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Pressure broadening of SiI lines in a hydrogen plasma jet Beck, Reginald John 1970

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PRESSURE BROADENING OF S i l LINES IN A HYDROGEN PLASMA JET by REGINALD JOHN BECK  B.Sc,  U n i v e r s i t y o f B r i t i s h Columbia, 1968  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF M.Sc. i n the Department of PHYSICS  We accept t h i s required  THE  t h e s i s as conforming  to the  standard  UNIVERSITY OF BRITISH COLUMBIA May,  1970  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  f u l f i l m e n t o f the requirements f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, the L i b r a r y s h a l l I  make i t f r e e l y a v a i l a b l e  f u r t h e r agree t h a t p e r m i s s i o n  for  I agree  r e f e r e n c e and  f o r e x t e n s i v e copying o f t h i s  that  study. thesis  f o r s c h o l a r l y purposes may be granted by the Head o f my Department o r by h i s  representatives.  of this  thesis  written  permission.  It  i s understood that copying o r p u b l i c a t i o n  f o r f i n a n c i a l gain shall  Department The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada  Columbia  not be allowed without my  -ii-  .  ABSTRACT  A p r e s s u r i z e d hydrogen  plasma j e t i s developed f o r  p r e s s u r e broadening experiments -20 atmospheres. plasma which was  a t p r e s s u r e s of from 4 t o  O p e r a t i o n at low flow r a t e s produced  homogeneous i n c r o s s s e c t i o n w i t h r e s p e c t  to e l e c t r o n d e n s i t y and temperature,,with w e l l s u i t e d f o r broadening  axial gradients,  experiments.  o  0 The broadening of two was  studied.  electrons  Widths and  S i l lines,  s h i f t s due  X3905 A and A2881 A  to broadening  by  (Stark e f f e c t ) and a l s o by n e u t r a l hydrogen  were measured.  a  atoms  The e x p e r i m e n t a l r e s u l t s were compared  w i t h the theory of Griem i n the case of the Stark broadening and w i t h the Unsold theory of Van der Waals broadening f o r the case of the hydrogen  perturbers.  Comparison i s a l s o  made between the e x p e r i m e n t a l r e s u l t s and o t h e r e x p e r i m e n t a l r e s u l t s f o r broadening by argon atoms. disagreement  was  Significant  found, e s p e c i a l l y i n the case o f the  broadening by hydrogen  atoms.  -iii-  TABLE OF CONTENTS PAGE CHAPTER I  INTRODUCTION  1  CHAPTER I I  THEORY  4  CHAPTER I I I  APPARATUS  27  CHAPTER IV  THE EXPERIMENT  42  CHAPTER V  THE PLASMA PROPERTIES  50  CHAPTER VI  RESULTS AND DISCUSSION  55  BIBLIOGRAPHY  . ..  - APPENDIX I APPENDIX I I  APPENDIX I I I  . ...  64  THE PULSE TRANSFORMER  65  ABEL TRANSFORM PLASMA COLUMN  66  FOR A CYLINDRICAL  H-D CURVE FOR- CALIBRATING THE PLATE EMULSION  70  -i'v-  LIST OF TABLES PAG PAGE TABLE I  RECIPROCAL DISPERSION OF THE SPECTROGRAPH ••« ao aa a« «« «e e* *o o» »« «« «« o« ot ot ot t««a oo aoaa»aoo««* * SPECTP.OGP-A.PH  TABLE I I  40 40  EXPERIMENTAL AND THEORETICAL REDUCED WIDTHS AND SHIFT-TO-WIDTH RATIOS DUE TO INTERACTIONS WITH ELECTRONS  TABLE I I I  58  MEASURED REDUCED WIDTHS AND SHIFTS DUE TO INTERACTIONS WITH HYDROGEN ATOMS .  TABLE IV  59  COMPARISON BETWEEN THE INTERACTION CONSTANTS AND SHIFT-TO-WIDTH  RATIOS  FOR BROADENING BY HYDROGEN AND ARGON  61  -v-  LIST OF FIGURES PAGE FIGURE 1  PLASMA PARAMETERS FOR BROADENING MEASUREMENTS  FIGURE 2  24  A SIMPLIFIED DIAGRAM OF THE PLASMA JET  . .•  28  FIGURE 3  POWER SUPPLY  33  FIGURE 4  THE STANDARD LINE SOURCE  38  FIGURE 5  DISPLAYING NON-NEUTRALITY OF STEP FILTER  39  FIGURE 6  BASIC OPTICAL APPARATUS  43  FIGURE 7  THE GAS SYSTEM  44  FIGURE 8  THE ELECTRONICS  45  FIGURE 9  RADIAL VARIATION OF N  FIGURE 10  AXIAL VARIATION OF N  e  51  e  AT VARIOUS  PRESSURES  53  FIGURE 11  TEMPERATURE VERSUS PRESSURE  54  FIGURE 12  ELECTRON AND HYDROGEN DENSITIES VERSUS PRESSURE  FIGURE 13  FIGURE 14  54  CYLINDRICAL COLUMN GEOMETRY FOR ABEL TRANSFORM  66  TYPICAL H-D CURVE  71  ACKNOWLEDGMENT  I wish t o express my s i n c e r e a p p r e c i a t i o n f o r the encouragement  and guidance given t o me by Dr. J . Meyer.  As my s u p e r v i s o r , h i s i n t e r e s t and u n d e r s t a n d i n g o f t h e problems were o f prime importance i n c a r r y i n g out the work. I a l s o wish t o thank the members o f t h e plasma group f o r much u s e f u l d i s c u s s i o n and h e l p f u l s u g g e s t i o n s .  In  p a r t i c u l a r , s p e c i a l thanks t o Dr. D.E. Roberts f o r h i s p a t i e n t c o n s i d e r a t i o n o f many q u e s t i o n s MacLatchy  and t o Mr. Cy  f o r h i s i n t e r e s t and encouragement.  I am a l s o indebted machine work and d e s i g n  t o Mr. Tony Knop f o r h i s expert c o n s i d e r a t i o n s d u r i n g the  developement o f the j e t .  -1-  . CHAPTER I INTRODUCTION  The phenomenon o f l i n e broadening i s w e l l known and has been i n v e s t i g a t e d f o r many y e a r s .  Because so much  b a s i c p h y s i c s i s i n v o l v e d i n the theory, l i n e  broadening  o f f e r s a convenient b a s i s f o r e x p e r i m e n t a l and t h e o r e t i c a l work on concepts of the atom and i n t e r - p a r t i c a l  forces.  However, the u s e f u l n e s s o f work on l i n e broadening i s not c o n f i n e d t o these a s p e c t s , but i s a l s o apparent f o r plasma d i a g n o s t i c purposes.  Here, w i t h the use of s p e c t r o g r a p h i c  equipment f o r a n a l y s i s , one comes as c l o s e as i s p o s s i b l e to a d e t a t c h e d probe; i . e . , one which does not p e r t u r b the plasma light  d u r i n g measurement.  In the case of the study of  from the s t a r s and the nebulae, a s t r o p h y s i c i s t s must  r e l y on l i n e broadening measurements as a source of much of t h e i r d a t a r e g a r d i n g p a r t i c l e d e n s i t i e s , temperatures and interactions.  T h i s d a t a must, n e v e r t h e l e s s , remain a  c o l l e c t i o n o f numbers u n l e s s c o n t r o l l e d l a b o r a t o r y  experi-  ments a r e made t o determine cause and e f f e c t . The o b j e c t o f the experiment r e p o r t e d i n t h i s i s t o study the p r e s s u r e broadening of s i l i c o n radiation. broadened  thesis  line  T h i s work i s m o t i v a t e d by the o b s e r v a t i o n of metal l i n e p r o f i l e s o r i g i n a t i n g  of c e r t a i n c o o l s t a r s .  These atmospheres  i n the contain  atmospheres hydrogen  -2-  and the study o f the p r e s s u r e broadening of these by i n t e r a c t i o n w i t h hydrogen  lines  atoms may p r o v i d e i n f o r m a t i o n  u s e f u l i n p r e d i c t i n g the hydrogen  densities.  To f a c i l i t a t e t h i s i n v e s t i g a t i o n , i t seemed t h a t a p r e s s u r i z e d hydrogen l i g h t source.  plasma j e t would p r o v i d e an i d e a l  One would expect d e n s i t y and  temperature  g r a d i e n t s i n the plasma and thereby o b t a i n v a r i a t i o n s i n the l i n e p r o f i l e s due t o both these e f f e c t s . such a j e t was developed and two S i l l i n e s , o  2881 A, were s t u d i e d .  To t h i s end o  3905 A and  The s i l i c o n was i n j e c t e d i n t o the  system i n the form o f s i l a n e gas  (SiH ). 4  In Chapter I I , t h e o r e t i c a l aspects needed f o r t h i s experiment  are d i s c u s s e d .  temperature  These i n c l u d e l i n e  broadening,  and d e n s i t y d e t e r m i n a t i o n , and the deconvolu-  t i o n o f the p r o f i l e s .  The dynamics o f the j e t are a l s o  discussed. Chapter  I I I i s concerned w i t h the c o n s t r u c t i o n and  o p e r a t i o n o f t h e l i g h t sources and the d e s c r i p t i o n o f the o p t i c a l equipment.  C o n s t r u c t i o n of the D.C. power supply  f o r the j e t and the a s s o c i a t e d e l e c t r o n i c s i s a l s o discussed. Chapter procedure. plates i  s  IV i s devoted t o the e x p e r i m e n t a l set-up and Exposure  and a n a l y s i s o f the p h o t o g r a p h i c  outlined.  The plasma p r o p e r t i e s are d e s c r i b e d i n Chapter V.  -3-  E l e c t r o n d e n s i t i e s o f the order o f a few  times 1 0  temperatures i n the v i c i n i t y of 12000 °K are  found.  Homogeneity of the plasma w i t h r e s p e c t t o d e n s i t y temperature i s The  also  Chapter VI,  d i s c u s s i o n of the r e s u l t s and  The  first  certain points  An  for  I t i s hoped t h a t the i n c l u s i o n  i n t h i s form r a t h e r than n o t i n g  w i l l provide  with  here.  appendices c l a r i f y  the b e n e f i t of the reader.  references  concerns i t s e l f  comparison w i t h theory.  error discussion i s also included  o f these p o i n t s  and  discussed.  f i n a l chapter,  F i n a l l y , three  and  1 7  them i n  b e t t e r c o n t i n u i t y i n the t h e s i s .  appendix d i f f e r s i n t h a t i t r e f e r s to a  t e c h n i c a l developement of p o s s i b l e i n t e r e s t .  -4-  CHAPTER I I THEORY  A)  PLASMA JETS In g e n e r a l a plasma j e t can be c o n s i d e r e d  as a flow  of gas through a p i p e w i t h energy i n p u t through the w a l l s of the p i p e .  C o l d gas e n t e r s one end and hot gas e x i t s  at the o t h e r end.  The equations  o f c o n s e r v a t i o n o f mass,  momentum, and energy from gas dynamics are used i n c o n j u n c t i o n w i t h a laminar  flow model t o d e s c r i b e the j e t .  In' the case o f a hydrogen plasma j e t w i t h a low flow r a t e conduction  ( a few cu. f t . p e r h o u r ) , h e a t i n g by thermal c o u l d be expected t o p l a y a prominent r o l e i n  the a c t u a l mechanism o f the formation  o f the plasma.  The  thermal c o n d u c t i v i t y o f a hydrogen plasma has r e c e n t l y been measured  (Behringer  to 7000 °K.  e t a l , 1968) i n the r e g i o n o f 2000 °K  T h e i r r e s u l t s show a sharp peak i n the  c o n d u c t i v i t y a t 4000 °K.  T h i s suggests the e x i s t e n c e o f a  boundary r e g i o n a t 4000 °K where the temperature would drop o f f very q u i c k l y s i n c e the i n c r e a s e d c o n d u c t i v i t y would r a p i d l y c a r r y the heat away.  One c o u l d then expect  a plasma w i t h a hot c e n t r a l core o f f a i r l y  constant  temperature o r a t l e a s t w i t h a slow temperature which would f a l l  gradient  o f f r a p i d l y a t the 4000 °K r e g i o n .  -5-  An e x c e l l e n t d i s c u s s i o n o f plasma j e t s i n g e n e r a l and o f a p a r t i c u l a r model developed  at the U n i v e r s i t y of  B r i t i s h . Columbia plasma p h y s i c s l a b i s g i v e n by M o r r i s (1968). W.  