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Spectroscopic diagnostic techniques for shock heated plasmas Simpkinson, William Vaughan 1961

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SPECTROSCOPIC FOR  SHOCK  DIAGNOSTIC HEATED  TECHNIQUES  PLASMAS  by  WILLIAM VAUGHAN SIMPKINSON B . A . S c , U n i v e r s i t y o f B r i t i s h Columbia, 1957  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.A.Sc. i n the Department of PHYSICS  W.e a c c e p t t h i s t h e s i s as conforming t o the required standard  THE UNIVERSITY OF BRITISH COLUMBIA October,  1961  In p r e s e n t i n g  t h i s thesis i n p a r t i a l fulfilment of  the r e q u i r e m e n t s f o r an advanced degree a t t h e British  Columbia, I agree t h a t the  a v a i l a b l e f o r reference  and  study.  University  of  L i b r a r y s h a l l make i t f r e e l y I f u r t h e r agree t h a t  permission  f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may g r a n t e d by  the  Head o f my  It i s understood t h a t f i n a n c i a l gain  Department o r by h i s  be  representatives.  copying o r p u b l i c a t i o n o f t h i s t h e s i s f o r  s h a l l not  be  a l l o w e d w i t h o u t my  Department o f P h y s i c s The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada.  Columbia,  Date  1960  September 29.  written  permission.  ABSTRACT  Photographic  and P h o t o e l e c t r i c measurements were  made on the shock e x c i t e d s p e c t r a o f Argon and H e l i u m .  The  plasma temperature and e l e c t r o n d e n s i t y i n the r e g i o n behind the shock wave were c a l c u l a t e d from the s p e c t r o s c o p i c measurements.  These q u a n t i t i e s were compared w i t h the v a l u e s o b t a i n e d  from the Rankine Hugoniot shock t h e o r y i n c l u d i n g the e f f e c t of i o n i z a t i o n .  C o n s i d e r a b l e disagreement was found between  e x p e r i m e n t a l r e s u l t s and t h e o r e t i c a l  (ii)  predictions.  TABLE OF CONTENTS Chapter  Page  I  INTRODUCTION  1  II  THEORY  h  S p e c t r o s c o p i c Theory (a) S t a r k B r o a d e n i n g o f Hydrogen L i n e s (b) S p e c t r a l L i n e S h i f t i n g (c) Temperature D e t e r m i n a t i o n from S p e c t r a l Intensities Shock Theory  V  8 12 17  I I I APPARATUS  IV  + k 7  !  17 18 19  Shock Tube S p e c t r o s c o p i c Equipment E l e c t r o n i c A n c i l l i a r y Equipment Arrangement o f the Equipment and M i s c e l l a n e o u s Details  20  EXPERIMENTAL  22  Preliminary Investigation Measurements Data R e d u c t i o n o f Time I n t e g r a t e d S p e c t r a Data R e d u c t i o n o f Time R e s o l v e d S p e c t r a l Intensities  22 2*+ 25  RESULTS  29  (A) ARGON Preliminary Time I n t e g r a t e d Measurements (a) Ne D e t e r m i n a t i o n from H^ B r o a d e n i n g and Line S h i f t i n g (b) Observed L i n e I n t e n s i t i e s (c) Temperatures from Observed L i n e I n t e n s i t i e s Time R e s o l v e d Measurements T h e o r e t i c a l Temperatures and D e n s i t i e s (B) HELIUM Preliminary Time I n t e g r a t e d Measurements Time R e s o l v e d Measurements (a) Hydrogen and H e l i u m L i n e I n t e n s i t i e s (b) N and kT Behind Shock T h e o r e t i c a l Temperatures and D e n s i t i e s  (iii)  27  29 30 30 31 32 33 35 36 37 37 37 39 kO  TABLE OF CONTENTS ( c o n t ' d ) Chapter VI  Page  CONCLUSIONS  hi  Appendix I  THEORETICAL LINE STRENGTHS  hh  Argon L i n e S t r e n g t h s Helium Line Strengths  hh h6  BIBLIOGRAPHY  hQ  ILLUSTRATIONS  Page  lo 2. 3. h. 5. 6. 7. 8. 9.  pkT v e r s u s L One D i m e n s i o n a l Shock Wave Shock Tube Arrangement o f A p p a r a t u s E l e c t r o d e l e s s Discharge C i r c u i t Trace Photograph Filtered Profiles v e r s u s Log I n t e n s i t y Spectrophotometer S e n s i t i v i t y 10. I ( t ) f o r A l l 329^ A° 11. I ( t ) f o r AIII 3285 A  12 13 17 20 21 25 27 27 28  13. K t ) a t U-835 A Ih. I ( t ) f o r H e l 5876 15. K t ) f o r H e l l h686 16. kT and N v e r s u s t  38 38 38 39  33  33  0  12.  I ( t ) a t hQ55  AO  38  0  e  TABLES  Page  I II I I I Plasma Temperature (ev) IV L i n e I n t e n s i t i e s f o r V a r i o u s Shock v ( i n cm/microsecond) V Plasma Temperature kT (ev) VI VII s  (iv)  30 31  Velocities  32 3*+ 35 36  hO  ACKNOtfLEDGEMEM TS  I am very g r a t e f u l to Dr. A. J . Barnard f o r the i n v a l u a b l e d i r e c t i o n and a s s i s t a n c e g i v e n throughout the course o f t h i s work. S p e c i a l thanks are extended  to Mr. G.D.  Cormack who  designed and c o n s t r u c t e d most of the apparatus used i n t h i s i n v e s t i g a t i o n while working f o r h i s MSc degree. indebted scopic  to Dr. A.M.  I am a l s o  Crooker f o r the generous l o a n of s p e c t r o -  equipment.  (v)  I INTRODUCTION  In  the g r e a t l y expanding  f i e l d of h i g h  temperature  or  plasma p h y s i c s much e f f o r t i s g o i n g i n t o the development  of  d i a g n o s t i c techniques.  The development o f plasma d i s g n o s t i c s  i s rendered d i f f i c u l t by t h e t r a n s i e n t n a t u r e o f the l a b o r a t o r y plasmas produced, typical.  l i f e t i m e s o f the o r d e r o f microseconds  being  B r o a d l y s p e a k i n g , plasma d i a g n o s t i c t e c h n i q u e s can be  d i v i d e d i n t o two c a t e g o r i e s , t h e f i r s t being those  techniques  which p e r t u r b t h e plasma and then measure the e f f e c t o f the p e r t u r b a t i o n , t h e second plasma.  b e i n g those which do n o t p e r t u r b the  P e r t u r b i n g t e c h n i q u e s as a r u l e i n t r o d u c e some u n c e r -  t a i n t y i n t h a t the p e r t u r b a t i o n may change the e f f e c t b e i n g measured. S p e c t r o s c o p i c t e c h n i q u e s , which do n o t i n v o l v e plasma p e r t u r b a t i o n s , a r e a u s e f u l and p o w e r f u l means o f i n v e s t i g a t i o n . Study o f the e m i s s i o n s p e c t r a from a plasma can l e a d to i d e n t i f i c a t i o n o f the elements  p r e s e n t and y i e l d a q u a n t i t a t i v e  e s t i m a t e o f the e l e c t r o n d e n s i t y , e l e c t r o n temperature, and degree o f i o n i z a t i o n . temperature  I n a d d i t i o n to the above, the i o n k i n e t i c  can be o b t a i n e d f o r plasmas a t very h i g h tempera-  t u r e s (T ~ - 1 0  6  °K).  The approach  employed i n t h i s experiment  was to d r i v e  a s t r o n g shock wave down a q u a r t z tube and observe  the emission  s p e c t r a from the heated  r e g i o n behind the shock. - 1 -  The v a l u e s o f  -  2 -  e l e c t r o n d e n s i t y , e l e c t r o n temperature, and the degree o f i o n i z a t i o n obtained  from s p e c t r o s c o p i c o b s e r v a t i o n s  were compared  w i t h those expected from theory f o r the shock v e l o c i t i e s o b s e r v e d . From the above comparison some i n f e r e n c e may be made of c o n d i t i o n s i n the plasma being  studied.  The most  q u e s t i o n i s whether o r n o t the plasma i s i n thermal  important equilibrium.  Here e q u i l i b r i u m i m p l i e s the e x i s t e n c e o f : (1) a M a x w e l l i a n  velocity  distribution for electrons, i . e . , a  u n i q u e e l e c t r o n temperature, and (2)  a d i s t r i b u t i o n o f atoms and/or i o n s i n v a r i o u s energy s t a t e s , E , n  the p o p u l a t i o n o f each d e s c r i b a b l e by a term c o n t a i n i n g  a Boltzmann f a c t o r ,  e x p ( - E / k T ) , i n which the temperature, n  T, e q u a l s the e l e c t r o n temperature (k i s the Boltzmann constant). S p e c t r o s c o p y i s e x t r e m e l y w e l l - s u i t e d to i n v e s t i g a t i o n s o f energy level  populations. The  s p e c t r o s c o p i c measurements to be made a r e o f l i n e  b r o a d e n i n g , l i n e s h i f t i n g , and o f t h e r e l a t i v e i n t e n s i t i e s o f l i n e s of various adjacent  atomic and i o n i c s p e c t r a * .  I t will  be seen t h a t i n t h i s experiment the temperature and d e n s i t i e s are such t h a t measurable l i n e broadening and s h i f t i n g a r e due o n l y to. t h e e l e c t r i c m i c r o f i e l d s w i t h i n the plasma, so t h a t measurement o f these o b s e r v a b l e s and i o n d e n s i t i e s .  permits  determination  The measurement o f r e l a t i v e l i n e  of e l e c t r o n intensities  "•Adjacent s p e c t r a a r e the s p e c t r a o f an atom and an i o n Cor o f two i o n s ) each p o s s e s s i n g the same n u c l e u s but whose complements of e l e c t r o n s d i f f e r by one.  - 3 from a d j a c e n t s p e c t r a , i n an e q u i l i b r i u m plasma o f known e l e c t r o n d e n s i t y , y i e l d s the plasma temperature. Other workers (McLean e t a l , i 9 6 0 ) have done the above type of experiment w i t h a h e l i u m plasma produced by a magnetically  d r i v e n shock wave.  I n the p r e s e n t experiment  both h e l i u m and argon plasmas have been i n v e s t i g a t e d . work on h e l i u m a l l o w s  The  some comparison w i t h t h a t of McLean as  the c o n d i t i o n s a r e r o u g h l y s i m i l a r though the a n a l y s i s d i f f e r s somewhat.  N o t h i n g was found i n the l i t e r a t u r e on s t u d i e s of  argon s p e c t r a e x c i t e d by m a g n e t i c a l l y  d r i v e n shock waves.  I I THEORY  Spectroscopic  Theory  (a) S t a r k Broadening: o f Hydrogen L i n e s I n an assembly o f e m i t t i n g atoms and i o n s the p r i n c i p a l s p e c t r a l l i n e broadening  mechanisms a r e :  ( 1 ) p e r t u r b a t i o n o f one o r both o f the a s s o c i a t e d energy l e v e l s o f the atom o r i o n * by the e l e c t r i c m i c r o f i e l d s due to surrounding  i o n s and e l e c t r o n s ( S t a r k e f f e c t ) ,  (2) Doppler e f f e c t on e m i s s i o n f r e q u e n c i e s due to random t h e r m a l m o t i o n o f the r a d i a t i n g atom o r i o n , and (3) p e r t u r b a t i o n o f energy l e v e l s by van der Waals f o r c e s between atoms and/or i o n s ( P r e s s u r e  effect).  The above mechanisms have been d i s c u s s e d i n many a r t i c l e s , the most u s e f u l o f which was found t o be a review a r t i c l e by R.G. Breene J r .  (1957)*  I t can be shown, t h a t a t the temperatures  and d e n s i t i e s a t t a i n e d i n t h i s experiment, p r e s s u r e broadening  t h e Doppler and  a r e l e s s than a few t e n t h s o f an angstrom.  T h i s l e a v e s o n l y t h e S t a r k e f f e c t as s i g n i f i c a n t ;  I t should  be p o i n t e d o u t here t h a t t h e S t a r k e f f e c t has two m a n i f e s t a t i o n s , l i n e broadening  and l i n e s h i f t i n g .  L i n e broadening  without  s h i f t i n g r e s u l t s from the energy l e v e l p e r t u r b a t i o n s changing s i g n w i t h the f l u c t u a t i n g m i c r o f i e l d  ( l i n e a r Stark  effect).  •The a s s o c i a t e d energy l e v e l s , E^ and E^, a r e r e l a t e d to the s p e c t r a l f r e q u e n c y , V , by the well-known r e l a t i o n : hV=Ei-E* where h i s P l a n c k ' s c o n s t a n t (6.6 x 1 0 ^ 7 e r g - s e c ) . m n  - k -  -  5 -  The most pronounced the  l i n e a r S t a r k e f f e c t i s seen i n  spectrum o f hydrogen which i s p r e s e n t as an i m p u r i t y i n  a l m o s t a l l plasmas.  I n t h i s experiment broadening measurements  were made o n l y on hydrogen  lines.  A t h e o r y f o r t h e l i n e a r S t a r k broadening o f hydrogen l i n e s was f i r s t developed by Holtsmark (1919). the  He assumed t h a t  p e r t u r b a t i o n s o f the energy l e v e l s were due e n t i r e l y to the  q u a s i - s t a t i o n a r y f i e l d s o f the i o n s , the f r e q u e n c y o f p e r t u r b a t i o n by t h e e l e c t r o n f i e l d s b e i n g too h i g h to cause t h e energy l e v e l s t o respond.  H o l t s m a r k c a l c u l a t e d the p r o b a b i l i t y f o r a  g i v e n f i e l d a t an e m i t t i n g atom due to s u r r o u n d i n g , s t a t i o n a r y , s i n g l y charged i o n s o f number d e n s i t y , N j . I f the f i e l d was expressed i n u n i t s o f F , where F Q  (1)  F  = 2.6leNj  Q  0  i s g i v e n by:  J  (where e i s the e l e c t r o n i c charge, h.8  x 10"10 coulombs), the  p r o b a b i l i t y d i s t r i b u t i o n s coincided f o r a l l N j . F r e f e r r e d to as the Holtsmark normal f i e l d .  0  i s usually  S i m i l a r i l y , the  p r o f i l e s o f a hydrogen l i n e f o r d i f f e r e n t N j can be r e p r e s e n t e d on a s i n g l e c u r v e by p l o t t i n g the s p e c t r a l i n t e n s i t y v e r s u s the parameter  <?C=  ^3  (where &\  i s the d i s p l a c e m e n t i n ang-  o stroms from the l i n e c e n t r e ) . r  From work by Chandrasekhar  (19 +3) t h e Holtsmark theory 1  can be extended to m u l t i p l y charged i o n s s i m p l y by r e p l a c i n g Nj  i n E q u a t i o n (1) by an "effective™ d e n s i t y g i v e n by: (2)  N  E  F  F  = N  X  +  2  3  /  2  N  2  +  3  3 / 2  N  .... =£;'i V 3y  3  +  i=l  - o where N  i s the number d e n s i t y of i - t h stage i o n s .  1  moderately  i o n i z e d gas, N , g  For a  the e l e c t r o n d e n s i t y , i s given by  N j>f to a f i r s t approximation. e  The a c c u r a t e e x p r e s s i o n f o r the  electron density i s :  N = N-_ + 2 N + 3N3 +  (3)  e  =  2  ^L  i r L  i=l Recent work was  done by Griem, Kolb, and Shen (1959)  on hydrogen l i n e broadening  due  to e l e c t r o n i c and i o n i c  i n a plasma of atoms, e l e c t r o n s , and e l a b o r a t e numerical a n a l y s i s was  s i n g l y charged  made and  fields  ions.  the t h e o r e t i c a l  p r o f i l e s obtained have shown b e t t e r agreement with  An line  experiment  than the p r e v i o u s Holtsmark theory. The (where F theory.  Q  t h e o r e t i c a l p r o f i l e s of Griem, Kolb, and Shen 2/3  = 2.6leN  ) are moderate c o r r e c t i o n s to the Holtsmark  e  Therefore, i t w i l l be assumed that f o r the purposes  t h i s experiment  the theory of Griem et a l may  i n c l u d e m u l t i p l y charged Equation  (2)) f o r  be extended  i o n s by s u b s t i t u t i n g N ff Q  of  to  (given by  N . e  In t h i s work, values of F  Q  were determined  the experimental l i n e p r o f i l e s with the t h e o r e t i c a l for  temperature  and  d e n s i t y n e a r e s t that estimated  The  constant by which P C i s m u l t i p l i e d  F  which y i e l d s  by  fitting  profiles to occur.  to get the best f i t i s  N ff. e  A simple method of making the above f i t i s to r e p l o t the p r o f i l e s on l o g - l o g  s c a l e with  f o r the t h e o r e t i c a l  profile  - 7 on the same s c a l e as  A X  abscissae). the p r o f i l e s i s F  (b)  Q  f o r the e x p e r i m e n t a l  profile  The h o r i z o n t a l s h i f t r e q u i r e d  to a l i g n  ( v e r t i c a l s h i f t i s unimportant).  Spectral Line Considering  Shifting  again  the S t a r k e f f e c t , l i n e s h i f t i n g as  w e l l as b r o a d e n i n g o c c u r s when the energy l e v e l p e r t u r b a t i o n i s a f u n c t i o n o n l y o f t h e magnitude o f the f l u c t u a t i n g m i c r o f i e l d (quadratic Stark e f f e c t ) . field  The f u n c t i o n a l r e l a t i o n s h i p between  s t r e n g t h and s h i f t o f the s p e c t r a l l i n e wavelength o r  f r e q u e n c y i s known from experiments i n x^hich a gaseous i s m a i n t a i n e d i n a steady^: u n i f o r m e l e c t r i c  discharge  field.  I n the s p e c t r a o f argon the s t a r k s h i f t i s r e a d i l y measured.  The s h i f t s o f many argon l i n e s have been i n v e s t i g a t e d  by Minnhagen  (19^8) and  Maissel  (1958) and  been found more o r  l e s s p r o p o r t i o n a l to the square o f the f i e l d the S t a r k e f f e c t i s more c o m p l i c a t e d result i t i s d i f f i c u l t line shifting.  strength.  I n helium  than i n argon and as a  t o o b t a i n u s e f u l i n f o r m a t i o n from h e l i u m  I n t h i s experiment l i n e s h i f t data w i l l be used  o n l y i n the work on argon. I t remains t o r e l a t e the l i n e s h i f t observed i n the shock s p e c t r a t o t h e e l e c t r o n ( i o n ) d e n s i t y i n t h e plasma. frequency s h i f t ,  A V , o f a g i v e n l i n e w i l l be assumed to be  r e l a t e d t o the f i e l d (-+)  A N  The  s t r e n g t h F by:  = CF  2  where C i s a c o n s t a n t known from S t a r k e f f e c t e x p e r i m e n t s . l i n e i n t e n s i t y d i s t r i b u t i o n f u n c t i o n I ( /\~~)) ) i s r e l a t e d the n o r m a l i z e d H o l t s m a r k * p r o b a b i l i t y  K A V )d(A\>  (5) where I  Q  to  d i s t r i b u t i o n W(F/F ) by: 0  ^'w(F/F )dF  ) =  0  i s the t o t a l s p e c t r a l  discussion,  The  i n t e n s i t y o f the l i n e  under  /-yt-©o  I(A\) )d(ZaV)) -oo  The Holtsmark f u n c t i o n W ( ^  ) i s o b t a i n e d from  (19^3). WC/  p-  3  ) vanishes at  has a h a l f w i d t h o f /\p<^2,25<,  I(A\V  (6)  I )  =  D  Chandrasekhar  0,©O^ peaks a t  = 1.6  From E q u a t i o n s (h)  and (5) •  W(F/F )  T2~ 2CFg  G  -*/F  o  Thus the i n t e n s i t y d i s t r i b u t i o n f u n c t i o n K^^V W(P  ) .  When p l o t t e d  and  ) peak s as  from the curve f o r W ( )  i s found to be a t  the peak of  W(P)  For a g i v e n l i n e , the f r e q u e n c y  s h i f t o f the i n t e n s i t y d i s t r i b u t i o n maximum i s measured s p e c t r o scopically.  