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Multiwire proportional counters Westlund, Wayne Arthur 1970

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MULTIWIRE PROPORTIONAL COUNTERS by WAYNE ARTHUR WESTLUND B . S c , Univers i ty of B r i t i s h Columbia, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF• THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE . i n the Department of Physics We accept this thesis as conforming to the required standard The Univers i ty of B r i t i s h Columbia September, 1970 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver 8, Canada ABSTRACT The aim of this work i s twofold: f i r s t , to develop a mult i layered mult iwire proport ional chamber which would be useful as a pos i t ion-sens i t ive detector i n tracking the path of a beam of elementary pa r t i c l e s and iden t i fy ing the pa r t i c l e s by thei r energies; and second, to measure the operating charac te r i s t i cs of such a chamber. A chamber has been developed which consists e s sen t i a l l y of a stack of printed c i r c u i t board frames to which are soldered separately many p a r a l l e l f ine wires . A s igna l plane at ground po ten t ia l has on e i ther side planes at high voltage. The chamber i s made gas- t ight by mylar f i l m on both ends and gas i s flowed through at atmospheric pressure. The e l ec t ros t a t i c s of th i s type of chamber follows exactly the theory derived for the f ami l i a r proport ional counter, of which the m u l t i -wire proport ional chamber i s an extension. The pulse charac te r i s t i cs measured for the chamber agree c lose ly with those values predicted by the theory. Such a chamber with s igna l wires of .0005 inch (12.7yUm) spaced .10 inch (2.5 mm) apart with planes separated by inch (3.2 mm) runs 4 we l l at 1800 vo l t s with a gas ampl i f i ca t ion factor of about 10 , g iv ing a pulse 5 mv high with r ise t ime of 25 nsec. The energy reso lu t ion shows a FWHM of 1 kev for the 5.9 kev x-ray of Fe"'"', while the time reso lu t ion i s at leas t 25 nsec. The pos i t i ona l s e n s i t i v i t y i s at least as f ine as the wire spacing. TABLE OF CONTENTS Page CHAPTER I INTRODUCTION 1 CHAPTER I I THEORY 5 A. Qua l i t a t ive Descr ipt ion . . . . 5 B. A n a l y t i c a l Descr ipt ion 7 (1) Ion iza t ion Counters 7 (2) Proport ional Counters 11 (3) Mul t iwire Proport ional Chambers 13 C. Numerical Calculat ions 14 CHAPTER I I I CONSTRUCTION 20 A. P l a s t i c Frame Chambers 20 B. Pr in ted C i r c u i t Board Chambers 22 CHAPTER IV READ-OUT SYSTEM 25 CHAPTER V OPERATION AND TESTING OF THE CHAMBERS 27 A. P l a s t i c Frame Chambers 27 B. Pr in ted C i r c u i t Board Chambers 28 (1) P a r a l l e l or Perpendicular Mode 28 (2) Wire and Plane Spacings 29 (3) Energy and Resolution 29 (4) Time Resolution 30 (5) Spat ia l Resolution . 30 (6) Pulse Height, Risetime, and Decay Time. . 30 (7) Gas Ampl i f i ca t ion Factor , A 31 CHAPTER VI DISCUSSION AND CONCLUSIONS 33 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . 38 i i i L I S T OF FIGURES To F o l l o w Page 1. S i m p l e V e r s i o n o f a P r o p o r t i o n a l C o u n t e r 1 2. Number of E l e c t r o n s C o l l e c t e d , n, V e r s u s H i g h V o l t a g e f o r a Gas C o u n t e r 5 3. P a r a l l e l P l a t e Geometry 9 4. C o a x i a l C y l i n d e r Geometry 10 5. Time Development o f a P u l s e f r o m a P r o p o r t i o n a l C o u n t e r H a v i n g - = 500 12 a 6. S i m p l e D i f f e r e n t i a t o r 13 7. D i f f e r e n t i a t e d P r o p o r t i o n a l C o u n t e r P u l s e s f o r — = ! a 500 and S e v e r a l V a l u e s o f S' = — 13 RC 8. E q u i p o t e n t i a l s i n a M u l t i w i r e P r o p o r t i o n a l Chamber 14 9. S c h e m a t i c Diagrams o f E a r l y V e r s i o n o f M u l t i w i r e P r o p o r t i o n a l Chamber 20 10. S c h e m a t i c Diagrams of P r i n t e d C i r c u i t B o ard Type o f Chamber 22 11. S i m p l e E l e c t r i c a l C o n n e c t i o n s o f E a r l y Chambers . . 25 12. " S c h e m a t i c Diagram o f D i g i t a l A m p l i f i e r 25 13. S c h e m a t i c Diagram f o r Energy R e s o l u t i o n Measurement. 25 14. S c h e m a t i c Diagram f o r Time R e s o l u t i o n Measurements . 25 15. S c h e m a t i c Diagram o f Chamber Gas F l o w 27 i v L I S T OF FIGURES (Cont'd.) To F o l l o w Page 16. Energy R e s o l u t i o n , P e r p e n d i c u l a r Mode 29 17. E n e r g y R e s o l u t i o n , P a r a l l e l Mode 29 18. T y p i c a l P u l s e s f r o m Fe"'"' S o u r c e , A m p l i f i e d by O r t e c 101/201 29 19. Energy R e s o l u t i o n , F e 5 5 S o u r c e . FWHM 1.37 k e v . . . 29 20. E n e r g y R e s o l u t i o n ' 29 21. E n e r g y R e s o l u t i o n . FWHM 1.71. k e v 29 22. E n e r g y R e s o l u t i o n . FWHM 1.23 k e v 29 23. Time R e s o l u t i o n . FWHM 56 n s e c ' 29 24. Time R e s o l u t i o n . FWHM 42 n s e c 29 25. Time R e s o l u t i o n ; C a l i b r a t i o n o f 128 Channel Mode . . 29 26. Time R e s o l u t i o n . FWHM 55 nsec 29 27. Time R e s o l u t i o n . FWHM 34 n s e c •, 29 28. Time R e s o l u t i o n . FWHM 25 n s e c 29 29. To Measure Time R e s o l u t i o n 30 30. Time R e s o l u t i o n ; C a l i b r a t i o n o f 256 Channel Mode . . 30 31. _ Time R e s o l u t i o n ; w i t h D e l a y 30 32. R i s e t i m e o f P u l s e D i r e c t l y f r o m Chamber 30 33. Decay Time o f P u l s e D i r e c t l y f r o m Chamber 30 34. L e a s t Squares F i t o f E x p e r i m e n t a l Data P o i n t s f o r 9 0 % A r g o n - 10% Methane M i x t u r e t o T h e o r e t i c a l Curve w i t h oL = 0.100 . . . . 31 v L I S T OF FIGURES (Cont'd.) To F o l l o w Page 35. L e a s t Squares F i t s o f E x p e r i m e n t a l D a t a P o i n t s f o r A r g o n - I s o b u t a n e M i x t u r e s to T h e o r e t i c a l Curves 31 vi LIST OF TABLES .To Follow Page I , Comparison of Features of Some Types of Radiat ion Detectors 2 I I . Rate of Increase of the Ioniza t ion Cross Section with Energy 15 I I I . Chamber Operation with Different Quenching Agents 28 IV. Comparison of Chamber Operation with Signal Wires P a r a l l e l and Perpendicular to HV Wires 28 V. Comparison of Chamber Operation with Different Wire and Plane Spacings 29 V I . Rough Estimation of Spat ia l Resolution of Chamber 30 V I I . Results of F i t t i n g Experimental Points to Theoret ical Formula 32 v i i ACKNOWLEDGEMENTS I should l i k e to express my appreciat ion to my supervisor, Dr. David A. Axen, for h is great in te res t , encouragement, and advice throughout the course of this work. Also I should l i k e to thank Dr. G, M. G r i f f i t h s and the Van de Graaff group for the i r f r i end ly encouragement and support. v i i i CHAPTER I INTRODUCTION The fami l i a r type of proport ional counter consists of two coaxia l cy l inders , the inner one being a f ine wire a few tens of microns i n diameter and the outer one having a diameter of several centimeters. The outer cyl inder i s f i l l e d with a gas and, as shown i n F i g . 1, i s kept at ground po ten t ia l while the inner wire i s charged to a high pos i t ive v o l t -age. Charged pa r t i c l e s entering through the window ionize atoms or molecules of the gas by Coulomb in te rac t ions . The resul tant electrons t r ave l toward the central electrode and the pos i t ive ions t rave l toward the outer electrode. The c o l l e c t i o n of these ions consti tutes an e l e c t r i c current i n the central wire for a b r i e f period of time, which pers i s t s u n t i l a l l of the ions from this pa r t i cu la r event have been co l l ec t ed . This current causes a voltage pulse across the r e s i s to r shown i n F i g . 1, which then may be displayed on an osc i l loscope or converted into a data pulse. The mult iwire proport ional chamber consists of planes of wires stretched i n p a r a l l e l array. In th i s case the wires of the central s igna l plane are kept at ground poten t ia l while the planes on e i ther side are maintained at high negative voltage. In this work the high voltage planes consist of p a r a l l e l wires . Chambers using th in me ta l l i c f o i l or mesh for HV planes are reported i n the l i t e r a t u r e . ^ ' ^ ' ^ ' ^ ^ " ^ A number of planes may be sandwiched together by a l te rna t ing s igna l planes and HV planes, g iv ing several advantages: Output FIG. 1--Simple Version of a Proport ional Counter (a) Two orthogonal s ignal planes afford two-dimensional s e n s i t i v i t y ; three or more s ignal planes may f i x the th i rd coordinate and so give the complete path of the i n i t i a l p a r t i c l e . (b) Having a mul t ip le chamber instead of several s ingle chambers reduces the number of mylar windows which the p a r t i c l e must traverse, thereby reducing the d i s s ipa t ion of energy. (c) The construction and operation of a mul t ip le chamber are simpler than those of an equivalent number of s ingle chambers. Another type of pos i t ion - sens i t ive detector i s the mult iwire spark chamber. The operating voltage of a spark chamber i s above the breakdown voltage and so the high voltage is 1 pulsed only after a p a r t i c l e has traversed the chamber, as detected by supplementary counters. A spark then develops at the pos i t ion of the ion i za t ion l e f t by the incident p a r t i c l e . The