He d i s c u s s e s t h e l a m i n a r f l o w model developed  Neuman  (1962)  and by B. A h l b o r n  (1965)  by  and i n v e s t i g a t e s  the o p e r a t i o n o f argon and h e l i u m plasma j e t s u s i n g  this  theory. The  h e a t i n g mechanism f o r p r o d u c i n g  t h e plasma used  i n t h i s e x p e r i m e n t i s n o t known and has n o t been i n v e s t i g a t e d here.  The plasma p a r a m e t e r s were measured  e x p e r i m e n t a l l y and found s u i t a b l e f o r t h e l i n e experiment. combination  broadening  The a u t h o r b e l i e v e s t h e mechanism t o be a o f l a m i n a r f l o w and t h e r m a l c o n d u c t i o n  w i t h c o n v e c t i o n e f f e c t s and suggests  heating  t h a t f u r t h e r work be  done t o d e t e r m i n e t h e a c t u a l mechanism and t o d e v e l o p  a  theory.  B)  LINE BROADENING a)  Pressure  broadening  I n a source o f l i n e r a d i a t i o n t h e atomic o r i o n i c r a d i a t o r s a r e s u r r o u n d e d by an atmosphere o f charged and neutral particles.  I n t e r a c t i o n between t h e r a d i a t o r s and  t h e s e p a r t i c l e s p e r t u r b s t h e shape o f t h e r a d i a t e d l i n e profiles.  -6-  The Lorentz  e a r l i e s t treatment of t h i s problem i s t h a t of (1905).  oscillator  He  considers  a classical radiating  as the model f o r the r a d i a t i n g atom.  atoms are assumed to have a d e f i n i t e c o l l i s i o n  The radius  and  each r a d i a t i n g atom undergoes an i n e l a s t i c c o l l i s i o n which stops  the r a d i a t i n g p r o c e s s .  The  Fourier integral analysis  of the wave t r a i n y i e l d s the observed frequency t i o n o f the  distribu-  spectral intensity; 1  1  I(u)) =  (1) (o3-w )  TT T  with  0  a half-width y = Lindholm  2  +  (1/T)  2/T.  (1941) extends t h i s treatment f o r the  of e l a s t i c c o l l i s i o n s  (the c o l l i s i o n  phase change) o f s h o r t d u r a t i o n by exp{ico t  case  causes an a r b i t r a r y  c o n s i d e r i n g the  function  - i A (t) }  0  (2)  t where A(t) = Z n 0  (3)  and  (0,t).  n are the phase s h i f t s o c c u r r i n g i n the i n t e r v a l  Fourier analyzing I(OJ) =  (2) leads  to;  [/ exp{i(u)-w ) t + i A ( t ) } dt] o CO  2  00  = . / / exp{i(aj-u ) ( t " - t ' ) + i[A(t")-A(t»)] } d t ' d t " 0  — 00 —  00  (4)  -7-  and  t" f o r A ( t " ) - A ( t ' ) = I r, and t " - t ' = t , f  I(OJ) =  / exp{i (u-wo) > t d t / exp{ i [ A (t+t' ) - A ( t ) ] } d t 1  —  CO  ...  —  CO  (5)  I f the mean time between c o l l i s i o n s  i s T „ . the  expected number of c o l l i s i o n s i n the i n t e r v a l T i s T / T and  ,  the p r o b a b i l i t y o f Z c o l l i s i o n s i s g i v e n by; ( T / T  A number, and  0  0  )  Z  exp(-T/T ) 0  1/z:  (6)  a, o f c o l l i s i o n s w i t h d i f f e r e n t phase s h i f t s  c r o s s s e c t i o n s leads t o an average  correlation  function (7)  exp{i[A ( t + f )-A (t') ] } = exp{t[-a+i3] } whereby,  a I(w) = — TT  1 •• (u-a) + (3) + a 0  2  (8) 2  where the h a l f width Y = 2a = 2vN Z2a s i n a / 2 3. a  (9)  z  and  with  the s h i f t  6 = vN Z o s i n a a a  1/x = avN where a i s the c o l l i s i o n  (10)  cross s e c t i o n ,  v the mean r e l a t i v e v e l o c i t y between e m i t t e r and p e r t u r b e r and. N i s the number d e n s i t y o f the p e r t u r b e r s .  1  -8-  It  i s seen then, t h a t w i t h t h i s treatment both  e l a s t i c and  inelastic collisions  lead to L o r e n t z i a n  shapes w i t h widths p r o p o r t i o n a l to the p e r t u r b e r density.  In the  case of e l a s t i c c o l l i s i o n s , a  a l s o r e s u l t s which s i m i l a r l y perturber  shift  i s p r o p o r t i o n a l to  of the  the  i n t e r a c t i o n f o r c e s i n the  form of an i n v e r s e power law,  Aca(r) =  2 l T  C  p  w i t h s t r a i g h t l i n e o r b i t s f o r the p e r t u r b e r s  /  r P  '  permits  c a l c u l a t i o n of the c o l l i s i o n c r o s s s e c t i o n s and e v a l u a t i o n of the widths and  i)  values  Stark  number  number d e n s i t y .  Consideration  various  line  of  hence  s h i f t s c o r r e s p o n d i n g to  p,  broadening *  Griem e t a l theory  (1962a) b e g i n treatment of the modern  o f Stark broadening of i s o l a t e d l i n e s by  t h a t the p e r t u r b e r s trajectories system.  This  assuming  are c l a s s i c a l p a r t i c l e s moving  independent of the  s t a t e of the  along  emitting  " C l a s s i c a l Path Approximation", f o r the  case  of e m i t t i n g n e u t r a l s , i m p l i e s s t r a i c h t l i n e paths f o r e l e c t r o n s and Two and  ions.  l i m i t s are now  e l e c t r o n broadening.  recognized, For  low  corresponding to ion  v e l o c i t y ions,  the  " Q u a s i - S t a t i c " assumption i s made t h a t d u r i n g  an  all  Electronic  i o n i c perturbers  are at f i x e d p o s i t i o n s .  emission  -9-  collisions  are t r e a t e d by the e l e c t r o n impact  approximation.  ( collision)  T h i s leads t o both the S t a r k h a l f - w i d t h s  and s h i f t s b e i n g p r o p o r t i o n a l t o the e l e c t r o n d e n s i t y , N , e and t o L o r e n t z i a n Griem  profiles.  (1964) develops the theory f o r hydrogen  and f o r i s o l a t e d l i n e s of c e r t a i n elements which  i s of i n t e r e s t here.  For hydrogen  lines  including  lines,  silicon  the  combined width due to both i o n and e l e c t r o n broadening s c a l e s q u i t e c l o s e l y as the t w o - t h i r d s power o f the electron density. 2  Y  = e  where 2 y  e  [ N  e  Griem w r i t e s the hydrogen  / C ( N  , T ) J  e  2  /  (12)  i s the f u l l S t a r k width and C i s a c o e f f i c i e n t  i s o n l y a weak f u n c t i o n of N  which  l i n e width as;  3  and T.  Tables o f  e v a l u e s o f t h i s c o e f f i c i e n t f o r the hydrogen  l i n e s and o f  widths and s h i f t s t a b u l a t i n g r e s u l t s o f c a l c u l a t i o n s i n which both e l e c t r o n impact and i o n broadening are c o n s i d e r e d a l o n g w i t h i o n - i o n i n t e r a c t i o n s are g i v e n i n the  1964  reference. i i ) Van der Waals broadening The impact theory of Lindholm (1946), assuming  (1941) and o f F o l e y  the Van der Waals i n t e r a c t i o n  (p=6),  p r e d i c t s a Lorentzian i n t e n s i t y d i s t r i b u t i o n with a h a l f width o f Y  6  =17.0  v  3  /  5  C  2  e  /  5  N  H  (13)  where v i s the mean r e l a t i v e v e l o c i t y between e m i t t e r and p e r t u r b e r ,  C  = C  6,k  6  initial  , - C  (k and k d e s i g n a t e 1  6,k'  and f i n a l l e v e l s ) i s an atomic  the number d e n s i t y o f hydrogen atoms.  c o n s t a n t and N i s The r a t i o o f  s h i f t t o width p r e d i c t e d by the theory i s ±0.36, + sign i f C  i s p o s i t i v e and the - siqri i f C 6  The  i s neqative. 6  T h e o r e t i c a l l y , the s h i f t t o width r a t i o , f o r e i g n gas p e r t u r b e r s , i s independent i n t e r a c t i o n constant C  f o r the case o f  o f both the  and the mean r e l a t i v e v e l o c i t y , v. 6  In  o r d e r t o f i n d a v a l u e f o r the i n t e r a c t i o n  c o n s t a n t , C , i t i s necessary  t o c o n s i d e r the i n t e r a c t i o n  6  energy  i n a system c o n s i s t i n g o f a hydrogen atom p e r t u r b e r  and a r a d i a t i n g atom. in  W r i t i n g the i n t e r a c t i o n  Hamiltonian  terms o f s p h e r i c a l wave f u n c t i o n s and u s i n g p e r t u r b a t i o n  t h e o r y , the i n t e r a c t i o n energy, E, can be w r i t t e n as E % E V/r . The f i r s t non-zero term i n the expansion n n  appears  f o r n = 6, and n e g l e c t i n g h i g h e r o r d e r terms i n n  yields; 6  E = — r in  kk' ee' — E -E , + E -E , z  I 6  k',e'  z  k  k  e  (14)  e  Hartree u n i t s , w i t h k d e n o t i n g the r a d i a t i n g atom and e,  the n e u t r a l p e r t u r b e r .  Here the E^ are a l l the l e v e l s f o r  the r a d i a t o r and the p e r t u r b e r and the Z s are the 1  c o o r d i n a t e s f o r the c o n n e c t i n g l i n e between the two n u c l e i .  -11-  Unsold E -E , >> e e between  (1955) makes t h e a p p r o x i m a t i o n  that  E -E, .; i . e . , t h a t t h e d i f f e r e n c e k k ' 1  i n energy  t h e l e v e l s o f t h e h y d r o g e n atom w i l l  much l a r g e r t h a t t h a t o f t h e r a d i a t i n g atom. a p p r o x i m a t i o n , he e x p r e s s e s polarizability  of the  •  a l w a y s be By  this  (14) i n t e r m s o f t h e  h y d r o g e n atom, a, a s ;  3a E = -  Z Z r  or  k'  6  ,  2  k  (15)  k  i n terms o f t h e average Bohr r a d i u s e a  r  2  2  E = -  i n cgs u n i t s . r  This y i e l d s  the expression f o r C ; 6  e = - — e ft  2  C  a r  _  rad. sec  2  e  U s i n g t h e B a t e s a n d Damgaard n* r  2  - 1  cm  (17)  6  (1949) e x p r e s s i o n f o r r ; 2  2  = a  e  (16)  6  (5 n * + l - 3 x ( i + l ) } ,  (18)  2  o  2  Z  2  t h e Van d e r Waals  constant C  6,k  ,•corresponding to a  level  k c a n be e s t i m a t e d a s ; e = - —  C  2  a a—2- n * { 5 n * + l - 3 \ (i+l) } r a d . s e c " 2  2  1  cm  6  (19) where a  o  i s the f i r s t  Bohr r a d i u s , n *  q u a n t u m number o f t h e l e v e l  k, and  2  i s the  \ i s the  effective angular  -12-  momentum quantum number o f the o p t i c a l e l e c t r o n i n the l e v e l k. In  the experiment these i n t e r a c t i o n c o n s t a n t s , C , o  e  o  c o r r e s p o n d i n g t o the S i l l i n e s A 3 9 0 5 A and A 2 8 8 1 A, are measured. iii)  Resonance broadening D i p o l e i n t e r a c t i o n between two atomic systems o f t h e  same k i n d w i t h one i n an e x c i t e d s t a t e and the o t h e r u s u a l l y i n the ground s t a t e leads t o energy exchange between the systems.  Broadening occurs s i n c e the r a d i a t o r  i s damped by i t s i n t e r a c t i n g  partner.  T h i s form of broadening must be n e g l i g i b l e i n t h i s experiment because the h i g h r a t i o o f hydrogen d e n s i t i e s and the low m o b i l i t y of  the s i l i c o n  those w i t h hydrogen  atoms very s m a l l compared  atoms.  b) Non-pressure-dependent Due  (due t o the g r e a t e r mass)  atom would make the number o f encounters  between r a d i a t o r s and s i l i c o n to  to s i l i c o n  effects  t o the h i g h p r e s s u r e s used i n t h i s  experiment  these p r e s s u r e independent mechanisms a r e n o t l i k e l y t o c o n t r i b u t e a p p r e c i a b l y t o the observed broadening and s h i f t . They a r e mentioned i)  here f o r t h e sake o f completeness.  