The c o r r e s p o n d i n g f i e l d  from E q u a t i o n (^f),  and d i v i d i n g F  m a x  can then be found from E q u a t i o n (1)  (°) Temperature  s  by 1.05  fflax  ,  calculated  yields F . D  (with N f f replacing e  D e t e r m i n a t i o n from S p e c t r a l  Assuming e q u i l i b r i u m *W(y3) i  strength, F  between e l e c t r o n  N  e f f  Nj_ ).  Intensities and i o n i c temp-  n o r m a l i z e d by the r e q u i r e m e n t t h a t the p r o b a b i l i t y f o r  w( j 3 ) d p = 1).  -9 e r a t u r e s , the temperature o f a plasma can be determined from i n t e n s i t i e s o f l i n e s w i t h i n a g i v e n spectrum o r from l i n e s o f adjacent spectra.  However, because o f the l a r g e d i f f e r e n c e  between e n e r g i e s o f i o n i z a t i o n f o r s u c c e s s i v e i o n s p e c i e s compared w i t h the s m a l l d i f f e r e n c e s between energy s t a t e s w i t h i n a s p e c i e s , the temperature i s most s e n s i t i v e l y determined from comparison o f measurements from a d j a c e n t s p e c t r a . The a b s o l u t e i n t e n s i t y o f a s p e c t r a l l i n e  resulting  from a t r a n s i t i o n between the energy l e v e l s W~ and  o f an  i - t h s t a g e i o n i s g i v e n by (see f o r example Condon and S h o r t l e y ) : ( n  ,  (7)  T  I  x  i _  =  N  1  —-  g g  (m) f f l r TT^c ;  1  m  i  —r-rr  S  ,v  (m,n;  3A%,n)  " ' "l  where N^(m) i s the d e n s i t y o f i - t h stage i o n s o f energy E*, g^ i s the degeneracy o f the energy s t a t e E^,  ~\(m,n,)±s  the  w a v e l e n g t h o f t h e l i n e , c i s the speed o f l i g h t , and S (m,n) i s 1  the t h e o r e t i c a l l i n e s t r e n g t h o f the t r a n s i t i o n E^-E?: (Ei; w i l l m n m always be taken as the upper l e v e l ) .  F o l l o w i n g Condon and  •Shortley the term l i n e s t r e n g t h i s t a k e n to be the sum o f the squares o f the e l e c t r i c d i p o l e m a t r i x elements.  The l i n e  strengths  f o r t h e h e l i u m and argon l i n e s s t u d i e d i n t h i s experiment a r e t a b u l a t e d i n Appendix I . Now i n t h e r m a l e q u i l i b r i u m , a t temperature T, the N (m) can be expressed as the p r o d u c t o f the s t a t i s t i c a l weight., 1  g^, f o r t h e energy l e v e l  and the Boltzmann f a c t o r ,  (k i s the Boltzmann c o n s t a n t ) .  Therefore  exp(-E^/kT)  -  (8)  fe=^ m  where Z N (0) 1  for  1  10  N ( i n ) = ^ g e x p ( - 2 m ) = ^S^l fe mm i fe o i  ,  i  k T  g exp(-=fra) ^ i - f P l kT g o  g  =  1  i s the p a r t i t i o n f u n c t i o n f o r i - t h stage i o n s ,  and g^ a r e the d e n s i t y and s t a t i s t i c a l weight i - t h stage i o n s i n the ground s t a t e (E^ = 0 ) . (9)  s i M i m  = NiLoj. i o  P g  e  and E q u a t i o n (7)  _ % kT  (  g  r£ i  =  Z  i  m  (  *  2  1  and  respectively,  From E q u a t i o n ( 8 )  _  ^ kT  becomes on s u b s t i t u t i n g I ^ C f e / g : 1  rn  i i ,6i^tosi  ( ) 10  m  '  3X1^,11)  n  A second  Z  (  . ^  }  kT  1  r e l a t i o n i n v o l v i n g the N  i s o b t a i n e d by  1  i n t r o d u c i n g Saha's e q u a t i o n which g i v e s the r a t i o of the. numbers of i o n s i n the v a r i o u s stages o f i o n i z a t i o n :  NV+I  (11)  i+l i  N  where M  _  2  N  z  e  2 m (  }  h  i s the e l e c t r o n mass and E  electron).  E  2  the i - t h stage i o n (the energy  for  _  e^kT 3/2  1  i "kT  )  i s the i o n i z a t i o n energy  r e q u i r e d to remove the  of  (i+l)-th  Combining E q u a t i o n ( 1 1 ) w i t h E q u a t i o n ( 1 0 ) taken  i - t h and  ( i + l ) - t h stage i o n s :  (12) m.n T  =  i ± + 1  nfen  1  A -ZTh jh + , li „"u ^ V„" Ai(m,n)  )^  1^2mJTkTtiv §v  2  2  1  fe  h  ;  "  \  os'cm>i) f e ..*\  EEi ++EE i  ^  x i + 1  kT  -- E l xi  - 11 Taking l ° g  (13)  M  °? E q u a t i o n (12) :  1 0  =  (1/2-TOD 3/21og kI 1 0  ( ~ * m E  E  - K)  +1  t  3/21og (S2|a) + 10  +  l  O  g  1  0  (  where S (m,n) and /\. (m,n) have been r e w r i t t e n  and  1  . I n s e r t i n g n u m e r i c a l v a l u e s i n E q u a t i o n (13)  d^)  k  T  .(I/2.303) (  =  >  £ i l ^ L _  /\. •  gives:  J|2  3 / 2 1 o g k T + 21.8 + l o g ( 10  1 0  where kT i s i n e l e c t r o n v o l t s . I t i s seen t h a t E q u a t i o n (1*+) has the form: (15)  kT =  A ._ 3/2 l o g k T ~ + B 10  and thus l e n d s i t s e l f best a c c o m p l i s h e d  e a s i l y to graphical s o l u t i o n .  This i s  by i n t r o d u c i n g a s c a l i n g parameter p, such  t h a t pA i s c o n s t a n t .  F o r convenience  pA w i l l be s e t e q u a l t o  10, and E q u a t i o n (15) then becomes:  ( l 6 )  J k f •  3  /  2  1 O g  10  p  k  T  =  ( B  +  3  /  2  l 0 g  1 0 TV  )  =  L  F i g u r e 1 i s a graph o f L v e r s u s pkT from which kT can be o b t a i n e d f o r -given B and A.  •*> 12 — Figure 1 - pkT vs. L pkT  It should be added here that an exact value of H for i n s e r t i o n i n Equation (Ik)  w i l l not always be available  from l i n e broadening and s h i f t i n g measurements. measurements give only ^ ff  e  I f these  as defined by Equation (2), a f i r s t  e  approximation to kT can be obtained ,by inserting N f f f o r TS e  i n Equation (Ik).  N^, N  2  &  etc. are found from Sana's equation  using these approximations y i e l d s a better value f o r N  to kT and N .  Equation (3) then  which i n turn w i l l improve the  approximation f o r kT.  Shock Theory We w i l l consider here a strong, one dimensional shock  -  wave p r o p a g a t i n g  -  13  with velocity  v  g  i n t o a gas a t r e s t .  the n o t a t i o n on F i g u r e 2, the s u b s c r i p t before  the shock.  pressure,  Q  Following  w i l l denote q u a n t i t i e s  The symbols p, T, U, N, v, denote r e s p e c t i v e l y  temperature, i n t e r n a l energy per p a r t i c l e , number  d e n s i t y o f i o n s and/or atoms combined, and f l o w v e l o c i t y .  F i g u r e 2 - One D i m e n s i o n a l  Shock Wave  Vo  p,T,U,N  T  and U <C< UJ and the eequatj quations o momentum, and energy a r e :  (17)  N v OS  (b) (c)  0  Po> o> o> o U  N  As i t i s assumed t h a t the shock i s s t r o n g :  (a)  =  p pv  P <K p D  f o r c o n s e r v a t i o n o f mass, l i n e a r '  = N(v -v) s  = mN v v 0  s  = N v (U + imv ) 2  Q  s  where m i s the mass o f an atom o r i o n ( n e g l e c t i n g e l e c t r o n mass), From E q u a t i o n (18)  ( 1 7 ) (b) and ( c ) : U = imv  2  To proceed f u r t h e r w i t h t h i s development the processes o c c u r r i n g behind  the shock must be c o n s i d e r e d .  The p r i n c i p a l  -  _  11+  processes i n t h i s r e g i o n are c o l l i s i o n a l tion.  i o n i z a t i o n and  excita-  From the o v e r a l l charge n e u t r a l i t y of the plasma we  may  write:  (19)  1^= N + 2N + 3 N x  2  where the symbol e>C^ denotes atoms ( oC  =  +  3  =  + . .)=N 2ic?C = N<£  +2  the f r a c t i o n of  1  i  i times  ionized  NV ). N  Assuming thermal e q u i l i b r i u m between i o n s and (i.e.  T.  (17)  = T ) Equations  ( a ) , (b) and  mented with the equation of s t a t e and i n t e r n a l energy  of an i d e a l  (18)  electrons,  can be  supple-  the equation f o r the  gas:  (a)  p = (N+N )kT = (l+oC)NkT  (b)  U = 3/2  Q  (20)  where U ^  e  (1+oOkT +  i s the i o n i z a t i o n and (17)  S o l v i n g Equations  U  i e  the e x c i t a t i o n energy  ( a ) , ( b ) , (18)  and  (20) f o r N  per i o n . and  Q  v , s 2  and i n t r o d u c i n g n u m e r i c a l v a l u e s : {1+cC), (a)  N  =  N  e  (ifd+cO  +  2U  i e / k T  (21) (b)  v  2  _ s  where kT and U^ weight  e  (,2XT(l+<£) + lQ,). J-^M 3/2 k T ( l + « C ) + U U  1  9  2  (cm./microsec.) ^ «/ -'  2  2  /  c m  i e  are i n e l e c t r o n v o l t s and M i s the  of the r e s t  m i c r o s e c  atomic  gas.  For comparison  with v a l u e s of kT and N  s p e c t r o s c o p i c measurements i t i s necessary  g  obtained  from  to express kT and  N  e  - 15 i n terms o f t h e o b s e r v a b l e s , v l  and U. i e  experiment and  a r e themselves  s  and N .  I t should be noted  f u n c t i o n s o f kT and N .  In this  eQ  t h e temperature  that  i s o f t h e o r d e r o f a few e l e c t r o n v o l t s  so t h e e x c i t a t i o n energy o f an i o n , g i v e n by:  e  ,g  «*-  ^  E e x p ( - _n)  VgJ  &  1  i s s m a l l compared w i t h the i o n i z a t i o n energy. the e x c i t a t i o n e n e r g i e s , U.  (22)  can be expressed  = X , E ° + o4(E°+ E ) +  U.  1  i n terms o f the xP^  + c/T(E°+...+E -l) + ...  1  ie  Thus, n e g l e c t i n g  r  2  r  Assuming t h e r m a l e q u i l i b r i u m , the © £ a r e g i v e n by the Saha equations:  -B  (23)  r + 1  2 z ^ l 2 - k T 3/2 •  -  e  E  r  and by: (2h)  £e£  = 1  To s o l v e E q u a t i o n s f o r kT, N  g  (21) ( a ) , ( b ) , ( 2 2 ) , (23) and (2k)  and t h e c?