The Production and Use of Proton-Induced Ultrasoft X-rays Jones, Elizabeth Anne The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author For additional information about this publication click this link. http://qmro.qmul.ac.uk/jspui/handle/123456789/1487 Information about this research object was correct at the time of download; we occasionally make corrections to records, please therefore check the published record when citing. For more information contact [email protected]
Transcript
The Production and Use of Proton-Induced Ultrasoft X-raysJones, Elizabeth Anne
The copyright of this thesis rests with the author and no quotation from it or information
derived from it may be published without the prior written consent of the author
For additional information about this publication click this link.
A thesis submitted for the degree of Doctor of Philosophy
of the University of London'.
Dept. of Medical Electronics and Physics The Medical College of St. Bartholomew's Hospital Charterhouse Square London EC1 June 1988
2
ABSTRACT
A 700 keV Van de Graaff accelerator was used to accelerate protons
onto solid targets of different light elements to produce ultrasoft,
characteristic X-rays (< 5 keV). The proton energies were calibrated
using the (p, y) resonances at 633 keV in Aluminium and at 340 and
483 keV in Fluorine.
The X-ray emission characteristics of Aluminium, Carbon, Gold,
Silicon/Carbon, Silicon/Nitrogen and Titanium/Boron were studied as
a function of incident proton energy, angle of inclination of the
target (30° - 60° to the proton beam) and angle of detection of the
X-rays (40° - 130° to the beam). Detection of the X-rays was achieved
using a gas-flow proportional counter directly coupled to a low-noise
pre-amplifier. The resulting spectra, recorded on a multichannel
analyser, were well fitted by linear combinations of single Gaussian
curves to give peak position (X-ray energy), width and area (X-ray
intensity).
Carbon contamination of the target surface was studied in detail
for the Aluminium target. A number of low beam currents onto the
target (10 - 70 nA) were used for total irradiation times of up to
17 hours in order to establish the degree of overall X-ray energy
mixing.
The information gained from the study of both the Carbon
contamination and the X-ray emission characteristics was used to
propose practical optimum conditions for the production of ultrasoft
X-rays by proton bombardment in their application to biological and
biochemical irradiations.
A computer code, capable of following the electron track histories
resulting from ultrasoft X-ray interactions has been used to compare
the details of such energy deposition with the results of mammalian
cell irradiations made at the M. R. C. Radiobiology Unit for a number,
of different ultrasoft X-ray energies. Such a-comparison has been used
to try to identify the mechanisms of radiation action. Included in this
work is the application of the computer code to a variety of. characteris-
tic X-ray photon energies, thus extending the available, calculated data.
3
ACKNOWLEDGEMENTS
I am deeply indebted to many people for their help towards the
completion of this work. Foremost among these is my supervisor, Dr. F. A. Smith, who has patiently steered me throughout the duration
of this study and has been a constant source of inspiration,
encouragement and advice. Sincere thanks are also due to Dr. D. T. Goodhead at the M. R. C. Radiobiology Unit (Chilton, Didcot) who was always available for discussion and guidance on all aspects of the
work.
My thanks are also due to Prof. N. F. Kember for making the facilities at the Physics Department of the Medical College of St. Bartholomew's Hospital available, and I am grateful for the
comradeship afforded to me by him and all the members of the department during my three years there. Special thanks must go to Len Eastgate for constructing various parts of the equipment and James Oriel for his
constant advice and help with the electronic equipment (and breakdowns! ).
I am also grateful to Peter Browne and his colleagues for their assis- tance with the computing side of the work.
During the duration of this study I made several visits to the M. R. C. Radiobiology Unit and I am grateful to all those who made these
visits possible. I am especially grateful for being allowed access to
the computing facilities at the Unit and appreciate the help given by
members of the Computer Services Division. I also appreciate the friend-
ship and advice given by members of the Cell and Molecular Biology
Division. In particular, I would like to mention Dave Charlton (now at Concordia University, Montreal, Canada) and Hooshang Nikjoo - who was
an invaluable source of advice and information concerning the use of the
Monte-Carlo track structure codes. They, along with Dr. Goodhead, also
provided me with unpublished data, for which I am very grateful.
I am indebted to the Science and Engineering Research Council for
the award of a research studentship and to the Medical Research Council
for covering the cost of the visits to the Radiobiology Unit. I am also
grateful to Mrs. D. Boyle for deciphering my writing and typing the
thesis.
4
Finally, I would like to thank my family. My brother, Hefin
has always been ready with his support and helpful advice, and
submitted himself willingly (? ) to reading the final versions of
this work. My parents have given continual encouragement, support
and devotion over the years and this was reiterated by their
willingness to help check the data presented in Appendix 2. It is
as a token of my appreciation that I dedicate this work to my parents
and brother.
Diolch o galon i'bob un ohonoch!
5
TABLE OF CONTENTS Page
Abstract 2
Acknowledgeme nts 3
Table of Contents 5
List of Figures 7
List of Tables 10
Chapter 1 Introduction 11
Chapter 2 Expe rimental Apparatus 22
2.1 The Van de Graaff accelerator 22
2.1.1 The Generator 22
2.1.2 The Accelerator 24
2.1.3 The Pressurised Tank 25
2.2 The Beam Line 26
2.2.1 Accelerator tube extension 26
2.2.2 Collimators 29 2.2.3 The Scattering Chamber 29
2.3 The Target System 30
2.4 The Detection System 34
2.4.1 The Proportional Counter 34
2.4.2 Associated Electronics 43
Chapter 3 Calib ration of the Van de Graaff machine 45
Chapter 4 Data Analysis 55 4.1 Subroutine SIMPLX 56
5.1.3 Proton energy dependence of 62 X-ray emission
5.2 Results 62 5.2.1 Surface contamination study 79
5.2.2 Angular distribution study 85
5.2.3 Proton energy dependence of 92 X-ray emission
6
Pace
Chapter 6 Theoretical Treatment of Results 96
6.1 Compensation for target surface 96 contamination
6.1.1 Example of surface contamina- 101 tion calculations
6.2 Calculation of theoretical angular 103 distribution
6.2.1 Example of the theoretical 108 angular distribution calculation
Chapter 7 Application of Monte-Carlo Track Structure 115 Codes
7.1 Introduction 115
7.2 Local Energy Deposition of Radiation 116 Tracks
7.3 Calculations using a Monte-Carlo structure 118 code'
7.3.1 Track Structure and Scoring 119 Programme
7.3.2 Results 120
Chapter 8 Discussion 141
8.1 Comparison of the observed angular 141 dependence of proton-induced ultrasoft X-rays with theoretical calculation
8.2 A practical beam line for proton- 143 induced ultrasoft X-rays
8.3 Monte-Carlo electron track structure 150 data
Bibliography 154
Appendices:
Appendix 1 Subroutine FCN 165
Appendix 2 The absolute frequency of energy depositions 169 greater than a given amount in each elemental cylinder per Gray of absorbed dose to the
medium
7
LIST OF FIGURES Figure Page
1.1 Frequencies of dicentric exchange aberrations 12 in human lymphocytes after irradiation with high and low L. E. T. radiations.
1.2 Dominant mode of absorption of Aluminium K X-rays 14 by an Oxygen atom.
1.3 Energy deposited locally by electrons from low 15 L. E. T. radiations.
1.4 Typical X-ray energy spectrum from a hot-filament 18 X-ray tube.
2.1 Simplified drawing of the AN700 Van de Graaff 23 accelerator.
2.2 Schematic diagram of the beam line. 27
2.3 Schematic drawing of the target system. 31
2.4 The effect of applying a positive bias voltage 32 to the electron suppression shield.
2.5 The angular dependence of the target charge 33
collection time.
2.6 The Manson Gas-flow Proportional Counter. 35
2.7 The transmission of ultrasoft X-rays through the 36 VYNS window.
2.8 The effect of adding Polypropylene filters above 38
the detector window.
2.9 Magnetic deflection of scattered protons. 39
2.10 Calculation of the magnetic field required to 40 deflect the scattered protons away from the hole in the steel shield.
2.11 The correction to the required magnetic field due 42
to the limited extent of the available field.
2.12 Schematic drawing of the ultrasoft X-ray detec- 44
tion system with the associated electronics.
3.1 Proton capture. 46
3.2 Schematic diagram of the beam line as used during 48 the calibration of the Van de Graaff.
3.3 An example of the energy spectrum from the CaF2 50 target.
3.4 Thick target y-ray yield curve for 19F (p, y)
20Ne. 51
3.5 Thick target y-ray yield curve for 27A1 (p, y)
28Si. 52
8
Figure Page
3.6 Calibration graph for the proton energy as 54 a function of the generating voltmeter reading.
4.1 A two dimensional simplex. 57
5.1 Examples of the spectra obtained for each of 65 the targets when bombarded with 500keV protons.
5.2 Derivation of the BK X-ray intensity. 73
5.3 The transmission characteristics of 6 pm 74 Polypropylene at low energies.
5.4 Energy calibration graph for the proportional 76 counter and MCA system.
5.5 The variation of the CK X-ray yield with 82 collected charge on the target.
5.6 The variation of the A1K X-ray yield with 83 collected charge on the target.
5.7 The A1K : CK X-ray intensity ratio as a function 84 of the charge collected on the target.
5.8 The build-up of Carbon contamination X-ray 86 intensity with the total amount of charge collected on an Al target.
5.9 The rate of Carbon contamination build-up as a 87 function of the proton beam current.
5.10 The relative X-ray intensity as a function of 89 the detector angle.
5.11 The mass attenuation coefficient of low energy 93 X-rays in Carbon, Silicon and Gold targets.
5.12 The measured X-ray intensities of CK and A1K X-rays. 94
5.13 The ratio of the measured Carbon-to-Aluminium 95 K-shell X-ray intensity as a function of proton energy.
6.1 The mass attenuation coefficient of low-energy 97 photons in Carbon.
6.2 Calculation of the depth of Carbon contaminant 100 on the target surface.
6. ý Simplifying assumptions used for the calculation 104 of the theoretical angular dependence of the emitted X-rays from a thick target.
6.4 The variation of proton energy with depth into 105 the target.
6.5 The K-shell X-ray production cross-section for 106
proton bombardment of various low Z targets.
9
Figure
7.1 Diagram illustrating the virtual sphere enclosing the simulated electron track(s) and crossed by the scoring cylinders arranged at random.
7.2 The frequency of energy depositions obtained when considering the interaction of CK X-rays with soft tissue.
7.3 The frequency of energy depositions obtained when considering the interaction of A1K X-rays with soft tissue.
7.4 The frequency of energy depositions in a 2 nm x2 nm cylinder by simulated electron tracks from various low Z characteristic X-rays.
7.5 The frequency of energy depositions in a 10 nm x5 nm cylinder by simulated electron tracks from various low Z characteristic X-rays.
7.6 The frequency of energy depositions in a 25 nm x 25 nm cylinder by simulated electron tracks from various low Z characteristic X-rays.
7.7 An inter-elemental comparison for the frequency of energy deposition in a2 nm x2 nm cylinder.
7.8 An inter-elemental comparison for the frequency of energy deposition in a 10 nm x5 nm cylinder.
7.9 An inter-elemental comparison for the frequency of energy deposition in a 25 nm x 25 nm cylinder.
8.1 The sin 6 dependence of the difference in the distance travelled within the target at either end of each pm increment.
8.2 A schematic diagram summarising some of the properties of a practical beam line for biological irradiation by proton-induced ultrasoft X-rays.
Pace
122
124
128
133
134
135
137
138
139
142
149
10
LIST OF TABLES
Table Page
5.1 The energies of the characteristic X-rays studied. 64
5.2 The average parameter values for the various 71 targets.
5.3 The observed yield of X-rays. 78
5.4 Comparison between the observed and documented 80 yields of proton-induced ultrasoft X-rays.
6.1 The linear attenuation coefficient of ultra- 98 soft X-rays in Carbon.
6.2 The A1K intensity - correcting for surface contami- 102 nation.
6.3 The energy loss experienced by a 500 keV 109
proton in an Al target.