N a t u r a l broadening Even i f a l l e x t e r n a l i n f l u e n c e s are removed from an  emitter i t w i l l  still  r e a c t w i t h i t s own r a d i a t i o n  field.  -13-  T h i s e f f e c t g i v e s the lower l i m i t t o the width o f a spectral ii)  line.  Doppler broadening and s h i f t This e f f e c t arises  because  of the s h i f t i n frequency  of the l i g h t r a d i a t e d from p a r t i c l e s moving w i t h r e s p e c t to the o b s e r v e r . velocity  and  radiator  i s too low f o r t h i s e f f e c t t o c o n t r i b u t e  appreciably iii)  The plasma temperature  (see f i g . l  and the d i s c u s s i o n on p.23  ).  Broadening due to s e l f a b s o r p t i o n In f i n i t e d i m e n s i o n a l plasmas a photon may  absorbed b e f o r e i t has a chance t o escape. the plasma i s s a i d t o be  "optically thick"  be  In t h i s and a  case  photon  w i t h a frequency near t h a t or l i n e c e n t e r becomes trapped w h i l e those w i t h f r e q u e n c i e s i n the wings escape.  This  tends to f l a t t e n out the p r o f i l e , thereby i n c r e a s i n g i t s width. Unfolded p r o f i l e s of the l i n e s observed i n t h i s experiment c)  i n d i c a t e t h a t these l i n e s were o p t i c a l l y  thin.  S u p e r p o s i t i o n of broadening mechanisms  The L o r e n t z i a n p r o f i l e s c h a r a c t e r i s t i c  of S t a r k and  Van der Waals broadening are examples of a f a m i l y of p r o f i l e s known as V o i g t p r o f i l e s . p r o c e s s e s are s t a t i s t i c a l l y  I f the two  independent,  broadening  as i s the case  w i t h the p r o c e s s e s under c o n s i d e r a t i o n , then the observed  line  shape i s s i m p l y  line  shapes;  the  convoluted  product  of  the  two  . CO  I, °  (AX)-='/  b  _co  S  When t h e is  two  profiles  = AX  o b g  (AX-AX )  I ( A X ) dAX  1  1  1  also Lorentzian.  AX A  I  2  are In  AX  i +  (20)  1  Lorentzian,  this  c a s e one  the  resultant  adds t h e  (21)  , obs  where Y~ w i d t h due Since the  y  e  H  + Y  sees  f o r two  A N  e  are  +  B  the  half-width  to both  the  half-  h a v e b e e n shown t o be  proportional  obtains;  '  N  ( 2 3 )  sets of N  and  N„  , calculation  of  H  and  B permits  e v a l u a t i o n of broadening  one  may  the  due  effects.  Similarly, S,  and  h y d r o g e n atoms, r e s p e c t i v e l y .  H  A  of  that;  Stark  independent  constants  data  (22)  half-widths  =  experimental  H  d e n s i t i e s , one  *obs  the  e  the  by  TT  t o b r o a d e n i n g by  these  A  and  = Y  and  E  to  to a n a l y z i n g  e x p e r i m e n t , one  AX  i s given  (1969).  With r e s p e c t this  half-widths  2  more c o m p l e t e d i s c u s s i o n o f V o i g t p r o f i l e s  Burnett  profil  obs  =  S e  N  e  + S N  H  write  H  shifts , ,v 0  ( ) 2 4  -15-  When the observed s h i f t s are s m a l l , i t i s h e l p f u l to c o n s i d e r the observed s h i f t to width r a t i o , parameter, T =  g e +  Y  HH _ HNh  for Y  a n  e  H  e  e  /  ^^ 25  from the f i n a l e x p e r i m e n t a l  d Y n  d) Instrument  profile  l i n e broadening theory as d i s c u s s e d e a r l i e r  predicts profiles  i n t r i n s i c a l l y c h a r a c t e r i s t i c of the  l i n e r a d i a t i o n e m i t t e d by a plasma. measuring profile  H  a  TT  where a i s determined  The  as a  whereby;  Ye Ne results  r,  apparatus may  alter  The r e c o r d i n g and  the t r u e shape of the  to a d i f f e r e n t observed  shape because o f f i n i t e  r e s o l v i n g powers and o t h e r e f f e c t s . T h i s "instrument broadening" may  be removed by the  d e c o n v o l u t i o n procedure p r e v i o u s l y d i s c u s s e d . narrow l i n e  A very  from an e l e c t r o d e l e s s d i s c h a r g e lamp, f o r  i n s t a n c e , i s sent through the system.  Considering i t s  i n t r i n s i c shape as a d e l t a f u n c t i o n as f a r as the apparatus i s concerned i m p l i e s t h a t i t s observed shape i s the  instrument p r o f i l e . Allen  (1964) o u t l i n e s a procedure f o r s e l e c t i n g the  nearest Voigt p r o f i l e  and p e r f o r m i n g the d e c o n v o l u t i o n .  T h i s procedure showed t h a t the instrument p r o f i l e  -16-  affected  the widths o f the narrowest s i l i c o n l i n e  observed i n t h i s experiment by 5% a t the most. on the width o f H  was e n t i r e l y 6  nealigible. . •  -  The e f f e c t  I t was  -  thought t h a t no improvement was t o be made i n deconv o l u t i n g t h e s i l i c o n l i n e s t o remove the instrument width as the e r r o r i n t r o d u c e d by the computer program would be at l e a s t 5%. e)  A b e l u n f o l d i n g o f a c y l i n d r i c a l source  intensity  profile The i n t e n s i t y  observed i n a s p e c t r a l  integrated intensity emissions.  l i n e i s the  a l o n g the l i n e of s i g h t  I f t h e plasma  o f the l o c a l  c r o s s s e c t i o n i s not homogeneous  w i t h r e s p e c t t o e l e c t r o n d e n s i t y and temperature, a d e c o n v o l u t i o n p r o c e s s must be undertaken t o o b t a i n the unfolded p r o f i l e . T h i s can be done f o r a symmetrical, o p t i c a l l y  thin  c y l i n d r i c a l source by u s i n g the A b e l t r a n s f o r m (Griem, T h i s procedure i s g i v e n i n Appendix C)  thesis.  THE PLASMA PARAMETERS In an experiment  the  I I I of this  1964).  the apparatus imposes r e s t r i c t i o n s on  experimental conditions o r , vice  v e r s a , the r e g i o n o f  e x p e r i m e n t a l i n t e r e s t w i l l impose r e s t r i c t i o n s ating  parameters.  These r e s t r i c t i o n s  on the oper-  may be severe i n the  case o f apparatus f o r l i n e broadening experiments where more than one broadening mechanism i s important.  Such i s t h e case  -17-  for  the experiment r e p o r t e d  here.  For t h i s experiment i t was necessary r e g i o n of i n t e r e s t w i t h  t o d e f i n e the  r e s p e c t t o the temperatures and  d e n s i t i e s so as t o enable r e s o l v i n g the broadening mechanisms as w e l l as t o permit parameters. versus  spectrographic  determination  o f the  To t h i s end a t h e o r e t i c a l graph of p r e s s u r e  temperature was drawn up which d e f i n e s the o p e r a t i n g  parameters f o r the experiment. a)  L o c a l Thermodynamic E q u i l i b r i u m and the Saha equation  I f the e x c i t e d l e v e l s o f the atoms or ions i n a s m a l l r e g i o n i n a plasma are populated statistics,  a c c o r d i n g t o Boltzmann  then the r e l e v a n t temperature  i s t h a t of the  s p e c i e s which dominates the r e a c t i o n r a t e s .  A  c o n s i d e r a t i o n o f the p o p u l a t i o n d i s t r i b u t i o n s formula state  statistical leads t o a  f o r the r e l a t i v e p o p u l a t i o n i n any g i v e n quantum  (Griem, 1964); g^ exp(-E / k T ) 2 Z (T)  N N where;  N  n  (26)  i s the sum o f the d e n s i t i e s i n a quantum s t a t e s ^ of a g i v e n energy E , n  the g^ are the s t a t i s t i c a l weights equal t o the number o f quantum s t a t e s having  energy E , n  N i s the t o t a l number o f atoms or ions o f the same s p e c i e s and i o n i z a t i o n Z i s the p a r t i t i o n f u n c t i o n .  stage,  -18-  The r a t i o of the d e n s i t i e s o f atoms or i o n s o f the same s p e c i e s and stage o f i o n i z a t i o n , w i t h e n e r g i e s E  n  and  E , m  i s then; N  g exp(-E /kT) ^n  n  nn  \  g  (27)  exp(-E /kT)  m  m  The numerator and denominator are c a l l e d Boltzmann a s s o c i a t e d w i t h the e n e r g i e s E  n  factors  and E .  For the case o f a time independent and homogeneous plasma, L o c a l Thermodynamic E q u i l i b r i u m  (LTE) holds i f  e l e c t r o n c o l l i s i o n p r o c e s s e s are more important than r a d i a t ive processes.  In t h i s case, the c h a r a c t e r i s t i c temperature  i s t h a t o f the e l e c t r o n s .  LTE may  be expected f o r e l e c t r o n  d e n s i t i e s of N  e  > 9xl0  1 7  /AE (: j  3  kT ^/ |— J  2  cm  -3  (28)  (Griem, 1964), where E„ i s the i o n i z a t i o n energy of hydrogen n  and AE i s the d i f f e r e n c e i n energy of the l e v e l s . optically  t h i n hydrogen plasma, t h i s  e l e c t r o n density of N  e  > 1.2x10  17  cm  For an  i n d i c a t e s t h a t .an -3  i s n e c e s s a r y t o ensure  LTE. The Saha e q u a t i o n , which expresses the e l e c t r o n and i o n d e n s i t i e s i n terms of the p a r t i t i o n f u n c t i o n s and the i o n i z a t i o n energy may  be  d e r i v e d from e q u a t i o n s (26) and (27).  In terms o f s i n g l y i o n i z e d p a r t i c l e s the Saha equation  -19-  may b e w r i t t e n N N e  N  (Griem,  196 4 ) ;  2Z (T)  i  MM  ±  Z (T)  Q  where;  E  i s the ionization  q  AE  D  and N  1  N  kT  2)  ' j  (29)  energy,  i s t h e l o w e r i n g o f t h e i o n i z a t i o n due t o s h i e l d ing  N.  exp(--i?  * 2 Trn '  Q  effects, o  a r e t h e number, d e n s i t i e s  o f i o n s a n d atoms  respectively, Z^(T)  a n d Z ( T ) a r e t h e i o n a n d atom p a r t i t i o n Q  functions  respectively.  For Hydrogen, e q u a t i o n  (29) may b e w r i t t e n ;  K —£ N  =  S  *(T,  AE )  (30)  Q  H  w h e r e S* ( T , AE_) i s t h e b r a c k e t e d p a r t o f e q u a t i o n ti o  (29).  table  i s given  o f v a l u e s o f S* f o r a w i d e r a n g e o f T a n d A E  by D r a w i n a n d F e l e n b o k  (1965).  In order t o i n d i c a t e value of N which  = 1.2x10 cm" 1 7  g  the r e g i o n i n which 3  i s substituted  then gives t h e values o f N  Debye f o r m u l a AE  H  Q  i n t o e q u a t i o n (30)  as a f u n c t i o n  o f T.  The  Q  1 3  cm"  1  PD  where p  LTE h o l d s , t h e  i s used f o r A E , whereby,  = 1.16xl0-  Q  Q  A  i s the Debye radius given by,  (31)  -20-  P  =  D  T —  6.895  V  x  2  )  cxn  (32)  e ( D r a w i n and Now, P  Felenbok,  1965).  the pressure balance equation; =  (2N  + N )kT, n  e  (33)  using quasi-neutrality  (N =N-j_) , g i v e s t h e c o r r e s p o n d i n g  v a l u e s o f P.  representing  equations b)  The  for N  line  e  = 1.2xl0  g  Dissociation  cm"  1 7  the s o l u t i o n of  i s plotted  3  these  i n f i g . 1.  of H 2  At  low t e m p e r a t u r e s , h y d r o g e n m o l e c u l e s  c o n t r i b u t e to the broadening. diagram  This r e g i o n i n the  ( f i g . 1) i s mapped o u t by  equilibrium  equation for H  will P-T  s o l v i n g the d i s s o c i a t i o n  m o l e c u l e s and  atoms.  