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UBC Theses and Dissertations

Preliminary experiments for the study of the absorption spectra of plasmas Budd, Sinclair Edwards 1961

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PRELIMINARY STUDY  OF  THE  EXPERIMENTS  ABSORPTION  FOR  SPECTRA  THE OF  PLASMAS  by SINCLAIR B.Sc,  A  University  THESIS THE  EDWARDS  BUDD  of British  Columbia,  i960  S U B M I T T E D I N P A R T I A L F U L F I L M E N T OF REQUIREMENTS  FOR T H E D E G R E E OF  M.Sc.  in  t h e Department of PHYSICS  We  accept  required  THE  this  thesis  as conforming  tothe  standard  UNIVERSITY  OF B R I T I S H  October,  1961  COLUMBIA  In p r e s e n t i n g the  t h i s thesis i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t t h e U n i v e r s i t y  British  Columbia, I agree t h a t the  a v a i l a b l e f o r reference  and  study.  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  s h a l l not  be a l l o w e d w i t h o u t my w r i t t e n  T — '  ffij  1  representatives.  c o p y i n g or 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  The U n i v e r s i t y o f B r i t i s h Vancouver 3, Canada. Date  be  IS  Columbia,  Of  permission.  A B S T R A C T  A F l a s h U n i t to supply a pulsed source of continuum r a d i a t i o n has been constructed to provide the l i g h t required f o r the study of absorption spectra of plasmas. The u n i t which contains the plasma has been designed to produce a gas of h i g h p u r i t y .  Several t r a n s i t i o n s i n the excited neon  were seen i n absorption. previously.  At l e a s t two have not been reported  A p r e l i m i n a r y determination of t r a n s i t i o n temper-  atures has been made.  TABLE OF CONTENTS Page 1  INTRODUCTION Chapter I  1. 2„ 3. 4. 5o II  3  THEORY Introduction Transition Temperatures Relative A Values Correlation of Electron Temperature to Excited Level Populations Neon Spectrum  3 7 12 15 18  APPARATUS  20  1. 2. 3. h. 5.  20 20 36 38 40  Introduction Flash Unit Plasma Unit Shutter Unit Electronic Units  ^3  III RESULTS AND CONCLUSIONS 1. 2. 3.  *+3 *+3 48  Introduction Experiment Future Work  Appendix I  II  TRANSFER EQUATION  50  1.  Definitions and Fundamental Notions  50  2.  Equation of Transfer  57 58  DISCHARGE MODEL  6l  BIBLIOGRAPHY FIGURES 1. 2. 3. h. 5. 6. 7. 8. 9.  following page 61 Neon Spectrum Apparatus Flash Unit Window Geometries Trigger Geometries Waveforms Plasma Unit Shutter Unit Trigger Unit iii  ACKNOWLEDGMENT  I would l i k e to extend my thanks to Dr, R. Nodwell whose guidance and understanding have been of immeasurable a s s i s t a n c e to me i n t h i s work; to other members of the plasma physics group with whom discussions have been most i n f o r m a t i v e ; to John Turner f o r the time devoted to discussions of e l e c t r o n i c s and whose a b i l i t y has made much of t h i s experiment p o s s i b l e ; to Johnny Lees f o r h i s e x c e l l e n t glass blowing, and to Alex Eraser and other members of the t e c h n i c a l s t a f f f o r t h e i r cooperation.  iv  INTRODUCTION  In the recent surge of i n t e r e s t i n plasma physics research one of the major d i f f i c u l t i e s connected w i t h determining the p r o p e r t i e s of the plasma has been the development of s u i t a b l e d i a g n o s t i c techniques.  Four w e l l - d e f i n e d techniques  are p r e s e n t l y i n common use i n plasma physics l a b o r a t o r i e s . 1. R-E.technique using microwaves 2. D.C. probes 3 . Photographic techniques 4-. Spectroscopic techniques The f i r s t two of these, while p r o v i d i n g much accurate, i n t e r e s t ing and u s e f u l data have the major disadvantage that they introduce p e r t u r b a t i o n s i n t o the plasma, and the e f f e c t of these perturbations may mask or a l t e r the e f f e c t which i s being measured.  Photographic techniques provide i n f o r m a t i o n about  the l o c a t i o n of the plasmas and t h e i r approximate  densities,  but very l i t t l e d e t a i l e d knowledge-. Spectroscopic techniques, used i n t h i s l a b o r a t o r y f o r observations of both emission and absorption s p e c t r a , have a decided advantage over the f i r s t two techniques mentioned i n that the measurements have very l i t t l e e f f e c t on the plasma i t s e l f ; and over the photographic technique i n that much more i n f o r m a t i o n other than approximate density and p o s i t i o n can be gathered.  Besides these advantages - 1 -  spectroscopy i s capable of  giving information about the l o c a l properties of a plasma, and when combined with electronics, time resolution. In the i n t e r p r e t a t i o n of the data obtained by the study of emission spectra, i t i s often necessary to know the r e l a t i v e population densities of two levels and the p r o b a b i l i t y of a t r a n s i t i o n between these l e v e l s .  Unfortunately i n many cases  these t r a n s i t i o n p r o b a b i l i t i e s are not well-known and the d i s t r i b u t i o n of electrons among the energy l e v e l s may depart s i g n i f i c a n t l y from the usually assumed Boltzmann d i s t r i b u t i o n , due to presence of impurities, because of the p a r t i c u l a r e x c i tation mechanism or because of i n s u f f i c i e n t time to reach thermal equilibrium.  I t i s therefore desirable that experimental  investigations into t r a n s i t i o n p r o b a b i l i t i e s and electron densities be undertaken. determined  Ladenberg has shown that these quantities may be  through measurement of anomalous dispersion and  absorption spectra.  I t i s also foreseeable that, using an  appropriate modern pulse technique to trigger a short duration continuum source, we might study the time evolution of the absorption spectrum of a plasma. This thesis describes the preliminary experimental work which has been done i n preparation of the study of absorption spectra of ionized gases.  Namely, the construction of the back-  ground source the design of which was inspired by the work of W.R.So Garton who has improved upon the many previous attempts to achieve a high b r i l l i a n c e discbarge with the continuum i n the ultra violet.  Chapter I THEORY 1.  Introduction As was pointed out i n the i n t r o d u c t i o n , considerable  information about a plasma or a hot gas may be obtained by the study of i t s absorption spectrum.  The absorption spectrum i s  obtained by passing l i g h t from a source of continuum r a d i a t i o n through the gas under i n v e s t i g a t i o n .  The source may be a carbon  arc o r , as i s used i n t h i s experiment, a f l a s h discharge.  Since  t h i s gas i s self-luminous the spectrum may e x h i b i t b r i g h t l i n e s upon the darker continuum background or dark l i n e s upon the b r i g h t e r continuum background.  The r e s u l t depends upon whether  the background r a d i a t i o n i s r e s p e c t i v e l y hotter or cooler than the gas. These observations can be deduced q u a n t i t a t i v e l y by rearranging and s o l v i n g equation Al*+.  d's  Now w r i t e the f i r s t term on the r i g h t .  At t h i s point we should r e c a l l two important r e l a t i o n s h i p s between E i n s t e i n c o e f f i c i e n t s L  L  = Ub^L  BUL.  - 3 -  (2)  -  where  h  -  gj_ i s the m u l t i p l i c i t y of quantum state  i .  Using equation 2, equation 1 becomes NU„ A« hvuu = (NuVuuB^u -MutfuuBQ I h ^ L h U , , Tj t  L  C  (4)  N<-v>m. b\-t<. _ ^  2-  I f the gas i s i n thermal e q u i l i b r i u m  £  then  2 where  T  i s the temperature of the gas, N  the t o t a l number  of atoms present and £. the p a r t i t i o n f u n c t i o n of the gas; hence  From equation A6 and 3 we have K  "  =e— •  L  (5)  S u b s t i t u t i n g equation 5 i n t o equation 4, we get (6)  The s p e c i f i c i n t e n s i t y i n s i d e a black body at a temperature T i s  —1 Define  b  Kviu.  Kv.  L  =  -D  ( ) T  (7)  y  =  hv^(  N ^ B _  -A/.v^B_).  (8)  This,  f r o m i t s a p p e a r a n c e i n e q u a t i o n 9,  absorption  coefficient.  6,  equation  and  e q u a t i o n Alh  where  now  transfer  ( 1 , m,  gration.  the r e s u l t i n g  solve this  to the p r e s e n t  equation of  S u b s t i t u t e equations  8  7 and  e x p r e s s i o n to  into  transform  into  We cable  use  o b v i o u s l y i s the  n)  ¥e  are  e q u a t i o n under c i r c u m s t a n c e s  experiment.  In Cartesian coordinates  the d i r e c t i o n  cosines of  choose to i n t e g r a t e a l o n g  the  the path  of  y -axis,  the  solution  J . ^ If  the  and  external  this  Cs e  equation  a  source  +  y  Kv> v>u.<_  ^d  3,(1]  .  i s constant are  constant,  y direction.  emitting radiation Xco)  the  solution i s  a t the y =  0  I f t h e r e i s no  i n the p o s i t i v e  , i n the p o s i t i v e  along  the  are c o n s i d e r i n g s t a r t  i n the p o s i t i v e  a t y = 0,  ;  equation i s  J  t h e p l a s m a we  extend  the i n t e n s i t y hence  =  t h a t i s (slcci;^  Let plane  of  absorption coefficient  y-axis,  inte-  ;  general  the  is  becoming  The  appli-  y  direction,  d i r e c t i o n i s zero  I.(y)  BJ;T)(I  =  - e '  K  v  do  j  y  The e x p o t e n t i a l term represents s e l f - a b s o r p t i o n . black body of temperature  I f there i s a  r a d i a t i n g i n the p o s i t i v e y  d i r e c t i o n from y = 0 then I(o) = B(T^) and the s o l u t i o n to the t r a n s f e r equation i s  = B X T ) ( i - e ^ ) +- BCr'le-"'*  I D  _K  Equation 11 shows that 1^  (  at the point of observation  w i l l equal B^CT ) f o r any frequency away from those corresponding 1  to atomic t r a n s i t i o n s , f o r at these frequencies K thus see that i f  Xy '<  Btf(T')  the  J ^ B^>. i~T^ l i n e w 1 1 1  t h e  be d a r k and  l  i  n  lf  e  w  i  l  1  b e  ly =  b  r  = 0.  v  l  §  n  t  ?  i  We f  B (T'j I f the temperature  l i n e w i l l be merged with the background.  t h e  w  of the background r a d i a t o r i s greater than that of the plasma the  l i n e w i l l be seen i n absorption.  To show t h i s we f i r s t  note that from the monatomic behavior of B(T)  B(f)  > BCD  T'>T  From equation 11 we have  (Iv-B„(T>) but  i s  to ( o jcOO ) .  T'>T  =  [BJT'J - BJCDJ  e'*'^  r e s t r i c t e d to (0,1) because  i s restricted  Hence i f  l  v  lv  - j? ) v(T  >  >  B  jj'j _  QUJ  B , ( T V  S i m i l a r l y , we can show that i f the temperature of the black body i s lower than that of the plasma, the l i n e w i l l appear i n emission.  - 7  If  -  T = T , i t f o l l o w s immediately 1  I = B d ) , that i s , 1  there w i l l be n e i t h e r a b r i g h t l i n e nor a dark l i n e .  It will  have blended i n t o the background. I t might seem that these r e s u l t s were dependent on the  assumption of thermal e q u i l i b r i u m i n the plasma since t h i s  was invoked i n the d e r i v a t i o n of equation 5*  However, the  plasma temperature which we have been using to c h a r a c t e r i z e the  emission of the plasma at the frequency corresponding to a  t r a n s i t i o n between a p a i r of l e v e l s ition  1  and  u  can be a t r a n s -  temperature, T^, defined i n such a way that the ratio', of  population between these two l e v e l s i s given by !L  -  This temperature i s d i f f e r e n t f o r each p a i r of l e v e l s and a p p l i e s only to the t r a n s i t i o n occurring between those p a r t i c u l a r l e v e l s . .2. T r a n s i t i o n  Temperature  G a r t o n , because of u n c e r t a i n t y i n the temperature of 2  his  continuum source, was unable to o b t a i n an exact value f o r  BCT ) 1  so he used a procedure which would at l e a s t i n d i c a t e how  w e j l a common temperature could be ascribed to h i s plasmas. The t o t a l energy  P  falling  on the photographic plate  per u n i t time i s given by cos 8 du>  dv  which f o r an emission l i n e becomes by equation 10 P =  C  (12)  - 8 where  "B (J)  slowly  varying  the  integral  measured  a  v  b  taken  e  source  Iv  a  Jvo  d  out o f the i n t e g r a l  f u n c t i o n o f v>  over  C  and  5  an a p p r o p r i a t e lines,  (or equivalent  now n  a  for different  absorption by  m  V  angle.  only  breadth)  o f temperature  i s a constant  solid  need  -  i ti s a  representing  The v a l u e  be r e l a t i v e .  of a line  from  o f P,  The  a gas  total  backed  T l i s  BJl'J e " * v y  ^  because  i f H is »  B o(T'J  s  v  T  o  VA/  thus  The  -1  the  Planck  and  T  term  representing formula  This  L-n:'J^,g-i  it  c a n be c o n c l u d e d have  The a  time  the  t  a  , that  emission  i n the denominator o f £  <T  10 f o r  ^  o f the plasmas  =  7000 A  we a r e  finally  V  the l e v e l s  transition  results  D  i n a  corresponding  temperature  given  straight  line,  to these  trans-  by t h e r e c i p -  o f the l i n e .  the present  photographic  since  typical  against  that  a common  o f the slope  In  have  ?  a plot  rocal  of  done we  If  emission  c a n be d r o p p e d  8000 Ox °K, c o n d i t i o n s  =  studying.  itions  forced  plate  experiment  i s exposed  a different  to the absorption  i s , f o r the duration  spectrum  method  i s superimposed  spectrum f o r  o f the f l a s h , f o r a time  t  i s used.  after e  .  which  I ti s  -  9  p o s s i b l e to adjust the time  t  -  e  u n t i l n e i t h e r an absorption  nor an emission l i n e i s seen on the photographic p l a t e .  In an  experiment one must take n o t i c e of the i n t e r m i t t e n c y e f f e c t which w i l l be pronounced with such short exposures. discussed more f u l l y i n Chapter I I I . c a l l e d the disappearance time. f i l l s i n the absorption l i n e .  This time,  This i s  t = td, i s e  E s s e n t i a l l y the emission l i n e I t i s d i f f i c u l t to expose the  plate f o r the exact time td so two p i c t u r e s are taken with different  t s , allowing the disappearance time to be i n t e r -  polated.  The r e l a t i o n s h i p between the disappearance time and  5  e  the t r a n s i t i o n temperature T  where T  T  h  >A  T  is  L  (13)  v  l i s the black body temperature.  I n t e r p r e t i n g the  t r a n s i t i o n temperature as a parameter expression the r e l a t i v e population d e n s i t i e s , we have 9L.  »V<-  t^+td  These formulas are derived from the f o l l o w i n g considerations.  Define  P  as the t o t a l energy entering the spectro-  graph s l i t per u n i t area from one l i n e . a density on the photographic p l a t e . d e f i n i t i o n of  l  v  P - J Xv = c f ( l  v  P  w i l l be manifest a s  The exposure  ;  P  i s , by the  , given by COS  dv)  9  dt  d^  1  dv> cl"t  (15)  - 10  where  C  we have  -  From equation 11  allows f o r the geometrical i n t e g r a l . P  of the f l a s h exposure given by  a  P*. - C t ,  BJT)jl-e^ > y  The i n t e g r a l over  c t . eyorr) f  ,  £ ~ ^ v  (16)  i n equation 15 i s obviously j u s t the time  t  t . As before, ~BJJ)  exposure  H-  and  a  B^T) are removed from the  i n t e g r a l and replaced by t h e i r values at the centre of the l i n e and  B (T') Vi  respectively.  spectrum of exposure time  t  e  P  e  i n c i d e n t from the emission  is  The t o t a l exposure i s then c(-t^ t J +  I f the time  t  e  c  B ,(T;/(i-c-  K v  y  V  Y  ct.  B (j')[e'^c/v V6  i s equal to the disappearance time  t^  (17)  then  This equation combined with equation 17 r e s u l t s i n a r e l a t i o n s h i p between the temperature and time  t<j namely  or  Neglecting the term f o r forced emission i n the plasma and using Wein's law f o r the black body (a d o u b t f u l step), we have  By taking logs we have equation 13«  - l i l t remains only to determine  P i and P 2 of a p a r t i c u l a r l i n e (of f r e -  s c a l e , the exposures quency  t<j. We measure on an a r b i t r a r y  ) i n the two d i f f e r e n t p i c t u r e s mentioned above.  VXAC  Me  know from equation 11 that  and Pi-  where times.  C(t^t  S i  t -j_ and t e  BJTJ / ( i - c - ^ ) ^  ) g  t c t . Svo(^;  K  2  e~ </p M  are the corresponding emission exposure  These equations are a r r i v e d at i n a manner i d e n t i c a l to  that used f o r equation 1 5 . With the above two equations we can solve f o r ,  C 6 (vf(i-  and  e'<'>  Vo  C  O lr')  [e-^dy  v  Lint  • enabling us to w r i t e an equation'; f o r the i n t e n s i t y as a f u n c t i o n of the exposure time P(j, we f i n d  t  e  . I f we measure the background exposure  t ^ , by s o l v i n g the general equation, to be  Another determination of t r a n s i t i o n temperature may be made by exposing a p l a t e separately to an absorption spectrum f o r a time  t and to an emission spectrum f o r a time a  exposure f o r the absorption l i n e i s  The exposure f o r the emission l i n e i s  The exposure f o r the continuum i s  t . The e  - 12  The d i f f e r e n c e between  Po  P  -  and  0  P  [C * « . BUT') - C ( L V  =  The r a t i o of the d i f f e r e n c e to P  Po-a  ± ^  f  te L  Pc  M L }  is  a  t e , ) Six)]  +  l?l - e - " ^ . k  v  i s given as  e  _  Bvirj  By e s t a b l i s h i n g the exposures P , P , P Q  a  e  on an a r b i t r a r y scale,  from the observed d e n s i t i e s on the photographic p l a t e (remembering t  e  the i n t e r m i t t e n c y e f f e c t ) and knowing the exposure time  t  a  and t _ , we can c a l c u l a t e the r a t i o of the continuum r a d i e 1  ancy to the plasma radiancy. I f we know the continuum  temperature  we can f i n d the t r a n s i t i o n temperature. Both these .methods are used i n the experiment to estimate the t r a n s i t i o n temperature. 3 . R e l a t i v e A Values"' The measurement of the anomalous d i s p e r s i o n i n the neighbourhood of an absorption l i n e but outside the region of absorption combined with the measurement of the t r a n s i t i o n temperature allows us to c a l c u l a t e the r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s for lines  i  which correspond to t r a n s i t i o n s to a common  3  level  .  The anomalous d i s p e r s i o n i s given by (see  K o r f f and B r e i t )  where F  M ; t  -  M  Since we know  A*cu  n^lj^)--  wc  l  „  A  -  corresponding to the l i n e s i ,  1 +  - 13 we know  F  M  I  >  F  J  S  L  Then  _^ AU,L  h U i L  9  ^  ^ . J i - e KIT  that i s , we can f i n d a l l the t r a n s i t i o n p r o b a b i l i t i e s with respect to that of l i n e 1 . The absorption spectrum a f f o r d s another method of determining the r e l a t i v e A values.  From equation 1 1 we see that,  i f the black body temperature i s much higher than the t r a n s i t i o n temperature and the absorption c o e f f i c i e n t i s small (conditions which c e r t a i n l y e x i s t i n the present experiment) the i n t e n s i t y i s given by  thus  il  ' S^^ •  u  <  18)  K  But from equation 9  since  = Nu  S  , 5  from t h e i r r e s p e c t i v e d e f i n i t i o n s .  J A U ^ - A/, From equations 3> 5 and 1 8  we have  J_ P y J  " ^  L  J  ^  M ^ f | - e ^ ) (19)  QTTVJ-  "err  /  which gives us the same information as does a measurement of anomalous d i s p e r s i o n .  - 15  -  gives us y e t another advantage i n that i t i s not necessary to calculate  the true i n t e n s i t y as Ladenberg had to, i n order to  determine the r e l a t i v e A values f o r t r a n s i t i o n s with a common upper l e v e l .  Supposing we have measured the anomalous d i s p e r s i o n  f o r s e v e r a l of these l i n e s  j (a measurement of the integrated  absorption c o e f f i c i e n t would serve as well) we have r  hu  w  r  A  A  ' ^* v  , s>^_ (\) (  but we know  ULi  y. l - g  v*.Li Lj Ii  i --  i  e  t_  K  T  j  w.  and A/  so  That i s  In summary, we gain two advantages which Ladenberg did not have when we know the t r a n s i t i o n temperature. we can c a l c u l a t e  Firstly,  the r e l a t i v e A values f o r common lower l e v e l  t r a n s i t i o n s when there i s a high t r a n s i t i o n temperature and secondly, we can c a l c u l a t e  the r e l a t i v e A values f o r common  upper l e v e l t r a n s i t i o n s without evaluating the i n t e g r a l of equation 1 9 . h. C o r r e l a t i o n  of E l e c t r o n Temperatures to Excited Level  Populations^'6. The  equilibrium  d i s t r i b u t i o n i n the populations of the  -  -  16  l e v e l s of e x c i t e d atoms i s dependent upon the e l e c t r o n d i s t r i bution f u n c t i o n ; . transfer  This f u n c t i o n i s governed by Boltzmann s 1  equation  i£ -r  + eX  v • Vr-F  v  n  where the number o f e l e c t r o n s dy  7 f - -^V enclosed by the volume dx  dz a t the point xyz and with v e l o c i t y between v ^ ^ ^ + d ^ ,  V/ , \J^+AVj and Vj , \Zj +- d y  dn.  =  n  i s given by  -f(%  ^ J  dv  d x dy  x  dVj dV  }  n i s the density of e l e c t r o n s . I f the f i e l d i s i n x  d i r e c t i o n only and  i s a constant i n  space the equation reduces to  On the assumption that the plasma can be modelled a f t e r a Lorentz gas, that i s one where  m  e l e c t r o n i s much l e s s than the mass  of the molecules and the  M  the mass of an  d e n s i t y of the e l e c t r o n s i s small as i n a weakly i o n i z e d gas, the v e l o c i t y d i s t r i b u t i o n i s n e a r l y i s o t r o p i c except f o r small d e v i a t i o n s due to e l e c t r i c f i e l d and d i f f u s i o n . solved by expanding corresponding for  The equation i s  f i n s p h e r i c a l harmonics and 'equating  terms.  The answer depends on our approximation  ±A 2t  /Collisions  Margenau, considering only e l a s t i c c o l l i s i o n s and a constant e l e c t r o n mean f r e e path, found that f o r small high frequency f i e l d s of amplitude x  0  and tngular frequency  which i o n i z a t i o n can be neglected the 3  Maxwellian  with  T  e  =  +•  W in  distribution function i s  M e*  X „ y e K m  l  W S  - 17  Though the have a  model u s e d was  only  -  a p p r o x i m a t e we  d i s t r i b u t i o n which i s n e a r l y Under c e r t a i n g e n e r a l  erations  show t h e  existence  of  and  excited  atoms and  B o l t z m a n n law  the  excited  atoms.  it  i s necessary  only  that  the  the  To  validity  of  demonstrate  v e l o c i t i e s of  the  electrons  density  second  between the  electrons  approximately lisions.  the  tical  equilibrium  pressures  in the  the  say,  two  of  excited  two  atoms,  at  by  per  those of  current  kind  electronic  processes of  the  second col-  excitation  collisions  and  with  spontaneous r a d i a t i o n  the  electron  rate  of  This  atoms, w i t h a  temperature.  equilibrium  i s a natural  d i f f u s i o n to  responsible  i t i s shown t h a t  atomic l e v e l s corresponds  this statistical  densities.  electrons  conditions  two  pressure i s raised,  excited  the  atoms d e s t r o y  are  these  with other  these  populations  current  excited  of  the  in  the  and  excitation. With  of  and  collisions  must p r e d o m i n a t e o v e r  collisions  radiant  that  a s many atoms as  T h a t i s to  de-excitation walls,  so  the  this,  that  very high  consid-  equilibrium  p l a s m a have a n e a r M a x w e l l i a n d i s t r i b u t i o n and be  to  theoretical  statistical  between e l e c t r o n s for  expect  Maxwellian.  conditions, a  can  and  for rise  will  statis-  higher  reached  for  of  atoms  the  increase of  pressure  to a  the  walls  of  ratio  consequence of  the  collisions  be  At  the  the  excited  i n the the  at  decrease  number o f  second k i n d  constant  lower  as slow  with  current.  the  - 18 5. The Neon S p e c t r u m The gives  rise  stable the cms  lowest  to the s i n g l e  and a l a r g e  first  o f neon i s the c o n f i g u r a t i o n  state  excited  130,000 and 174,000 c m s " from 1  gives 78O  rise  lowest  electron  assigned  2p5.3s,  According  to Shortley, to only  the f i r s t  The • • ' P 1  1  bine  with  lines  the normal  74-3 and 736 A*.  same p o p u l a t i o n  since  state  a t room  t h e same o r d e r  o f t h e n e o n i o n i s 2p5 w h i c h with a doublet ofneutral  o  separation of  neon i n a f i r s t the a d d i t i o n o f an  2p^ s t a t e .  r  l e v e l so f  t h e i n v e r t e d 3p  3 p . The 3p  above  1  the  Q  2  and i P i l e v e l s com-  the u l t r a a  lowest  form  1070 c m s "  c a n be  configurations,  The t h r e e  d e n s i t i e s , even  as that  state.  the L S d e s i g n a t i o n  togive  into  betx^een  The l e v e l s ^P210  temperature  the.atom  l i e i n the r e g i o n  the f o l l o w i n g  is  i s very  130,000  configuration,  state  2p^, w ^ i c h  over  the  2p5.ns.  excited  to bring  t o a r i s e from  ^PQl e v e l s are metastable while  and  of  states  i n either  3P££.$.  state,  p state,  to the core  significantly  configuration  the normal  c a n be c o n s i d e r e d  2p5.3p and t h e s e r i e s  the  the  2  Thus t h e e x c i t e d  approximation  states  configuration  t o an i n v e r t e d  cms'l.  This  2p5.3is w h i c h l i e s  state  A l l the e x c i t e d  The  -'-SQ.  energy i s required  possible  higher.  - 1  state  1  1  violet  have  resonance  approximately  t h o u g h 3p^ ±  unstable,  s  t h e mean e n e r g y o f t h e n e o n atom i s o f the energy d i f f e r e n c e  between  these  1, levels, by  allowing  collision  configuration  with  the population  o f t h e ^p-^ term  the m e t a s t a b l e  states  gives  rise  to ten l e v e l s ,  t o be r e p l e n i s h e d  3 p and 3p „ 2  1  S  Q  , 3s1? p 1  0  Q  )  The  2p^.3p  3p  ,  ol2  - 19 l  -  ^  and  D]_23*  ^  n e  "terms of the above c o n f i g u r a t i o n combine  to give about t h i r t y s p e c t r a l l i n e s .  In f i g u r e 1,  the l i n e s  which were observed i n the experiment are i n d i c a t e d .  Chapter I I APPARATUS 1. I n t r o d u c t i o n The general arrangement of the equipment used f o r the i n v e s t i g a t i o n s described i n t h i s t h e s i s i s i l l u s t r a t e d i n f i g u r e 2.  L i g h t from a high temperature source of continuum r a d i a t i o n ,  the f l a s h u n i t , passes through a plasma generated unit.  i n the plasma  In t h i s experiment the plasma i s created by a Radio f r e -  quency discharge but the plasma source could be replaced by other sources such as a shock wave.  The l i g h t , having passed  the plasma, i s photographed with a spectrograph r e s u l t i n g absorption spectra.  through  to record the  I n one phase of the experiment  i t i s necessary to c o n t r o l the r e l a t i v e exposure times of the plasma and f l a s h u n i t s .  This can only be accomplished with'rapid  s h u t t e r i n g of the spectrograph since the plasma u n i t i s a continuous r a d i a t o r and the f l a s h u n i t a pulsed r a d i a t o r . u n i t has to be synchronized with the shutter unite  The f l a s h  This i s  achieved by f i r i n g the f l a s h u n i t with a pulse from the t r i g g e r u n i t which i s t r i p p e d by the output pulse of the delay u n i t . This delay u n i t pulse i s i n i t i a t e d by a s i g n a l from the shutter u n i t which occurs at a f i x e d time i n advance of the opening of the spectrograph shutter. 2. The F l a s h U n i t The f l a s h u n i t , to f u l f i l l i t s f u n c t i o n adequately, was constructed with many d i f f e r e n t operating c h a r a c t e r i s t i c s . - 20 -  From  a  preliminary  employing  the  radiation  with  5000°K b l a c k higher to  tures an  of  also in  tens  of  advantageous  either  integrals may  high  be  compared  In this  be  in  the  short an  do have  of  a  to  with  the  of  source  free  of  continuum  of  is  hoped  to i n  tempera-  source  spectral  even  to  use  Besides  lines  black  a  hoped  at  i t  and  absorption  a  of  decided  our  and  require i t  was  unit  that  plasmas  from  decaying  is bands  coefficient distribution  body.  investigate the  order  with  of  time  resolution  only  microseconds.  However  i n  the  described  proved  the  would  i t  the  is  of  for  radiation.  that  good  plasma  future  other  and  i t  duration  we  Kelvin  that  plasmas  experiment  the  to  so  evaluated  this  i n  spectrum  emission  arc  that  source  experiments  state  duration  the  transient To  steady  or  easily  should  to  be  this  more  a  the  pulse  thesis nuisance  than  advantage.  In the  have  the  approximating  steradiancy  conveniently  technique,  discharge  to  future  milliseconds.  the  spectral  absorption may  Since  degrees  for  i n  carbon  technique  thousands  discharge  a  obvious  steradiancy,,  diagnostic  the  of  neon  steradiancy  became  this  impulsive  requiring  i t  -  using  crater  spectral  body,  spectral  apply  experiment  positive a  21  order  absorption  charge  light  position ferably  of  to  spectrum  through at  four,  determination  produce  least are of  a  useful  resulting  the  plasma  four  from  unit,  exposures.  required population  to  provide  densities  photographic the i t Two  passing  required  of  the  the  pictures,  sufficient and  record  transition  dis-  super-  and  data  of  for  prethe  probabilities.  -  22 -  We must thus have the f l a s h u n i t output i d e n t i c a l f o r at l e a s t eight discharges. As was pointed out i n the i n t r o d u c t i o n to t h i s chapter i t i s necessary to t r i g g e r the discharge at a p r e c i s e moment. In the present experiment a j i t t e r time of the order of twenty microseconds between the t r i g g e r i n g pulse and the discharge i n the f l a s h tube i s t o l e r a b l e .  However future experiments dealing  with t r a n s i e n t plasmas w i l l require much smaller j i t t e r times. Hence i t was decided to design the t r i g g e r i n g system with as small a j i t t e r as p o s s i b l e . In the experimental e v a l u a t i o n of the f l a s h u n i t e l e c t r o n i c measurements are made simultaneously with the discharge i n .'the f l a s h tube and f o r t h i s reason i t i s d e s i r a b l e to choose a geometry f o r the e l e c t r i c a l leads which has a low r a d i a t i n g efficiency.  The choice of c o n s t r u c t i o n m a t e r i a l s and design of  the f l a s h u n i t was made also with the purpose of assuring i t a long l i f e , of f a c i l i t a t i n g i t s alignment with the other u n i t s and making i t e a s i l y replaced or r e p a i r e d . f l a s h u n i t i s i l l u s t r a t e d i n f i g u r e 3»  The design of the  This f i n a l choice was  made i n an attempt to embody a l l the considerations mentioned above and to a r r i v e a t a compromise where c o n f l i c t s e x i s t e d . In p r i n c i p l e , the operation of the u n i t i s very simple. The aluminum electrode connected  cemented to the discharge tube i s  to the copper c o l l a r  by means of eight r a d i a l screws.  9  4.8  cm. long,  2.7  cm.  I.D.^,  This copper c o l l a r i s connected  - 23 to  the  centre  of  the  aluminum e l e c t r o d e E by  a w i r e gauze  condenser  i s attached  2  soldered  to  the  electrode  where i t i s s e c u r e d  connected  to  the  Thus when the TL,  the  down the eight  outside  outside  s c r e w s to  the  quartz  flash  the  electrode E 2 , 2  and  The the  close  observed  the  collar  by  the  and  strap.  