UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Optimization studies of the TRIUMF biomedical pion beam Poon, Michael Nai-Chiu 1977

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1977_A6_7 P66.pdf [ 4.85MB ]
Metadata
JSON: 831-1.0085194.json
JSON-LD: 831-1.0085194-ld.json
RDF/XML (Pretty): 831-1.0085194-rdf.xml
RDF/JSON: 831-1.0085194-rdf.json
Turtle: 831-1.0085194-turtle.txt
N-Triples: 831-1.0085194-rdf-ntriples.txt
Original Record: 831-1.0085194-source.json
Full Text
831-1.0085194-fulltext.txt
Citation
831-1.0085194.ris

Full Text

OPTIMIZATION STUDIES OF THE TRIUMF BIOMEDICAL PION BEAM by ^ MICHAEL NAI-CHIU |POON B . S c , U n i v e r s i t y o f B r i t i s h Columbia, 1975 A THESIS SUBMITTED IN PARTIAL. FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Physics) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1977 (c) M i c hael Nai-Chiu Poon, 1977 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t ha t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . o n Depar tment o f P h y s i c s The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date August 15, 1977 i i ABSTRACT Studies have been made to procure a flux-maximized and contaminant-minimized T T - beam f o r radiotherapy at the Batho Biomedical F a c i l i t y at TRIUMF. The dependence of the pion y i e l d on the i n c i d e n t proton energy bombarding the pion production t a r g e t and on the mi d - l i n e momentum of the pion t r a n s p o r t system have been measured. We have determined the transmiss i o n e f f i c i e n c y of the pion t r a n s p o r t system: both i t s momentum and angular acceptance and a l s o i t s phase space acceptance along the length of the t a r g e t . Based on a s u f f i c i e n t understanding of the mechanism of gamma production from ir° decay, a model has been made to account f o r the e l e c t r o n contamination measurements. An optimum ir~ production t a r g e t f o r radiotherapy i s recommended. We conclude t h a t the a c t u a l performance of the pion t r a n s p o r t system i s approx-imately three times below the design expectation. However, the reduced pion f l u x can be increased by changes i n the present o p e r a t i n g mode of TRIUMF. The i n c i d e n t proton energy should be decreased from 500 MeV to 450 MeV, where the expected proton current can be increased to between 22 0 and 450 yA by maintaining the c y c l o t r o n tank pressure between 1 x 10 8 and 5 x 10 8 t o r r . A 7.4 cm b e r y l l i u m t a r g e t , w i t h i t s top surface exposed, would r e s u l t i n an e i g h t f o l d decrease i n the e l e c t r o n contamination i f the proton beam were steered to the top surface of the t a r g e t . With t h i s o p e r a t i n g mode,. the maximum i r - flux at 2 00 MeV/c i s expected to l i e between 2.3 x 10 8 and 4.8 x 10 8 per second with a corresponding electron and muon contamination of 3% and 10%. i v TABLE OF CONTENTS Page TITLE i ABSTRACT i i TABLE OF CONTENTS v i v LIST OF TABLES v i i LIST OF ILLUSTRATIONS v i i i ACKNOWLEGEMENTS • x i i CHAPTER 1 Introduction • 1 CHAPTER 2 Experimental Techniques 3 2.1 General description of the production and transport of a proton beam to TT production area 3 2.2 The pion-production target 5 2.3 The bio-medical channel**** 8 2.4 The data a c q u i s i t i o n system * 10 2.5 Proton beam monitors 19 CHAPTER 3 Study of negative pion y i e l d s 22 3.1 P a r t i c l e y i e l d s at a proton energy of 500 MeV 22 3.2 Dependence of the pion y i e l d on incident proton energy 26 3.3 The e f f e c t i v e thickness of the production targets 26 3.4 Recommendations on the optimum proton proton energy for therapy 29 V TABLE OF CONTENTS(CONTINUED) Page 3.4.1 Limitations imposed on the maximum extractable proton current 3 0 3.4.2 Optimum extracted proton energy for therapy 32 CHAPTER 4 Determination of the channel characteristics•35 4.1 Determination of the momentum acceptance O f M8 3 5 4.1.1 Method 36 4.1.2 Results and discussion of accuracies 38 4.2 Determination of the angular acceptance of M8 41 4.2.1 Determination of the pion production cross-section for C at a proton energy of 500 MeV • 43 4.2.2 Corrections for pion nuclear interaction loss in the target f i 47 4.2.3 Corrections for pion nuclear interaction loss outside the target f i 48 4.2.4 Results and discussion of uncertainties 48 CHAPTER 5 Study of the electron contamination of the pion beam 51 5.1 Experimental findings 52 5.2 Explanation of the experimental findings 56 v i TABLE OF CONTENTS(CONTINUED) Page 5.2.1 Sources of electrons 57 5.2.2 Determination of the gamma-energy spectrum and d i f f e r -e n t i a l cross-section for y-emission at 30° 58 5.2.3 Determination of the pair production cross-sections U ( E J • 68 PP 5.2.4 A model for electron and pion production i n the target*•••72 5.2.4.1 Correction for the water jacket 75 5.2.4.2 Correction for the energy degradation of p a r t i c l e s 77 5.2.5 Results of the calc u l a t i o n s of the p a r t i c l e production 7 9 CHAPTER 6 Study of the pion production target material••85 CHAPTER 7 Recommendations, summary and conclusion 93 B I B L I O G R A P H Y 9 8 APPENDIX I Data analysis of the evaluation of the TT production cross-section 103 1.1 Reduction of the input data to N (H.) 103 IT 1 1.2 Reduction of N (PL) to cross-section p l o t s . . 103 APPENDIX II Correction to P g due to energy degradation of electrons i n water 110 v i i LIST OF TABLES Table Page I Parameters of the T2 targets 7 II Dimensions of the s c i n t i l l a t o r s 13 III Dependence of the pion y i e l d on Be target thickness with a 5 00 MeV proton beam 28 IV u° production t o t a l cross-sections and gamma d i f f e r e n t i a l cross-sections for various elements 65 V A comparison of the significance of each region of the T2 target i n negative pion and electron production 78 VI Pertinent data i n the choice of target 91 VII Dependence of the maximum pion y i e l d per proton on the target material at various proton energies 92 VIII A comparison between the design and achieved s p e c i f i c a t i o n s of the M8 channel 96 IX Recommendations for changes i n the operating mode of TRIUMF for pion therapy • 97 X Parameters and variables i n KIOWA analysis • 105 XI Values of h and k for electron energies 30<T<200 M e V * 1 1 2 v i i i LIST OF ILLUSTRATIONS Figure Page 2.1 A plan view of TRIUMF 4 2.2 The T2 target area of TRIUMF-*** 6 2.3 The bio-medical beam l i n e M8 9 2.4 A schematic representation of the p a r t i c l e detection system * 11 2.5 A t y p i c a l beam p r o f i l e at the exit of M8 12 2.6 A schematic representation of the e l e c t r o n i c s * 1 5 2.7 A d i f f e r e n t i a l range curve of a 63.8 MeV (148 MeV/c) pion beam 16 2.8 The ti m e - o f - f l i g h t spectrum of a 148 MeV/c beam 18 3.1 Negative p a r t i c l e y i e l d s detected at the end of the M8 channel, produced by a 500 MeV proton beam impinging on:(a) a 10 cm Be target; (b) a 10 cm C target; (c) a 1 cm Cu target* 2 3 3.2 A comparison of the po s i t i v e and negative pion y i e l d for a 10 cm Be target 25 3.3 Dependence of pion y i e l d on the k i n e t i c energy of a proton beam incident on (a) a 10 cm Be target; (b) a 10 cm C target 27 3.4 Dependence of the maximum extractable current on the H extraction energy plotted with the tank pressure as a parameter • • • 31 ix LIST OF ILLUSTRATIONS(CONTINUED) Figure p a g e 3.5 Dependence of the maximum pion y i e l d per second on the incident proton energy at a tank pressure of 5 x 10~ 8 t o r r " ••••••••33 3.6 Dependence of the maximum pion y i e l d per second on the incident proton energy at a tank pressure of 1 x 10 8 t o r r 34 4.1 A sketch of the process of transforming the d i f f e r e n t i a l range curve to the corresponding momentum acceptance curve 37 4.2 Typical d i f f e r e n t i a l range curves (a), (c) and t h e i r corresponding momentum acceptance curves (b), (d) at respective s l i t openings of 0.64 cm and 11.4 cm 39 4.3 Dependence of the momentum acceptance of the M8 channel on the blade width 4 0 4.4 A schematic representation of the apparatus for pion production cross-section measurements • 44 4.5 The d i f f e r e n t i a l cross-section of negative pion production on carbon from a 500 MeV proton beam* • • 4 6 4.6 The particle-transmission e f f i c i e n c y curve of M8 —the angular acceptance versus the momentum acceptance of the channel 50 5.1 Dependence of the electron contamination i n (a) a 148 MeV/c; (b) a 170 MeV/c beam as an incident 500 MeV proton beam with v e r t i c a l standard deviation of 0.22 cm i s steered v e r t i c a l l y along the 10 cm Be target •••••••53 5.2 Negative p a r t i c l e y i e l d s at the end of M8 from a 500 MeV proton beam of v e r t i c a l standard deviation of 0.22 cm impinging the top and the bottom of a 10 cm carbon target at T2 54 X LIST OF ILLUSTRATIONS(CONTINUED) Figure Page 5.3 Relative electron and positron y i e l d s from a 10 cm Be target with a centered 500 MeV proton beam 55 5.4 Dependence of TT° t o t a l cross section on the incident proton energy 63 5.5 The gamma energy spectrum at a laboratory angle of 30° for an incident 475 MeV proton beam 67 5.6 Dependence of the pair production cross-section on electron energy for beryllium 7 0 5.7 Dependence of the pair production cross-section on Z of the nucleus as calculated from equation 5.12 71 5.8 A schematic representation of the electron and pion production model 73 5.9 A cross-sectional view of the pion production target T2 76 5.10 Dependence of the electron contamination on the channel momentum for a 10 cm Be target at T2. The incident proton energy i s 500 MeV • 80 5.11 Dependence of the electron contamination on the incident proton energy on a 10 cm Be target 8 3 5.12 The e f f e c t on the electron contamination by changes i n the target design 84 6.1 Dependence of the maximum allowable target thickness at T2 on the incident proton energy 87 x i LIST OF ILLUSTRATIONS(CONTINUED) Figure Page 1.1 A flowchart of the KIOWA a n a l y s i s ' * " 106 1.2 Dependence of (Aft./A^io)' on the hodoscope counter number 10 9 II.1 A schematic representation of a gamma ray impinging on a slab of material producing an electron v i a pair production 113 x i i ACKNOWLEGEMENTS I wish to thank my thesis supervisor, Dr. R. M. Henkelman, for his continual guidance, utmost patience,and incessant encouragement throughout the project. I am also grateful to Dr. R. R. Johnson, Dr. K. Y. Lam, Dr. L. D. Skarsgard and Mr. R. W. Harrison for reading the manuscript and providing me with many valuable comments. For the many hours spent i n tuning the TRIUMF BL1 and the useful suggestions in the experimental work, I am indebted to Dr. Patrick Walden. Thanks are also due to Dr. Garth Jones and Dr. Ed Auld for t h e i r guidance and contribution i n the IT cross-section measurements. Futhermore, I wish to acknowledge Dr. T. G. Masterson for the many hours of discussions that we spent together. The f i n a n c i a l support from the National Research council of Canada i n the form of a postgraduate scholarship and the research f a c i l i t i e s provided by the B r i t i s h Columbia Cancer Foundation are very much appreciated. I w i l l treasure the fellowship established during the past two years with my colleagues Ken Shortt and Larry Watts. The many stimulating ideas from Dr. Jan Nordin are gr a t e f u l l y acknowledged. Thanks are due to Mr. Bruno Jaggi, the e l e c t r o n i c s "expert" of the Batho Bio-medical F a c i l i t y , for his technical assistance. I also wish to express my appreciation to T r i c a Watt for typing the manuscript. x i i i Most o f a l l , I am i n d e b t e d t o my p a r e n t s f o r t h e i r n u r t u r e and i n e s t i m a b l e l o v e t h r o u g h o u t t h e y e a r s . May t h i s work be used t o t h e g l o r y o f Him, the C r e a t o r and S u s t a i n e r o f t h e u n i v e r s e , who by H i s N a t u r e i s our God, and by H i s Grace has a l s o become my F a t h e r . 1 CHAPTER 1  INTRODUCTION Radiotherapy u s i n g n e g a t i v e pions w i l l soon be i n i t i a t e d a t the Batho Biomedical F a c i l i t y a t TRIUMF ( T r i -U n i v e r s i t y Meson F a c i l i t y ) with the a v a i l a b i l i t y o f an a n t i c i p a t e d 100 yA 500 MeV proton beam by S p r i n g 1978. Since the r a t i o n a l e f o r pi o n therapy of cancer has been w e l l docu-mented by many authors [1,2,3,4], i t w i l l not be presented i n t h i s study. Dose c a l c u l a t i o n s r e l a t i n g t o the use of neg a t i v e pions f o r r a d i o t h e r a p y have a l s o been performed [5]. However, s i n c e p i o n r a d i o t h e r a p y i s s t i l l embryonic, much p h y s i c s r e s e a r c h i s needed be f o r e treatment can be s t a r t e d . Although t h i s r e s e a r c h i s motivated by the immediate c l i n i c a l needs of the b i o m e d i c a l f a c i l i t y a t TRIUMF, i t w i l l a l s o be of value i n the design o f new channels f o r p i o n r a d i o t h e r a p y . Since any movement of the p a t i e n t d u r i n g i r r a d i a t i o n reduces the r e l i a b i l i t y o f the dose l o c a l i z a t i o n , the t r e a t -ment time should be as short as p o s s i b l e . Hence, the a v a i l a b l e p i o n f l u x needs to be maximized. The i n e v i t a b l e contamination o f t h e . p i o n beam by muons and e l e c t r o n s needs to be minimized. Because these contaminants have lo n g e r ranges than pions they cause unwanted damage to normal t i s s u e s o u t s i d e the tumour volume and e f f e c t i v e l y l i m i t the maximum tumour dose when c r i t i c a l , r a d i a t i o n - s e n s i t i v e organs border the tumour. Moreover, s i n c e e l e c t r o n s are low L i n e a r Energy T r a n s f e r (LET) p a r t i c l e s , they d i l u t e the high LET 2 radiation produced by the pion stars, and thus reduce the effectiveness of the damage incurred by the tumour. For these reasons, i t i s important that the incident pion beam be as intense and as pure as possible. This thesis presents studies on the production of pions and contaminants and recommends methods of optimizing the biomedical pion beam for radiotherapy. The process of pion production at TRIUMF, the biomedical beam transport system and the experimental techniques used throughout t h i s study are outlined i n chapter 2. Chapter 3 investigates the pion y i e l d . 