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A low energy Beta-ray spectrometer Brown, Harry 1948

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3  3 7  3 7 <- 6  A LOW ENERGY BETA-RAY. SPECTROMETER by Harry Brown  A thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree of MASTER OF ARTS i n the department of PHYSICS  The University of B r i t i s h A p r i l , 1948  Columbia  ACKNOWLEDGEMENT  This research has been carried out under a granti n - a i d from the National Research Council to Dr. K. C. Mann of the Physics Department, University of B r i t i s h Columbia. The author i s the holder of a National Research Council studentship f o r the year 1947-48, The author g r a t e f u l l y acknowledges the.continued advice and assistance of Dr. K. C. Mann under whose d i r e c t i o n the project was established. Further acknowledgement i s made of the assistance given by Dr. J . G. Hooley of the Department of Chemistry, University of B r i t i s h Columbia, i n the preparation of the Radium D solution and of the valuable help and advice of Mr. A* Fraser and Mr. Wm. Pye of the Physics Department i n the machining and glass blowing connected with the project.  t ABSTRACT  The ray is  c o n s t r u c t i o n and p r e l i m i n a r y t e s t s o f a B e t a -  spectrometer described.  focussing  designed  t o w o r k a t e n e r g i e s below 100  The i n s t r u m e n t  i s of the small  type u s i n g f o u r counter p a i r s .  Kev  semi-circular  The d e s i g n i s f o r  r e a s o n a b l y h i g h r e s o l u t i o n and h i g h t r a n s m i s s i o n a n g l e . The m a g n e t i c f i e l d plane than  coils  1%.  designed  to maintain f i e l d  homogeneity t o b e t t e r  The magnet c u r r e n t i s h e l d t o  means o f a n e l e c t r o n i c amplification double  i s p r o d u c e d by a c o m b i n a t i o n o f  triodes The  circuit  part i n  composed o f D.C.  stages c o n t r o l l i n g  10,000  c o u n t e r windows a n d s o u r c e .  by  and A.C.  t h e g r i d s o f a bank o f  i n s e r i e s w i t h t h e magnet  d i o n f i l m s o f t h e o r d e r o f 0.1JA is continuing.  1  6AS7  windings. backing are c o l l o -  Work o n t h i s  instrument  TABLE OF CONTENTS  Page I.  INTRODUCTION  II.  APPARATUS A. The S p e c t r o m e t e r  III.  B.  The Magnet  C.  The C u r r e n t  1  *  . . . . . .  13 16  C o n t r o l Apparatus  RESULTS A. Tests o f the Uniformity of the Magnetic F i e l d B. Tests o f the Current Control Apparatus C.  7  Tests o f the Spectrometer  19 20 .  22  IV.  CONCLUSION  25  •V.  BIBLIOGRAPHY  21  TABLE OF  ILLUSTRATIONS  FIGURE 1  F a c i n g Page Internal  C o n s t r u c t i o n o f the 9  Spectrometer 2  The  3  C o n s t r u c t i o n o f t h e Magnet  4  Schematic  5  Circuit Block Diagram o f Current  Field  o f a Plane  Circular  . . . .  14  . . . . . . . . .  15  Diagram o f Current  Coil  Control 16  Control  Circuit 6  . . ..  V a r i a t i o n o f Magnetic Spectrometer  Field  in 20  PLATE  Page  I  The  Spectrometer P a r t i a l l y Assembled  II  The  Magnet and  III  The  Current Control Panel  IV V  16  The Magnet a n d The  Field  Testing Coils  28  . . . .  29 30  Spectrometer Assembled  6AS7 R e g u l a t o r C h a s s i s  . . .  .  ....  31 32  A LOW ENERGY BETA-RAY SPECTROMETER  I..  INTRODUCTION  In extending the range of ordinary methods of Betaray  spectroscopy to low energies a number of d i f f i c u l t i e s  arise. (a)  The most important of these are as follows: The scattering of electrons from parts of the ap-  paratus increases greatly at lower electron energies.  From  t h e o r e t i c a l considerations the scattering, i n the two processes important at low energies, i o n i z a t i o n and e l a s t i c scattering, varies inversely as the energy to the f i r s t power, at l e a s t , and d i r e c t l y as the atomic number of the scattering material. Experimentally the work of Sehonland" " on the scattering of 1  cathode rays has shown that approximately t h i s holds true. (b)  The detection of low energy Beta p a r t i c l e s also  presents d i f f i c u l t i e s .  I f the ordinary Geiger counter i s  used the 'window' must be made extremely t h i n i n order to B.J.F. Schonland,  Proc.Roy.Soc. A113. 87,  19-6.  2.  allow the passage of the p a r t i c l e s into the counter chamber. 2  Even here scattering i s s t i l l the major problem as Crowther has found that Beta p a r t i c l e s are strongly scattered by f i l m s so t h i n that absorption i s inappreciable. The method of mounting the radioactive source becomes very important at low energies.  Unless i t i s mounted  on a very t h i n f i l m an excess of low energy electrons i s caused by scattering from the support. The work of •z 4 Flammersf eld- and Tyler 7  has shown the importance of t h i s  back scattering. (c)  At low energies i t becomes d i f f i c u l t to measure the  d e f l e c t i n g magnetic f i e l d to the accuracy required.  In an  ordinary large scale spectrometer f i e l d s of less than 30 gauss may be required to focus electrons of 10 Kev  energy.  Thus c a l i b r a t i o n to one percent e n t a i l s measurement of a f r a c t i o n of a gauss. (d)  At these low f i e l d strengths the effect of extra-  neous magnetic f i e l d s becomes important.  In p a r t i c u l a r ,  compensation f o r the earth's magnetic f i e l d i s c r i t i c a l part i c u l a r l y when i t has a component perpendicular to the focussing f i e l d . For  these reasons very few authors have quoted-re-  sults f o r Beta spectra below 100  Kev.  