sens i t ive time of th i s chamber i s of the order of one micro-second so that a l l pa r t i c l e s which have traversed the chamber wi th in this i n t e r v a l w i l l be recorded. The energy dissipated i n the spark must be stored i n condensers. The recharging time of these condensers i s of the order of mi l l i seconds ; hence, counting rates of up to one k i l o h e r t z are possible with the spark chamber. In contrast , a mult iwire proport ional chamber can be operated at rates up to 10^ counts per wire per second. Some features of d i f ferent types of rad ia t ion detectors have been (3) compared by Charpak and are summarized i n Table I . The advantages of mult iwire proport ional chambers include operation at high counting rates , TABLE I . Comparison of Features of Some Types of Radiation Detectors (3) (from Charpak ) S c i n t i l l a t i o n Hodoscope Wire spark Chamber Mul t iwire Proport ional Chamber S e l f - t r i g g e r i n g yes no yes Minimum space reso lu t ion 2 mm to 1 cm (depending on length) 0.5 mm 1 mm Time reso lu t ion Dead-time 5 nsec less than 100 nsec 500 nsec 100 nsec 25 nsec less than 100 nsec Unit p r ice ( r e l a t ive ) 50 Minimum thickness ( r e l a t ive ) 100 1 2 5 1 Magnetic f i e l d s sens i t ive sens i t ive in sens i t ive 3 good spa t i a l r e so lu t ion , and short time reso lu t ion . When th is work was started only single-coordinate chambers with HV planes of s ta in less s tee l mesh or aluminum f o i l had been reported i n the l i t e r a t u r e . One purpose of this work was to invest igate the p o s s i b i l i t y of making a mult iplanar , mult iwire proport ional chamber so that more than one coordinate could be measured with a beam traversing the minimum number of f o i l s , namely two. The other purpose was to measure the pulse height and pulse reso lu t ion time i n order to determine the spec i f ica t ions for the ampli f iers of a data acqu i s i t i on system. The parameters have been invest igated as a function of gas mixture and chamber geometry, i . e . wire spacing, plane spacing, and or ien ta t ion of the planes with respect to one another. These charac te r i s t i cs were measured wi th in the framework of t ry ing to bu i ld a robust, mult i layered system with the smallest possible number of c r i t i c a l operating parameters, which would be useful i n p r a c t i c a l experiments. While this work was being carr ied on, groups at other i n s t i t u t i o n s were making good progress i n the development of mult iwire proport ional chambers. Several of the groups benefited from working d i r e c t l y with Charpak, to whom much of the c red i t i s due for the development of these chambers. Bemporad et a l ^ have recent ly reported achieving a spa t i a l reso lu t ion of one-quarter the wire spacing, which i n the i r case was 3 mm. Their time reso lu t ion was 150 nsec. Simanton et a l have reported on.a low-cost ampl i f ier for these c h a m b e r s . T h i s looks quite promising and may be t r i ed here i n the near future. 4 An e x c e l l e n t d e s c r i p t i o n o f t h e s e m u l t i w i r e p r o p o r t i o n a l chambers i s g i v e n i n an a r t i c l e by Charpak e t a l ^ where t h e y u n f o l d the t h e o r y i n some d e t a i l and p r e s e n t the l a t e s t r e s u l t s of t h e i r measurements. They r e p o r t p u l s e s o f more tha n 200 MV f r o m chambers w i t h 2 mm w i r e s p a c i n g , and 25 n s e c maximum time j i t t e r . A l s o they say t h a t time r e s o l u t i o n o f 7 n s e c can be a c h i e v e d by means o f t i m e - p o s i t i o n c o r r e l a -t i o n u s i n g a d r i f t chamber. I n the n e x t c h a p t e r some b a s i c t h e o r y b e h i n d the o p e r a t i o n o f p r o p o r t i o n a l c o u n t e r s i s p r e s e n t e d . I n the t h i r d c h a p t e r the c o n s t r u c t i o n o f the chambers i s d e s c r i b e d , w h i l e the e l e c t r o n i c s used w i t h the chambers i s d e s c r i b e d i n the f o u r t h c h a p t e r . I n the f i f t h c h a p t e r d e t a i l s o f the o p e r a t i o n and t e s t i n g o f the chambers a r e g i v e n . F i n a l l y , i n the s i x t h c h a p t e r d i s c u s s i o n o f r e s u l t s and c o n c l u s i o n s a r e p r e s e n t e d . CHAPTER II THEORY This chapter presents some d e t a i l s of how a pulse i s formed i n a proportional counter, how the pulse develops under p a r a l l e l plate and c y l i n d r i c a l geometries, and how some parameters such as pulse height and time r e s o l u t i o n may be estimated. A q u a l i t a t i v e d e s c r i p t i o n i s given f i r s t , followed by a more a n a l y t i c a l d e s c r i p t i o n . A. Q u a l i t a t i v e Description The number of ion pairs produced by an incoming p a r t i c l e i s pro-p o r t i o n a l to the amount of energy deposited i n the chamber, which may be a l l of i t s k i n e t i c energy i f the p a r t i c l e i s stopped i n s i d e the chamber i or may be only part of i t s energy i f the p a r t i c l e passes r i g h t through. The negative ions produced by c o l l i s i o n s of the incoming p a r t i c l e with atoms of the counter gas d r i f t toward the p o s i t i v e electrode, and .the p o s i t i v e ions d r i f t toward the negative electrode. The mode of operation of the counter i s dependent on the voltage applied to the electrodes. F i g . 2 shows a t y p i c a l voltage curve. As Wilkinson s h o w s , i n the voltage range from V^, which i s a few tens of v o l t s such that the i n i t i a l ions do not recombine, to V^, which i s about 200 v o l t s f o r h i s case, only the i n i t i a l ions are c o l l e c t e d at the electrodes. Above gas a m p l i f i c a t i o n takes place; that i s , the primary electrons from the i n i t i a l i o n i z a t i o n acquire enough energy from the e l e c t r i c f i e l d to i n t e r a c t with other atomic electrons and cause secondary i o n i z a t i o n . This a c t i o n takes place very close to the central wire, p r i n c i p a l l y within one wire diameter, where the e l e c t r i c f i e l d i s 5 FIG. 2--Number of Electrons Collected, n, Versus High Voltage for a Gas Counter 6 strongest. From to the gas a m p l i f i c a t i o n factor i s independent of the number of i n i t i a l electrons and so the voltage pulse produced i s proportional to the i n i t i a l i o n i z a t i o n . From to the gas a m p l i f i c a -t i o n i s increasing. From to V,_ the subsequent i o n i z a t i o n s cause avalanches of ions to spread the whole length of the tube, and the v o l t -age pulse s i z e i s uniform and independent of the number of i n i t i a l electrons. Above the device breaks down and goes into a state of con-tinuous discharge. In the proportional region the e l e c t r i c f i e l d near the c e n t r a l electrode i s s u f f i c i e n t f or the electron to gain 'more energy between atomic c o l l i s i o n s than that required to i o n i z e another atom. A small avalanche of secondary i o n i z a t i o n r e s u l t s close to the central wire. A l l of the electrons i n the avalanche are then c o l l e c t e d by the central wire i n the very short time of about 10 ^ sec.because of the high e l e c t r o n m o b i l i t y . The much heavier p o s i t i v e ions d r i f t toward the outer electrode i n a time which i s about 1000 times greater than that of the electrons. In f a c t , the p o s i t i v e ions are p r a c t i c a l l y stationary while the electrons are being c o l l e c t e d . However, because the p o s i t i v e ions are so close to the wire, they e f f e c t i v e l y cancel the pulse contributed by c o l l e c t i o n of the electrons. As the p o s i t i v e ions move away i n the high f i e l d region they induce on the c e n t r a l wire a negative pulse with a f a s t rise-time. This pulse f l a t t e n s out as the p o s i t i v e ions t r a v e l f u r t h e r away and i t i s completed when the p o s i t i v e ions f i n a l l y reach the negative electrode. In the Geiger case the p o s i t i v e ions form a sheath surrounding the central wire, which spreads along i t s e n t i r e length. This sheath reduces the e f f e c t i v e e l e c t r i c f i e l d around the wire, thereby quenching the avalanches and rendering the counter i n s e n s i t i v e to any more incoming p a r t i c l e s u n t i l such time as the p o s i t i v e ions have d r i f t e d f ar enough away from the ce n t r a l wire for the f i e l d around i t to r e b u i l d i t s e l f . In the proportional case, however, the avalanches do not f i l l the whole counter tube and so the proportional counter does not have a dead time i n the Geiger sense. Rather what happens i s that successive pulses may be reduced i n height i f the counting rate i s quite high, 10^ per second. In both cases avalanche propagation i s kept i n check by the addi t i o n of a small percentage of a polyatomic gas or vapour, such as ethyl alcohol, to the counter gas. This ad d i t i v e serves to absorb u l t r a -v i o l e t photons which are produced i n the c o l l i s i o n processes and which might otherwise cause avalanches to breed incessantly. I t also helps by absorbing energy from metastable states which are prevalent i n noble gas atoms and which would undesirably prolong the counter's recovery 4 ' - 4 