'Dependence of the pion flux on momentum, on the target material, and on the incident proton energy are characterized. Calculations of the transmission e f f i c i e n c y of the pion transport system and measurements of the pion production cross-section by 500 MeV protons on carbon are summarized in chapter 4. Chapter 5 explores the mechanism of production of the electron contamination i n the pion beam. It i s shown that the electron contamination can be s i g n i f -i c a n t l y reduced by a change i n the design of the pion produc-t i o n target. Chapter 6 discusses the l i m i t a t i o n s imposed on the material and dimensions of the target by the TRIUMF beam transport systems and safety requirements and recommends an optimal target. F i n a l l y , a proposal for an optimized operat-ing mode at TRIUMF for radiotherapy i s summarized i n chapter 7. 3 CHAPTER 2  EXPERIMENTAL TECHNIQUES 2.1 General D e s c r i p t i o n of the p r o d u c t i o n and t r a n s p o r t  of a proton beam to TT~ p r o d u c t i o n area The TRIUMF c y c l o t r o n i s a meson f a c t o r y t h a t f e a t u r e s the hig h duty c y c l e o f an isochronous c y c l o t r o n w i t h h i g h e x t r a c t i o n e f f i c i e n c y , combined w i t h the simultaneous and independent e x t r a c t i o n o f two beams de s i g n a t e d as Beam Li n e 4 (BL4) and Beam L i n e 1 (BL1) a t e n e r g i e s v a r i a b l e between 18 3 and 52 0 MeV and i n t e n s i t i e s up to 100 uA. S p l i t r a t i o s (BL4/BL1) of 1/1 t o 1/5000 have been achieved. U n p o l a r i z e d or p o l a r i z e d beam of H~ i o n s are produced a t 3 00 kV i n an e x t e r n a l E h l e r s source or a Lamb-shift source r e s p e c t i v e l y . The H~ i o n s are then i n j e c t e d i n t o the c e n t e r of the sectoir-focussed c y c l o t r o n v i a a s p i r a l i n f l e c t o r . They are a c c e l e r a t e d on c r o s s i n g the v o l t a g e gap i n a r a d i o -frequency c a v i t y d r i v e n at 23.05 MHz and are maintained i n a s p i r a l o r b i t by the a z i m a t h a l l y v a r y i n g magnetic f i e l d . At the d e s i r e d f i n a l energy, protons are e x t r a c t e d w i t h good energy r e s o l u t i o n (3 MeV f u l l width f o r a 500 MeV beam) by i n s e r t i n g a carbon or aluminum f o i l to s t r i p the two bound e l e c t r o n s from the H~ i o n s . The proton beam i s c o l l e c t e d by a combination magnet which s t e e r s the beam down an e x t e r n a l beam l i n e . For Beam Li n e 1, the proton beam i s t r a n s p o r t e d t o the south-east corner of the c y c l o t r o n v a u l t , i s bent through a 30-degree angle i n t o the beam t u n n e l , and i s subsequently F i g u r e 2.1 A p l a n v i e w o f TRIUMF The l o c a t i o n s o f the p r o t o n c u r r e n t m o n i t o r s : (1) t h e p o l a r i m e t e r ; (2) t h e s t r i p p e r f o i l s i g n a l ; (3) t h e Cerenkov c o u n t e r ; (4) t h e beam dump m o n i t o r are as shown i n t h e f i g u r e . The p i T a r e a i s i n d i c a t e d by t . B L l B and M i l are new c h a n n e l s under c o n s t r u c t i o n . 5 transported v i a a series of bending magnets, quadrupoles and steering magnets to T2, the pion production target (see Figure 2.1). The spot size of the proton beam on the target i s 40 mm2. More detailed descriptions of the cyclotron's c h a r a c t e r i s t i c s and performance, as well as i t s present status are published elsewhere [6,7,8,9,10]. 2.2 The pion-production target There are three secondary meson beams produced at T2: the Biomedical channel, the stopped Tr/y channel and the polarized muon channel; designated M8, M9 and M2 0 respectively. The pion production targets are mounted i n cassettes fixed on the target ladder (see Figure 2.2). The targets a v a i l -able for t h i s present study consist of nominal 3 cm Be, 10 cm Be, 14 cm Be, 10 cm C and a 1 cm Cu targets. With the exception of the 10 cm carbon target, a l l targets are encased in thin-walled (^0.01" wall) stai n l e s s steel cassettes and are water-cooled. ZnS s c i n t i l l a t o r s are placed i n front of the 3 cm Be and 10 cm C targets to allow v i s u a l i z a t i o n of the proton beam spot on the target. The p r o f i l e and location of the proton beam can be manipulated using the two quadrupoles (1Q12, 1Q13) and the two steering magnets (1SM6, 1SM7) immed-i a t e l y upstream of T2 on Beam Line 1. Specifications of each target are summarized i n Table I. 6 F i g u r e 2.2 The T2 t a r g e t area of TRIUMF TABLE I PARAMETERS OF THE T2 TARGETS Target Material Physical Size Density(gm/cm ) Comments Be Be Be Cu 2.54 x 1.5 x 0.5 cm" 10.16 x 1.5 x 0.5 cm" 13.97 x 1.5 x 0.5 cm" 1.00 x 1.5 x 0.5 cm" 10.40 x 1.56 x 6.56 cm" 1.848 1.848 1.848 8. 96 1.85 -ZnS s c i n t i l l a t o r mounted at the front -three s l o t s are cut i n the target for more e f f i c i e n t cooling -ZnS s c i n t i l l a t o r mounted at the front -the target i s uncooled 8 2.3 The biomedical channel The M8 channel i s constructed at a v e r t i c a l angle of 3 0° with respect to the d i r e c t i o n of the incident proton beam. It i s 7.2 meters long to the vacuum window with nine beam l i n e elements capable of transporting beams of momentum up to 22 0 MeV/c. As i l l u s t r a t e d i n Figure 2.3, the channel i s a double bend system. Ql and Q5 are 8" aperture quadru-poles; Q2, Q3, Q4 are 12" aperture quadrupoles. Sextupoles SI and S2 are used for second order correction of the beam optics. Bl and B2 are 45° bending magnets. Ql, which i s approximately one meter from the production target, c o l l e c t s a collimated beam of 23 msr angular acceptance and focusses i t i n the Y-direction (perpendicular to the beam plane) to optimize the flux passing through B l . Bl separates the pos-i t i v e l y charged p a r t i c l e s from the negatively charged p a r t i c l e s , and also disperses the p a r t i c l e s according to t h e i r momenta. Q2 then focusses the beam i n the X-direction to a dispersed l i n e focus at the mid plane of the beam l i n e . The remainder of the beam l i n e serves to recombine the d i f f e r e n t momenta into an achromatic f i e l d after Q5 i n the experimental area [11]. Q5 i s mounted on r a i l s with a possible range of movement of over 40 cm, thus providing v a r i a b i l i t y i n the beam focus. The magnetic f i e l d s in the beam l i n e elements have been adjusted to maximize the flux transported by the channel. STEPPING-MOTORS FOR F i g u r e 2.3 The bio-medical beam l i n e M8 10 2.4 The data a c q u i s i t i o n system The p a r t i c l e detection system i s i l l u s t r a t e d in Figure 2.4. The pions are stopped i n a water tank, with the range being determined by the incident momentum. The size and shape of the beam spot can be monitored by means of a multiwire proportional counter located between the two s c i n t i l l a t o r s SI and S2. For the present study, the diameter of the beam spot used i s t y p i c a l l y 2.0 ± 0.2 cm with the beam divergence of less than 50 mR. Figure 2.5 gives a p r o f i l e of the beam. S c i n t i l l a t o r s SI, S2, S3 and S4 are made of NE102A p l a s t i c coupled with l i g h t pipes to photomultipliers (type RCA 8575). The physical dimensions of the s c i n t i l l a t o r s are summarized in Table I I . The large dimensions are chosen so that a l l the p a r t i c l e s are intercepted by the counters. Due to the f i n i t e size of the beam and i t s small angular divergence, beam loss due to multiple scattering i n the water i s n e g l i g i b l e . In addition, the p a r t i c l e flux rate in t h i s work i s less than 10 5 per second, well within the l i m i t a t i o n s imposed by the counters, thus saturation e f f e c t s are also n e g l i g i b l e . The entire beam l i n e operation as well as the data ac q u i s i t i o n i s handled by means of a Data General NOVA 2/10 system, running under RDOS (Real-Time-Disk Operating System). The computer i s linked to the motor d r i v e r s , the potentio-meters for pos i t i o n measurements, the set points of the magnet PHYSICAL MEASUREMENT: Counter Arrangement Variable Position S3 S4 Beam a a 9 a a a • a a a a S1 MWPC S2 Plastic Box [Not to scale] Water Tank F i g u r e 2.4 A schematic r e p r e s e n t a t i o n of the p a r t i c l e d e t e c t i o n s y s t TABLE I I DIMENSIONS OF THE SCINTILLATORS S c i n t i l l a t o r Number M a t e r i a l S i z e Comments 1 2 3 4 NE102A NE102A NE102A NE102A 10" x 10" x 1/8" 10" x 10" x 1/8" 11" x 11" x 1/8" : 12" x 12" x 3/16": -S3 and S4 are packed together with no a i r gap i n between 14 power s u p p l i e s and t h e d a t a a c q u i s i t i o n system t h r o u g h CAMAC. A more d e t a i l e d d e s c r i p t i o n o f t h e b i o m e d i c a l beam l i n e c o n t r o l system i s g i v e n i n r e f e r e n c e 12. F i g u r e 2.6 g i v e s a sche m a t i c r e p r e s e n t a t i o n o f t h e e l e c t r o n i c s . The t o t a l f l u x o f p a r t i c l e s t r a n s p o r t e d t o t h e end o f M8 i s measured by t h e l o g i c c o i n c i d e n c e 1.2. The s i g n a l 1.2.3.4 measures t h e p a r t i c l e s s t o p p i n g i n S3. The d i f f e r e n t i a l range c u r v e as shown i n F i g u r e 2.7 i s a measure o f t h e number o f p a r t i c l e s s t o p p i n g as a f u n c t i o n o f d e p t h . The f i g u r e r e p r e s e n t s t h e s t o p p i n g d i s t r i b u t i o n i n water o f an i n c i d e n t monoenergetic 63.8 MeV p i o n beam. The l a r g e s t peak a t a d e p t h o f a p p r o x i m a t e l y 13 cm c o r r e s p o n d s t o t h e r e g i o n o f t h e s t o p p i n g p i o n , whereas t h e s m a l l e r peak near 20 cm c o r r e s p o n d s t o t h a t o f t h e s t o p p i n g o f muons produced b e f o r e B2. The p a r t i c l e c o m p o s i t i o n i s d e t e r m i n e d by means o f t i m e - o f - f l i g h t (TOF) measurements t h a t u t i l i z e t h e f a c t t h a t t h e c y c l o t r o n produces p r o t o n b u r s t s a t 43.8 nsec i n t e r v a l s ( w i t h a s t a b i l i t y o f ± 7.5 p a r t s i n 10 8) w i t h FWHM o f 3 nsec. Thus, t h e p a r t i c l e s (Tr,y,e) t r a n s p o r t e d t o t h e e x i t o f M8 pos s e s s e x a c t l y t h e same m i c r o s t r u c t u r e as t h e p r o t o n beam b u t w i l l be s h i f t e d i n time r e l a t i v e t o each o t h e r , a c c o r d i n g t o the time needed f o r t h e p a r t i c l e s t o t r a v e l down t h e c h a n n e l , where t h e time s e p a r a t i o n At between two t y p e s o f p a r t i c l e s w i t h masses m2 and m 2 i n u n i t s o f MeV/c 2 a r e g i v e n by proton monitors P Q L A R 8 M E T E R c-C E R E S S S K O V o— B E A M D U M P STOPFER FOSL ^ SI S2 o-S3 o-5 4 o-R F coincidence gate discriminator delay box D D D D 1 - 2 3> D D •mv— 1 - 2 - 3 WD s start 1 - 2 - R F ._.-J=D delay time s on T D C particle selection for norma! beam profile operation F i g u r e 2.6 A schematic r e p r e s e n t a t i o n o f the e l e c t r o n i c s 16 F i g u r e 2.7 A d i f f e r e n t i a l range curve of a 63.8 MeV (148 MeV/c) pi o n beam y i d e s i g n a t e s the muons produced from IT decay before B2 17 At [sec] = _ X L _ [ ( P 2 C 2 + m ^ ) V 2 - ( p 2 c 2 + m ^ ) ^ ] P C 2 (2.1) where D i s the length of the channel i n meters and p i s the mid-line momentum of the channel i n MeV/c. Clean time separation between the pions and the electrons i s possible for momenta ranging up to 2 00 MeV/c. Moreover, by putting i n a proper time delay between the R.F. and the 1.2 coincidence i t i s possible to gate the MWPC to obtain either the electron or pion beam p r o f i l e s at the end of M8. A t y p i c a l TOF spectrum at a channel momentum of 148 MeV/c i s shown i n Figure 2.8. The three components of the beam are pions, muons and electrons. The muon contamination i s further subdivided into two components. The f i r s t com-ponent yi consists of muons with the same momentum as the pions. These are mostly produced from TT decay (TT -*• uv, C T = 7.804 meters) near the target T2 and along the beam l i n e before B l . The second component \Xi consists of muons produced from TT decay afte r B2, and therefore d i f f e r s i n momentum from the rest of the beam, but possesses exactly the same time signature as the pions. Thus, t h i s u 2 component i s buried i n the TOF spectrum under the pion peak. The contribution of y 2 i s estimated to be six percent of the pion peak for channel momentum va r i a t i o n from 100 to 200 MeV/c. F i g u r e 2.8 The t i m e - o f - f l i g h t spectrum of a 14 8 MeV/c beam 19 2.5 Proton beam monitors Absolute measurements of the p a r t i c l e y i e l d s require that the proton current be measured. This monitoring has been done with four types of detectors. The f i r s t i s a polarimeter located between pir area and T2 (see Figure 2.1) [13]. A thin polyethelene (CH2) f o i l (^ 5 mg/cm2) i s inserted i n the proton beam. By monitoring the flux of the scattered and reco i l e d protons in coincidence, a r e l a t i v e measure of the proton current can be obtained. The pol a r i z a t i o n of the beam, which can also be monitored, i s irre l e v a n t ' t o t h i s work and i s thus ignored. The polarimeter can be calibra t e d absolutely by a carbon a c t i v a t i o n technique, using the reaction 1 2C(p, p n ) 1 ^ ; 1 1 C ( B + ) 1 1 B . During the ca l i b r a t i o n process, a f o i l of 1 2 C with areal density 3 04.6 6 mg/cm2 was inserted into the beam. After approximately two minutes