The  2  equation, derived  i n an a n a l o g o u s manner t o t h e  e q u a t iN o n , i s ; Z*(T) =  /TTkTm \  2  where;  2  3 / 2  H  exp(-x /kT)  \ ~ h ~ ^  H  H  Saha  (34)  D  H2  Z  H  ^ g  = 2 i s the p a r t i t i o n  Q  function  f o r hydrogen  atoms, Z„  =  iiz  Zgxc H  x  z  2  partition Xrj  l s  t  ^  i e  osc H  x  z£  2  o t  H2  function  dissociation  (Z  e x c  H2  % 1)  is  f o r hydrogen molecules,  energy.  -21-  This reduces N —  to  2  =  2.35xl0  T /  2 2  1  [1-exp(-hv/kT)]  2  exp(- /kT) X n  (35)  H 2  I f N^/N^  i s written  equation,  P =  (N  N^g , + N  u  terms  an e q u a t i o n f o r t h e p r e s s u r e  ri2  of $ i s obtained; t  =  P  )kT,  TT  tl  in  then from the p r e s s u r e  2  2  _£ • N  H  W h i c h c a n be  F  ([_—  kT  k T  M  »  ^  2  ++  R  —  ft2  e  — ))  (36)  '  written, (T)  (  —  J  +  3  B  (37)  :  where F(T)  =  3.25xl0  6  T / 3  2  [1-exp(-6.35x10 /T)] 3  exp(-5.2  XIOVT)  (38) Equation  (37) i s p l o t t e d  c)  Comparison  in f i g . 1 for 3 =  2,5,10.  of d i f f e r e n t broadening  mechanisms o  For the f o l l o w i n g is  considered.  following and  Kusch, C / e,A 2  5  calculations  the S i l l i n e  For broadening w i t h Argon  c o n s t a n t was 19 67) ; = 3.7xl0"  atoms,  A3905 A the  found e x p e r i m e n t a l l y (Feldhausen 1 3  -22-  C  « a  and a  6  6.6 3 >. 16.3  =  H  cu  where a i s the p o l a r i z a b i l i t y .  A  T h e r e f o r e a lower l i m i t  (broadening by H atoms i s always  found t o be much g r e a t e r than broadening by Argon atoms) can be expected t o be;  C / e 2  =  s  2.6xl0 . 1 3  The h a l f - w i d t h of the l i n e i s g i v e n by e q u a t i o n the  velocity v  =  ("  6  =  1.4xl0-  From Greim  T  9  3  /  4  P  Now,  nipr  m„  1/2  ,  (39)  ./  N  0  T T  H  1.4x10"  =  N  6  implies N / N e H  =  T I  6  G  effect  f o r the l i n e . 6xl0~  3  T  3  /  /  L0  ( 4 Q )  (3 3) we have;  =  N  =  N  / j  e 2— N  +  > % R  u s i n g equations  from e q u a t i o n  1  Y^  6 = Y /Y  Using e q u a t i o n  _L)\  (1964), broadening due t o the Stark  gives a half-width of Defining  +  1.48x10* T  = Y  +  I  —kT  \  as  (13) w i t h  (26xl0  - 3  \ 1  T / 3  kT  1 0  +  l ) kT  (41)  (30) and (40), N„ can be e l i m i n a t e d  (41) w i t h the r e s u l t ;  P = 1.4xl0"  1 9  6~  2  '  S*(T, AE ) [ 2 6 T  ? / l  O  ^  °.+ 1 0 T / ] a t . 3  2  5  (42)  -23-  Equation . Drawin  (42) i s p l o t t e d i n f i g .  and Felenbok, f o r ' 6 = 1,  1, u s i n g the d a t a from 10.  The h a l f - w i d t h due t o the Doppler e f f e c t i s g i v e n by; 2w Y  kT  =  2 • In 2 rn .  c  D  (43)  Si which, Y  f o r the case o f the s i l i c o n atom, reduces to  D  = 6.25xl0  T / .  8  1  (44)  2  The r e g i o n where the broadening due  to the Doppler  i s e q u a l to t h a t due to broadening by hydrogen found by e q u a t i n g P = 62.5  T / 6  Y 5  a n n  ^  Y  dyne-cm  which i s p l o t t e d i n f i g .  (45)  -2  1,  sees t h a t t o the l e f t o f the  profiles  atoms i s  r e s u l t i n g i n the r e l a t i o n ;  Looking a t the Pressure-Temperature • one  effect  6=1  diagram  (fig.l)  l i n e the Doppler  should p o s s i b l y be deconvoluted from the  combined p r o f i l e of the p r e s s u r e broadening mechanisms, a t l e a s t f o r the p r e s s u r e r e g i o n below 4 However, to the r i g h t o f the  6=1  atmospheres.  l i n e i n the LTE r e g i o n ,  the l i n e width due to the Doppler e f f e c t , up to about 15000 *K,  i s a s m a l l percentage of the combined widths and  i g n o r i n g the Doppler width would o n l y i n t r o d u c e a s m a l l c o n s t a n t e r r o r i n the r e s u l t i n g w i d t h s .  2000  4000  6000  8000  10000  12000  14000  16000  TEMPERATURE I N °K FIGURE 1  PLASMA PARAMETERS FOR BROADENING  MEASUREMENTS  18000  20000  d)  Spectre-graphic d e t e r m i n a t i o n o f t h e parameters  R e w r i t i n g e q u a t i o n (12) a s ; N  e  = C ( N , T)  (2y )  e  3  e  /  (46)  2  i n d i c a t e s t h e method o f o b t a i n i n g t h e e l e c t r o n d e n s i t y , N e  .J  M e a s u r i n g t h e h a l f - w i d t h o f t h e hydrogen  l i n e , H^, p e r m i t s  d e t e r m i n a t i o n o f N e t o w i t h i n a t h e o r e t i c a l e r r o r o f 5% (Griem, 1 9 6 4 ) . Having d e t e r m i n e d N , T may be c a l c u l a t e d from t h e Saha e q u a t i o n f o r a plasma i n LTE, i f , the percentage of i m p u r i t i e s i s s m a l l . similar to that outlined i n section  as i s t h e case h e r e , The p r o c e d u r e i s  (a) f o r d e t e r m i n i n g t h e  r e g i o n i n w h i c h LTE h o l d s , e x c e p t t h a t i n t h i s case b o t h and T a r e unknown.  The p r e s s u r e b a l a n c e e q u a t i o n  ( w i t h N.: = N ); i . e . e q u a t i o n ( 3 3 ) , P = (2N "  Saha's e q u a t i o n , ^ '  N /N e 2  H  =  hi  S* (T, AE ) , a r e s o l v e d H °  g r a p h i c a l l y u s i n g an average v a l u e o f A E t u r e range  + N ) kT and 6  Q  o v e r t h e tempera-  ( t h i s i n t r o d u c e s an e r r o r o f l e s s than 5 % ) ,  The method o f s o l u t i o n i s seen more c l e a r l y by w r i t i n g equation N.  H  (33) i n t h e form; P  -  2N  kT  e  (47)  and Saha's e q u a t i o n i n t h e form; N.  e  (48)  -26-  Equations  (47) and  (48) a r e p l o t t e d  diagram f o r each value of N  g  on an  and P and t h e  - T intersection  of  each p a i r of curves g i v e s the corresponding v a l u e o f  N  and  H  T.  CHAPTER I I I APPARATUS  A)  THE PLASMA J E T The d i f f i c u l t y  hydrogen  lies  i n c o n s t r u c t i n g a j e tf o r use with  i n o v e r c o m i n g anode c o r r o s i o n c a u s e d by t h e  h i g h t e m p e r a t u r e s e x p e r i e n c e d a t t h e anode c h a n n e l  surface.  The f i r s t m o d e l u s e d a w a t e r c o o l e d c o p p e r a n o d e w h i c h burned o u t a f t e r . a minute o r so o f t o t a l o p e r a t i n g t i m e . The f i n a l  model d e s c r i b e d here used a t h o r i a t e d t u n g s t e n  insert, force f i t t e d  i n t o a l a r g e copper heat sink.  Some  w a t e r c o o l i n g was e m p l o y e d t o p r o t e c t r u b b e r o - r i n g b u t t h e anode was p r i m a r i l y r a d i a t i o n a)  seals  cooled.  Design  The b a s i c d e s i g n o f t h e j e t was c a r r i e d o v e r f r o m i n u s e a t t h e U n i v e r s i t y Of B.C. p l a s m a  lab.  Some  jets  radical  a l t e r a t i o n s w e r e made a s t o anode s t r u c t u r e a n d a t u r r e t was p l a c e d o v e r t h e anode t o p e r m i t o b s e r v a t i o n o f t h e plasma of  from f o u r p o r t h o l e s d u r i n g o p e r a t i o n under p r e s s u r e s  f r o m 4 t o 15 o r 2 0 b)  atmospheres.  Construction  A s i m p l i f i e d d i a g r a m o f t h e j e t c a n be f o u n d o n t h e f o l l o w i n g page  (fig.2).  No a t t e m p t h a s b e e n made t o  p r e s e n t a s c a l e d r a w i n g a s i t was t h o u g h t t h a t c e r t a i n k e y f e a t u r e s w o u l d be o b s c u r e d i n s u c h a d i a g r a m .  -28-  EXHAUST OUTLET  TURRET  WINDOW ANODE INSERT  COPPER ANODE HEAT SINK CATHODE  GAS INTAKE ANODE BASE O-RING SEALS CATHODE INSULATOR  FIGURE 2 V  A S I M P L I F I E D DIAGRAM OF THE PLASMA J E T  The  dimensions  ,i n general, are not c r i t i c a l  and those  w h i c h a r e i m p o r t a n t may be f o u n d i n t h e d i s c u s s i o n . R e f e r r i n g t o f i g . 2 , one sees t h a t t h e j e t c a n b a s i c a l l y be b r o k e n down t o f o u r u n i t s ; lucite  with  i n s u l a t o r a n d h o l d e r , t h e anode b a s e , t h e a n o d e ,  and t h e o b s e r v a t i o n i)  t h e cathode  Cathode  turret.  assembly  Th'e c a t h o d e i s made f r o m a p i e c e o f 5 / 8 t h i n c h b r a s s rod  t h r e a d e d on one end and w i t h a c l a m p i n g a s s e m b l y  o t h e r end.  on t h e  A p i e c e o f 1 cm. d i a m e t e r t h o r i a t e d t u n g s t e n r o d  is  ground  t o a p o i n t a t one end (an a n g l e o f about  is  a d v i s a b l e here) and i s i n s e r t e d  i n t h e clamp.  15 d e g r e e s The  t h r e a d e d end f i t s t h e t h r e a d e d i n s u l a t o r and a r u b b e r in  the insulator provides a pressure seal.  of  cathode length a r e p o s s i b l e .  o-ring  Two a d j u s t m e n t s  A r o u g h a d j u s t m e n t made  d i r e c t l y on t h e t u n g s t e n t i p and a f i n e a d j u s t m e n t w h i c h c a n be made e x t e r n a l l y b y s c r e w i n g t h e t h r e a d e d p o r t i o n i n a n d out o f the i n s u l a t o r .  This f i n e adjustment i s f a c i l i t a t e d  by t h e 3/4 i n c h b e a r i n g s u r f a c e w h i c h e x t e n d s i n t o t h e insulator. Originally  t h e c a t h o d e was w a t e r c o o l e d b u t due t o t h e  l o w c u r r e n t u s e d i t was f o u n d p o s s i b l e t o d i s p e n s e w i t h w a t e r c o o l i n g w i t h no c h a n g e i n p e r f o r m a n c e .  -30-  ii)  The a n o d e  base  C o n n e c t i o n s t o t h e gas l i n e made t o t h e anode b a s e .  and w a t e r c o o l i n g l i n e a r e  Water c h a n n e l s i n t h e base  permit  a f l o w o f w a t e r t h r o u g h t h e anode h e a t s i n k t o p r o v i d e some cooling  f o rthe turret  seals.  The d i m e n s i o n s a r e u n c r i t i c a l y e t s h o u l d p r o v i d e e n o u g h c l e a r a n c e f o r t h e cathode trigger  s o a s t o a v o i d a r c i n g o f t h e 15 k . v .  pulse.  I t t u r n e d o u t t h a t no t u r b u l e n c e was e x p e r i e n c e d i n b r i n g i n g t h e gas d i r e c t l y  i n t o t h e chamber r a t h e r t h a n t h r o u g h  a p e r f o r a t e d b a f f l e which i s o f t e n used t o produce symmetrical flow. r a t e o f about  T h i s i s p r o b a b l y due t o t h e l o w f l o w  3 c u b i c f e e t p e r hour used i n t h e experiment.  The a n o d e b a s e was m a c h i n e d  from commercial brass  s t o c k a n d t h e w a l l s w e r e n e v e r l e s s t h a n 1/4 i n c h to ensure against iii)  a  thick  rupture.  Anode The a n o d e h e a t s i n k was m a c h i n e d  diameter copper r o d . insert,  f r o m a 2 1/2  To a l l o w a - f o r c e f i t  inch  of the tungsten  t h e i n s e r t h o l e was made a f e w t h o u s a n d t h s o f a n  i n c h s m a l l e r t h a n t h e 1 cm. d i a m e t e r o f t h e i n s e r t . Circular sink,  grooves were m i l l e d  i n t h e t o p surface o f the heat  i n c r e a s i n g t h e s u r f a c e a r e a f o r more  efficient  cooling. The i n s e r t s w e r e c u t f r o m a p i e c e o f t h o r i a t e d t u n g s t e n r o d i d e n t i c a l t o t h a t used f o r t h e cathode t i p .  -31-  A d i a m o n d w h e e l was  used to cut the  erosion cutter d r i l l e d  t h e b o r e and  s u r f a c e of the i n s e r t s . d e p e n d i n g on out  bore diameter  w  spark  the  as  bottom  1 or 2  maximum d i a m e t e r  during  mm.  opened  operation,  Turret The  t u r r e t i s a brass  threaded in  hollowed  a  t h e c o p p e r c u t t i n g t o o l a v a i l a b l e and  t o a b o u t 3 mm.  iv)  The  s l u g s and  c y l i n d e r hard  chuck which h o l d s  place.  soldered to  the cathode heat s i n k  Four o b s e r v a t i o n p o r t s are spaced ;  a r o u n d , t h e c a n n i s t e r and  s u r f a c e i s l e v e l with-', t h e e d g e o f t h e w i n d o w . inch quartz blanks,  held  threaded  i n by  permits fit.  colletts  anode The  1 i n c h i n diameter  windows and  against o-ring seals.  r e m o v a l f o r c l e a n i n g and  Thin polyethelene  rigidly  symmetrically  p o s i t i o n e d so t h a t the  a r e o f 1/4  the  gaskets  This  ensures a pressure between the q u a r t z  are  tight and  b r a s s p r o t e c t a g a i n s t c h i p p i n g t h e window e d g e s . A small brass  c o u p l i n g i s soldered i n the center  t h e t o p o f t h e t u r r e t and c) i)  Associated  Power To  to the exhaust  system.  equipment  supply  a v o i d f l u c t u a t i o n s i n l i g h t i n t e n s i t y i t was  necessary a D.C.  connects  of  to operate  c u r r e n t source  phase f u l l  the  j e t f r o m as p u r e and  as p o s s i b l e .  wave b r i d g e has  stable  Consequently a  wave b r i d g e p o w e r s u p p l y was  t h r e e phase f u l l  as  built  three  (fig. 3).  i n h e r e n t l y the  best  The  -32-  ripple  f a c t o r and a l a r g e choke and e l e c t r o l y t i c  f u r t h e r reduced the current r i p p l e typical operating current. experienced used w i t h the  capacitor  t o l e s s t h a n 1% a t  I t was n o t i c e d t h a t  using the b a l l a s t r e s i s t o r  stacks  ripple  normally  l a r g e b a t t e r y s u p p l i e s i n t h e l a b was l e s s t h a n  s m a l l amount o f i n s t a b i l i t y  Hence, w i t h r e s p e c t good as o t h e r  to ripple,  introduced this  by t h e b a l l a s t .  s u p p l y was a t l e a s t as  supplies s u c c e s s f u l l y i n current use.  r e g u l a t i o n was a c h i e v e d  by r u n n i n g  the supply  Good  a t about -  l/5th of i t s capacity. ii)  Ballast A ballast resistor  r u n a w a y was c o n s t r u c t e d resistors  f o rthe prevention  o f 1 ohm r i b b o n wound p o w e r  (Ohmite #2312).  connected t o provide  of current  Nine o f these  were s e r i e s  up t o 9 ohms i n 1 ohm s t e p s  a t up  t o 32 amps c u r r e n t . iii)  Electronics Gap  b r e a k d o w n b e t w e e n a n o d e a n d c a t h o d e was  electronically transformer. primary  The p u l s e  of high voltage  discharge in  using a thyratron discharge transformer  initiated  u n i t and a p u l s e  consisted of a 1 turn  insulated wire  connected t o t h e  u n i t a n d a 10 t u r n s e c o n d a r y o f h e a v y w i r e  s e r i e s w i t h t h e power s u p p l y  transformer  and t h e j e t cathode.  was wound o n a l a r g e t o r r o i d a l  (see A p p e n d i x I ) .  placed  ferrite  The  core  25 KVA DELTA TO  ISOLATION  WYE  TRANSFORMER  CONTROL RELAY j  O  TIMER AND TRIGGER 6:  S I L I C O N R E C T I F I E R DIODES  100 AMP BREAKER THREE PHASE TRANSIENT SUPPRESSOR DIODE ASSEMBLY  THREE -PHASE 240 V*A.C.  FIGURE 3 POWER SUPPLY  *  3 SPRAGUE 36D I N PARALLEL  A  ,Tektronix  pulse generator  ;  #162  wave f o r m g e n e r a t o r  turned  s w i t c h o p e r a t i o n of the on  iv)  Exhaust  system  The  e x h a u s t gas  was  was  allowed  discharged  Gas  f o r p e r i o d s o f f r o m 0 t o 15  then  conducted out of the  to bubble through  hydrogen. the j e t .  t a n k was  flow  l a b o r a t o r y where, before  being  an  vapors.  employed w h i c h p e r m i t t e d  t o mix  A needle  A v a c u u m pump a l l o w e d  Operation  amps.  of pressure  in  e m p t y i n g o f t h e j e t chamber  of the j e t j e t was  achieved  at  currents  T h i s p r o d u c e d a v o l t a g e d r o p o f 110  t h e b a l l a s t r e s i s t o r and  7 0 v o l t s between  electrodes.  This represents  to  T y p i c a l o p e r a t i n g time  the a r c .  control  with  system.  Stable o p e r a t i o n of the o f a b o u t 23  a measured  t o a measured f i n a l p r e s s u r e  valve permitted  o r of the whole  across  cooled  v a l v e and  T h i s p r o v e d t o be toxic  the  seconds.  a water bath  o f d i s p o s i n g o f any  amount o f s i l a n e  d)  turned  f r o m t h e t u r r e t chamber was a needle  until  system  A mixing  alone  #163  single  A timer c i r c u i t  i n t o the atmosphere.  e f f e c t i v e way v)  This permitted  a water j a c k e t , passed through  m e t e r , and it  on.  system.  power s u p p l y  by  a  were used t o d e l a y the t r i g g e r p u l s e  t h e p o w e r s u p p l y was  hot  and  a b o u t 1600  watts  of the  the  o f power  j e t was  volts  input  from 5  -35-  to  10 s e c o n d s d e p e n d i n g o n t h e p r e s s u r e . Once a s t a b l e anode b o r e s h a p e h a d b e e n a c h i e v e d  initial  set-up  procedure, l i t t l e  what e r o s i o n d i d o c c u r  during  . e r o s i o n was e x p e r i e n c e d  d i dnot impair operation.  and  After  l e n g t h l y o p e r a t i o n , however, t h e accumulated e f f e c t s o f e r o s i o n a n d o c c a s i o n a l p i t t i n g d i d make r e p l a c e m e n t o f t h e tungsten The  insert  necessary.  t i p of the tungsten  of molten tungsten  c a t h o d e became a s m a l l  during operation  and l i t t l e  ball  erosion .  o f t h i s e l e c t r o d e was o b s e r v e d . The  p r e c i s e p o s i t i o n i n g o f the cathode turned  the most c r i t i c a l a d j u s t m e n t .  o u t t o be  P l u s o r m i n u s 20 d e g r e e s  v a r i a t i o n o f t h e cathode screw would correspond  i n many  i n s t a n c e s t o a d i r e c t anode t o c a t h o d e s h o r t o r a n o n sustained arc.  An i m p r o v e d f u t u r e d e s i g n  should  have a  b e t t e r method f o r t h e a d j u s t m e n t o f t h e e l e c t r o d e s . may b e v e r y  difficult  t o achieve  This  b e c a u s e of. t h e n e e d t o  p r e s s u r i z e t h e chamber. Stable operation  o f t h e j e t was n o t p o s s i b l e a b o v e  a b o u t 20 a t m o s p h e r e s a n d d i f f i c u l t  a b o v e a b o u t 15 a t m o s p h e r e s .  Up t o 15 a t m o s p h e r e s , o p e r a t i n g c o n d i t i o n s w e r e q u i t e r e p r o d u c i b l e a n d c o u l d b e e x t e n d e d t o 18 a t m o s p h e r e s some  success. The  1000  with  g a s was m i x e d i n t h e r a t i o o f 5 p a r t s s i l a n e t o  parts t o t a l mixture  with  hydrogen.-  At t h i s p o i n t the reader use  of silane.  Great  T h i s gas i s h i g h l y t o x i c  c a r e m u s t be t a k e n  t h a t t h e exhaust ignites  i s cautioned regarding the  t o prevent  and c o r r o s i v e .  l e a k s a n d t o make  fumes a r e c o m p l e t e l y  disposed of.  i n c o n t a c t w i t h a i r and i n a m i x t u r e w i t h  i s doubly  tricky.  sure  Silane  hydrogen  A l l p o s s i b l e p r e c a u t i o n s s h o u l d be  taken. B)  THE STANDARD L I N E SOURCE  In order a source  t o m e a s u r e l i n e s h i f t i t was n e c e s s a r y  of narrow, u n s h i f t e d s i l i c o n l i n e s .  constructed with a tungsten silicon  An a r c was  anode a n d a lump o f f u s e d  i n a copper h o l d e r as a cathode.  operated  t o have  T h i s a r c was  i n a 200 t o r r a r g o n a t m o s p h e r e a t 50 v o l t s a n d  a c u r r e n t o f 4 amps.  The p o w e r s u p p l y u s e d was a c o n s t a n t  c u r r e n t N o b a t r o n DCR 150-15A.  A 12 ohm b a l l a s t  was p l a c e d i n s e r i e s ' w i t h t h e power s u p p l y . i n i t i a t e d b y a C e n c o BD#10 t e s l a  resistor  B r e a k d o w n was  coil. o  The h a l f - w i d t h o f t h e S i l 3905 A l i n e f r o m t h i s  source  e  was 0.15 A. line  A s t h i s was t h e same a s t h a t o f a n i t r o g e n  from-an e l e c t r o d e l e s s d i s c h a r g e  lamp r e c o r d e d w i t h t h e  same o p t i c s a n d m e a s u r e d w i t h t h e same e q u i p m e n t , t h i s  width  o  o f 0.15 A c a n be assumed t o be due t o t h e i n s t r u m e n t profile. Due t o t h e l o w p r e s s u r e current,  atmosphere and t h e low a r c  any s h i f t i n w a v e l e n g t h o f t h e s e  standard  lines  -37-  lnust be n e g l i g i b l e  i n comparison  w i t h t h a t of the  lines  from the j e t . A mask o f b r a s s mesh p l a c e d i n f r o n t o f spectrograph  s l i t caused  the standard l i n e  d o t t e d t r a c e superimposed  the  t o a p p e a r as  on t h e t r a c e f r o m t h e j e t .  This  p e r m i t t e d a c c u r a t e m e a s u r e m e n t as t h e t r a c e s a p p e a r as a r c s on t h e p h o t o g r a p h i c See  fig.4  C)  CARBON  of the standard  source.  ARC Hoyer carbon  N o b a t r o n p o w e r s u p p l y and  a r c was  continuum r a d i a t i o n  used w i t h  f r o m t h e anode s p o t , i n c o n j u n c t i o n  c a l i b r a t i o n of the photographic  tungsten  p l a t e s (see A p p e n d i x I I I ) .  c a l i b r a t e d i n a set-up  (model #2400) and For a comparison  c a t i o n s see  f i g . 5.  The  a sensitive  consisting of  galvanometer  measured d e n s i t i e s agree (1966) who  specifivery  used the  well  same  filter. D)  OPTICAL EQUIPMENT  a) H i l g e r E742 p r i s m The  silicon  and  a  Spectro-  w i t h the manufacturer's  w i t h t h o s e m e a s u r e d by C a m p b e l l step  enabled  r i b b o n lamp p i n h o l e s o u r c e , a Beckman DU  photometer readout.  was  A  a u n i f o r m anode s p o t .  w i t h a H i l g e r F1273 n e u t r a l d e n s i t y s t e p f i l t e r  step f i l t e r  the  a b a l l a s t r e s i s t o r o f 6 ohms.  c u r r e n t o f a b o u t 10 amps p r o d u c e d  The  slight  plates.  f o r a drawing  A S p i n d l e r and  The  a  spectrograph  h y d r o g e n l i n e r a d i a t i o n was  recorded  -38-  FIGURE 4 THE STANDARD L I N E SOURCE  _ J  3800  I  4000  !  4200  I  4400  J  4600  1  4800  I....  5000  I  5200  L  5400  WAVELENGTH I N ANGSTROMS MANUFACTURER'S SPECS. o FIGURE 5 D I S P L A Y I N G NON-NEUTRALITY'OF STEP F I L T E R '  EXP. MEASUREMENTS  -40-  on Kodak I F p l a t e s e x p o s e d i n t h i s  spectrograph.  The r e c i p r o c a l d i s p e r s i o n o f t h e s p e c t r o g r a p h 'was determined  f o r t h e g l a s s o p t i c s a t 3900 A a n d 4850 A  u s i n g an i r o n a r c .  With  f o r 2880 A a n d 4850 A.  thequartz These v a l u e s  o p t i c s , t h i s was r e p e a t e d G  r  e  g i v e n . i n " the t a b l e  below.  .TABLE I  RECIPROCAL DISPERSION OF THE SPECTROGRAPH  A u s e f u l acessory source  t o the spectrograph  c o n s i s t i n g o f an i n c a n d e s c e n t  replaced the plate holder. pass through'the  lamp o n a f r a m e w h i c h  This permitted white  spectrograph  p l a t e and o u t through  was a l i g h t  from t h e r e g i o n o f t h e  t h e normal entrance  p r o d u c e d an image o f t h e s l i t  light to  slit.  This  at theposition of the  d i s c h a r g e a n d was v e r y u s e f u l i n a l i g n m e n t . c)  Photodensit.o eter m  The p l a t e s w e r e s c a n n e d o n a J a r r e l l - A s h speed photodensitometer. recorder recorded 0.25  A Bristol's  the line profiles.  t o 2 5 mm./min. w e r e a v a i l a b l e .  variable  Dynamaster c h a r t Scan speeds o f from The s i l i c o n  lines  w e r e s c a n n e d a t 0.5 mm./min., Hg a t 5 o r 1 0 mm./min.  -41-  A  fine vernier  s c a l e on t h e p l a t e c a r r i a g e  permitted  m e a s u r e m e n t o f p l a t e p o s i t i o n t o 2 / 1 0 t h s o f a mm. d i s p l a y of the p l a t e with  a magnification  p r o v i d e d good c o n t r o l o f t h e s c a n n i n g  Visual  f a c t o r o f 15  operation.  CHAPTER I V THE EXPERIMENT A)  EXPERIMENTAL SET-UP A diagram  f o l l o w i n g page  of the o p t i c a l (fig.6).  s e t - u p i s g i v e n on t h e  Two s u r f a c e c o a t e d m i r r o r s ( M l a n d  M2 i n f i g . 6 ) o n h e a v y m o u n t s w e r e so a r r a n g e d  t h a t they could  be i n t e r c h a n g e d w i t h o u t a f f e c t i n g t h e a l i g n m e n t o f t h e optics.  This permitted interchange of the j e t with the  standard source o r carbon  a r c when e x p o s i n g t h e p l a t e s . "  The l e n s e s u s e d p r o v i d e d a m a g n i f i c a t i o n o f 2 o f t h e light  f r o m t h e j e t when o b t a i n i n g t h e d a t a f o r A b e l  unfolding.  In this  c a s e t h e j e t was m o u n t e d o n i t s s i d e .  One-to-one images were used  f o r the a x i a l exposures.  A  m a g n i f i c a t i o n o f a b o u t 30 p e r m i t t e d t h e c e n t r a l a r e a o f e v e n i n t e n s i t y o f the carbon plate  a r c a n o d e s p o t t o be s e l e c t e d f o r  calibration. The g a s s y s t e m  (fig.  7) a n d t h e e l e c t r o n i c s  ( f i g . 8)  are s t r a i g h t f o r e w a r d . The a n o d e b a s e was m o u n t e d o n a s w i v e l permitted Axial  which  t h e j e t t o be o p e r a t e d u p r i g h t o r on i t s s i d e .  and r a d i a l  exposures  c o u l d be t u r n e d t h r o u g h a t a n g l e s o f from lowered  stand  c o u l d t h u s be t a k e n .  an a n g l e o f 45 d e g r e e s  0 t o 30 d e g r e e s .  alignment  and t i l t e d  I t c o u l d be r a i s e d o r  8 i n c h e s on l a r g e t h r e a d e d b o l t s .  facilitated  The s t a n d  These  adjustments  f o r either axial or radial operation.  HILGER E742 PRISM SPECTROGRAPH.  FIGURE 6 BASIC OPTICAL APPARATUS  MANIFOLD  I  I.  MIXING TANK  FIGURE 7 THE GAS SYSTEM  0  NEEDLE VALVE  C*)  GAUGE  JET  ELECTRODES  _8  THYRATRON DISCHARGE UNIT  DELAY  BALLAST RESISTOR  POWER SUPPLY  MANUAL TRIGGER  FIGURE 8 THE ELECTRONICS  -46-  In  t u r n , t h e s t a n d was b o l t e d t o a h e a v y w e i g h t e d  ensure  frame t o  stability.  B)PROCEDURE B e f o r e t a k i n g any d a t a t h e c o r r e c t e x p o s u r e all  t h e s o u r c e s were d e t e r m i n e d  necessary  empirically.  I t was  to f i t pieces of gelatin neutral density  i n t h e p l a t e h o l d e r i n o r d e r t o reduce light  times f o r  from both  j e t and c a r b o n  found filter  the intensity  a r c a t wavelengths  of the  near  H . -  The cathode. PSIG  a r c was b u r n e d i n h y d r o g e n f o r a d j u s t m e n t This adjustment  intervals until The  of the  was u s u a l l y made a t 180 t o 200  ( t h e gauges were c a l i b r a t e d  above a t m o s p h e r i c  p  i n pounds p e r square  inch  p r e s s u r e ) w i t h t h e j e t on f o r s h o r t  a s t a b l e p l a s m a was a c h i e v e d .  photographic  p l a t e s were exposed i n t h e s p e c t r o 0  g r a p h w i t h a s l i t w i d t h o f 25y f o r t h e 3905 A l i n e for  t h e 2881 A l i n e .  The f u l l  slit  used w i t h t h e j e t and s t a n d a r d l i n e of  9 mm.  l e n g t h o f 18 mm. source.  of the j e t with the standard l i n e  traces.  superimposed  one o f t h e c a r b o n  all  r e l e v e n t d a t a f o r a n y one p r e s s u r e s e t t i n g o n a s i n g l e The w a v e l e n g t h  a plate,  length  and  plate.  arc filled  was  A slit  gave t h e b e s t p a t t e r n s f o r t h e c a l i b r a t i o n  One e x p o s u r e  a n d 20u  thereby recording  range o f the spectrograph w i t h the a  g l a s s p r i s m e a s i l y . c o v e r e d b o t h Hp a n d t h e 3905 A  line. o  I t was a l s o p o s s i b l e t o r e c o r d b o t h I-I  p  on a s i n g l e p l a t e when u s i n g t h e q u a r t z  a n d t h e 2881 A prism.  line  -47-  After  f l u s h i n g t h e system w i t h hydrogen,  t h e gas  m i x t u r e was made i n t h e r a t i o o f 2.5 l b s . o f s i l a n e t o 500 lbs.  o f t o t a l mixture w i t h hydrogen.  introduced  i n t o a r e s i d u e o f hydrogen  .The s i l a n e was a t atmospheric  p r e s s u r e a n d t h e n t h e m i x i n g t a n k was f i l l e d pressure with Exposure typically  to the final  hydrogen. t i m e s f o r t h e s p e c t r a o f t h e j e t were  2 t o 8 seconds.  The s t a n d a r d s o u r c e r e q u i r e d  about  1 minute o f exposure and t h e carbon a r c , 1 t o 5 seconds. C)  EXTRACTING  AND ANALYZING  THE DATA  The p h o t o g r a p h i c p l a t e s w e r e d e v e l o p e d a n d d r i e d i n a c c o r d a n c e w i t h t h e s t a n d a r d p r o c e d u r e a s recommended b y Kodak. E x p o s u r e s w e r e made w i t h t h e j e t i n o p e r a t i o n a t p r e s s u r e s o f 9 0 , 1 2 0 , 1 5 0 , 1 8 0 , 210 a n d 240 P S I G , w i t h a maximum f l u c t u a t i o n o f ' 5 P S I G .  C o n v e r s i o n i s made t o  d y n e s p e r s q u a r e cm. f o r b e t t e r p r e s e n t a t i o n o f t h e r e s u l t s . a)  Radial  exposures  These were t a k e n t o f a c i l i t a t e A b e l u n f o l d i n g .  Each  l i n e was s c a n n e d o n t h e p h o t o d e n s i t o m e t e r a t 2 0 o r more p o s i t i o n s a c r o s s t h e p l a t e p r o d u c i n g a t l e a s t 20 p r o f i l e s per  l i n e on t h e r o l l  chart read out.  The s t e p wedge t r a c e .  was s c a n n e d a t 3905 A a n d a t 4861 A o n e a c h p l a t e , 7 density  steps f o r each l i n e .  W i t h t h i s d a t a a n H-D  was d r a w n f o r e a c h l i n e , p e r m i t t i n g e a c h p r o f i l e transformed  providing  i n t o an i n t e n s i t y p r o f i l e  curve  t o be  (see Appendix  III).  -48-  B a r r ' s method  (1962) o f A b e l u n f o l d i n g r e q u i r e s 20  d a t a p o i n t s f o r e a c h w a v e l e n g t h t o be u n f o l d e d . t h e s e p o i n t s , " t h e d a t a were a r r a n g e d manner.  the l i n e The  as a f u n c t i o n o f t h e r a d i u s o f t h e plasma  a normalized  a l l t h e p o i n t s and  spaced i n t e n s i t i e s were r e a d o f f t h i s  for the unfolding process.  - T h i s was r e p e a t e d  wavelengths across the p r o f i l e s . was u s e d t o u n f o l d t h e s e  The  graph  at several  An .IBM 360/67 c o m p u t e r  intensities  (a r e p r e s e n t a t i v e  i s i n c l u d e d i n t h e t h e s i s ) a n d t h e now  unfolded  constructed. r a d i u s was n o r m a l i z e d  by t a k i n g as t h e c e n t e r ,  t h e p o s i t i o n o f t h e p r o f i l e w i t h t h e most i n t e n s e center.  profile  radius of the  A s m o o t h c u r v e was d r a w n t h r o u g h  20 p e r i o d i c a l l y  profiles  column.  a t one p a r t i c u l a r w a v e l e n g t h f o r e a c h  i n a s e t was p l o t t e d v e r s u s  readout  i n t h e a b o v e manner  a record of the i n t e n s i t y versus wavelength of  intensity  column.  i n the following  Each s e t o f p r o f i l e s o b t a i n e d  represented  To p r o v i d e  line  E s t a b l i s h i n g t h e o u t e r boundary o f t h e column  required a cut-off of the l i n e p o s i t i o n o f low i n t e n s i t y .  c e n t e r i n t e n s i t y a t some  T h i s was, o f c o u r s e ,  by t h e l e a s t i n t e n s e p r o f i l e  determined  scanned, i . e . , the f i r s t  p r o f i l e w h i c h c o u l d be r e s o l v e d o u t o f t h e b a c k g r o u n d density of the plate.  The i n t e n s i t y o f t h e l i n e  t h i s p r o f i l e was c o n s i s t e n t l y p l o t t o z e r o by f i t t i n g essentially,  center of  l o w enough t h a t e x t e n d i n g t h e  d i f f e r e n t curves  t o t h i s p o i n t - made,  no d i f f e r e n c e t o t h e u n f o l d e d  intensities.  -49-  b) A x i a l  exposures  The a x i a l  s h o t s were scanned a t s e v e r a l p o s i t i o n s  across the plate. profile  correspondina  ( a t t h e same h e i g h t a b o v e t h e anode) was  These p r o f i l e s case  For each s i l i c o n p r o f i l e , a  were t r a n s f o r m e d  into  intensities  recorded.  as i n t h e  o f t h e r a d i a l ones and t h e h a l f - w i d t h s measured and  recorded.  -50-  CHAPTER V PLASMA PROPERTIES  A)  ELECTRON DENSITY U s i n g a v a l u e o f C (N , T) = 3 . 0 x l 0  196 4)  and  the measured w i d t h s o f H ,  A~  l l f  values of N  D  r , were c a l c u l a t e d shows N  and  as  a  the plasma column r a d i u s ,  f o r the r a d i a l measurements.  v e r s u s r f o r an a x i a l p o s i t i o n o f 0.5  the anode, f o r 2 r e p r e s e n t a t i v e p r e s s u r e s . graph,  (Griem,  3  e  p  f u n c t i o n o f t h e p r e s s u r e , P,  cm"  3 / / 2  Fig. 9 cm.  above  Looking  at  this  i t i s c l e a r t h a t the e l e c t r o n d e n s i t y i s constant  a c r o s s the plasma column a t t h i s p o s i t i o n . profiles  a t a p o s i t i o n o f 1,0  h a l f - w i d t h s which  taken  t h e e l e c t r o n d e n s i t y was  position.  i s a graph  a t 0.5  cm.  This graph  , except  axial  t h o s e a t 0.5  s h o t s c e n t e r e d on shows t h e  the  height.  x  T h i s c r o s s s e c t i o n a l homogeneity of the  electron  i f the plasma c o n s i s t e d of a  c e n t r a l core of constant temperature boundary r e g i o n from a c o o l e r r e g i o n .  cm.,  expected  behavior of density f a l l i n g o f f w i t h increased a i a l  d e n s i t y w o u l d be e x p e c t e d  that  cross  of e l e c t r o n d e n s i t y versus  were o b t a i n e d from the f o l d e d a x i a l (r = 0 ) .  the  axially.  