r i s e s up  to  C  down to  trigger  is  2  t h e n down t h e  L . 2  leads  through plane l e a d  and  the  plane lead  L  travels  1 ?  t u b e t h r o u g h CQ_, i n t h r o u g h  electrode E ^ ,  The  2  Collar C  the  the  L-j_.  collar  necked  c o n d e n s e r by  i s applied  flash  plane lead  copper  a metal  where i t r e t u r n s  the  i n s i d e of  to  the  1.5  mm.  condenser  v i a the  to wire  L . 2  i n s u l a t i n g p l a t e Ip,  together. the  Finally  the  window W ,  the  p l a t e s Lj_ and  light  while  2  t h i c k , i s cemented  from  the  L  to  to  be  discharge  is  2  t h r o u g h window W]_,  the  unit  aligned. the  c o n s i d e r a t i o n was temperatures. discharge  showed  occurred  course of designing given  tube. the  because  cooler.  to a c h i e v i n g  Contributing  s p e c t r u m was  discharge  always  was  the  t u b e , i n i t i a l l y u n d e r a vacuum o f .1 m i c r o n s  through  In  the  the  to  i n s u l a t i n g cylinder Ic, allowing  placed  is  current of  the  gau.ze t o C  of  t r i g g e r pulse  condenser  through  The  the  a uniform  g r e a t l y to  the use  sodium D l i n e s  c o n t i n u u m and  instead  tube the  of  of  glass  discharge  t u b e showed no  g l a s s near strong  high  the for  spectrum  strongly i n absorption.  sodium f r o m decomposed quartz  primary  the u n i f o r m i t y  of quartz  With a glass  flash unit,  the  This  walls  absorption  lines.  -  2h  -  As i s well-known from the work of Anderson' , the par7  ameter which determines  to a l a r g e extent the u n i f o r m i t y of the.  continuum i s the current density i n the discharge channel. From h i s i n v e s t i g a t i o n s i t i s seen that a current of twenty or t h i r t y thousand amperes per square centimeter i s necessary.  The  current which flows during the discharge i s given by the expression  As i s seen from t h i s formula a low inductance i s important f o r high current d e n s i t i e s .  For t h i s reason c o a x i a l geometry was  i n i t i a l l y considered f o r the f l a s h u n i t .  The low r a d i a t i n g  e f f i c i e n c y of c o a x i a l geometry added appeal f o r the choice of t h i s form. I t i s f o r t u n a t e that a uniform continuum and a high temperature  are products of the same c o n d i t i o n s . An equation  expressing the conservation of energy f o r the discharge can be written  where  dE dt  i s the r a t e of change of the t o t a l energy of the tube;  i R i s the rate at which energy i s added to the discharge; E(tT) i s the energy of the discharge at a given time and given temperature.  Since the plasma i s a gas, i t i s an i n c r e a s i n g f u n c t i o n  of temperature; f(T) i s the f r a c t i o n of t o t a l energy l o s t per second by mechanisms other than r a d i a t i o n .  I t i s most p l a u s i b l e h.  that t h i s i s an i n c r e a s i n g f u n c t i o n of temperature; the term A <rT  - 25 -  represents i.e.  dE _ dt  the power l o s s by r a d i a t i o n . I n a steady 0 5  state  we see that we would have an increase i n temper-  ature with an increase i n current.  From the foregoing consid-  e r a t i o n s we conclude that to achieve a uniform continuum and high temperature l a r g e currents generated by the use of low inductance  c i r c u i t s i n the leads and discharge tube, high  voltages, and l a r g e capacitances are r e q u i r e d . used was a 1.6 m,f.d. low inductance,  The condenser  25 m^uh, high voltage,  25k.v.7. manufactured by C o r n e l l - D u b i l i e r , model NRG 323. The use of l a r g e currents creates a major problem. Since the currents are flowing i n opposite d i r e c t i o n s i n the two p l a t e s which are separated  by only 1/16 inch of.perspex  (to keep the s e l f - i n d u c t a n c e low) a strong r e p u l s i v e force e x i s t s between them.  The magnitude of t h i s f o r c e can be e s t i -  mated by using a very simple c a l c u l a t i o n .  Supposing the.current  i s damped out i n two periods we have approximately  one-quarter  of the stored energy d i s s i p a t e d i n a h a l f period.  I f a l l of  t h i s energy were converted  i n t o the k i n e t i c energy of the p l a t e s  t h e i r f i n a l v e l o c i t y would be  v  =  t  where E i s the condenser voltage and m the mass of one p l a t e . These p l a t e s acquire the v e l o c i t y ino.half period. f o r c e from  F.AT = m.AV  is  F - f i ^ where  P  i s the p e r i o d .  Hence the  (21)  - 26 In  This  s u b s t i t u t i n g values  f o r c e would be a p p l i e d  to the q u a r t z - e l e c t r o d e  the  gauze c o l l a r  which absorbs  the  electrode E  to the p l a t e P .  black  2  we h a v e  t h e shock were n o t u s e d  the e l e c t r o d e E  2  e l e c t r o d e E-j_ had t o be cemented w i t h used  to connect  easy  alignment.  the e l e c t r o d e  Even with tube.  a few f i r i n g s crazing not  caused  craze  since  high  2  electrode occur  screws were  cylinder,  f o r c e i s exerted  force  tends  The e l e c t r o d e s junctions  recessed  enabling  on t h e  to s h a t t e r i t a f t e r  I t was f o u n d  This i s another  Figure  The  o f t h e g l a s s i s r e d u c e d by-  as g l a s s a l l o w i n g  voltages  precautions.  E-j_ and E .  epoxy b e c a u s e  that  the tube to  quartz d i d withstand  reason f o r the choice of  g l a s s i n the c o n s t r u c t i o n o f the discharge  The ation  this  by t h e d i s c h a r g e .  as r e a d i l y  over  tube.  to the copper  the strength  many more d i s c h a r g e s . quartz  to the quartz  t h e gauze a s m a l l  I f the tube i s g l a s s  to j o i n  T h i s made i t p o s s i b l e t o u s e  2  wax t o cement  junctions i f  employed  necessitate  ha shows t h e d e t a i l s a r e grooved  so t h a t  special  insul-  o f the electrodes the quartz-  i n s i d e t h e vacuum o f t h e d i s c h a r g e  i n the electrodes,  tube.  tube  a r e g i o n o f low e l e c t r i c Q  field.  This i s i n accordance with  The tube gauze  hollow  t o be e a s i l y  t h e f i n d i n g s o f Kofoid••.  c y l i n d e r I c of perspex allows  w i t h d r a w n and r e p l a c e d  s t r a p and t h e s c r e w s .  simply  ' :•"  the discharge  by u n d o i n g t h e  The c y l i n d e r e x t e n d s 3 cms. on e i t h e r  side of air  the i n s u l a t i n g  between t h e  increase flush cm. of  the  r e m o v a l and  order  t h e demanded first  the  electrode.  and  of  it  tube.  tube.  output to  electrode.  be  decided of  different had  The  two  with  such  in  acid.  The  (figure  pitting. walls  nitric was  4b)  end  a t one  deposited l i g h t l y centered  on  the o p t i c a l  image o f  dependence o f  10°  second  the  I t was  o f f the  axis.  made  t h a t , placed near  the in  attached  paper.  t r y was  over  the a x i s of  c o n f i n e d to a c i r c l e  sensitized  size  of  deposition  t h e p i n h o l e camera was  i n mind, a of  resulting  t h e windows w i t h  constant f o r at l e a s t  with a glass b a f f l e  because  from  to m e a s u r e t h e d i r e c t i o n a l using  shots  with  t h e e l e c t r o d e s and  e b u l a t i o n was  t h e d i s c h a r g e by  tried.  from  m a t e r i a l was  While  reproducible  a r r a n g e m e n t s were  f o r a dense r i n g  t h e window.  essentially  simplification  t h e windows p l a c e d f l u s h  corresponded  These f i n d i n g s he)  f o r the  problems.  dissolved  The  .8  myah, w i t h i t removed by  part with h y d r o f l u r i c  This ring  centre of was  t o 12  c o n s t r u c t i n g a p i n h o l e camera  the d i s c h a r g e  opposite the  conductor  d e p o s i t was  t h e whole windoxi/ e x c e p t the  myuh.with t h e r e t u r n  i n f o g g i n g and e m u l a t i o n  p a r t c o u l d be  e f f e c t i v e path i n The  They became opaque a f t e r  that this  examined by  five  ( f i g u r e ha)  another  the  to have the d i s c h a r g e spectrum  resulting  appeared  s i n c e one  insulating  degree,  trial  deposition  acid  extending  c o n s i d e r e d worth the s a c r i f i c e  The  It  tube  by  breakdown i s p r e v e n t e d .  3*6  from  the d i s c h a r g e  In to  and  plates,  i n inductance  with  was  plate  copper  -  27  light found  (figure one  -  -  28  e l e c t r o d e , part of the nearby window could not see the f a r electrode.  This f a i l e d because there was d i f f u s i o n and s c a t -  t e r i n g of electrode m a t e r i a l . In the next attempt a window was moved from the main discharge path by p l a c i n g i t on the end of a branch of a wye ( f i g u r e 4-d).  A f t e r one shot, the window became contaminated  due to the condensation  of the discharge d e b r i s .  From t h i s  observation a mechanism by which the main discharge tube keeps clean i s suggested.  I t appears that the discharge evaporates  the m a t e r i a l condensed during the l a t t e r part of the previous discharge.  At present experiments are being concluded to  develop a window system which e x p l o i t s t h i s s e l f - c l e a n i n g process. In the f o u r t h design i t was hoped to make use of electrostatic deflection.  One window was moved away from the  end of the discharge tube and electrode by adding a s e c t i o n of glass tubing ( f i g u r e H-e).  Two m e t a l l i c d e f l e c t i o n p l a t e s D,  length L^, were placed d i a m e t r i c a l l y opposite on the outside of the extension thus separating them by a distance S ~ l cm. They had a voltage placed across them equal to that of the condenser p o t e n t i a l .  Assuming that a p a r t i c l e would convert a l l  of i t s p o t e n t i a l energy to k i n e t i c energy, that i s  where V i s condenser voltage. By the equation of motion, and assuming plane p a r a l l e l electrodes f  - %&  ~-  It  -  m  c  ^  •S  where E i s the e l e c t r o s t a t i c f i e l d i n s i d e the extension  tube.  - 29 Hence the time required f o r a p a r t i c l e to t r a v e l from one side of the extension to the other i s  The time to go from one end of the extension to the other, a distance  L_  is  I f these times were equal no p a r t i c l e would reach the window. That i s i f  L = 2S.  When such dimensions t h i s suggested  were used no improvement was n o t i c e d .  Thus  the discharge was i n the form of a n e u t r a l plasma  since the p a r t i c l e s could not have recombined to form n e u t r a l molecules i n the short t r a n s i t time. The f i f t h  design ( f i g u r e 4-f) and the one used i n the  present experiment was a p a r t i a l success.  