Any measurements  that have been obtained i n t h i s region"have been the r e s u l t J.A. Crowther, Proc.Roy.Soc. A80, ^A. Flammersfeld, Zeits.fur.Physik 2  4  A. W. Tyler,  Phys.Rev.  jj6,  125,  186, 112, 1939.  1908. 727, 1939.  of s p e c i a l techniques. The work of Backus<5 on the Beta spectrum of illustrates this.  Cu^  In investigating t h i s spectrum down to  5 Kev he used an e l e c t r o s t a t i c focussing spectrometer.  His  counter windows, and source backing were collodion films about 0*1 micron thick. The small amount of work done below 100 Kev i s due e n t i r e l y to the experimental d i f f i c u l t i e s involved and not because of any lack of importance.  On the contrary i t i s  essential f o r the development of consistent nuclear theory that r e l i a b l e information be available i n the low energy region. The quantum mechanical equation f o r the energy spectrum of Beta p a r t i c l e s does not d i f f e r e n t i a t e between positrons and electrons with the exception of an expression r e lated to the Coulomb f i e l d of the nucleus. i s n e g l i g i b l e except at low energies.  This expression  Even on a c l a s s i c a l  picture i t i s evident that an electron spectrum should have some intensity even at zero energy while a positron spectrum should drop to zero i n t e n s i t y at an energy equivalent to the potential energy of a positron at the 'surface nucleus.  1  of the  Backus^ i n his i n v e s t i g a t i o n of the electron and  positron spectra of C u ^ found a d e f i n i t e deviation from the low energy positron to electron r a t i o given by nuclear theory. A knowledge of the low energy spectra of many isotopes i s essential to the development of a s a t i s f a c t o r y nuclear theory. V.  Backus,  Phys.Rev.  6_8, £9, 194.5.  4. In addition i t i s highly probable that there are numerous undiscovered 100 Kev.  Beta groups whose end points are below  Also the energy and i n t e n s i t y of Gamma rays i n  this region are uncertain and require further i n v e s t i g a t i o n . For these reasons i t was decided to build a small spectrometer expressly to measure Beta spectra below 100 Kev. I t could also be used to measure Gamma spectra i n t h i s region since the work of Robinson^ on photo effect's of X-rays below 10 Kev shows that the 'photo-electron radiator' technique of Beta-ray spectroscopy  can be applied even at very low  energies.. The design of the spectrometer was governed by the following f a c t o r s : (a)  I n order to use current control apparatus already  b u i l t f o r the large spectrometers magnetic focussing was chosen - u t i l i z i n g the. well known semi-circular focussing property of a magnetic f i e l d . (b)  An air-cored magnet must be used i f possible so  the f i e l d would be a l i n e a r function of the current - thus only one point c a l i b r a t i o n would be required. (c)  The spectrometer had to be as small as possible to  give a small radius of electron path, to l i m i t the size of the f i e l d producing  c o i l s and so that the entire apparatus  could be l i n e d up p a r a l l e l to the earth's magnetic f i e l d i n order to eliminate the need f o r compensating c o i l s . l i m i t i s imposed by the minimum size of the Geiger ^H. Robinson,  Proc.Roy.Soc.  104, 453, 1923.  A lower counters.  (d)  A l l surfaces i n the spectrometer must be made of a  substance of low atomic number i n order to reduce the scatt e r i n g of electrons. (e)  In order to eliminate the use of heavy lead b a f f l e s  to prevent gamma ray background the counters should be so arranged that a coincidence technique could be used i f necessary . (f)  As large as possible a s o l i d angle of the r a d i a t i o n  from the source should be u t i l i z e d so that weak sources could be investigated. (g)  As a preliminary f i g u r e a r e s o l u t i o n of 1% was l a i d  down, but the design of the spectrometer was to be such that changes i n the b a f f l e system, etc., could r e a d i l y be made. (h)  The technique developed by B a c k u s f o r t h i n counter  windows was to be used i f possible. As the spectrum of Radium D has been found to cons i s t of Beta's and 'Gamma's of very low energy, t h i s substance was chosen to make preliminary tests of the instrument. Radium D has been investigated by several workers, a l l using rather special techniques.  G. von Droste'' using  a Wilson cloud chamber and magnetic d e f l e c t i o n , together with measurements of path lengths, obtained a series of y_? l i n e s a l l attributable to the action o f one Y energy.  l i n e of 47.2 Kev  Richardson and Leigh-Smith^ d i s t r i b u t e d Radium D as  -*J. Backus,  loc. c i t .  ^G. von Droste, Zeits.fur.Physik 84, 17, 1933. 8 H.O.W. Richardson & A. Leigh-Smith, Proc.Roy.Soo. l60. 454, 1937.  a gas i n the form of tetra-methyl lead throughout a cloud chamber.  The Beta spectrum was then calculated from electron  path lengths and range-energy measurements.  Lee and L i b b y 9  using magnetic d e f l e c t i o n and aluminum abosrbers found a p r i mary Beta-ray d i s t r i b u t i o n of very low energy with an end point o f 2 5 . 5 ± 1 Kev.  Considerable work on the Gamma radia-  t i o n of RaD has been done by Tsien San-Tsiang, F r i l l e y , et. al.  1 0  , who report the existence of several nuclear Gamma rays  of various i n t e n s i t i e s .  By a number of methods, such as  c r y s t a l analysis, cloud chamber path.lengths, absorption measurements, etc., they show the existence of seven Gamma l i n e s of energies from 7 . 3 Kev to 6 5 Kev.  9  1 0  D.D. Lee and W. V. Libby, Phys .