Most of the v a l u e s o f N  plasma column  yielded  This indicated  constant i n a p a r t i c u l a r  s e c t i o n of plasma but v a r i e d 10  above t h e anode  w e r e e q u a l t o t h e f o l d e d o n e s a s was  case w i t h the p r o f i l e s  Fig.  cm.  Some u n f o l d e d  s e p a r a t e d by a  hot  sharp  xlO  6 1 7  o O  S3  u  15.5x10  6  DYNES/CM  JO.  2  \  H  \  0)  I m H  o  i  EH H  CO  W Q  o  O  7^2x10  6  DYNES/CM  o  2  o.  >Q  EH U  H  h3  \  W  0.0 FIGURE 9  0.1  0.2 0.3 0.4 RADIUS OF PLASMA COLUMN I N CM. RADIAL VARIATION OF N  e  0.5  0.6  -52-.  B)  TEMPERATURE Saha's e q u a t i o n and t h e p r o c e d u r e  permitted calculation of the electron Fig.  11 shows T  given i n the theory temperature.  as a f u n c t i o n o f t h e pressure  f o r t h e 0.5  e cm. p o s i t i o n .  S i n c e t h e p l a s m a was i n L T E , t h e  can  be c h a r a c t e r i z e d by a s i n g l e v a l u e , T.  C)  HYDROGEN DENSITY A r e p r e s e n t a t i v e graph o f N  is  g i v e n i n f i g . 12.  position. N  H  H  and N  shifts  Since the pressure  i s constant £  exposures provide a continuous changing  the pressure  T h i s a l s o r e f e r s t o t h e 0.5 cm.  i n c r e a s e s w i t h a x i a l h e i g h t as N  axial  versus  temperature  w i t h N , N_ a n d T.  above t h e anode  decreases.  Thus, t h e  r e c o r d o f w i d t h s and  \  \  b  \  o  ©\ \*  V \  \  \  \ \  °  \  Y \  \  o  \>  *  x  7.2^10  o  \  ©  6  9.3x10  \  \  \°  o  13.^5x10  6  \  '  \  ^  \  .\  \  \  o  15.5\<10  6  DYNES/CM  6  \  \ \  \  o  o  \  \  1  x  1  o  .  h  V  • \  V  8  fl  1  8  1  2  3  4x10  ELECTRON FIGURE  10  AXIAL  VARIATION  DENSITY, OF  N  N  '  A T VARIOUS  e  PRESSURES  \  _ 1 7  cm"  3  2  -5413000 K  12000 rt  s FIGURE 11  TEMPERATURE VERSUS PRESSURE  11000 10 {= 9  XlO . xlO  1 7  1 8  FOR N  {  FOR N H  a u H  >H EH M CO  w Q  2 1 0  X  10  X  X  X  X  X  11 12 13 14 15 : 16 17 PRESSURE I N DYNES/CM  X  18  19  ?f  FIGURE 12  ELECTRON AND HYDROGEN D E N S I T I E S VERSUS PRESSURE  20x10'  -55-  1  CHAPTER V I RESULTS AND DISCUSSION A)  THE PLASMA J E T The  experimental  developed broadening run  evidence  indicates that the j e t  h e r e i s a good p l a s m a g e n e r a t o r  for line  measurements a t h i g h p r e s s u r e s .  When t h e j e t i s  i n t h e l o w f l o w r a t e mode, t h e p l a s m a w h i c h r e s u l t s i s  homogeneous i n c r o s s s e c t i o n w i t h r e s p e c t t o N fairly  constant  axially  upper e x t r e m i t y .  until  much t h e same b e h a v i o r  t h e l i n e s i n v e s t i g a t e d showed That i s ,  u n i f o r m l y throughout t h e plasma  with the i n t e n s i t y dropping  o f frapidly  at the outer  layer.  LTE  i s ensured,  pressures permits  i n the form o f  a s t h e h y d r o g e n l i n e H^.  t h e r a d i a t i o n was e m i t t e d  boundary  f a l l i n g o f f rapidly a t the  With the impurity i n j e c t e d  a gas as w i t h t h e s i l a n e ,  and T and  a s p r e v i o u s l y d i s c u s s e d , by t h e h i g h  and hence t h e v a l u e s  of N  t h e u s e o f Saha's e q u a t i o n  encountered.  This  f o r the calculation of T  (for a small percentage of i m p u r i t i e s ) .  A f u r t h e r step f o r  f u t u r e i n v e s t i g a t i o n m i g h t i n v o l v e an i n d e p e n d e n t m e t h o d o f m e a s u r i n g T.  T h i s was a t t e m p t e d i n t h e e x p e r i m e n t b y  i n g some a r g o n i n t o t h e j e t b u t f a i l e d which d i f f e r e d  sufficiently  inject-  a s no l i n e s w e r e  i n excitation  energy.  found  -56-  B)  ELECTRON  BROADENING  The m e a s u r e d v a l u e s Stark effect  f o r reduced s h i f t and w i d t h  i n t e r a c t i o n w i t h e l e c t r o n s a r e compared  •theoretical values (see T a b l e I I ) .  p r e d i c t e d by t h e G B K O - t h e o r y  sections f o r elastic  This  collisions  between e l e c t r o n s and are well predicted  1  the  as o n l y these  agree  i n d i c a t e s that the  s i l i c o n atoms e x c i t e d i n t h e 4 s P ° l e v e l by t h e t h e o r y ,  with  ( G r i e m , 1964)  F o r b o t h l i n e s t h e measured s h i f t s  well with the t h e o r e t i c a l values. cross  due t o  collisions  are responsible f o r  shift. In the case of the widths,  t h e agreement w i t h t h e theory o  xs n o t s o g o o d . only  slightly  The m e a s u r e d w i d t h  t h e 3905 A l i n e i s  of  smaller than the t h e o r e t i c a l value, but the  l i n e a t 2881 A i s s e e n t o be a b o u t f o u r t i m e s predicted.  This d e v i a t i o n from theory  s u p r i s i n g a s some s e v e r e the  i s not too  section f o r inelastic  responsible f o r the broadening.  s e c t i o n i s p r o p o r t i o n a l t o t h e sum o f  c a l c u l a t i o n of these approximation  level  This  strengths  For the  t h e Coulomb  Both t h e 3 p D and t h e 3 p 2 1  2 1  S  levels,  however, have e q u i v a l e n t e l e c t r o n s and t h e r e f o r e t h e Coulomb a p p r o x i m a t i o n  i s not applicable.  cross  t o and from both  of the observed l i n e .  oscillator  i s used.  collisions,  the o s c i l l a t o r  strengths of a l l the possible t r a n s i t i o n s the upper and t h e lower  than  s i m p l i f i c a t i o n s h a v e b e e n made f o r  calculation of the cross  which are mainly  wider  Secondly, the  -57-  multiplet  splitting  is neglected the  adn these  calculation  especially  o f t h e 4p l e v e l i n t o terms a r e taken  neglects  forbidden  4 p * P , 4p*D a n d 4p*S  as one l e v e l .  Finally  t r a n s i t i o n s , of which  some s i n g l e t - t r i p l e t t r a n s i t i o n s  i n S i l are  observed w i t h l a r g e i n t e n s i t i e s i n normal d i s c h a r g e s . is  likely  t h a t t h e agreement between t h e o r y  and experiment  w o u l d be i m p r o v e d i f m e a s u r e d o s c i l l a t o r , s t r e n g t h s used f o r t h e j c a l c u l a t i o n , C)  r a t h e r than  these  c o u l d be  simplifications.  BROADENING BY HYDROGEN ATOMS Here, t h e measured s h i f t t o w i d t h  the  I t  theoretical  values  within  the error  t e m p e r a t u r e , one c a n c a l c u l a t e  r a t i o s agree limits.  the constants  with  Knowing t h e  C  from t h e G  reduced h a l f - w i d t h s i n Table Values  forC  2 / / s  I I I (using equation 13).  , d e t e r m i n e d i n t h i s manner, a r e compared  with  6  measurements by F e l d h a u s e n and Kusch broadened by a r g o n atoms.  interactions  interactions to  the blue Using  try  1967) t h e c o n s t a n t s  w i t h hydrogen a r e l a r g e r  with argon.  lines  As i n t h e case o f t i t a n i u m  ( M e y e r , 1964 a n d K u s c h a n d M e i n h o l d , for  (1967) o n s i l i c o n  than  those f o r  F u r t h e r , t h e l i n e 3905 A i s s h i f t e d  by h y d r o g e n a n d t o t h e r e d by a r g o n . Unsold's approximation  to estimate  the constants  (equation  1.9) o n e c a n  f o r a l e v e l , m; i . e . , C . m  6  a t r a n s i t i o n m-n one o b t a i n s c  mn 6  =  c  m  _ n c  6  e  6  For  TABLE I I EXPERIMENTAL AND THEORETICAL REDUCED WIDTHS AND SHIFTTO-WIDTH RATIOS. DUE TO INTERACTIONS WITH ELECTRONS  -59-  TABLE I I I MEASURED REDUCED WIDTHS AND SHIFTS DUE TO INTERACTIONS WITH HYDROGEN ATOMS„  (RED SHIFTS ARE COUNTED P O S I T I V E )  /  -60-  Calculated values of C ^ 2  5  6  a r e shown f o r b o t h  i n t e r a c t i o n w i t h hydrogen and w i t h argon While  f  cases,  j _ Table IV, n  t h e agreement between experiment  and t h e o r y i s q u i t e  good f o r a r g o n as p e r t u r b e r , i t b r e a k s  down c o m p l e t e l y f o r  the case  o f hydrogen.  action constant  The t h e o r y p r e d i c t s t h a t t h e i n t e r -  i n c r e a s e s w i t h the energy of the l e v e l  under c o n s i d e r a t i o n . the  3905 A l i n e  The m e a s u r e d s h i f t  to the blue of  shows, h o w e v e r , t h a t t h e l o w e r  3p  S  level  i s more a f f e c t e d . b y t h e i n t e r a c t i o n w i t h h y d r o g e n atoms than  t h e upper 4s P° l e v e l ,  than  the 3p  2881  A line.  w h i c h i n t u r n i s more a f f e c t e d  1  2 1  D  level  a s i n d i c a t e d by t h e r e d s h i f t  of the  o  T h i s means; 3p C "  S  2 1  6  C / e 2  5  than  4s P°  >  C  2 1  >  6  m e a s u r e d f o r t h e 2881 A l i n e theory predicts.  constants  3p  2 1  from combination  i s a b o u t 20 t i m e s  those  e s t i m a t e d by  can form s t a b l e s i l i c o n  time  electronic  hydride  2 i  2  S)  that molecules.  o f ground s t a t e hydrogen w i t h s i l i c o n e x c i t e d  Si(3p D).+ H ( S ) + SiII( A) or 2 1  5  states of SiH resulting  observed  e t a l , 1969);  Si(3p  Unsold s  due t o t h e f a c t  i n two o f t h e t h r e e s t u d i e d l e v e l s h a v e b e e n (Herzberg  larger  1  T h i s may be p a r t i a l l y  Up t o t h e p r e s e n t  6  D a n d 4 s P ° a r e more t h a n two  o r d e r s o f magnitude l a r g e r than  hydrogen and s i l i c o n  C  This implies that the i n t e r a c t i o n  f o r the levels  approximation.  3p D  1  + H( S) + 2  2  SiH( Z ) 2  +  SiH( E ) 2  +  TAELE I V  .  COMPARISON BETWEEN THE INTERACTION CONSTANTS AND SHIFT-TOWIDTH RATIOS FOR BROADENING BY HYDROGEN AND ARGON  C  6  (10 Exp,  Shift-to-v/idth  (Argon)  2 / / s  1 3  cm  1 2 / 5  /sec  2 / 5  ratio  (Exp. )  )  Th,  Hydrogen  Argon  3,2  -0.63  + 0.29  3,3  + 0. 32  + 0.83  (RED SHIFTS ARE COUNTED P O S I T I V E )  -62-  Molecular the  binding  forces  a r e o f c o u r s e much l a r g e r  a t t r a c t i v e forces estimated At  by.Unsold's  approximation.  a n y r a t e , i t i s c l e a r t h a t due t o t h e a b s c e n c e  of molecular bonding, the i n t e r a c t i o n w i t h argon should  than  atoms  be V a n d e r W a a l s t o a g o o d a p p r o x i m a t i o n , w h i l e  the p r e s e n c e o f m o l e c u l a r bonds i n t h e c a s e o f i n t e r a c t i o n with D)  hydrogen should  be e x p e c t e d t o c r e a t e  complications.  ERRORS In t h e r e s u l t s and g r a p h s , t h e .error b a r s and  tolerances  are standard  deviations  derived  from  the  data.  Factors  a)  An e r r o r o f 5% i s p o s s i b l e i n t h e v a l u e s  c o n t r i b u t i n g to these errors are; of N  from the h a l f - w i d t h s  with  o f H^.  A further e r r o r i n these  i s i n c u r r e d by t h e p r o c e d u r e o f s c a n n i n g t h e p r o f i l e s  t h e p h o t o d e n s i t o m e t e r and a v e r a g i n g .  density  of the n e u t r a l density  a f u r t h e r e r r o r o f 5%. used i n transforming also introduce  filters  the p r o f i l e s  V a r i a t i o n s i n the  used w i l l  Small deviations  i n t h e H-D  curves  to i n t e n s i t y p r o f i l e s  to the s i l i c o n  will  half-widths.  