6.4 The AlK production cross-section. 110
6.5 The distance travelled by the X-ray within the 111 target.
6.6 The product of the A1K X-ray production cross- 112 section and the attenuation of the X-ray in the target.
6.7 The contribution of the A1K X-rays produced in 114
the first pm of the target.
7.1 Input parameters for the electron generating 121
code, MOCA7.
8.1 The mass attenuation coefficients of low energy 152 X-rays in Oxygen.
11
CHAPTER 1
INTRODUCTION
In 1938 K. Sax published the results of a study of chromosome
aberrations induced in cells by ionising radiations. These results,
together with further studies (for example : Sax, 1940,1957; Evans,
1962; Revell, 1974; Savage, 1975), showed that ionising radiations were
capable of inducing the exchange of chromosome material and it was
suggested that an aberration arose as a consequence of two radiation
damaged chromosomes undergoing an exchange. Radiations of different
ionisation density or linear energy transfer, L. E. T., (L. E. T. is a
measure of the energy imparted to a medium along the path of a charged
particle [ICRU, 1970]) were observed to have varying degrees of effect
on the irradiated cells (Figure 1.1). Combining this information with
the size of the chromosome structures involved led to the suggestion
that the required distances between pairs of damaged chromosomes for
aberration induction (termed the interaction distances) were of the
order of 0.1 to 1 pm (Lea and Catcheside, 1942; Lea, 1955; Wolff, 1959;
Heddle and Wolff, 1966; Neary, Preston and Savage, 1967). In comparison,
the diameter of cell nuclei is typically of the'order of 10 Pm and the
diameter of a DNA double helix is approximately 2 nm.
During the same time period, developments in experimental physics,
particularly with the introduction in the late 1950s of the low-
pressure (Rossi) proportional counter (Rossi and Rosenzweig, 1955),
enableddirect measurements to be made of the energy deposited by
radiation within a small simulated tissue volume. Such measurements,
and their analyses, became known as microdosimetry - the study of the
properties of radiation in small tissue volumes usually smaller than
the nuclei of mammalian cells.
12
m 0 16.
d CL U) C 0
IM I- 0
vý "L
C
0 0
HIGH LET LOW LET
Fission neutrons Y- rays
Dose (Gy)
Figure 1.1 Frequencies of dicentric exchange aberrations in human lymphocytes after irradiation with radiations of high L. E. T. (Lloyd et al., 1976) and low L. E. T (Lloyd et al., 1975). Above each curve is a diagrammatical representation of the track of ionisation produced by a typical secondary charged particle from each radiation (from Goodhead, 1982 with permission, copyright by Academic Press, Inc. ).
02468
13
By using microdosimetric techniques attempts could be made to
measure some physical properties of ionising radiations that corres-
ponded to the properties of radiation resulting in chromosome
aberrations and other biological effects in cells. Such studies
might then elucidate the mechanisms of radiation action, enabling
the radiological risks to human beings to be better understood and
quantified.
As mentioned earlier, L. E. T. is often varied within studies of
radiation mechanisms. The radiations used frequently deposit energy
along tracks which are long in comparison with sub-cellular dimensions,
thus making it difficult to pinpoint the cause of any specific damage.
Radiations which produce tracks of short, defined lengths have been
available, but practical limitations such as their attenuation co-
efficient have limited their use.
However, ultrasoft X-rays of less than ti 5 keV, although having
very large attenuation coefficients and a limited availability, have
been used intermittently since the late 1920s (Goodhead and Thacker,
1977). The interaction of ultrasoft X-rays with matter takes place
almost entirely by photoelectric absorption (Figure 1.2) leading to
the production of photo- and Auger- electrons of low, well defined
energies, capable of producing only very short tracks (< 0.1 pm).
Recent studies on mammalian cells have shown that ultrasoft X-rays are
highly effective in inducing biological damage (Cox et aZ., 1977;
Goodhead et al., 1979,1981a; Virisk et al., 1980; Thacker et al., 1983;
Brenner et al., 1987; Raju et al., 1987) and have been found, in general,
to be more effective per unit dose than hard X-rays and gamma (y) rays.
Although other ionising radiations, such as hard X-rays and y-rays,
produce a large number of low energy electrons (Figure 1.3), the effect
14
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o,
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JC I,
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ti0/ `tai ry/
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Figure 1.3 Energy deposited locally by electrons from low L. E. T. radiations (D. T. Goodhead and H. Nikjoo, (pers. cormn. ) based on data by Burch (1957) and R. J. Munson (unpublished data) using the method of Burch). 35 - 45 % of the energy is deposited by electrons of 5 keV energy or less.
1 10 100 1000 Electron Energy
, keV
16
of the low energy electrons cannot be studied in isolation from the
effect of the higher energy electrons (Raju et al., 1987). The effec-
tiveness of ultrasoft X-rays was also observed to increase with
decreasing photon energy.
Numerous models and concepts attempt to explain radiation-induced
Silicon/Carbon (SiC), Silicon/Nitrogen (Si/N) and Titanium/Boron
(TiB2). were clamped onto an insulated, semi-cylindrical brass holder
which entered the scattering chamber through one of the removable lids
(Section 2.2.3). The TiB2 (Borax Consolidated) SiC and Si/N
(Morganite Special Carbons Ltd. ) targets were hot compressed, the
Si/N target believed to be predominantly Si3N4 (ti 90%) and the remainder
consisting of an unknown ratio of Si to N atoms. The target holder
could accommodate all six targets together, each target being suffi-
ciently wide (> 1 cm) to allow the proton beam to strike at least
two positions. Movement from one target position to another was
possible without breaking the vacuum in the scattering chamber as was
varying the target orientation with respect to the beam. This latter
facility permitted a complete 360° rotation about the target holder's
axis although in practice, the need for electrical connections res-
tricted it to < 180°. The angle which the target made to the beam
could be monitored from outside the scattering chamber.
The target holder was surrounded by an electron suppressor shield
which was insulated from the target holder and the scattering chamber.
Using a similar design to that used by Sterk, Marks and Saylor (1967),
31
O vº 3C
Z'
a 4- rn ý
vi C
_ý .. m r- .r tV NN
Nr =a or -
L0
CCP to
w
"C
VN N
U)
C .` 1
0
io
w cm a) 0 ou-
mN N
. 92 Co Co
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2
öC to 0u
0 a
01 C
N ýp t0 ++ h.
9 Q) u Co U)
v 00
4J
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v u
M
C,
lJ..
32
N
0 r
U
N CV
V ,4
0 0
O
d
.xg
m E
d rn cv m
Figure 2.4 The effect of applying a negative bias voltage to the electron suppression shield with the target at 45° to the beam. The points shown are the average values (± s. d. ),
over five readings, for the time taken to collect a charge of 25 pC on the target.
0 10 20 30 40 50 60 70 80 90 Target bias voltage (V
33
`n 5 N Q
v
U
U, c, 1 4-
04 a, ö 0
0
c YI c9
. 6. -
(D E
4-
d Of
(9 0 b. i d
Figure 2.5 The angular dependence of the target charge collection time for an unbiased electron suppression shield (") and with a -90 V bias voltage on the shield (0). The points shown are the average values (± s. d. ) taken over five readings.
Target-to-beam angle
34
the target was biased at +90 V relative to the electron shield using
a power supply operated with its output floating (but referenced to the
shield). This was found to be sufficient to prevent secondary electrons
from escaping (Figure 2.4) thereby causing a false indication of beam
current - an effect which was observed to be target-angle dependent
(Figure 2.5).
The current onto the target was monitored using a charge integrator
(Figure 2.2) constructed in the Physics Department of St. Bartholomew's
Hospital Medical College. The current onto the target was transferred,
through a coaxial cable, to the integrator where a2 NF capacitor was
charged. The voltage across the capacitor was measured and monitored
on a 25 V full scale deflection (f. s. d. ) meter, thus giving a charge
measurement of 50 pC f. s. d. The integrator had a number of different
capacitors (1 nF to 2 pF) in its circuitry such that a suitable value
could be chosen for the particular current being measured.
2.4 The Detection System
2.4.1 The Proportional Counter (Figure-2.6)
The emitted X-rays were detected using a gas-flow proportional
counter (Model 04, J. E. Manson Co., Inc. ) directly coupled to a low
noise pre-amplifier (Manson Model PAL-01). The counter had a Nickel
plated brass body with cylindrical internal symmetry of 1.95 cm diameter
and length 7.3 cm. The 3 mm x 10 mm slotted window consisted of a VYNS
(a copolymer of 90% Vinyl chloride and 10% Vinyl acetate: C22H2302C19)
window of 28pg. cm 2 nominal thickness ('11 0.1 Nm) on a 60% open 400
lines per inch (ti 160 lines per cm) Nickel mesh. The transmission
characteristics of the window at low photon energies (Manson literature)
are shown in Figure 2.7. The X-rays transmitted through the window
were absorbed in the cylindrical cavity (maximum diametric gas path
35
A. Position of anode
wire
3mm x 10mm slotted V YN S window
EXX
Anode high voltage "
Output PAL-01 Pre-amplifier E
±15 and Gnd
B.
Window <--- Gas supply
-AAA4Aý[ Anode wire v ray
r-4 ý-
Pre -amplifier
Figure 2.6 The Manson Gas-flow Proportional Counter : A. Showing the 3 mm x 10 mm slotted VYNS
window. B. Cross-section through the centre of the
counter, showing the window, anode wire and gas path.
36
100
80
60 0 I::
Figure 2.7 The transmission of ultrasoft X-rays through the VYNS window (28 pg. cm 2 film on a 60 % open mesh). The position of some light element K-lines are indicated.
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Photon Energy, keV
37
length of 2.05 cm) by P10 (90% Argon and 10% Methane) gas at a flow
rate of 12.5 cm3. min-l. A bias voltage of +1700 V was used on the
central 50 um diameter stainless steel anode for all the X-rays except
Titanium K-shell (TiK) X-rays, for which, because of their higher energy
(4.5 keV), a bias voltage of +1600 V was used to produce less amplifi-
cation. The collecting area was defined by a1 mm diameter hole in a
Cadmium disc placed in front of the counter window. This also reduced
the X-ray intensity and hence the counting rate, avoiding pile-up.
Directly above the counter window was placed 6 pm of Polypropylene
(CH2 = CHCH3) which, when combined with the counter window, was found
to be sufficient to prevent backscattered protons entering the counter.
The thickness of Polypropylene used was determined experimentally by
observing the X-ray emission spectra from a Carbon target, when
bombarded with 500keV protons, for varying thicknesses of 'filter'
above the detector window. The optimum condition was taken to be the
point at which additional layers of filter served only to attenuate
the X-rays being produced with no effect on the background (Figure 2.8).
An alternative, magnetic method was used in the earlier stages of the
work (Figure 2.9). Using the expression for the magnetic field, B,
required to deflect charged particles of rest energy Wo and kinetic
energy T, through an arc of a circle with radius r (Rosenblatt, 19'68):
1
IT (T +2 Wo)] 2 2.1
300 r
where T and ö are in MeV, it was possible to estimate the field
strength required to deflect any scattered protons away from the
window. A simplified drawing is shown in Figure 2.10 (A). With the
magnet pole pieces 7 mm apart (Figure 2.9 (A)) and the steel shielding
(present to prevent the magnetic field affecting the operation of the
pre-amplifier) having a3 mm aperture, the maximum value of 'x' was
38
1
1
1
U)
O V
0 ö z
1
of Polypropylene
Figure 2.8 The effect of adding Polypropylene filters above the detector window. The spectrum from a Carbon target bombarded with 500 keV protons is shown with filters added in 2 pm increments from 0 to 10 pm of Polypropylene.
0 100 200 300 400 Channel no.
39
A.
ý7mm
Spac
B. Target
tt tt tI
; scattered , protons
Nt TS
-ff
r
out of page
X-rays
Proton be-am
Al collimator
UMNII-Steel shielding -Cd pinhole
Proportional counter
Figure 2.9 Magnetic deflection of scattered protons : A. Schematic diagram of the magnet (with
a magnetic field of 0.3 T between the pole pieces).