time. For instance, He has a metastable state with a l i f e t i m e of r^r 10 sec, much longer than the sort of time r e s o l u t i o n one wishes to obtain from a counter. B. A n a l y t i c a l Description (1) I o n i z a t i o n Counters The p o s i t i v e electrode w i l l be considered to be the one connected to the external a m p l i f i e r and hence the one whose p o t e n t i a l changes are of i n t e r e s t . F i r s t a simple i o n i z a t i o n counter w i l l be considered. A f t e r the formation of an i n i t i a l ion pair and the beginning of separation of the charges +e and -e, these induce at time t charges q^_(t) and q (t) on the p o s i t i v e electrode so that i t s p o t e n t i a l , o r i g i n a l l y zero, i s now q, (t) + q (t) P(t) = 2t : — , (1) C becoming n o t j u s t -— a t a time t , when the e l e c t r o n has been c o l l e c t e d , C 1 b u t r a t h e r -e + q,(t ) P ( t x ) = ^—— , (2) where C i s the t o t a l c a p a c i t a n c e of the e l e c t r o d e . I t i s n o t u n t i l the l a t e r time t ^ when the p o s i t i v e i o n has been c o l l e c t e d a t the n e g a t i v e e l e c t r o d e t h a t the p o t e n t i a l of the s i g n a l e l e c t r o d e becomes P ( t 2 ) = - f . Thus to o b t a i n the f u l l p u l s e b o t h i o n s must be c o l l e c t e d . I n t h e l i g h t o f t h e s e f a c t s , q_^_(t) and q ( t ) must be c a l c u l a t e d f o r the d i f f e r e n t g e o m e t r i e s and c o n d i t i o n s i n o r d e r to g a i n a p r o p e r u n d e r s t a n d i n g o f the p u l s e f o r m a t i o n . W i l k i n s o n ^ ^ p r o c e e d s by means of Green's theorem, x^here-by i f c h arges q^, q^> ••• a r e p l a c e d on an i s o l a t e d s y s t e m of c o n d u c t o r s 1, 2, .... so t h a t t h e i r p o t e n t i a l s a r e P^, P^, . .., and t h e n i f t h e s e I I I I a r e changed to q^ , q^ , ... and P^ , P^ , t h e n P n ' = £ % P n ' <3> ( s e e , f o r i n s t a n c e , r e f e r e n c e 8, page 83.) T h i s theorem has q u i t e s i m p l e forms f o r the c a s e s o f two i n f i n i t e p a r a l l e l p l a t e s and of i n f i n i t e co-a x i a l c y l i n d e r s . L e t the e l e c t r o d e s be l a b e l l e d 1 and 2, and suppose the c h a r g e e i s somewhere between them, r e s i d i n g on an i n d e f i n i t e l y s m a l l e l e c t r o d e l a b e l l e d 3. The f i r s t s e t of p o t e n t i a l s a r e t a k e n to be P^ = P^ = 0, P^ u n s p e c i f i e d ; the c o r r e s p o n d i n g c h arges a r e q^ and t o be c a l c u l a t e d , and q^ = e. The second s e t o f p o t e n t i a l s a r e t a k e n as t h o s e e x i s t i n g i n i i t the chamber under i t s o p e r a t i n g c o n d i t i o n s , P^ , P^ , and P^ ; the new i charges on e l e c t r o d e s 1 and 2 a r e u n s p e c i f i e d w h i l e q^ = 0. Then Green's theorem g i v e s i i, i q l P l + q 2 P 2 + e P 3 = 0 ' ( 4 ) o r , s i n c e q^ + q^ + e = 0 by the i n i t i a l a s s u m p t i o n , I I I I P -P P -P q = - e — ; r , q 2 = -e j r • (5) P -P P -P 1 2 1 V2 T h i s m e r e l y says t h a t the charge i n d u c e d on a g i v e n e l e c t r o d e i s p r o -p o r t i o n a l to the p o t e n t i a l d i f f e r e n c e between the p o i n t i n the chamber where the i n d u c i n g c h a r g e was c r e a t e d and the o t h e r e l e c t r o d e . Thus, i n o r d e r to f i n d the i n d u c e d c h a r g e s i t i s n e c e s s a r y t o examine the e q u i -p o t e n t i a l s i n the chamber. I t was p r e v i o u s l y p o i n t e d o u t t h a t the e l e c t r o n o f an i o n p a i r i s c o l l e c t e d about 1000 t i m e s f a s t e r t h a n i t s p o s i t i v e p a r t n e r . Then f o r a f a s t chamber w i t h a s h o r t c l i p p i n g time so t h a t t ^ >^ R C ^ t ^ ( o f w h i c h more w i l l be s a i d l a t e r i n t h i s s e c t i o n ) , E q u a t i o n (1) becomes q ( t ) + Q P ( t ) = — ± , (6) where Q = q ( 0 ) , the p o s i t i v e i o n i n d u c t i o n , i s e f f e c t i v e l y c o n s t a n t . The p u l s e r e a c h e s i t s maximum v a l u e , -e + Q p = — c — • • a t time t ^ and t h e n f a l l s w i t h time c o n s t a n t RC. Q + v a r i e s w i t h the p o s i t i o n where the i o n p a i r was formed, and so i t would appear t h a t the chamber f a i l s t o a c h i e v e the d e s i r e d p r o p o r t i o n a l i t y between i o n i z a t i o n and p u l s e h e i g h t . However, i t w i l l be shown t h a t t h i s f e a r i s unfounded. Now, f o r the p a r a l l e l p l a t e geometry as i n F i g . 3, q + ( 0 ) = Q + = e (1 - ^ ) = - q _ ( 0 ) ; (7) - s » to a m p l i f i e r O x,. FIG. 3 - - P a r a l l e l Plate Geometry 10 x i s the distance from the c o l l e c t i n g plate where the ion pair i s formed. At time t the electron is at x, where x - x = v t, v being the e lect ron d r i f t v e l o c i t y , and so q_(t) = -e (1 - J ) . (8) Then from Equation (1), p ( t ) - ! a - j ) + a - f)} e v t C d ' *0 Thus, the pulse r i se s l i n e a r l y u n t i l t.. = — , when 1 v (9) e *0 P l = " I f <10> After this time, for RC ^ t , P(t) r i ses very s lowly, reaching - i n time t^ ^ 1000 t . With a smaller but s t i l l large RC such that t )>) RC t^, the pulse drops exponential ly. For an i on i za t i on chamber consis t ing of coaxial cyl inders as i n F i g . 4, the f i e l d at x i s V x i n & Si (11) where V i s the high voltage on the central wire . Assuming that the e l ec t ron -d r i f t v e l o c i t y i s described by ( f )2 , where ZXT i s the f i e l d strength i n vol ts /cm, and p i s the gas pressure i n v = (constant) p ) 2 , (12) mm. Hg, then the electron migration v e l o c i t y may be wr i t t en -ft* K- ' FIG. 4 --Coaxial Cylinder Geometry Proceeding as before, Green's theorem gives b _b_ i n * ' i n *0 q_(x) = -e g , Q + = e — -jy ( 1 4 ) o — Xx\ a. X n a ! 3 A x 0 - A ( x 0 2 -1 K_ (TTT) 2 t ) 2 and P(t) = - £ ^ ^ f L _ - _ i §^ (15) C b a u n t i l 3 3 2 2 fcl = — U r ' (16) 2 K - ( ^ n b } a By d e f i n i n g a parameter f such that \ on the f scale, t h i s can be written p ( r ) = TxTi ^ n ( r ^ F " ) ' ( 1 7 ) a 3 a 2 The l a r g e s t value of f i s 1 - (—) which i s ^ 1 for the usual case X Q ) ^ The f i n a l height of the pulse i s A ? P = -J-f (18) a (2) Proportional Counters The foregoing c a l c u l a t i o n s have been concerned with i o n i z a t i o n chambers; for a proportional counter the mechanism of pulse formation i s quite d i f f e r e n t because of the electron m u l t i p l i c a t i o n which takes place i n the gas, mostly near the central wire where Q e. Hence the pulse from electron c o l l e c t i o n i s r e l a t i v e l y small and the major contribution comes from the slower p o s i t i v e ion c o l l e c t i o n . Since most of the i o n i z a -t i o n occurs close to the c e n t r a l wire the pulse si z e i s independent of the pos i t ion of the o r i g i n a l track of the p a r t i c l e i n the chamber., This i s an important advantage, for a l l the pulses w i l l have the same form and the same f rac t ion w i l l be recorded even though the RC c l ipp ing time may be much shorter than the pulse length. To determine the shape of the pulse the ca lcu la t ion s tar ts with -e + q (t) P(t) = ^ (19) For pos i t ive ion mob i l i t y the expression v = K X (20) i s used, where K i s the ion ic mobi l i ty which incorporates the pressure dependence. Then, s i m i l a r l y to the p r io r ca lcu la t ion for the ion i za t ion chamber, the ion mobi l i ty can be wr i t ten d x 0 K V dt * n A * ' ( 2 1 ) 0 a which leads to C 2KVt ^ An (a^ Jlxv —• p(t) = * uJ ' ' a ,.2 2, p b (b - a ) X n — u n t i l t = a , (23) 2VK when the pos i t ive ion i s col lec ted and P = — . As before, th is can be wr i t t en i n terms of the to ta l pulse height and length, F(r) " 7A^- M\7r + '}'• <24) a a 2 b with the maximum T value being 1 - — . F i g . 5 shows the pulse for — = 500. I t i s in te res t ing to look at the effects of d i f f e r e n t i a t i o n on P ( T ) 0.4 -0.3 -0.2 -0.1 _ 0 I 1 1 1 1 1 i i i i I I I ' ' i 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 FIG. 5--Time Development of a Pulse from a Proport ional Counter Having — = 500. T i s a parameter such that t o t a l pulse height and length are approximately un i ty . 13 the pulse. From F i g . 6, ^ - ^ ~ = 2- (25) d r R C using the form i n which pulse length and height are unity. For R C « 1 t h i s reduces to d ? " R C ( 2 6 ) i l l u s t r a t i n g the d i f f e r e n t i a t i n g property of the R C c i r c u i t . I t i s con-venient to set -—^ = S , the r a t i o of ion c o l l e c t i o n time to c l i p p i n g time, K C a measure of the sharpness of d i f f e r e n t i a t i o n . Then, f or the proportional counter, Equations (24 and (25) lead to the s o l u t i o n 2 _ r 2 E i f ( r + f z ) j 7 . - E i [ f 2 s ] v ( r ) = 7 7 7 1 r a * 7 " ' a exp r + where E i i s the exponential i n t e g r a l (tabulated, f o r instance, by Jahnke and Emde, 1945 e d i t i o n ) . This tends f o r small S to P(<T) and for large S to v ( T ) = — \ —±—2 . (28) b 2 F i g . 