£ a method o f s u c c e s s i v e  was adopted.  We w i l l f i n d i t c o n v e n i e n t  i n form: (a) (25)  kT  = -b -V s/l.92'1/7 +  Mv  8(1+^0  approximations  to r e w r i t e Equation  (21)  - 16 where b and c a r e g i v e n by: b = (IfU, -3/2MV ,  y  c = (^U. 9 A M v  )  2  le  s/i.92  J /  ie  + + 7 /  2  )  s/i.92  7  I n s e r t i n g estimated values f o r the (25) g i v e s a f i r s t a p p r o x i m a t i o n of these f i r s t approximations values f o r the o C . consistent  i n Equations  t o kT- and N^*.  (22) and  Substitution  i n Saha's e q u a t i o n y i e l d s  This process i s continued u n t i l  better  self  values of o £ are obtained. The above method o f s o l u t i o n s i m p l i f i e s i n p r a c t i c e  for  v a l u e s o f kT such  that:  ,  , T r r l 15.1? +  kT ^= minimum  (a—~S—)  At such temperatures  o n l y the  need be c o n s i d e r e d .  T h i s i s a t once apparent  equation. in  f o r which  from Saha's  Thus, i n most cases o n l y two o f the  the a p p r o x i m a t i n g  precedure.  However, i f  need be used or « ^  + 2  a r e s i g n i f i c a n t as c a l c u l a t e d from Saha's e q u a t i o n u s i n g t h e a p p r o x i m a t e v a l u e s o f kT and N  then t h e a p p r o x i m a t i n g  must be c a r r i e d one s t e p f u r t h e r . whichever  o f ©£. -. o r o £ 1 —J-  i s repeated  I n s e r t i n g i n E q u a t i o n (2*+)  i s s i g n i f i c a n t , the above  found.  procedure  i+2  giving better values f o r  process i s continued u n t i l a c o n s i s t e n t is  procedure  and <^\+i> T h i s whole value of  or °^+2  Ill  APPARATUS  Shock Tube The shock tube used f o r t h i s work c o n s i s t e d o f a q u a r t z tube o f 2 . 5 cm i n s i d e d i a m e t e r , a p p r o x i m a t e l y 100 cm l o n g , and f i t t e d w i t h an e l e c t r o m a g n e t i c d r i v e r .  The g e n e r a l  d e t a i l s o f t h e d r i v e r , energy s t o r a g e c i r c u i t and v e l o c i t y measuring a p p a r a t u s a r e shown i n f i g u r e 3 ( n o t t o s c a l e ) . F i g u r e 3 - Shock Tube RCA Type 931  The s p a r k s w i t c h , when t r i g g e r e d , f e e d s c u r r e n t to the d r i v e r from the c a p a c i t o r bank which i s r a t e d a t f o u r mfd. a t 15 KV.  I t can be seen from the d r i v e r geometry t h a t the  a r c c u r r e n t i s t i g h t l y coupled to t h e c u r r e n t i n t h e bac&strap and i s thus g i v e n a s t r o n g magnetic r e p u l s i o n which i n a d d i t i o n - 17  -  - 18 -  to  sudden e x p a n s i o n  by h e a t i n g causes a shock wave to be p r o -  pagated down t h e tube.  The shock v e l o c i t y i s c a l c u l a t e d from  the time i n t e r v a l between the p h o t o m u l t i p l i e r responses t o t h e l i g h t from t h e luminous f r o n t f o l l o w i n g the shock. The  d e s i g n , 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 i s shock  tube a r e f u l l y d e s c r i b e d by Cormack  (i960).  S p e c t r o s c o p i c Equipment Time i n t e g r a t e d s p e c t r a were o b t a i n e d u s i n g a H i l g e r El  spectrograph.  This spectrograph  c o u l d be f i t t e d w i t h a  seven s t e p n e u t r a l d e n s i t y f i l t e r f o r d e t e r m i n a t i o n o f t h e emulsion  d e n s i t y v e r s u s l i g h t i n t e n s i t y r e l a t i o n f o r any p l a t e  required. To study time v a r i a t i o n o f s p e c t r a l i n t e n s i t i e s a H i l g e r constant d e v i a t i o n spectrograph  was m o d i f i e d by the  a d d i t i o n o f an a d j u s t a b l e s l i t i n t h e f o c u s p l a n e , f o l l o w e d by a photomultiplier.  The r e s u l t i n g spectrophotometer  be used i n the v i s i b l e s p e c t r a l r e g i o n .  This  could only  spectrograph  was l a t e r r e p l a c e d by a Bausch and Lomb g r a t i n g monochromator when one became a v a i l a b l e . For time i n t e g r a t e d s t u d i e s , t h e wavelength range 2000-7200 A  0  c o u l d be covered  by t h e H i l g e r E l s p e c t r o g r a p h .  By u s i n g an RCA I P 28 p h o t o m u l t i p l i e r i n the  spectrophotometer,  time r e s o l v e d measurements c o u l d be made i n the range 2500-6000A . 0  The d i s p e r s i o n o f t h e E l s p e c t r o g r a p h approximately  1.2A°/mm a t 2000A  0  ranges from  to i+SAO/mm a t 66OOA0 w h i l e  - 19 t h a t o f t h e g r a t i n g s p e c t r o p h o t o m e t e r i s l6A°/mm throughout the spectrum.  The s l i t w i d t h used on the E l i n s t r u m e n t and  the average g r a i n s i z e o f p l a t e e m u l s i o n a l l o w e d  resolution  of l i n e s on t h e p l a t e s e p a r a t e d by a p p r o x i m a t e l y .1 mm. g r a t i n g s p e c t r o p h o t o m e t e r w i t h the s l i t w i d t h s used slit two  The  (entrance  •^-.0+ mm, e x i t s l i t '"-s09 mm) was c a p a b l e o f r e s o l v i n g o l i n e s o f h a l f w i d t h 1.5A° separated by h to 5A°. s  i  %  E l e c t r o n i c A n c i l l i a r y Equipment The voltage  s t a n d a r d e l e c t r o n i c s used c o n s i s t e d o f a p l a t e  supply, a v a r i a b l e , c a l i b r a t e d 0 - 1 . 5  the p h o t o m u l t i p l i e r s  and a T e k t r o n i x  KV. s u p p l y f o r  type 551 d u a l beam o s c i l -  loscope f i t t e d with a single input preamplifier, a difference p r e a m p l i f i e r , and a Dumont t r a c e r e c o r d i n g  camera.  The photo-  m u l t i p l i e r c i r c u i t s were made up i n t h e l a b o r a t o r y . The  o u t p u t o f t h e v e l o c i t y measuring  was f e d through s h i e l d e d the o s c i l l o s c o p e .  photomultipliers  c a b l e to t h e d i f f e r e n c e a m p l i f i e r on  The o u t p u t o f t h e p h o t o m u l t i p l i e r on the mono-  chromator was f e d i n t o a cathode f o l l o w e r o f s t a n d a r d The  o u t p u t o f t h e cathode f o l l o w e r was f e d through  cable  to the s i n g l e input p r e a m p l i f i e r .  design.  shielded  The r i s e time o f the  p h o t o m u l t i p l i e r , cathode f o l l o w e r and p r e a m p l i f i e r c i r c u i t was of t h e o r d e r o f .1 m i c r o s e c o n d .  The o s c i l l o s c o p e was t r i g g e r e d  by a p i c k - u p c o i l coupled to the c u r r e n t i n the shock tube d i s charge. The  v a r i a b l e high voltage  m u l t i p l i e r s allowed  power supply to the photo-  adjustment o f spectrophotometer  sensitivity  - 20 to  accommodate a g r e a t range of s p e c t r a l i n t e n s i t i e s without  changing the spectrophotometer entrance  slit.  Arrangement of the Equipment and M i s c e l l a n e o u s D e t a i l s The apparatus was scale).  arranged as i n f i g u r e h (not to :  F i g u r e k - Arrangement of Apparatus  RCA IP28  / T h o tomul t i p l i er Quartz objective lens V e l o c i t y measurin pho t o m u l t i p l i e r s Shock_ driver  Electrodeless discharge tube  Cathode ^/"follower T o ^/oscilloscope n  K ^ h i eld with s l i t to define object region 110 v o l t s d.c. Removable m i r r o r f o r use with e l e c t r o d e l e s s discharge source Displacement of o b s e r v a t i o n p o i n t from shock tube d i s c h a r g e (variable)  The i r o n a r c and e l e c t r o d e l e s s d i s c h a r g e tube y i e l d comparison  s p e c t r a which can be superimposed  by use of a Hartmann  -  2 1 -  diaphragm on the time i n t e g r a t e d shock s p e c t r a o b t a i n e d by the H i l g e r E l instrument. connected  The e l e c t r o d e l e s s d i s c h a r g e tube was  to the shock tube vacuum system so t h a t the p r e s s u r e  o f t h e gas being e x c i t e d c o u l d be r e g u l a t e d by the same v a l v e s as c o n t r o l l e d the p r e s s u r e i n the shock tube.  The c i r c u i t  diagram f o r the e l e c t r o d e l e s s d i s c h a r g e i s g i v e n i n f i g u r e 5 » F i g u r e 5 - E l e c t r o d e l e s s Discharge  Circuit  Spark gap  220  Discharge tube  v o l t s a.c:  50KV X - r a y transformer Capacitors .0025  to  .0'  IV EXPERIMENTAL  Preliminary  Investigation  S e v e r a l time i n t e g r a t e d shock s p e c t r a were taken on I l f o r d HP3 p l a t e s o f the i l l u m i n a t i o n o f a s t a t i o n 10 cm from the d r i v i n g e l e c t r o d e s . shock v e l o c i t y .  Each s p e c t r a was taken a t a d i f f e r e n t  The shock v e l o c i t y c o u l d be changed r e a d i l y  by a d j u s t i n g t h e i n i t i a l v o l t a g e on the c a p a c i t o r bank.  After  f i f t e e n to twenty f i r i n g s the i n s i d e o f the shock tube became b l a c k e n e d and i t was n e c e s s a r y to remove the d r i v e r and c l e a n the tube (see f i g u r e 3 ) . F i f t e e n f i r i n g s o f the tube were found ample f o r a good exposure.  