As i n t r i a l f o u r ,  extensions are used but t h i s time, to keep the windows clean, a g l a s s tube at one end of which there i s a c o n s t r i c t i o n i n the form of a s l i t , was placed i n s i d e each window extension with the s l i t towards the e l e c t r o d e s .  This arrangement kept the  windows clean f o r twelve discharges. tension, 3 cms. i s determined tages.  The length of the ex-  by a compromise between two advan-  The f u r t h e r away the windows are from the discharge the  cleaner they stay because they subtend a smaller s o l i d angle to the discharge? however the nearer the windows are to the s l i t the smaller the  f number . they a l l o w f o r the system.  This design  does not take advantage of the l a r g e diameter of the discharge  - 30 tube which for  the  c o u l d be u s e d  entirely  it  to p r e s e n t  a source  extended  i n area  experiment.  In order  to u s e  -  to a c h i e v e  satisfactory  d i f f e r e n t methods were t r i e d .  ultra violet light  would  be  between t h e denser.  very  s a f e as  triggering  For  this  had  t o be  fell  on  t h e r e would  s y s t e m and  the n e g a t i v e  to t r i g g e r  first  two  was  an  be no  electrical  the h i g h  voltage of  passed  attempt  t h a t i f i t worked,  through  connections the a  aluminum e l e c t r o d e E ^  the d i s c h a r g e  s e t too n e a r  The  r e c o g n i z i n g the f a c t  L i g h t from a t r i g g e r e d spark  window and  triggering  the v o l t a g e o f  the  t h e breakdown v a l v e , c a u s i n g  con-  quartz 5a).  (figure condenser  spurious  discharges.  T h i s method was trigger  5b.  to  to  Initially the  one  discharge  negative  polarity  of  the  that  electrons emitted  the  necessary  electron  discharge  from  pulse. the  i t into  the  work e q u a l l y w e l l ) .  towards  the  ( I t was  the  were  not  the  p o l a r i t i e s of  the  F o r more r e l i a b l e  E  2  electric field  far electrode.  trigger  concluded  discharge  to i n t r o d u c e a n o t h e r  s p a c e where t h e  allowing i t  only  Hence i t was  trigger  s p a c e between E j and  shown i n  r e g a r d l e s s of  the f l a s h d i s c h a r g e .  necessary  used  T h i s would  r e s p e c t to E2?  of i n t r o d u c i n g  t u b e as  e l e c t r o d e was  e l e c t r o n s from E j , s i n c e both  i t was  i n this  trigger  kv, . t r i g g e r  p u l s e do n o t  triggering running  with  to i n i t i a t e  photo-electric trigger  32  the  e l e c t r o d e E]_.  when E ^ was  occur  abandoned i n f a v o u r  electrodes d i r e c t l y into  figure arc  then  and  trigger to h a v e  would  electrode the  arc  a c c e l e r a t e the  T h i s arrangement i s used  in  the f i n a l  design.  electrodes  to  the  they  are  immersed  i n the  will  not  rise  high.  too  several of i t s operating  figure at  6a.  the  c a t h o d e Ej_ as  of  discharge  the f l a s h u n i t  characteristics  photographed  a sweep speed o f one in a  This voltage i s given  coil  these  their  trigger  t h a t when potential  determinations  were made. time  The  of time  i s shown i n  f r o m an o s c i l l o s c o p e d i s p l a y  microsecond,  search  to keep  p o s s i b l e so  c u r r e n t as a f u n c t i o n o f  T h i s was  v o l t a g e induced  however  resulting  Upon c o m p l e t i o n  of  -  I t i s necessary  as n e a r  derivative  31  per  centimeter  placed near  the  between the  coil  of  the  discharge.  by V = M di dt  where M i s the m u t u a l i n d u c t a n c e charge  circuit.  to  the  calculated  to  derive equation  in  t h e a p p e n d i x and  s e c o n d s and  = 1.52  -  .07  we  = 3.3*+ x 1 0  L  =  56  R  =  .087  -  t  considered. by  and  not  6  Using  dis-  accurately  values  t h e method o u t l i n e d  o f P = 19«6  -  .09  x  10"^  find i  .i5  .007  seconds henries  ohms. c a l c u l a t i o n must be  from  the  time  zero  and  s i n c e t h e r e i s a phase a n g l e  Using  the  shows t h a t the model used  x 10-9  5.6  the p e r i o d i n the  as h a l f a p e r i o d  corresponds  i s q u i t e good.  ^  successive zeros  -given to 30$  This  the observed  two  be  waveform  i n AV7.  Al5  value  to  observed  one  The  zero  of  LD  The  and  the v a l u e s  o f L and  R  the  taken  from  the  first  (equation A 1 7 ) current i s  - 32  -  = 82,700 x  i  di = 0 at t = .6 x 10° seconds. dt Hence the maximum c u r r e n t i s 4 8 , 7 0 0 amperes. From By  we  observation  see  the  current  amps./ cm.  .  d e n s i t y i n the  i s 75  discharge  T h i s i s w e l l above t h e  threshold  these -  for  11  x  values K)3  continuum  radiation. The  change i n o u t p u t  condenser v o l t a g e low  current  was  examined.  d e n s i t i e s there  r e a c h e s 15  voltage  s p e c t r u m as At  are  '-kv . the  low  lines  multiplier time.  spectral steradiancy  sensitivity  T h i s was  o f w h i c h was  microsecond  The  appearance of  One  must f i r s t  i s long  The  total  is  given  per  out  with  note  compared  the  after to  the  equivalently  bands, b u t  as  the  uniform  o r i g i n a t i n g from  silicon.  i n t e g r a t e d o v e r a 931  the  and  i n t e n s i t y u n i t , the  photo-  a l l the period  (figure  peak i s e a s i l y f o r the  e n e r g y has of  the  of  6b).  explained. decay of  the  been pumped i n t o  discharge  s y s t e m as  output  a sweep speed  photographed  time c o n s t a n t  e n e r g y P pumped i n t o the by  or  the  i n v e s t i g a t e d as a f u n c t i o n o f  second h i g h e r  that  and  an o s c i l l o s c o p e w i t h  centimeter  the  intensity,  it,  was  d i s p l a y e d on  one  discharge  curve  carried  voltages  c o n t i n u u m becomes q u i t e  e x c e p t f o r s e v e r a l bands most l i k e l y The  a f u n c t i o n of  current.  a f u n c t i o n of  time  - 33  -  where to a f i r s t approximation R i s assumed constant during the discharge. This i n t e g r a l i s evaluated g r a p h i c a l l y below  -t  Allowing f o r the e x p o t e n t i a l decay of the discharge energy at regions A and B i n the graph above we f i n d the energy of the discharge as a f u n c t i o n of time i s shown i n the f o l l o w i n g graph  -t  - 3^ I f the rate of r a d i a t i o n i s p r o p o r t i o n a l  to the energy content  of the discharge, as i t most l i k e l y i s , t h i s i d . l l be the observed l i g h t output s l i g h t l y d i s t o r t e d by the response curve of the photomultiplier.  This d i s t o r t i o n r e s u l t s from change i n the  d i s t r i b u t i o n of energy as the temperature of the discharge i s lowered. As S p i t z e r ^ shows, the temperature of a plasma can be deduced from a measurement of i t s r e s i s t i v i t y . of a plasma i n which e l e c t r o n - e l e c t r o n i s given by "I  The r e s i s t i v i t y  c o l l i s i o n s are considered  = 4^  (22)  where y . i s a f u n c t i o n of the state of i o n i z a t i o n of the gas. :  2  2 = 1  ^ and  =  .582  3  .683 .785  i s the t h e o r e t i c a l r e s i s t i v i t y of a Lorentz gas. ^*L_ i s  given by -n where  e  3/z  m 2. c - c i i A 2 ( Z KTJ H 1  i s the e l e c t r o n i c charge i n esu, K the Boltzmann  constant, m  e  temperature.  the mass of the e l e c t r o n , and >.  n  Q  T  the absolute  i s given by 2-  where  (23)  e  B e  \ rr r\ J  3  &  i s the e l e c t r o n density.  d i f f e r e n t values of T and n  g  A table of Ln 7 A  i s given by S p i t z e r .  for  Substituting  the numerical values f o r the constants i n equations 22 and 23 for a s i n g l y i o n i z e d gas we f i n d T = 3.4-9 / L n X \ i  (24)  - 35 A more convenient v a r i a b l e than  Ln X  is K =  Ln X  /T ^.  The table below gives t h i s f o r d i f f e r e n t values of T and T°K  ELECTRON DENSITY 1  10 2  10^  1.6xlO-  9.4-3xl0  2  IO*  n . e  e l e c t r o n s /cc. 10 ?  2  10  1  10  1 8  3  6.21x10"^  4.04xlO~  1<A  2.32x10"^  1.63x10-?  9.4-3x10 ~  10?  8.41x10-7  6.21x10-7  4.04x10-7  2.97x10-7 1.87x10-7  IO  2.97x10~  2.28xlO"  1.59x10"  1.24x10-8 8 . 9 6 x 1 0 " ^ 5.54x10-9  IO  3  6  8  lf  8  1.88x10"^ 6  8  5.57x10"  6  The temperature i s best found by p l o t t i n g log]_QT against log-j^K f o r the value of n n  Q  during the discharge- n  e  can be found by  = 3.22 x 1 0 ? P 2 1  e  where P i s the f i n a l pressure of the discharge i n mm., of Hg. H  i s the degree of i o n i z a t i o n . K = 1.53  x 10  -I+  and  K i s given by  RA/L  (see equation 24)  where R is- r e s i s t a n c e of the discharge; A i s cross s e c t i o n . d f . discharge; L i s l e n g t h of discharge. the assumption  that the discharge has uniform cross s e c t i o n . 15  For the present f l a s h tube K  This equation i s based on  has the value  n  g  has the value  K = 3=9 x 10^.  n  e  10  y  and  This r e s u l t s i n an estimate  of the temperature at 40 - 10 x 10  3  °K.  I t should be noted that t h i s r e s u l t depends upon a t h e o r e t i c a l expression f o r d e n s i t i e s and high temperatures.  which i s good only f o r low Furthermore  the theory requires  - 36 that  the  energy  gained  field  be much l e s s  check  shows t h a t the  between c o l l i s i o n s  than  the average  c o n d i t i o n s of  domain o f a p p l i c a b i l i t y  This the  spectral  of  estimate  approach  the  was  distribution  a more d i r e c t  from  kinetic  steradiancy of  standard  carbon  A  quick  t h e d i s c h a r g e a r e i n the  theory.  made i n an  curve  attempt  to  establish  f o r the d i s c h a r g e .  the i n t e n s i t y  At  used.  t h e d i s c h a r g e i s compared  arc using  electric  energy.  to the problem i s b e i n g  spectral  the  present The  to t h a t o f a  unit attached  to a  mon-  ochromator. 3.  Plasma U n i t The  plasma u n i t  p l a s m a i n a gas  o f any  absorption  i n which  two  tube  was  desired purity  shown i n f i g u r e  7a.  light  a r e welded  The  and  P and  With  the  D.C.  discharge of  arms, and  tube.  The  Because  the plasma  uniform The  of  rest  of  i n length,  the a b s o r p t i o n  B  be  present be  generated  i n the  i n the  obstruct  the e l e c t r o d e s are w a t e r c o o l e d  t h e l a r g e amount o f h e a t  two  the p l a s m a i n the  the e l e c t r o d e s w i l l not  spite  tube.  respectively.  