B. The experimental arrangement used.
Pole piece
40
A. r
---ý x-
For y»»x, y=I and a. tan'' xl Cyl
r . 180 ,1 Fa
B. 7mm E-r
Magnet pole Epiece p
--ý 5tnm(-
`ý Shield
3mm
2.2
Figure 2.10 Calculation of the magnetic field required to deflect the scattered protons away from the hole in the steel shield.
A. The simplifying assumptions used for the calculation of the radius of the arc of the circle through which the protons are deflected.
B. The maximum distance over which the protons are deflected (x).
41
taken as 5 mm, where a proton at the edge of the field just avoids the
edge of the aperture (Figure 2.10(B)). The distance between the magnet
and the shielding was 6 cm (_y). Using the approximations that the arc
length, Zwy, and ax tan-1 (x/y) in Equation 2.2 gave a value of r
0.7 m. When used in Equation 2.1 for 500 keV protons this then gave
a required magnetic field of 0.15 T.
Since the magnetic field used was 0.3 T, it should have been more
than sufficient to deflect even the most energetic backscattered protons.
This was not, however, found to be the case. The presence of the magnet
between the target and the detector proved to be largely ineffective in
reducing the amount of backscattered projectiles entering the counter.
There are three possible-reasons for this:
(i) It is possible that the protons reached the magnet pole pieces at
an angle other than parallel to the axis, and that therefore some protons
which were originally well off-course from the 3 mm aperture were curved
back to it.
(ii) In the preceding calculation it was assumed that the proton was
subjected to the field B throughout the distance y. In practice how-
ever, the field only extends for the 7 mm within the pole pieces, after
which the proton will continue on a tangential path to the curve it was
following. As a result the field required would be higher if the same
eventual deflection was to be achieved (Figure 2.11).
(iii) Buck, Wheatley and Feldman (1973) showed that for proton energies
ti 100 keV, a large fraction of the backscattered projectiles were
neutralised. Consequently any attempt to remove the recoil particles
from the X-ray flux by electrostatic (or magnetic) deflection techniques
would be expected to be only partially successful.
It was therefore concluded that an absorbing filter was necessary to
prevent back-scattered protons and Hydrogen atoms from entering the
proportional counter.
42
r i
I.
4 - X-ý
Path of a proton subjected to a magnetic field over a distance: (a)--t y
(b)--f--- Z
Figure 2.11 The correction to the magnitude of the required magnetic field due to the limited extent of the available field (z =7 um).
x' x tan a=-=z z ry
For xz =5 mm (i. e. xz =x)
z. xz MI= = 0.6mm WU
V
Assuming Zzz (Figure 5.10(A)) and using Equation 2.2, r=8.5 cm which, when substituted into Equation 2.1, gives B=1.2 T.
*- XZ -4
43
2.4.2 Associated Electronics (Figure 2.12)
The bias voltage to the counter anode was provided using a
Harwell 2000 Series E. H. T. Unit, Type 2147-2 with a variable output
from 0 to 3 kV. The Manson PAL-O1 pre-amplifier required a+ 15 V and
a- 15 V input which was obtained from a Harwell 2000 Power Supply
Unit, Type 2015-4.
The input stage of the pre-amplifier was a junction field-effect
transistor followed by quasi-Gaussian double differentiating and
integrating filters with time constants of 0.75 ps. The output pulse
was bipolar with the positive lobe leading. The output from the pre-
amplifier was fed into the input of a Norland IT-5300 Multichannel
Analyser (MCA) (Norland Instruments/Ino-Tech. Inc. ). Using the pulse
height analysis mode of the MCA the energy distribution of the output
from the pre-amplifier was obtained and recorded onto the GOULD PN6000
mini-computer.
44
r. 0
. r., 41 u v a)
w 0 Co t+
a
U) U
Ö
c) N
a) b N
U O y y
N
a (1) 41 U)
0 co
cd i+
"d
U " rl 1-i td E
C) U)
N I
N
a,
Li
45
CHAPTER 3
CALIBRATION OF THE VAN DE GRAAFF MACHINE
The potential at the high-voltage terminal of the Van de Graaff
accelerator was monitored using an in-built generating voltmeter. The
voltmeter assembly consisted of a motor-driven rotor, with four equally
spaced, 45° sectors cut out of it and a stator plate divided into
eight insulated 45° sectors. As the rotor rotates, it alternately
exposes the high voltage terminal to the stator and shields from it
each sector. Triangular wave alternating current (a. c. ) voltages are
thus electrostatically induced between adjacent sectors of the stator,
the voltages being directly proportional to the terminal voltage.
Four alternate stator sectors of the voltmeter are connected in parallel
to the a. c. terminal of a bridge-rectifier circuit, located on the
voltmeter housing, which is connected to the generator voltage meter
on the control console of the accelerator.
The generating voltmeter was calibrated using the (p, y) resonances
method (Hunt and Jones, 1953). A low-energy proton may be captured by
a nucleus which is thereby transformed into a residual nucleus in a
highly excited state (Figure 3.1). Instead of expelling the incident
particle again (scattering), the residual nucleus may decay to the
ground state and rid itself of the binding energy of the particle by
the emission of one or more gamma (y) rays. The capture of a proton
depends upon the energy being of the correct amount needed to enable
the residual nucleus to be formed in one of its excited states, and is
thus resonant in nature.
For the calibration of the Van de Graaff accelerator, resonant
proton energies were looked for in Fluorine and Aluminium. Strong
46
M( A+lY *)
on energy
M(A+1Y)
0
Figure 3.1 Proton capture : the target nucleus (AX)
captures a proton (rest-mass, M(p), kinetic energy, T(p)) to form a residual nucleus in an excited state, A+ ly*.
47
resonances have been observed at 340.4 keV and 483.1 keV in Fluorine
(Hornyak et at., 1950) and at 633 keV in Aluminium (Meyer, Venter and
Reitmann, 1975). For these cases the expected reactions are as given
below, with the available excitation energy, E. being calculated from:
EM (AX) +M (p) +T (p) _M (A+1 Y) 3.1
where M, the rest mass, was obtained from the Table of Isotopes, 1978,
and T (p) was the kinetic energy of the proton.
For Fluorine, the resonance reaction is given by
19F (P, Y) 20Ne 3.2
with M (19F) = 17697.032 MeV, M (20Ne) = 18622.977 MeV and M (p) =
938.280 MeV. Thus for a proton of energy T (p) = 340.4 keV, the
excitation energy was calculated to be 12.675 MeV, and for T (p) =
483.1 keV, E= 12.818 MeV. For Aluminium, the reaction is given by
27A1 (p, Y) 28Si 3.3
with M (27 Al) = 25133.333 MeV and M (28Si) = 26060.537 MeV giving an
excitation energy of 11.709 MeV for a 633 keV proton.
For both Fluorine and Aluminium the calculated excitation energies
are such that the energy levels of the residual nucleus are very close
together. For example, for the 20Ne nucleus there are over 125 energy
levels in the region of E= 11 to 23.5 MeV. As a result, an increase
of only 0.14 MeV in the energy of the protons interacting with the
Fluorine nuclei is sufficient to give rise to a second resonance
position.
The emission of y -rays'from thick (2,6 mm) targets of Aluminium
and Fluorine (in the form of a Calcium fluoride, CaF2 target) was
studied using a 3" diameter x 3" length (75 mm x 75 mm) cylindrical
Thallium activated Sodium iodide (NaI(Tl)) crystal detector in
conjunction with a Norland IT-5300 MCA. As is shown in Figure 3.2 the
48
ti
CD
N
9 0 w E
m C7 m
oý ýv oý
a
L() a
oº c
aý d Aý vA Nt
OV H
r. 0 M 41 Co Ei 1+ u r1 N(0
H G4 >lb cu Co 0 C) U
b0
.C Cl O Hrl
I+ q 41 q R1 N O
'O I oO O d 1-i u
.t P td C3 aý a E-4
Co O Rf .a
cSt a
Ki 0 e-i H
W
cd 'L3 1.1 C1 Gl 0
a) u > +-
b Co 4-+w > O 4-+ .. 41
cu oo > aý cu H r-I 41
cd }a _1 '-' C C O ýH p o0
ý Co N Cl z 0) ý,
ý 41 w b x: Co Co 0 NM GO '-I u td rl
.rA> b DC F+' 'r 4. + W -rl x
H. ä
Cn 0 -4 r1 ºr1 r-
N
M
V
ü_1 M
49
target was positioned at 45° to the proton beam with the detector at
900. In order to eliminate most of the background counts the NaI(Tl)
detector was encased in 5 cm Lead shielding. The accelerator
terminal voltage was varied in 10 kV increments around the expected
keV for 27A1). The energy spectrum from the NaI(Tl) detector was
collected and, using the integrating facility on the MCA, the number
of emitted Y-ray counts measured (Figure 3.3) as a function of the
accelerating voltage. As shown in Figure 3.3, for the Fluorine
resonances it was possible to integrate a specific Y-ray peak which,
using the two 1-rays from a60Co source for calibration, was found at a
photon energy E1 ti 7 MeV. However, for the Aluminium target, no such
peak was observed - the 1-ray energy believed to be > 10 MeV (High
Voltage Ltd. literature) thus extending beyond the range of the 1024
channels of the MCA. However, for a 75 mm x 75 mm cylindrical NaI(Tl)
crystal a large proportion of the photon interactions would be
expected to be of the Compton effect kind, where only a portion of the
energy of the photon is deposited in the crystal thus giving rise to a
range of reduced height pulses which would appear on the MCA scale.
The resonance position for the Al target was therefore deduced by
integrating the total energy spectrum above channel 100 (thus eliminating
most of the low energy, accelerator voltage independent noise).
Having normalised all the measurements to the proton beam current,
thick target y-ray yield curves were obtained (Figures 3.4 and 3.5).
The resonance positions were identified at the point of maximum gradient
of the thick target yield curves versus accelerating voltage (Khan and
Potter, 1964):
19F(p, Y)
20Ne - 340 ± 10 kV
480 ± 10 kV
27Al (p, y) is Si - 640 ± 10 kV " 14,
?! äff ý``
50
kV independent noise
N 2.0 0 r
x u) 1.5 c 0
1.0 0 Position of Y-rays
from60Co source
-130 5 - . E z
ON I 0 200 400 600
Channel number 800 1000
Figure 3.3 An example of the energy spectrum obtained from the Ca12 target with an accelerating voltage of 350 kV. The y-ray counts were obtained by integrating the peak between the 'Start' and 'Stop' positions. An energy calibration based on the y-rays from a 60Co
source (at 1.17 and 1.33 MeV) gave the energy at channel 800 as z7 MeV (assuming a linear energy scale through the origin).
kV dependent peak
Stop Start
51
Jfl)$/SIUflO3) oI
`aonino i96VJe; )10! 43 J0 3ua! peiE)
0 LD ICJ -0
Ln a) G)
+' Fi co 0 U)
cv u O ý3 O +' Ln 3p
Co 10 Z O
O > aW
C o r1 44 4. J
O d Nä O u al
-v-4 Ö
E . ý. r N
O 0 >
4 Nv LU C! OO. L]
4J OO d0+- N ý+ D N4) rl
a) 0 x10 as 0 uvn M ý O H
b 0+ ý
cr Om N N
m U.
N0 Co Co 'e c4 O (zOi. x) e `anano 1e6aei )1oiy1'swunoo I(ei-A,
In order to calibrate the proton beam energy against the accelerating
voltage, as monitored by the generating voltmeter, the observed
resonance positions were compared with the known resonance energies as
given by Hornyak et al., 1950 and Meyer, Venter and Reitmann, 1975.
This information was then used to produce a calibration graph for the
actual proton beam energy in terms of the generating voltmeter reading
(Figure 3.6). The vertical error bars were smaller in magnitude than
the size of the plotted points.
From the three resonance positions observed it was seen that the
terminal voltage as measured by the generating voltmeter was within
t5 kV of the proton beam energy, thus lying within the experimental
accuracy of t 10 kV under which the major part of this work was
undertaken (Chapter 5).
54
701
060,
>I 50 rn
c 40
30 0
20 a
10
Figure 3.6 Calibration graph for the proton energy as a function of the generating voltmeter reading. The regression line is shown (y = O. 99x + 1.59) with a correlation coefficient, r=1.0.