The p h o t o g r a p h i c p l a t e so  o b t a i n e d was a n a l y z e d u s i n g the i r o n a r c spectrum as a r e f e r e n c e . R e l a t i v e i n t e n s i t i e s o f the l i n e s were e s t i m a t e d from the emulsion d e n s i t i e s .  From the s p e c t r a l l i n e s i d e n t i f i e d on the  p l a t e some were chosen f o r f u r t h e r s t u d y .  The c r i t e r i a f o r  the s e l e c t i o n were freedom from i m p u r i t y i n t e r f e r e n c e ,  proxi-  m i t y to o t h e r l i n e s o f the same and a d j a c e n t s p e c t r a and a v a i l a b i l i t y i n the l i t e r a t u r e o f S t a r k s h i f t  coefficients.  The second c r i t e r i o n was d e s i r a b l e as no ready means was a v a i l a b l e f o r c h e c k i n g the m a n u f a c t u r e r s ' s p e c t r a l  sensitivity  v e r s u s wavelength r e l a t i o n f o r the s p e c t r o p h o t o m e t e r .  I t may  be added t h a t s p e c t r a l l i n e s which were expected and n o t found on the p l a t e s were l o o k e d f o r w i t h the s p e c t r o p h o t o m e t e r .  This  was t r i e d because i n the r e g i o n 2500 - 5000A the s p e c t r o p h o t o 0  meter gave a s t r o n g response to s p e c t r a l l i n e s which were very weak on the p l a t e . - 22 -  -  23  -  As the S t a r k broadening o f the to  l i n e s were  be used f o r the d e t e r m i n a t i o n o f e l e c t r o n d e n s i t y i t was  d e s i r a b l e to know t h e i r time h i s t o r i e s . at  and  Their a r r i v a l  times  the 1 0 cm s t a t i o n and p u l s e shape were observed u s i n g the  s p e c t r o p h o t o m e t e r and compared w i t h h i s t o r i e s o f the l i n e i n t e n s i t i e s of the r e s t gas being used. A f t e r the e x p l o r a t o r y work above had been completed the s p e c t r o p h o t o m e t e r was a d j u s t e d and c a l i b r a t e d f o r the l i n e s to  be s t u d i e d .  1200  The p h o t o m u l t i p l i e r s u p p l y v o l t a g e was  v o l t s and the e n t r a n c e s l i t w i d t h was  s e t to  s e t f o r "on scale'"'  responses from the weakest l i n e to be i n v e s t i g a t e d .  Then the  e x i t s l i t was a d j u s t e d by s e t t i n g the spectrophotometer on the w i d e s t l i n e and n a r r o w i n g the e x i t s l i t by s m a l l i n c r e m e n t s u n t i l the response showed a sudden d e c r e a s e .  Next, the r e l a t i o n  between spectrophotometer s e n s i t i v i t y and p h o t o m u l t i p l i e r s u p p l y v o l t a g e was  determined by s e t t i n g the i n s t r u m e n t on a s p e c t r a l  l i n e whose response was e l e v e n to t h i r t e e n v o l t s and then dec r e a s i n g the supply v o l t a g e by one hundred the response a g a i n . 1100,  v o l t s and  taking  I n t h i s manner i n t e n s i t i e s t a k e n a t 1 2 0 0 ,  1 0 0 0 v o l t s e t c e t e r a c o u l d be r e l a t e d .  I t was  assumed  t h a t the p h o t o m u l t i p l i e r - c a t h o d e f o l l o w e r c i r c u i t gave l i n e a r response w i t h s p e c t r a l i n t e n s i t y below the s a t u r a t i o n p o i n t (output "^-16  volts).  F i n a l l y , the e l e c t r o d e l e s s d i s c h a r g e was a d j u s t e d to g i v e the b e s t p o s s i b l e r e f e r e n c e spectrum f o r the gas b e i n g s t u d i e d , i . e . narrow u n s h i f t e d s p e c t r a l l i n e s o f the same s p e c t r a  -  as were observed  2k -  i n t h e shock tube.  The best c o n d i t i o n s were  chosen by comparing s e v e r a l exposures taken w i t h v a r i o u s c a p a c i t a n c e s and spark gaps i n the d i s c h a r g e c i r c u i t  ( f i g u r e 5)  and w i t h the gas p r e s s u r e a t a low v a l u e (p ^ 2 0 m i c r o n s ) .  Measurements The o b s e r v a t i o n s were a l l made a t t h e 10 cm s t a t i o n and a t t h r e e v a l u e s o f shock v e l o c i t y c o r r e s p o n d i n g v o l t a g e s o f 10 KV, 11.25 KV and 12.5 KV. neutral density f i l t e r almost  completed,  to d r i v i n g  As the seven step  was n o t a v a i l a b l e u n t i l the work was  o n l y one exposure was made through  a t a d r i v i n g v o l t a g e o f 12.5 KV w i t h argon.  the f i l t e r ,  Some o f the time  i n t e g r a t e d s p e c t r a were exposed i n j u x t a p o s i t i o n w i t h e l e c t r o d e l e s s d i s c h a r g e s p e c t r a i n o r d e r t o measure S t a r k  shifts.  Whenever p o s s i b l e , time i n t e g r a t e d and time r e s o l v e d data were o b t a i n e d from the same f i r i n g s .  Quadruple P o l a r o i d  exposures were taken o f t h e o s c i l l o s c o p e t r a c i n g s t o average out random f l u c t u a t i o n s i n i n t e n s i t y and v e l o c i t y .  In this  manner the average shock v e l o c i t y was r e c o r d e d f o r each time i n t e g r a t e d spectrum and any abnormal d e v i a t i o n f o r a s i n g l e shot c o u l d e a s i l y be seen.  A t y p i c a l oscilloscope trace  photo i s p i c t u r e d i n F i g u r e 6. upper t r a c e s a r e t h e responses  R e f e r r i n g t o F i g u r e 6, the o f t h e spectrophotometer  r a d i a t i o n i n t h e v i c i n i t y o f the l i n e . had been made o f the spectrophotometer  to  A f t e r f o u r exposures response  to a given  s p e c t r a l l i n e t h e background c o n t i n u a was r e c o r d e d .  The s p e c t r o -  - 2 5-  photometer  was t u r n e d to a nearby wavelength r e g i o n f r e e from  s p e c t r a l l i n e s and f o u r more exposures were taken ( w i t h the lower t r a c e removed).  The lower t r a c e i s the response o f the  two v e l o c i t y measuring p h o t o m u l t i p l i e r s taken through the d i f f e r ence p r e a m p l i f i e r .  The shock v e l o c i t y i s o b t a i n e d from the  lower t r a c e , the s e p a r a t i o n o f the d i s c o n t i n u i t i e s i n the t r a c e marking the time f o r shock passage through 5 cm. F i g u r e 6 - Trace Photograph volts^  \ \\// i  V  \  3*"  time  Where p o s s i b l e time r e s o l v e d p r o f i l e s were o b t a i n e d of the  and  lines.  T h i s was done by r e c o r d i n g average  time h i s t o r i e s a t 5A° i n t e r v a l s r a n g i n g from the l i n e c e n t r e to a p o i n t where o n l y the background  s i g n a l was o b s e r v e d .  Data R e d u c t i o n o f Time I n t e g r a t e d S p e c t r a A J a r r e l - A s h microphotometer coupled w i t h a B r i s t o l pen r e c o r d e r was used to scan the l i n e s o f i n t e r e s t on the time i n t e g r a t e d s p e c t r a f o r s p e c t r a l i n t e n s i t y and the broadening o f the  and ELg  lines.  These pen r e c o r d e r t r a c e s were made f o r  the exposure t r a n s m i t t e d through each segment o f the seven step filter.  The maximum e m u l s i o n d e n s i t i e s read from the above t r a c e s ( e x c e p t i n g those f o r hydrogen l i n e s ) were p l o t t e d f o r each s p e c t r a l l i n e a g a i n s t the l o g a r i t h m of the i n t e n s i t y ( t a k i n g the u n f i l t e r e d i n t e n s i t y as u n i t y and the l o g a r i t h m s of All  f i l t e r e d i n t e n s i t i e s as the n e g a t i v e of the f i l t e r the curves so o b t a i n e d were f i t t e d  densities).  to a s i n g l e curve by  s h i f t i n g p a r a l l e l to the l o g i n t e n s i t y a x i s .  From t h i s  the r e l a t i v e i n t e n s i t y v e r s u s e m u l s i o n d e n s i t y was  curve  read.  The procedure f o r d e t e r m i n a t i o n of hydrogen l i n e broadening  d i f f e r e d from the above.  density,  f o r each f i l t e r  I n t h i s case the  s t e p was  p l o t t e d versus  (on the same s c a l e ) as sketched i n F i g u r e 7»  emulsion wavelength  Next, p l o t s of wave-  l e n g t h v e r s u s l o g i n t e n s i t y were made f o r s e v e r a l v a l u e s of c o n s t a n t P,  the f i l t e r d e n s i t y d i f f e r e n c e and hence Z \ ( l o g i n -  t e n s i t y ) b e i n g known between each two s t e p s . versus  As the p l o t s o f I  ~\ w e r e s y m m e t r i c a l , o n l y a h a l f p r o f i l e was used as i s s  seen i n F i g u r e 8.  The p r o f i l e of l o g i n t e n s i t y v e r s u s / \ i s ob-  t a i n e d by v e r t i c a l l y s h i f t i n g the curves o f F i g u r e 8 to a b e s t f i t s i n g l e curve.  - 27 F i g u r e 8 - Avs  Figure 7 - F i l t e r e d Profiles  Data Reduction of Time Resolved S p e c t r a l The spectrophotometer  Log I n t e n s i t y  Intensities  t r a c e s were p l o t t e d on a l a r g e r  s c a l e with t h e i r r e s p e c t i v e backgrounds.  