7 shows v ( T ' ) f o r — = 500 and some values of S . I t i s seen that a very sharp d i f f e r e n t i a t i o n i s possib l e , giving short pulses i n s p i t e of the f a c t that they are generated by p o s i t i v e ion mobi l i t y . (3) Multiwire Proportional Chambers Now, with regard to the s p e c i a l case of a multiwire proportional chamber where the s i g n a l wires are l y i n g p a r a l l e l i n a f l a t plane between two s i m i l a r planes of wires at high voltage, Charpak et a l ^ give the v ( f ) P ( T ) FIG. 6--Simple D i f f e r e n t i a t o r ) 14 e l e c t r o s t a t i c potent ia l at any point ins ide the chamber as V = ) + sinh (• (29) where q i s the charge per un i t length of each wire , w i s the spacing between the wires , x i s i n the plane of the wires , y i s the perpendicular coordinate, and the coordinate system i s centered on one wire . F i g . 8 shows a sketch of the f i e l d l ines and equipotentials i n the chamber. I t i s seen that, near the wire where most of the electron m u l t i p l i c a t i o n takes place, the equipotentials are c y l i n d r i c a l and so the preceding theory developed for the c y l i n d r i c a l proport ional counter applies equally we l l to the mult iwire proport ional chamber. C. Numerical Calculat ions The pulse height, P, obtained from a proport ional counter may be expressed as P = ^ . . (30 where A i s the gas ampl i f i ca t ion fac tor , n i s the number of ion pairs produced i n the i n i t i a l i o n i z a t i o n , e i s the e lec t ron ic charge, and C i s the to ta l apparent capacitance of the s ignal wire and i t s external attachments. Equation (30), which follows from the simple formula V = , assumes that the pos i t ive ions have been co l l ec ted . Korff (9) gives the fol lowing formula for the gas ampl i f i ca t ion factor i n terms of measurable quant i t ies : FIG. 8--Equipotentials i n a Multiwire Proportional Chamber 15 A = exp 1^  2(fNcVa)2 j^( | - ) 2 . i j J ( 3 1 ) where f i s a parameter depending on the pa r t i cu la r gas used i n the counter, 3 N i s the number of molecules of gas per cm i n the counter, -|c i s the capacitance per un i t length of the s ignal wire , V i s the high voltage applied to the electrodes, a i s the radius of the s igna l wire, and Vp i s the electrode voltage at which gas ampl i f ica t ion commences. This formula i s expressed i n Gaussian un i t s , which means that c i s dimensionless and V must be expressed i n s t a tvo l t s . Equation (31) may be wr i t t en An A = 2(fNca)2 I - X - . v 2 I (32) Korff has compiled Table I I which gives f for various gases, In the case of a mixture of gases the factors fN become fN = ^ f . N. (33) l 1 where and N^ per ta in to the ind iv idua l gas components. Now, at room temperature 6.02 x 1 0 2 3 molecules 273 „ , , i r > 19 1 , 3 N = ~ x » Q R = 2.46 x 10 molecules per cm . 2.24 x 10 cm (34) For a 90% Ar - 10% CH^ mixture, then, 19-17 ? fN = (1.81 x 2.22 + 1.24 x 0.246) x 10 = 4.32 x 10 molecules per cm. v o l t . (35) For the chamber used, - |c was measured as approximately 8.1 picofarad per TABLE I I . Rate of Increase of the Ion iza t ion Cross Section with Energy (from K o r f f ( 9 ) ) Gas f ( I O " 1 7 cm 2 /vol t ) Ar 1.81 Ne 0.14 He 0.11 H 2 0.46 °2 . 0.66 N 2 0. 70 NO 0.74 CO 0.83 C 2 H 2 1.91 CH. 4 1.24 1 6 - 4 cm £ ^ 7 . 3 ( u n i t l e s s ) i n the Gaussian system. a = 6 . 3 x 1 0 cm. Hence putting these values into Equation ( 3 2 ) gives 1 0 • „ „ 4 . 3 2 x 2 x 7 . 3 x 6 . 3 x 1 0 " 2 2 X. n A = 2 ( T— ) A = 0 . 2 3 0 3 where V i s now i n conventional v o l t s ; or, since /v'n u = 2 . 3 0 2 6 1°S-^Q U > log A = 0 . 1 0 0 / - ~ T - V 2 / ( 3 6 ) Equation ( 3 6 ) , which was derived for a coaxial cylinder proportional counter, has been tested for the multiwire proportional chamber by measuring and p l o t t i n g output pulse height versus high voltage. Such an experimental curve may be r e l a t e d to Equation ( 3 6 ) by means of Equation ( 3 0 ) . However, since the experimental pulse heights were measured by means of an external a m p l i f i e r the gain, G, of this e l e c t r o n i c device must be taken into consideration, so that Equation ( 3 0 ) becomes P = G_A_n_e ( 3 ? ) where P represents the e x t e r n a l l y amplified pulse height. The number, n, of i n i t i a l ion pairs can be estimated by assuming 3 0 ev as the average energy given up i n producing one ion pair by a p a r t i c l e slowing to a stop i n argon. Dealing with the 5 . 9 kev x-ray from Fe , then 5 9 0 0 ev „„„ . . y 2 0 0 ion pairs ( 3 8 ) 3 0 ev/ion pair are produced by one event. As described i n Chapter V , the gas a m p l i f i c a t i o n for a 1 0 wire per inch double chamber with -r inch spacing between planes, operating on a o mixture of 90% argon - 10%, methane, at a high voltage of 1800 v o l t s , 3 was found to be approximately 1 x 10 . Also, the capacitance C was measured as 110 pf. Hence by Equation (30) the unamplified pulse height expected from t h i s chamber i s 1 x 10 3 x 200 x 1.6 x 10" 1 9 P = — v o l t s 110 x 10 = 0.3 m i l l i v o l t s • ^ 3 9' ) To estimate the pulse risetime, Equations (23) and 24) may be used. Equation (23) gives f _ ( b 2 - a 2) An b •a 2VK = C ( 0 - 3 ) 2 - (6.3 x 10"4)27^C?n 500 2 x 1800 x 12.6 £3 12 yUsec. (40) (Wilkinson, on page 48 of Reference 1, gives 12.6 as the value of K for argon.) This 12^Asec. i s the time for formation of the whole pulse, i . e . u n t i l the p o s i t i v e ions have been c o l l e c t e d . F i g . 7 shows that the f a s t r i s e of the d i f f e r e n t i a t e d pulse i s accomplished by the time the pulse has reached h a l f i t s maximum height. Then by Equation (24), a 2 . a 2 T 1 + l L i — ' ¥ ^ 3T3U 2 18 S i n c e f has been c a l c u l a t e d as 12 y ^ s e c , t h e n the e x p e c t e d r i s e t i m e of the p u l s e i s a p p r o x i m a t e l y 1 x 12 y ^ s e c = 24 n s e c . (41) 500 The decay t i m e o f the d i f f e r e n t i a t e d p u l s e may be e s t i m a t e d s i m p l y f r o m the RC t i m e c o n s t a n t . A l t h o u g h n o m i n a l l y 3.3 KJT~, t h e v a l u e o f the r e s i s t o r on t h e w i r e used f o r t h i s d e t e r m i n a t i o n was measured as 5K-P-. The t o t a l c a p a c i t a n c e o f the w i r e and a t t a c h m e n t s was measured as 110 p f . Hence t h e decay time t a k e n f o r the p u l s e t o d e c l i n e t o ~ 37% o f i t s peak h e i g h t s h o u l d be 5 x 1 0 3 x 110 x 1 0 " 1 2 s e c = 0 . 5 5 / < s e c . (42) The t i m e r e s o l u t i o n i s governed by the t i m e j i t t e r i n the s i g n a l p u l s e s ; t h a t i s , the range o f t i m e s t a k e n by t h e e l e c t r o n s p r o d u c e d by i o n i z i n g p a r t i c l e s i n d i f f e r e n t ' p a r t s of the chamber to r e a c h the s i g n a l w i r e , be a m p l i f i e d and t h e n be t r a n s m i t t e d t h r o u g h t h e e x t e r n a l c i r c u i t to the a n a l y z e r . I n o r d e r to e s t i m a t e the t i m e r e s o l u t i o n , the e l e c t r o n d r i f t v e l o c i t y must f i r s t be c a l c u l a t e d ; t h i s can be done by means of E q u a t i o n ( 1 2 ) . F o r t h e chamber w i t h 4 mm s p a c i n g between p l a n e s , o p e r a t i n g a t 2000 v o l t s w i t h t h e gas f l o w i n g t h r o u g h a t a t m o s p h e r i c p r e s s u r e , ^ = L 200°7ZltS H - 6.58 - (43) p .4 cm x 760 mm Hg W i l k i n s o n ^ ^ p o i n t s o u t t h a t E q u a t i o n (12) tends toward l i n e a r i t y f o r moderate v a l u e s o f — — and t h a t e x p e r i m e n t e r s have shown t h a t f o r a gas P m i x t u r e of a r g o n w i t h a l i t t l e q u e n c h i n g gas, E q u a t i o n (12) i s a p p r o x i m a t e by 19 6 yz v = 1.6 x 10 x — — cm/sec. (44) Then f o r the case a t hand the e l e c t r o n d r i f t v e l o c i t y i s a p p r o x i m a t e l y 6 7 v = 1.6 x 10 x 6.58 cm/sec Si£ 1 x 10 cm/sec . (45) Hence an e l e c t r o n t r a v e l s one c e n t i m e t e r i n about 100 nanoseconds. W i t h p l a n e s p a c i n g o f 4 mm the p o s i t i o n o f the p r i m a r y i o n i z a t i o n r e l a t i v e t o the s i g n a l w i r e i s u n c e r t a i n to a t l e a s t 2 mm, and so one may e x p e c t the time j i t t e r t o be a p p r o x i m a t e l y 20 nanoseconds. To sum up, t h e v o l t a g e . p u l s e r e s u l t i n g f r o m the d e t e c t i o n o f the 55 5.9 k e v x - r a y o f Fe by the m u l t i w i r e p r o p o r t i o n a l chamber h a v i n g 10 w i r e s p e r i n c h , \ i n c h between p l a n e s , 907o A r - 107o CH. gas m i x t u r e , o 4 1800 v o l t s o f p o t e n t i a l d i f f e r e n c e on the e l e c t r o d e s , and a 5 K-/1- r e s i s t o r t e r m i n a t i n g t h e s i g n a l w i r e o f i n t e r e s t s h o u l d have the f o l l o w i n g c h a r a c t e r -i s t i c s a c c o r d i n g to the f o r e g o i n g t h e o r e t i c a l c o n s i d e r a t i o n s : P u l s e h e i g h t 0.3 mv T o t a l p u l s e l e n g t h 12 yUsec P u l s e r i s e t i m e 24 n s e c Decay t i m e o f d i f f e r e n t i a t e d p u l s e 0.55y^sec Time r e s o l u t i o n 20 n s e c I n v i e w o f the many a p p r o x i m a t i o n s made, t h e s e e s t i m a t e d v a l u e s may be i n e r r o r by as much as 100%. CHAPTER I I I CONSTRUCTION A. P l a s t i c Frame Chambers I n i t i a l l y the chambers were b u i l t s i m i l a r l y to t h o s e d e s c r i b e d by (2) Charpak e t a l , as shown i n F i g . 