CK X-rays in a Carbon target, than for higher energies such as SiK X-rays
in a Silicon target (Figure 5.11). A further anisotropy in the emission
of M-shell X-rays might also be expected because of the angular momenta
change which occur in the system upon the emission of M X-rays.
5.2.3 Proton energy dependence of X-ray emission
The variation in X-ray intensity with proton energy (at constant
current and for a fixed amount of charge onto the target) was measured
for the Aluminium and Carbon targets. Three sets of data were taken
for each target, the average values being shown in Figure 5.12\ with the
uncertainties (± s. d. ) being less than the size of the plotted points.
Whilst the X-ray production cross-section for 500 keV protons onto
a Carbon target is 15 times that for an Aluminium target (Figure 6.5)
only a factor 4 difference was observed in practice. This may however
be explained by the decreased transmission of the CK X-rays through the
VYNS window and the Polypropylene filter compared to A1K X-rays -a
factor of 2 in each case (Figures 2.7 and 5.3). It was also seen that
whilst the intensity of the A1K X-rays continued to be increasing
rapidly as the proton energy approached 700 keV, the intensity of the
CK X-rays appeared to be levelling off. As a result the measured ratio
of the Carbon-to-Aluminium intensity decreased with energy (Figure 5.13).
93
1
i
% 1=f
: icr C !
r "
ý ý f " "
w Qt
f t
"i ý" i"ý
0 it "iý,
C i" fr
m 1O "" i""i
N
ai
i
Ck S! kAum%%
"1 1 10 X- ray energy, keV
Figure 5.11 The mass attenuation coefficient of low energy X-rays in Carbon (" ), Silicon (A and Gold ( ) targets with the positions of the CK, SiK and AuM X-rays indicated.
94
1
N C
O C. )
T
N C d C
I-
X
1
CK
ýýK
Figure 5.12 The measured X-ray intensities of CK from a Carbon target ( ) and A1K from an Aluminium target (A) as a function of proton energy.
U 2UU 400 600 Proton Energy, keV
95
12
10
oý E cý
.NE C d r+ C
Q
0
C
Figure 5.13 The ratio of the measured Carbon-to-Aluminium K-shell X-ray intensity (as given in Figure 5.12) as a function of proton energy.
Proton Energy, keV
96
CHAPTER 6
THEORETICAL TREATMENT OF RESULTS
6.1 Compensation for target surface contamination
The results'of the surface contamination study (Section 5.2.1)
showed that most, if not all, of the observed target surface contamina-
tion was Carbon. Whilst this would appear to be of no relevance for
a CK X-ray beam (Figure 5.5) it most certainly does affect the intensity
of other photon energies. (Figure 5.6) because of their absorption in
the Carbon layer. In order to ensure that any intensity variations
occurring in the angular distribution study (Section 5.2.2) was a result
of changing the target and/or detector angle, and not due to the build-
up of Carbon on the target surface, corrections were applied to the
angular distribution data to take into account the depth of Carbon the
proton beam had to traverse on leaving the target.
Using the data taken with the detector at an angle of 90° to the
beam at the start and end of each target angle scan, it was possible to
deduce the effective depth of Carbon on the target surface. If the ini-
tial intensity of the target's characteristic X-rays was II and this falls
to an intensity 12 by the end of a scan then, using the expression for
the attenuation of a homogeneous X-ray beam in traversing a thickness
'x' of matter (Harnwell and Livingood, 1933):
12=1II. exp (- ux) 6.1 where u is a constant of proportionality known as the linear attenuation
coefficient.
The u-values used were derived from the mass attenuation co-
efficients (u/p) as given by Hubbell '(1977) (Figure 6.1), taking the
density, p, of Carbon as 2300 kg. m-3 (Science Data Book, 1978). The
linear attenuation coefficients used for the surface contamination
97"
ýCD N
E u1
w
C
v
d
81
c 0 co c
cv U) Cl) cti
Figure - 6.1 The mass attenuation coefficient of low- energy photons in Carbon.
Energy, keV
98
Characteristic Energy W X-ray (keV) (cm 1)
BK 0.183 1.38 x 104
CK 0.278 4.95 x 103
NK 0.392 5.75 x 104
A1K 1.487 1.56 x 103
SiK 1.740 989
AuM 2.120 575
TiK 4.511 57.5
Table 6.1 The linear attenuation coefficient, p,
of ultrasoft X-rays in Carbon (derived
from Hubbell, 1977).
99
correction are given in table 6.1. These values were then used in
Equation 6.1 to give the depth, x, of Carbon laid down on the target
surface between the measurements of I1 and I2. In doing this, it was
assumed that the incoming proton energy loss in the Carbon layer was
negligible. Calculations (Section 6.1.1) showed this assumption to
hold within 5%.
Knowledge of the amount of charge which had been collected on the
target between the measurements of 11 and 12 enabled the Carbon contami-
nation to be expressed in terms of 'thickness per charge' (nm/pC).
It was therefore possible to deduce the depth of Carbon on the target
surface at any stage of the angular scan. However, as this calculation
gave the thicknesslat 90° to the beam (in line with the detector position),
a geometrical correction factor had to be included when the detector
angle was varied before the depth of Carbon through which the X-ray
photon had to traverse on leaving the target could be calculated
(Figure 6.2).
Having calculated the amount of Carbon on the target surface at
any particular stage of the angular scan it was possible to modify
the intensities obtained for the characteristic X-ray yield to com-
pensate for any attenuation occurring in the Carbon layer. If IM was
the measured intensity, as given by MINUIT (Chapter 4), at target
angle, 0, and detector angle, a, then the real intensity, before
absorption in the Carbon layer, IX, was given by
IM (8, a) = Ix (6, a) . exp (-u. ye, a) 6.3
where m is the linear attenuation coefficient of Carbon for the X-ray
energy and Yea is the calculated Carbon thickness on the target surface
as given by Equation 6.2 (Figure 6.2). The actual X-ray intensity was
therefore taken as I
IX (e, a) -- M (B, a)
6.4 exp (-p. ye, a)
100
T----. --.
:e
P
Detector
Figure 6.2 Calculation of the depth of Carbon contaminant on the target surface.
ß= 900 -a, y= 900 -0
Using the Sine theorem :
x sin (180 - (ß+y)) sin y
X. cos 9 6.2 sin (a+A) yA,
a
101
6.1.1 Example of surface contamination calculation
An example of a set of data for the Aluminium target is shown in
Table 6.2, with the measured AlK X-ray intensities given in the second
column. In order to calculate the thickness, x, of Carbon laid down
on the target surface between the first (I1 - 164269 counts) and last
(12 a 159694 counts) measurements, Equation 6.1 was rearranged to give Zn (I2/Il)
. x-6.5 u
Substituting the values of I1 and I2 and using p=1.56 x 103 cm 1
(Table 6.1) gave
x=1.81 x 10-5 cm (181 nm).
Since all the measurements were normalised to the charge collected on
the target, each spectrum being collected for 25 pC, the total charge
collected between the measurements of 11 and 12 was 300 pC. This gave
a Carbon build-up depth of 0.6 nm. pC 1
or, alternatively, 15 nm per
25 pC of charge collected on the target.
Taking the geometrical correction factor given in Equation 6.2 into
consideration, the thickness, y, of Carbon through which the AlK X-rays
had to traverse on leaving the target was calculated for each detector
angle (Table 6.2, column 6). It was then possible to use Equation 6.4
to calculate the real intensity of the AlK X-rays having compensated for
the absorption in the surface Carbon layer (Table 6.2, column 7).
Finally, the intensities were normalised to the theoretical maximum
flux at 6= 30° and a= 60° (Section 6.2) - Table 6.2, column 8.
As can be seen from Table 6.2, the total Carbon depth at the end
of the scan was 195 nm at 90° to the proton beam. This corresponds to
a depth of 0.3 pm in the direction of the beam (a = 0°) which would
result in the proton beam losing - 20 keV in the Carbon layer (Figure 6.4),
with-a 5% reduction in the X-ray production cross-section (Figure 6.5).
102
0
t! º N . ti C ß (x 0
O O O*,
CO C%
O O
0 O
O O
O O
o OA
o O%
in O,
in 00
-7 O O
C to- 0 IIM
.- O O . - r- '- ^ ö .
O O .
O .
O -- C *' m
+ý+ In L -t L/1
00 -e
O C%
r_ M
ul 1-
Ul O
rý CV
-e 1"
%D .O
M 00
-Y' '-
00 1ý
r N
±ä 'c X O ýC -7
ýD
C% 1- LM
%D . - C
u1 -
0% M
-t ýt
%D -7
in M
%M N
in LM
ýt ON
O, %m
%D t
2 + C_ W "- "-
' "--
% r-
%D %O . -
ýO "-
%D "-
% "-
in r-
M . -
O %D
Or 4- O
0 ,Q
92 O %M N O 00 (D %D M LM V) N O 4'' in N. c N lD N u1 N Oa 1z 00 in 0
++ _
fa + - N M in % 00 O
"- M 00 in O-. C\
Q + . - . - N - 00 . -
Z3 F O
O N Oa
00 00
fl, 00
00 00
N C%
O O
M . -
in M
M r
C' vl
Q ON
O O
ÜC '" O O O O O r- . - N . to
U 0 +
0 a) s E5 ,n ä c, w`
ö ý- in "-
O M in - O .O in N. 0 a in O O
cv in M O ºn in
.o O 00 in v% n, W c'
r- r "- r r- ._ . -
LZ tu el
coaom -% Z: L V8 tu
tj : 3.
in N
0 LO
vl N.
0 O
in N
O vi
in r-
0 O
in cV
O L
in O in
-70 O "' . - cV N
n N
r- N
O M
CV (n
VO 0 H
"ý 3
Q% ,m -t M O
0 N -
0 tu N
r18 -t
cV I.
'O O
N M N N
0 - 0
- 00
N
C'4 to C%
.W %M in %0 'G % % %0 N -t m 0' in
I-
++ C 0% - ý
%M N. O O O O . CD
Co 0% p
103
6.2 Calculation of theoretical angular distribution
K-shell characteristic X-rays are emitted isotropically as a
result of the initial state having an angular momentum of 1/2 (Folkmann,
Cramon and Hertel, 1984). The only angular dependence therefore expected
is a geometrical effect due to the self-absorption of the X-rays in
the target.
The complete description of, the effect of self-absorption in the
target would require detailed information on the-energy and X-ray produc-
tion cross-section of the proton beam as a function of the distance
travelled within the target. However, for the purpose of comparison
with the experimental data a more simplified approach, outlined below,
was used (Figure 6.3).
Using the 'Stopping Power' graphs of Anderson and Ziegler (1977)
the energy of the proton beam, Ep, at 1 pm increments within the target
was calculated, with EP = 500 keV at the target surface (Figure 6.4).
This does assume a constant stopping power within each 1 pm interval
and will therefore cumulatively underestimate the energy loss in each
interval. However, the range of the proton as calculated in this manner
was within 3% of the range as given by Anderson and Ziegler (1977)
and therefore the underestimation in the energy loss was deemed negli-
gible. The average energy of the proton beam in each um, EZ, was taken
to be that of a proton at the centre of the increment, that is for
xi = x1 + (i - 1) Ax 6.6
with x1 = 0.5 pm, Ax =1 pm and i=1 to 6. Using the analytical cross-
section formula of Paul (1984), the K-shell X-ray production cross-section
at each position, ai(E. ), were calculated (Figure 6.5): 71
SC X
10' Q 6.7
Z2.2
where f and S, are functions of proton energy, E, and target atomic
number, Z.
104
0
Xi E-
ýýa `" .ý .ý
d i
P
Figure 6.3 Simplifying assumptions used for the calculation of the theoretical angular dependence of the emitted X-rays from a thick target.
d2 xi . sin 0
= sin (A + a)
x Xý X . ýcL
0= 30 °, 45 ° and 60 °; 400 4a< 1300
105
500 "�
400- 6.. Error bar for "'"ý '", ý each point
300 '° "' ''ý
. d0
o. rn
w 200 '° '"o ö
'ý '" 0
100 '". q
00 23456 Depth Into target, Nm
Figure 6.4 The variation of proton energy with depth into the target.