-Rev. £ 5 _ , 2 5 2 , 1939. T s i e n Sah-Tsiang, Comptes Rendus 2 1 6 , 7 6 5 , 194-3* Oxiang Te TchaO, J . Suruque, Tsien San-Tsiang, Comptes Rendus 217, 5 3 5 , 194-3. Tsien San-Tsiang, Comptes Rendus 2 1 0 , 5 0 3 , 1944. M. F r i l l e y , Comptes Rendus 2 1 8 , 50TT 1 9 4 - 4 . Tsien San-Tsiang and C. Marty, Comptes Rendus 2 2 0 , 6 8 8 , 1945.  Tsien San-Tsiang and C. Marty, Tsien San-Tsiang,  Phys.Rev.  Comptes Rendus 69_, 3 8 , 1 9 4 6 .  221, 177,  1945.  7.  II.  The three parts,  a p p a r a t u s may the  control  A.  SPECTROMETER The  ( c ) , ( f ) and  as f o l l o w s :  in  the center o f a c i r c l e .  The  cumference o f t h i s  source  circle  whose p a t h s  i t s e l f Is  (g) a b o v e .  The  the  design  spaced  thread  on t h e  source t r a v e l  B a f f l e s a r e p l a c e d so t h a t  plane in cir-  only electrons  equal to the d i s t a n c e from  s o u r c e t o t h e c o u n t e r window w i l l  cir-  counters.  f i e l d p e r p e n d i c u l a r t o the  e l e c t r o n s e m i t t e d by t h e  e n t i r e apparatus  basic  there are four Geiger  have d i a m e t e r s  governed  i s mounted on a v e r t i c a l Symmetrically  the a c t i o n o f a magnetic  c u l a r paths.  i t s e l f , t h e magnet, a n d  design of the spectrometer  is  'of- t h e c i r c l e ,  into  apparatus.  by r e q u i r e m e n t s  By  c o n v e n i e n t l y he d i v i d e d  spectrometer  current  THE  APPARATUS  r e a c h the counter.  i s enclosed i n a c y l i n d r i c a l  box  the The  which i s  evacuated. P l a n and shown i n F i g . 1.  s e c t i o n views o f the The  spectrometer  are  a c t u a l d i m e n s i o n s "were c a l c u l a t e d  in  i n c h e s b e c a u s e o f d i f f i c u l t i e s w i t h m a c h i n e work and m a t e r i a l s available. The  e n c l o s i n g box  i s a b r a s s c y l i n d e r o f 6_; i n c h e s  8. inside diameter with walls i inch thick. of 5/16 inch brass. seals.  . The end plates are  Soft rubber rings are used as vacuum  A one inch copper pipe passes through the center of  one end plate (hereafter c a l l e d the base plate) f o r connection to the vacuum pump.  Through the wall of t h i s pipe there are  several small tubes for counter f i l l i n g and evacuating, elect r i c a l connections and vacuum gauge. * One inch above the base plate there i s mounted a 1/8 inch brass disc to which are fastened the b a f f l e system and the source holder.  When a l l four counters are used a  U shaped bracket holds the thread on which the course i s deposited, v e r t i c a l l y above the center of t h i s plate.  This  may possibly lead to d i f f i c u l t y i n some instances because of back-scattering from the thread.  An alternative method which  has been used i n preliminary tests using only one counter i s to mount a t h i n (.004  inch) brass sheet with a . 0 1 0 inch s l o t  d i r e c t l y over the center.  The source i s formed by evaporating  a solution of RaD chloride on a t h i n collodion f i l m so that the source covers an area 1 inch by J inch.  The f i l m i s  then mounted behind the brass sheet so that electrons passing through the s l o t are focussed on the counter window.  This  method eliminates the back-scattering e n t i r e l y and i n addit i o n gives a much greater i n t e n s i t y of Beta radiation. The distance from source to counter window i s 2 . 4 inches so that the electrons t r a v e l i n paths whose radius i s 1.2  inches ( 3 . 0 5 cm.).  inches radius, 1% greater.  The b a f f l e s are cut to  1.212  I In fact  making the b a f f l e s ,  t h a t each p a i r  For the i n s i d e  a d v a n t a g e was  form approximately  baffle a.solid  a quadrant  The to  the absorbing grooves  o u t s i d e b a f f l e s w e r e made f r o m the exact i n s i d e diameter  1-1/2  handled  Two  four blocks of  h o l e s 5/8  parallel  inches  e a a h o f t h e s e on c e n t e r s  b l o c k s w e r e t h e n t r i m m e d down t o a shaper.  Particular  f a c e i n w h i c h t h e window was of  this  face only  .030  turned These  c a r e was  t o be  set.  i n c h e s o f m e t a l was  s u r f a c e s were t h e n p o l i s h e d w i t h  brass  diameter  21/32.inch  apart.  the  cut  shaper.  t h e same way.  through  size with  then  cut i n w i t h a  were d r i l l e d The  circle.  was  a hollow c y l i n d e r  c o u n t e r s w e r e made f r o m  inches long.  I t was  the  1(a).  b a f f l e s a r e shown i n F i g . The  and  of a  2 inches long  cylinder  t u r n e d on t h e l a t h e t o t h e e x a c t d i a m e t e r . i n t o q u a r t e r s and  taken of  reasonable  taken w i t h  the  I n the  center  line  left.  The  inside  emery p a p e r and  crocus  i n c h e s l o n g and  .035  cloth  u n t i l q u i t e smooth. 3/4-  Next a narrow s l o t w i d e was  cut through  the f r o n t  parallel  to the a x i s o f the h o l e .  t h e c o l l o d i o n window. windows w i l l  be d e s o r i b e d  Glass caps, to  the  may  through  emits  no  the  This slot  counter,  i s covered  with  p r e p a r a t i o n and m o u n t i n g o f t h e s e '  later.  a s shown i n F i g . 1 ( b ) ,  ends o f t h e f i r s t  extended gated  The  f a c e o f the f i r s t  inches  h o l e and  center..  a  .005  are then  i n c h tungsten  I f the source  being  wire  investi-  Gamma r a y s o r o n l y v e r y weak o n e s , t h i s  be mounted i n p o s i t i o n on t h e b a s e p l a t e and  sealed  counter  connections  2/3 FIGURE  Scale  1.  INTERNAL CONSTRUCTION OF THE SPECTROMETER *  10. made t o t h e f i l l i n g if  system and s c a l i n g  circuits.  