Si
reaction . . .

6-6 Determination of k at the 922.6 keV resonance


xiii


. . 56


138




140



142

147








Determination of k at the 937.2 keV resonance

Determination of k at the 991.88 keV resonance

Determination of k at the 1025.0 keV resonance

Determination of k at the 1118.4 keV resonance


6-11 Block diagram of the K261 current source


6-12 Illustration of the virtual ground type of
current-measuring instrument .

6-13 Photon energy spectrum of calibration source

6-14 Typical spectrometer calibration graph .


6-15 Specific detected photon yields of
targets . .

6-16 Correction factor for tilted wires

6-17 Specific detected photon yields of
targets of 0.127 mm diameter .

6-18 Measurement of beam profile (I)
(beam direction: into the page) .

6-19 Measurement of beam profile (II)
(beam direction: into the page) .

6-20 Measurement of beam profile (III)
(beam direction: into the page) .

6-21 Measurement of beam profile (IV)
(beam direction: into the page) .

6-22 Measurement of beam profile (V)
(beam direction: into the page) .

6-23 Measurement of beam profile (VI)
(beam direction: into the page) .


laminiform


filiform
* *


6-7

6-8

6-9

6-10


. 183

186


S. 192


S 197


S. .. 198


S. .. 199


S. 200


S. .. 201


S. 202


7-1 Illustration of the method used to determine
the values of Ati used in Equation 7-2 .

7-2 Universal graph of proton energy vs. target
penetration . .

7-3 Specific detected photon yields for thick
laminiform targets . .

7-4 Geometry for filiform targets .


. 210


. 213


. 216

. 218


xiv


S 148

S 149

S 150

S 151

S 156


S 157

S 163

S 165


.








7-5 Specific detected photon yields (K-series)
for 0.127 mm filiform targets . .

7-6 Specific detected photon yields (L-series)
for 0.127 mm filiform targets . .

7-7 Specific detected photon yield as a function of
wire diameter . .

7-8 Specific detected photon yield and energy loss
vs. energy for 0.001 mm gold wires bombarded


with high-energy protons


A-i Construction of 0.004" Mylar windows .

A-2 Setup for pressure-testing of Mylar windows

A-3 Exploded view of Mylar window modified with
aluminum disc . .

A-4 Fabrication of aluminum blanks .

A-5 Jig for machining thin aluminum windows
(material: cold rolled steel) .

A-6 Alignment of the jig . .

A-7 Mounting the blank on the jig .

A-8 Measuring the baseline with the depth gauge
before beginning the cutting operation .

A-9 Window cutting operation . .

B-1 Specifications of the K485 current meter .

B-2 Calibration certificate of the K485
current meter . .

C-1 Datalog form . .


. 235

. 236


S. 239

S. 240


241

243

. 245


. 246

. 247

. 250


. 251

S. 253


220


221


222


. 224















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


DEVELOPMENT OF A MULTI-ELEMENT X-RAY EXCITATION PROBE
FOR THE MEASUREMENT OF SPATIAL DISTRIBUTIONS OF
ENERGETIC IONS, ATOMS, AND MOLECULES

By

Angelo M. Ferrari

December, 1991

Chairman: Dr. Samim Anghaie
Major Department: Nuclear Engineering Sciences

The multi-element x-ray excitation probe is a new

device to measure spatial distributions of energetic

particle fields such as ions, atoms, and molecules using the

characteristic x-ray spectra of multi-element targets to

determine location of the point of measurement, and the

intensity of the spectral lines to determine the particle

flux. The probe consists of several thin wires or other

small targets of different elements mounted on a supporting

frame. The probe is placed in the field of energetic

particles which interact with the atoms of the targets,

causing the emission of characteristic x-rays. The

radiation produced by the targets is detected in a high-

purity germanium detector located in the vicinity of the

probe. The signals generated by the detector are processed

and stored in a computer-based x-ray spectrometer. The high


xvi







resolution inherent to this instrument provides x-ray

spectra with sharply defined lines which are used to

identify the element which generated them and, therefore,

their location of origin. Because in the case of particle-

excited targets the production of characteristic x-rays is

directly proportional to the number of particles that

directly interact with the wire, the integral of the

characteristic x-ray spectrum is a direct measurement of the

particle flux at the given location. In this manner, if the

location of the different targets is known with respect to a

given frame of reference, and the probes have been

calibrated with beams of known intensities, the information

provided by the characteristic x-ray spectrum can be

directly reduced to the quantity of interest: particle flux

vs. location.

Multi-element x-ray excitation probes have a

potentially wide range of applications, from the

characterization of particle accelerator beams to the

determination of densities in fields of energetic particles

with quasi-stationary orbits.

Some of the probes built to perform the proof-of-

principle experiments have been used to measure proton beam

profiles with resolutions of approximately 10 Am and to

detect less than 105 protons per square millimeter per

second.

A theoretical model is developed which describes the

basic principles of operation of the probe (characteristic


xvii









x-ray production). This theoretical model is based on well-

established theories of interaction of energetic particles

with matter. This allows a priori calculations of the

expected results, at least within one order of magnitude for

absolute values and within substantially narrower limits for

relative measurements.


xviii














CHAPTER 1
INTRODUCTION



The multi-element x-ray excitation probe is an

instrument used in the measurement of spatial distributions

of energetic particles such as ions, atoms, and molecules.

The probe consists of an array of targets of several

elements (usually, but not necessarily, in the form of thin

metallic wires arranged in a parallel configuration) placed

in the field of energetic particles whose spatial

distribution is to be measured. The particles that strike

the targets excite its atoms and these, in turn, emit

characteristic x-rays. A high-resolution photon

spectrometry system records their spectrum. The location of

the emission is determined by the characteristic spectrum

and the number of particles striking each target by the

intensity of the x-ray lines. By calibration of the probes

in controlled experimental conditions it is possible to

establish a quantitative relationship between position and

particle flux.

One important feature of the multi-element x-ray

excitation probe method is that it is based on well-

established principles of low-energy photon spectrometry

used in a novel manner.









In the past, high resolution x-ray spectrometry has

been used mainly in the field of elemental analysis. In

this application, the quantities to be measured are the

amounts or concentrations of the elemental constituents of a

sample. The sample is excited with photons or charged

particles, and the energy spectrum emitted by the sample

yields the desired information. In contrast, in the method

developed in the present work the composition of the sample

(probe) is well known, and the obtained x-ray spectrum is

used to characterize the particle-beam used in the

excitation.

Another important aspect of the new method is that it

is applicable not only to measurements involving particle-

beams discussed in Chapters 2 and 3, but also to the

determination of particle distributions of other ordered

energetic particle systems described in Chapter 2, such as

the Self-Collider Fusion Reactor (SCFR) under development at

the University of Florida.

A third significant feature of the method is the

possibility of building probes that are essentially

transparent to the beam. This is particularly true for

highly energetic particle beams, as discussed in Chapter 7.

Finally, the potential for its application to the

measurement of multi-dimensional particle distributions

is mentioned in Chapter 8.

The material presented here is organized as follows:









In Chapter 2, the diagnostic needs of the SCFR, which

were the original motivating force for the development of

the x-ray excitation probe, are discussed. To place these

diagnostic needs in their proper context, a description of

the SCFR precedes them. Also in Chapter 2, a review of

existing methods for particle distribution methods is

included. This review highlights the desirability for a

novel approach in the case of the SCFR experiments.

In Chapter 3, the multi-element x-ray excitation method

and its applicability to the SCFR diagnostic requirements

are described in detail. This leads to the discussion of

other potential applications of the newly developed probe to

other experimental situations, such as characterization of

accelerator beams, particle-beam optics, neutral particle

beams, etc.

In Chapter 4, a study of the interaction of energetic

particles with matter and the production of characteristic

x-rays is presented. This is done with the purpose of

arriving at the definition of the concept of specific

detected photon yield ysd, which is later used in the

calculation of particle density distributions from the

information contained in the characteristic x-ray spectra of

the probes. Some of the expressions derived in this chapter

are also used in Chapter 7 for the calculation of Ysd in

those cases in which the probes cannot be calibrated

experimentally.







4
In Chapter 5, the physical implementation of the multi-

element x-ray excitation system is presented. The fabri-

cation of the probes is described, and the specifications of

the x-ray spectrometer necessary to perform the measurements

are discussed.

In Chapter 6, a presentation of the experimental work

performed for the development, calibration, and application

of the multi-element x-ray excitation probes is made. This

includes a description of the experimental facility used in

the measurements, the calibration procedure of the Van de

Graaff accelerator, the calibration of probes using totally

and partially ionized beams, measurements of proton beam

profiles, and measurements of neutralized particle beams.

In Chapter 7, the concept of specific detected photon

yield developed in Chapter 4 is applied to the calibration

of probes. Calculations are shown for targets that were

previously used in Chapter 6 and for targets that could not

be calibrated experimentally.

In Chapter 8, the general conclusions derived from this

development work are presented, and possible new areas for

further development of the method are mentioned.