Gold target 0 Titanium target
A Carbon target (a similar curve is obtained for Boron)
E3 Aluminium target " Silicon target
106
1
1
E1 u
N
70 r
K
w
C 0
a) N
N N 01 L.
C 0
4.1 V
01 1- a
cv
X 1
1
Proton Energy, MeV
Figure 6.5 The K-shell X-ray production cross-section for proton bombardment of various low Z targets (using the method of Paul (1984))
0 Boron Carbon
A Aluminium Q Silicon
" Titanium
107
The proton flux was assumed to be constant over the whole
of the proton range, which is generally the case provided EP » Ik,
the electron ionisation energy (-1 keV). No account was taken of the
divergence of the proton beam, the assumption being that this will only
be of major importance towards the end of the proton range and that
even if divergence is occurring it may still be assumed that on average
the protons follow a central path.
The number of K-shell photons emitted from a thick target into a
solid angle 0 per N incident protons of energy E and range R0 is given by
(Lewis, Simmons and Merzbacher, 1953):
Ro - ud(x)
I (Ro) _2. Nnp fe. a {E (x) } dx 6.8 4 ir 0
where n represents the number of target atoms per gram, p represents the
density of the target, ji is the absorption coefficient of the target for
its own characteristic X-rays (Hubbell and Veigele, 1976; Hubbell, 1977)
and d is the distance which the X-ray travels in the target. In the
simplified calculation considered here, the photon flux in the direction
of the detector was taken to be proportional to:
6- ud. 0 0, a=
E Q. (E. ) .e6.9 i=1
where a (Z) was calculated using Equation 6.7 and dZ (Figure 6.3) was
calculated from
x" sin A d. Z 6.10
Z sin (A + a)
00, a
was calculated for each target/detector angle combination and
normalised to the maximum flux (found at 0= 30° and a= 60°).
Also calculated were the normalised flux when considering only the
first interval of the proton's interaction within the target, that is
for the first 1 pm only. In this case the photon flux was taken to be
108
represented by
-ud1 ýeý a Q1 (E1) .e6.11
and all values normalised to 1030,60
In the case of the Gold M-shell X-rays a similar treatment was
considered but with the production cross-section, a (Ederived from
the total M-shell ionisation cross-section, a M, (Johnson, Basbas and
McDaniel, 1979) combined with the M-shell average fluorescence yield,
wM, (Bambynek et at., 1972):
I vZ = am .w6.12
6.2.1 Example of the theoretical angular distribution calculation
For 500 keV protons penetrating an Aluminium target, the energy
of the protons along their range (- 5.5 pm) was calculated using the
stopping power data of Anderson and Ziegler i(1977), (Table 6.3).
These values were plotted (Figure 6.4) and used to find the energy
of the proton beam at the centre of each pm increment (Table 6.4,
column 2). The X-ray production cross-section at each energy was
then derived from Figure 6.5 (Table 6.4, column 3).
Using Equation 6.10, the distance travelled by the X-ray through
the target (d2) was calculated for a given target and detector angle
combination for each of the distances travelled by the proton
(xi, i=1 to 6) (Table 6.5). Taking the Aluminium self-absorption
coefficient as 1.08 x 103 cm- l (Hubbell and Veigele, 1976) the
product, OZ, of the production cross-section (a2) and the attenuation
in the target (e-sdi) was calculated (Table 6.6).
For each target/detector angle combination, 0 e, a
(Equation 6.9)
was calculated from 6
Sýeý a ZEI
of 6.13
109
Depth into Proton energy Stopping Power Proton energy target of Aluminium after 1 pm
(um) (keV) (keV/um) (keV)
0 500.0 69.3 430.7
1 430.7 74.1 356.6
2 356.6 81.3 275.3
3 275.3 90.3 185.0
4 185.0 105.4 79.6
5 79.6 125.3 -
Table 6.3 The energy loss experienced by a 500 keV proton
on entering an Aluminium target, assuming a
constant stopping power within each 1 um interval.
110
Depth into Proton X-ray production target Energy cross-section
xi E. ci (awn) (keV) tx10'24 cm2)
0.5 466 190
1.5 392 130
2.5 316 75
3.5 230 32
4.5 132 6
5.5 14 < 10-5
Table 6.4 The AlK production cross-section for the
proton as it penetrates the target.
111
Detector di (pn) Angle i123456
a° xi 0.5 1.5 2.5 3.5 4.5 5.5
40 0.266 0.798 1.330 1.862 2.394 2.926
50 0.254 0.762 1.269 1.777 2.285 . 2.792
60 0.250 0.750 1.250 1.750 2.250 2.750
70 0.254 0.762 1.269 1.777 2.285 2.792
80 0.266 0.798 1.330 1.862 2.394 2.926
90 0.289 0.866 1.443 2.021 2.598 3.175
100 0.326 0.979 1.632 2.284 2.937 3.590
110 0.389 1.167 1.945 2.723 3.500 4.278
120 0.500 1.500 2.500 3.500 4.500 5.500
130 0.731 2.193 3.655 5.117 6.579 8.040
140 1.440 4.319 7.198 10.078 12.957 15.837
Table 6.5 The distance travelled by the X-ray, d., within the
target for a target angle, 0= 30°.
112
Detector
Angle
a° i1
X. It. : 0.5
2 1.5
3 2.5
d1
4 3.5
5 4.5
6 5.5
46 30, a
(ERZ) 46 30. a
30,60
40 185 119 65 26 5 N 400 1.00
50 185 120 65 26 5 E 401 1.00
60 185 120 66 26 5 G 402 1.00
70 185 120 65 26 5 L 401 1.00
80 185 119 65 26 5 I 400 1.00
90 184 118 64 26 5 G 397 0.99
100 183 117 63 25 4 I 392 0.98
110 182 115 61 24 4 B 386 0.96
120 180 111 57 22 4 L 374 0.93
130 176 103 51 18 3 E 351 0.87
140 163 82 34 11 2 (< 1) 292 0.73
Table 6.6 The product, of the AlK X-ray production
cross-section, aand the attenuation of the X-ray
in the target (exp [-µd ]) for a target angle,
0= 300.
113
and the intensities normalised to the maximum flux occurring at 0- 30°
and a= 600. Finally 06, a
(_ 01) was considered (Table 6.6, column 2)
and normalised to 0 30,60
(Table 6.7).
114
Detector 30, a Angle 1
a° 30, aß 30,60
40 185 1.00
50 185 1.00
60 185 1.00
70 185 1.00
80 185 1.00
90 184 0.99
100 183 0.99
110 182 0.98
120 180 0.97
130 176 0.95
140 163 0.88
Table 6.7 The contribution of the AlK X-rays
produced in the first pm of the
target normalised to those produced
at a target angle, 0= 30° and
detector angle, a= 60°.
115
CHAPTER 7
APPLICATION OF MONTE-CARLO TRACK STRUCTURE CODES
7.1 Introduction
This chapter sets out to consider the microtopography of the
radiation tracks produced by the interactions of ultrasoft X-rays
of varying energy in soft tissue. Significant differences in patterns
of energy deposition may result in differences in biological effective-
ness which are open to experimental investigation.
Whenever photons interact with matter they create secondary elec-
trons by means of three competing interactions :
(a) the photoelectric effect, in which most of the incident photon's
energyAs expended in the ejection of an orbital electron;
(b) the Compton effect, in which part of the primary photon's energy
is transferred to a single atomic electron and a 'Compton scattered'
photon is emitted with energy and direction determined from relativis-
tic momentum-energy conservation;
and
(c) pair production, requiring a minimum of 1.02 MeV, in which an
electron-positron pair is produced. The relative importance of each
interaction type shifts with increasing energy such that for photon
energy, lhu < 30 keV the photoelectric effect is dominant (in low
atomic number material) whilst for hu > 10 MeV it is pair production
which is most important. Thus the energy deposition by X- or y- ray
fields on a microscopic scale is determined almost exclusively by the
energy loss of their secondary electrons. The importance of the energy
deposition of electrons is in fact common to all radiation fields,
including heavy ions and neutrons (Paretzke, 1980). A detailed theore-
tical understanding of the microtopography of events occurring within
the track of a charged particle is consequently important. The
116
availability of the necessary cross-section data (for example Opal,
Beaty and Peterson, 1972) and the development of sufficiently powerful
computers has contributed towards an increase in our knowledge of the
energy deposition by ionising radiation by permitting the calculation
of the local concentrations of activations on a nanometer scale using
Monte-Carlo track structure simulation codes (Berger, 1974; Heaps and
Green, 1974; Hamm et at., 1976; Paretzke, 1978).
Ionising radiations can induce in cells a variety of biological
changes. The cell nucleus appears to be the main region of radio-
sensitivity. However, a large proportion of the ionisations, excitations,
and their products, produced by the radiation appear to have no permanent
effect on the cell (Goodhead and Brenner, 1983a; Goodhead et aZ., 1985).
Permanent effects such as cell death (loss of proliferation capacity),
mutations and chromosome aberrations appear to be caused by some'rare,
critical damage induced by the radiation. Differing types ('qualities')
of ionising radiations have differing efficiencies in producing biological
effects thus underlying the need for information on the physical proper-
ties of radiation interaction which may be correlated with the biological
effect of practical radiations and assist in the understanding of the
mechanisms of radiation action.
7.2 Local Energy Deposition of Radiation Tracks
Previous experiments with ultrasoft X-rays have shown that complete
biological effects can be efficiently produced by small amounts of highly
localised energy depositions (Goodhead, Thacker and Cox, 1979;
Goodhead et at., 1980; Thacker, Goodhead and Wilkinson, 1983). For
example, the photo-electron produced as a result of the absorption of
a CK X-ray photon in soft tissue deposits < 280 eV in <7 nm. These
studies indicate that the damage produced by ultrasoft X-rays is similar
in nature to that produced by conventional low L. E. T. radiations such as
hard X-rays and y-rays (Goodhead, Cox and Thacker, 1981).
117
The small dimensions (down to < 10 nm) involved in the energy
deposition of low-energy electrons, including those produced by ultra-
soft X-rays are, unfortunately, below the region of most experimental
measurement techniques ( -1 - 10 pm). However, a possible way of
identifying the critical characteristics of radiation action is by the
use of Monte-Carlo track structure codes. These simulate the radiation
tracks in the form of complete atomic, interaction-by-interaction
histories, recording all spatial and energy transfer information
(Paretzke, 1980). This information can then be compared with the
observed relative biological effectiveness (R. B. E. ) of the different
radiations.
During the late 1950s analyses of the relative effectiveness
of heavy ions of different L. E. T. indicated that it might be possible
to describe their mechanism of action in terms of a threshold energy
deposition in small sites (- hundreds of eV in- nm) (Howard-Flanders, 1958).
The availability of Monte-Carlo track structure calculations (Paretzke
et al., 1974; Hamm et al., 1978; Terrisol, Patau and Eudaldo, 1978;
Wilson and Paretzke, 1980) supported by low-pressure cloud chamber
measurements (Budd and Marshall, 1980; Kwok, Budd and Marshall, \, 1981;
Brenner, 1982) has enabled the threshold energy concept to be reassessed.
Previously reported experiments (Cox, Thacker and Goodhead, 1977;
Goodhead et at., 1980; Thacker, Cox and Goodhead, 1980;: Virsik et at., 1980;
Goodhead, Thacker and Cox, 1981a) have shown that very low energy photons
have considerably greater effectiveness per unit dose than hard X-rays
or y-rays, the lowest energy X-rays having the greater biological
effect. Since the X-rays deposit energy throughout the irradiated cells
only in highly localised, small quantities, complete biological lesions
may be produced by these well defined energy concentrations. Goodhead
and Brenner (1983b) set out to investigate the threshold energy concept
in terms of a distance and an energy such that the probability of this
118
amount of energy (or greater) being deposited by the X-rays within a
volume correlated with the observed R. B. E. of the radiation. By com-
paring data obtained from experiments (Goodhead and Brenner, 1983b and
references therein) with those calculated using the Monte-Carlo track
structure codes (Brenner, 1982; Brenner and Zaider, 1982; Zaider, Brenner
and Wilson, 1983) it was concluded that, for low L. E. T. radiations at
least, there was correlation for threshold energies of about 100 eV in
a spherical volume of diameter -3 nm. This correlation did not hold
for high L. E. T. radiations.