However,  t h e s o u r c e e m i t s s t r o n g Gamma r a y s , a r e c t a n g u l a r h o l e  _• i n c h b y f i n c h s h o u l d be c u t t h r o u g h t h e w a l l between t h e two  holes, t h i s  s l o t f o r m i n g t h e window f o r t h e s e c o n d  G l a s s cap's a r e t h e n s e a l e d t o i t a n d t h e c e n t e r w i r e The  two c o u n t e r s a r e t h e n c o n n e c t e d  cuit,  i . e . a count  both counters.  i s registered  use o f t h i s  inserted.  i na 'coincidence' c i r -  o n l y i f an e l e c t r o n  traverses  T h i s u s u a l l y happens o n l y f o r e l e c t r o n s  whioh a r e f o l l o w i n g t h e c i r c u l a r The  counter.  path through the b a f f l e s .  c o i n c i d e n c e method o n o t h e r s p e c t r o m e t e r s  has r e s u l t e d i n a g r e a t l y r e d u c e d  background  Gamma r a y s f r o m t h e s o u r c e , s c a t t e r e d  c o u n t c a u s e d by  e l e c t r o n s , and cosmic  rays. The  c o u n t e r s and t h e i r a r r a n g e m e n t a r e shown i n  Fig. 1(c). Because o f t h e t h i n n e s s o f t h e c o l l o d i o n f i l m s i t is  n e c e s s a r y t o e v a c u a t e t h e c o u n t e r s a n d t h e vacuum e n -  closure simultaneously, as a pressure d i f f e r e n t i a l greater t h a n 10 cms o f m e r c u r y w i l l e n t i r e system  F i g . 1) a n d f i l l e d  1 / 7 " a l c o h o l a n d 6/7 The last  After the  i s e v a c u a t e d t o 10"^ mm t h e c o u n t e r s a r e c o n -  nected t o the f i l l i n g ((d)  r u p t u r e t h e window.  t o 5 cms p r e s s u r e w i t h a m i x t u r e o f  argon.  filling  f l a s k o f about  s y s t e m by means o f t h e s t o p c o c k  system i s standard except that  4 liters  capacity  a bal-  i s included as the mix-  ture o f argon and a l c o h o l s l o w l y d i f f u s e s through t h e counter window,.  I n t h i s way r u n s o f s e v e r a l h o u r s  c o u l d be made  1  1  •  without the c h a r a c t e r i s t i c s of the counter changing appreciably. The collodion windows are prepared as follows: Collodion i s diluted with an equal volume of amyl acetate. Two drops of t h i s solution are dropped i n rapid succession into a pan of d i s t i l l e d water.  The solution spreads i n a  t h i n f i l m over a c i r c u l a r area about one foot i n diameter of the surface of the water and d r i e s i n a few seconds.  I t can  then be cut into sections by sawing a wire through i t with a rapid up and down motion.  The sections can be l i f t e d out by  means of a rectangular wire frame which i s s l i d under a sect i o n of the f i l m and l i f t e d gently so that the f i l m f a l l s on both.sides of the frame.  Thus the f i l m i n i t s f i n a l state  consists of two thicknesses of the o r i g i n a l f i l m .  In t h i s  way a more uniform f i l m , free from pinholes, i s produced.  It  has been found that when the films dry, they are sometimes marked with straight l i n e s .  Care should be taken to select  films that are clear as the marks seem to indicate breaks i n one side of the f i l m . The f i l m i s mounted i n the following way:  The  front face of the counter i s covered with a t h i n coating of vacuum wax  (Apiezon Qj so that the color of the brass shows  through the wax.  A t h i n sheet of brass .004 inches thick  i s cut to the size of the counter face and a slot cut i n i t .010 inches wide and % inch long, so that t h i s s l o t i s approximately i n the middle of the s l o t i n the counter wall when the brass sheet i s placed exactly on the f l a t face.  . T h e n one  side of this  f i l m of  wax. The  brass  counter  h o r i z o n t a l and  bright  i s covered w i t h a  i s held firmly  a film  The  brass  s h i n i n g through  the  slot  flows over the  slots.)  brass  to l i n e  s l o t s without  no  (A i s of  t o c h e c k t h a t no  sheet can  damaging t h e  wax  be moved a r o u n d  collodion film i f  pressure i s applied. When t h e a l i n e m e n t  held firmly rod  the  s u r f a c e to melt  surfaces together.  s m a l l amount o f wax.  counter  slot  t h e wax  Then t h e  I t i s then  installed  a t the f o c u s o f the  the spectrometer  a heated and w e l d  i s thoroughly  s y s t e m and  i t i s ready The  entire  glass the  two  with  cool  the  of 7 to 1 0  spectrometer  cms  with  beam. the source are  t o t h e magnet and  spectrometer  w h i c h were made o f b r o n z e  number and  and  is  the  installed vacuum  for operation.  the e x c e p t i o n o f the copper  size.  i n the  electron  i s connected  brass sheet  edges a r e c o v e r e d  When t h e wax  ' When t h e f o u r c o u n t e r s  correct  the  i s tested with a pressure d i f f e r e n t i a l  of mercury. the  i s completed,  i n p l a c e w i t h a b l u n t o b j e c t and  i s run over  inside a  counter  around  the  coincide.  i n the  also later  up t h e  i s p l a c e d on  slots  great assistance i n a l i n i n g , The  face i s  so t h a t i t breaks  sheet  s i d e down, so t h a t t h e two  light  similar  so t h a t t h e f l a t  l a i d ..on t h e wax  t h e edges o f t h e f a c e . f i l m , wax  sheet  12.  i s made o u t o f b r a s s  t u b i n g and  baffles  not a v a i l a b l e  i n the  I n o r d e r t o p r o v i d e a s u r f a c e o f low  atomic  thus reduce  the  a s b r a s s was  the o u t e r  with  s c a t t e r i n g o f e l e c t r o n s a s much  13. as p o s s i b l e a l l exposed s u r f a c e s were coated w i t h a t h i n f i l m o f vacuum s e a l i n g was.  B.  