CHAPTER 2
MOTIVATION AND BACKGROUND



In several areas of experimental particle physics, atomic

and molecular beam studies, accelerator design, and applied

accelerator technology, it is necessary or desirable to know

the particle flux distribution over a given area or in a given

volume. The need for new methods and systems to measure such

distributions is discussed later in this chapter when existing

methods are reviewed. However, a few applications can be

mentioned at this time to illustrate this need. For instance,

the map of particle flux over the cross section of an

accelerator or microprobe beam can be used in the design and

adjustment of particle optics systems. Also, measurements of

distribution of atomic and molecular beams are useful in the

study of neutralization methods. Other situations in which

the quantitative knowledge of particle flux distribution is

advantageous are diagnostic applications in some nuclear

fusion experiments involving colliding beams. The diagnostic

requirements of one of such experimental fusion projects,1

the University of Florida Self-Collider Fusion Reactor (SCFR)

[1,2], motivated the development of the method and system



'In this work, the word fusion indicates any of several exoergic
nuclear reactions.







6

presented here. In the first part of this chapter, the SCFR

and its diagnostic needs are discussed. In the second part,

existing methods of particle distribution measurement are

described.



2.1 Motivation

2.1.1 The Self-Collider Fusion Reactor

The SCFR is a beam-confinement fusion system currently

under development at the University of Florida. In this

system, fusionable particles injected by an electrostatic

accelerator into a reaction chamber describe rosette-shaped

trajectories that are contained within a bi-concave thin

disk under the influence of strong axially and radially

focusing magnetic fields. The purpose of this arrangement

is to create a high density of particles moving in colliding

trajectories within a small volume near the center of the

distribution. This situation establishes a favorable

environment for the occurrence of fusion reactions such as

(d,d), (d,t), (d,3He), and (p,1"B) (Figure 2-1). To coerce

the particles into the desired trajectories, it is necessary

to realize a magnetic field with the following characteris-

tics:

1. It must have cylindrical geometry (the axis of

symmetry is called the z-axis).

2. It must increase from nearly zero at the z-axis to a

high intensity near the periphery.















DEUTERON DEUTERON
t
ENERGY GAIN+I ^P\
3.269 MeHEUUM-3


NEUTRON




a. 2H + 2H 3He + n


HELIUM-3


DEUTERON


ENERGY GAIN ALPHA
18.353 MeV


PROTON



c. 3He + 2H a + p


DEUTERON


ENERGY GAIN TRITIUM
4.033 MeVTRITIUM


PROTON




b. 2H + 2H 3H + p


PROTON


B-11 -.

BORON -11


ENERGY GAIN
8.681MeV


ALPHA


d. 11B + p 3a


Figure 2-1. Examples of exoergic nuclear reactions
which could be produced with colliding beams


ALPHA


DEUTERON







8

3. Also, it must have a small radial component near the

periphery.

Figures 2-2 and 2-3 show the building up of this field

configuration by using superconducting solenoid arrays, and

Figure 2-4 illustrates the approximate shapes of the

trajectories. Attention is called to the fact that, as

shown in Figure 2-3, the combination of the three

superconducting solenoids creates a magnetic field with a

radial as well as an axial component near the periphery of

the reaction chamber. This radial component is necessary

for axial focusing of the trajectories.

Computer simulations have been performed to determine

the shape of the self-colliding trajectories, and, based on

those simulations, calculations of the particle density

distribution and of the probability of the occurrence of

fusion reactions have been carried out [3]. The particle

density distribution calculations show that the concen-

tration of particles will vary as 1/r2, where r is the

distance from the point of intersection of the trajectories

(Figure 2-5); and the results of calculations of the

probability of fusion calculations indicate that it should

be possible to realize a system with positive energy

balance. A number of fusion reactions are possible

candidates for the proposed system, and some of those being

considered are shown in Figure 2-1. One of the most

attractive is the (p,"B) reaction which yields three alpha
























Central rectangle
indicates outline
of reaction chamber
I I I


a. Fiel of solenoid set #1 only


Central rectangle
indicates outline
of reaction chamber
I I I- I


b. Resultant field of solenoids #1 and #3


Figure 2-2. Approximate diagram of the field lines of
the superconducting magnets used in the SCFR






















I Solenoid set #1


.0=-- ISolenoid set #3


Central rectangle
indicates outline
of reaction chamber


Figure 2-3. Complete array of the superconducting
magnets used in the SCFR and approximate
diagram of the field lines


i













Radial focusing effect
of axial (Z) component
of magnetic field


Z-axis perpendicular to the paper Magnification of center region


a. View on the radial plane



AR



Axial focusing effect
of radial component
of magnetic field

... .. .. .


Horizontal scale is
greatly exaggerated
with respect to that
of top diagram.


b. View on a plane through the z-axis


Figure 2-4. Representation of the trajectories of the
particles in the SCFR showing the focusing effects
of the axial and radial field components















































Figure 2-5. Particle density as a function
of the radial distance







































Electron
Collector
Grids


Figure 2-6. SCFR concept with direct
energy conversion system


Ion
Collectors
biased at
high voltage







14

particles, a net energy gain of 8681 keV per reaction, has a

cross section of almost one barn at 650 keV (energy of

protons striking a stationary "B target), and is completely

aneutronic.

Whatever the reaction selected, the charged fusion products

will leave the reaction chamber spiraling around the z-axis,

under the influence of the axial magnetic field. Figure 2-6

shows a simplified diagram of a kinetic-to-electric direct

conversion scheme which has been proposed to extract power

from the system without any intermediate thermal conversion

stage.

The SCFR differs significantly from proposed generators

based on the production of energy by the fusion of randomly

colliding particles in a confined thermonuclear plasma. In

those systems it is necessary to reach a critical state

(ignition) of temperature and pressure at which a

sufficiently high fusion rate is attained to generate the

energy necessary to maintain the conditions of criticality.

At that point the reactor continues to operate without

further addition of external energy. In this conventional

mode of operation it is necessary to prevent the extinction

of the reaction. This is accomplished by appropriate

design. On the other hand, in the SCFR there is neither

criticality nor ignition. In principle, the reactor can

operate at any power level as long as energetic particles

continue to be injected into the reaction chamber in

sufficient quantities.









A fraction of these particles will undergo fusion and

generate energy. As mentioned before, it is theoretically

possible to design a system that will generate more energy

than it consumes. In this sense, the SCFR is an energy

amplifier rather than a generator.

In summary, the SCFR has the advantages of being

inherently stable (no energy output unless there is some

energy input), of scaling very well (a relatively small

system should be substantially as efficient as a much larger

one), and, by the proper selection of fusionable particles,

of being essentially aneutronic.

Three distinct subsystems can be identified in the

SCFR: particle injection, particle fusion, and energy

extraction. The particle injection subsystem consists of

the particle accelerators, the beam optics, and the

components specifically required for injecting the beams of

fusionable particles into the reaction chamber. The

particle fusion subsystem consists of the reaction chamber

itself and of the superconducting magnets necessary to

create the desired magnetic field configuration. The energy

extraction system consists of the means for collecting the

energetic particles generated in the fusion reactions, the

system for converting the kinetic energy of these particles

into usable electrical energy, and, in some cases, the

subsystem for breeding new fusionable particles.

One of the first engineering problems that must be

solved in the SCFR is the difficulty of injecting charged









particles at the center of a magnetic field configuration

such as the one previously described. Direct injection is

not realizable because the charged particles would be

deflected by the strong magnetic field in the annular region

close to the periphery of the reaction chamber and would not

be able to describe the desired quasi-stationary

trajectories. Two solutions are proposed for this problem:

One is off-center injection, the other is beam

neutralization.

The first method consists in directing the beam of

charged particles off-center so that the magnetic field

bends it into an orbit that passes through the geometric

center of the reaction chamber (Figure 2-7a). By design,

the magnetic field keeps the particle in this center-

intersecting trajectory. The beam neutralization method

consists in converting the charged particles into neutral

species (atoms or molecules) before injecting them directly

into the center of the reaction chamber, and then providing

means of reionizing them within the volume of acceptance

for quasi-stationary orbits (Figure 2-7b). In principle,

off-center injection is the most desirable method because of

its simplicity and efficiency (theoretically, all the

particles in the beam can be directed to the center).

However, experimental constraints sometimes preclude the use

of this method, and beam neutralization becomes the only

available option. In the early stages of the SCFR project,














CHARGED-PARTICLE BEAM
FROM ACCELERATOR


a. Off-center injection


NEUTRALIZED-PARTICLE
BEAM


b. Neutral beam injection


Figure 2-7. Methods of particle injection in the SCFR









it will be necessary to use an existing superconducting

magnet system previously designed for other applications.

There are restrictions in the access to the central space of

this magnet in its present form that make it impossible to

inject a beam at the necessary distance from the center to

achieve off-center injection. Modification of the magnet to

allow for off-center injection is one of the options

currently being considered, but beam neutralization remains

a distinct possibility [4].

In the first series of proof-of-principle experiments,

protons will be used as the orbiting particles to test the

magnetic field configuration. If the method of beam

neutralization is used, a beam of neutral hydrogen atoms

will be obtained by directing an H2* beam through a thin

carbon film. By interacting with the carbon lattice, some

of the H2 ions will be dissociated into H* ions and H atoms.

These ions, as well as the remnant H2+ ions, will be

deflected from the beam with a sweeping magnet, and the H

atoms will proceed to the center of the reaction chamber.

Some of the H atoms will be ionized through collisions with

existing electrons as they travel through the reaction

chamber; a few of them will become ions at, or very near,

the center of the chamber. These ions will be trapped by

the magnetic field and will describe the quasi-stationary

orbits. The atoms that are not ionized, or that are ionized

at other locations within the chamber, will be lost. Once

the process of ionization begins, a gradual buildup will









take place because of the preferential ionizations in the

center. Eventually, the system reaches a steady state in

which the charge density at the center remains constant.