Whilst spherical volumes are mathematically convenient, intra-
cellular structures at the nanometer level of organisation (such as
the D. N. A. double helix, nucleosome, chromatin fibre) are better
modelled by cylindrical volumes. Since 1983 a method for scoring
energy depositions in randomly orientated cylinders has been developed
(Charlton et al., 1985a, 1985b; Goodhead et al., 1985) and using a
Monte-Carlo track structure code, based on that of Wilson and Paretzke
(1980), an extensive calculation and tabulation of absolute frequencies
of energy deposition by mono-energetic protons and a-particles has
already been produced (Charlton et al., 1985a). The process is being
extended to include mono-energetic electrons and photons (H. Nikjoo,
pers. comm. ).
7.3 Calculations using a Monte-Carlo structure code
The energy deposition in small cylindrical targets by simulated
electron tracks from the absorption of Carbon, Aluminium and Titanium
K-shell X-rays has already been calculated (Nikjoo, Goodhead and
Charlton, 1987). The Monte-Carlo technique employed has the capability
of dealing with extensive input-tables on the relative photo-absorption
and atomic de-excitation probabilities for a given irradiated medium,
such as soft tissue. However, the construction of complete input
119
tables to include all modes of absorption of an ultrasoft characteristic
X-ray by atoms of all elements in soft tissue, weighted to take account
of the photoionisation cross-sections and the percentage by weight of
each element in soft tissue, is very time consuming. It would therefore
seem practical to try to reduce the time taken by considering only
the most significant contribution(s). In this way a wider range of
photon energies may be investigated and any discontinuities in local
energy deposition as'a function of photon energy observed. ' These may
have biological consequences and therefore be open to experimental
investigation with appropriate proton-induced ultrasoft X-ray beams.
Goodhead and Thacker (1977) have shown that Carbon, Nitrogen and
Oxygen atoms are responsible for - 99% of the absorbed dose when
mammalian soft tissue is'irradiated by AlK X-rays. The most signifi-
cant contribution (- 90%) is the result of absorption in the Oxygen
atom's K-shell - Oxygen accounting for - 75% by mass of soft tissue
of the same atomic composition as spleen of 'reference man' (I. C. R. P.,
1975). It might therefore be expected that an input table which
showed the production of electrons resulting from the absorption of
characteristic X-rays in the Oxygen atoms only would approximately
simulate the effects taking place in soft tissue having its full atomic
composition.
7.3.1 Track Structure and Scoring Programme
Using a Norsk Data mini-computer at the M. R. C. Radiobiology Unit
and the electron track simulation code 'MOCA7' contained within the
charged-particle track structure code 'MOCA14' (Wilson and Paretzke,
1981) along with the scoring programme 'ESCORE' (D. E. Charlton and
H. Nikjoo, pers. comm. ) it was possible to carry out scoring for
energy deposition in small cylindrical volumes for the K-shell
characteristic X-rays of selected elements within the atomic number
range 45Zä 20.
120
A number of photons were considered for each X-ray energy, taking
only absorption by the Oxygen atom into account. This resulted in
either one or two electrons, depending on whether the photon energy was
sufficiently large to cause the release of an Auger electron as well as
the initial photo-electron (Coghlan and Clausing, 1973) (Figure 1.2).
A minimum amount of energy required to free an electron ('residual
potential energy') of 32 eV was assumed for Oxygen in soft tissue
(H. Nikjoo, pers. comm. ). The resulting input parameters for all the
elements considered are given in Table 7.1.
The code MOCA7 was then used to generate the tracks of electrons
in water vapour adjusted to a density of 1 g. cm 3 (103 kg m73), the
electron histories being followed until their energies had fallen to
10 eV. Although liquid water is of greater biological relevance than
water vapour (the cell consisting of - 80% water), there are fewer
experimentally measured cross-sections on which to base a liquid
water transport code. Although it is known that there are differences
between macroscopic cross-sections in the liquid and vapour phases
(Goodhead, 1987d) a comparison of spatial patterns of energy deposi-
tion, -for electrons, between liquid water codes (Hamm et al., 1976;
Terrisol, Patau and Eudaldo, 1978) and those obtained from a water
vapour code (Turner et aZ., 1982,1983a, 1983b) indicate significant
differences only in energy deposition over small (< 1 nm) distances
(Paretzke et al., 1986).
7.3.2. Results
Scoring of the energy deposition of the electrons was carried out
within a gross volume defined by a virtual sphere whose radius was at
least 1.1 times that of the length of the longest electron track.
Chords cutting the virtual sphere were generated using 'p-randomness'
(Kellerer, 1971) and these served as the axes of the cylindrical
121
Element Atomic No.
z
Photon Energy
(eV)
Residual potential energy
(e V)
Photo- electron energy
(eV)
Auger electron energy
(eV)
Be 4 109 32 77 -
B 5 183 32 151 -
C 6 278 32 246 -
N 7 392 32 360 -
0 8 525 32 493 -
F 9 677 32 140 505
Na 11 1041 32 504 505
Mg 12 1254 32 717 505
Al 13 1487 32 950 505
Si 14 1740 32 1203 505
C1 17 2622 32 2085 505
Ca 20 3692 32 3155 505
Table 7.1 Input parameters for the electron generating code,
MOCA7, considering the interaction of characteristic
K-shell X-rays with Oxygen.
IlIAoujl a iesiduai polenl; al e ieºtgq of 32eV
was used to all Ae aLove eases a al; 9yýý JoweI
value would be oioýc aPPýcP{ýaýe ýaý
e sinj j io n; seal cases (Be - O)
122
Figure 7.1 Diagram illustrating the virtual sphere enclosing the simulated electron track(s) and crossed by the scoring cylinders arranged at random.
123
volumes in which the energy deposition was scored (Figure 7.1).
Each cylinder was then divided into small sections, beginning at a
random point along its length, and the total energy deposited in each
section recorded. The lengths of the sections were chosen as multiples
of the radius of the cylinder. The frequency of deposition of given
amounts of energy in each cylindrical section was recorded and normalised
to the frequency which would have occurred had the macroscopic region
containing the cylinder been subjected to an electron flux delivering
one Gray (Gy). As a check on the sampling accuracy, the ratio of the
volume of the virtual sphere to the volume sampled was compared with the
ratio of the energy deposited in the virtual sphere to the energy
deposited in the target cylinders. These two ratios were generally
within 5% of each other. The diameter and length of the target cylinders
could be varied and data were collected for dimensions similar to those
of biological structures:
Biological Structure Cylinder diameter (nm)
Element of DNA 2 Nucleosome 10
Element of chromatin fibre 25
In each case, energy deposition was calculated for four cylinder
lengths, 1, given by
1=nxd7.1
where d represents the cylinder diameter and n=0.5,1,2 and 4.
Scoring was initially carried out for Carbon and Aluminium
(Z =6 and 13 respectively) to enable a comparison to be drawn between
the data obtained from considering absorption by the Oxygen atoms only
and those-already obtained by H. Nikjoo (pers. comm. ) from considering
the full elemental composition of soft tissue (as given for spleen of
'reference man' (I. C. R. P., 1975)). The results obtained are shown in
Figures 7.2 and 7.3. The error bars shown on these and following
figures were calculated from the assumption that the statistics of the
124
Figure 7.2 The frequency of energy depositions greater than a given amount, E in cylinders of various sizes, per Gray of dose to the surrounding medium. Shown are the frequencies obtained when cosidering the interaction of CK X-rays with the full elemental composition of soft tissue (o) (H. Nikjoo (pers. corrnn. ))
and, where they differ by more than the size of the plotted points, considering the interaction of CK X-rays
with Oxygen atoms only (A). The error bars were cal- culated using Equations 7.2 and 7.3 in the text.
Figure 7.3 The frequency of energy depositions greater than a given amount, E in cylinders of variousisizes, per Gray of dose to the surrounding medium. Shown are the frequencies obtained when considering the interaction of A1K X-rays with the full elemental composition of soft tissue (Q) (H. Nikjoo (pers. corrnn. ))
and, where they differ by more than the size of the plotted points, considering the interaction of A1K X-rays with Oxygen atoms only (o ). The error bars
were calculated using Equations 7.2 and 7.3 in the text.
data were represented by the number of hits within the target cylinders.
If 'H' represents the total number of hits within the target cylinders
and 'f>E' denotes the frequency of energy deposition greater than E per Gy,
then the percentage error on each frequency was calculated using:
nE = f>E
xH7.2 f>0
% error =� nE x 100 = (rtE) 2x 100 7.3
nE
If the entire track of a CK X-ray absorption in soft tissue is
approximated as a highly localised ('point') event in a large scoring
cylinder, then as the cylinder length increases the frequency of energy
deposition greater than a given amount, E, would be expected to increase
proportionally. From Figure 7.2, (ii) and (iii), it is seen that the
frequency of energy deposition does double with cylinder length for the
larger diameter cylinders, but for the smallest cylinder diameter (Figure
7.2, (i)) as the cylinder length is doubled the frequency increases by
more than a factor 2 at high threshold energies (E > 50 eV) and less
than 2 at lower energies. This suggests that as the target cylinder
length increases it is more likely to contain large energy depositions
(large hits) and less likely to have just a small amount of energy
deposited in it. Figure 7.3 shows that AlK X-rays follow the same
tendency but, because of the larger dimensions of the tracks, a larger
sized target (> 25 nm diameter) is required before the approximation
holds that doubling the target size doubles the chance of hitting it.
The results of scoring the CK and AlK X-rays showed sufficient
agreement between the data considering absorption in Oxygen atoms only
and the data taking the complete elemental composition of soft tissue
into account to warrant the continuation of scoring using absorption by
Oxygen only. Using the data of Table 7.1 as input, scoring was there-
fore carried out for the remaining elemental characteristic energies using
the code ESCORE. A limit of Z <_ 20 was set because efficient scoring
133
1
1I
C, U; Al
O
O a
rn
c d
. 1.1 O
0 c
v d I- LL
Figure 7.4 The frequency of energy depositions greater than a given amount, E in a2 nm diameter, 2 nm long
cylinder by simulated electron tracks from various low Z characteristic X-rays.
O BeK X-rays
A CK X-rays
A1K X-rays
" CaK X-rays
Threshold Energy 'E'. key
134
I- C
W
A c c
1
Figure 7.5 The frequency of energy depositions greater than a given amount, E in a 10 nm diameter, 5 nm long cylinder by simulated electron tracks from various low Z characteristic X-rays.
o BeK X-rays
A CK X-rays
A1K X-rays
" CaK X-rays
0 .' .2 ,3 .4 .5 Threshold Energy 'E ý. keV
135
a t9
w A C 0
U, 0 a m v
rn m C m w 0
0 c m
c 0 I- U.
Figure 7.6 The frequency of energy depositions greater than a given amount, E in a 25 nm diameter, 25 nm long cylinder by simulated electron tracks from various low Z characteristic X-rays.
O BeK X-rays
A CK X-rays
A 0K X-rays
A1K X-rays
" CaK X-rays
0 "1 "2 "3 "4 "5 -6 Threshold Energy 'E '. keV
136
can only be carried out for low-energy electrons, where the entire
electron track is confined to a relatively small volume. For high-
energy electrons, multi-stage sampling procedures have proved necessary
to enhance the scoring efficiency (H. Nikjoo, pers. comm. ). The com-
plete energy deposition data are given in Appendix 2, with selected
samples, including the lowest and highest (Z =4 and 20) photon energies,
plotted in Figures 7.4,7.5 and 7.6. The target cylinder sizes were
chosen to represent:
(i) element of DNA
(ii) nucleosome
(iii) element of chromatin fibre
2nm diameter x 2nm length
: 10nm diameter x 5nm length
25nm diameter x 25nm length
The cylinder lengths chosen for the elements of DNA and chromatin
fibre are arbitrary.