THE MAGNET The  spectrometer r e q u i r e s a uniform magnetic  field  over a c y l i n d r i c a l volume" 12 cms. i n diameter and roughly 2 cms. deep.  An a r b i t r a r y l i m i t o f one peroent was s e t on  the v a r i a t i o n o f the f i e l d over t h i s r e g i o n .  Field  strengths  o f 75 t o 360 gauss were r e q u i r e d t o measure s p e c t r a from 5 Kev t o 100 Kev (Hr 230 t o 1100  gauss-cms).  F u r t h e r r e s t r i c t i o n s were imposed by t h e l i m i t a t i o n s o f the c u r r e n t c o n t r o l c i r c u i t .  I t was determined by e x p e r i -  ment t h a t the l a r g e r the l o a d r e s i s t a n c e the g r e a t e r t h e t o t a l power a v a i l a b l e , but the .less the a c c u r a c y o f c o n t r o l .  Thus  a compromise had t o be made and a r e s i s t a n c e o f approximately 12 ohms and a c u r r e n t o f 10 amperes was chosen i n order t o g i v e the maximum f i e l d It  o f 360 gauss and the best p o s s i b l e c o n t r o l .  i s usual t o use a p a i r o f Helmholz c o i l s t o p r o -  v i d e a uniform magnetic f i e l d i t was f e l t  over a c o n s i d e r a b l e  volume, but  that i n t h i s case, s i n c e the uniform f i e l d was  r e q u i r e d only over a t h i n d i s c shaped volume, t h a t i t c o u l d be provided  by a c o i l o r c o i l s  i n one plane.• For a c i r c u l a r  coil  o f r a d i u s a t h e f i e l d H Q a t the center i s _LZ__L . where I i s the a . c u r r e n t through the c o i l .  Con-  14. sider  the p o i n t P  This  i s an  from t a b l e s . in  Fig.  i n the  A  plane  elliptic  curve  o f the  coil  at a  i n t e g r a l and  must be  obtained  p l o t t i n g Hp / H Q a g a i n s t x / a  i s shown  2. By  coplanar  use  coils,  of t h i s one  curve  i t was  determined that  ampere t u r n s  approximately mum  two  gauss a t t h e i r  coil  the  second c o i l  i s i n the  opposite  cms  and  a  common c e n t e r , w i t h of radius  sense to the  current  cms,  third  would g i v e a f i e l d  i n d i c a t e s that the  a  of  maxi-  6 cm.  (The  current i n the  in other  coils. These c a l c u l a t i o n s ,  and  cms  i n h o m o g e n e i t y o f 0 . 2 8 f . o v e r an a r e a  minus s i g n o n this  3o0  of radius 8.5  three  of radius 17.5  o f +14000 ampere t u r n s  a s e c o n d o f - 2 7 0 0 ampere t u r n s o f r a d i u s 1 1 o f +120  distance  would not  section  necessarily hold f o r c o i l s  such as As  however, were f o r i d e a l  i s necessary  to c a r r y the  a maximum c u r r e n t  o f 10  of a f i n i t e current  amperes had  coils cross-  required. been  decided  15. upon, c o i l s of 1400,  270,  and 12 turns were needed.  liminary c a l c u l a t i o n indicated that $14 wire was  A pre-  the  smallest  that would r e s u l t i n the required resistance of 12 ohms. By t r i a l and error calculations the c o i l arrangement shown i n F i g . 3 was form f i e l d .  selected as giving a reasonably uni-  There are two possible causes f o r the  deviation  of the f i e l d of t h i s magnet from the f i e l d of the i d e a l magnet discussed above.  The f i r s t i s the f i n i t e width of  the c o i l s i n the r a d i a l d i r e c t i o n , the other i s the thickness of the  finite  coils.  The f i n i t e width of the c o i l s i n the r a d i a l d i r e c t i o n was  taken into account i n calculations by d i v i d i n g the  outer c o i l into 4 annular rings, the next into two  annular  rings and leaving the inner c o i l as one.  For each of these  annular rings, by use of the graph F i g . 2,  the f i e l d at the  center and at r = 1,  calculated as a  2,- 3> 4, 5> 6 cms was  f r a c t i o n of the f i e l d H  0  at the center of an i d e a l c o i l of  14000 ampere turns and 17.5  cms.  The resultant f i e l d  ob-  tained by adding the i n d i v i d u a l f i e l d s a l g e b r a i c a l l y for each value of r was  equal to 70 ± 1% o f . H Q .  I t i s evident because of the symmetry of the magnet that the f i n i t e thickness of the ©oils w i l l have only a n e g l i g i b l e effect on the d i r e c t i o n of the f i e l d i n the considered.  And further the uniformity  region  of the f i e l d w i l l  not be changed over the small central region since i n any plane through t h i s region and perpendicular  to the axis of  the magnet the turns r a t i o of the c o i l s i s unchanged.  The  1400  12 Turns  270 Turns Turns  m y.'///////////////77.  1/4 Scale FIGURE 3. CONSTRUCTION OF THE MaGNET  16. only possible way that the thickness of the c o i l s could i n fluence the f i e l d would be to change i t s o v e r - a l l value. Consider a solenoidal c o i l of radius a with n turns per unit length and carrying a current i .  The f i e l d at the  point P on i t s axis i s given by Hp  = 2 7rni (cos 0 2 - cos 0 _ )  where 0 i and 0 2 equal one h a l f of the angles subtended at the point P by the ends of the solenoid.  In the worst possible  case for the magnet constructed 0 _ = 78°, 0 2 =  1 0 2  ° which  gives. Kp  = .832 7T n i .  The t o t a l current around the loop i s 2nia tan 12° and i f t h i s were concentrated i n a single turn the f i e l d H at the center would be «*  .848 7r n i .  -  *  Thus H  p  8 5 2  -  982  The f i n i t e thickness reduces the f i e l d by 1.8%.  Therefore  the f i e l d given by t h i s magnet i s equal to 69 * 1% of the f i e l d H Q at the center of an i d e a l c o i l of radius 17.3 cms and of 14000 ampere turns.  C.  THE CURRENT CONTROL APPARATUS The schematic and block diagrams of the current  control apparatus are shown i n Figs. 4 and 5 respectively. The system i s e s s e n t i a l l y that used by Dr. L. G. E l l i o t t i n  FIGURE 4. SCHEMATIC DIAGRAM OF CURRENT CONTROL CIRCUIT  500  i i  mf.  