of i r r a d i a t i o n , the f o i l was placed between two 1/16 inch CH 2 f o i l s so that the B + would promptly annihilate. A Nal c r y s t a l located 2 0 cm from the f o i l then measured and recorded the 0.511 MeV gamma spectra repeatedly four times during approximately one and a half hours. Then, from the measured number of gamma rays together with the known 1 2C(p, p n) J 1C cross-sections, the integrated proton flux during the ac t i v a t i o n process was determined. This c a l i b r a t i o n allowed the observed count rate from the scatter and r e c o i l arms of the polarimeter to be used as an absolute proton current monitor for proton currents less than 10 yA with an 20 error of less than 1 10%. The second proton current monitor i s the signal from the stripper f o i l [4]. If the stripped electrons are captured by the f o i l , the current developed i n the stripper i s proportional to the extracted proton current (in f a c t , i t i s twice the proton current). Since the beam s p i l l i n BLl i s less than 10 nA, the proton current at T2 can be assumed to be the same as that at the stripper f o i l . One l i m i t a t i o n of t h i s monitor i s radiofrequency interference at low proton energies (T < 3 00 MeV) where the stripper f o i l i s located near the resonators i n the cyclotron. Another drawback i s that some of the electrons may be l o s t due to the presence of the magnetic f i e l d and the geometry of the stripper f o i l . Generally, for a proton energy of 500 MeV, these e f f e c t s are small, and the stripper f o i l signal can be used to give an absolute measure of the proton current with errors of ± 10% for proton currents above 100 nA. Besides the two absolute proton current monitors mentioned above, two other r e l a t i v e current monitors are available. The f i r s t one i s a Cerenkov counter located downstream of the f i r s t dipole of M9 which measures the Y - r a Y s produced by the protons at the T2 target, thus giving a measure of the amount of proton beam impinging upon the target. Unfortunately, t h i s signal i s found to be dependent on the magnetic f i e l d strength of the dipole. Possible misalignment of the counter also means that the signal cannot be compared 21 o v e r an e x t e n d e d p e r i o d o f t i m e . T h e s e l i m i t a t i o n s hamper t h e e f f e c t i v e n e s s o f t h e C e r e n k o v c o u n t e r as a beam m o n i t o r . The l a s t i s a s c i n t i l l a t i o n c o u n t e r l o c a t e d i n t h e beam l i n e 1 t u n n e l a t a p p r o x i m a t e l y t e n m e t e r s u p s t r e a m f r o m T2. I t me a s u r e s t h e r a d i a t i o n f r o m t h e beam dumped i n T2 and t h u s g i v e s a measure o f t h e p r o t o n beam c u r r e n t d e l i v e r e d t o t h e T2 a r e a . However, beam s p i l l a l o n g B L l and r e s i d u a l r a d i a t i o n i n t h e t u n n e l w i l l i n c r e a s e t h e l e v e l o f t h e d e t e c t e d s i g n a l , t h u s t h e u s e f u l n e s s o f t h i s c o u n t e r i s a l s o l i m i t e d . 22 CHAPTER 3  STUDY OF NEGATIVE PION YIELDS With M8 channel'adjusted to maximize the pion flux, the pion y i e l d per yA of proton current on the target delivered to the i r r a d i a t i o n area i s determined by three factors: the channel momentum, the incident proton k i n e t i c energy and the target material for the pion production. Besides the consideration of flux maximization, a knowledge of the momen-tum dependence of pion y i e l d and of the corresponding contam-inant y i e l d s i s important i n the selection of the operating momenta for radiotherapy. Discussions on the choice of target material for pion production w i l l be reserved for a l a t e r chapter. The following sections contain studies of the dependence of the pion y i e l d on the channel momentum •( p<200 MeV/c ) and the incident proton energy( T <500 MeV ). P 3.1 P a r t i c l e y i e l d s at a proton energy of 500 MeV A 500 MeV proton beam s t r i k i n g the center of the T2 target i s normally used i n pion production. Figure 3.1(a), (b) and (c) show graphs of momentum dependence of negative p a r t i c l e y i e l d s at the end of M8 for various T2 production targets. The composition consists of TT -, e~ as well as the two types of muons, y-r and y 2 as defined i n Chapter 2. For momenta less than 2 00 MeV/c, a l l the y i e l d curves have the trend of decreasing electron contamination with increasing channel momentum. For the 10 cm Be target, electron CHANNEL MOMENTUM (MEV/C) Figure 3.1 Negative p a r t i c l e y i e l d s detected at the end of the M8 channel, produced by 500 MeV proton beam impinging on:(a) a 10 cm Be target;(b) a 10 cm C target; (c) a 1 cm Cu target 24 contamination amounts to 42% of the t o t a l beam, which decreases to l g % as the momentum changes from 14 8 MeV/c to 200 MeV/c. The f r a c t i o n of the. combined pion and muon flux, that i s i d e n t i f i e d as u x by t i m e - o f - f l i g h t , also decreases as the momentum increases, as expected. Although the u 2 component cannot be resolved by the t i m e - o f - f l i g h t technique, i t s contribution can be estimated by kinematic considerations. In fact, c a l c u l a t i o n shows y 2 i s approximately 6% of the pion flux. Maximization of the pion f l u x i s not the only factor in selection of the momentum of the beam i n radiotherapy. The pion density at the stopping region i n the i r r a d i a t e d tissue depends also on the momentum acceptance (see Chapter 4) and the nuclear i n - f l i g h t i n t e r a c t i o n of the pions. In f a c t , consideration o f . a l l the factors discussed above leads to the conclusion that the operating range of the channel momentum w i l l be between 160 and 200 MeV/c [15]. Positively-charged p a r t i c l e y i e l d s can also be measured by reversing the p o l a r i t i e s of a l l the magnets of the channel. Figure 3.2 shows the i r + y i e l d s along with the TT~ y i e l d s from a 10 cm Be target. I t should be noted that there i s no constant scaling factor between the TT + and ir~ y i e l d . In f a c t , the r a t i o TT + y i e l d / f r - y i e l d increases from four to six as the momentum increases from 100 MeV/c to 170 MeV/c. 25 1 0 CM BE C H A N N E L fvlOIVIENTUM (MEV/C) F i g u r e 3.2 A comparison o f t h e p o s i t i v e and n e g a t i v e p i o n y i e l d from a 10 cm Be t a r g e t (The symbols used t o r e p r e s e n t t h e d a t a p o i n t s a r e l a r g e enough t o i n c l u d e t h e e r r o r b a r s from c o u n t i n g s t a t i s t i c s .) 26 3.2 Dependence of the pion y i e l d on incident proton energy Figure 3.3 summarizes the dependence of the negative pion y i e l d on the incident proton energy. The pion y i e l d s per yA of incident proton current are plotted against the proton energy i n the range of 300 to 500 MeV, with the pion momentum as a parameter. A l l muon components have been removed from the pion y i e l d s . Uncertainties a r i s i n g from counting s t a t i s -t i c s are too small to be shown i n the graphs. However, there i s a ±10% uncertainty due to the uncertainty i n the measured proton current. Nevertheless, i t i s informative to r e a l i z e that the I T - y i e l d i s monotonically increasing with proton energy. Moreover, the y i e l d of higher momentum pions decreases more sharply as proton energy decreases than that of lower momentum pions. The y i e l d s approach zero at a proton energy of 300 MeV. These are consistent with calculated thresholds based only on kinematic considerations. 3.3 The e f f e c t i v e thickness of the production targets Due to the limited phase space acceptance of the M8 channel, the e f f e c t i v e thickness of the production target i s less than i t s physical thickness. Table III shows the r e l a t i v e pion y i e l d s from the 3 cm, 10 cm and 14 cm Be targets. It i s important to r e a l i z e that although the pion y i e l d as a function of momentum can be scaled by some constant factor for various target thicknesses, t h i s factor i s less than the r a t i o of the 27 1-5 1 0 0-5 a. cc uj CL. o UJ co C£ a. a _ i UJ 7Z O (a.) 01 •0 0-5 (b) 0 300 0 200MEV/C MEV/C MEV/C MEV/C MEV/C 200MEV/C 180 MEV/C 70 MEV/C 48 MEV/C 0 0 MEV/C 40 0 5 0 0 INCIDENT P ROTON ENERGY ( M E V ) F i g u r e 3.3 Dependence o f p i o n y i e l d on t h e k i n e t i c e n e r g y o f a p r o t o n beam i n c i d e n t on (a) a 10 cm Be t a r g e t ; (b) a 10 cm C t a r g e t 28 TABLE I I I DEPENDENCE OF THE PION YIELD ON BE TARGET THICKNESS WITH A 500 MEV PROTON BEAM Thickness (cm) R e l a t i v e Y i e l d (±5 2.54 1.00 10.16 2.33 13.97 2.33 target thicknesses. In f a c t , no s i g n i f i c a n t change in the pion y i e l d i s observed as the target thickness i s increased from 10 cm to 14 cm. By assuming an e l l i p t i c a l phase space acceptance along the target length with the maximum acceptance at the centre of the target, i t i s possible to calculate the e f f e c -t i v e target thickness of the 10 cm target using the data i n Table III a f t e r appropriate corrections have been made to compensate for both the energy and i n t e n s i t y degradation of the proton beam as i t travels through the target. The r e s u l t i n g e f f e c t i v e thickness of the 10 cm target i s 5.8 - 0.5 cm, that i s , the equivalent thickness of the 10 cm target i s 5.8 cm i f the phase space acceptance of the channel along the target length were uniform. Similar c a l c u l a t i o n also shows that a target of thickness more than 7.4 ± 0.7 cm w i l l not contribute any increase i n the pion y i e l d . It should be pointed out that Monte-Carlo simulation shows the e f f e c t i v e thickness of a 10 cm target i s 8.9 cm, i n disagreement with the estimated value based on experimental data. This might indicate that some beam l i n e element i s misaligned or malfunctioning or more l i k e l y that the shape of the phase-space acceptance i s not s t r i c t l y e l l i p t i c a l as assumed. 3.4 Recommendation oh the optimum proton energy for therapy Although the r e s u l t s as shown i n Figure 3.3 show a 30 decrease i n pion y i e l d with decrease i n proton energy, the determination of the optimum proton energy for treatment requires a knowledge of the dependence of the maximum extractable proton current on i t s energy. 3.4.1 Limitations imposed on the maximum extractable proton  current The l i m i t a t i o n s imposed on the maximum extractable proton current to BLl are well documented [16, 17]. The three factors which determine these l i m i t s are radiation due to electromagnetic s t r i p p i n g (the tendency for the weakly bound H~ ion to dissociate in intense magnetic f i e l d s ) , gas stripping (the loss of beam due to ne u t r a l i z a t i o n of H~ ions in c o l l i s i o n s with the residual gas i n the cyclotron) and f i n a l l y the maximum beam i n t e n s i t y which can be produced by the H~ ion source and transmitted into the cyclotron that i s at present limited to an extracted beam of 450 yA. By combining these three factors with a maximum beam loss of 15 yA i n the cyclotron, the dependence of the maximum extractable H~ current on i t s energy can be calculated [18]. The results are shown i n Figure 3.4 with the tank pressure as a parameter. The sharp drop i n the maximum extractable current at 400 MeV can be attributed mainly to electromagnetic stripping loss. At a constant tank pressure of 5 x 10~ 8 t o r r , the TRIUMF cyclotron i s capable of 31 MEAN D E E V O L T A G E 7 5 KV T E M P INSIDE C Y C L O T R O N 3 0 0 ° K B E A M L O S S INSIDE C Y C L O . 15 LIA 1 0 0 0 < 3. z w or or z> o LU _J 03 < h-O < 01 h-X UJ X < 2 4 5 0 max. a I lowable c u r r e n t 2 0 0 3 0 0 4 0 0 H" E N E R G Y (MEV) 5 0 0 F i g u r e 3.4 Dependence o f the maximum e x t r a c t a b l e c u r r e n t on the H e x t r a c t i o n energy p l o t t e d w i t h the tank pressure as a parameter 32 d e l i v e r i n g 100 yA at 500 MeV and 300 yA at 400 MeV. 3.4.2 Optimum extracted proton energy for therapy The TRIUMF cyclotron i s expected to operate with a tank pressure between 1 x 10 8 and 5 x 10 8 t o r r ; the pressure which i t can maintain depends on how often the tank has to be opened for service and also on new i n s t a l l a t i o n of helium cryogenic pumps. Combination of the res u l t s from Figure 3.3(a) for a 10 cm Be target and Figure 3.4 shows the dependence of the maximum TT flux on proton energy with the pion momentum and tank pressure as parameters. The r e s u l t s for a 10 cm Be production target are shown i n Figures 3.5 and 3.6. Increases of 1.4 and 2.0 times i n the flux of 200 MeV/c pions at tank pressures of 5 x 10 8 and 1 x 10~ 8 t o r r respectively are obtainable by decreasing proton energy from 500 MeV to 450 MeV. Therefore, i t can be concluded that the maximum M8 pion flux can be achieved by s h i f t i n g the proton energy to 450 MeV and by maintaining the highest possible vacuum i n the tank. F i g u r e 3.. 5 Dependence o f the maximum pion y i e l d per second on the i n c i d e n t proton energy a t a tank pressure of 5 x 10 8 t o r r 00. r 5 o X o LU CO Ql LU a. o _ l LU X < 2 P= IXIO"8 TORR 2 0 0 MEV/C I80MEV/C 170 MEV/C. 148 MEV/C 100 MEV/C 3 0 0 4 0 0 INCIDENT PROTON 5 0 0 ENERGY (MEV) Figure 3.6 Dependence of the maximum pion y i e l d per second on the incident proton energy at a tank pressure of 1 x 10 8 t o r r u> 35 CHAPTER 4 DETERMINATION OF THE CHANNEL CHARACTERISTICS An adequate understanding of the biomedical channel requires a knowledge of i t s particle-transmission e f f i c i e n c y i n terms of the momentum and s o l i d angle acceptances. This chapter deals with the measurements of these c h a r a c t e r i s t i c s . The experimental results are then compared with t h e o r e t i c a l predictions based on ray-tracing techniques. 