the d i s c h a r g e w i l l  them to the g l a s s w i t h De  as  unit  t a k e s p l a c e between  column w i l l  to s e a l  tube  which the f l a s h  s i d e arms, o n l y  possible of  a  composition.  centimeters  to e a c h end  the p o s i t i v e  furthermore  path.  fifty  s e t in, s i d e arms A and  e l e c t r o d e s i n the  absorption  optical  N,  and  G l a s s windows t h r o u g h  d i s c h a r g e which produces  electrodes  to g e n e r a t e  the p l a s m a i s formed i s a g l a s s  centimeters i n diameter  i s passed  designed  Khotinsky  side  the i t is  Wax,  i n the o r d e r  in of  - 37  -  400 watts at the cathode f o r a D.C. discharge and of 10  watts  for each electrode i n an A.C. discharge. A t t a i n i n g a discharge of s u f f i c i e n t p u r i t y presented a d i f f i c u l t problem.  During a D.C. discharge a metal f i l m i s  sputtered onto the w a l l of side arm B.  Gases w i l l occlude on  t h i s f i l m and when the next discharge i s run the heating of the w a l l b o i l s them o f f ,  r e l e a s i n g them to the discharge.  This  source of i m p u r i t i e s i s eliminated by making side arm B U-shaped and immersing i t i n a bath of l i q u i d n i t r o g e n . also freezes out a l a r g e amount of oxygen.  This procedure  When there i s an A.C.  discharge t h i s problem occurs at both side arms A and B. However there was not s u f f i c i e n t time to modify side arm A. To remove the remaining a c t i v e gases, a chamber to contain f i n e l y divided uranium was appended to the absorption tube.  This  f o l l o w s the method of G. H. D i e k e ' . 1 0  1 1  Two grams of uranium turnings, cleaned i n n i t r i c acid s h o r t l y before, are introduced i n t o the chamber and baked f o r two hours a t a high temperature under vacuum.. Hydrogen gas i s then allowed to f i l l atmosphere.  the system to a pressure of about one  The r e a c t i o n of the uranium with the hydrogen was  started by an i n i t i a l hard heating of the turnings a f t e r which the  temperature i s maintained a t about 250°C.  I n about one-half  hour the e f f e c t of the r e a c t i o n can be seen - whiskers form on the  turnings.  A f t e r several hours the r e a c t i o n goes to com-  p l e t i o n leaving uranium hydride powder.  The hydrogen i s then  pumped o f f and the uranium hydride i s heated to 4-00°C to reduce  - 38 it  to  a finely  entering  the  powder can  the  three  major  the  litre  G a t a p h o r e s i s i s the  minor The it  desired swept  gas  toward  may  the  side  arm  t u b e pumped o u t , again.  This  i s an  the  gas,  i n the the  fills, the  the  active  Once the be  introduced  4.  Shutter  of  p l a s m a and  gas  through  H.  wool that  a ready  cathode of  supply  near  the  .  the  works w h e t h e r  h a v e the  the  to a i r .  Dieke  a monatomic  will  minor the  molecule.  impurities  in  powdered u r a n i u m where t h e y  resevoir  until  G.  from  i n the  arm  B,  i s shut o f f , the  r e o p e n e d and the  side  desired  the  two  main p r o c e s s e s are used  for  the  i n e r t g a s e s and  i f inert.  absorption  process  purity i s  are  started  reached.  in purifying  gettering  by  gases.  i s p u r i f i e d the the  arrangement  desired  impurities  shown i n f i g u r e  can  7b.  Unit The  duction  the  noted  It i s located  This or  be  glass  guarantees  the  concentrated  resevoir  summary,  at  gases.  resevoir  of  i f exposed  exploited,  c a t h o d e and  cataphoresis  uranium f o r  be  i n e r t gas  i s repeated  In  study.  concentration  removed, i f a c t i v e , and If  a wad  I t should  resevoir  under  a mixture of  constituent  placing  tube.  glass  constituent  of  powder i s p r e v e n t e d  i g n i t e spontaneously  anode where c a t a p h o r e s i s  constituent  This  t u b e by  chamber and  A of  uranium.  absorption  between t h e uranium  divided  shutter  unit  t h i s chapter, to  time the  ( f i g u r e 8)  i s used  to  t r i g g e r i n g of  as  mentioned  control the  the  i n the  intro-  exposure of  flash unit.  There  the are  -  39  -  two d i a m e t r i c a l l y opposite s l o t s A and B i n the r o t a t i n g d i s c ; S l o t A, near the rim, to c o n t r o l the exposure by adjustment of i t s width, and S l o t B, near the a x i s , to c o n t r o l the  timing.  The minimum exposure i s three milleseconds, t h i s being f - 20 of the spectrograph, the speed of the  determined by the disc r.p.s. = 1725,  and the distance  spectrograph s l i t and the d i s c . *min ~  s = 3 cm. between the  The minimum exposure i s given by  l s  f 2 TTR x r.p.s.  where R = 3«7 cm. i s the mean distance from the axis to S l o t A. Since S l o t A w i l l expose the spectrograph about twentyeight times per second, a compur shutter, which i s open f o r j u s t under the time of one r e v o l u t i o n of the d i s c , i s placed i n f r o n t of the d i s c , thus l i m i t i n g the number of exposures to one.  This exposure w i l l occur when the shutter i s open. The f l a s h u n i t f i r i n g i s timed by a pulse from the  photomultiplier  PT_ produced by a burst of l i g h t from the lamp  L, as S l o t B passes i n f r o n t of the p h o t o m u l t i p l i e r . event i s arranged  This  to take place i n advance of the coincidence  of S l o t A with the spectrograph s l i t by placing the photom u l t i p l i e r o f f the diameter formed by the spectrograph s l i t the d i s c a x i s .  The p h o t o m u l t i p l i e r  and  pulse i s delayed by the  Tektronix 5*+5-A o s c i l l o s c o p e u n t i l the spectrograph s l i t opens. This pulse gets through to the t r i g g e r u n i t only i f the compur shutter i s open.  -  hO  -  Low j i t t e r i n the order of ten microseconds i s assured by having a l a r g e slope to the p h o t o m u l t i p l i e r pulse. This slope of .2 v o l t s per microsecond i s achieved by imaging lamp B i n the p l a i n of the d i s c with lens L and p l a c i n g stops on both sides of the image.  The synchronization of the f l a s h  f i r i n g and the spectrograph opening i s accomplished lowing procedure.  The pulse from the p h o t o m u l t i p l i e r , P j  t r i g g e r s the d i s p l a y sweep of the o s c i l l o s c o p e . connected  by the f o l -  to another p h o t o m u l t i p l i e r P  p o s i t i o n of the spectrograph.  2  Input A i s  located at the p l a t e  A carbon arc used to simulate  the plasma produces a pulse (displayed on the o s c i l l o s c o p e ) when the spectrograph s l i t i s open.  The delayed output pulse  of the o s c i l l o s c o p e i s fed to input B and d i s p l a y e d .  Synchroni-  z a t i o n takes place when these two pulses c o i n c i d e , as the delayed pulse f i r e s the discharge tube. 5. E l e c t r o n i c Units The two remaining u n i t s of the s i x used i n the e x p e r i ment, namely the t r i g g e r u n i t and the i n t e n s i t y u n i t are e l e c t r o n i c i n nature. The t r i g g e r i n g u n i t was designed a f t e r the work of G.A. Theophanis-*-3  0  Two three-meter  long, type R.G. 58U  c o a x i a l cables, i n p a r a l l e l , are charged to 1 6 kv. with a high frequency and high voltage supply of the type used i n t e l e v i s i o n receivers.  The f a r end of the cables i s terminated with a  50 /^yK farads 2 0 kv. condenser i n s e r i e s with ten one-megohm r e s i s t o r s , i n p a r a l l e l , arranged about the condenser. e s s e n t i a l l y an i n f i n i t e termination.  This i s  The sheaths of the c o a x i a l  - 4-1 cables  a r e grounded w h i l e  connected signal end  t o t h e anode o f a h y d r o g e n f i l l e d  i s a p p l i e d to the g r i d  o f the attached  cable.  this  s e n d s a - 16 kv  with  a coefficient  the  condensor  must f a l l  a t 16 k v " . a r e  the i n n e r conductors  thyatron.  When a  o f the t h y a t r o n i t s h o r t s the t h e c a b l e s a r e a t 16 fcv' .  Since  • p u l s e down t h e c a b l e w h i c h i s r e f l e c t e d  o f +1.  In order  remains constant,  that the v o l t a g e  e.g. l 6 k v " . ,  t o -32 kv' .  T h i s p u l s e i s then  The  thyatron i s f i r e d  across  the f a r s i d e  taken o f f across the  resistors.  fired  i n t u r n from  nected  to the g r i d  exercised the  hydrogen  over  the o s c i l l o s c o p e ,  The  the  output  of this  a carbon  931A  so a u n i v i b r a t o r  this  distribution  a brass  (type  i s completely  box.  time o f  jitter  to determine  and w i l l  consisting  2N1177, 144  enclosed,  I t i s necessary  This  time  microseconds.  of the output  This unit  from  duration.  with a j i t t e r  j i t t e r , the t o t a l 25  pulse  was i n t r o d u c e d i n t o t h e  i n t e n s i t y u n i t i s used  arc.  The t u r n on t i m e o f  p u l s e o f 50 m i c r o s e c o n d s  With  and a t r a n s i s t o r  frequency)  tube.  the d u r a t i o n of the delayed  f o r the f l a s h u n i t ,  spectral  s h u t t e r i s con-  o f t h e 2D21 so t h a t c o n t r o l i s  t h e s y s t e m mounts t o a b o u t  light  The compur  a d e l a y o f 35 m i c r o s e c o n d s  f i v e microseconds.  of  than  w i t h an o u t p u t  introduced  of  circuit  the f i r i n g  2D21 i s l o n g e r  circuit  a delay pulse.  w i t h a 2D21 w h i c h i s  be u s e d  the i n t e g r a t e d to  as compared  determine  with  that  of a photomultiplier mc.  alpha  w i t h i t s power  to use t h i s  cut o f f supplies, i n  particular  design i n  - k2 order The  to avoid  transistor  matching with it  pickup  -  o f the e l e c t r i c a l n o i s e from  i s i n t h e common c o l l e c t o r  the high generator  impedence o f t h e c a b l e s  t o t h e o s c i l l o s c o p e i s made p o s s i b l e .  ence m a t c h a t t h e o s c i l l o s c o p e end a l s o , from  the c a b l e .  Besides experiment, They a r e :  one  connecting  By a r r a n g i n g  an imped-  there i s very  loxtf n o i s e  works v e r y  the u n i t s designed  satisfactorily.  and c o n s t r u c t e d f o r t h e  pieces of available  a T e k t r o n i x o s c i l l o s c o p e type  megacycle o s c i l l a t o r , automatic  This u n i t  several other  c o n f i g u r a t i o n , so  impedence o f t h e p h o t o m u l t i p l i e r 931^  t h e 52 ohm c h a r a c t e r i s t i c  pickup  the discharge.  equipment a r e u s e d .  