Generator  I Magnet j  it i  A.C. Amplifier Rubicon Potentiometer 3ta. •tes.  Calibration Cell  C  6AS7»S 6AS7  Bias D.C. Amplifier and Phase Sensitive Deteotor  Tube  (6L6)  C5a l i b r a t i o n lvanometer |Ga.  Standard Battery  JL FIGURE  5.  B L O C K D I A G R A M O F CURRENT CONTROL C I R C U I T  17. the N a t i o n a l Research C o u n c i l l a b o r a t o r i e s at Chalk with  some m o d i f i c a t i o n s r e q u i r e d There are  paratus will  with  10  a c t u a l l y two  different  the  'A.C  c y c l e s per  ranges.  from zero  circuit will  can  be  The  t o a b o u t 10  equipment. i n the  'D.C  c y c l e s per  ap-  circuit  cycles  handle frequencies  s e c o n d t o a b o u t 1000  q u e n c i e s above t h i s  differences of  control circuits  frequency  handle f r e q u e n c i e s  second;  by  River,  per from  second.  Fre-  removed by means o f s u i t a b l e  filter  networks. I n t h e D.C. by  t h e magnet c u r r e n t  (.08  ohms) i s b a l a n c e d  potentiometer cell.  The  i n t o a 60  control circuit i n passing  which i n t u r n can  d i f f e r e n c e i n these  to the  cycle voltage  t h e D.C.  output The  t r i o d e s on  db. and  the  voltages  is  i n order  grid.  standard  converted converter. by means o f  r e s u l t a n t D.C.  t o ensure the  r e g u l a t o r tubes are  a separate  parallel  then r e c t i f i e d the  a  voltage  The  proper  a  phase biased  polarity  by in  voltage.  exception  individual two  Rubicon  i s m e r e l y a f u l l wave d e t e c t o r  chassis.  cathodes, r e s p e c t i v e l y of these with  two  developed resistor  c a l i b r a t e d by  g r i d s of the r e g u l a t o r tubes.  sensitive detector 60  be  from a  c y c l e s q u a r e wave by means o f a Brown  'phase s e n s i t i v e d e t e c t o r *  a  voltage  through a small  against a voltage  T h i s i s a m p l i f i e d a b o u t 100  applied  the  of a g r i d The  thirty-eight The  banks o f 19  grids, plates,  tubes are  tubes,  connected  across  the  twin and  connected i n  ' s t o p p e r ' _of 1000  filaments are  6AS7  115  parallel  ohms i n e a c h i n series, volt  A.C.  in  18. lines.  The  t o t a l rated plate current capacity of these  i s r o u g h l y 10 up t o 18  amperes h u t t h e y a p p e a r  feedback  amplified  t o work s a t i s f a c t o r i l y  amperes. The A.C.  tive  c o n t r o l c i r c u i t c o n s i s t s o f a.normal nega-  loop.  by a  A.C.  fluctuations  6AC7, t h e n by a 6L6  the g r i d s o f the  and  a c r o s s t h e magnet applied  T  To p r e v e n t o s c i l l a t i o n due  response  stage i s reduced  o f one  ( g r e a t e r t h a n 1000  condenser  a d d i t i o n i t was  directly duced  with  to the brushes.  sporadic o s c i l l a t i o n s  the  to phase s h i f t  the  Fluctuations  of  are eliminated to a great extent  found n e c e s s a r y t o bypass  t h e commutator  to  across the generator t e r m i n a l s .  the g e n e r a t o r t o ground  are  greatly at high frequencies  cycles per second).  higher frequency than t h i s mf  directly  6AS7 s i n the p r o p e r phase to reduce  fluctuations.  by a 500  tubes  .1  mf  each t e r m i n a l o f  condensers  Larger condensers  'hash* of the  In  connected than t h i s  re-  even f u r t h e r but r e s u l t e d i n system.  19.  Ill.  RESULTS  A number o f t e s t s were c a r r i e d  out t o check t h e  u n i f o r m i t y o f t h e .magnetic f i e l d a n d t o c h e c k t h e o p e r a t i o n of  the c o n t r o l c i r c u i t .  counters  A.  I n a d d i t i o n the operation of the  was t e s t e d i n v a r i o u s ways.  TESTS OF THE UNIFORMITY OF THE MAGNETIC F I E L D The  mentally  u n i f o r m i t y o f t h e f i e l d was  i n t h e f o l l o w i n g way:  t u r n s o f #28  s q u a r e o f 0.5  cm s i d e .  galvanometer.  magnet c i r c u i t  the process  was  a  at  placed  'infinity . 1  broken and the d e f l e c t i o n o f t h e Then t h e c o i l s were  repeated.  interchanged  The d e f l e c t i o n s d i f f e r e d  by  less  0.5f».  than  T h e n one c o i l was and  100  W i t h a measured  o f 4 amperes t h r o u g h t h e magnet one c o i l was  galvanometer observed. and  of  The t w o . c o i l s w e r e c o n n e c t e d i n  t h e c e n t e r o f t h e magnet a n d t h e ' o t h e r  The  coils  1 cm a n d t h e c o i l w i n d i n g s o c c u p i e d  . s e r i e s and t o a b a l l i s t i c s  at  identical  experi-  w i r e were wound o n b a k e l i t e f o r m s so t h a t t h e  i n s i d e d i a m e t e r was  current  Two  checked  the other,  i n opposite  fixed  a t t h e c e n t e r o f t h e magnet  s e n s e t o t h e f i r s t was p l a c e d a t  a p o i n t i n t h e r e g i o n t o be o c c u p i e d while  t h e magnet c u r r e n t was  by t h e  interrupted.  spectrometer The  galvanometer  20. deflections in  observed  the f i e l d s  were t h u s  proportional to thedifference  a t t h e two p o i n t s o c c u p i e d  by t h e c o i l s ,  a n d by  c o m p a r i n g t h e d e f l e c t i o n t o t h a t due t o one c o i l  alone the  percent v a r i a t i o n o f the f i e l d  A large  number  o f r e a d i n g s were t a k e n  second c o i l *  The r e s u l t s  This the as  field  a r e g i v e n by c u r v e s A i n F i g . 6.  was a b o u t 2% a n d t h a t t h e f i e l d  the d i s t a n c e from the center  spectrometer  and thus  the larger values  disconnected. 