4.1 Determination of the momentum acceptance of M8 The momentum acceptance of the M8 channel was determined from the d i s t r i b u t i o n s of the stopping-pion i n water. The momentum blades were set to a series of f i v e s p e c i f i c s l i t openings centered at the mid-line of the channel. 1 2 3 4 D i f f e r e n t i a l range curves * ^ * 2 *— for each blade setting were obtained. These measured d i f f e r e n t i a l range curves were then transformed to momentum acceptance curves a f t e r correction for range straggling and the momentum dependence of the pion y i e l d . The experiment was performed using a 2 nA 425. MeV proton beam i n beam l i n e 1. The pion production target at T2 was 10 cm Be. The M8 channel was tuned to accept p o s i t i v e -l y charged p a r t i c l e s with a mid-line momentum of 148 MeV/c. The composition of t h i s beam was 77% pions, 10% type 1 muons (Ui)/ 5% type 2 muons (y 2) and 8% positrons. 36 4.1.1 Method Figure 4.1 summarizes the steps involved i n trans-forming a d i f f e r e n t i a l range curve to i t s corresponding momentum acceptance curve. The d i f f e r e n t i a l range curve measured the f r a c t i o n of p a r t i c l e s stopping in S3, and was thus proportional to ^•(x) where x was the equivalent distance t r a v e l l e d by the pions i n water. No pions were l o s t by multiple scattering due to the f i n i t e size of the beam and the large area of the s c i n t i l l a t o r s . Before the raw spectrum was analysed, the background due to beam losses from pion i n - f l i g h t nuclear interaction and from the stopping muons (1J2) had to be subtracted. Range straggling tended to broaden the pion stopping peak. The d i s t r i b u t i o n function cj) (x) of the path lengths due to t h i s process can be expressed by <|>(x) = [ ( 2 T T 0 2 ) - 1 / 2 exp(-(x-x 0) 2/2a 2) ] dx (4.1) where x 0 i s the range of the pions and o - 0.0207 x 0 for the present analysis [19]. The i n i t i a l spectrum g~( x) was then deconvoluted to remove the range straggling using the i t e r a t i v e response method as described in M.S. Freedman et a l [20]. An important correction that had to be made to the 37 l « 2 - 3 - 4 \1 vs X hacEcgd. s u b t r a c t i o n dN dX _JL_ c o r r e c f i o n fo r r a n g e s t ragg l ing d X d N _ dfrS d X dT d F " d X d T d P \1» r e l a t i v e no. of j p ' part icles per mev/e in te rva l 1 •EorrscHon f©r vie i per mev/c interval j N , r e l a t i v e no. of p a r t i c l e s a c c e p t e d a t m o m e n t u m P n o r m a l i z a t i o n | r a n g e - e n e r g y curve T ,energy of the p ions Pc T + 2 M c 2 J : P, m o m e n t u m of the pions m o m e n t u m aeoej at the s p e c i f i c bHade se t t ing since Figure 4.1 A sketch of the process of transforming the d i f f e r e n t i a l range curve to the corresponding momentum acceptance curve 38 deconvoluted spectrum ^ ( x ) was to account f o r the i n c r e a s e of the p i o n y i e l d w i t h i n c r e a s i n g momentum. Thus, u s i n g the pio n y i e l d curve obtained f o r 10 cm Be at an i n c i d e n t proton energy of 425 MeV, the r e l a t i v e p i o n y i e l d per momentum-bite i n t e r v a l as a f u n c t i o n of momentum was ob t a i n e d and t h i s c o r r e c t i o n was a p p l i e d to the spectrum g ^ ( x ) • 4.1.2 R e s u l t s and d i s c u s s i o n o f a c c u r a c i e s F i g u r e s 4.2(a) and (c) i l l u s t r a t e t y p i c a l d i f f e r e n -t i a l range c u r v e s . The backgrounds and the peak h e i g h t s ob-served are as p r e d i c t e d by theory. The cor r e s p o n d i n g f i n a l n ormalized s p e c t r a are i l l u s t r a t e d i n F i g u r e s 4.2(b) and (d). From these s p e c t r a , the dependence of the momentum acceptance of the channel on the momentum blade width i s obtained as shown i n F i g u r e 4.3. The momentum acceptance o f the channel i n c r e a s e s w i t h s l i t opening from ±1.3% t o an asymptotic v a l u e of ±6.6% when the bla d e s , a r e completely wide open. The measured momentum r e s o l u t i o n o f ±1.3% i s l i m i t e d by the beam o p t i c s . In f a c t , the momentum r e s o l u t i o n can be improved by sextupole t u n i n g which reduces the width of the focus formed by a given momentum a t the d i s p e r s i o n plane. From the viewpoint of r a d i o t h e r a p y , the r e s o l u t i o n o f the channel i s not a ve r y important parameter because i t i s unnecessary to d e f i n e the st o p p i n g range of the pions t o a gr e a t e r accuracy than t h a t which i s allowed by the range 39 •05 cvi — _L -05 (a) •04 •03 02 •01 (c) • • A* 1 (b) 10 •0 >-s-> < _ l U J cc 5 10 15 20 25 DEPTH IN WATER (CM.) Figure 4.2 Typical d i f f e r e n t i a l range curves (a),(c) and t h e i r corresponding momentum acceptance curves (b),(d) at respective s l i t openings of 0.64 cm and 11.4 cm i L I I J ! 2 4 6 8 10 12 MOMENTUM BLADE FULL WIDTH (CM.) gure 4.3 Dependence of the momentum acceptance of the M8 channel on the blade width 41 straggling. For a 180 MeV/c pion beam, the f u l l width of the stopping range i s approximately 1.08 cm, which corresponds to a momentum resolution of ±1.8%. The inaccuracies attached to the re s u l t s arise from s t a t i s t i c a l fluctuations i n the data, which i n turn govern the accuracy in the deconvolution process. This s t a t i s t i c a l f l u c t u a t i o n appears as o s c i l l a t o r y behavior i n the deconvolved spectra, which i s apparent i n Figure 4.2(d). Fortunately, the f u l l widths of the spectra are not p a r t i c u l a r l y dependent on these fluctuations. Typical uncertainties of the f i n a l r e s u l t s are i n the range between ±3 to ±6%. I t can be seen from the d i f f e r e n t i a l range curves that the e f f i c i e n c y of S4 i s greater than 99% which, therefore, introduces n e g l i g i b l e error, whereas i n e f f i c i e n c y i n S3 would not be expected to af f e c t the r e s u l t s . F i n a l l y , the e f f e c t of beam contamination i s n e g l i g i b l e , since the electrons and ]i\ muons have greater ranges than the pions; and the y 2 muons, with a wide momentum d i s t r i b u t i o n , add a low and nearly uniform background. 4.2 Determination of the angular acceptance of M8 The angular acceptance AO, of the channel can be calculated from the following equation, ^ = N N f f • f* AT ,d'a , ( 4 ' 2 ) ' P 1 2 (dTd^ 42 where i s the pion flux detected; i s the corresponding e f f e c t i v e proton flux i n t e r a c t i n g with the carbon n u c l e i . Due to nuclear interactions of the protons with the target, N i s less than the incident proton current. N. i s the P t ef f e c t i v e number of carbon n u c l e i per unit area presented to the proton beam (see Section 3.3). AT i s the pion energy acceptance of the channel determined from the measured momentum acceptance in the l a s t section (Section 4.1). f D i s the non-decay p r o b a b i l i t y of the pions. f. and f. are 1 i x 2 the corresponding p r o b a b i l i t i e s that a pion w i l l not be l o s t inside or outside the target because of nuclear absorption or scattering. aTflo, i s the pion production cross-section at 30°. Due to energy degradation of the proton beam i n the target, the mean proton energy for pion production i s less than the incident proton energy. In fa c t , the mean proton energy i n a 10 cm C target from an incident 500 MeV beam i s 475 MeV. The r e s u l t s from Figure 3.3(b) indicates that the pion production cross-section at 47 5 MeV i s approximately 0.8 5 times that at 500 MeV for pions with momentum above 150 MeV/c. The pions w i l l also be degraded i n energy before emerging from the target. Thus, correction has be applied do-to match the values of N with r( -.m at a pion energy IT ,dTdfi * ^ J corresponding to the production energy. This correction i s small as w i l l be shown i n the following section that the production cross-sections vary only s l i g h t l y for pion energies between 60 and 100 MeV. Losses due to multiple scattering 43 of the pions are assumed to be n e g l i g i b l e since approximately the same number of p a r t i c l e s are scattered into as out of the detected beam. 4.2.1 Determination of the pion production cross-section  for 1 2C at a proton energy of 500 MeV Figure 4.4 i l l u s t r a t e s the physical set-up used i n the determination of the pion-production cross-section at a laboratory angle of 34° for carbon with an incident 500 MeV proton beam. A carbon target (0.147 gm/cm2) was placed at 45° with respect to the incident proton beam. The pions produced were accepted by a magnetic spectrometer set at 34° with respect to the d i r e c t i o n of the incident protons [.21]. The magnetic spectrometer consisted of two pole faces of 5 0 cm radius separated from each other by 0.7 5 inch,, providing an uniform magnetic f i e l d that was varied from 5 KG to 10.8 KG. The pions were bent through the spectrometer and were sub-sequently analyzed by a 2 4 - s c i n t i l l a t o r hodoscope and two s c i n t i l l a t i o n counters. The proton current was monitored by means of the polarimeter described in Section 2.5. An event i s defined by the lo g i c coincidence AC.2H..(C + C ) where the H.'s are the hodoscope bin numbers and C_. = C_.D.CTr.; C T = C n T .C T T are set up so as to avoid K U K I K Li U J J _L±J time j i t t e r and to r e j e c t random events. S i m i l a r l y , a random event i s defined by ( A C ) ^ e i a y > 2 H j • ( C R + * F O R EVERY event registered, the f i r i n g pattern of the hodoscope counters, the Beam- \ line i E in.stainless steel window sn. acceptarce carbon .counter A target / at 45° / poSarirrseter downstream A ntiSSaf ion ters hodoseopi s O f T O S C A L E ] gure 4.4 A schematic representation of the apparatus for pion-production cross-section measurements 45 pulse heights of the signals registered at counters C Q L , C Q R , C^ L, C^ R, Hj's, as well as the timings between the signals were a l l recorded and stored i n a computer [22]. The r e a l pion d i s t r i b u t i o n as a function of hodoscope bin number at each magnetic f i e l d setting of the spectrometer was obtained afte r appropriate timing cuts were applied to r e j e c t electrons and muons. Random events were subtracted with the aid of the program KIOWA [23] . These pion d i s t r i b u t i o n spectra were then converted into cross-section plots a f t e r corrections were made to account for pion decay, misalignment of the hodoscope bins, energy loss of pions i n the production target and i n the acceptance counter AC, as well as the v a r i a t i o n of the solid-angle acceptance along the hodoscope counters. A more detailed description of t h i s process i s recorded i n Appendix I. Figure 4.5 gives the f i n a l r e s u l t of the a n a l y s i s — the plot of pion production cross-section as a function of pion energy. The cross-section plateaus at approximately 5.9 yb/(MeV - sr) for pion energies between 60 MeV and 100 MeV. S t a t i s t i c a l f l u c t u a t i o n i n the number of counts i s r e f l e c t e d i n the uncertainty in the cross-section, giving f l u c t u a t i o n of approximately ±14%. There i s very l i t t l e experimental data for TT- production at 3 0° available. The only other measurement that exists to date i s the r e s u l t s from Cochran et a l for a proton energy of 730 MeV [24]. Their data show 8 d2<r dTdfl Mb (Mev-sr) A A ^ O A o o o o 0 00, A ^ A A A 1 A A A A J» A<=> O r A A 0 0 0 , A o°0 0 0 ^ ,00 A ^ v data from B= 5-0 KG B= 6-3 KG B= 7-7 KG B= 9-2 KG BHO-8 KG 20 40 60 80 PION KINETIC ENERGY (MEV) 100 120 F i g u r e 4.5 The d i f f e r e n t i a l c r o s s - s e c t i o n of negative pion p r o d u c t i o n on carbon, from a 500 MeV proton beam at 34° 47 lower cross-sections for which there i s as yet no explana-ti o n . 4.2.2 Corrections for pion nuclear in t e r a c t i o n loss i n the target f. • 1 1 For pion energies below 100 MeV, the negative pion interaction losses are mainly through absorption processes. Loss through e l a s t i c scatter may be considered n e g l i g i b l e , as can be demonstrated by the following argument. There i s no loss i n the number of detected pions i f the pion production i s i s o t r o p i c i n the laboratory frame. For the worst case, i f a l l the pions were produced at a forward angle of 30°, which i s the angle seen by the M8 channel, calculations using Rutherford cross-section formula combined with e x i s t i n g data show that a pion energy of 100 MeV [25], over 7 5% of the e l a s t i c scattered beam i s detected by the M8 channel; t h i s f r a c t i o n increases to over 91% at a pion energy of 50 MeV. Therefore, there i s enough j u s t i f i c a t i o n to assume a l l i n t e r -action losses are through the i n e l a s t i c channels. In e l a s t i c cross-sections for TT- on 1 2 C at energies below 100 MeV can be deduced from both e x i s t i n g experimental data and t h e o r e t i c a l calculations [26, 27, 28, 29, 30]. It i s calculated that f i ranges from 0.97 at 5 0 MeV to 0.94 at 107 MeV for the present work. 48 4.2.3 Corrections for pion nuclear i n t e r a c t i o n loss outside the target f^ Pions emitted from the carbon target towards the M8 channel are p a r t i a l l y screened by the target mounted above in the target ladder. Hence, there w i l l be pions l o s t through nuclear interaction external to the carbon target. Assuming a l l losses are v i a the i n e l a s t i c channels, and by scaling the i n e l a s t i c cross-sections by A 0 - 8 [29] , where A i s the atomic number of the material, together with due consideration to the phase space acceptance of the M8 channel, i t i s possible to estimate the amount of pion l o s s . Calculation shows f. 1 2 for a 30 MeV pion beam i s 0.993, decreasing to 0.982 for a 100 MeV pion beam. This correction i s also n e g l i g i b l e . 