54-5A,  a  tuned  g r i d "28  a J a r r e l l - A s h microphotometer, H i l g e r  glass-quartz spectrograph  f o r t h e plasma u n i t  capable  and two h i g h v o l t a g e s u p p l i e s ,  of delivering  two amperes a t  1200 v o l t s , t h e o t h e r f o r t h e f l a s h u n i t c a p a b l e o f 30,000 a t 30 m i l l i a m p e r e s .  volts  Chapter I I I RESULTS AND CONCLUSIONS 1. I n t r o d u c t i o n Upon completion of the c o n s t r u c t i o n of the present apparatus, a preliminary experiment was run to demonstrate the e f f e c t i v e n e s s of the theory and apparatus.  There follo\tfs  i n t h i s chapter an account of the experiment with i t s r e s u l t s and conclusions  suggesting  e f f i c i e n t operating conditions  p o s s i b l e improvements i n the equipment.  and  In a d d i t i o n , experiments  i n which the f l a s h u n i t could e f f e c t i v e l y be used are proposed. 2. Experiment Neon was  chosen as the gas i n which the  discharge  occurs, since i n f u t u r e experiments i t s use w i l l enable the r e s u l t s to be compared with the i n v e s t i g a t i o n s of Kopfermann and Ladenberg.  The discharge,  taking place i n the neon at a  pressure of 2.2 m i l l i m e t e r s , was excited by the radio frequency o s c i l l a t o r generating  about 20 watts, an unknown f r a c t i o n being  d i s s i p a t e d i n the discharge.  This energy was  through the two electrodes P and N.  introduced  The neon was not f r e e of  i m p u r i t i e s i n s p i t e of the aids employed since the metal components of the absorption tube outgassed too r a p i d l y . be noted that the apparatus was  I t should  c a r e f u l l y arranged so that a l l  portions of i t would f l o o d the spectroscope prism. The data obtained i s derived from one p l a t e containing four spectrograms. Two  One  consisted of an emission  spectrum only.  consisted of s i x shots each of the spectrum r e s u l t i n g from - 4-3  -  - 44 -  the passage of the continuum l i g h t through the neon plasma. These twelve shots were taken through the same discharge tube window.  These two spectrograms d i f f e r e d by having an exposure  time t , equal to . 4 5 m i l l i s e c o n d s f o r one and . 7 6 m i l l i s e c o n d s e  for  the other.  The f o u r t h spectrogram consisted of a twenty-five  shot exposure of the continuum source only through a seven step graded f i l t e r (platinum on g l a s s , e s s e n t i a l l y a n e u t r a l f i l t e r for  the wave length range studied).  Uniform i l l u m i n a t i o n of the  p l a t e was assured by forming an image of the discharge on the collimator lens of the spectrograph with a lens i n close proximity to the step f i l t e r and spectrograph s l i t .  The f l a s h  continuum,  rather than other sources, was used to e s t a b l i s h the characteri s t i c curve by exposure of the plate through the step xvedge since t h i s exposure must be made under the same conditions as were the spectrograms to which the curve would be applied. The p e r t i n e n t data and r e s u l t s f o r the d i f f e r e n t l i n e s examined are given i n the table below. Line 6163 Trans- From 3 P ( 3 P I ) 3s(3p ) i t i o n To  3s(3P )  3P(3P )  3P(3P )  3S(3P )  3S(3PI)  3s(3p )  2  2  .76xlO~3sec.  td B(T)/B(T )  . 4 5 x l O s e c . 5 4 x 1 0 ~ s e c . .65x10-6  1  _b  .0044  b  .0036  .0030  .57x10"  2  x  4730  4240  .58x10^ s  6  .0034  1.02  P  T  0  .45xlO""3 sec.  e i  tep  R  6096  3P(3D ) 2  c  t  6074  6334  S143  .0034 1  4000  4220  - 4200  - 45 F o r t h e two p a i r s o f t r a n s i t i o n s w i t h d i f f e r e n t common lower l e v e l s 3p  and 3 p 2 ?  1  the r a t i o r  o f the v a l u e s B ( T ) / B ( T ) 1  p  g i v e s the r e l a t i v e p o p u l a t i o n o f the upper s t a t e s o f each p a i r . The temperature T i s c a l c u l a t e d on t h e assumption t h a t the d i s c h a r g e i s a 40,000 °K b l a c k body.  The t r a n s i t i o n temperatures  appear to be q u i t e r e a s o n a b l e , s i n c e when a carbon a r c a t a temperature o f about 5000 °K was used as a continuum s o u r c e , the l i n e s were seen f a i n t l y i n a b s o r p t i o n . D u r i n g the c o n s t r u c t i o n o f the apparatus'many  plates  were t a k e n upon i^hich no c a l i b r a t i o n exposures were made but which d i d show i n t e r e s t i n g r e s u l t s .  One p l a t e r e v e a l e d  sixteen  t r a n s i t i o n s i n a b s o r p t i o n between the 3p5»3p n d 3p5»3s cona  f i g u r a t i o n ^ w h i l e another p l a t e showed two t r a n s i t i o n s which, to the b e s t o f our knox^ledge, have never been r e p o r t e d as seen i n absorption.  These t r a n s i t i o n s o c c u r r e d betv>een the s t a t e s  3p (2p?.3p) - P (2p5.5s) and 3p ( 53p) . 3p (2p55s). 3  1  2  0  2p  1  The v a l u e s o f BCD/BCT ) a r e i n e r r o r by a t most 30$ 1  e s t i m a t e d by t r a c i n g the maximum e r r o r s i n measurements through the c a l c u l a t i o n s i n v o l v e d .  There a r e t h r e e i m p o r t a n t sources  o f random e r r o r ; a r i s i n g from measurements o f t i m e , d e n s i t y and i n t e n s i t y .  The g r e a t e s t d i f f i c u l t y i n the measurement o f  the time t , r e s u l t i n g i n an e r r o r o f 5$, i s caused by the e  f i n i t e m e c h a n i c a l opening time o f the s l i t .  I n the determination  o f the p e r c e n t a g e t r a n s m i s s i o n o f t h e p l a t e an e r r o r o f about 2% a r i s e s , n o t from t h e J a r r e l l - A s h m i c r o d e n s i t o m e t e r which i s used f o r t h e measurement, but r a t h e r from the g e n e r a l n o i s e l e v e l o f the p l a t e .  - 4-6 The absorption l i n e appears as only a h% v a r i a t i o n of the continuum, and since the d i f f e r e n c e between the absorption and background exposures i s used i n these c a l c u l a t i o n s , a l a r g e source of error i s introduced.  This error could be diminished  considerably by shortening the exposure time t e l .  T n e  third  error a r i s e s from the g r a p h i c a l e v a l u a t i o n of the exposure from the transmission of the photographic  plate.  The twenty-five  shots used to e s t a b l i s h the c h a r a c t e r i s t i c curve r e s u l t e d i n over-exposure, allowing only the lower p o r t i o n of the curve to be w e l l e s t a b l i s h e d .  However, only an approximate curve i s  needed, since small v a r i a t i o n s i n exposure are measured. Unfortunately, t h i s inaccurate curve did not allow the second method, mentioned i n Chapter I and r e q u i r i n g a measurement of both emission and absorption spectra, to be used since large v a r i a t i o n s i n exposure are i n v o l v e d . Besides the above random e r r o r s , several systematic ones were present.  A l l the formulas developed i n Chapter I  were dependent upon an i n t e g r a l over l i n e width, but since the l i n e s are so s l i g h t l y i n absorption or emission, the maximum depth or height of the l i n e s was taken as a measure of t h e i r i n t e g r a l s , that i s , i t was assumed that they a l l have the same l i n e shape.  Another e r r o r i s introduced by the progressive  darkening of the window from the discharge d e b r i s . allowed f o r i n a f i r s t approximation  This was  by assuming that the two  sets of exposures were taken with black bodies of d i f f e r e n t temperatures, n e c e s s i t a t i n g the use of the s l i g h t l y modified formula  -  td = ( P  b n  -  47  - i ) ( e 2 + t ) - (P2 p  t  b  a  (P2  -  - P2)(t i + t ) e  _ ta  a  rPi)  instead of equation 1 7 a where r = P 2 / P ] _ b  b  and  P i and  are background intensities of the exposures 1 and 2. symbols are the same as those i n Chapter I .  b  P  b 2  The other  I f i t i s assumed  that a f i x e d quantity of m a t e r i a l i s deposited on the window a f t e r each discharge, then the exposure of the p l a t e from the n^h discharge i s given by P  = cT " 111  m  1  where T i s the transmission. By measuring the above p l a t e we f i n d T = .9938. I t has been e x p l i c i t l y assumed i n c a l c u l a t i n g the temperature of the plasma that the plasma column examined was uniform and at a common temperature.  The diameter of the absorption tube,  2 cms., may make t h i s assumption i n v a l i d .  Another error which  i s as yet undetermined r e s u l t s from the time behavior of the temperature of the f l a s h discharge. Since the source peaks at a very high temperature t h i s error would be r e l a t i v e l y small. Other errors which may be important r e s u l t from an i n t e r m i t t a n c y e f f e c t and the f a i l u r e of the R e c i p r o c i t y Law. The i n t e r m i t t a n c y e f f e c t w i l l a r i s e from the superposition of the s i x shots, with a time i n t e r v a l of about one minute, to form a s i n g l e spectrogram.  The R e c i p r o c i t y Law may f a i l  because  of the d i f f e r e n t exposure times of the continuum and plasma; and of the step wedge and spectrograms.  I t i s believed however  . 1+8 -  that t h i s error w i l l be s l i g h t because of the short times and high i n t e n s i t i e s involved. 3. Future Work A f t e r running the experiment, areas which are open to improvement became evident. To observe t r a n s i t i o n s at higher temperatures i t w i l l be necessary to construct a s h u t t e r i n g mechanism with an open time approaching that of the duration of the f l a s h .  This short time w i l l p a r t i a l l y e l i m i n a t e the  d i f f i c u l t i e s caused by the i n t e r m i t t a n c y e f f e c t since the exposures of the plasmas which at present are f o r time t , w i l l e  be composed of a s e r i e s of exposures each of duration t but a  which w i l l t o t a l to time t . e  To avoid d i f f i c u l t i e s encountered  with the p u r i t y of the neon, i t i s suggested that an absorption tube be b u i l t which w i l l be e n t i r e l y f r e e of electrodes but s t i l l incorporates uranium as a g e t t e r .  In t h i s tube the plasma would  be generated by an e l e c t r o d e l e s s R.F. discharge. From a d e t a i l e d study of the time behavior of the discharge spectrum a better estimate of time t able.  a  \rould be a v a i l -  I t i s also recommended that the s p e c t r a l radiancy of the  source be compared to that of a standard black body so that t r a n s i t i o n temperatures may be determined with a degree of certainty.  