'Fig.  f o r various positions o fthe  shows t h a t t h e maximum h o r i z o n t a l v a r i a t i o n o f  As t h e i n n e r c o i l  for  c o u l d be f o u n d .  6.  The r e s u l t s  steadily  increased.  o f 12 t u r n s was v e r y  had a f a i r l y of T  increased  large effect  close tothe on t h e f i e l d  a t r i a l was made w i t h t h i s a r e shown by t h e c u r v e s  The maximum v a r i a t i o n o v e r  a cylindrical  coil  Bin region  6 cms i n r a d i u s a n d 2 cms t h i c k i s s e e n .to be 1% w h i c h i s t h e value o r i g i n a l l y  specified.  I t was t h e r e f o r e d e c i d e d  the  c i r c u i t with the inner c o i l  but  i n t h e f u t u r e f u r t h e r measurements w i l l  different  B.  disconnected  numbers o f t u r n s o n t h e i n n e r  t o use  f o r the present, be c o n d u c t e d  with  coil.  TESTS OF THE CURRENT CONTROL APPARATUS An a m p l i f i e r  o f about  90 db. g a i n was c o n n e c t e d  to  an o s c i l l o s c o p e .  Using  .001 v o l t s  (.0028 v o l t s p e a k t o p e a k ) was f e d i n t o  r.m.s*  the a m p l i f i e r  a v o l t a g e d i v i d e r a n A.C. s i g n a l o f  a n d a s i g n a l h e i g h t o f 3 i n c h e s was o b s e r v e d  the o s c i l l o s c o p e  on  s c r e e n when t h e g a i n c o n t r o l was s e t a t t h e  1/2 maximum g a i n p o i n t .  . The l i n e a r i t y  of the gain  control  21. was  checked  setting.  a n d no c o r r e c t i o n s were n e c e s s a r y t o t h e d i a l Thus a t f u l l  gain a signal of .001 volts  peak  s h o u l d g i v e a d e f l e c t i o n o f 2 . 2 i n c h e s on t h e s c r e e n . The  amplifier  standard r e s i s t a n c e  i n p u t was t h e n c o n n e c t e d  i n t h e magnet c i r c u i t .  across the  When t h e c o n t r o l  c i r c u i t was i n o p e r a t i o n a n d magnet c u r r e n t f l o w i n g random p u l s e s o f a maximum h e i g h t o f 1 i n c h were o b s e r v e d . is  e q u i v a l e n t t o a p e a k v o l t a g e o f .0004 v o l t s .  s u r g e s were v e r y n a r r o w , l e s s f r e q u e n c y was a b o u t  These  t h a n 100 m i c r o - s e c o n d s ,  and t h e  100 times p e r second.  No a p p a r e n t was  This  change i n t h e a m p l i t u d e  o f these  surges  n o t i c e d b e t w e e n magnet c u r r e n t s o f 50 m;a. t o 1 0 amperes A t l e s s t h a n 50 m.a. t h e  so l o n g a s c o n t r o l was m a i n t a i n e d . system  started  to oscillate  s m a l l condensers  because  of the effect  connecting the generator brushes  of the t o ground.  When t h e s e were, d i s c o n n e c t e d t h e s y s t e m d i d n o t o s c i l l a t e f o r any  v a l u e o f t h e c u r r e n t , but t h e v o l t a g e surges  above i n c r e a s e d i n a m p l i t u d e evident  that A  by a f a c t o r o f 2 o r 3 ,  c u r r e n t o f 50 m.a. d e v e l o p s  the pulses v a r i e d maximum r a t i o  current  It is  t h e s e r a n d o m s u r g e s a r e due t o commutator  i n 50.  from 1 p a r t  i n 10 t o 1 p a r t  f o r c u r r e n t s t o be u s e d F u r t h e r i t i s thought  'hash'.  .004 v o l t s a c r o s s t h e  s t a n d a r d r e s i s t a n c e w h i l e 10 amperes d e v e l o p s  1 part  mentioned  .8 v o l t s .  Thus  i n 2000.  Their  i n t h e magnet i s a b o u t that  t h e a c t u a l magnet  does n o t f o l l o w t h e f o r m o f t h e v o l t a g e a c r o s s t h e  standard resistance 1 Henry i n d u c t a n c e .  s i n c e t h e magnet h a s a p p r o x i m a t e l y The h i g h f r e q u e n c y components o f t h e  22. voltage are probably  short-circuited  a c r o s s t h e magnet by t h e  inter-turn capacity. A s f a r a s D.C. o r l o w f r e q u e n c y concerned  none o f g r e a t e r t h a n  oscilloscope table. as  C.  They c e r t a i n l y  1 part  i n c h e s were o b s e r v e d  c o u l d have been o b s e r v e d  T h u s t h e D.C. c o n t r o l  in  10,000  i f as g r e a t  i s accurate to a t  over the e n t i r e usable current  range.  TESTS OF THE SPECTROMETER The  a small table parallel  entire  apparatus  so t h a t  was a s s e m b l e d a n d mounted o n •  the magnetic f i e l d  t o the earth's magnetic f i e l d .  o f t h e c o i l was Connections  t h e n made t o t h e vacuum pump a n d t o t h e c o u n t e r system. tight,  The a p p a r a t u s but s p e c i a l  the rubber  was f o u n d  sealing rings  A test  as f a i r l y  approximately  t o operate  75 v o l t s  a tight  joint.  large  source  strengths  o f t h e c o u n t e r was made w i t h t h e  e m i t t i n g s t r o n g gamma r a y s was u s e d appeared  vacuum  o n l y one c o u n t e r a n d one s e t  window c o m p l e t e l y s e a l e d w i t h a b r a s s p l a t e .  filled  filling  t o be r e a s o n a b l y  i n o r d e r t o ensure  b a f f l e s were i n s t a l l e d  were a v a i l a b l e .  were  c a r e was r e q u i r e d i n t h e p o s i t i o n i n g o f  For p r e l i m i n a r y t e s t s of  on t h e  s c r e e n and a t low c u r r e n t s t h e y were n o t d e t e c -  .05 i n c h e s .  least  .1  fluctuations are  A  source  a n d t h e c o u n t e r when  efficiently, with a plateau o f  s t a r t i n g a t a b o u t 850  volts.  A s o u r c e o f R a d i u m D was t h e n p u t i n t h e s p e c t r o meter u s i n g t h e a l t e r n a t i v e method d e s c r i b e d i n I I A.  