4.2.4 Results and discussion of uncertainties The angular acceptance of the M8 channel i s c a l c -ulated using the data from the pion y i e l d s at six channel momenta between 148 MeV/c and 2 00 MeV/c afte r the y 2 compon-ent of the y i e l d s has been deleted (see Figure 3.1(b)). The average Afl from these cal c u l a t i o n s i s 7.5 - 0.4 msr where the uncertainty quoted refers to the standard deviation about the average. Systematic errors i n the deduced angular acceptance arise from uncertainties i n the cross-section measurements and from the proton current c a l i b r a t i o n , giving errors of ±14% and ± 10% respectively. In addition, there i s ±10% 49 error i n the determination of the e f f e c t i v e length of the carbon target. Errors a r i s i n g from other sources are i n s i g -n i f i c a n t . Thus, the root mean square error in the angular acceptance i s ±2 0% obtained by summing i n quadrature the component errors. Combining angular acceptance measurements with the r e l a t i v e momentum acceptance curve (see Figure 4.2(d)) y i e l d s the Aft - (Ap/p) curve for the M8 channel, as shown i n Figure 4.6. It should be noted that there i s a ±20% uncer-tain t y in the Aft-axis for the experimental r e s u l t s . Results from ray-tracing simulation of the M8 channel which i s also plotted i n the same figure, shows good agreement between the t h e o r e t i c a l and experimental r e s u l t s [31]. 50 12 10 8 A H . (msr) expt'l .theoretical prediction Figure 4.6 The particle-transmission e f f i c i e n c y curve of M8 —the angular acceptance versus the momentum acceptance of the channel error bars have been plotted on several points to indicate the permitted span of An for that p a r t i c u l Ap/p 51 C H A P T E R 5 STUDY OF THE ELECTRON CONTAMINATION OF THE PION BEAM In radiotherapy, i t i s important that the contam-inants i n the beam be kept at a minimum. As can be seen from Chapter 2, the three contaminants i n the negative pion beam are muons from pion decay before B2 (yi type muons), muons from pion decay afte r B2 (y 2 type muons), and the electrons. The muons are i n t r i n s i c i n a pion beam and, therefore, cannot be eliminated e n t i r e l y . For operation of the beam l i n e above 160 MeV/c, y i ' s contribute to less than 8% of the t o t a l beam. Thus, the corresponding dose deposited i n the normal tissue i s small. In addition, y 2's w i l l not s i g n i f i c a n t l y reduce the e f f i c i e n c y of pion therapy. Being dispersed i n momentum and emitted predominantly at a r e l a t i v e l y large opening angle (approximately 14° for a 160 MeV/c pion beam) with respect to the incident pions, they deposit a low dose uniformly i n the v i c i n i t y of the stopping pions. On the other hand, the electrons pose a problem for radiation treatment. Once the pions and the muons are stopped i n the tissue, the radiation damage to the normal tissue i s completely determined by the ioni z a t i o n from the electrons. Presently, a 18 0 MeV/c pion beam produced from a 10 cm Be target at T2 t y p i c a l l y contains 28% of the t o t a l f l u x as electrons. Furthermore, the discrep-ancy between t h i s large contamination and the low electron contamination of 9% at 18 0 MeV/c reported by the SIN TTE3 medical channel [32] requires explanation. It i s es s e n t i a l 52 to minimize the electron contamination, and to do so, i t i s necessary to understand the mechanism of electron production. 5.1 Experimental findings Figures 5.1(a) and (b) show the electron component in 148 MeV/c and 17 0 MeV/c beams as the proton beam i s v e r t i c a l l y steered up and down the 10 cm Be target. At both momenta, i f the beam i s steered to the top of the target, the electron contamination can be reduced by 2 0% from the value obtained when the beam i s centered on the target. The theor-e t i c a l curves are predictions of a model which w i l l be described subsequently i n t h i s chapter. This steering e f f e c t can also be appreciated from the y i e l d curves shown i n Figure 5.2. The ' TT~ u~ e~ rates are monitored with the proton beam steered to the top and bottom of a 10 cm carbon target. For the carbon target, at pion momenta above 18 0 MeV/c, the electron contam-ination i s approximately halved. I t should be noted that the s l i g h t decrease i n the pion flux as the beam i s steered to the bottom of the target i s consistent with nuclear i n - f l i g h t i nteraction losses of pions i n the target. Another experimental r e s u l t that i s important to an understanding of the electron production.process i s the equi-valence of the detected flux of electron and positrons. Figure 5.3 shows the channel momentum dependence of the r e l a t i v e e + and e~ flux from a 10 cm Be target with a 500 MeV proton beam. TOP WM Be BOTTOM ~ -7 w a t e r j a c k e t w a t e r j a c k e t Figure 5.1 Dependence of the electron contamination i n (a)a 148 MeV/c;(b)a 170 MeV/c beam as an incident 500 MeV proton beam with v e r t i c a l standard deviation of 0.22 cm i s steered v e r t i c a l l y along the 10 cm Be target 54 0 100 2 0 0 C H A M N E L MOMENTUM ( M E V / C ) F i g u r e 5.2 N e g a t i v e p a r t i c l e y i e l d s a t t h e end o f M8 from a 500 MeV p r o t o n beam o f s t a n d a r d d e v i a t i o n o f 0.22 cm i m p i n g i n g t h e t o p and t h e bottom o f a 10 cm c a r b o n t a r g e t a t T2 I ' i J _ L_ J 0 5 0 1 0 0 1 5 0 2 0 0 CHANNEL MOMENTUM (MEV/C) F i g u r e 5.3 R e l a t i v e e l e c t r o n and p o s i t r o n y i e l d s from a 10 cm Be t a r g e t w i t h a centered 500 MeV proton beam 56 The e + data i s obtained with a l l the p o l a r i t i e s of the magnets reversed from the normal mode of operation. A t h i r d piece of evidence r e l a t i n g fcO the electron production i s the s i m i l a r i t y of the pion and eletron beam p r o f i l e s observed at the end of the channel as detected by the multiwire proportional counter. In addition, variations in the widths of the openings of the Y - s l i t s and the momentum s l i t s do not s i g n i f i c a n t l y change the electron contamination of the beam at the exit of M8. 5.2 Explanation of the experimental findings In view of the above findings, the following hypo-thesis i s formulated: A l l detected electrons a r i s e from pair  production processes i n the T2 pion production target. The equivalence of the electron and positron y i e l d s and the observed v a r i a t i o n of the electron contamination as the proton beam i s steered up and down the target are both consistent with the mechanism of pair production. Furthermore, i f the hypo-thesis were v a l i d , variations of the s l i t openings of the M8 channel would not change the electron contamination. This agrees with the experimental r e s u l t s . Since there i s assumed to be no non-target source of electrons, minimization of the electron contamination can be accomplished with changes only i n the target design. In the 57 following sections, a model of electron production w i l l be constructed based on the above hypothesis and i t w i l l be shown to be completely i n agreement with a l l the experimental res u l t s and to be consistent with the findings from the TRIUMF M9 and SIN TTE3 channels. 5.2.1 Sources of electrons As the proton beam str i k e s the target, the following reaction sequences give r i s e to y-rays, which in turn can produce positrons and electrons by Y - c o n v e r s i ° n -(1) TT° production p + X •> p + X + TT0 (X i s the target • nucleus) TT0 2y y -*• e + e~ Due to the very short l i f e - t i m e of IT° (CT * 2.5 x 10 - 6cm), the TT° decays into two gamma rays within a few atomic l a t t i c e s i t e s i n the target. (2) Radiative capture by neutrons of protons i n f l i g h t np ->• Y Y •> e + e~ (3) Radiative absorption of pions i n nuclei TT + X X* + Y (x* represents the + _ nucleus i n an Y ->- e + e , , , , , s 1 excited state) 58 (4) Bremsstrahlung from pp and np c o l l i s i o n , etc. (pp •> ppy\ np •> npy/ Y e +e~ In the proton and electron energies under considera -h t i o n (T * 500 MeV, T > 100 MeV), processes (2), (3), and (4) p e have very small cross-sections compared to the f i r s t process [35, 56 - 61]. Thus i t s h a l l be assumed a l l gamma rays that contribute to the production of the detected electrons are from TT° decay. 5.2.2 Determination of the gamma-energy spectrum and d i f f e r e n t i a l cross-section for y-emission at 30° Theoretical prediction of the electron contamination necessitates a knowledge of the energy spectrum and d i f f e r e n -t i a l cross-section for Y - e m i s s i ° n a t a laboratory angle of 30°. Consider a proton impinging on a nucleon in a target nucleus which i s at res t . Due to the Fermi motion of the nucleons i n the nucleus (average Fermi momentum = 220 MeV/c), there i s no unique center of mass system for t h i s process. Fortunately, i f the momentum of the incident proton i s large compared to t h i s Fermi momentum (for example, at a proton energy of 500 MeV, the corresponding momentum i s 1090 MeV/c), the spread of the center of mass v e l o c i t y i s obviously small. In f a c t , Bayukov et a l and Crandall et a l v e r i f i e d that at 59 proton energies between 300 and 500 MeV [35, 39], the "re-production process can be viewed as r e s u l t i n g from protons bombarding independent nucleons that are t r a v e l l i n g i n the opposite d i r e c t i o n from the incident proton. Therefore, the center of mass v e l o c i t y i s given by 8 ^ c = . y 8- - 0.223 c of m 'p p c (K -\\ Y + 1.025 v - x ; The process of 7T°-photon emission has been studied extensively i n the period 1950-1964 [33-44]. The following i s a summary of the res u l t s that are relevant to the prediction. Unless otherwise stated, a l l conclusions are related to the center of mass frame. 1. The Tr° energy and angular d i s t r i b u t i o n s can-be treated independently. Bombardment of the nucleus by protons of laboratory energy of 470 MeV re s u l t s i n T T O I S produced predominantly at t h e i r maximum possible energy allowed by kinematics. At higher proton energies, the TT°'S are produced at energies considerably lower than the maximum allowable energy [38, 39]. 2. The TT° angular d i s t r i b u t i o n ty^ {Q Q £ m) can be repre-sented by Ea p (cos0 £ ) where 9 £ i s the polar J n n rn* c of m c of m v angle with respect to the proton beam d i r e c t i o n in the center of mass frame. At proton energies below 500 MeV, cj) (6 c ) i s dominated by a cos 20 - contribution. TT c or m -1 c of m 60 However, as the proton energy increases beyond 600 MeV, ^ T T ^ C Q f m) becomes more i s o t r o p i c due to the manifestation of the 3-3 resonance behaviour. In fact, i t has been shown that for a 1 2C nucleus [38], 2.5 + cos 20 at T = 660 MeV, P II c of m I 0.2 + cos 2 9 at T =47 0 MeV. And for a 9Be nucleus, W6 - ) * 0.15 + cos 26 at T = 47 0 MeV. " c of m ^ P 3. The y energy spectrum and angular d i s t r i b u t i o n are completely determined by the TT? energy and angular d i s t r i -butions. If Tr°-mesons are created with v e l o c i t y 8 Q C / then assuming that there i s no screening e f f e c t s , the photon spectrum and angular d i s t r i b u t i o n i n the center of mass frame can be represented by [40] c c of m c of m Ho' c of m 1 E a P, (cose c )P ( 1 [1 - k o ]) — n n c of m n -r— po Yo p o T o c of m dftdk _ (5.2) c of m where Y 0 = (1 - B^ 2 )" 1 ' 2 ^c of m = P h ° t o n energy i n the center of mass frame dft = observer's s o l i d angle i n the center of mass frame k = 1/2 m c 2 o T T 0 Using a r e l a t i v i s t i c transformation, the Y - s P e c t r u m in the laboratory frame I(k, 9, 3 ) i s related to I (k £ , o c c of m e - ,3 ) by [35] c of m *o •* I (k , 6 - , 3 ) = Y 4= (1 - B * cosf c c of m c of m o 'c of m c of m Kk,e,3 0) (5.3) k ^ = k v _ ( l - 3 _ cosG) (5.4) c of m 'c of mv M c of m ' cos6 c of m (cose - t - 3 ^ ) c o i m ( 1 - 3 ^ cose-)7 c of m (5.5) The y-energy spectrum i s in s e n s i t i v e both to the type of nucleus and to the v a r i a t i o n i n the Tr° angular d i s t r i b u t i o n at y energies above 12 0 MeV. Due to meson scattering and nuclear screening of the protons by the nucleus, the Y - a n ,?ular d i s t r i b u t i o n becomes more anisotropic as-the mass number of the nucleus increases. However, t h i s screening e f f e c t becomes weaker as the angle of emission of the Y's increases. It has been shown experimentally that the Y - a n i 3 u l a r d i s t r i b u t i o n i s i s o t r o p i c 62 for the case of 1 2C bombarded by protons of energy 470 MeV in the laboratory frame [3 6]. 6. The TT° production t o t a l cross sections have been measured for 1 2C as a function of proton energies between 17 5 MeV and 660 MeV in the laboratory frame (see Figure 5.4) [44]. Moreover i t i s v e r i f i e d experimentally that over the range from hydrogen to lead, a^o (total) °= [Z+N/a \ ] 2 / 3 (5.6) where a = 6.3 i 0.4 mb np IT 0 a = 3.22 ± 0.17 mb for T = 665 MeV PP P Z, N are the number of protons and neutrons per nucleus. 7. The y-emission emission cross section da^(6) i n the laboratory frame can be expressed by da IB) = 1/dcose . m \ (2o,) (5.7) an " Vdcos 'e \ (2a i of m j TT where 9. depends on the angular and energy d i s t r i b u -tions of the TT0 meson i n the center of mass frame. For an i s o t r o p i c IT 0 angular d i s t r i b u t i o n , Q equals 4TT; whereas 200 300 400 500 PROTON KINETIC ENERGY (MEV) 600 F i g u r e 5.4 Dependence of TT° t o t a l c r o s s s e c t i o n on the i n c i d e n t proton energy(see r e f e r e n c e no. 44) 64 for a cos 2 6 d i s t r i b u t i o n , ft reduces to 2.5TT. In p a r t i c u l a r , for 470 MeV protons impinging on beryllium, ft i s approx-imately equal to 2.76TT. The- term / dcos8 c Q^ A arises \dcos6 / from s o l i d angle transformation between the center of mass and the laboratory frame, which i s given e x p l i c i t l y by /dco.s.0. r „\ 1 - 8 . . .c. „ ,c o\ [ c of m\ = H c of m (5.8) Vdcos0 J ( i - 8 C Q f mcos9.) * For 475 MeV protons on beryllium, i t can be shown that d a X (30°) * 0.4220^0 (5.9) dft Using the r e s u l t that the Tr° production process at proton energies near 4 75 MeV can be viewed as protons impinging on independent nucleons, for f i r s t order approximation, ^TT 0 ^ c of m^  w o u l d b e independent of the type of target nucleus. Therefore, for the present study, i t i s assumed that Equation 5.9 holds true for a l l types of nucleus at a proton energy of 475 MeV. The TT° production cross-section and the gamma emission d i f f e r e n t i a l cross section at 30° are tabulated i n Table IV. Based on the above summary of experimental r e s u l t s , the Y - e m i s s i ° n energy spectrum at a laboratory angle of 3 0° can be approximated, as follows. TABLE IV TT° PRODUCTION TOTAL CROSS-SECTIONS AND GAMMA DIFFERENTIAL CROSS-SECTIONS FOR VARIOUS ELEMENTS Element N L + « J : ^ - ' 3 b PP (mb) a,b da .mb> a, b &Qy [sr> 5 6 8 30 34 125 6 8 26 29 82 0. 