The backgrounds  s u b t r a c t e d l e a v i n g the net i n t e n s i t y of each s p e c t r a l The i n t e n s i t y  s c a l e was a r b i t r a r i l y  were  line.  chosen so that the responses  i n v o l t s f o r the h i g h e s t p h o t o m u l t i p l i e r supply v o l t a g e could be p l o t t e d without change.  Traces f o r which the supply v o l t a g e  was reduced to avoid s a t u r a t i o n of the e l e c t r o n i c s were c o r r e c t e d using  the s e n s i t i v i t y versus supply v o l t a g e r e l a t i o n  previously  determined. C o r r e c t i o n s f o r v a r i a t i o n i n spectrophotometer t i v i t y with wavelength  were r e q u i r e d f o r comparison of two l i n e s  separated by more than 100-200°A.  A spectrophotometer  v i t y curve ( F i g u r e 9) was drawn from the g r a t i n g curve f o r the Bausch  sensi-  sensiti-  efficiency  and Lomb monochromator combined with the  - 28 -  spectral sensitivity  c u r v e f o r the I P 28 p h o t o m u l t i p l i e r taken  from RCA tube d a t a . F i g u r e 9 - Spectrophotometer  Sensitivity  Relative Sensitivity  Time r e s o l v e d hydrogen l i n e p r o f i l e s  were o b t a i n e d  d i r e c t l y from the P o l a r o i d t r a c e photographs by p l o t t i n g  the  response a t a g i v e n time from each averaged t r a c e a g a i n s t the wavelength a t which the t r a c e was taken ( a f t e r background  signal  s u b t r a c t i n g the  f o r the g i v e n time from each r e s p o n s e ) .  V RESULTS  This c h a p t e r w i l l be d i v i d e d i n t o two p a r t s (A) Argon and (B) H e l i u m . (A)  Argon  Preliminary The p r e l i m i n a r y p l a t e s o f the argon shock s p e c t r a contained Impurity  a generous number o f s t r o n g A l l and A I I I l i n e s p r e s e n t were H ^  lines,  the stronger  lines,  *+650.l6  for intensity  , Hg, , many C I I , S i l l , C u l  C a l l l i n e s and o n l y the s t r o n g e s t  and +-65l«35A° ( u n r e s o l v a b l e ) .  CIII  The l i n e s  l  chosen  measurement were: All  AIII  3 2 9 3 . 9 5 A °  3 2 8 5 . 8 5 A °  3307.2*+A°  3301.88A°  33 50 .9^A°  33H.  3376A6A°  3336.13A°  3388.17A  0  25A°  3 3 M f . 7 2 A ° 33  while  lines.  those f o r measurement o f S t a r k  5 8 A 1 A  0  s h i f t were:  All 3 5 5 9 . 5 3 A °  356l.O*rA° 3 5 7 6 . 6 2 A ° 3588.M+AO  The HP3 p l a t e c u t o f f i n s e n s i t i v i t y a t about  6 5 7 0 A  0  so t h a t measurement o f t h e H^ p r o f i l e n e c e s s i t a t e d an exposure w i t h a Kodak type F p l a t e which has r e l a t i v e l y vity i n this  region.  -  29  -  constant  sensiti'  - 30 Time r e s o l v e d a n a l y s i s c o u l d n o t be made o f the Hg l i n e because many A l l l i n e s o v e r l a p i t s p r o f i l e and the H ^ 1 l a y o u t s i d e t h e s e n s i t i v e r e g i o n o f the s p e c t r o p h o t o m e t e r . The e l e c t r o d e l e s s d i s c h a r g e tube was found t o y i e l d s t r o n g A l l and A I I I l i n e s w i t h C = .0075 mfd. and a spark gap o f one i n c h .  Time I n t e g r a t e d Measurements (a) Ne D e t e r m i n a t i o n from H ^ The H ^  Broadening and L i n e S h i f t i n g  p r o f i l e as o b t a i n e d by the procedure o u t l i n e d  i n Chapter IV ( F i g u r e s 7 and 8) was f i t t e d b e s t i n t h e wings by the t h e o r e t i c a l p r o f i l e f o r T=20,000°K and We=10 7 m~3.  The  1  C  =F  ratio  n  f o r b e s t f i t was (212±2*f) s t a t v o l t s / c m which  y i e l d e d , from F = 2 . 6 l e N / 3 , N 2  Q  (  N'  eff  = (.7-.D10  17  cm" ,  The A l l l i n e s h i f t i n g gave F v a l u e s t a b u l a t e d  3  below;  Table I L i n e (A°)  F ( s t a t volts/cm)  Weighted* Average F  7h7 1001 llk7 1900 977  833stv/cm  3588.tf 3576.6  3561.0 3559.5  Taking average F=833 s t a t v/cm, F = 0  Ne?iN  = ( 5 ± l ) 1 0 7 cm-3.  1.05  =793 s t a t v/cm and  1  eff  •Average i s weighted i n f a v o u r o f A l l k +7 +.8A which showed b e s t agreement w i t h <£>V= C F and a g a i n s t A l l 356lA° which showed worst agreement. ]  2  )  u  - 31 I t i s seen t h a t the two e s t i m a t e s o f N  d i f f e r by  e  a f a c t o r o f seven, though both w i l l be lowered a f t e r o b t a i n i n g an a p p r o x i m a t i o n f o r kT and the oC^ and then s o l v i n g e q u a t i o n s (2) and (3) f o r a second a p p r o x i m a t i o n to N .  (a) Observed  Line Intensities  The A l l and A l l time i n t e g r a t e d t o t a l l i n e  intensities  were taken as the p r o d u c t o f the i n t e n s i t y c o r r e s p o n d i n g to the peak o f the l i n e e m u l s i o n d e n s i t y p r o f i l e as taken from the pen r e c o r d e r t r a c i n g and the w i d t h o f the p r o f i l e taken a t a d e n s i t y r e a d i n g c o r r e s p o n d i n g to o n e - h a l f peak i n t e n s i t y .  These i n t e n -  s i t i e s observed a t V =1.92 cm/microsecond, a r e t a b u l a t e d below s  w i t h upper energy l e v e l s , E *  and i o n i z a t i o n energys, E , as 1  v  taken from Moore (19*+9) • Table I I All Multiplet Line (A°)  El=2?.5ev Intensityy,  AIII  E*(ev),  Mu^.tiplet L i n e (AO)  E =H-0.7ev 2  Intensity  E|(ev)  83 3293.9  kk  23.53  1 3285.8  83 3307.2  52.5  23. k5  1 3301.9  ko  25.26  109 3350.9  ko  2k.72  1 33H.2  23  25.25  109 3376.5  k5  2k ,71  3 3336.1  25  27.98  96 3388.1  50  23.53  3 33^.7  19  27.96  3 3358. »f  12  27.9^  25.28  - 32 (c) Temperatures  from Observed  Line  Intensities  S o l u t i o n s t o e q u a t i o n (1*+) u s i n g l i n e s t r e n g t h s , S^, from Appendix I , energy l e v e l s , i o n i z a t i o n e n e r g i e s , and p a i r s o f l i n e i n t e n s i t i e s from (b) above and f o r each v a l u e o f Ne i n (a) above a r e t a b u l a t e d belox-/. o f kT f o r Ne=5xl0 ' cm"3, 1  7  The l o w e r numbers a r e v a l u e s  t h e upper numbers v a l u e s f o r Ne=.7x-10 'c 1  Table I I I - Plasma Temperature (ev)  \AIII L I N E S All  (AO^  3293.9  3307.2  3350.9  3376.5  3388.1  3285.8  3301.9.  3311.2:  3336.I  33M+.7  3358 A  2.06  2.10  2.10  2.11  2.13  2.13  2.36  2A2  2Al  2.39  2A2  2A1  1.93  1.97  1.97  1.97  1.99  1.97  2.19  2.2k  2.2k  2.22  2.25  2.2^  2.18  2.17  2A6  2A6  1.39  1.3^  1.61  1.58  l A  1.3^  1.62  1.61  2.11  2.16  2.15  2.15  2A1  2A9  2A8  2A5  '  Only a few temperature c a l c u l a t i o n s were made u s i n g A l l 3350.9A° and 3376.5A° as t h e l i n e s t r e n g t h t h e o r y seemed to break down f o r these l i n e s and g i v e i n c o n s i s t a n t r e s u l t s (see Appendix I ) . A b e t t e r a p p r o x i m a t i o n to the h i g h e r e s t i m a t e o f N  e  was made u s i n g the average v a l u e o f kT from Table I I I ( d i s -  c o u n t i n g c a l c u l a t i o n s i n v o l v i n g A l l 3350.9 and 3376.5A°),  - 33 solving f o r c ? ^ , J^i") £2  stituting  (assuming i  n  c/C^ + &0> = 1) and then sub-  e q u a t i o n s (2) and ( 3 ) .  This c a l c u l a t i o n  y i e l d e d N = 3» 9xl0-*-' cm""3 which i n t u r n caused the second 7  e  a p p r o x i m a t i o n t o kT t o be reduced. - .O'+ev (a 2% r e d u c t i o n ) .  Time R e s o l v e d Measurements In t h e work w i t h argon time r e s o l v e d h i s t o r i e s c o u l d n o t be o b t a i n e d from t h e  and  lines.  The A l l and A I I I  i n t e n s i t y h i s t o r i e s c o u l d , however, be used t o check t h e t o t a l i n t e n s i t y v a l u e s o b t a i n e d from the time i n t e g r a t e d  spectra.  T y p i c a l averages o f A l l and A I I I i n t e n s i t y are  histories  r e p l o t t e d i n F i g u r e s 10 and 11. F i g u r e 10 - I ( t ) f o r A l l 329>+A  F i g u r e 11 - I ( t ) f o r A I I I 3285A  Kt)  I(t)  0  0  t ( m i c r o s e c o n d s , from d i s c h a r g e ) The second peak, which i s q u i t e apparent i n A l l 329 *-, i s caused 1  by a second shock which o c c u r s due t o r i n g i n g i n t h e d i s c h a r g e circuit  (see Cormack, i 9 6 0 ) .  F o r comparison w i t h time i n t e g r a t e d  - 3h intensities  the i n t e g r a l  Jl(t)dt was c a l c u l a t e d  f o r each i n t e n s i t y  v e r s u s time c u r v e .  The  i n t e g r a t e d i n t e n s i t i e s a r e t a b u l a t e d below f o r the t h r e e d r i v i n g v o l t a g e s ( i . e . f o r shock v e l o c i t i e s v ) . s  Table IV - L i n e i n t e n s i t i e s f o r v a r i o u s shock v e l o c i t i e s v ( i n cm/microsecond) s  All Intensity  Line (A°)  AIII  10KV v =1.5 s  Line  11.25KV v =1.72 s  12.5KV v =1.92  (AO)  Intensity 10KV v =1.5  s  s  11.25KV 12.5KV v =1.72 v =1.92 s  s  329-+  2k.1  36.5  »f 5.0  3286  k.6  25.6  If2.5  3307  20.1  29.9  33.6  3302  5.9  11.9  22.3  3351  21  22.7  k2.7  3336  8.7  12.1  kl.2  33^5  8.2  8.6  3388  no readj ngs t a k e n  3358  8.7  'From Tables I I and IV i t can be seen t h a t the two methods o f measuring ment.  total line intensity  show o n l y rough agree-  However, when the temperature c a l c u l a t i o n  i s made u s i n g  the i n t e n s i t i e s o f Table IV t h e v a l u e s o f kT o b t a i n e d cover the same range as those i n Table I I I . C a l c u l a t i o n s were made o f average t e m p e r a t u r e s , kT, a t v = 1 . 