9. S i g n a l p l a n e s and h i g h v o l t a g e p l a n e s were made by s t r e t c h i n g w i r e s i n p a r a l l e l on the i n c h P l e x i g l a s f r a m e s . The w i r e used was g o l d - p l a t e d t u n g s t e n , 0.0005 i n c h i n d i a m e t e r (12.7 yUra), o b t a i n e d f r o m T h e r m i o n i c P r o d u c t s Co., P l a i n f i e l d , New J e r s e y . F i r s t i t was wound c o n t i n u o u s l y on a d e v i c e c o n s i s t i n g o f f o u r b r a s s r o d s , t h r e a d e d w i t h 20 t h r e a d s p e r i n c h , mounted i n a s c i s s o r s - l i k e frame. When the frame was f u l l y wound w i t h r o u g h l y 128 p a r a l l e l l i n e s of w i r e , the d e v i c e was expanded s l i g h t l y by means of screws so as to make the w i r e s e v e n l y t a u t . F i r s t , o f c o u r s e , t h e t h r e a d e d b r a s s r o d s were l u b r i c a t e d w i t h m e t h a n o l so t h a t the w i r e would n o t b r e a k under uneven t e n s i o n somewhere i n i t s w i n d i n g s . A l t h o u g h the w i r e i s e x t r e m e l y f i n e , i t was p o s s i b l e a f t e r p r a c t i c e to t a u t e n the w i r e s y s t e m to a d e g r e e j u s t s h o r t of b r e a k i n g , judged by f e e l . Then t h e d e v i c e was l a i d on a ~" P l e x i g l a s frame so t h a t t h e 4 p a r a l l e l w i r e s s t r a d d l e d the o p p o s i t e ends w h i c h had been c o a t e d w i t h an epoxy one q u a r t of w h i c h had been g r a c i o u s l y s u p p l i e d f r e e by R e i c h h o l d C h e m i c a l s (Canada) L i m i t e d , P o r t Moody, B r i t i s h C o l u m b i a . When the epoxy had d r i e d , the p a r a l l e l w i r e s were the n s e c u r e l y f i x e d to the P l e x i g l a s f r a m e , e v e n l y t a u t and e q u a l l y spaced a t .05 i n c h (1.27 mm). S i n c e the s t r e t c h e r was c o n t i n u o u s l y wound, i t c o u l d t h e n be t u r n e d o v e r and the p r o c e d u r e was r e p e a t e d on a n o t h e r P l e x i g l a s frame. ( T h i s t u r n i n g o v e r 20 — P l e x i g l a s .005" w i r e ,030" A l guard s t r i p ,040" p l a s t i c i n s u l a t i o n s t r i p t m y l a r 0016 w i r e .0005" HV w i r e s w i r e s .0016" HV n e g a t i v e g u a r d s t r i p s F I G . 9--Schematic Diagrams o f E a r l y V e r s i o n of M u l t i w i r e P r o p o r t i o n a l Chamber sometimes ended i n d i s a s t e r . ) When d r y , the two frames were c u t from the s t r e t c h e r and the w i r e ends trimmed. F o r a s i n g l e chamber, t h r e e o f t h e s e w i r e d frames were assembled as i n F i g . 9. A l s o the f i g u r e shows aluminum g u a r d s t r i p s , whose f u n c t i o n i s t o p r e v e n t e l e c t r i c a l breakdown a c r o s s the d i e l e c t r i c f r a m e s . On e i t h e r s i d e of the a s s e m b l y a P l e x i g l a s frame was added to w h i c h was f a s t e n e d a t h i n m y l a r f i l m to p r o v i d e a window and to make the chamber g a s - t i g h t . The whole chamber was g l u e d t o g e t h e r w i t h the same epoxy men-t i o n e d b e f o r e . S m a l l - b o r e h o l e s were d r i l l e d h o r i z o n t a l l y t h r o u g h the edges o f the o u t e r frames and copper t u b i n g i n s e r t e d to p r o v i d e a gas i n l e t a t the b o t t o m and o u t l e t a t t h e t o p of the chamber. The c o u n t e r gas was f l o w e d t h r o u g h a t e s s e n t i a l l y a t m o s p h e r i c p r e s s u r e . The e l e c t r i c a l c o n n e c t i o n s were q u i t e s i m p l e . The w i r e s o f the two o u t e r HV p l a n e s were j o i n e d t o g e t h e r by means of a w i r e s o l d e r e d a c r o s s them a l l and l e d o u t t o the HV s u p p l y . The w i r e s of t h e m i d d l e s i g n a l p l a n e were s o l d e r e d i n d i v i d u a l l y to s e p a r a t e l i n e s of a p r i n t e d c i r c u i t b o a r d s t r i p w h i c h was f a s t e n e d to the end of the s i g n a l frame. 3 T h i s s t r i p , m e a s u r i n g 8 i n c h e s l o n g by 1-r i n c h e s wide s i m p l y had 128 p a r a l l e l s t r a i g h t l i n e s of g o l d - p l a t e d copper a c r o s s i t s w i d t h , thus a f f o r d i n g a s i m p l e r e a d - o u t method. The p r i n t e d c i r c u i t b o a r d s t r i p was m a n u f a c t u r e d to the a u t h o r ' s d e s i g n by Johns & A s s o c i a t e s Co. L t d . , South Burnaby, B r i t i s h C o l u m b i a . Some m i n o r v a r i a t i o n s i n the c o n s t r u c t i o n of t h e s e chambers were a l s o t r i e d . The aluminum guard s t r i p s were o m i t t e d and t h e i r l o s s d i d n o t seem to have a p p r e c i a b l e e f f e c t . I n s t e a d o f epoxy, g l u i n g was done by means of e t h y l e n e d i c h l o r i d e w h i c h m e l t s the P l e x i g l a s s u r f a c e s l i g h t l y , 22 a f t e r which the p l a s t i c material fuses together again. This method has the great advantage that i t s drying time i s only a few minutes as com-pared with several hours f o r epoxy. However, i n some cases, the wires were not so securely fastened as with epoxy. This method was much less messy and produced a neater chamber. The biggest disadvantage of the foregoing construction methods was that, once glued together, the chamber could not be dismantled for possible r e p a i r s . Consequently, these methods were abandoned i n favour of a simpler construction. B. Printed C i r c u i t Board Chambers Instead of gluing the wires to a P l e x i g l a s frame i t was decided to solder them d i r e c t l y to a printed c i r c u i t board frame as shown i n F i g . 10. These frames were made to the author's design by Johns & Associates Co. Ltd., out of ordinary ~-r inch printed c i r c u i t board material. The wires were simply stretched by hand and soldered into place i n d i v i d u a l l y . Now the gold-plated copper l i n e s are r i g h t on the frame, making i t easy to solder the wires i n d i v i d u a l l y to the l i n e s and also making the s i g n a l read-out easy. Once strung, the boards are stacked together--three for a s i n g l e chamber, f i v e f or a double, and so on--with rubber gaskets between boards to stop gas leakage. On e i t h e r side i s placed a ^ inch P l e x i g l a s frame with i t s thin mylar window and i t s inserted copper tubing for gas i n l e t or o u t l e t . F i n a l l y a ~ inch thick aluminum frame i s added on e i t h e r side to give strength and to ensure f l a t n e s s of the planes. The whole sandwich i s fastened together by means of four b o l t s near the corners; this provides ample gas-tightness. In a l l of these chambers i t i s important that the planes be as FIG. 10--Schematic Diagrams of Printed C i r c u i t Board Type of Chamber 23 f l a t as possib l e , that the wires be evenly spaced and evenly taut, that the chamber be free of any sharp points which might lead to corona d i s -charge, and that the inner chamber be free of d i r t which might f l o a t onto a wire and provide a point f o r corona discharge. This l a s t d e t a i l i s extremely important for a l l i t takes to cause trouble of this kind i s an almost microscopic b i t of dust, f i b r e from the printed c i r c u i t board frames, or a ti n y piece of the almost i n v i s i b l e .0005 inch wire. The e l e c t r i c a l connections f o r these P.C. board chambers are l i k e those of the p l a s t i c frame chambers. The l i n e s of the HV planes are joined by a wire soldered across them and then lead out to the HV source. For the si g n a l planes, the p a r a l l e l conducting l i n e s terminate at the edge of the board which juts out inch from the side of the chamber, allowing a standard connector to be slipped on. I t i s obvious that the l a t t e r method of chamber construction lends i t s e l f very well to easy r e p a i r s . Adjustments were also simple: f o r example, i n s e r t i n g or removing planes to make a double or a sing l e chamber, r o t a t i n g the si g n a l planes to be p a r a l l e l or perpendicular to the HV plane wires, i n s e r t i n g planes with d i f f e r e n t wire spacing, or changing the spacing between planes. The l a s t adjustment was t r i e d i n two d i f f e r e n t ways: the more v e r s a t i l e way was to i n s e r t spacers i n the form of frames of epoxy-fibre board, the same sort of board used f o r printed c i r c u i t s but with no m e t a l l i c coating. These spacers were cut from the material 1 " 1" which was obtained i n sheets of — and -r thickness. The other way was l o o 1" 1 to s t r i n g the wires on — thick P.C. frames as well as on the — thick o l o frames. Since the standard P.C. board e l e c t r i c a l connectors are made 1 " to f i t — boards, i t was necessary to shave h a l f of the thickness from lo 24 1" •the edges of the -3- board when i t was used for s i g n a l planes. This o 1" l a t t e r method i s not advised because the non-standard -jr P.C. board 1 " material i s not so r e a d i l y a v a i l a b l e as the standard — board. j CHAPTER I V READ-OUT SYSTEM W i t h the e a r l y P l e x i g l a s t y p e of chamber the s i g n a l w i r e s were r e a d one a t a time by a s i m p l e d i f f e r e n t i a t o r c o n n e c t e d t o an o s c i l l o -s c o p e , as i n F i g . 