This is because the number of particles that are injected

equals the number of particles that undergo fusion reactions

or that are lost through mechanisms discussed in Reference

2. The particle fusion subsystem consists of a reaction

chamber and the superconducting magnets that provide the

field necessary to maintain the particles in the center-

intersecting quasi-stationary trajectories.

The first stage of the SCFR experimental program is

aimed at verifying the computer predictions of spatial

particle-density distributions within the reaction chamber.

These measurements are expected to yield valuable

information necessary for the design on the magnetic field

configuration and methods of particle injection to be used

in subsequent stages of the project.

2.1.2 Diagnostic Instrumentation Requirements of the SCFR

In the different phases of the SCFR project (proof-of-

principle, prototype design and testing, optimization of

fusion rate, extraction of energy, and optimization of

energy production), it will be necessary to perform

measurements of a number of system variables. In the early

stages, some of these measurements will be the verification

of the magnetic field configuration and of the existence of

quasi-stationary orbits, the measurement of particle flux









distribution, the verification of the existence of fusion

reactions, and the measurement of fusion products. In

particular, during the proof-of-principle experiments the

following diagnostic needs must be addressed:

1. Measurement of beam profiles and mapping of

accelerator beam cross section to optimize

particle beam optics to achieve a beam sharply

focused at the center of the reaction chamber.

2. Measurement of the efficiency of the

neutralization system to optimize its performance.

3. Measurement of the efficiency of the reionizing

process in the reaction chamber.

4. Measurement of the charged-particle flux

distribution in the reaction chamber.

These diagnostic needs require instrumentation capable

of measuring beams before and after neutralization and

probes that are minimally intrusive in the reaction chamber.

The method for the measurement of spatial particle

distributions that has been developed and that is presented

here was motivated by these diagnostic needs and addresses

all of these requirements.

2.2 Background: Existing Methods of Particle
Density Distribution Measurement

The existing methods of particle density distribution

measurements may be divided into two broad categories:

plasma diagnostics and particle-beam diagnostics. Systems

for plasma diagnostics will not be discussed here because







21

they are not directly related to the subject matter of this

work. On the other hand, a description of current methods

for particle-beam diagnostics highlights the needs for novel

approaches to this measurement problem and provides the

background necessary for the discussion of the method

developed in this work.

Several techniques are or have been used for the

characterization of particle-beams in accelerators,

microprobes, and colliding-beam systems. These include beam

current, secondary emissions, particle backscattering, and

induced charge measurement methods. Typical devices used in

the implementation of these methods are described below.

2.2.1 Beam-current Measurements

Probably the most common method of determining

particle-beam intensity and profile consists in measuring

the current from beam-intercepting electrodes [4-13]. These

will be generically referred to as current probes.

The systems based on this method are usually

implemented with single- or dual-wire probes moved across

the beam to obtain one- or two-dimensional profiles in a

sequence of measurements [5-13]. Also, stationary two-

dimensional wire arrays have been used [14]. Some of the

most representative systems based on current probes

described in the literature are discussed below.

Nielsen and Skilbird designed a beam-profiling

instrument which had two 0.2 mm-thick tungsten wires

(needles) at 900, separately driven by oscillators. The









needles scanned the beam at approximately 25 cps in either

direction [13]. Currents down to the level of 10-9 A were

measured with this system. This is equivalent to

approximately 1010 singly charged ions per second.

Takacs devised a simple single-wire scanner system that

had the ability of scanning the beam sequentially in two

orthogonal directions [12]. The wire was bent at 900 and

attached by its vertex at the tip of a rod of much greater

length than the diameter of the beam cross section; the

sides of the right angle formed by the wire were positioned

at 450 with respect to the axis of the rod. The probe was

placed on the beam path with the plane formed by the bent

wire normal to the beam. The rod was driven back and forth

on the wire plane causing both sides of the angle formed by

the wire to intercept the beam on each complete cycle. The

position of the probe was determined by a piezo-electric

transducer. The current for each position of the probe was

recorded, and the beam profile was reconstructed from these

values.

Hortig built a single-electrode probe that consisted of

a wire mounted at 450 with respect to the axis of a drive

motor [11]. In one revolution the wire scanned the beam

cross section in two directions. Also here, a two-

dimensional mapping of the cross section was obtained from

the acquired information.

Variations and improvements of these methods have been

implemented by Stensgaard and Korbjerg [5], Meier and









Richter [6], Duport and Jaccard [7], Bond and Gordon [8],

Wegner and Figenbaum [9], and Jagger, Page and Riley [10],

among others.

Stover and Fowler have constructed probes in the form

of orthogonal arrays of 16 x 16 wires, each wire connected

to a current-measuring amplifier [14]. The plane of the

array is placed perpendicular to the beam axis. Two-

dimensional profiles are obtained with the probe at a fixed

position.

In general, no great amount of information is given in

the literature about the lower limit of detection of the

wire probes. It appears that the probes were constructed

for operation in relatively high intensity beams where the

main concern was to protect the wires from being destroyed

by heating rather than to measure extremely low particle

flux. It is reasonable to assume, however, that the

sensitivity of the probes will be limited by the

capabilities of state-of-the-art of current-measuring

instruments, by the noise introduced by insulator leakage,

by particles of spurious origin striking the wire, and by

the time available for the measurement.

All of the current probes require that the charged

particles be fully stopped by the electrode(s). Therefore,

no matter what the energy of the beam, the particles that

contribute to the measurement are permanently removed from

the beam.









2.2.2 Secondary Emissions Measurements

Another approach to particle beam characterization is

to measure the secondary emissions from targets that

intercept the beam partially or totally. Some of the

techniques found in the literature are described below.

Martin and Goloskie have used a probe to measure

aberrations of quadrupole lenses designed to focus 600 keV

protons [15]. The probe consisted of a tungsten wire

inserted in the beam path. The measured quantity was the

charge of the backscattered protons.

Field described measurements of the beam sizes of the

Stanford Linear Collider using the bremstrahlung from carbon

filament probes [16].

Struve, Chambers, Lauer, and Slaughter have also

implemented bremstrahlung probes. In their case, the

targets were tantalum rods and tungsten powder [17].

A method for profiling proton beams by measuring the Ka

radiation from copper deposited on an iron wire has been

described by Jenson, Hill, and Mangenson [18].

Bosser et al. have constructed probes with thin carbon

fibers that are scanned across the beam to obtain a one-

dimensional profile of protons and anti-protons. Secondary

particle emissions from the filaments are detected and

counted by scintillator-photomultiplier tube assemblies, and

the number of counts is used as a measurement of the beam

intensity at the chord intercepted by the probe [19].








25

Odom et al. [20] have used thin film and grid probes to

map beam cross sections by obtaining an image of it from the

secondary emissions focused by charged-particle optics.

2.2.3 Other Methods of Particle Beam Characterization

A commonly used method of characterizing pulsed-

accelerator beams is to measure the current transient

created by the induced charge as the burst of particles

passes between electrodes (stripline pick-ups). This method

has been most recently discussed by Ross [21], by Kuske et

al. [22], and by Webber et al. [23]. Electrostatic pick-up

yields information on beam intensity and beam position.

In the case of electron beams, it is also possible to

measure the synchrotron radiation if the beam is bent by

magnetic fields. Kuske et al. [22] and Coombes and Neet [24]

have made use of this method.

Images of beams' cross-sections can also be obtained by

intercepting them with charge-coupled devices (CCD), as

described by Beavis et al. [25], or with scintillation

screens with or without shadowing grids, or with filament

arrays [21, 24, 26, and 27].

Coombes and Neet have measured the emissions of the

interactions of particles with gerenkov cells to monitor

linear accelerator beams [24].

In colliding beam systems, it is possible to derive

some information about them from the bremstrahlung emitted

at the point of collision [21].









2.2.4 Applicability of Existing Methods to the SCFR
Diagnostic Requirements

Some of the existing methods could meet some of the

diagnostic needs of the SCFR. For instance, several of the

techniques described above could be used to adjust the

particle optics system necessary to produce a beam spot of

the required size at the center of the quasi-stationary

orbits. Also, some of the instrumentation just discussed

could be used to perform measurements in the neutral beams

used in one of the SCFR methods of injection. However, the

measurement of particle density distribution inside the

reaction chamber poses particular challenges, such as the

need for minimal interference with the orbiting particles

and the desirability of performing simultaneous measurements

at different locations, that are not easily met with the

existing devices. As an example, the possibility of using

thin wires at various points within the chamber to implement

the current-measuring method does not appear feasible

because the allowable wire size (of the order of 1 Am in

diameter) would be smaller than the range of the energetic

particles, and no charge would be deposited on the probes.

Therefore, a new method of charge particle distribution

measurement that has potential advantages for some of the

SCFR measurements, and that also may be applicable to other

experimental situations, has been developed and is

introduced in the next chapter.















CHAPTER 3
THE MULTI-ELEMENT X-RAY EXCITATION PROBE METHOD



The operation of the multi-element x-ray excitation

probes for the measurement of spatial distributions of

energetic ions, atoms, and molecules developed in this work

is based on the one-to-one correlation existing between

elements and their characteristic x-ray spectra as a means

of obtaining position and particle flux information

simultaneously from several locations within the

distribution [28].