85 1.00 1.21 2.84 3.07 6. 97 9.5 11.1 13.4 31.5 34.1 77.4 4.0 4.7 5.7 13.3 14.4 32.7 Notes: a. for a 475 MeV proton beam b. a l l data are normalized with respect to the data for carbon y-emission at a laboratory angle of 30° corresponds to emission at 42.5° i n the center of mass frame for an incident proton energy of 475 MeV. To a f i r s t order approx-imation i t can be assumed that no nuclear screening e f f e c t i s present, and that the shapes of the Y ~ e n e r g y spectrum for a l l types of n u c l e i are i d e n t i c a l . Therefore, i f the Y - e n e r g y spectrum for a p a r t i c u l a r angle of emission i n the center of mass frame were known, the shapes of the Y - e n e r g Y spectra at a l l angles would be completely determined through equation 5.2 Moreover, since the TT 0'S are produced at the maximum allowable energy when the nucleus i s bombarded by protons of energies near 470 MeV i n the laboratory frame, the variables Yo a n<i Bo in the equation can be treated as constants. In f a c t , i t can be deduced from reference 38 that 8 0 i s approximately 0.8. Thus, for the process of 475 MeV protons impinging on a nucleus, i t can be shown that I (k , 0 „ , 8 0 ) ? 0.48 + (1.55y2 - 0.33)A c c of m c of m ° ^ J (5.10) where y = (1 - 4 0.5 ) c of m A = P 2(cos e c o f m j Since the shape of I(k, 180°) at a proton energy of 470 MeV on Be i s known [38, 39], the shape of the Y - e n e r ( ? y spectrum at 30°, I (k, 30°), can be deduced by applying equa-tions 5.3, 5.4, 5.5 and 5.10. The r e s u l t of t h i s c a l c u l a t i o n 4 , derived from Baiukov et o!{!957) INTENSITY -\ T p = 475MeV \ lab. angle 3 0° INTENSITY > RELATI / i 1 < 0 100 200 GAMMA 300 400 ENERGY (MEV) F i g u r e 5.5 The gamma energy spectrum a t a l a b o r a t o r y angle of 30° f o r an i n c i d e n t 475 MeV proton beam 68 i s shown i n Figure 5.5. 5.2.3 Determination of the pair production cross sections ( E J 'PP Production of electrons with t o t a l energy E_ (kinetic energy T) requires Y - energy k greater than (E_ + 0.511) MeV. Neglecting the e f f e c t of the repulsion of the positrons by the nucleus, which s l i g h t l y favours e + production, then according to reference 45 (azo \ (k, E_) dE_dk \dkdT/ PP In /2 E+ E- - | - c(c)\ dkdE V 3k 2 ' for 2 < C < 15 and = I (k)cj) 1 k (E+z + E_ 2 ) {<h (c) - t l n Z ) + 2 E + E -J J 3 k 2 |<P2 (C) " flnZ}J dkdE for 0 $ C ^ 2 (5.11) where E + + E electron. = k; m Dc 2 i s the rest mass of the 69 c (C) 100kmoc' E +E_Z 1/3 0.58637C _ 1.3 9 2 8 3 <J>1,2 (?) 20.774 exp (-0.1798^) cf>i (?) -{exp - ( C + 0.1165)/0.2966) 0 < C $ 0.8 19.6720 exp (-0.1163C) 0.8 < C << 2 (5.793 x 10~ 2 8)Z 2cm 2 Thus, I(k) i s the normalized gamma energy spectrum where I(k) = I (k) /0°°I(k)dk da dT (E )dE PP U: d 2a dk E dkdT dE (5.12) It should be noted that since E_ i s usually much greater than m 0c 2, the electron produced w i l l i n general t r a v e l in the same d i r e c t i o n as the i n i t i a l y-rays. The opening angle for an 150 MeV electron i s approximately three m i l l i -radians. Calculations were performed using the derived gamma spectrum (Figure 5.4) at a proton energy of 475 MeV. Figure 5.6 shows the electron energy dependence of the pair production 5 I -_» I I —_J 1 1 —I— 0 100 120 140 160 180 200 ELECTRON ENERGY (MEV) F i g u r e 5.6 Dependence of the p a i r p r o d u c t i o n c r o s s - s e c t i o n on e l e c t r o n energy f o r b e r y l l i u m 3 CM > LLl o 0 ) X CVJ N I b|}-•oj-o 0 1 0 0 MEV 150 MEV 180 MEV 2 0 0 MEV 2 0 4 0 6 0 8 0 Figure 5.7 Dependence of the pair production cross-section on Z of the nucleus as calculated from equation 5.12 72 cross section for the case of beryllium. The cross-section decreases with increasing electron energy. In p a r t i c u l a r , the cross-section at 200 MeV i s approximately two and a half times less than that at 100 MeV. Figure 5.7 i l l u s t r a t e s nucleus, which i s as expected for pair-production processes. 5.2.4 A model for electron and pion production i n the target by taking the simple case of a proton beam s t r i k i n g a long N o production target characterized by the parameter a = —J-^; where p, A are the density and the atomic number of the material, and N 0 i s the Avogadro number. The e f f e c t i v e length of the target as seen by the channel i s denoted D. Assume the channel to have a fixed angular acceptance Afi about an angle of 3 0° to the proton beam and a fixed momentum acceptance (Ap/p) about a mid-line momentum p, which gives corresponding electron and pion energy acceptances of AT g and AT^. P a r t i c l e production i s considered to be i n the X-Z plane only (see Figure 5.8). Furthermore, i t i s assumed that none of the p a r t i c l e s lose energy i n t r a v e l l i n g through the target. Then, the Z 2 dependence of the cross-section on the type of The basic concepts i n the model can be i l l u s t r a t e d (5.13a) o (5.13b) where N e ( x 0 ) , N ^ t x J are the number of electrons and pions TO MS CHAMNEL Figure 5.8 A schematic representation of the electron and pion production model (see text for details) 74 detected; N (x 0, x) i s the proton i n t e n s i t y p r o f i l e i n the x-direction with the centroid at x 0 , i n s p e c i f i c , for a gaussian d i s t r i b u t i o n . N (x c,x) = N^ exp -(x - X0)2/2CT 2 /o~2 a/Tn Np i s the proton current a i s the standard deviation of the of the proton spot i n the x-direction. i s the pr o b a b i l i t y of gamma ray production, P = (do \ AftaD [see section 5.2.2] V dft / P g(x) i s the p r o b a b i l i t y of electron production given that the gamma exi s t s , P g (x) = 1 - exp(-aaxsec30°) (d?) a = (do) ( T e ) A T e [see section pp 5.2.3] T e i s the energy of the detected electron. P^ i s the pr o b a b i l i t y of IT - production, P / d 2 g \ AT AftaD \ dTdft ) 7 7 note that / d 2 g ) aN 2 / 3 and / d 2 g | i s known for carbon [chapter 4] VdTdjW (x) i s the p r o b a b i l i t y that the pions w i l l not be l o s t due to nuclear interaction (see Chapter 4), P^ (x) = exp(-mxsec30°) m •= N pp xs the i n - f l i g h t in t e rac t ion coe f f i c i en t . P D i s the non-decay p r o b a b i l i t y of the pions a f t e r traversing the channel of length d , c P_(x) = exp(-d m C 2/PT) D c TT ' " ' CT = 7.804 meters (decay length of pions) Since N e(x Q) and 1ST (x 0) can be evaluated numerically, the pion and electron production from the target can be calculated. 5.4.2.1 Correction for the water jacket Refinements to the above model are necessary before proceeding with the c a l c u l a t i o n s . One correction i s to account for the water jacket that encompasses the target (see Figure 5.9). The target i s wrapped i n s t e e l wire providing a snug f i t i n the cassette. The r a t i o of water to s t e e l i n region 2 0«5 0 - 0 2 5 4 CM W A L L !-5 C M STABMLESS STEEL ( REGION I ) WATER & STEEL WIRE C REG80M 2 ) ( R E G I O N 3 ) [ N O T T O S C A L E ] O - S C M F i g u r e 5.9 A c r o s s ^ - s e c t i o n a l view of the pio n - p r o d u c t i o n t a r g e t T2 77 by volume i s approximately 1.7. Since t h i s water jacket i s of high Z material i t provides a very e f f e c t i v e source for y-conversion to electrons. Table V summarizes the r e l a t i v e merits of each material of the target i n terms of electron and pion production. From the tabulated r e s u l t s , i t can be seen that the water jacket generates a considerable number of electrons while i t produces comparatively few pions. The equivalent thickness for Y - c o n v e r s i ° n from the upper portion of the water jacket i s 2.22 cm of beryllium (compared with the height of the beryllium target which i s only 1.5 cm). 5.2.4.2 Correction for the energy degradation of p a r t i c l e s Due to degradation, the energies of the pions and the electrons at the point of production i n the target are higher than t h e i r detected energies at the end of M8. Over the momentum range under consideration (150 - 200 MeV/c), t h i s w i l l have n e g l i g i b l e e f f e c t on the predicted number of pions produced since the pion production cross-section i s approximately constant i n t h i s energy range. However, t h i s i s not so for the electrons. The pair production cross section decreases sharply with an increase i n the electron energy. Therefore, a correction has to be applied to obtain the mean pair production cross-section i n the electron production process. The parameter P , which describes the p r o b a b i l i t y of electron production (see Section 5.2.4) i s to be modified to TABLE V A COMPARISON OF THE SIGNIFICANCE OF EACH REGION OF THE T2 TARGET IN NEGATIVE PION AND ELECTRON PRODUCTION ci b C cl G Region Material Relative a Relative Relative Relative Relative m vdT ;pp .dfi 'V vdTdfT ir 1 Fe 0.687 39.2 3.31 9.65 4.32 ^ oo 2 Fe+H20 0.427f 17.2 f 2.13f 2.10f 2.77f 3 Be 1.000 1.0 1.00 1.00 1.00 Notes: a. a <=c Nop/A b. see Figure 5.7 c. see Table IV d. e. d 2 a , a 2/3 dTd^ J / " m a A (see f. the e f f e c t i v e 29) i , n fra c t i o n of Fe 3 ilated with T—. C „ ,. = — f r a c t i o n of H O 5 79 P e = 1 - exp(-£sec30°) (5.14) where as defined in Appendix I I , i s a function of the thicknesses of the various regions of the target cassette assembly. 5.2.5 Results of the calculations of p a r t i c l e production With the above corrections included i n the model, ca l c u l a t i o n of the pion and electron production from the water-cooled beryllium target was carr i e d out. The pion y i e l d was adjusted to account for muon contamination i n the beam. Results of these calculations are summarized i n Figures 5.1(a), (b) and 5.10. Experimental data are also presented for comparison. It can be seen that there i s escellent agreement between the predictions of the model and the actual measurements. As an independent check, calculations were repeated for the pair production cross-sections, gamma energy spectrum and production cross-section at 135° for the M9 channel. Along with the interpolated r e s u l t s of the pion production cross-sections from the ex i s t i n g data [46, 47, 48], positron contamination was calculated to be 13% and 1.8% at 100 MeV/c and 140 MeV/c respectively, comparing favourably with the measured values of 10% and 2% at the corresponding momenta [4 9]. This theory of electron production explains the contamination r e s u l t s obtained at other incident proton energies. 80 z o < Z < H Z O O 60 40 z o IT H 20 o LU _ J LU EXPT L THEORETICAL CO o J_ 100 F i g u r e 5.10 125 150 175 200 CHANNEL MOMENTUM (MEV/C) 225 Dependence of the e l e c t r o n contamination on the channel momentum f o r a 10 cm Be t a r g e t a t T2. The i n c i d e n t proton energy i s 500 MeV 9 81 Examination of Equations 5.1 and 5.8 indicates that the solid-angle transformation i s i n s e n s i t i v e to v a r i a t i o n i n proton energy, and for energies below 500 MeV, 0. stays approximately constant. Thus, the dependence of<^^- on proton energy i s completely determined by o^0. Furthermore, the y-energy spectrum observed in the laboratory frame w i l l be shifted to lower energies as the proton energy decreases, reducing the pair production cross-sections for electron energies above 100 MeV. Hence, as the proton energy decreases, the electron production also decreases due to both the decrease in o^0 and the pair production cross-sections. However, Figures 3.3 and 5.5 show that for Tf" momenta above 150 MeV/c, the TT- production cross-section decreases more rapidl y than o^0 with decreasing proton energy. Thus, the reduced prod-uctions of both the electrons and negative pions compensate each other. Hence, the electron contamination of the pion beam should be i n s e n s i t i v e to v a r i a t i o n in the proton energies below 500 MeV, as confirmed by the experimental r e s u l t s shown in Figure 5.11. Since there i s excellent agreement between the experimental findings and the predictions derived from the t h e o r e t i c a l framework based on the hypotheses stated i n the beginning of t h i s section (Section 5.2), minimization of the electron contamination can be accomplished by changes i n the target design. Figure 5.12 shows the predicted electron contamination plotted against the channel momentum 82 for various target configurations. If the production target i s completely exposed on the top, the electron contamination becomes less than 10% for a 120 MeV/c beam. This greatly enhances the possible momenta that could be used for radio-therapy. For the case of the 10 cm Be target with top surface completely exposed, the electron contamination would be reduced to less than 3% at 180 MeV/c, which i s approximately an eigh t f o l d improvement over the present value. F i n a l l y t h i s understanding of electron production, makes the reported low contamination for the SIN TTE3 biomedical channel no surprise. Since the geometrical configuration of the TTE3 production target i s complicated, and since the gamma energy spectrum at proton energies of 550 MeV i s not a v a i l -able, c a l c u l a t i o n of the electron contamination for the TTE3 channel has not been performed. However, i t can be seen from the theory established i n t h