Having generated the basic data it was possible to draw an inter-
elemental comparison by selecting a particular size of target cylinder
and plotting the frequency of events depositing more than a given energy,
E, in the target as a function of characteristic X-ray energy. Such
data are presented in Figures 7.7,7.8 and 7.9. Whilst comparison with
existing experimental data (Goodhead and Brenner, 1983b; D. T. Goodhead,
pers. comm. ) would suggest that threshold energies of the order of 100 eV
within targets of - 2nm diameter is the important region in terms of low
L. E. T. radiations such as X-rays, larger sized targets are of particular
interest when considering high L. E. T. radiations such as a-particles
(Goodhead et al,, 1985).
Figure 7.7 shows that low energy X-ray photons (< 1 keV) are the
most efficient in depositing small, localised amounts of energy within
a target. Within this region, the data show varying degrees of struc-
ture, the more pronounced being at the higher energy of deposition
(E - 200eV). The decrease observed at the lowest X-ray energies
(BeK, BK and CK) is probably due to the limit set by the X-ray energy
137
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140
itself; as E approaches the X-ray energy the frequency of energy
deposition greater than E will obviously fall. Assuming the uncertain-
ties are represented by Equations 7.2 and 7.3, the fluctuations in the
region of the NK, OK and FK X-ray energies are more than can be accounted
for by scoring statistics alone. Referring to Table 7.1 it is seen that
for Fluorine, an Auger electron is emitted as well as the photo-electron.
Looking in particular at a threshold energy, E- 200eV, the photo-
electron (at 140eV), if acting independently, should be incapable
of depositing energy > 200eV within the target and hence the probability
of energy deposition should be dominated by the Auger electron (505eV).
The Auger electron is similar in energy to the photo-electron from the
interaction of OK X-rays with the Oxygen atoms in soft tissue, yet the
probability of energy deposition > 200eV per Gy for the FK X-rays is
double that for the OK X-rays. This would suggest that there might be
a substantial combined effect resulting from the overlapping of the
electrons as opposed to each electron acting independently.
Figures 7.8 and 7.9 again show that the low energy photons are the
most efficient at depositing small amounts of energy within a target.
With a target size of 25nm x 25nm (Figure 7.9) the electrons produced
by the low energy photons are usually entirely enclosed within the
targets (for example, the CK X-ray (278eV) gives rise to an electron
with a range of < 7nm (I. C. R. U., 1970)). As the photon energy increases,
whilst the electrons produced are still enclosed by the targets there
will be fewer of them per unit dose, and hence the efficiency of deposit-
ing a threshold energy falls (from BK to Na, X-rays). Further increase
in the photon energy (> 1 keV) leads to electrons starting to 'escape'
from, or enter into, a target and so targets are more likely to be hit
(from Na K to higher energy X-rays). As the threshold energy increases
(from 150eV to 600eV) the benefit of additional hits is lost because
these higher energy (lower L. E. T. ) electrons have a low probability of
depositing large energy in a target even if they do pass through it.
141
CHAPTER 8
DISCUSSION
8.1 Comparison of the observed angular dependence of proton-
induced ultrasoft X-rays with theoretical calculation
Both the observed and calculated angular dependence of proton-
induced ultrasoft X-rays are shown in Figure 5.10 ((i) - (vi)).
For K-shell X-rays the agreement between the experimental data and
the theoretical estimate, based upon the consideration of X-ray
production over the total proton range in the target, is best when the
target is inclined at an angle of 30° to the proton beam. As the target-
to-beam angle decreases the experimental data becomes more in agreement
with that calculated from consideration of the X-rays produced in the
first 1pm of the proton range only.
A certain amount of disagreement between experimental data and
theoretical estimates might be expected because of the limited (fpm)
resolution steps of the calculations and the simplifying assumption
that the proton energy remained constant over each fpm increment
(Section 6.2). In fact, the proton energy (and therefore the X-ray
production cross-section) would be greatest at the target edge side
of each increment where self-absorption effects would be less. The
effects would be expected to be more pronounced at larger target angles,
0, due to the sin 0 dependence (Figure 8.1). Further reasons for dis-
agreement might also be expected as the result of an irregular target
surface profile. Studies by Gaines (1981) have shown that anisotropy
additional to that produced due to self-absorption in a smooth target
can be expected for surface roughness with average peak-to-valley
distances greater than -0.1Nm. Methods of quantifying the effect of
target roughness were considered, the most promising being the intro-
duction of regular rulings onto a smooth target having an average
142
e=so'
Y- x= sin B 1
Figure 8.1 The sin 0 dependence of the difference in the distance travelled within the target at either end of each 1 pm increment.
143
peak-to-valley distance of, < 0.05pm. However, the cost of producing
such a high specification target meant that such a study extended
beyond the scope of this work.
8.2' A practical beam line for proton-induced ultrasoft X-rays
From the results of the angular distribution study (Section 5.2.2)
it is seen that for the maximum intensity of characteristic X-rays a
small target-to-proton beam angle is desirable. Whilst practical limita-
tions in this work, resulting from the need for electrical connections,
have meant that the narrowest target angle studied was 30°, geometrical
considerations (Equation 6.10) show that narrower angles would maximise
the X-ray yield still further. For any particular target angle, the
optimum detector angle, that is the irradiation position, would appear
to be perpendicular to the target surface with the X-ray yield decreasing
as the irradiation position moves further away from the perpendicular.
With particular reference to the target angles and detector angle varia-
tions used in this work, the maximum X-ray yield occurred for a target
angle of 30° and a detection angle of 60° to the beam. These effects
become less important as the X-ray energy increases -a direct conse-
quence of the reduction in the target self-absorption of the X-rays.
Whilst increased proton energy does, in general, lead to an
increased X-ray production cross-section (although for the lowest Z
elements such as Boron and Carbon, the cross-section does reach a
plateau at proton energies of a few 100 keV (Figure 6.5) before falling
as the energy increases further towards 1 MeV and greater), the
advantage thus gained must be weighed against the necessity of elimi-
nating all scattered protons from the photon beam. Since this would
appear to require some form of filtration (Section 2.4.1), the higher
the proton energies the greater will be the filter thickness required
to stop the scattered protons. This will result in a corresponding
144
decrease in the transmission of the photon beam thereby offsetting the
increased production at high proton energies.
Previous work (Sterk, 1965; Khan, Potter and Worley, 1965; Gaines,
1981) has shown that Carbon contamination of the target surface is a
common problem when studying proton-induced ultrasoft X-rays. The
indications are, however, (Section 5.2.1) that this may at least be
reduced by making use of high (> NA) proton beam currents. Beam currents
of the order of 500 pA have been used at the M. R. C. Radiobiology Unit
and whilst Carbon deposition was still observed on the target surface,
the rate of build-up of Carbon and the subsequent reduction in charac-
teristic X-ray yield (from an Aluminium target) is far less pronounced
(D. T. Goodhead, pers. comm. ) than with beam currents of - 35 nA as used
in this work. The beneficial effects of high target currents may be
due to target heating.
When considering the irradiation of biological systems, and in
particular, mammalian cells, additional factors have to be taken into
account. Although all the measurements in this study were made within
the evacuated scattering chamber (Section 2.2.3) the detection/
irradiation position for mammalian cell irradiations would almost
certainly need to be at atmospheric pressure in order for the cells
to be able to survive. It is necessary to irradiate an attached mono-
layer of cells such that their position is well-defined and there is
minimum attenuation across the cell layer. The subsequent removal,
counting and biological assay of the cells necessitates the irradia-
tion of a large number ( -. 104 - 105) of cells and hence an irradiation
dish base of the order of 3cm in diameter is required. A well-defined
entrance surface is required for dosimetry purposes and therefore
irradiation cannot be from the air side (as opposed to the dish base
side) of the cells since, even if the growing medium was poured away
there would remain an unmeasurable, variable layer of liquid, and if
145
the dishes were dried the cells would die. As a result of these
considerations the preferred system in use is to make an irradiation
dish with a thin plastic base on which cells are grown, and irradiate
through the dish base (First International Ultrasoft X-Ray Workshop,
1987). A typical experiment (for example, to obtain a dose-response
curve) would require the irradiation of many such dishes.
Whilst cells may be grown on a variety of materials, the best
combination of small, well-defined attenuation across the irradiation
dish base and cell growth compatibility appears to be provided by
1.5Nm Polyethylene terephthalate, C10H8 0 4,
('Mylar' (Du Pont))
(D. T. Goodhead, pers. comm. ). In order to achieve uniformity of dose
to a large area monolayer of cells, very little distortion of the dish
base can be tolerated and so to avoid a pressure differential across
the dish base, atmospheric pressure is required on both sides of the
irradiation dish. This leads to the requirement of a 'vacuum window'
to bring the photon beam out of the vacuum chamber, in which the target
is positioned, into atmospheric pressure. There will, therefore, be a
'flight-path' between the vacuum window and the dish base.
Assuming an irradiation dish base size of - 3cm diameter, a
required uniformity of 14
beam across the base means that the vacuum
window has to be of comparable diameter. However, the vacuum window
also needs to be able to tolerate the pressure differential of
10"3 - 104 Pa on the vacuum side and atmospheric pressure (105 Pa)
on the other, and an unsupported window thick enough to tolerate such
a, pressure differential over a circular area - 3cm in diameter would
greatly reduce the X-ray flux. A thin window (for example, 2.5pm
'Hostaphan', '(Hoechst)) on a supporting grid would therefore appear to
be more 'appropriate. There is then the additional problem resulting
from the 'shadowing' of the transmitted beam by the grid wires.
146
The irradiation dish must not therefore be too near the vacuum window
in order that the natural divergence of the photon beam from the finite-
sized source will cancel out any shadowing effects.
some filtration of the scattered protons, additional filtration will be
required in order to ensure that no protons enter the irradiation dish.
The vacuum window-to-dish base separation may be used as a flight tube
with low atomic number gas (Hydrogen, H2, or Helium, He) flowing at
atmospheric pressure. Whilst Helium would be preferable from the safety
point of view, the increased attenuation in Helium at energies <1 keV
would make Hydrogen a better choice at the lowest energies. Both H2 and
He are efficient at stopping protons (500 keV protons having a range of
< 10cm in both gases) and have lower attenuation coefficients, p, for
ultrasoft X-rays than air. For example (Hubbell and Veigele, 1976):
for CK X-rays
Whilst the vacuum window and the irradiation dish base will offer
'AIR 6.2 cm-1
u-H - 3x10-2cm1 2
PHe 0.6 cm- 1
and for A1K X-rays
For the X-ray beam to achieve a uniformity within 5- 10% over the
' 'AIR 1.3 cm 1
PH - 1.6x10cm1 2
pHe 3x 10-3 cm 1
base of the irradiation dish, the photons need to be produced over a
large target area. The nearer the vacuum window is to the target
position, the larger the required production area since there will be
less distance over which the photon beam may diverge. In terms of
maximising the dose rate to the cells however, the nearer the vacuum
window and the dish base are to the target, the better. One possible
alternative to using a large diameter proton beam bombarding the
target would be to scan the proton beam across the target surface such
that the overall production surface area is larger.
147
Finally, consideration must be given to the Carbon contamination
X-rays, the elimination of which will require additional filtration to
that offered by the window, dish base and flight tube gas. Whilst it
was possible in this study to deduce the BK X-ray yield by subtracting
the CK X-ray yield (taken from the Aluminium target data) from the
combined peak, for biological irradiations deduction of effectiveness
by subtraction of observed effectiveness of mixed beams would introduce
very large errors and would usually not be practical. The necessity of
growing cells on some material, usually polymers, and the need for a
vacuum window (both of which will in general have transmission charac-
teristics dominated by the CK edge) means that it would also be very
difficult to filter out the CK X-rays from a combined beam of Carbon
and some other low Z elemental X-ray without removing the X-ray energy
actually required. X-rays from targets of atomic number lower than
Carbon (Z = 6) have the added disadvantage of having higher attenuation
coefficients in the flight tube gases than Carbon. Hence, even if it
were possible to filter out the CK X-rays produced along with, for
example, the BeK X-rays from a Beryllium target using a Be filter
(X-ray Data Booklet, 1986) it is unlikely that a sufficiently intense
beam of BeK X-rays could be obtained at a practical irradiation position.