Targets bombarded by energetic particles, or excited by

electromagnetic radiation, emit the characteristic x-ray

spectra of their constituent elements. It follows that

single-element targets such as pure-metals emit the

characteristic spectrum of that element only. Also, the

intensity of a spectrum is directly proportional to the

number of particles or photons that excite the target.

Therefore, if different pure-element targets are placed at

various locations within a field of excitation agents, the

energy of the generated x-ray lines yields information on

their place of origin, and their intensity on the intensity

of the excitation.








28

The production and detection of x-rays will be analyzed

in the next chapter. Here, the general manner in which

single- and multi-element probes can be used in experimental

situations will be discussed, and the features that make

them potentially applicable to measurements such as those

required in the SCFR will be described.



3.1 Operation of the Multi-element X-ray
Excitation Probe System

The principle of operation of the system briefly

described above will be illustrated with a hypothetical

example.

A beam of particles, such as the one shown in Figure

3-1 has a certain cross section, and the number of particles

per unit area passing by two points within this cross

section during an interval t is to be determined. For the

purposes of this discussion, it will be assumed that the two

points are at distances dI and d2 from a reference axis.

The application of the multi-element x-ray excitation probe

method to this experimental situation is shown below.

Two targets in the form of small disks of equal cross-

sectional area a made of the pure elements El and E2 are

placed at the desired locations. The targets, excited by

the particles, emit their characteristic x-ray spectra which

are accumulated for the interval t. Assuming that the x-ray

spectrometer has been properly calibrated in terms of

energy, the spectral lines corresponding to each of the




















PARTICLE BEAM


- El


REFERENCE LINE


a. Location of the targets with
respect to the beam


X-RAY ENERGY


b. Characteristic x-ray spectra of the
pure elements El and E2



Figure 3-1. Illustration of the principle of operation
of the multi-element x-ray excitation method


-----








30
targets are identified and the counts under the peaks of the

respective spectra are integrated. Again, assuming that the

targets have been calibrated according to the procedure to

be discussed in Chapter 6, the number of particles

intercepted by each of the disks is computed. Therefore, at

the conclusion of the measurement it has been determined

that the intensity of the beam is n, and n2 particles per

unit time per unit area at the distances d, and d2,

respectively, from the reference line. Simultaneous

measurement of beam intensity at a larger number of

locations only requires the use of a larger number of

targets.



3.2 Targets for Use with the Multi-element Probes

In principle, there is no limit to the shapes and sizes

of the targets that can be used with the multi-element x-ray

excitation probes. In practice, the characteristics of the

targets are dictated by the requirement of the measurement,

the compatibility of the materials with the experimental

environment, the availability of the pure materials in the

required forms and sizes, and the feasibility of fabricating

them to the required specifications.

In the experimental part of this work, only metallic

targets in the form of foils and wires have been used, but

there are several other possibilities. Some of these are

mentioned below.









1. Small metallic disks attached to wires of a

different metal. The support wire must have an x-

ray spectrum that doesn't interfere with the

spectra of the disks. For instance, iron wires

(principal x-ray lines below 7 keV) could be used

to support niobium, molybdenum, rhodium,

palladium, silver, and cadmium disks (all elements

with principal lines above 16 keV). Bonding

techniques used in the semiconductor industry

could be applied to the fabrication of the probes.

2. Alternately, short sections of the supporting wire

could be electroplated with other metals.

3. If the target materials can be attached to the

substrate by vacuum deposition, low-Z supports

such as fused silica or carbon fibers could be

used. In this case, the choice of target elements

widens to include some of the metals with atomic

numbers below 40 (Ti, V, Cr, Mn, Fe, Co, Ni, Cu,

and Zn) which still have x-ray spectra with

energies sufficiently high (>4.5 keV) to make

possible the use of windowless detectors (see

Chapter 5).

4. Disposable probes in the form of silicon chips

with a mosaic (or other suitable pattern) of

different elements could be mass produced with

semiconductor fabrication techniques (chemical

vapor deposition -CVD- or ion implantation, for









instance), calibrated with x-ray fluorescence

systems, and then used to characterize ion-beam or

x-ray lithography instruments. A derivative

application of this technique could be found in

single-event upset (SEU) studies of semi-

conductors: Fiduciary marks could be implanted on

a large scale integrated (LSI) circuit chip and

then used for precise registration of the probing

microbeam.

5. At the expense of sacrificing some of the

intrinsic simplicity of the probes, they could be

attached to mechanical drives to generate two- and

three-dimensional maps of particle distributions.



3.3 Applicability of the Method to the SCFR
Diagnostic Needs

The method of particle density determination using

multi-element x-ray probes is not limited to the

measurements that need to be performed in the SCFR but is

also applicable to other experimental situations as can be

inferred from the previous discussion. However, since the

SCFR diagnostic requirements initially motivated its

development, some of the features of the method that help

meet those requirements will be mentioned.



1. Passivity. The multi-element probes are passive.

No leads need to be brought out of the reaction









chamber, as it is the case with current probes,

for instance. This simplifies the insertion of

the probes into the chamber which has very limited

access.

2. Remote sensing. In most cases, the elements that

are selected as target materials emit x-rays

sufficiently energetic to be detected through thin

windows. Therefore, it is not always necessary to

mount the detector inside the chamber itself, as

required with backscatter or secondary particle

emission probes.

3. Low intrusiveness. Any probe inserted to

intercept the particles affects their

distribution. This is particularly true near the

center of the chamber where particle density is

expected to reach very high values. It is

therefore desirable to use probes with physical

dimensions as small as compatible with their

ability to perform the measurement. A wire

diameter of less than 1 gm is the maximum

acceptable at distances of the order of 1 mm from

the center of the distribution. Platinum and gold

wires of this size are commercially available and

could be used for this purpose. Current-measuring

probes of this dimension would not be suitable

because they would be smaller than the range of









the particles to be measured; they would collect

no charge and yield no output.

4. Simplicity of implementation. Particle dis-

tributions can be measured at small or large

number of locations with the x-ray probes with

equal ease. Only the number of targets mounted

on the probe need to be changed as necessary.

Because of the probe passivity mentioned above,

this is a relatively simple procedure. Probes

with up to four different elements were

implemented in the experimental part of this work,

but there are approximately 12 metals that are

compatible with the chamber environment, that have

characteristic x-ray with sufficiently high energy

to be detectable through windows, and that can be

drawn into thin wires. Therefore, in principle,

probes with this number of targets could be built.

When many elements are used simultaneously,

partial overlap of their spectra may occur. This,

however, is not a serious problem as shown in

Chapter 6 for the case of four-wire probes with

partially overlapping spectra. There, a simple

correction technique was used in the measurement

of beam profiles. For cases were more complex

spectral overlap is found, readily available

spectral deconvolution software can be used.









5. Partially ionized and neutral particle detection.

Atoms become ionized and molecules dissociated

shortly after they collide with the target. From

that point on they are ionic species, interact

with the target material, and generate

characteristic x-rays in the manner described in

Chapter 4. Therefore, x-ray probes are equally

applicable to the measurement of charged or

neutral particles. This is a feature that they

share with all secondary emission probes; however,

this property combined with some of the other

characteristics already mentioned makes the x-ray

probes especially well-suited for the neutral-

particle measurements needed in the SCFR. In

Chapter 6, the application of the method to the

measurement of partially ionized molecules (H2+)

and neutral atoms (H) is reported.



3.4 Other Applications for X-ray Excitation Probes

The minimal intrusiveness, relative simplicity, and

capability for multi-dimensional mapping of particle

distributions are properties that could make multi-element

x-ray excitation probes also attractive in applications

other than those that motivated their development.

Some of the potential applications of multi-element x-

ray excitation probes have already been mentioned, either in

the discussion of the SCFR diagnostic requirements or in the









description of possible probe configurations. Here, these

applications are recapitulated and additional ones are

mentioned.

1. Characterization of charged-particle beams in

accelerators (particularly, in very high energy

accelerators), ion microprobes, and colliding and

self-colliding beam systems.

2. Adjustment of particle optics systems.

3. Alignment and quality control of semiconductor ion

implanters, ion-beam lithography systems, and

other production ion-beam equipment used in

semiconductor fabrication and testing.

4. Specialized semiconductor testing, such as single-

event upset (SEU) studies.

5. Characterization of experimental heavy-particle

therapy systems.

6. Atomic and molecular beam studies.















CHAPTER 4
PRODUCTION AND DETECTION OF X-RAYS FROM
TARGETS BOMBARDED BY ENERGETIC PARTICLES


The measurement of spatial distributions of particles

using the characteristic x-ray excitation probes developed

in this work requires that a correspondence be established

between the measured x-ray intensity and the number of

particles that strike the targets. This correspondence can

be established experimentally by using particle beams of

known intensity, or it can be calculated from the geometry

of the probes and from published values of x-ray production

cross sections. Later in this work, experimental

determinations of the relationship between number of

striking particles and x-ray intensity are described. In

this chapter, an expression for the correspondence between

the measured parameter (x-ray intensity) and the unknown

variable (number of particles) is derived. This expression

is later used (Chapter 7) to calculate particle flux with

probes that were not experimentally calibrated and to cross-

validate the results obtained from the experimental

calibrations. The discussion begins with considerations

regarding the interaction of energetic particles with matter

and proceeds from that point.