11. Then i t was f o u n d t h a t t h e c a p a c i t o r c o u l d be o m i t t e d as s t r a y c a p a c i t a n c e a f f o r d e d ample d i f f e r e n t i a t i o n o f the p u l s e . I n t h e l a t e r t e s t s each s i g n a l w i r e was c o n n e c t e d to ground t h r o u g h a 3K-/L r e s i s t o r . T h i s r e s i s t a n c e was chosen i n o r d e r t o s i m u l a t e th e i n p u t impedance o f a p o s s i b l e a m p l i f i e r . F i g . 14 g i v e s a d i a g r a m of t h e e l e c t r o n i c c i r c u i t used f o r m e a s u r i n g t i m e r e s o l u t i o n w h i l e F i g . 12 shows a d e t a i l e d s c h e m a t i c d i a g r a m o f the a m p l i f i e r . S i n c e t h i s a m p l i f i e r g i v e s a d i g i t a l o u t p u t , f o r energy measurements the c i r c u i t o f F i g . 13 was us e d . The d i g i t a l a m p l i f i e r was b u i l t l o c a l l y by T e c h c a l E l e c t r o n i c S e r v i c e s a t a c o s t o f a p p r o x i m a t e l y $12.50 each, f r o m a d e s i g n by t h e RHEL E l e c t r o n i c s Group. Fou r a m p l i f i e r s a r e mounted on each b o a r d w h i c h measures 3^ i n c h e s s q u a r e . F o u r o f t h e s e b o a r d s f i t i n t o a s m a l l r a c k w h i c h i s t h e n mounted near t h e end of the chamber. Power i s l e d to the r a c k and d a t a i s l e d f r o m the r a c k by means of c a b l e s w i t h a p p r o p r i a t e t e r m i n a t i o n s . The a m p l i f i e r s r e c e i v e t h e p u l s e s f r o m the s i g n a l w i r e s t h r o u g h the 3KJ1. r e s i s t o r s w h i c h a r e s o l d e r e d t o a 64-way c o n n e c t o r , s u p p l i e d by U l t r a E l e c t r o n i c s (Components) L i m i t e d , w h i c h s l i p s o n t o the edge of the P.C. frames o f the chamber. 25 *nal Wires CRO FIG. ll--Simple E l e c t r i c a l Connections of Ea r l y Chambers + Vcc a + 12v FIG. 12--Schematic Diagram of D i g i t a l Amplifier Signal Wires Ortec 101 Preamplifier Ortec 201 Ampl i f ie r Kicksor ter CRO FIG. 13—Schematic Diagram for Energy Resolution Measurement Signal Wires inm$ Each3 K D i g i t a l Amplifier i I (see F i g . 12) 1 HI-Discriminator Delay Nal Crystal C Z Z Z Z Z 3 — Chamber I I 90 Sr Source Photomultiplier Kicksorter Discriminator TAC Delay S t oP Star t FIG. 14--Schematic Diagram f o r Time Resolution Measurements 26 The ampl i f ier features a d i g i t a l output pulse of 4 vo l t s ampli-tude, 150 nsec duration with a delay of 300 nsec, and a d iscr iminator l e v e l of 0.5 mv. Future work w i l l include further development of the read-out system. CHAPTER V OPERATION AND TESTING OF THE CHAMBERS A. P l a s t i c Frame Chambers The f i r s t part of the experimental work was devoted to the P l e x i g l a type of chamber previously described, constructing several models, deter-mining the i r operating voltages under conditions of d i f ferent gas mixtures and measuring pulse heights and r i se t imes . The basic experimental set-up was as shown i n F i g . 15. The gas, argon with a small admixture of a polyatomic quenching agent, was fed into the bottom of the chamber through ^ inch Po ly f lo tubing with appropriate f i t t i n g s ; i t was vented at the top of the chamber and thence allowed to bubble in to a f lask par t ly f i l l e d with ethanol. The l a t t e r served as an exhaust indica tor and also as a preventative against the p o s s i b i l i t y of electronegative gases flowing back into the chamber to contaminate i t . The gas flow was control led by a pressure gauge on the gas cyl inder and a needle valve followed by a flowmeter. When l i q u i d quenching agents such as ethanol, pentane and heptane were used, a branch tube allowed argon to bubble through the l i q u i d and the r e su l t i ng gas mixture was then led to j o i n wi th a pure argon branch and thence into the chamber. Each branch had i t s own needle valve and flowmeter. The quenching agent f lask was kept at 0°C by means of an ice bath i n order to r e s t r i c t the amount of quenching agent vapor izat ion as otherwise the excessive vapour tended to hinder operation of the chamber. The gas mixture was flowed through the chamber e s sen t i a l ly at atmospheric pressure and at a rate of 0.5 cu f t . per hour t y p i c a l l y . 27 > To Exhaust Flask I A Flowmeter Needle Valve Argon 5* To HV Supply To CRO Flowmeter % Needle Valve T Other Gas With Gaseous Quenching Agent - Po ly f lo Tubing I Flowmeter Needle Valve Argon 1 Flowmeter 1 Needle Valve With L iqu id Quenching Agent FIG. 15--Schematic Diagram of Chamber Gas Flow 28 The HV planes were kept at a constant but v a r i a b l e p o t e n t i a l by means of a Northeast S c i e n t i f i c regulated high voltage power supply. A Tektronix Model 585A o s c i l l o s c o p e was used to display the pulse generated across the read-out r e s i s t o r attached to the p a r t i c u l a r wire of i n t e r e s t . 137 The r a d i o a c t i v e source used most often was Cs ; i t was positioned roughly above the wire of i n t e r e s t . .Table I II shows a comparison of some r e l a t i v e pulse c h a r a c t e r i s t i c s 137 using the Cs source with several d i f f e r e n t gas mixtures. The data of Table I II give an idea of the r e l a t i v e behaviour to expect with these d i f f e r e n t quenching agents. The chamber used had 20 wires per inch with inch spacing between planes. B. Printed C i r c u i t Board Chambers As-mentioned i n the construction section, the l a t e r chamber models were easy to dismantle f o r repa i r s or adjustments, and so experimentation concerning d i f f e r e n t wire and plane spacings or configurations was r e a d i l y c a r r i e d out. (1) P a r a l l e l or Perpendicular Mode In order to in v e s t i g a t e the e f f e c t s of p o s i t i o n i n g the signal plane with i t s wires p a r a l l e l to, or a l t e r n a t i v e l y perpendicular to, the wires of the HV planes, a s i n g l e chamber was assembled with a 10 wire per inch s i g n a l plane f i r s t i n the p a r a l l e l mode and subsequently i n the perpendicular mode. In each case, before t e s t i n g , the counter gas was allowed to flow f o r several hours to allow the chamber conditions to s t a b i l i z e , since, when a chamber i s opened, unwanted gases l i k e oxygen enter into i t and must be flushed out. Table IV shows some r e s u l t s of t h i s t e s t i n g , which used a 100 microcurie source of Fe"'"' whose spectrum TABLE I I I . Chamber Operation with Different Quenching Agents The f i r s t three addit ives l i s t e d are l i qu ids and thei r proportion was not measured or ca lcula ted . Gas or Vapour Added to Argon Optimum Operat-ing Voltage (vol ts) Rela t ive Maximum Pulse Height ( m i l l i v o l t s ) Rela t ive Pulse Rise-time (nanosec.) ethanol 1750 02 1.0 pentane heptane methane 10% 2850 1250 2250 2.0 1.0 .33 2.0 1.0 acetylene 17%, isobutane 207o 2650 2650 .6 1.0 33 33 TABLE IV Comparison of Chamber Operation with Signal Wires P a r a l l e l and Perpendicular to HV Wires P a r a l l e l Mode Perpendicular Operating HV used 1600 v . 1600 v. Breakdown HV 1700 v. 1900 v . Max. pulse height 8 v . 4 v . Kicksor ter data: 3 kev peak i n channel 5.9 kev peak i n channel FWHM of 5.9 peak, channels , kev 114 296 137 2.18 111 338 91 1.16 Using Ortec Model 201 ampl i f ier on un i t gain se t t ing . 29 shows a 3 kev and a 5.9 kev x - r a y peaks. A l t h o u g h t h i s t e s t was done o n l y once i n t h i s f a s h i o n , o t h e r measurements were made on d o u b l e chambers w i t h o r t h o g o n a l s i g n a l p l a n e s . F o r i n s t a n c e , F i g s . 16 and 17 show the en e r g y r e s o l u t i o n s o f a w i r e on each o f the o r t h o g o n a l s i g n a l p l a n e s o f a 10 w i r e p er i n c h d o u b l e chamber w i t h i n c h e x t r a s p a c e r s between p l a n e s . F i g . 16 i s f o r the p e r p e n d i -c u l a r mode: the f u l l w i d t h a t h a l f maximum of the 5.9 k e v peak f r o m the Fe"'"' s o u r c e measures 1.09 kev; v i s u a l l y the r e s o l u t i o n i s q u i t e n o i s e -f r e e . F i g . 17 i s f o r the p a r a l l e l mode: the c o r r e s p o n d i n g FWHM i s 2.16 kev; v i s u a l l y the peaks show c o n s i d e r a b l e n o i s e . (2) W i r e and P l a n e S p a c i n g s W i t h r e g a r d t o the e f f e c t s o f d i f f e r e n t w i r e and p l a n e s p a c i n g s , T a b l e V summarizes the s i g n i f i c a n t d a t a . I n some cases more tha n one e n t r y i s shown f o r a g i v e n measurement. These a r o s e f r o m r e a d i n g o u t d i f f e r e n t w i r e s , w h i c h may g i v e s l i g h t l y d i f f e r e n t r e s u l t s , o r f r o m d i f f e r e n t a m p l i f i e r s on s e p a r a t e w i r e s . These r e a d i n g s w h i c h do n o t d i f f e r a p p r e c i a b l y , a r e i n c l u d e d to g i v e an i d e a o f the range o b s e r v e d i n some measurements. The b r a c k e t e d numbers r e f e r t o the f i g u r e s , w h i c h d i s p l a y p h o t o g r a p h i c a l l y the r a t h e r n i c e r e s u l t s . (3) E n e r g y R e s o l u t i o n The energy r e s o l u t i o n measurements were made by s i m p l y f e e d i n g the s i g n a l f r o m the 3K_/T- r e s i s t o r a t t a c h e d t o the end of a s i g n a l w i r e i n t o an O r t e c Model 101 p r e a m p l i f i e r , t h e n t o the Model 201 a m p l i f i e r , and f i n a l l y i n t o a N u c l e a r D a t a p u l s e h e i g h t a n a l y z e r . T h i s s e t - u p i s s k e t c h e d i n F i g . 