The  c o u n t e r , now w i t h a c o l l o d i o n v/indow i n s t a l l e d , was mounted  23. in  the spectrometer  and a l i n e d w i t h t h e b a f f l e  system, and  c o n n e c t i o n s made t o t h e h i g h v o l t a g e power s u p p l y a n d t o t h e scaling  circuits. A g r e a t d e a l o f d i f f i c u l t y was t h e n  The  mixture  appeared  o f argon  and a l c o h o l u s e d  to l e a k through  for filling  5 cms o f a i r was a l l o w e d  argon  t o enter the counter  out and t h e c o u n t e r f i l l e d  and a l c o h o l m i x t u r e  dicated  without  t h e vacuum gauge i m m e d i a t e l y i n -  a leak.  m a i n t a i n t h e 3 cms p r e s s u r e i n t h e c o u n t e r  ballast  y e t when  w i t h 5 cms o f  T h e s e l e a k s were s o l a r g e t h a t i t was to  air-  On s e v e r a l o c c a s i o n s  t h e d e g r e e o f vacuum i n t h e s p e c t r o m e t e r ,  t h i s was pumped  the counters  t h e window e v e n t h o u g h i t was  t i g h t a s f a r a s c o u l d be a s c e r t a i n e d .  changing  encountered.  f l a s k attached As  to the f i l l i n g  impossible  even w i t h t h e  system.  a r e s u l t when t h e v o l t a g e was  counter,  i t went i n t o a l m o s t  possible  e x c e p t i o n o f a few s h o r t i n t e r v a l s when i t a p p e a r e d  to  be o p e r a t i n g  was  operate  installed  were c a r r i e d  successfully.  a c r o s s t h e window was k e p t  at a l l times.  window  that the pres-  t o a very low  T h i s was done by ' t h r o t t l i n g ' t h e  None o f t h e s e a t t e m p t s consequently  thicker  t o ensure  vacuum pump w i t h a c l a m p o n t h e r u b b e r  and  o u t t o make t h e  A slightly  and extreme c a r e t a k e n  sure d i f f e r e n t i a l level  discharge with the  normally.  Further attempts counter  continuous  applied to the  hose  connection.  have a s y e t b e e n s u c c e s s f u l  no r e a d i n g s o f t h e B e t a - r a y  spectrum  of  Radium D have been t a k e n .  It i s felt,  c e s s f u l o p e r a t i o n o f the apparatus velopment o f the p r o p e r dion films.  technique  A t the time  however,  that  suc-  depends o n l y on t h e deof d e a l i n g with the  of writing,  collo-  c o u n t e r s have b e e n •  p r e p a r e d w i t h a p p a r e n t l y l e a k p r o o f windows and work i s c o n tinuing.  25.  IV.  While tested  the spectrometer  successfully,  a s i t now  CONCLUSION  stands  the p r i n c i p l e s  the apparatus  measurements o f l o w  a s a u n i t has  energy  involved  should give  not y e t been  a r e sound,  satisfactory  Beta-ray spectra,  once t h e  proper  t e c h n i q u e s o f m o u n t i n g t h e c o l l o d i o n windows have b e e n v e l o p e d and  i m p r o v e m e n t s and m o d i f i c a t i o n s  i n c r e a s e the f l e x i b i l i t y o f the spectrometer  others w i l l  while  make i t e a s i e r o f o p e r a t i o n .  A h i g h e r v o l t a g e magnet power s u p p l y w o u l d the range 200 rise  Kev.  de-  mastered.  However, c e r t a i n will  and  o f the spectrometer The  limit  o f the copper  could r e a d i l y  be  t o be  extended  almost  o f c o u r s e depends on t h e  enable to  temperature  i n t h e magnet b u t w a t e r c o o l i n g  coils  attached.  It w i l l  p r o b a b l y be n e c e s s a r y t o d e v e l o p a s i m p l e r  method o f a t t a c h i n g t h e c o l l o d i o n windows t o t h e c o u n t e r s i n order t o reduce setting niques  while  up t h e c o u n t e r and a t t h e same t i m e m a k i n g t h e t e c h r i n v o l v e d l e s s p a i n s t a k i n g and The  readily  the danger o f b r e a k i n g the f i l m s  be  delicate.  u n i f o r m i t y o f the magnetic  improved- t o a l m o s t  by changing t h e t u r n s r a t i o  any  field  can  d e s i r e d degree  of the c o i l s .  I t may  quite  of  accuracy  also  be  necessary  t o c l a m p t h e s i d e s o f t h e magnet t o g e t h e r more  f i r m l y as a s l i g h t warping developed  when t h e c o i l s  were  b e i n g wound. The  development o f t h i s  spectrometer  t i n u e d a n d when i t i s s u c c e s s f u l l y o p e r a t e d  i s being con  i t should  prove  t o be a v a l u a b l e t o o l f o r t h e i n v e s t i g a t i o n o f l o w e n e r g y B e t a - a n d Gamm-ray  spectra.  27.  V.  BIBLIOGRAPHY  BOOKS H. A.  "Elementary Nuclear Theory", John W i l e y & Sons, 1947.  Bethe  E . R u t h e r f o r d , J . Chadwick, "Radiations from R a d i o a c t i v e C. D. E l l i s , Substances".  REFERENCES 1.  B. J . F.  2.  J . A.  3.  A.  Schonland,  Crowther,  Flammersfeld,  4 . . A. W.  Tyler,  A113.  Proc.Roy.Soc.  A 8 0 , 186, 1908.  Zeits.fur  __6_, 1 2 3 , 1 9 3 9 68,  Phys.Rev.  6.  H.  Proc.Roy.Soc.  7.  G. v o n D r o s t e ,  8.  H. 0. W.  9.  10.  D. D. L e e & W. F. L i b b y , T s i e n San-Tsiang, Ouang Te T c h a o , J . Suruque, & T s i e n San-Tsiang, T s i e n San-Tsiang, M. F r i l l e y , T s i e n San-Tsiang, & C. M a r t y , T s i e n San-Tsiang, & C. M a r t y , Tsien San-Tsiang,  Proc.Roy.Soo.  Phys.Rev.  1939.  59,-1943. 455, 1923.  104,  8_4, 1 7 , 1 9 3 3 .  Zeits.fur Physik  Richardson Leigh-Smith,  727,  P h y s , Rev.  J". B a c k u s ,  & A.  112,  Physik  5.  Robinson,  87, 1 9 2 6 .  Proc.Roy.Soc.  l 6 0 , 454, 1937.  _5_5, 232,  1939.  Comptes Rendus  216,  765, 1943.  Comptes.Rendus Comptes Rendus Comptes Rendus  2JL7,  1943.  21b, 2__T,  535, 503, 505,  Comptes Rendus  2j_0, 688,  1945.  221,.  1945.  Comptes Rendus Phys.Rev. 6__,  r  177,  3&T1946.  1944. 1944.  PLATE I . THE SPECTROMETER PARTIALLY ASSEMBLED  PLATS I I . THE MAGNET AND  F I E L D TESTING COILS  PLATE IV. THE MAGNET AND SPECTROMETER ASSEMBLED  P L A T E Y. THE 6AS7 RECrUI_'LTOR CHASSIS  

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