i s chapter that most of the electrons detected by the M8 channel comes from the water-jacket of the T2 target. Since the production target employed by SIN i s radiatively-cooled, the electron contamination i s expected to be much lower. | 6 0 < z o o LU LU 0 10 CM BE 300 00 MEV/C 148 MEV/C I80MEV/C 200 MEV/C J_ 400 500 INCIDENT PROTON ENERGY (MEV) Figure 5.11 Dependence of the electron contamination on the incident proton energy on a 10 cm Be target 10 CM BE 60 O < < 40 "Z. o o o cc l~ 20 o UJ _1 UJ no change in target design target with region 2 removed 100 F i g u r e 5.12 120 140 160 !80 200 CHANNEL MOMENTUM (MEV/C) 220 The e f f e c t on the e l e c t r o n contamination by changes i n the t a r g e t d e s i g n . For a l l t a r g e t c o n f i g u r a t i o n s , ^ 500'MeV proton beam with standard d e v i a t i o n of 0.2 cm i s impinging the t a r g e t a t 0.2 cm below i t s top su r f a c e 85 CHAPTER 6 STUDY OF THE PION PRODUCTION TARGET MATERIAL Prudent choice of the pion production target i s needed i n order that an intense pion beam with low contam-ination may be obtained. Studies had already been made in 1971 i n the design stage of the cyclotron regarding the target material at T2 [50, 51]. However, with a better know-ledge of pion production cross-sections and the l i m i t a t i o n s imposed by the M8 channel, a survey of the r e l a t i v e merits of various targets i s needed. Ba s i c a l l y , there are three constraints on the choice of target imposed by the beamlines, as follows, 1. The maximum target length i s to be less than 7.4 cm (see Chapter 3). Further increase in the length of the target w i l l not contribute to any increase i n the pion flux and w i l l only increase the neutron radiation background, en-hance the beam s p i l l , and degrade the in t e n s i t y and the energy of the proton beam. 2. After passing through T2, the proton beam i s to be trans-ported through a series of quadrupoles to the Thermal Neutron F a c i l i t y (TNF). Calculations regarding the beam s p i l l beyond T2 are being carried out by TRIUMF beam phy s i c i s t s . The beam emittance at T2 i s not to be degraded more than that from a 10 cm Be target at a proton energy of 500 MeV. For a f i r s t order c a l c u l a t i o n , assuming no 86 decrease i n proton energy as the beam traverses the t a r -get, the multiple scattering angle i s given by <02> V* 17.5 P8c 1 + 0.1 logi Ol'0x (6.1) where x i s the target thickness L^ . i s the radiation length of the target material p i s the momentum of the protons i n MeV/c 6c i s the v e l o c i t y of the protons [52] # Thus, for a 10 cm Be target, < 0 . 2 > 1 / 2 equals 11.7 mrad. The corresponding beam s p i l l at the collimators immediately downstream of T2 amounts to 12.5% of the i n i t i a l beam cur-rent. Since <Q,2>V2 increases with decreasing proton energy the maximum allowable target thickness decreases with decrease i n proton energy. Figure 6.1 gives the dependence of (x/L ) on proton energy. For an incident proton K max energy of 450 MeV, the maximum allowed thickness of Bef? C; Cu are 8.43 cm; 4.44 cm (assuming p = 2.3 gm/cm3); and 0.35 cm respectively. 3. In order that the radiation l e v e l i n the v i c i n i t y of T2 be minimized and that the transmission to TNF be optimized, the maximum proton beam loss at T2 must be less than 25%. Assuming losses only through i n e l a s t i c processes, the maximum target thickness t max i s given by 300 400 500 PROTON ENERGY (MEV) Figure 6.1 Dependence of the maximum allowable target thickness at T2 on the incident proton energy (x and L R are as defined i n the text) 88 t [cm] = 4.7764 x 1 0 - 2 5 A (6.2) where p, A are the density [gm/cm3] and atomic number of the material respectively. a_ i s the reaction cross-sections [cm3] tabulated in l i t e r a t u r e [53]. Note that a D, hence t , i s i n s e n s i t i v e to v a r i a t i o n i n proton K max energy beyond 250 MeV. In practice, t h i s i s a weaker constraint than the second one. The beam s p i l l for a 10 cm Be target i s 22%, which i s c e r t a i n l y below the previous imposed l i m i t . If there were no constraints imposed by the beam s p i l l s , the sole figure of merit for pion y i e l d would be determined by the luminosity index P , which i s the pion l i y i e l d per MeV-steradian per proton per unit target length, P T = d 2g N 0p (6.3) dTdft A Since the cross-section i s proportional to N2^3 >[24, 46], the r e l a t i v e merit of each material i s determined by (N2/3 p/A) , which would favour the high Z elements and c e r t a i n inorganic compounds. However, minimized electron contamination favours low Z material (see Chapter 5). Therefore, choice of the target i s a balance between these two factors. In pion therapy, the maximum tolerable l e v e l of electron contamination i n a 180 MeV/c beam i s approximately 89 20%. Assuming a gaussian-shaped proton beam with v e r t i c a l standard deviation of 0.2 cm incident on an uncooled target at 0.2 cm below i t s top surface, i t i s calculated that aluminum oxide i s the best choice; for the same dimensions, there i s a 1.5 times increase i n the TT~ f l u x over that obtainable from a beryllium target. Chapter 5 shows that the corresponding electron contamination in a 18 0 MeV/c beam would be 4% i f a beryllium target were used. On the other hand i n view of the above three con-s t r a i n t s , a new figure of merit for pion y i e l d P has to be used, where P = p L x e f f i - s the maximum allowed pion flux constrained by x which i s the e f f e c t i v e maximum err target thickness allowed by the three constraints. The maximum physical target thickness x , determined by the — ^ max 2 multiple scattering i s further reduced by the non-uniform acceptance of M8 along the length of the target as described in Chapter 3 to give an e f f e c t i v e maximum thickness x e f f In determining P, the cross-section at proton energy T^ i s scaled from that at 500 MeV by (T - 350)/(500-350) , as established from Figure 3. Pertinent data used i n t h i s analysis i s given i n Table VI. Table VII gives the resu l t s at proton energies of 500, 450 and 430 MeV. These r e s u l t s conclude that a beryllium target i s most desirable with the present imposed l i m i t s . I t i s 90 favoured f o r both IT - flux-maximization and contaminant-min i m i z a t i o n . Carbon i s the next best choice. Because i t i s more porous than b e r y l l i u m , the produced gas w i l l escape e a s i l y when the t a r g e t i s i r r a d i a t e d at high i n t e n s i t y . Furthermore, Table VI shows t h a t i f more beam s p i l l were allowed at the c o l l i m a t o r s downstream of T2, a more luminous t a r g e t , (for example, aluminum o x i d e ) , would be favoured. TABLE VI PERTINENT DATA IN THE CHOICE OF TARGETS Element Z p (gm/cm3) A (gm/mole) L R (gm/cm2)a a R (mb) fo r e l a t i v e TT Xsec Be 4 1.848 9. 01 66 200 1.00 C 6 2.3 12.01 43. 3 220 1.13 Al 13 2.7 26.98 24.3 420 1.99 Fe 26 7. 87 56 13.9 690 3.31 Cu 29 8. 96 63. 54 13.0 750 3.67 Pb 82 11.35 207.19 6.4 1780 8.66 A1 20 3 - 3. 97 101.96 29. 5 C - 8.07° FeB - 7.15 66.66 48.54° - 4.40° Notes: a. from reference no. 54 b. scaled with N 2 / / 3 c. values estimated from the composition of the constituents of the compound 92 TABLE VII DEPENDENCE OF THE MAXIMUM PION YIELD PER PROTON ON THE TARGET MATERIAL AT VARIOUS PROTON ENERGIES Element 500 MeV 45 0 MeV X (cm) max r e l a t i v e P X (cm) max 430 MeV r e l a t i v e P X (cm) max r e l a t i v e P 12.5% beam loss at the collimators Be 7.4 1.00 7.4 0. 67 7.4 0.53 C 5.27 0.87 4.44 0.51 4.14 0.38 Al 2.52 0.41 2.12 0.23 1.98 0.18 Fe 0.49 0.19 0.41 0.11 0.39 0.08 Cu 0.41 0.18 0.35 0.10 0.32 0. 07 Pb 0.16 0. 06 0.13 0. 03 0.12 0. 03 A1 20 3 2. 08 0.60 1.76 0.34 1.63 0.25 FeB 1.90 0.83 .1. 6.1. 0.47 1.49 0.35 25% beam loss at the collimators Be 7.4 1. 00 7.4 0.67 7.4 0.53 C 7.4 1.06 7.4 0.71 7.4 0.56 Al 4.77 0.74 4. 03 0.43 3.74 0.32 Fe 0.93 0.36 0.78 0.20 0.73 0.15 Cu 0.78 0.34 0. 66 0.19 0. 61 0.14 Pb 0.30 0.12 0.26 0. 07 0.24 0. 05 A1 20 3 3.94 1.10 3.33 0.63 3. 09 0.47 FeB 3.60 1.52 3. 04 0.87 2.82 0. 65 93 CHAPTER 7 RECOMMENDATIONS, SUMMARY AND CONCLUSION The r e s u l t s presented i n t h i s study serve as a basis for understanding some of the c h a r a c t e r i s t i c s and performance of the biomedical channel at TRIUMF. It i s in s t r u c t i v e at t h i s point to compare the design s p e c i f i c a t i o n s with the actual attainable values for the channel character-i s t i c s , as summarized i n Table VIII. From the table, i t can be concluded that the actual achieved pion f l u x i s approx-imately three times less than what was expected. Therefore, with no change i n the status of operation i n terms of incident energy, beam tunes and target configurations, i t i s question-able whether the pion flux i s f e a s i b l e for treatment. This i s beyond the scope of t h i s study but should be seriously considered by the radiotherapists. The three-fold reduction i n the anticipated pion flux due to the poor transmission e f f i c i e n c y of the biomedical channel and also the high electron contamination in the pion beam can be corrected by changing the operating mode of TRIUMF. A summarized proposal i s presented i n Table IX. The proton current delivered to T2 i s limited by gas str i p p i n g and electromagnetic d i s s o c i a t i o n of the H~ ions, and i s ultimately limited by the capacity of the ion source. By maintaining the tank pressure below 5 x 10~ 8 t o r r and by decreasing the proton energy to 450 MeV, the extracted proton beam could be inten-s i f i e d . I t i s shown i n Chapter 3 that the maximum pion flux 94 delivered to M8 would be increased s i g n i f i c a n t l y . In part-i c u l a r , at a tank pressure of 1 x 10 - 8 t o r r , the maximum pion flux would increase to 4.8 x 10 8 per see, which i s a three-fold increase over the presently anticipated value attainable with a 100 yA, 500 MeV proton beam. No change in the material of the pion production target i s needed. From Chapter 6, i t i s also shown that carbon and aluminum oxide should be considered as alternative candidates i f increased beam s p i l l i n the v i c i n i t y of T2 i s allowed. The proton beam p r o f i l e at the T2 target should be changed from a v e r t i c a l spot to a horizontal one bombarding the top surface of the target in order to minimize the electron contamination. This change i n the beam p r o f i l e can be accomplished r e a d i l y by adjusting the magnetic f i e l d s of elements 1Q12, 1Q13, 1SM6 and 1SM7 i n Beam Line 1. In s t a l l a t i o n s of any extra quadrupoles i n Beam Line 1 i s unnecessary. A complete redesign of the cooling system of the target i s necessary. At the present, the electron contamination i s mainly due to y-conversion i n the water cooling jacket. The top surface of the target should be bared to minimize the electron production. In t h i s manner, the electron contamination can be reduced to a l e v e l that i s no longer a concern i n pion therapy. F i n a l l y , the proposed operating mode w i l l require adequate shielding for 450 yA to be i n s t a l l e d i n the meson h a l l . 95 In conclusion, through t h i s study, a basic under-standing of the pion flux and contamination of the biomedical channel has been achieved. This knowledge has been s u f f i c i e n t to allow recommendations to be made for changes i n the mode of operation of Beam Line 1 and the Biomedical channel, so that they w i l l be better suited for radiotherapy. 96 TABLE VIII A COMPARISON BETWEEN THE DESIGN AND ACHIEVED SPECIFICATIONS OF THE M8 CHANNEL Spe c i f i c a t i o n Design Achieved Momentum resolution Acceptances (i) momentum (i i ) angular Total length of the channel Pion production target thickness Pion production cross-section for carbon(100 MeV pions) ±1% ±10% 10 msr 7 meters 10 cm l i b MeV-sr ±1.3% ±(6.6+0.4)% 7.5±0.4 msr 7.2 meters 5.8±0.5 cm 5.9±0.8 yb MeV-sr Notes: a. from reference no. 11 97 TABLE IX RECOMMENDATIONS FOR CHANGES IN THE OPERATING MODE OF TRIUMF FOR PION THERAPY Spe c i f i c a t i o n Present Status Proposed Cyclotron tank pressure —8 5 x 10 tor r (1-5) x 10~8torr Proton energy . 500 MeV 450 MeV current lOOyA 220-450yA beam p r o f i l e at T2 1.5(H)x0.5 (W) cm2 <0.3 (H)xl.5 cm2 striking.the center s t r i k i n g -0.2 cm of the target from the top surfj of the target T2 target: material Be Be physical dimension 1.45 (H.)x0.5 (W)x 10(T) cm3 1(H)x2(W)x8(T) cm with bare top encased i n water surface jacket Maximum TT flux at 2 00 MeV/c 8 1.6 x 10 per sec 2.3 to 4.8 x 108 per sec Electron contamination 16% at 200 MeV/c 42% at 150 Mev/c -3% at 200 MeV/c ^5% at 150 MeV/c 98 BIBLIOGRAPHY P.H. Fowler and D.H. Perkins, "The P o s s i b i l i t y of Therapeutic Applications of Beams of Negative TT-Mesons". Nature 18 9, 524 (1961). P.H. Fowler, "1964 Rutherford Memorial Lecture: Tr-Mesons versus Cancer?". Proceedings of the Physical Society (London) , 8_5, 1051 (1965) . C. Richman, H. Aceto, M.R. Raju and B. Schwartz, "The Radiotherapeutic P o s s i b i l i t i e s of Negative Pions". American Journal of Roentgenology, Radium Therapy and Nuclear Medicine, 96, 777 (1966). M.R. Raju and C. Richman, "Negative Pion Radiotherapy: Physical and Radiobiological Aspects". Current Topics in Radiation Research Quarterly 8_, 159 (1972). M.I. Henry, "Dose Calculations r e l a t i n g to the use of negative pi-mesons for radiotherapy". M.Sc. Thesis, University of B r i t i s h Columbia, 1973. J.R. Richardson, E.W. Blackmcre, G. Dutto, C.J. Kost, G.H. Mackenzie and M.K. Craddock, "Production of Simultaneous, Variable energy beams from the TRIUMF cyclotron". IEEE Transactions on Nuclear Science, NS-22, No. 3, 1402 (1975). R.M. Pearce, ed., "Experimental F a c i l i t i e s at TRIUMF" TRIUMF Internal Report, TRI-75-2, (1975). M.K. Craddock, E.W. Blackmore, G. Dutto, C.J. Kost, G.H. Mackenzie, J.R. Richardson, L.W. Root and P. Schmor, "Properties of the TRIUMF cyclotron beam'. Invited Paper at the V l l t h .International cyclotron conference, TRI-PP-75-8 (1975). W.M. Brobeck and Associates, "The Conceptual Design of the beam transport magnets for Beam Line 1". TRIUMF external report, TRI-70-1 (1970). M.K. Craddock, "Recent Developments at the TRIUMF Meson Factory". Invited Paper at V Ail-Union National Conference on P a r t i c l e Accelerators, Dubna, TRI-PP-76-10, (1976). R.W. Harrison, "A beam transport system for the medical f a c i l i t y at TRIUMF". M.Sc. Thesis, University of V i c t o r i a 1972. 