For elements with Z near, but greater than 6, a similar problem
exists. - Whilst it might be possible to use a Nitride or Oxide filter
to transmit the NK or OK X-rays respectively at the expense of the CK
X-rays, these elemental X-rays would have had to have been produced
from compound targets such as Si3N4 or A1203, SiO2 and MgO, 2and
hence the'photon beam would also consist of the higher energy charac-
teristic X-rays which could not be filtered out efficiently whilst
still leaving the lower energy X-rays. However, once the characteris-
tic photon energies are >1 keV it should be possible to use a filter,
ideally of the same Z as the target, such that the CK X-rays are removed
148
without over-reducing the yield of the required X-rays. Additional
filters would also reduce the gas tube length required to ensure the
removal of all scattered protons from the photon beam.
Because of the difficulty in achieving a total removal of the
contaminant CK X-rays from other characteristic low energy (< 1 keV)
X-rays, it would appear that, other than for Carbon targets, there is a
very limited biological use for proton-induced low target Z charac-
teristic X-rays. It may however, in a well characterised system where
the Carbon build-up is kept to a minimum and in which a detailed study
is made on the rate-of build-up under specific operating conditions,
be possible to look at the effect of a combined energy photon beam on
biological systems and then, by comparison with the effectiveness of
CK X-rays alone, "deduce the additional effects due to a second X-ray
energy.
A schematic diagram summarising some of these practical considera-
tions is shown in Figure 8.2. Specific distances (such as target-to-
window, window-to-dish base) will vary according to particular systems.
Proton beam energy, available beam diameter, supporting grid wire size
and separation, and practical limitations on target and irradiation
angles all have to be considered.
The beam line shown in Figure 8.2 is by no means a unique solution
to the practical problems of biological irradiation with proton-induced
ultrasoft X-rays. Different systems can be, and are being, used (First
International Ultrasoft X-Ray Workshop, 1987). Attenuation problems
are greatly reduced by actually growing the cells on the vacuum window,
thus eliminating the need for a flight tube. However, in this case it
would be necessary to incorporate filters into the vacuum system to
ensure that scattered protons do not reach the cells and, other than
for Carbon targets, to absorb the CK X-rays. Also, assuming that an
149
jEPi H2 01
3
.1
.
. '_Kra
ý �
1
z
r
Figure 8.2 A schematic diagram summarising some of the properties of a practical beam line for biological irradiation by proton-induced ultrasoft X-rays.
1. Target 2. Window (2.5 pm Hostaphan 3. Flight Tube ( =; 10 cm in length), with H2
or He gas flowing to prevent scattered protons from reaching the irradiation position
4. Variable filter - depending on target - to absorb CK X-rays
5. Irradiation dish (cells grown on 1.5 pm 'Mylar)
\i
150
irradiating beam area of - 3cm diameter is required, the vacuum window
would still need to be supported by a grid so that the cells would have
to be grown carefully in between the grid wires if they were to be
uniformly irradiated. Growing the cells on the vacuum window would
also mean that the area immediately inside the window would have to be
let up to atmospheric pressure prior to the irradiation of each sample
for the window to be changed.
The pressure'differential across the vacuum window could be reduced
by irradiating the cells under reduced pressure. Instead of bringing
the photon beam out into atmospheric pressure the cells could be enclosed
in a 'wet irradiation chamber' where saturated water vapour, at a pressure
of. - 10 4
Pa (0.1 atmospheric pressure), was admitted into an evacuated
chamber. Another alternative would be to bring the photon beam out
through a much smaller vacuum window, such as a narrow slit, and then
scan the irradiation dish across the slit. The reduced area of the
vacuum window might also eliminate the need for a support grid.
8.3 Monte-Carlo electron track structure data
Previous comparisons (Goodhead and Brenner, 1983b; D. T. Goodhead,
pers. comm. ) between experimental data and the calculated frequencies
of energy deposition using Monte-Carlo simulated tracks of randomly
emitted photo- and Auger-electrons generated by ultrasoft X-rays seem
to suggest that energy deposition of > 100 eV in small volumes
( -2nm diameter) may be a critical property when considering the
biological effectiveness of low ionisation density radiation such as
X-rays. The effectiveness of various K-shell X-rays at depositing
threshold energies of - 100 eV within small cylindrical (2nm diameter
x'2nm'length) targets is shown in Figure 7.7, where a certain degree
of structure is observed at the low (< 1 keV) photon energies. This
suggests that biological irradiations with these characteristic X-rays
151
would be an useful indication of the validity of the threshold energy
concept.
However, biological irradiations with proton-induced ultrasoft
X-rays in the region of interest (CK to FK X-rays) are subject to a
number of experimental problems. Irradiations with proton-induced
CK X-rays (278 eV) have been undertaken at, for example, the M. R. C.
Radiobiology Unit. The main problem at this energy is one of attenua-
tion within the cells, the absorbed dose being reduced by 50% over 1.2Nm
depth of the cell (Goodhead, Thacker and Cox, 1979). This compares with
an average 'flattened' cell thickness of - zum (Goodhead and Thacker,
1977). Using the data of Henke et al. (1982) for the mass attenuation
coefficients (p/p) for the various X-ray energies in Oxygen (Table 8.1)
to represent the attenuation in soft tissue, the attenuation coeffi-
cient for FK X-rays is found to be twice that for CK X-rays. FK X-rays
would therefore be a very unsuitable choice for practical irradiations.
From Table 8.1, it is seen that in terms of attenuation, NK and
0K X-rays would be a better choice of low energy photons, but there are
further practical difficulties concerning their production. If proton
bombardment is to be used as a means of producing the characteristic,
ultrasoft X-rays then, as has been already discussed in Section 8.2,
there are problems with scattered proton filtration and the elimination
of contaminant CK X-rays as well as the higher energy characteristic
X-rays, such as SiK, A1K or MgK X-rays, which will inevitably be
produced from the compound target.
It would therefore appear necessary to use an alternative method
to proton bombardment of solid targets for the production of low
energy photons (other than CK X-rays) if these particular biological
irradiations are to be undertaken. A strong contender would be the
use of synchrotron radiation sources which are capable of producing
152
X-ray Photon u line energy p
(e V) (cm2. g-1)
BK 183 1.65 x 104
CK 278 6.04 x 103
NK 392 2.53 x 103
0K 525 1.20 x 103
FK 677 1.24 x 104
Table 8.1 The mass attenuation coefficients (u/p)
of low energy X-rays in Oxygen (from
Henke et aZ., 1982).
153
high intensities of monochromatic ultrasoft X-rays. These are not
confined to producing characteristic energies and would eliminate the
need for filtration of scattered protons and contaminating X-rays.
There are, however, other practical difficulties such as a small
beam size and the requirement for vacuum windows capable of with-
standing ultra high vacuum on one side and atmospheric pressure on
the other, but these problems are not insurmountable. It might, there-
fore, be possible, 'using'synchrotron produced ultrasoft X-ray energies,
to carry out biological irradiations at low photon energies such as
NK (392 eV) and'OK (525 eV) X-rays and compare their biological effec-
tiveness with the frequency of threshold energy depositions within
small volumes as calculated by Monte-Carlo techniques. Such informa-
tion would aid the further elucidation of the critical properties of
ionising radiation action.
154
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165
APPENDIX 1
SMBRO TINE FCN(NPAR, G, F, X, IFIAG) C C GAUSSIAN FITTING: T1 GAUSSIANS ON A CONSTANT BAC[E(JND C
IF (IFLAG. GT. 1) GO TO 25 READ(5110) (TITLE(I), I=1,40) BEAD(5,10) (DESCP(I), I=1,40) READ (5,15) NPI'S K=(NPTS/5)+1 DO 30 J=1, K NUJ*5-4 N=J*5 IEAD(5,20) RUB, ZERO, (SPEC(I), I=M, N)
10 FORMAT (40A1) 15 FORMAT (14) 20 FORMAT(/, A1, I4,1X, I6,1X, I6,1X, I6,1X, I6,1X, I6) 30 CONTINUE 25 CONTINUE
DO 35 I=26, NPTS R=DFLD1T(SPEC (I) ) ERR(I)=DSQRT(DABS(R)) IF (DABS(ERR(I)). LT. 1.0D-03) ERR(I)=1. OD+00
35 CONTINUE C C COMFTTE ! IHE RETICAL FUNCTION C
166
C C FIRST PE1K C
DO 40 I=26, NPTS 1N=I-1 IF(AVXI. EQ. O. OD+00) CO To 50 FAC1=AVX1-DFLOAT (M) IF (PS HM. LT. 1. OD-03) FWHM 1. OD+00 F1=FAC1/F HMJ. ARG1=-2.7726D+00*F1*F1 IF(ARG1. LT. -10) GO TO 50 S1=0.9394/FWHM1 THEOl(I) AR1*Sl*EXP (ARGl) GOT040
50 THEM (I) =0. OD+-00 40 CONTINUE
C C SECOND PEAK C
DO 42 I=26, NPIS N=I-1 IF(AVX2. EQ. O. OD+00) GO 'P0 52 FAC2 AVX2-DFLOAT(M) IF(FWHM2. LT. 1. OD-03) FVDV=1. OD+00 F2=FAC2/PS 7HM2 ARG2=-2.7726D+00*F2*F2 IF (AI 32 . LT. -10) GO TO 52 S2=0.9394/FWHM2 THE02(I) AR2*S2*EXP(AI32) GO TO 42
52 THEO2(I)=O. OD+00 42 CONTINUE
c C THIRD PEAK c
DO 44 I=26, NPTS ICI-1 IF(AVX3. EQ. O. OD+00) GO TO 54 FAC3 AVX3-DFLO T(M) IF(FWHM3. LT. 1. OD-03) FWHM3=1.0D+00 F3=FAC3/FWHM3 ARG3=-2.7726D+00*F3*F3 IF (ARG3 . LT. -10) GO TO 54 S3=0.9394/MUM 'HE03(I) AR3*S3*EXP(ARG3) GO TO 44
54 THEO3(I)=O. OD+00 44 CONTINUE
C C CALQJLATE TOTAL =RETICAL VAIÜES C
DO 60 I=26, NPrS SUM (I) =TH]. (I) +'I%ä702 (I) +'IHID03 (I) +BCi(
The absolute frequency of energy depositions greater than a given
amount in each elemental cylinder per Gray of absorbed dose to the
medium
The tables are headed by the photon energy for the particular
scoring run, and the number of interactions considered. The diameter
of the target cylinder is given and also the number of infinitely long
cylinders that were hit (a measure of the statistics of the run). The
body of the table shows the frequency of hits of energy greater than
E, and data for four different lengths of cylinders are given. The
frequencies apply to a single target cylinder placed at random in water
irradiated uniformly with an absorbed dose of 1 Gy. In some cases, the
last values in each column are subject to very large uncertainties
(Equation 7.3) resulting in the repetition of the same value, and may
therefore be ignored.
The frequency averaged mean specific energy in the targets, z, is
given at the base of each column. This was calculated from the full
frequency distribution of hit sizes and independently of the absolute
normalisation of the scoring frequencies in the Table. Let f(E) be the
frequency of energy depositions ('hits') of energy between E and E+ dE.
Then the frequency mean hit size, E, is given by
Co E_0E. f(E). dE
A2.1
ö f(E). dE
irrespective of the normalisation of the frequency distribution.
Hence, the frequency mean specific energy is
z=E A2.2 m
where m is the mass of a target (I. C. R. U., 1983; -Goodhead, 1987d).
170
(In I. C. R. U. notation this frequency mean specific energy is written
as ZF (I. C. R. U., 1983)). The probability of a hit of any size is given
by z-1 and should, with ideal scoring, equal the frequency of a hit
greater than 0 eV (f>o). The difference between these values is a
measure of the statistical uncertainty of the data. The 'scoring
efficiency', S, is defined by:
f>o - z-1 I S (%) _ -1
x 100 A2.3 z
Finally, the number of hits from which the statistics are dervied is
given at the bottom of each column.
171
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