4.1 Introduction

The acquisition of the characteristic x-rays spectrum

of a target bombarded by a beam of energetic particles is

the result of a process which consists of four distinct

parts:

1. Stopping: The loss of energy of the beam in

the target.

2. Production: The emission of characteristic x-rays

by the target material.

3. Self-absorption: The attenuation of the photons by

the target material.



4. Detection: The x-ray detection process itself in

which variables such as solid angle, detector

efficiency, attenuation by windows, and attenuation

by the detector dead layer must be considered.

These four parts will be separately discussed, and the

effect of earlier processes on following ones will be

analyzed. Finally, the results of the individual steps will

be brought together under a single mathematical expression.



4.2 Stopping of Energetic Ions by Matter

The phenomenon of stopping of heavy ions' by matter is

a topic that has been extensively studied since H. Geiger



1 In accordance with common usage, the term heavy ion applies
to any charged particle heavier than the electron [29,30].









39
and E. Marsden published the results of their experiments on

the scattering of alpha particles by gold foils in 1909 and

1910 [29,30]. These experiments had been carried out under

the direction of E. Rutherford for the purpose of testing

the validity of J.J. Thomson's atomic model'. Thomson's

model predicted that the scattering of heavy charged

particles by thin metallic foils would be the resultant of

many random individual collisions with the atomic electrons

and would follow a narrow bell-shaped distribution about

zero.

Although the most significant (if unexpected) result of

Geiger and Marsden's experiments was that a few alpha

particles underwent an anomalously high scattering, they

also showed, as Thomson's model predicted, that most of the

particles were indeed scattered with a very small angle.

The exceptional instances of large angle scattering are

the most important from the standpoint of their impact on


atomic physics because they led Rutherford to the

postulation of the nuclear atom [33], but the multiple small

angle scattering by the atomic electrons is the most

significant mechanism from the standpoint of the stopping of

heavy ions by matter. The dominance of this mechanism of

interaction has been confirmed by all experiments to date.


'This was the so-called "plum pudding" model because it represented
the atom as a positive charge uniformily distributed throughout the
entire volume, with the discrete negatively charged electrons
embeded at different points within it.











Conservation of energy and linear momentum in ion-

electron encounters requires that small scattering angle

corresponds to low energy transfer in each collision, so the

energy loss of heavy ions is the result of a very large

number of small energy loss events. The energy loss

(stopping) of heavy ions in matter and the spread in the

values of this energy loss are subjects of direct interest

to the study of x-ray production.

The study of the mechanism of interaction of heavy ions

with matter was initiated by N. Bohr in 1913-15 [34,35] and,

although refinements continue to be made to this day

[36,37], Bohr's basic results are still applicable [38].

In 1932, H. Bethe developed an expression for the

stopping of heavy ions by matter, which is applicable to

high energy projectiles (E > ~ 400 kev/amu) [39]. This

expression is known as Bethe's formula and is shown below.


dE 4ne4z2 N[ n2mov2 n(l-2)_
x mov2 I


(4-1)


where dE = differential of particle energy

dx = differential of distance travelled by
particle

z = charge of particle in electronic charge
units

e = electronic charge

N = atomic density of the target material

Z = atomic number of the target material

mo = rest mass of electron











v = velocity of the particle

8 = v/c (c = velocity of light)

I = geometric mean of the excitation and
ionization potential of the target atoms


Other formulas for the stopping of lower energy

particles in dense materials have also been developed.

Anderson and Ziegler have fitted these formulas to existing

experimental data and have arrived at semi-empirical

expressions for the stopping power and range for a number of

heavy ions in pure elemental targets. They have published

their results in a set of tables and graphs [40]. As an

example, their curves for protons in tungsten are shown in

Figure 4-1.

As mentioned above, the two quantities that will be of

interest later, when the production of characteristic x-rays

is discussed, are the energy loss of the heavy ions as they

penetrate the target and their energy distribution about the

average value at each point along their path. The energy

loss as a function of penetrated distance is readily derived

from the data of Anderson and Ziegler, and the variance of

the distribution is given by the expression derived by Bohr

for interaction of the particle with the orbital electrons

in the Rutherford's atomic model (Equation 4-2) [35].


E2 41cz2e4NZt


(4-2)













Zzu-
200-

.=. 180


.n 140 --------
160
.-2 140
E
1120

S100- -- /


60
60--

400

1 ib 10o 10 ii o 10'0ooo
PROTON ENERGY [keV]

a. Stopping





1000


100


C 10

2
E
w
0.1!



0.0 1 ... ,,,, ,,,,

1 10 100 1000 10000
PROTON ENERGY [keV]

b. Range



Figure 4-1. Stopping and range of protons in tungsten











where t2 = variance

t = thickness of material layer

and the other quantities are as indicated in Equation 4-1.

As an example, the graph of the energy of protons of

initial energy E0 = 1 MeV vs. their penetration in a thick

tungsten target is shown in Figure 4-2. In this graph, the

energy loss was calculated from the range curves of Anderson

and Ziegler, and the standard deviation of the distribution

at several points (vertical bars) was computed with Equation

4-2.

As shown in the graph, the distribution of energies

about an average value is quite narrow until the penetration

equals a substantial fraction of the range; it doesn't

become significantly broad until the particles have lost

most of their initial energy. As will be discussed later,

the x-ray production cross section is a very strong function

of the particle energy; therefore, a very large percentage

of the x-rays are produced in the first few layers of the

target where the beam is essentially mono-energetic. It

also will be shown later that this phenomenon, combined with

the still relatively narrow distribution of energies close

to the end of the range, leads to the conclusion that the

beam can be considered strictly mono-energetic (no

distribution about an average value) at each point along the

range without introducing a significant error in the

calculated value of x-ray production.

























S0.7


> 0.6-

z
m 0.5


O
< 0.4-

0
z 0.3


0.2-


0.1



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
NORMALIZED PENETRATION (x/range)


Figure 4-2. Energy loss of a proton beam with initial
energy E0 = 1 MeV as it penetrates a thick tungsten target,
graphed from data of Andersen and Ziegler. Curve is a fifth
order polynomial fit. Vertical segments are standard
deviations calculated with Bohr's formula.










4.3 Production of Characteristic X-rays

In principle, the energy transferred to the atomic

electrons by the energetic particles in the manner just

described may result in excitation or ionization. In

practice, the latter mechanism is strongly dominant; in

discussing the production of characteristic x-rays there is

no need to discuss the former. The probability of the

occurrence of ionization is given by the ionization cross

section, a,.

Most of the ionization events involve electrons from

the outer atomic orbits and this results in the emission of

low-energy photons (visible and ultraviolet). These are

reabsorbed within the target material and their energy

dissipated as heat. However, some of the ionization events

involve the ejection of inner-orbit (K, L, or M) electrons.

In this case, when the vacancies are refilled one of two

phenomena may occur: emission of characteristic x-rays or

emission of Auger electrons. These two processes are

competitive. The emission of characteristic x-rays is the

topic that will be discussed in this section.

Since the binding energies of the atomic electrons are

well defined, the characteristic x-ray energies, which are

equal to the differences in binding energies between

electrons at different levels, also have precisely defined

values. In addition, because the energy levels are unique

for each atomic species, the emitted x-rays also have











energies uniquely associated with each element. The term

characteristic indicates this fact.1

Usually, in each element there are several possible

transitions that result in the emission of x-rays. When the

atoms of the element are ionized by the energetic ions, a

number of x-rays of well defined energies will be produced.

The set of these x-rays is the characteristic x-ray spectrum

of the element. While some individual spectral line of a

particular element may be quite close to a line from the

same or another element and this may make them difficult to

resolve, the characteristic spectrum of an element taken as

a whole is easily distinguishable from that of a different

element. In this respect, characteristic x-ray spectra may

be considered to be the signatures or fingerprints of the

elements to which they belong. This has led to the present

situation in which, just as it was the case for over one

hundred years with its optical counterpart, x-ray

spectrometry is now a routinely used method of elemental

analysis. The widespread application of x-ray spectrometry

as an analytical tool was the progress made in semiconductor

devices in the 1950s and 60s. This resulted (among many

other things) in the development of two components that

launched a new era in non-destructive testing technology:



'The qualifier characteristic will be generally omitted in the
rest of this work since this the only kind of x-ray discussed here.
If bremstrahlung needs to be mentioned, it will be explicitly so
indicated.









the lithium-drifted silicon photon detector and the low-

noise field-effect transistor. In later sections, these and

other aspects of x-ray spectroscopy instrumentation will be

discussed in greater detail.

For the sake of completeness it must be mentioned

that, besides the heavy ions discussed here, other modes of

target excitation are widely used in x-ray spectroscopy.

These include excitation with the bremstrahlung from x-ray

tubes, with low energy gamma rays, with characteristic x-

rays from other elements, and with electron beams. Each of

these modes has its particular advantages and shortcomings,

and all have specific applications for which they are best

suited. The excitation with heavy ions discussed in this

work is usually known by the acronym PIXE, which stands for

particle-induced x-ray emission.

At this point a digression will be made to discuss the

notation used in x-ray spectroscopy.