13. F i g . 18 shows a t y p i c a l s e t o f p u l s e s f r o m t h e O r t e c 201, as d i s p l a y e d on the CRO. The 5.9 k e v and the 3 k e v p u l s e s a r e TABLE V. Comparison of Chamber Operation with Different Wire and Plane Spacings 10 wire / inch 20 wi re / inch Extra Spacers none 1/16 i n . none 1/16 i n . 1/8 i n . Operating HV 1680 2500 1950 2500 3900 Energy Resolution 1.37 (19,20) 1.09 (16) 1.42 1.41 too poor to measure (FWHM of 5.9 kev peak, measured i n kev) 1.71 (21) 1.23 (22) 1.97 Time Resolution (nsec) 56 (23) 42 (24,25) 55 (26) 34 (27) 25*(28) 91 92 101 80 A l l measurements were made using methane as quenching agent except that marked * which used isobutane. The bracketed numbers refer to the photographic f igures . FIG. 17--Energy Resolution, P a r a l l e l Mode. FIG. 18--Typical Pulses from Fe Source, Amplif ied by Ortec 101/201. 20 v / d i v . ; 5 y " s e c / d i v . p r — , • j - -FIG. 19--Energy Resolution. Fe Source. FWHM 1.37 kev. See Table V. FIG. 20--Energy Resolut ion. As F i g . 19 but d i f ferent wire and more counts. FIG. 21--Energy Resolut ion. FWHM 1.71 kev. FIG. 22--Energy Resolution. FWHM 1.23 kev. 1 1 1 1 FIG. 23--Time Resolution. FWHM 56 nsec. - — 1 FIG. 24. Time Resolution. FWHM 42 nsec. Peak channel 83. I 1 Jv!vv>>, » FIG. 25--Time Resolution; Ca l ib ra t ion of 128 Channel Mode. As F i g . 24, but peak shif ted to channel 78 by inse r t ion of 47 nsec delay. FIG. 27--Time Resolution. FWHM 34 nsec. FIG. 28--Time Resolut ion. FWHM 25 nsec. (best achieved) 30 c l e a r l y distinguished. (4) Time Resolution For measuring the time r e s o l u t i o n , F i g . 14 gives a schematic diagram of the e l e c t r o n i c s . The s t a r t pulse f o r the time-to-amplitude converter (TAC) i s provided by a sodium iodide s c i n t i l l a t o r while the stop pulse comes from the slower proportional chamber. The p r i n c i p l e of operation i s sketched i n F i g . 29. The variance i n t i s due to discriminator timing j i t t e r which arises because the pulse heights may d i f f e r by s l i g h t amounts, as well as to the f a c t that i n i t i a l i o n i z a t i o n may occur anywhere wit h i n the chamber. To c a l i b r a t e the apparatus a delay box was inserted on each arm of the c i r c u i t . These were varied by a known amount and the r e s u l t i n g s h i f t i n the time peak was observed, as shown by F i g s . 30 and 31. Thus, fo r the case of the Nuclear Data pulse height analyzer operating i n the 256-channel mode, one channel was found to equal 63 nanosec , „ =4.2 nanosec . (46) 114.5 - 129.5 (5) S p a t i a l Resolution L i t t l e information was gathered about the chambers' s p a t i a l r e s o l u t i o n , but Table VI shows an example of the e f f e c t of changing source p o s i t i o n on the count rate and time r e s o l u t i o n of a wire on the s i g n a l plane of a 10 wire per inch chamber with y^ r inch spacing between planes. (6) Pulse Height, Risetime, and Decay Time Fi g s . 32 and 33 aire photographs of the same pulse from a 10 wire per inch chamber operating at 1750 v o l t s on a gas mixture of 957c argon -Start Stop | < — A t — > | Number of Counts fwhm = r e s o l v i n g time A t from TAC (channels') FIG. 29--To Measure Time Resolution FIG. 30--Time Resolution; Ca l ib ra t ion of 256 Channel Mode. Peak i n channel 114. - ":' • ,n • -" . ' 1 l . j ' l t ^ l l l l " ! ! 1 FIG. 31--Time Resolution; With Delay. Inser t ion of 63 nsec delay shif ted peak to channel 129. FIG. 32--Risetime of Pulse D i r e c t l y From Chamber. 50 nsec/div; 5 mv / d i v . FIG. 33--Decay Time of Pulse D i r e c t l y From Chamber. 200 nsec/div. TABLE VI. Rough Estimation of S p a t i a l Resolution of Chamber 90 Sr Source Counts i n FWHM of Time P o s i t i o n . 1 Min. Peak (Channels) s | 2803 4 2543 4-J 2846 4-f 3428 24 4 4 | 4732 15 *4- | ' 4895 10 4 | 4245 12 o 4-7 3196 12 4 4-| 3350 24 5 2783 24 Apparently c l o s e s t to at this p o s i t i o n the wire. the source was 31 57. i s o b u t a n e w i t h the s i g n a l w i r e of i n t e r e s t t e r m i n a t e d by a 5K_/)_ r e s i s t o r . The p u l s e h e i g h t i s 5 mv. F i g . 32, where the time s c a l e i s 50 n s e c / d i v . , shows the p u l s e r i s e t i m e t o be a p p r o x i m a t e l y 25 n s e c . F i g . 33 w i t h a time s c a l e of 200 n s e c / d i v . shows t h a t the decay time where the p u l s e r e a c h e s of i t s peak h e i g h t i s a p p r o x i m a t e l y 0.8 sec. (7) Gas A m p l i f i c a t i o n F a c t o r , A F i g s . 34 and 35 a r e graphs of a m p l i f i e d p u l s e h e i g h t P v e r s u s h i g h v o l t a g e V, o b t a i n e d f r o m a 10 w i r e p e r i n c h chamber w i t h -\~ i n c h o between p l a n e s . F i g . 34 i s f o r a 9 0 % Ar - 107> CH^ gas m i x t u r e , w h i l e F i g . 35 i s f o r two c o n c e n t r a t i o n s o f A r - i s o b u t a n e . The marked p o i n t s r e p r e s e n t e x p e r i m e n t a l measurements; t h e s o l i d l i n e s a r e p l o t s o f the f o l l o w i n g e q u a t i o n w h i c h was a d a p t e d f r o m E q u a t i o n ( 3 6 ) : 1 l o g P = oL (,-^-r - V2) + l o g B . (47) P 2 E q u a t i o n (47) was f i t t e d to the e x p e r i m e n t a l p o i n t s by t h e L e a s t Squares method w i t h Vp and B as the v a r i a b l e p a r a m e t e r s . The f a c t o r oC was c a l c u l a t e d as 0.100 f o r t h e 10% methane m i x t u r e b u t oC i s n o t known e x a c t l y f o r the i s o b u t a n e m i x t u r e s as i t c o n t a i n s the f a c t o r f w h i c h i s n o t g i v e n f o r i s o b u t a n e i n T a b l e I I . A c c o r d i n g l y , f o r the i s o b u t a n e m i x t u r e s oC was v a r i e d i n s t e p s o f about 1% u n t i l the L e a s t Squares f i t was o b t a i n e d w h i c h gave the same B as had been found f o r the methane c a s e . Then f was d e r i v e d f r o m oC s i n c e by E q u a t i o n ( 3 6 ) , , 2 ,fNca. 9 , . . * = 275026 (ibo0 ' ( 4 8 ) I n v i e w o f the m a t c h i n g o f the s e m i l o g p l o t s , the r e l a t i o n s h i p between A and P may be w r i t t e n 5.0 Experimental points are marked O . S o l i d l i n e s are t h e o r e t i c a l curves. HV ( k i l o v o l t s ) 32 P = B A (49) E q u a t i o n (49) a l o n g w i t h E q u a t i o n (37) g i v e s B = £ f (50) G, the g a i n o f the O r t e c 101/201 a m p l i f i e r s y stem, was measured as 6500. The t o t a l c a p a c i t a n c e C was measured as f o l l o w s : s i g n a l w i r e 15 pf c o n n e c t i n g c a b l e 75 CRO i n p u t , and e s t i m a t e d i n p u t c a p a c i t a n c e f o r O r t e c 101/201 system 20 T o t a l 110 p f (51) Then, 6500 x 2 0 0 x 1.6 x 1 0 " 1 9 - T H 110 x 10 = 1.89 x 1 0 " 3 T a b l e V I I summarizes t h e s e r e s u l t s , TABLE VII. Results of F i t t i n g Experiment Points to Th e o r e t i c a l Formula 1 l o g P = ori (-^ -- - V 2) + log B V~2 P Ad d i t i v e 10% Methane 5% Isobutane 10% Isobutane o<_ 0.100 0.136 0.114 V 612 525 519 P B (expt.) 0.935 x 1 0 ~ 3 0.940 x I O - 3 0.919 x 1 0 _ 3 B (theor.) 1.89 x I O - 3 1.89 x I O - 3 1.89 x I O - 3 f (indicated) 1.24 ' 3 0 . 2 6.4 OC. for methane was calculated from Equation (48) . £>c^_ and thence f, were obtained for the isobutane mixtures by r e q u i r i n g that the three B's coincide. CHAPTER VI. DISCUSSION AND CONCLUSIONS On the b a s i s o f the t e s t i n g d e s c r i b e d i n the p r e v i o u s c h a p t e r i t i s e v i d e n t t h a t a p r o p o r t i o n a l chamber w i t h e x c e l l e n t c h a r a c t e r i s t i c s can be made q u i t e e a s i l y , c h e a p l y , and w i t h a minimum of c r i t i c a l p a r a m e t e r s . R e f e r r i n g to the d i f f e r e n t gas m i x t u r e s t e s t e d , the f i r s t t h r e e a d d i t i v e s l i s t e d i n T a b l e I I I a r e l i q u i d under normal c o n d i t i o n s and so the a r g o n had t o be b u b b l e d t h r o u g h them. T h i s p r o c e d u r e i s n o t amenable to a d e quate c o n t r o l and so t h e i r use i s n o t a d v i s e d . The a c e t y l e n e used was of a poor g r a d e , w h i c h f a c t c o n t r i b u t e d to i n s t a b i l i t y of.chamber o p e r a t i o n due to i m p u r i t i e s . The methane m i x t u r e , w h i c h i s v e r y common, worked q u i t e a d e q u a t e l y . However, i t wou l d seem t h a t the i s o b u t a n e , w h i c h i s a l s o e a s y t o o b t a i n , i s p r e f e r a b l e , f o r example, i n p u l s e r i s e -t i m e . T a b l e I V , w h i c h compares some measurements on two chambers t h a t d i f f e r e d o n l y by h a v i n g the s i g n a l p l a n e w i r e s e i t h e r p a r a l l e l o r p e r -p e n d i c u l a r t o t h o s e o f the HV p l a n e s , shows t h a t the p e r p e n d i c u l a r ' mode g i v e s b e t t e r e n e r g y r e s o l u t i o n . A l s o , i t a l l o w s a h i g h e r v o l t a g e to be u s e d , w h i c h would tend to improve p e r f o r m a n c e even more. T h i s d i f f e r e n c e i n b e h a v i o u r i s a l s o i l l u s t r a t e d b y . F i g s . 16 and 17 w h i c h p e r t a i n t o a d o u b l e chamber w i t h o r t h o g o n a l s i g n a l p l a n e s . F i g . 16 f o r the p e r p e n d i -c u l a r mode shows 1007» b e t t e r energy r e s o l u t i o n and much l e s s n o i s e t h a n F i g . 