The t e m p e r a t u r e s c a l c u l a t e d by S a h a ' s e q u a t i o n  to obtain  introduce  further errors.  These e r r o r s a l s o apply b)  obtained e  L  values  averaging  the constants  C  were used  and a l s o were u s e d i n t h e 6  pressure  equation.  deviations  Errors introduced  h e r e a r e due t o  f r o m LTE and t o t h e p r e s e n c e o f i m p u r i t i e s i n t h e  plasma up  ( S i g n i f i c a n t d e v i a t i o n f r o m LTE  t o 20%  I n our  i n the  c a s e LTE  c a l c u l a t e d temperatures. i s e n s u r e d by  the  d e n s i t i e s were always a t l e a s t than the  LTE  criterion  of N  e  c) will  The  appreciable  f a c t t h a t our  = 1.2x10*  cm" .  7  3  greater The  small  i n the plasma should  due  introduce e r r o r s i n the values.of  t o b r o a d e n i n g by  not  error.  t o l e r a n c e s i n the measured p r e s s u r e s  also introduce  )  electron  N  are  and  ±5%.  of T  and  H will  of  ( G r i e m , 1964)  a f a c t o r o f two  percentage of i m p u r i t i e s present introduce  produces e r r o r s  e r r o r s i n the measured hydrogen  atoms.  half-widths  Th  -64-  . BIBLIOGRAPHY  B. A h l b o r n , 1965;  Z. N a t u r f o r s c h u n g .  CW.  A l l e n , 1963; Athlone.  Astro-physical Quantities.  W.L.  B a r r , 1962;  D.R.  B a t e s and A. Damgaard, 1949? P h i l o s o p h i c . Roy. S o c (London) (A) 242, 1 0 1 .  K.  J.O.S.A. 52,  B e h r i n g e r , W. 215, 127.  K o l l m a r and MSc.  20a,  466. (2nd  Ed.)  885.  j . Mentiel,  Trans.  1968;  Z.  J.C  B u r n e t t , 1969; Columbia.  H.D.  Campbell,  H.W.  D r a w i n and P. F e l e n b o k , 1 9 6 5 ; D a t a f o r P l a s m a s i n L o c a l Thermodynamic E q u i l i b r i u m . ' G a u t h i e r - V i l l a r s . Paris.  1966;  H.  Feldhausen  and  H.  F o l e y , 1946;  Ph.D.  H.J.  Phys.  Thesis, U n i v e r s i t y of  Physic  Thesis, Univ. of B r i t .  Kusch, Rev.  6_9,  H.R.  G r i e m , M. B a r a n g e r , A.C. P h y s . Rev. 125, 177.  H.R.  Griem,  G.  H. J .  47_,  K u s c h and  M e y e r , 1964;  1977;  Z. A s t r o p h y s .  Col.  66_,  364.  616. K o l b and  Plasma Spectroscopy.  H e r z b e r g , A L a g e r q v i s t and Phys.  J.  1964;  British  G.  Oertel,  McGraw  B.J. McKenzie,  1962a;  Hill. 1969;  Can.  1899. G.  Meinhold,  1967;  Z. A s t r o p h y s . £0,  Z. A s t r o p h y s .  67_,  123.  94.  R.N. M o r r i s , 1966; MSc. T h e s i s , U n i v . o f B r i t . C o l . A. U n s o l d , 1955; P h y s i k d e r S t e r n a t m o s p h a r e n (2nd Ed.) Springer.  J.  . APPENDIX I THE PULSE TRANSFORMER T h i s i s i n c l u d e d a s an a p p e n d i x s i n c e i t r e p r e s e n t s important  improvement o v e r p r e v i o u s methods o f s t r i k i n g  an an  arc i n pressurized vessels. O t h e r m e t h o d s u s u a l l y i n v o l v e d some t y p e o f magnetically mechanical and  s c r e w e d down t o draw t h e a r c , o r  arrangement.  versatile.  another  The method d e s c r i b e d h e r e i s s i m p l e  The a r c i s s t r u c k e l e c t r o n i c a l l y  ing convenient With  striker  t i m i n g sequences and r e l i a b l e  t h i s method, a p u l s e t r a n s f o r m e r  permitt-  control.  couples  v o l t a g e p u l s e t o t h e j e t e l e c t r o d e s v i a t h e power The t r a n s f o r m e r secondary  i s c o n s t r u c t e d by w i n d i n g  bifilar  a high supply.  a primary  ( i n t e r l a c e d ) on a l a r g e t o r o i d  and  form.  F o r t h i s p a r t i c u l a r a p p l i c a t i o n a F e r r o x Cube* FX 1076 ferrite  c o r e , 4.1/2  i n . O.D.,  was u s e d . The c o r e  wrapped w i t h 4 l a y e r s o f good q u a l i t y p l a s t i c tape.  Ten t u r n s o f #10  to f i l l  formvar  The  c o n s i s t e d o f 1 t u r n o f 20 k . v . i n s u l a t e d  was  electrical  i n s u l a t e d wire:*  the c o r e , formed t h e secondary.  B8K  spacewound  primary  wire.  T h i s c o n f i g u r a t i o n p r o v i d e d a good impedance match t o t h e 50 ohm  cable f o r high frequency  16 k . v . p u l s e  from the t h y r a t r o n d i s c h a r g e u n i t .  components were t h e r e b y secondary and  winding  components o f t h e  s u p e r i m p o s e d o n t h e D.C,  connected  These through  i n s e r i e s w i t h t h e power  the  supply  t h e j e t . , c a u s i n g gap b r e a k d o w n .  * A v a i l a b l e through  d i s t r i b u t o r s of P h i l l i p s  (Netherlands).  -66-  APPENDIX I I •ABEL TRANSFORM FOR A C Y L I N D R I C A L PLASMA COLUMN Y  FIGURE 13  C Y L I N D R I C A L COLUMN GEOMETRY FOR ABI5L TRANSFORM  Whenever d e n s i t i e s a n d t e m p e r a t u r e s of  sight,  an i n t e g r a l  i n v e r s i o n procedure  recover l o c a l emission c o e f f i c i e n t s intensities. intensity  "  m u s t be u s e d t o  from t h e observed  I n o p t i c a l l y t h i n plasmas o f r a d i u s r , t h e o  i s , i n terms o f t h e e m i s s i o n (  I(v)  vary along the l i n e  r  = 2f  2 0  _y2)i/?-  r  e(r) r  e ( r ) d x = 21°  o  dr  —-  (r -y 2  r  coefficient;  f o r a c y l i n d r i c a l column observed  2  ) !/  2  i n the x direction  at a  d i s t a n c e y from t h e x z p l a n e where t h e e m i s s i o n i s a f u n c t i o n of  only the r coordinate.  The i n v e r s i o n  by t a k i n g t h e A b e l t r a n s f o r m  (Griem,  i s then  1964),  accomplished  -67-  e(r)  = •IT  1 —  r / r  0  I ' (y) d y (y -r ) 2  2  l  = /  1  r /  0  TT r  2  I ' (x) d x (x -r ) / 2  2  1  2  T h i s p r o c e d u r e i s m o s t e a s i l y done b y c o m p u t e r a n d a u s e f u l method h a s b e e n g i v e n by B a r r r e p r e s e n t a t i v e F o r t r a n 4 readout  (1962).  follows.  A  SCO MP I L fi C C 1 2 3 4 5 . 6 7 9 8 ..• 9 10 10 11 i i 12 13 13 14 15 16 1 17 18 19 2 20 21 • 22 23  24 25 26 27 28  .15 14  T H I S IS. BAR ?, S METHOD F O R - A R E L U N F O L D I N G OF R A D I A L P R O F I L E S ( N = ?.0) 20 P R O F I L F P O I N T S ( 0. 0 0' TO 0 . " 5 ) ARF FED I M U S I N G A F].O.n FORMAT D I M E N S I O N E ( 2 0 ) , BETA ( 2 0 , 2 0 ) , A R ( 2 ) 7 T I T L E ( 1 2 ) REA L I MS ( 2 0 ) PI = 3.14159 MPAGF = 0 OH - 0.0:? READ ( 5,9 1 ) BETA READ ( 5 , 9 6 ) T I T L E WRITE ( 6 , 97 ) T I T L E WRITE (6 ,90 } DO 13 I = ]. 2 0 READ ( 5 .92 ) IMS ( I ) I F { I M S ( I ) .LT.O.O) GO TO 9 9 9 CONTINUE AREA = I N S ( 1 J / 2 . 0 DO 1 I = 2 , 2 0 AREA = AREA + I M S ( I ) ' ' AREA = ? . 0 » A R F A * D H ' ' DO ?. I = 1 ,20 INS ( I ) = I K S ( I ) / AREA AR(2 ) = AREA NPAGE = N PAGE + 1 AREA = 0.0 no 14 i = 1,20 ] E ( I ) = 0.0 DO 15 J = 1 7 2 0 E ( I ) = E { I ) - B E T A ( I > J ) * IN S(J) E(I ) = E ( I )/(DH*PI ) AREA = AREA + E ( I ) :  7  ;  ;  - •  37 38 19 39 • 40 41 42 43 44 45 999 46 88 ^7 89 48 90 49 • 91 50 • 92  . A P. F A = (AP.FjA - E ( 1 )/?.. 0) *0H*2 . 0 00 16 I = 1,20 E ( I ) = F ( I ) /A R E A A R{1) = AREA OD 19 I = 1,20 R = D H' F L 0 A T ( I - l ) . X = in.O*R Y = 10 .0*F ( I ) . • • WRITE ( 6 , 9 3 ) R, E.( I ) , I N S ( I ) CONTI HUE WRITE (6 ,94 ) AR WRITE ( 6 , 8 8 ) IF ( M P A G E . N E . 2 ) GO TD 9 NPAGE = 0 WRITE ( 6 , 8 9 ) " •'.'~" GO TO 9 STOP FORMAT ( IH-//) FORMAT ( 1 HI ) FORMAT ( 1 4 X , 8HPOS I T I ON,4X,12HCALC.P ROE IL E > 5 X, FORMAT ( 1 0 F 8 . 0 ) FORMAT ( F 1 0 . 0 )  51  93  ' FORMAT  52 5? 54 55  94 9S 96 97  29 30 31 32 33 34 35  56..  16  ; :  •  I  "  :  3F15.4)  .  ; 1  :  (10X, F10.2,  ' . ' "  :  ;  11 H O B S . I M T E N S . / )  FORMAT ( 1 H 0 , 11X, 13HSCALE FACTORS, F 1 0 . 3 , 2 F 1 5 . 3 ) F 0 R M A T (1 ? X . ? OHSTAMOARO DEVIATION =• F 11. . 4 ) ' FORMAT (18A4) FORMAT ( 5 X , 1 8 A 4 ) END  •*  .  ''  g •  APPENDIX I I I H-D  CURVE FOR CALIBRATION THE P L A T E EMULSION  If  a n e u t r a l density step f i l t e r  of the s l i t by  a light  through  of a spectrograph source,  i s placed  and t h e s l i t  the exposure o f l i g h t  the i t h step of the f i l t e r  i n front  i silluminated  transmitted  i s g i v e n by;  E. = I t T. where; T — i s  the transmission of the i t h step,  I  i s the i n t e n s i t y of the l i g h t ,  t  i s the exposure  time.  An a p p r o x i m a t e m e a s u r e o f t h e d e n s i t y o f grains i n the emulsion  developed  i s c a l l e d D and i s m a t h e m a t i c a l l y  defined as; D = log  1  where; i  o  (i /i) o  i s the intensity of l i g h t transmitted  through  an u n e x p o s e d p o r t i o n o f t h e s p e c t r o g r a p h i c i  i s the i n t e n s i t y of l i g h t transmitted  t h e exposed and d e v e l o p e d P l o t t i n g D versus  log  plate  through  p o r t i o n of the p l a t e .  E. r e s u l t s  i n t h e H-D  (after  io r Hurter  and D r i f f i e l d )  curve which i s the t r a n s f o r m a t i o n  between d e n s i t y o f t h e exposed p o r t i o n o f t h e p l a t e and intensity  of the i n c i d e n t l i g h t .  of such a  curve.  Since  I and t a r e c o n s t n t  trace, plotting  a  log  Fig.14  shows an e x a m p l e  f o r any one  T. i n p l a c e o f l o g  10 1  1o  calibration  E. i s e q u i v a l e n t 1  LOG FIGURE 1 4  to  1 o(E)  T Y P I C A L H - D CURVE  c h o o s i n g a s c a l e l e n g t h as t h e i n t e n s i t i e s  These t r a n s m i s s i o n s of the f i l t e r or easily  are  elative.  are a function of the neutral density  a n d a r e u s u a l l y g i v e n by t h e m a n u f a c t u r e r  measured by a s e t - u p such as t h a t d e s c r i b e d on  p a g e 37 o f t h i s  thesis.  D r a w i n g a smooth c u r v e t h r o u g h t h e p o i n t s on t h e p l o t of D versus l o g T  gives a transformation  curve f o r a l l  1o 1 intermediate all  N o r m a l l y t h e maximum d e n s i t i e s o f  t h e l i n e s measured and t h o s e o f t h e s t e p  should to  exposures.  l i e on t h e l i n e a r  traces  p o r t i o n o f t h e H-D curve i n o r d e r  avoid errors introduced  f r o m B t o C.  filter  by t h e c o m p r e s s i o n  region  There i s a l s o reason t o doubt t h e v a l i d i t y o f  the t r a n s f o r m a t i o n  i n t h e s e dense  regions.  -72-  If the intensity H-D  o f t h e l i g h t used t o determine t h e  c u r v e i s known, a b s o l u t e i n t e n s i t i e s  o b t a i n e d by t h i s m e t h o d . this  can a l s o  However, i n t h i s  be  experiment,  i n f o r m a t i o n was n o t r e q u i r e d . Using a carbon a r c f o r the l i g h t source permitted  o b t a i n i n g t h e H-D  curve f o r a l lwavelengths  Since the i n t e n s i t i e s  and e x p o s u r e  studied.  times f o r the  p l a s m a a n d t h e c a r b o n a r c w e r e a p p r o x i m a t e l y t h e same, no d i f f i c u l t y w i t h r e c i p r o c i t y experiment.  f a i l u r e i s expected i n the  

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