Characteristic x-rays are usually identified by

symbolic expressions such as Ki,, M.2, etc. In this

notation, known as the Sigbahn notation, the first capital

letter indicates the atomic orbit in which the vacancy is

being filled [41,42]. All the x-rays that result from

filling vacancies in the first orbit (principal quantum

number, n = 1) are called K-series x-rays, in the second

orbit (n = 2), L-series x-rays, etc. Within a series, the

lines appear bunched into groups. The lines of some groups

are more intense than those from other groups. The







48

intensity of the group as a whole is indicated by the Greek

subindices (a indicates the most intense group, B the next

one, etc.). The numeric subindex indicates the relative

intensity of a line within a group (increasing numbers

indicate successively decreasing intensities). Because this

notation uses two classification criteria simultaneously

(atomic energy levels and spectroscopy intensity) it is

somewhat confusing. In addition, it is not used in a fully

consistent manner. Therefore, the International Union of

Pure and Applied Chemistry (IUPAC) has proposed an alternate

nomenclature ([42], p. 120). In the present work the

Sigbahn notation will be used exclusively because of its

present widespread acceptance. Figure 4-3 gives an example

of how this notation is applied. Figure 4-4 shows examples

of characteristic x-ray spectra acquired with a high-purity

germanium (HPGe) spectrometer.

The probability of production of characteristic x-rays

is given by the x-ray production cross section ax, which is

related to the ionization cross section ai by the

fluorescence yield (usually denoted by w); ax is a function

of the excitation method, the target material, and the

specific x-ray line being considered. For example, the

value of the cross section for the production of K x-rays by

tungsten when excited with the continuous radiation of an x-

ray tube is different from the cross section for the

production of the same x-rays when the target is bombarded

by 1 MeV protons.



























L-gamma-1 L-gamma-3






L-alpha-1 L-beta-1
L-alpha-2 L-beta2 L-gamma-2


K-calpla- 1 K



K-alpha-2




K


-b c a-1



K-bela-3



('


Figure 4-3. Characteristic x-ray nomenclature


















0
C



0
0.



0 I I -- --- i
(0 K- bea-1

150.24.938 eV 25452keV







S18 20 22 24 2 28 0
X-RAY ENERGY [keV]
a. K-lines of silver





L-alpha-1







fc KL-bets-2
09.68.15








0
1--,000
















0O L-gamma-1
z j10.893 ke.
500







S7 8 10 11 12 13 14 15
X-RAY ENERGY [keV]





b. L-lines of tantalum
Figure 4-4. Examples of characteristic x-ray spectra
E* 2000- [ 7]----------V ----------------

0 9.342 keV
&1500 LIIr^----



1 7000---------- / 1--14- 1








X-RAY ENERGY [keV]
b. L-lines of tantalum


Figure 4-4. Examples of characteristic x-ray spectra







51

To minimize the possibility of confusion, it is customary to

use as subindex for a the same letter as that of the series

being considered: the cross section for K-series x-rays is

indicated by aK, for L-series x-rays by aL, etc.

Measured values of the x-ray production cross section for

most elements, means of excitation, and a number of

excitation energies can be found in the literature [43,53].

For the purposes of this work, only those cross sections

pertaining to excitation with heavy ions are of interest,

and unless otherwise indicated, the term cross section will

be used only in this sense.

Besides the available experimental data, there are a

number of theoretical approaches to the calculation of x-ray

production cross sections [54-58]. Garcia et al. have

calculated and tabulated values of uKaK/ZL2 vs. E/AK, where

uK is the K-shell electron binding energy, aK is the K-

series x-ray production cross section, ZL is the atomic

number of the target, and A is the mass of the projectile in

amu [54]. Reuter et al. have fitted a logarithmic function

to the tabulated data [58]; their expression is given below

as Equation (4-3).





(log o 1 (lgo 2A (4-3)









where E = energy of the projectile

Ao = -19.04

A, = 0.03028

A2 = -1.11

A3 = 0.3771

A4 = 0.1923

A5 = 0.07459

A6 = -0.05084

A, = -0.005949

and the other variables have the meaning previously

indicated.

Reid has implemented Equation (4-3) with a computer

code, and Figure 4-5 shows examples of graphs of aK vs.

proton energy calculated with this code [59].

Computed values of cross section must be used only as a

general guideline, since in some cases they may differ

significantly from experimental data.

Figure 4-6 shows examples of graphs of aL vs. proton

energy plotted directly from experimental data [43].

As mentioned in section 4.1, a point to be noticed in

the graphs or tables is that the x-ray production cross

section is a strong function of the energy (approximately

fourth power above 500 keV, and even stronger below that

energy). This fact is of some help in simplifying

calculations of the x-ray yield, since it indicates that

only the first few layers of material need to be taken into

account. After the particles have lost about half of their

















Pd

0.1






0.001



0.0001



1E



1E-06-
100 200 300 400 500 600 700 800 900 100
PROTON ENERGY [keV]

a. Palladium







0.1
In





0.001





0.00010 5
-E g


200 300 400 50 00 700
PROTON ENERGY [keV]


e8o Beo 10oo


b. Indium



Figure 4-5. K-series x-ray production cross sections
computed with Reuter's formula and Reid's program


1;:
























.0



cn Crosses are published values.
O yCurve is fourth power function fit.
1 1




0.01 0 .
S500 1000 1500 2000 2500
PROTON ENERGY [keV]

a. Tantalum






Au L-series ,



10 0




+
0.0
/





-i 0.01
S: -- Crosses are published values.
............ Curve is fourth power function fit.




0.0001
I 500 1000 1500 2000 250(
PROTON ENERGY [keV]
b. Gold

Figure 4-6. L-series x-ray production cross sections
plotted from published data









initial energy, their contribution to x-ray production

becomes very small.

Another point that should be stressed is that the reported

values of the x-ray production cross sections are often

given with significant uncertainties (10, 20, or 30 percent,

and occasionally even higher), and that in some cases

discrepancies among independent measurements are larger than

could be expected from the stated errors. Mitchell and

Ziegler in the introduction to their table of cross sections

(compiled from different sources) state that "the thick

target data are specially prone to additional uncertainties

caused by energy loss, recoil, and absorption effects"

([43], p. 408).

As the energetic particles penetrate a thick target they

loose energy until they come to a complete stop at the end

of their range. This process was discussed in Section 4.1.

A plot of the average particle energy vs. penetration was

shown in Figure 4-2. This figure also showed the standard

deviation of the energy distribution about the average. For

the purposes of the discussion that follows, it is useful to

recast the plot of Figure 4-2 into a graph showing the

energy distribution of the particles at different average

energies (or at different penetration depths, which is

equivalent) as they travel through the target material.

This is shown in Figure 4-7.














TARGET PENETRATION [micro-meters]


0.6 0.4 0.
ENERGY [MeV]


Figure 4-7. Energy distribution of protons of initial
energy E0 = 1 MeV vs. average energy ,
as they penetrate a thick tungstan target.
The areas under the curves are equal.







57

As they loose energy through interaction with the target,

the particles generate characteristic x-rays at each point

along their path. Because at each penetration depth the

particles have a different average energy and energy

distribution, the production of x-rays varies with depth as

determined by these two parameters. The x-ray production

cross section at a distance t from the point of impact of

the particles on the target surface will be called

a(Eeff[t]), and is given by

Eo > [- o(E..[t]) o(E) e 2 dE


where E = Initial energy of the beam.

= Mean energy of the beam at a distance t from
the point of impact.

S= Standard deviation of the energy
distribution.

Eeff[t] = Is the effective energy of the beam at t,
which is defined as the energy of a mono-
energetic beam that would generate the same
number of photons as the beam with the given
distribution.

Equation (4-4) for protons of E0 = 1 MeV and the L-

series characteristic x-rays of tungsten was approximated

numerically using the expression


o(Eeff[t]) ] o (E) 1 -e E- AE (4-5)


and the obtained values of a(Eeff[t]) are shown in Table 4-1.

The example given is for 1 MeV protons (approximately

in the middle of the energy range of interest for this work)







58

striking a thick tungsten target. However, the conclusions

that can be derived from it are quite general because the

behavior of the cross section with energy is essentially the

same for all elements considered.

As Table 4-1 shows, the difference between the

effective and mean energies of the distribution is small,

Table 4-1. X-ray production cross-sections for protons
in tungsten, calculated with Equation (4-4)

X-Ray Production Cross-Section, a(Eeff[t]), Effective
Energy, Eeff[t], and Mean Energy of the Particle
Energy Distribution as a Function of the Target
Penetration Depth, t. Target: W. X-Rays: L-Series.
Depth o(Eefft]) Eeff[t] AE % of
[% of [cm ] [MeV] [MeV] {1}-{2} Total
Range] {1} {2} [%] Produc-
tion
2 1.31X10"23 0.989 0.990 0.1 38.1
15 8.95x10-24 0.901 0.900 0.1 64.1
29 5.95x1024 0.801 0.800 0.1 81.4
40 3.28x10"24 0.701 0.700 0.1 90.9
51 1.78x10'24 0.601 0.600 0.2 96.1
64 8.26x10"25 0.497 0.500 0.6 98.5
73 3.56x10-25 0.397 0.400 0.8 99.4
82 1.15x10"25 0.304 0.300 1.3 99.7
89 2.44x10-26 0.206 0.200 3.0 99.8
96 2.13x10"27 0.111 0.100 11.0 99.9

particularly for the first 70% of the particle range where

over 99% of the x-rays are produced (< 1%). This leads to

the observation that it is permissible to use a() instead

of a(Eeff[t]) in the computations of x-ray yields (see below)

without incurring a significant error. This substitution

simplifies matters considerably since it makes it









unnecessary to compute a(Ee f[t]) by carrying out the

integration of Equation 4-4 for every initial energy, target

material, and penetration depth. Instead, a() is

found through the following simpler procedure: The energy

at each depth is found in tables or graphs such as

that of Figure 4-2 which, in turn, are plotted from values

of stopping power computed by Anderson and Ziegler. The

cross section at those energies is then found from tables

published in the literature.