5 and 1 . 7 2 cm/microsecond u s i n g i n t e n s i t i e s o f A l l 329*f, 3307AO and A I I I  3286,  3302,  3336,  These v a l u e s a r e seen i n Table V. used i n the above c a l c u l a t i o n s  and 3 3 ^ A ° from Table IV. The average e l e c t r o n  densities  were e s t i m a t e d from shock t h e o r y ,  - 35 -  as time d i d n o t p e r m i t S t a r k s h i f t measurements a t t h e s e shock velocities.  At v =1.92 cm/microsecond s  the e l e c t r o n  densities  as c a l c u l a t e d from the shock t h e o r y and from the S t a r k differed significantly,  and t h e r e f o r e the e l e c t r o n  c a l c u l a t e d from shock t h e o r y were s c a l e d for  t h e l o w e r shock speeds.  shifts  densities  down i n p r o p o r t i o n  I n Table V the upper e n t r i e s a r e  kT v a l u e s f o r v =1.72 cm/microsecond, N =3» +x lO-^^cm"^ w h i l e !  the l o w e r ones a r e f o r v =1.5 cm/microsecond, N =2.95xl0^^cm~^. T a b l e V - Plasma Temperature  kT(ev)  \AIII Lines (A°) A l l :C\  3285.8  3301.9  3336.1  33^.7  2.25  2.19  2.21  2.25  2.05  2.12  2.15  2.09  2 0 1 -L  2.15  1.96  2.0M-  s  3293.9  3307.2  Theoretical  ^  Temperatures and D e n s i t i e s  The v a l u e s o f t h e plasma t e m p e r a t u r e , kT, and e l e c t r o n d e n s i t y , N , c a l c u l a t e d from the shock t h e o r y f o r e  v =1.5j 1.72, and 1.92 cm/microsecond  and i n i t i a l r e s t gas  d e n s i t y , N = 2 . 1 2 X 1 0 c m 3 (from p =.6 mm Hg a t 68°F) a r e d i s l6  Q  p l a y e d i n Table V I ,  _  0  A l s o shown i n Table VI a r e t h e average  v a l u e s o f s p e c t r o s c o p i c a l l y determined temperatures and densities.  - 36  -  Table VI  •v  s  (cm/microseconds)  Spectroscopic kT(ev)  1.92  2.32  1.72  2.18  1.50  2.0h  Values  N (10 cra-3) 17  e  3.9C-.8)  -  Shock Theory V a l u e s kT(ev) Ne(10 ^cm-3) 1  3.33  6.32  2.88  5.55  2.38  *f.75  (B) H e l i u m Preliminary On  the p l a t e s taken o f the h e l i u m  o n l y two He l i n e s were o b v i o u s l y p r e s e n t and H e l l +686. l  A v e r y f a i n t l i n e was  shock s p e c t r a  these were H e l 5876  seen a t 3888A  0  which  may  have been H e l 3888 (though t h e r e i s a weak C I I l i n e a t 3 8 8 9 A ) . 0  T h i s l i n e was was  c l e a r l y observed w i t h the spectrophotometer as  the l i n e H e l l 3203.  Impurity CII, Silll  No o t h e r He l i n e s c o u l d be f o u n d .  l i n e s p r e s e n t i n a d d i t i o n to  CIII, O i l , S i l l lines.  The  l i n e s and  and Hg  were many  the s t r o n g e r C u l , C a l l ,  i d e n t i f i c a t i o n o f these l i n e s was  by n o t i n g t h a t the i n t e n s i t i e s o f l i n e s o f the t h i r d showed a more r a p i d i n c r e a s e w i t h shock v e l o c i t y  and  verified spectra  than i n the  case o f the second s p e c t r a . H e l 5876, H e l l ^-686 impurity lines monochromator.  (5A°)  and 3203 were f a r enough from  to be r e s o l v e d by the Bausch and Lomb  An e s t i m a t e of the i n t e n s i t y o f H e l  3888A  0  - 37 c o u l d be made by c o r r e c t i n g f o r t h e response C I I 3889.  a t 3888A due t o 0  The i n t e n s i t y o f C I I 3889 was i n t u r n e s t i m a t e d  from t h e response  of other CII l i n e s of strength.  Both the H^- and Ep, l i n e s were f r e e from i n t e r f e r e n c e by o t h e r  lines.  Time I n t e g r a t e d Measurements No q u a n t i t a t i v e measurements were made on h e l i u m s p e c t r a as t h e n e u t r a l d e n s i t y f i l t e r was n o t a v a i l a b l e w h i l e t h i s work was i n p r o g r e s s .  Time R e s o l v e d  Measurements  U s a b l e measurements on h e l i u m were made o n l y a t a d r i v i n g v o l t a g e o f 1 2 . 5 KV.  Much e x p l o r a t o r y work i n the  v i s i b l e s p e c t r a l r e g i o n was done w i t h the m o d i f i e d H i l g e r c o n s t a n t d e v i a t i o n s p e c t r o g r a p h but no s p e c i f i c r e s u l t s came from t h i s work as t h e s p e c t r a l s e n s i t i v i t y o f the i n s t r u m e n t c o u l d n o t r e a d i l y be determined.  A f t e r the a r r i v a l o f the  Bausch and Lomb monochromator o n l y a l i m i t e d amount o f work was done on h e l i u m . (a) Hydrogen and Helium L i n e I n t e n s i t i e s Time r e s o l v e d o b s e r v a t i o n s o f s p e c t r a l i n t e n s i t y i n t h e v i c i n i t y o f t h e E^ f e r e n t times.  l i n e y i e l d e d Hg  profiles for dif-  T y p i c a l Ej^ i n t e n s i t y h i s t o r i e s a r e shown i n  F i g u r e s 12 and 13 f o r wavelengths near t h e l i n e c e n t r e and i n t h e wings.  (H-861A°)  - 38 F i g u r e 12  - I ( t ) a t H-855A  Figure H  0  I(t)  - I ( t ) at  W5A°  I(t)  It i s readily  seen from F i g u r e s 12 and 13 t h a t i f a time  i n t e g r a t e d i n t e n s i t y i s measured f o r t h e H^  l i n e ( i . e . from  a p h o t o g r a p h i c exposure) such a measurement w i l l be h e a v i l y weighted by t h e second p u l s e (caused by the second surge i n t h e r i n g i n g  o f the d i s c h a r g e ) .  current  The time i n t e g r a t e d  measurement would g i v e a much narrower p r o f i l e than i s a c t u a l l y the  case i m m e d i a t e l y behind the shock. T y p i c a l i n t e n s i t y h i s t o r i e s o f H e l and H e l l l i n e s a r e  shown i n F i g u r e s 1*+ and 15.  From t h e s e curves i t can be seen  t h a t the i o n i c l i n e s peak and decay sooner than do the atomic lines. F i g u r e l n - K t ) f o r H e l 5876  F i g u r e 1 5 - I ( t ) f o r H e l l ^686  ( m i c r o s e c o n d s , from d i s c h a r g e )  - 39 -  (b) N  p  and kT Behind Shock  Approximations to N ( i . e . N e  the H  e f f  ) were determined  from  p r o f i l e s a t v a r i o u s times a f t e r the p a s s i n g o f t h e  shock; these d e n s i t i e s a r e p l o t t e d i n F i g u r e 16. Having r e s o l v e d v a l u e s o f e l e c t r o n d e n s i t i e s , the plasma c o u l d be c a l c u l a t e d u s i n g the H e l and H e l l l i n e histories.  time  temperature  intensity  The temperatures so o b t a i n e d a r e a l s o p l o t t e d i n  F i g u r e 16. The o r i g i n o f the time a x i s i n F i g u r e 16 i s taken to be the p o i n t where the l u m i n o s i t y f i r s t begins t o r i s e as seen i n F i g u r e s 12 - 1 5 . ,  The temperatures and d e n s i t i e s shown  a r e such t h a t <^<$C 1 and thus ® f£  ^  =  Q  t o the a c c u r a c y o f t h i s  e  experiment. F i g u r e 16 - kT and N N  X -  N (cm^xlO-^)  0  _  k  e  versus t  e  kT(ev)  T  i.o  .5 time  (microseconds)  1.5  - ko T h e o r e t i c a l Temperatures and D e n s i t i e s The plasma temperature and e l e c t r o n d e n s i t y l a t e d from the shock t h e o r y f o r v N =1.17xlO  l 6  0  = l g  f.8  calcu-  cm/microsecond and  cm-3 (from p = . 3 3 mm Hg a t 68°F) a r e shown i n Q  Table V I I w i t h the s p e c t r o s c o p i c v a l u e s f o r comparison.  Table V I I  Spectroscopic Values kT(ev) 3.73  N (10 7cm-3) o  1  5.3(-D  Shock Theory V a l u e s kT(ev) 3.83  RedO^cm^) 1.52  V I CONCLUSIONS  F o r the gases used i n t h i s experiment, t h e temperature, measured s p e c t r o s c o p i c a l l y was i n a l l cases e q u a l t o o r l e s s than t h a t expected from the shock t h e o r y .  However, the  e l e c t r o n d e n s i t i e s determined from s p e c t r o s c o p i c measurements were g r e a t e r f o r h e l i u m and l e s s f o r argon than the shock theory p r e d i c t e d . The above r e s u l t s a r e a t v a r i a n c e w i t h those observed by McLean e t a l ( i 9 6 0 ) , t h e i r s p e c t r o s c o p i c temperatures b e i n g h i g h e r than e x p e c t e d .  A p o s s i b l e f a c t o r i n v o l v e d here i s the  d i s t a n c e from t h e d i s c h a r g e to the s t a t i o n a t which t h e o b s e r v a t i o n s were made.  McLean's o b s e r v a t i o n s were made a t 6 cm,  those h e r e a t 1 0 cm. With the l i m i t e d amount o f d a t a a v a i l a b l e from the work done to date no s p e c i f i c c o n c l u s i o n s can be drawn as to q u a n t i t a t i v e d e p a r t u r e from the shock t h e o r y .  Much more  i n v e s t i g a t i o n i s r e q u i r e d o f shock b e h a v i o r a t d i f f e r e n t speeds and s t a t i o n s i n o r d e r to determine i f the observed d i s c r e p a n c i e s a r e f u n c t i o n s o f the apparatus o r a r e due to i n v a l i d i t y o f the t h e o r y .  