99 12. H. Lang and R.W. Harrison, "The bio-medical beam l i n e control system at TRIUMF". TRIUMF i n t e r n a l report, TRI-I-75-2, (1975). 13. P. Walden, Private Communication, 1976. 14. E.W. Blackmore, Private Communication, 1977. 15. R.M. Henkelman, K.Y. Lam, R.W. Harrison, K.R. Shortt, M. Poon, H. Lang, B. Jaggi, B. Pa l c i c and L.D. Skarsgard, "Progress during the f i r s t year of operation of the Batho Biomedical F a c i l i t y , TRIUMF". TRIUMF External Report, TRI-77-2, (1977). 16. J.R. Richardson, "The Status of TRIUMF". , Invited paper at the VTIth International Cyclotron Conference, TRI-PP-75-7, (1975). 17. J.B. Warren, "The TRIUMF project" i n the Proceedings of  the 5th International Cyclotron Conference, ed. by R.W. Mcllroy, 73 (1969). 18. G.H. MacKenzie, Private Communication (1976). 19. F.H. A t t i x and William C. Roesch, Radiation Dosimetry Volume 1, 2nd Edition (New York: Academic Press, 1968), p. 217. 20. M.S. Freedman, T.B. Novey, F.T. Porter and F. Wagner, J r . , "Correction for phosphor back-scattering i n electron s c i n t i l l a t i o n spectrometry". Review-of S c i e n t i f i c Instruments, 2J7, 716 (1956). 21. K.C. Lee, "Optical properties of 50 cm Browne-Buechner Spectrograph". M.Sc. Thesis, University of B r i t i s h Columbia, 1975. 22. P. Walden, Private Communication, 1977. 23. A.W. Stetz, "KIOWA-Data histogramming and p l o t t i n g " . University of Alberta Nuclear Physics i n t e r n a l report, UAE-NPL #181, (1976). 24. D.R.F. Cochran, P.N. Dean, P.A.M. Gram, E.A. Knapp, E.R. Martin, D.E. Nagle, R.B. Perkins, W.J. Shlaer, H.A. Thiessen and E.D. Theriot, "Production of charged pions by 7 30-MeV protons from hydrogen and selected n u c l e i " . Physical Review D, 6, 3085 (1972) . 25. R.R. Johnson, T.G. Masterson, K.L. Erdman, A.W. Thomas, and R.H. Landau, " E l a s t i c scattering of po s i t i v e pions from 1 2 C at 30, 40 and 50 MeV". (to be published i n Nuclear Physics). 100 26. Jorg Hufner, "Pion Interact with Nuclei". Physics Report,: 21C, No. 1, (1975). 27. A.S. C a r r o l l , I.-H. Chiang, C.B. Dover, T.F. Kycia, K.K.Li, P.O. Mazur, D.N. Michael, P.M. Mockett, D.C. Rahm, and R. Rubinstein, "Pion-nucleus t o t a l cross sections in the (3,3) resonance region". Physical Review C, 14, 635 (1976). 28. S.A. Dytman, J.F. Amann, P.O. Barnes, J.N. Craig, K.G.R. Doss, R.A. Eisenstein, J.D. Sherman, and W.R. Wharton, "Scattering of 50 - MeV TT+ from 1 2C". Physical Review Letters, 38, 1059 (1977). 29. G. Burleson, K. Johnson, J. Calarco, M. Cooper, D. Hagerman, H. Meyer, R. Redwine, I. Halpern, L. Knutson, R. Marrs, M. Jakobson, and R. Teppersen, "Measurements of TT± nucleus t o t a l cross sections at energies below 200 MeV" i n Abstracts of Contributed Papers - Sixth International  Conference oh high energy physics and nuclear structure, ed. by R. Mischke, C. Hargrove and C. Hoffman, Paper # I. D.6, 1975. 30. A.W. Thomas, Private Communication, 1977. 31. R.W. Harrison and R'.M. Henkelman, Private Communication, 1977. 32. H. Appel, V. Bohmer, G. Buche, W. Kluge, and H. MattSy, " T T - - beam studies using t i m e - o f - f l i g h t methods". Atomkernenergie, 27, 177 (1976) . 33. J. Marshall, L. Marshall, V.A. Nedzel, and J.D. Warshaw, "rr° production cross section for 430-MeV protons on H and Be". Physical Review, 88, 632 (1952). 34. R.W. Hales and B.J. Moyer, "Atomic number dependence of neutral meson y i e l d from proton bombardment". Physical Review, 89_, 1047 (1953). 35. W.E. Crandall and B.J. Moyer, "Characteristics of neutral meson production i n the proton bombardment of carbon n u c l e i " . Physical Review, 92, 749 (1953). 36. Iu. D. Prokoshkin, "Investigation of neutral pion production by 390-660 MeV nucleons" (Review) i n CERN Symposium, 2, 385 (1956). 37. Iu. D. Prokoshkin, "Relation between the angular d i s t r i b u t i o n s of p a r t i c l e s and t h e i r decay products". JEPT (IT.S.S.R.), 31, 732 (1956). 101 38. Iu. D. Bayukov, M.S. Kozodaev and A.A. Tiapkin, "Investigation of the energy and angular d i s t r i b u t i o n of neutral pions produced by 470- and 660- MeV protons i n carbon". JEPT, 5, 552, (1957). 39. Iu. D. Bayukov, M.S. Kozodayev, Iu. D. Prokoshkin, and A.A. Tyapkin, "Production of neutral -rr-mesons by high energy protons". Nuclear Physics, 4_, 61 (1957). 40. B.J. Moyer and R.K. Squire, "Characteristics of TT° production from proton-proton c o l l i s i o n s near threshold". Physical Review, 107, 283 (1957). 41. A.M. Segar and R. Rubinstein, "Neutral Meson production by 93 0 MeV protons". Nuclear Physics, 14, 222 (1959/60). 42. A.F. Dunaitsev and Iu. D. Prokashkin, "The reaction p + p->p + p + Tr° i n the energy range from threshold to 665 MeV". JEPT 36^ , 1179 (1959). 43. R.J. Cence, D.L. Lind, G.D. Mead, and B.J. Moyer, "Neutral pion production from proton-proton c o l l i s i o n at 735 MeV". Physical Review, 131, 2713 (1963). 44. A.F. Dunaitsev and Yu. D. Prokoshkin, "Tr°-meson produc-ti o n by protons on complex n u c l e i " . Nuclear Physics, 56, 300 (1964). 45. H.A. Bethe and J. AshkinJ/ "Passage of Radiations through Matter" in Experimental Nuclear Physics, v o l . I, ed. by E. Segre, (New York: John Wiley and Sons, Inc., 1953) p. 325 f f . 46. P.W. James, "Low energy, large angle pion production by 580 MeV protons bombardment of various n u c l e i " . Ph.D. Thesis, University of V i c t o r i a , 1975. 47. E.L. Mathie, "Low energy pion production by protons with incident energies from 400 to 500 MeV". M.Sc. Thesis, University of V i c t o r i a , 1976. 48. J. Crawford, M. Daum, G.H. Eaton, R. Frosch, R. Hess, and D. Werren, "Measurement of the cross sections for charged pion production at 60° and 90° from various target materials by 585 MeV protons". SIN report PR-77-001, 1977. 49. D. Bryman, Private Communication, 1976. 50. T.A. Hodges, "Materials for meson production targets". TRIUMF in t e r n a l report, VPN-70-11, 1970. 51. T.A. Hodges, "Review of pion production target T3". TRIUMF in t e r n a l report, VPN-71-9, 1971. 102 52. V.L. Highland, "Some p r a c t i c a l remarks on multiple scattering". Nuclear Instruments and Methods, 129, 497 (1975). 53. D.F. Measday and C. Richard-Serre, "Loss of protons by nuclear interactions i n various materials". CERN 69-17, 1969. 54. P a r t i c l e Data Group, Review of Modern Physics, 4_5, S35 (1973) . 55. Studies i n Penetration Of charged p a r t i c l e s i n matter. U. Fano, Chairman, (Washington, D.C: National Academy of Science, NRC Publication no. 1133, 1964), p. 205. 56. D. Cohen, B.J. Moyer, H.C. Shaw and C.N. Waddell, "Bremsstrahlung from Proton Bombardment of Nuclei". Physical Review, 130, 1505 (1963) . 57. N.P. Samios, "Dynamics of Internally Converted Electron-Positron Pairs". Physical Review, 121, 275 (1961). 58. W. Panofsky, R. Lee Aamedt, and J. Hadley, "The Gamma-Ray Spectrum Resulting from Capture of Negative 7T-Mesons i n Hydrogen and Deuterium". Physical Review, 81, 565 (1951). 59. W.J. Kossler, and H.O. Funsten, "Nuclear Deexcitation y Rays i n 1'*N, 11*C, and 1 5N Following TT~ Capture on l 60". Physical Review C, 4, 1551 (1971). 60. J.A. B i s t i r l i c h , K.M. Crowe, A.S.L. Parsons, P. Skarek, and P. Truol, "Photon Spectra from Radiative Absorption of Pions i n Nuclei". Physical Review C, 5, 1867 (1972). 61. R. Bjorkland, W.E. Crandall, B.J. Moyer, and H.F. York, "High Energy Photons from Proton-Nucleon C o l l i s i o n s " . Physical Review, 7J7, 213 (1950) . 103 APPENDIX I DATA ANALYSTS OF THE EVALUATION OF THE TT PRODUCTION CROSS-SECTION The data analysis consists of two parts. F i r s t , the reduction of the input data to histograms N^(H^) where H^'s are the hodoscope bin numbers, and second, the trans-formation of these histograms for each magnetic f i e l d setting to cross-section plots. 1.1 . Reduction of the input data to N„r (H.. ) The input data, namely, the hodoscope f i r i n g pattern, the pulse height and timing are- stored i n arrays as tabulated i n Table X. The analysis i s performed using the TRIUMF version of KIOWA, which handles the timing cuts and random event subtraction. A flowchart of the KIOWA analysis i s given i n Figure 1.1. 1.2 Reduction of N^ (H.. ) to cross-section plots The d i f f e r e n t i a l cross-section i s related to N (H.) TT 1 by the following equation, 104 dN where ^ i s the number of pions per proton at each hodoscope bin H^, N (H.) or dN T T i -=77 = ; N being the number of protons dH N ' p • * P * bombarding the target, gj| i s the momentum width of each bin,where i t has been determined that dp_ = 1918.998 B [KG] dH (H.+72.47)4 l B i s the magnetic f i e l d , e i s the correction for pion decay, Nopt/2 A i s the number of target nuclei per unit area presented to the beam, i s the correction for the v a r i a t i o n of the Aft 1 o s o l i d angle acceptance for bin H^, from the geometry of the hodoscope counters . AQ. in r e l a t i o n to the spectrometer, has been calculated,: as shown i n Figure 1.2, Aftio i s the angular acceptance of the tenth bin, Using the pp->-Tr+d reaction, Afiro has been deter-mined to be equal to four msr. p i s the momentum of the pions, where p[MeV/c] = 3 [ - 4 ; , f j f 1 H.+22. 6 l Corrections are also made to account for energy degradation of the pions passing through the target and the :acceptance counter. Beam losses and multiple scatters of the 'pion and proton beams are small'and are ignored. 105 TABLE X PARAMETERS AND VARIABLES IN KIOWA ANALYSIS event pattern unit Storage Location D(l) to D(24) D(25) D (26) D(27) D(28) D(29) D(30) D(31)* D(32)* pulse-height] of the s i g -nal from the ADC D(33) [D(34) D(35) to D(40) Comments Hodoscope pattern(0 or 1 Real event Random event pOR pOL r l R plL p3R 3L , _ 1 = event 0 = non-event Odd no. hodoscope counters Even no. hodoscope counters C 0 R ; C 0 L ; C 1 R ; C 1 L ; C 3 R ; C 3 L note D(33) and D(34) determine i f two adjacent hodoscopes f i r e simultaneously timings from the TDC (D(41) to D(46) D(47) D(48) p . p . p . p . p . p U0R' 0 L ' U 1 R ' U 1 L ' ^ 3 R , C 3 L r f A.C. D (49) D(58) D(59) D(60) Hodoscope bin which r e g i s t e r s i g -nal or adjacent pairs of hodo^ scope which r e g i s t e r signal D(43) +D(44) - D(48) amt. of time which the p a r t i c l e takes i n t r a v e l l i n g from A.C. to C, D(587 i s independent of where the p a r t i c l e h i t s the hodoscope count-er D(43)-D(44) a measure of the location of where the p a r t i c l e passes through C, D(42)-D(41) a measure of the location of where the p a r t i c l e passes through C Q not used i n the present work 106 START ^ set a l l s p e c t r a to zero iEhodoscope b i n number from D(49) hodoscope spectrum f o r good " f i r e s " F i g u r e 1.1 A f l o w c h a r t o f the KIOWA a n a l y s i s 107 t h i s step i s used to delete non-target sources' p a r t i c l e r e a l spectrum with| r f timing cut a r r i v a l time at CI i s stored in D(58) t h i s step i s used to eliminate non-pions re a l spectrum with r f and {D(58) ,D(49) } cuts N 5 (i)=N 5 (i)+l Figure 1.1 — continued 108 f i n a l p ion spectrum N.7 ( i ) ~N 7 r(H i) N 7 ( i ) = N 5 ( i ) - N 6 ( i ) F i g u r e 1.1 -- continued 110 APPENDIX II CORRECTION TO P DUE TO ENERGY e • DEGRADATION OF ELECTRONS IN MATTER From the l i t e r a t u r e [ 5 5 ] , i t can be shown that the stopping power of electrons with energy T can be represented bY d T k =± = -hT MeV-cm2 (II.1) dx gm where h, k are non-negative constants dependent on the material. Table XI gives the values of h and k for various materials. Therefore, a f t e r traversing a material of thickness x, the f i n a l energy of the electron T g i s related to the i n i t i a l energy T 0 by • To ' 0 h dx (II.2) . r~ J , o _1 , n - v I 1-k or To = T [ 1+( 1 7 k ) hx ] 1 k (II.3) Introducing T=hT e; T e T [ 1 + ^ ] for I x « 1 (II.4) e e It can be generalized for electrons passing through J slabs of thicknesses x T, to x,, that 1 J T 0 - T [ 1+-^ Z T.x ] (II.5) / T e j=l. 3 provided =— 2 T i x - v K < 1 ' e j=l J 3 Consider now a gamma ray s t r i k i n g a slab of thickness x, undergoing pair production. Electrons of f i n a l energy T g are detected at the end of the slab(see Figure II.1). I l l Assuming the p a i r p r o d u c t i o n c r o s s - s e c t i o n ^ can be pp e m p i r i c a l l y expressed as | | = A exp(-BT) ( I I . 6) pp where A, B are p o s i t i v e s c a l a r s , then, i f the e l e c t r o n s are produced a t ( y, y+dy ), the c r o s s - s e c t i o n i s given by | § (T e,x,y) = A exp[-BT e( 1 + T ( * ~ y ) ) ] pp e = [Aexp(-BT ) ] [ l-BT(x-y)] (II.7) Thus, the p r o b a b i l i t y P e ( T g , x ) t h a t the gammas produce e l e c t r o n s of f i n a l energy T g i s giv e n by P e ( T e , x ) = l-exp[-aax( l - ^ J * - ) ] ( I I . 8) where a l l symbols are as d e f i n e d i n S e c t i o n 5.2.4. G e n e r a l i z i n g f o r the case when the gamma ray has to t r a v e r s e J s l a b s of v a r i o u s m a t e r i a l , the p r o b a b i l i t y t h a t an e l e c t r o n o f f i n a l energy T g i s de t e c t e d a t the end of the s e r i e s o f s l a b s given the photon e x i s t s ; i s rep r e s e n t e d by P - 1-expC (II.9) J T k x k where £ = E a k a k x k ( 1-B k-^ B k E T i x - } ) . k=l j<k J J 112 TABLE XI VALUES OF h AND k FOR ELECTRON ENERGIES 3 0< T <2 00 MEV M a t e r i a l 2 , / MeV-cm > h v — — ) gm k Be 0.3025 0.5046 C 0.3068 0.5612 Fe 0.1722 0.8442 H 20 0.3366 0.5736 r 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0085194/manifest

Comment

Related Items