In summary, for the purpose of computing x-ray yields

an initially mono-energetic particle beam can still be

considered mono-energetic at any point within the

penetration range; the distribution of energies about a mean

value can be ignored. The foregoing argument is found in

the literature in the form of simple statements such as the

following by Reuter et al.: "The beam energy straggling in

the target can be neglected over the effective excitation

range" [58], or by Campbell et al.: "The basic premise [for

the accuracy of the model] is a proton path which is linear

and affords a well-defined proton energy at any given depth"

[60].

In the remainder of the discussion of photon yields,

this correspondence between a penetration depth and a single

energy will be assumed.

The number of x-rays produced at a depth t over a path

length dt will be called the differential photon yield,

dY(t), and is given by














dY(t) pa o()dt (4-6)

where p, = atomic density (atoms of target material per
unit volume).

By integration of Equation (4-6), the total photon

yield, Y(Eo), is obtained:

R(40)
Y(E,) Pa f o()dt (4-7)
0

where R(Eo) = range of particles with initial energy
Eo.

Equation (4-7) can be written in terms of energy

instead of penetration depth with the relationship


dt (4-8)
S(E)

The stopping power S(E) can be calculated with the

expressions given by Anderson and Ziegler. Alternately,

the same conversion can be performed through the

relationship t = F(E) which can be found from curves such as

that of Figure 4-2. The procedures are equivalent, since

the curves are drawn from values of S(E). However, because

the expression for Y(Eo) must be later combined with the

expression for photon self-absorption that is a function of

t (the energy E of the particles ceases to play a role once

the photons have been generated), it is advantageous to

leave it in the form of Equation (4-7).









4.4 Absorption of X-rays in the Target Material


Not all the produced photons escape the target. Some

are absorbed within it. This phenomenon is called self-

absorption; it is discussed below.

In general, the attenuation of x-rays by matter is

governed by the relationship


I _oe-P" (4-9)

where I0 = Initial photon beam intensity.

y = Linear attenuation coefficient of the
absorbing material for photons of a given
energy.

T = Thickness of the absorber.

I = Intensity of the attenuated beam.

Extensive tables of attenuation coefficients have been

compiled by Hubbell [61]. Usually, the tabulated values are

those of the mass attenuation coefficients, m,. They are

converted into linear absorption coefficients by multiplying

them by the density of the material.

To compute the number of x-rays that actually emerge

from a target, Equation (4-9) is integrated along the path

of the ions within the target material. Often, the quantity

of interest is not the total number of photons that emerge

from the target but the number of photons that leave the

target within a defined solid angle or in a defined

direction. The manner in which the actual integration is

carried out depends on the target and detector geometry.









4.5. Detection of X-rays

The photons that leave the target within the solid

angle of acceptance of the detector may have to pass through

one or more external absorbing materials before they reach

the detector itself. For extremely low-energy photons, it

is sometimes necessary to construct a windowless detection

arrangement, including evacuation of the space between the

source of x-rays and the detector; in most other

circumstances the additional expense that this arrangement

entails is usually not warranted. When intervening windows

must be used, it is desirable to keep their attenuation to a

minimum to increase the detection efficiency.

When n windows exist between the point of production

and the point of detection, Equation (4-9) becomes



-I e (4-10)

where the i's stand for each of the absorbers.

Because for a given experimental situation and for a

given photon energy (indicated by the subindex j), the

exponential part of the equation is a constant, it will be

called the attenuation factor and simply expressed as Fj:


F I e ,' (4-11)
aj Ioe

Another factor that needs to be considered in the

detection process is the absolute efficiency of the









detector. In general, not all the photons that penetrate

the detector's sensitive volume are necessarily detected.

One of the causes of detection losses is the decrease

in photon total interaction cross section with energy. In

the case of gas-filled detectors particularly, the detection

efficiency decreases rapidly with x-ray energy. Therefore,

proportional counters used in x-ray diffraction and

spectrometry applications are practical only for detecting

very low energy photons.

A second reason for decreased efficiency may be simply

the small dimensions of the detector. For instance, if a

two millimeter-thick lithium-drifted silicon (Si(Li))

detector is used to detect the Ka line of Ag (approximately

22 keV), only 70% of the photons entering the detector

volume will be stopped and detected; the rest will emerge

without interaction.

A third factor that may adversely affect the efficiency

of the detector is attenuation by the entrance dead layer.

For practical reasons, semiconductor detectors for

applications involving relatively low-energy photons are

fabricated in the shape of flat cylinders (disks). The

contacts for the charge collecting electrodes are made on

the circular bases of the cylinder. To make a proper

contact it is necessary to add some dopant to the

semiconductor and to plate the surface (usually with Au).

This process creates thin conducting layers on the bases of

the cylinder, which for detection purposes are dead layers.









One of the bases of the cylinder is the entrance side, so

the photons must traverse it before they reach the sensitive

volume. This causes some of the x-rays to be absorbed in

the dead layer and results in a loss of efficiency. This

effect is only noticeable at photon energies below a few

keV, and, unless the detector is windowless, it is of

negligible importance compared to absorption by the window.

Another cause for loss of counts may be incomplete or

slow charge collection in regions of low field within the

detector volume. This phenomenon usually has a larger

impact on the resolution of the detector than in its

efficiency, and can be almost completely avoided by

restricting the photon beam to the high-field region of the

detector sensitive volume by means of suitable collimators.

As in the case of the attenuation factor, the

efficiency of the detector is a constant for a given set of

operating conditions. This constant will be indicated by e.



4.6 The Specific Detected Photon Yield.

In the method for the measurement of spatial

distributions of energetic particles developed in this work,

a quantity of particular importance is the specific detected

photon yield Ysd, defined as the number of detected photons

per particle per steradian:











Yd Xd (4-12)


where Xd = number of detected photons.

Pi = number of particles intercepted by the
target.

S= solid angle subtended by the detector with
vertex at the point photon emission.

For a given set of experimental conditions and x-ray

energy, Ysd is a constant. The value of Ysd is computed from

the production of characteristic x-rays (Equation (4-7)),

the self-absorption (Equation (4-9)), the attenuation factor

F, the detector efficiency e, and 4r.



YSd(Eo) Pa o()e-Pldt Faj e (4-13)
10
For geometries in which the angle of impact and the

take-off angle are both equal to 45 degrees, such as shown

in Figure 4-8, T = t.

As can be seen by re-arranging Equation 4-12, the

specific detected photon yield is the constant of

proportionality that, for a given set of experimental

conditions, relates the number of detected photons to the

number of particles intercepted by the target:


Xd (4-14)
YsdW

In other words, Ysd is the basic parameter used in the

determination of the number of particles from the values
























X-RAYS




NORMAL-,
Stake-off
Single =
45 deg


angle of incidence = 45 deg .


RANGE


Figure 4-8. Geometry for Equation 4-13








67
obtained from x-ray measurements. It can be computed from

Equation 4-13 for a given geometry, or it can be measured.














CHAPTER 5
IMPLEMENTATION OF THE MULTI-ELEMENT PROBE METHOD



The implementation of the multi-element x-ray emission

method may be divided into two parts: The mechanical aspects

of the probes and the test chamber, and the instrumentation

aspects of the acquisition and analysis of information. The

former include the design and construction of the test

chamber and the methods of fabrication of the probes, the

latter addresses the specification of the characteristics of

the detector and the electronic instrumentation used in the

detection of radiation, processing of the signals,

conversion of the analog information to digital form, and

storage, retrieval, and analysis of the acquired data. In

this chapter, all of these aspects of the implementation of

the system are addressed.

As indicated in Chapter 4, it is important to calibrate

the probes in conditions closely resembling those of the

actual measurements. On the other hand, as mentioned in

Chapter 3, there are many possible variations in the

geometrical configuration of the probes. Therefore, for the

initial implementation of the probes it was necessary to

choose configurations particularly relevant to the main

intended applications. Two configuration were selected:









Probes with targets made with thick metallic foils

(laminiform probes), and probes with targets made with thin

wires filiformm probes). The laminiform geometry was

selected because of its importance in establishing a

baseline for the measurement of specific photon yields. The

filiform geometry is of interest because of its wide range

of applications to particle distribution measurements in

general and to the planned SCFR experiments in particular.

The acquisition and analysis of even moderately complex

x-ray spectra requires the application of strict criteria in

the selection of the components of the spectrometry system.

These criteria must be applied both to individual module

specifications and to the system integration. A discussion

of the selection process is included in the sections that

deal with each system component, preceded by introductory

background material. First, a summary description of the

experimental system as actually implemented is given below.