A l s o , the e f f e c t o f i m p u r i t i e s ,  which has n o t been c o n s i d e r e d i n t h i s work, r e q u i r e s some s t u d y . F o r reasons o u t l i n e d i n t h e r e s u l t s , time i n t e g r a t e d or average v a l u e s o f N  e  (or N  e f f  ) can best be determined from  s h i f t o r broadening measurements made on the s p e c t r a o f the - kl -  -  1+2 -  p a r t i c u l a r r e s t gas being used.  Determination of e l e c t r o n  d e n s i t i e s from o b s e r v a t i o n o f i m p u r i t y s p e c t r a such as that of hydrogen must be made from time r e s o l v e d s p e c t r a .  The use  of the spectrophotometer i n o b t a i n i n g hydrogen l i n e p r o f i l e s and hence e l e c t r o n d e n s i t i e s appears  to be a v e r y promising technique.  While the techniques of measuring  line  intensities  are adequate f o r rough (- 10%) d e t e r m i n a t i o n of temperatures they r e q u i r e much refinement i n order to check the e q u i l i b r i u m assumption on which the s p e c t r o s c o p i c theory i s based.  To make  such a check, i n t e n s i t i e s of f a r separated l i n e s o f many d i f f e r ent m u l t i p l e t s must be a c c u r a t e l y determined and then compared. Such a comparison would r e q u i r e c a l i b r a t i o n o f the s p e c t r o s c o p i c apparatus f o r a b s o l u t e i n t e n s i t y versus wavelength.  Having  a b s o l u t e i n t e n s i t i e s f o r the s p e c t r a l l i n e s , Equations ( 3 ) , (10) and (11) can be solved f o r kT and N , e  mination of N  e  A separate d e t e r -  which i s independent of the e q u i l i b r i u m  assumption  can be made from measurements such as hydrogen l i n e broadening. Agreement between the two values of N  g  would s u b s t a n t i a t e the  o r i g i n a l assumption o f e q u i l i b r i u m . F u t u r e i n v e s t i g a t i o n s could  be d i r e c t e d  toxrards plasma  p r o p e r t i e s and behaviors which are s e n s i t i v e to the e x i s t e n c e or n o n - e x i s t e n c e of e q u i l i b r i u m .  Attempts could be made to  determine the time r e q u i r e d to e s t a b l i s h e q u i l i b r i u m  conditions.  In summary, the c o n c l u s i o n s to be drawn from experiment are that while spectroscopy i s a very u s e f u l  this tool  - ^3 f o r a i d i n g i n the d e t e r m i n a t i o n of c o n d i t i o n s w i t h i n a plasma, i t r e q u i r e s r e f i n e m e n t i n both t h e o r y and e x p e r i m e n t a l t e c h n i q u e . However, to f u r t h e r develop these t e c h n i q u e s r e q u i r e s a more thorough u n d e r s t a n d i n g o f the p r o c e s s e s w i t h i n a plasma.  APPENDIX I THEORETICAL LINE STRENGTHS The t h e o r e t i c a l l i n e s t r e n g t h s to be used i n c a l c u l a t i o n s f o r argon and h e l i u m w i l l be taken d i r e c t l y from p u b l i s h e d v a l u e s where a v a i l a b l e . for  As no v a l u e s a r e a v a i l a b l e  the s t r e n g t h s o f argon l i n e s used, these must be c a l c u l a t e d ,  Argon L i n e S t r e n g t h s F o l l o w i n g Condon and S h o r t l e y the l i n e s t r e n g t h , S, can be expressed as f o l l o w s :  ">  =^Zfe  s  where T ^ f i s a f a c t o r depending on t h e m u l t i p l e t * , ^ i s a f a c t o r depending on the p a r t i c u l a r l i n e i n the m u l t i p l e t , and where S *  2  i s r e l a t e d to the i n i t i a l e l e c t r o n a n g u l a r  momentum quantum number, J^, and to the r a d i a l wave f u n c t i o n s R^ and Rf o f the i n i t i a l and f i n a l s t a t e s by: poo ( 2 )  ^  2  =  Ifltl  ,  R  i f R  r  d r  *  The p r o d u c t s 7?fJ^ a r e e a s i l y found from the e l e c t r o n c o n f i g u r a t i o n s o f the a s s o c i a t e d energy l e v e l s (Moore, 1 9 ^ 9 and 1 9 5 9 ) and from f o r m u l a e and t a b l e s i n Chapter 9, Condon and S h o r t l e y . *A m u l t i p l e t i s a group o f l i n e s e m i t t e d by t r a n s i t i o n s from upper energy s t a t e s o f common p r i n c i p a l and o r b i t a l a n g u l a r momentum quantum numbers, (n,-#), but d i f f e r i n g t o t a l a n g u l a r momentum quantum numbers, ( j ; , to l o w e r energy s t a t e s h a v i n g the same r e l a t i o n s h i p to one a n o t h e r . -  Mf  -  - if5 Bates and Damgaard wave f u n c t i o n s which  (1950) have i n t e g r a t e d  (2) using  are s o l u t i o n s i n the Coulomb approximation*  to the Schroedinger e q u a t i o n .  Bates and Damgaard use the  expression:  where C i s the excess e l e c t r o n i c charge on the n u c l e u s (one f o r cP are  n e u t r a l atom, two f o r s i n g l y i o n i z e d atom, e t c . ) , and ^  = 2/3 C/n*  The q u a n t i t y n^ corresponding  Jl.  momentum  Y where ^ is for  =  R(n£ _ ,^-l,C)R(n^,i ,C)  i s the e f f e c t i v e p r i n c i p a l quantum number  to the s t a t e with e l e c t r o n o r b i t a l angular The n* and nJ^_]_ C  (g,)*»  n  a  r  e  g i v e n by the simple  the p a r t i c u l a r atom or i o n . ,A)  relation:  l&j)  ^ - i  the energy o f a l e v e l below the i o n i z a t i o n  and C^(n*£^r^  r dr,  ?  1  I n the above work  limit  thej^n*,^)  are t a b u l a t e d f o r g i v e n n* , ^ L i >  The c a l c u l a t e d l i n e  s t r e n g t h s f o r the argon  of i n t e r e s t are shown i n the t a b l e below.  a n (  3^.  lines  Values of /-.were  **In the Coulomb approximation the e l e c t r o n i s assumed to move i n a Coulomb p o t e n t i a l ( P o t e n t i a l energy = C where C i s excess e l e c t r o n i c charges on n u c l e u s ) . r  - h6 taken from Moore (19 +9). !  AIII  All  L i n e (A°)  Line ( A )  S  s  0  3293.6  5.26  3285.8  25.2  3307.2  2.10  3301.9  18.0 10.8  3350,9  .018  3311.2  3376.5  .025  3336.1  9.2  3388.5  33^.7  29.6  3358.5  20.0  The l i n e s t r e n g t h s f o r A l l 3350.9 and 3376.5 a r e a b n o r m a l l y low; the Coulomb a p p r o x i m a t i o n seems to break down f o r these lines. Helium L i n e S t r e n g t h s The l i n e s t r e n g t h s o f h e l i u m were o b t a i n e d from the absorption o s c i l l a t o r  strengths.  The a b s o r p t i o n o s c i l l a t o r  s t r e n g t h , f , i s r e l a t e d t o the l i n e s t r e n g t h , S, by f = K -  A where of  §.  §n  ^ i s the wavelength o f the l i n e , g  t h e lower energy  n  i s the degeneracy  l e v e l and K i s a c o n s t a n t which w i l l be  taken as u n i t y here as o n l y r a t i o s o f f o r S a r e used i n c a l culations . The o s c i l l a t o r s t r e n g t h s o f n e u t r a l h e l i u m were obt a i n e d from the work o f T r e f f e t z e t a l (1957) w h i l e those o f i o n i z e d h e l i u m a r e s i m p l y those o f hydrogen (see f o r example  - if7 -  Unsold). The v a l u e s o f f , g , and S f o r the h e l i u m l i n e s to n  be s t u d i e d i n t h i s experiment  a r e t a b u l a t e d below.  Hel  f  .057 .623  A( cmxlO^)  3.888 5.876  Hell  g  n  3 9  S= A g f n  .665 32.9  f  .151 .81+2  A( cmxlO^)  3.203 H-. 686  g  n  50  s= A  g n  2H-.2  32 126  f  BIBLIOGRAPHY  Bates,  D.R., and Damgaard, A., P h i l i s o p h i c a l T r a n s a c a t i o n s of the R o y a l S o c i e t y A2^+2, 101, 1950.  Breene, R.G.Jr.,  Reviews o f Modern P h y s i c s  2£,  1957.  Chandrasekhar, S., Review o f modern P h y s i c s 1_2, 1, 19^3 • C o n d o n , E.V., and S h o r t l e y , G.H., 1935. Cormack, G.D.,  Theory o f Atomic  Spectra,  MSc. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia,I960.  Griem, H.R., K o l b , A.C., and Shen, K.Y., P h y s i c a l Review 116, 1959. See a l s o N a v a l Research L a b o r a t o r y R e p o r t no. 5 ^55, I960. l  Holtsmark, J . , Z e i t s c h r i f t fiir Physik  20, 162, 1919.  M a i s s e l , L., J o u r n a l o f the O p t i c a l S o c i e t y o f A m e r i c a k-8, 853, 1958. McLean, E.A., F a n e u f f , C.E., K o l b , A.C., and Griem, H.R., P h y s i c s o f F l u i d s , 3, 8V3, i960. Minnhagen, L., A r k i v f o r Matematik, Astronomi o c h F y s i k ^5, no. 16, 191+8. Moore, C h a r l o t t e E., Atomic Energy L e v e l s , N a t i o n a l Bureau o f S t a n d a r d s , C i r c u l a r *+67, Volume 1, 19^9. Moore, C h a r l o t t e E., A M u l t i p l e t Table o f A s t r o p h y s i c a l I n t e r e s t , N a t i o n a l Bureau o f S t a n d a r d s , T e c h n i c a l Note 36,1959. T r e f f e t z , E., S c h l u t e r , A., Dettmar, K.H., and J o r g e n s , K., Z e i t s c h r i f t f i i r A s t r o p h y s i k kh, 1, 1957. U n s o l d , A., P h y s i k d e r S t e n i a tmosphar en, 1955.  - hQ -  

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