17 f o r t h e p a r a l l e l mode. Hence p l a c i n g t h e s i g n a l w i r e s p e r p e n d i -c u l a r t o the HV w i r e s i s a d v i s a b l e f o r b e t t e r r e s u l t s . W i t h r e g a r d t o w i r e and p l a n e s p a c i n g , T a b l e V shows t h a t the b e s t 33 3 4 energy and time resolutions from the chamber configurations tested came from the 1 0 wire per inch chamber with extra -— inch spacers between planes. A l l of these chambers have been made with . 0 0 0 5 inch signal wires. As Charpak points out, of. course, d i f f e r e n t wire diameters require d i f f e r e n t wire and plane spacings i n order to achieve the best e l e c t r i c f i e l d strength i n the chamber for maximum e f f i c i e n c y . Most of the measurements of Table V were made using argon: 9 0 7 ° -methane: 1 0 7 , as the counter gas. One entry, however, stands out: the best time r e s o l u t i o n of 2 5 nanoseconds was obtained by using argon: 8 0 7 o -isobutane: 2 0 7 , . Few measurements. were made with isobutane before the supply ran out, but i t seems clear that this gas mixture, perhaps i n d i f f e r e n t proportions, w i l l provide the best chamber operation. Although s p a t i a l r e s o l u t i o n was not adequately studied, the example of Table VI shows thatarandomly chosen wire e a s i l y distinguished l a t e r a l source s h i f t s of inch, which i s close to the wire spacing of o .100 inch. By measuring the source p o s i t i o n more accurately and by read ing adjacent wires simultaneously s p a t i a l r e s o l u t i o n of at l e a s t h a l f th wire spacing should be e a s i l y a t t a i n a b l e . F i g s . 3 2 and 3 3 show that the height of this t y p i c a l pulse i s approximately 5 mv. The calculated estimation of 0 . 3 v o l t s was for an Ar - CH^ mixture. Isobutane t y p i c a l l y gives pulses about ten times greater i n height. The observed risetime of 2 5 nsec i s very close to the calculated estimation of 2 4 nsec. The pulse decay length of about 0 . 8 y U sec i s only 4 5 7 , greater than the calculated value of 0 . 5 5 y ^ s e c . I t must be remembered that the equations used were derived for the co-a x i a l cylinder proportional counter and should not be considered exact. 35 A l s o many a p p r o x i m a t i o n s were made i n the c a l c u l a t i o n s , so t h a t p o s s i b l e e r r o r s o f up t o 1007, s h o u l d n o t be too d i s c o n c e r t i n g . F i g s . 34 and 35 show t h a t the t h e o r e t i c a l f o r m u l a f o r t h e gas a m p l i f i c a t i o n f a c t o r , E q u a t i o n ( 3 1 ) , works e x t r e m e l y w e l l . S i m p l y by v a r y i n g the v a l u e o f V , the e l e c t r o d e v o l t a g e a t w h i c h gas a m p l i f i c a t i o n i s e x p e c t e d to s t a r t , i t was p o s s i b l e to match e x a c t l y the s l o p e s of the e x p e r i m e n t a l and t h e o r e t i c a l c u r v e s . The o t h e r p a r a m e t e r , B, o n l y s e r v e d to match o r d i n a t e s , e s s e n t i a l l y . The v a l u e s o f V f o r the t h r e e cases P f i t t e d , namely 612, 525, and 519 v o l t s f o r the m i x t u r e s u s i n g 10% methane, 5% i s o b u t a n e , and 10% i s o b u t a n e r e s p e c t i v e l y , a r e i n the n e i g h b o u r h o o d to be e x p e c t e d , and f u r t h e r m o r e t h e i r r e l a t i v e m a g n i t u d e s a r e as e x p e c t e d : i t was d e t e r m i n e d p r e v i o u s l y t h a t i s o b u t a n e gave b e t t e r p e r f o r m a n c e t h a n methane, w h i c h a c c o u n t s f o r the f a c t t h a t the v o l t a g e a t w h i c h gas a m p l i -f i c a t i o n s t a r t s i s g r e a t e r f o r methane tha n f o r i s o b u t a n e . T a b l e V I I shows t h a t the v a l u e o f the pa r a m e t e r B o b t a i n e d by f i t t i n g E q u a t i o n (47) to the e x p e r i m e n t a l p o i n t s i s h a l f o f the v a l u e o f B d e r i v e d t h e o r e t i c a l l y f r o m E q u a t i o n ( 5 0 ) . T h i s r e s u l t i s j u s t i f i e d by n o t i n g t h a t E q u a t i o n ( 3 0 ) , f r o m w h i c h E q u a t i o n (50) f o l l o w e d , assumed t h a t the p o s i t i v e i o n s had a l l been c o l l e c t e d , whereas d i f f e r e n t i a t i o n i s q u i t e l i k e l y t o c u t the p u l s e h e i g h t i n h a l f , as seen i n F i g . 7. The o n l y i n c o n s i s t e n c y i n t h e s e r e s u l t s l i e s i n t h e a t t e m p t t o p r e d i c t t he v a l u e o f f f o r i s o b u t a n e , w h i c h i s n o t l i s t e d i n T a b l e I I . The d e r i v e d v a l u e s o f f shown i n T a b l e V I I a r e i n c o n s i s t e n t on two a c c o u n t s : f i r s t , t he two v a l u e s f o r the 5% and 10% c o n c e n t r a t i o n s o f i s o -b utane d i f f e r whereas t h e y s h o u l d a g r e e ; s e c o n d , t h e i r m agnitudes a r e s i g n i f i c a n t l y g r e a t e r t h a n t h o s e of the gases l i s t e d i n T a b l e I I . I t must 36 be concluded that the t h e o r e t i c a l formula, Equation (31), does not adequately p r e d i c t the e f f e c t s of using d i f f e r e n t kinds and concentrations of gases. To sum up, the chamber recommended here for use with s i g n a l wires of diameter .0005 inch (12.7yUm) should have wires spaced .10 inch ( ^ 2.5 mm) apart and planes separated by \ inch (^ v> 3.2 mm) with signal o wires perpendicular to HV wires, and be run on an argon-isobutane gas mixture. Such a chamber runs well at 1800 v o l t s with a gas a m p l i f i c a t i o n 4 f a c t o r of the order of 10 , giving a pulse 5 mv high with risetime of 25 nsec and decay length of 0 . 8 y U sec. The chamber features good energy 55 r e s o l u t i o n , g i v i n g a FWHM of almost 1 kev for the 5.9 kev x-ray of Fe , and an exc e l l e n t time r e s o l u t i o n of at l e a s t 25 nsec. The apparatus i s small, portable, and e a s i l y oriented to any s p a t i a l configuration so that i t s experimental use allows for great v e r s a t i l i t y . Some possible uses are as follows: (a) Beam p r o f i l e . Placed i n the beam from a p a r t i c l e accelerator, one or more multiwire proportional chambers could count the number of p a r t i c l e s i n the beam, i d e n t i f y the p a r t i c l e s by t h e i r energies, and determine th e i r p o s i t i o n a l d i s t r i b u t i o n . With the TRIUMF cyclotron, f or example, which has a pulse r e p e t i t i o n period of about 40 nsec, the chamber should be able to d i s t i n g u i s h the i n d i v i d u a l pulses emanating from the cyclo-tron. (b) Spectrometer. The exc e l l e n t p o s i t i o n a l s e n s i t i v i t y of the chamber makes i t i d e a l f o r use i n the f o c a l plane of a p a r t i c l 37 spectrometer. (c) P a i r a n n i h i l a t i o n . Suitably placed chambers could determine ••--.the t r a j e c t o r i e s and energies of photons o r i g i n a t i n g from the a n n i h i l a t i o n of positon-negaton p a i r s . (d) Photodisintegration. Since the chambers w i l l operate on many d i f f e r e n t gas mixtures, the photodisintegration of noble ..gases within the chamber could be investigated. (e) Medical use. A f t e r a radioisotope was i n j e c t e d into a sus- . pected tumor, the chamber could be used to determine the shape and extent of the tumor. J. Sperinde et a l at the Lawrence Radiation Laboratory have recently reported on the use of p l a s t i c s c i n t i l l a t o r s and wire spark chambers i n this regard. In conclusion, i t can be said that the operation of the multiwire proportional chamber conforms very n i c e l y to the theory developed primarily for the coaxial cylinder proportional counter. Also i t i s somewhat rewarding to note that the work described herein has achieved time, energy, and space resolutions which are quite comparable to those reported i n the l i t e r a t u r e . 38 L I S T OF REFERENCES 1 D. H. W i l k i n s o n , I o n i z a t i o n Chambers and C o u n t e r s (Cambridge: Cambridge U n i v e r s i t y P r e s s , 1950). 2 G. Charpak, R. B o u c l i e r , T. B r e s s a n i , J . F a v i e r and C. Z u p a n c i c , N u c l . I n s t r . and Meth. 62 (1968) 262. 3 G. Charpak, CERN C o u r i e r , No. 6, V o l . 9 (Ju n e , 1969). 4 P r o p o r t i o n a l Chambers, CERN C o u r i e r , No. 5, V o l . 10 (May, 1970). 5 G. Charpak, D. Rahm and H. S t e i n e r , N u c l . I n s t r . and Meth. 80 (1970) 13. 6 C. Bemporad, W. B e u s c h , A. C. M e l i s s i n o s and E. S c h u l l e r , N u c l . I n s t r . and Meth. 80 (1970) 205. 7 J . R. Siman t o n , K. R. B o u r k l a n d and R. F. M a r q u a r d t , N u c l . I n s t r . and Meth. 81 (1970) 13. 8 0. D. K e l l o g g , F o u n d a t i o n s o f P o t e n t i a l T h e o r y ( B e r l i n : V e r l a g von J u l i u s S p r i n g e r , 1929). 9 S. A. K o r f f , E l e c t r o n and N u c l e a r C o u n t e r s ( P r i n c e t o n : D. Van N o s t r a n d Company, I n c . , 1955). 10 J . S p e r i n d e , V. Perez-Mendez, A. J . M i l l e r , A. R i n d i , and M. R. R a j u , UCRL - 19376 Rev. P r e p r i n t ( F e b r u a r y , 1970). 11 L. J . K o e s t e r , J r . , U. K o e t z , and S. S i g l e r , N u c l . I n s t r . and Meth. 82 (1970) 67. 

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