All the experiments were performed in a test chamber

mounted at the end of one of the Van de Graaff accelerator

beam lines. The test chamber was constructed with one of

the beam line sections known as beam diagnostic assembly

(BDA) with a thin plastic window fitted on one of its ports

(see Appendix) plus other components. The probes consisted

of targets (foils or wires) mounted on holders which in turn

were attached to the tip of a vacuum-sealed linear motion

device (LMD). The LMD was inserted in the chamber through

one of the access ports. Details of the test chamber are









shown in Figure 5-1. The photons emitted by the targets

were detected by a high-purity germanium (HPGe) x-ray

detector with integral very low noise preamplifier. A

spectroscopy-grade linear amplifier with gaussian shaping

was used for signal amplification and conditioning, and a

pc-mounted multi-channel pulse-height analyzer for spectrum

acquisition and data reduction. A discussion of the main

components of the experimental system follows.



5.1 Construction and Assembly of Probes

5.1.1 Laminiform Probes

The laminiform probes consisted of metallic foil

mounted on aperture-type holders (Figure 5-2). A list of

the materials used as targets for these probes is given in

Table 5-1. The holder was attached to an LMD, as mentioned

above. The LMD provided the means for moving the targets in

and out of the beam path without having to open the test

chamber. The laminiform probes were made and tested to

determine thick-target x-ray yields of different materials

and to perform measurements with partially- and fully-

neutralized particle beams.

5.1.2 Filiform Probes

Single- and multi-element probes were implemented using

thin wires of niobium, molybdenum, palladium, tantalum,

tungsten, platinum, and gold. The diameter of the wires

used ranged from 0.010 to 0.127 mm. The single-element

probes were used for measuring photon yields and to profile


































u w
I



z
0 cc
I-- LU
o C
:E a
o 0^


7-
w

0

0
I-
I-
0
z


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HOLES FOR
MOUNTING
TO LMD


TARGET MOUNTING BEAM-THRU
APERTURE HOLES FOR APERTURE


a. Base


b. Ring clamp


LAMINIFORM TARGET


00


c. Complete assembly


Figure 5-2. Aperture-type holder









ion beams by sequential measurements. The multi-element

probes were used for simultaneous multi-position

measurements of beam profiles. The wires were mounted on

the aperture-type holders previously described or on fork-

type holders shown in Figure 5-3. In either case, the

holders were fastened to the end of the LMD shaft.

Table 5-1. Target materials used in the
laminiform probes


Range of 2.5 MeV
Material (Z) Thickness of protons in
foil material
[__m] [Am]
Nb (41) 300 32
Mo (42) 127 29
Pd (46) 60 27
Ta (73) 127 27
W (74) 220 22


A jig was designed and built for mounting uniformly-

spaced wires to the fork-type holders. This jig is shown in

Figure 5-4. As constructed, the jig can be used for

mounting up to six wires with spacings from zero to 2.54 mm.

The maximum spacing for six-wire assemblies is limited by

the spacing between the steel pins on the rotatable

platforms. If a lower number of wires is used, wider

spacing can be achieved by mounting them on alternate pins.

Intermediate wire spacings between zero and the maximum are

obtained by rotation of the platforms. The spacing between

wire centers is given by





















01] II ...

FRONT SIDE FRONT SIDE
BASE CLAMP

0






FRONT SIDE
COMPLETE ASSEMBLY


Figure 5-3. Fork-type holder












ROTATABLE PLATFORMS


a. Top view showing partially assembled probe


b. Front and side views


Figure 5-4. Jig for assembling filiform probes


REFERENCE LINE










s dcosa (5-1)

where = wire spacing.

d = distance between pin centers.

a = platform rotation angle.

To install wires with a given spacing, the platforms are

rotated symmetrically to the desired angle and secured in

place. Then the holder is mounted in position with the

hold-down screws. The wires are strung and made taut, and

their ends are clamped at the tie-down posts. When all the

wires are in place, they are fastened to the holder with the

clamping rods and screws. If necessary, aluminum foil shims

can be used under and over the wires before clamping to

ensure uniform compression. Even wires of nominally equal

diameters, have small size differences that may cause some

of them to be compressed before others; the aluminum shims

usually take care of this problem. The end of the wires are

then trimmed with small wire cutters and the frame is

removed from the jig. Wires as small as 0.010 mm in

diameter were successfully installed with this procedure.

The fork-type holders just described were designed for

use in profiling accelerator beams. For other applications

holders of different dimensions may be used. The jig that

was constructed may be adapted for other holder sizes, or

new jigs based on the same general design may be built.









5.1.3 Selection of Materials for Probe Construction

As mentioned in section 3.2, any element that can be

drawn into the required shapes, plated to wires or plane

surfaces, embedded in a matrix, or otherwise fixed in a

desired position, could be used as a component in a multi-

element x-ray excitation probe. In practice, there are

limitations imposed by the energy of their characteristic

photons, their x-ray production cross sections, the behavior

of the material in vacuum conditions, and the possibility of

interference of their characteristic spectra. In

particular, for the probes used in this work the choice of

materials was further limited to metals that can be drawn

into very thin wires. (Most metals are available in wire

sizes of 0.1 mm and larger; several, in sizes of 0.01 or

0.013 mm. Gold and platinum wires can be obtained in

diameters as small as 0.0006 mm in the form of Wollaston

wire). When all the requirements were taken into account,

the list of potential target materials reduced to those in

Table 5-2.



5.2 The X-ray Detector

A high-purity germanium x-ray detector was designed

specifically for the development work of the multi-element

x-ray excitation probes. The detector characteristics were

selected to meet the experimental requirements of the

calibration of the probes, the determination of intrinsic

photon yields, and the physical constraints of future SCFR




















Table 5-2. Reduced list of metals suitable as targets
in x-ray excitation probes


Atomic number Useful x-ray Energy of most
Element (Z) lines prominent line
[keV]
V 23 K-series 4.951
Cr 24 K-series 5.414
Co 27 K-series 6.929
Ni 28 K-series 7.477
Nb 41 K-series 16.692
Mo 42 K-series 17.476
Rh 45 K-series 20.213
Pd 46 K-series 21.174
Ag 47 K-series 22.159
In 49 K-series 24.206
Hf 72 L-series 7.898
Ta 73 L-series 8.145
W 74 L-series 8.396
Ir 77 L-series 9.174
Pt 78 L-series 9.441
Au 79 L-series 9.712









applications. The detector was built to these

specifications by Princeton Gamma-Tech, Inc. (PGT) of

Princeton, New Jersey.

The following considerations determined the

characteristic of the chosen design:

1. Non-continuous use.

2. Sufficient resolution.

3. Reasonable efficiency.

4. Physical configuration.

They are discussed in detail in the rest of this

section.

5.2.1 Non-continuous Use

It was anticipated that the development work of the

probes would require intermittent use of the detector:

Periods of intense use while measurements were being

performed in the Van de Graaff accelerator interspersed with

prolonged idling periods while work was being done in other

aspects of the project. This requirement made the choice of

a high-purity germanium (HPGe) detector mandatory. HPGe

detectors require cooling to liquid nitrogen temperature

only when in use, but they can be stored at room temperature

for indefinite periods of time. On the other hand, lithium-

drifted silicon (Si(Li)) detectors, which were the second

possible choice, require continuous cooling to avoid

permanent damage. No advantages were found in these

detectors to offset this serious shortcoming, so they were









withdrawn from consideration in the early stages of the

design.

5.2.2 Sufficient Resolution

The ability of a detector to separate x-rays lines of

different energies is measured by its resolution. The

resolution of a detector is usually expressed as the full-

width at half-maximum (fwhm) of spectral lines. This

definition is illustrated in Figure 5-5. The overall

resolution of a spectrometry system is usually lower (larger

fwhm) than the resolution of the detector itself. This is

because there are other factors that affect the resolution

in actual experimental conditions, such as preamplifier

noise, pulse shaping, and count rate; these will be

addressed in following sections. In principle, the

resolution of a detector should be specified so that

adequate separation between all the spectral lines of

interest could be obtained. In practice, it can't be

arbitrarily specified since it is limited by fundamental

physical processes and by conflict with other

specifications, such as efficiency. In addition, it is not

meaningful to specify a high detector resolution if

preamplifier noise, for instance, would ultimately determine

overall system resolution. Therefore, the resolution is

usually specified as the minimum required to meet the needs

of the experiment. In many cases, this is an important

point from the economy standpoint since the cost of

semiconductor detectors rises rapidly with resolution. The







































ENERGY


Figure 5-5. Definition of resolution









resolution of the detector acquired for this work was

specified with the goal of maximizing the number ofdifferent

targets that could be used in a probe and still being able

to resolve at least one prominent peak for each element.

Taking into consideration that the minimum spacing between

lines of interest is approximately 500 eV (the difference

between K-series of low-Z elements), a resolution of

approximately 250 eV at the low energy end of the spectrum

was deemed acceptable. It should be pointed out that this

specification is for the detector/preamplifier

combination since, by necessity, the two components are part

of an integral assembly. This is explained in section 5.3.

5.2.3 Reasonable Efficiency

To attain good sensitivity, it is desirable to make the

solid angle of detection as large as possible. For a

detector of small diameter compared to the target-to-

detector distance, the solid angle w is given by the ratio


Ad (5-2)
W steradianss)
r2

where Ad = area of detector

r = target-detector distance

This implies that for good efficiency the detector must

be placed very close to the point where the photons are

generated, or that the area of the detector must be very

large, or both. As it will be discussed later, there are

practical consideration that restrict the detector size.