Further i n v e s t i g a t i o n s of the discharge may suggest  changes i n the design of the f l a s h u n i t to improve on the u n i formity of the continuum. I t i s hoped that i n the f u t u r e several i n t e r e s t i n g and important experiments w i l l be conducted with t h i s f l a s h u n i t .  - 4-9 The  adaptation  plasmas since  is  i t  of  may  temperatures experiment tive  be  used  of  shock  w i l l  interest  studies  important tinuum  this  technique  considerable  population  current tion  of  of  check  densities  of  the  plasmas  are  effect a  technique  of  steady  very  available.  work  plasmas.  development are  to  study  assumptions  generated the  i n  the  interest  determine  diagnostic  sources  to  to  l i k e l y  now  i n  made  that  transient  this i n  laboratory  determining  Another  projected  impurities  state  of  of  plasma,  optical to  on  masers  become  high  a  a  the  rela  work «  of  Absor  very  temperature  con-  Appendix I THE EQUATION OF TRANSFER 1. Definitions and Fundamental Notions, (a)  The s p e c i f i c intensity of radiation at a point P and i n a  given d i r e c t i o n :  Consider a point i n a f i e l d of radiation.  Through this point construct a small elemental  surface d cr ;  i n a s p e c i f i c d i r e c t i o n s construct cones of solid angle d UJ , with apex on ds at every  point of do- ,  Then during the time  i n t e r v a l dt, the energy traversing the area do  -  and from the  semi-infinite volume so defined can be xvritten as dE = I cos 8 where 9  dco do~ dt.  (Al)  i s the angle between s and the normal to der .  -S  I obviously depends upon the point P and the direction s.  It i s  called the s p e c i f i c intensity or steradiancy at the point P^ and i n the d i r e c t i o n s.  In an i s o t r o p i c radiation f i e l d I i s inde-  pendent of s. (b) Monochromatic S p e c i f i c Intensity.  The monochromatic s p e c i f i c  i n t e n s i t y i s so defined that I  v  cos0 d r  dco  dt  i s the t o t a l energy i n the frequency  d^  i n t e r v a l ( \) , V + dV  which crossed the elemental area d <X i n a s o l i d angle d cj  and i n time dt.  - 50 -  (A2)  i n the direction Q From the d e f i n i t i o n  ) ,  it  follows  -  that I  Vie c a l l  51  d V  v  I the integrated  =  I .  intensity,  ( c ) Amount o f R a d i a n t E n e r g y F l o w i n g T h r o u g h  One E l e m e n t o f  Surface to Another. ^  L e t I be t h e s p e c i f i c P  1^2*  also  T l l e  e  n  e  r  g  y  traversed  w h i c h t r a v e r s e s dcr-^ i n u n i t t i m e and w h i c h d (T ,  i s from E q u a t i o n ( A l )  where d co i s t h e s o l i d d 6J 2_ =  dE  (d) E n e r g y  a t P-^, i n t h e d i r e c t i o n o f  intensity  dE = I c o s  so  A/,  Density  I  62  do"  d  a n g l e t h a t d 0~  cos  cos 6  A  0  dt  UJ  2  That i s ,  makes a t P-j_.  do~p  2  cos Q 2  dQ~2  do~i  of Radiation at a Point.  dt  (A3)  The e n e r g y  u , of the i n t e g r a t e d r a d i a t i o n a t a given  density,  point, i s the  amount o f r a d i a n t e n e r g y p e r u n i t v o l u m e w h i c h i s i n c o u r s e o f transit,  per u n i t time, i n the neighborhood  sidered.  Consider a p o i n t P surrounded  of convex  bounding  surface  0~  .  of the point  con-  by a s m a l l v o l u m e  Surround  t h e volume  with  V  a n o t h e r convex  52  -  s u r f a c e S such that  a r e l a r g e compared t o t h o s e o f cr intensity 2.  i n a given  , b u t s m a l l enough t h a t  A l l r a d i a t i o n c r o s s i n g V must h a v e c r o s s e d 2. through which  The  flowing across  energy  from E q u a t i o n  the  d i r e c t i o n i s constant f o r a l l points inside  an e l e m e n t  some o f t h e r a d i a t i o n h a s d2  and  der  , an e l e m e n t  Consider  dZ  passed. o f cr  , is  (A3)  =  dE  I cos 9  cos 6 r  L e t 1 be t h e d i s t a n c e The  the l i n e a r dimensions of 2  do-  2  2  traversed  t i m e o f t r a v e l i s 1/c  d  by t h i s  r a d i a t i o n through  where c i s t h e v e l o c i t y o f  Hence t h e amount o f r a d i a n t e n e r g y  due  ¥.  light.  to t h i s p e n c i l o f  light  is I  c o s (9  cosQ  do~  2  d 2  1  r^  = do  dV  The  solid  cos  -  angle subtended d  c  o f v o l u m e dv  But the element  = cos  U)  o f V i n t e r c e p t e d by  d  this  ray i s  1.  by d E  Q  ,  at P i s  d 2  r energy E i n t r a n s i t 2  Hence t h e t o t a l  E = 1 J J  I d V  c  The  energy  density  u  =  d u»  E  = 1  t h r o u g h the volume V i s = V c  J l  I I  dcJ.  V  If  u = h IT c  the r a d i a t i o n i s i s o t r o p i c  This f o l l o w s i d e n t i c a l l y  for I  v  ,and u  I.  v  also.  aco,  (A4-)  -  (e)  53  The E m i s s i o n C o e f f i c i e n t :  -  C o n s i d e r a n e l e m e n t o f mass  The amount o f e n e r g y e m i t t e d by t h i s e l e m e n t i n t o d CO  j  j  processes  du dt  Bi  v  +  dV,  the emission c o e f f i c i e n t .  interpretation  (A5)  To g e t a  physical  o f t h i s we d i s c u s s t h e d e t a i l s o f t h e a t o m i c  involved. If  t h e r e a r e t r a n s i t i o n s o f atoms o f t h e medium f r o m  quantum s t a t e u t o L t h e n t h e f r e q u e n c y o f r a d i a t i o n  h ~V where E  =  uL  E  - E  u  U  in  j  and  i s g i v e n by ( A 6 )  L  and E ^ a r e t h e e n e r g i e s o f t h e two c o r r e s p o n d i n g  u  T h i s e m i s s i o n p r o c e s s i s d e s c r i b e d by t h e E i n s t e i n A J  B  U  They a r e d e f i n e d as f o l l o w s .  L .  element of s o l i d radiation  V  u  ^  i n the d i r e c t i o n  a n g l e d U)  coefficients  s t a t e u emits  confined  , and i n t h e a b s e n c e o f an  U  d u) d t .  L  atom i s e x p o s e d  to a r a d i a t i o n  t r a n s i t i o n increases.  time dt  that  u i s stimulated  t o e m i t a quantum h  field  external  V  u  L  the p r o b a b i l i t y by a n e x t e r n a l  i n the d i r e c t i o n  If  the p r o b a b i l i t y of a  T h i s i s t a k e n c a r e o f by  d e f i n e d i n s u c h a way  atom i n s t a t e  in  to an  (A7)  This spontaneous emission i s uniform i n a l l d i r e c t i o n s .  U  that  field i s A  B L  states.  The p r o b a b i l i t y  an i n t e r v a l o f t i m e d t a n atom i n t h e e x c i t e d  a quantum o f e n e r g y h  the  angle  i n t i m e d t i n a f r e q u e n c y i n t e r v a l ( V , V* d x> ) i s g i v e n by  i s called  v  a solid  m.  introducing that  an  radiation  specified  excited field  by d o J ,  is B  uL  d  U  d t  -  ( A 8 )  - 54 where I ) V  the  i s i n the d i r e c t i o n defined  ( t L  emission  takes p l a c e i n exactly  incident  radiation.  per  time,  unit  h If can  by E q u a t i o n s  ^uL  (\  there are radiate  The t o t a l  +  N y ^ U  B  L  uL  at frequency V  JVuL where d i s t h e  (A7) and  }  =  u  uL  ( A  L  U  The  relationship  between t h e s e  The  t o t a l number  of t r a n s i t i o n s  the  s a m e T u n d e r any s y s t e m . \  u  u  V U L  U L  where a ^ and b j u  )  U  (A5) we  ^uL  h  c o e f f i c i e n t s are also  a b s o r p t i o n i n i s o t r o p i c energy  +  atom  (4-TTA L+B LJly  « L  U  volume i n t h e s t a t e  l^uL  I  and  uL  V  j  B  by a s i n g l e  M*iVuL d  see  u which that  (A9)  =  1  =  u L  ^  J  c  densities  f o r emission  and i n t e n s i t i e s .  c o e f f i c i e n t s i s shown below. per u n i t  time p e r atom must be  Hence n L  A  are defined  j  defined  I  v  u  B  +  u  L  J  V uL  1  ^  d  f o r i s o t r o p i c energy  U  L  densities  ^  d  so a  4  =  u L  TT A  U  and  L  b  u  L  =  C  B  U  L  Also a  where  uL  a ^  +  b  dw)  u L  density.  Einstein's  a  H  J , from E q u a t i o n  +  That i s ,  (A8) i s  =  atoms p e r u n i t  u  .  CJ  t h e same d i r e c t i o n as t h e  energy emitted  VuL  1  by d  uL  J  V  and b ^  U  L  =  h  A  uL  are defined  +  B  uL  j  V  1  U  L  d  ^  for isotropic intensities.  but  - 55 For  isotropic  intensities  dcj  I  I  4 TT .  ^ uL  Hence and  4-TTA. uL  (f)  The  sing  a  Absorption medium  intensity i t  has  I  Coefficient.  w i l l of  v  be  radiation  traversed  a medium  at of  dl•v It  should  emergent The  be  radiation  quantity  coefficient'  stationary  which  so  v  for  4  If  of  k  we  u  from  the  this  quantitatively  absorption  B ^ ,  an  the  atom  i n  absorbing  a  state  state  B  where  the  i n  of  phase  hV L U  is  then  the  from  the  i n  a  exposed i n  time  dt  v  specific +dly  as  of  incident the  the  radiation.  "mass  absorption  s  between  absorption of  state  Einstein that  is  given  the  u.  We  two  radiation atoms express  coefficient  the  radiation  of  of  probability  of  frequency  of V  U  by  (All)  'Lu  integral  after  write  intensity  absorption  way  to  I  can  the  excitation  the  the  V,  higher  such  the  defined  L,  of  we  with  frequency  the  If  traver-  (A10)  is  v  of  terms  L,  d l  case  to  L  defined  quantum  i n  radiation  becomes ds,  ,  u L  ds  the  and  arises  u  +  introduced  consider  \J ^  lower  is  Iv  v  4TTB  of  frequency  k I  radiation  states  frequency  that  =  L  absorption,,  thickness  -  remarked  by  u  pencil  A  weakened  b  is  extended  over  the  complete  sphere.  L ,  (g) T o t a l  Absorption.  to a r a d i a t i o n energy enclose  To c a l c u l a t e  cr  surface  energy  surface  d Z  an e l e m e n t  of o  d V  X  o f m has l i n e a r  p a s s i n g an element  o f mass m  t h e amount o f  i n frequency i n t e r v a l  t h e mass i n a l a r g e  bounding The  C o n s i d e r an e l e m e n t  field.  absorbed  56 -  time,  such t h a t the  dimensions  of Z  radiation  per u n i t  chosen  exposed  than 22 *  smaller  and i n c i d e n t  u p o n der ,  , i s from E q u a t i o n ( A 3 )  -  dE = I  cos Q  v  dcr d S  cos B  dv  r2 of  this  length  energy  t h e amount a b s o r b e d  l o f t h e mass: k  *v  1  v  c o s <9  from the p e n c i l  , dE  when  traversing  that i s  cos 9  do~  d,£ d v>  k  v  1  2 r =  I  k  v  dm  d V d c J  where dm = 1 c o s 6 .d ; d> i s an e l e m e n t o f mass o f m and dco= d S c o s 9 . t h e s o l i d a n g l e s u b t e n d e d a t t h e mass point  by d S  .  The t o t a l  d v JJ If  t h e number  can a b s o r b total  hence  I  energy  v  UL  _  k  y  dm  absorbed i s 6 00  =  dv  k  u  o f atoms i n s t a t e L p r e s e n t p e r u n i t at this  amount a b s o r b e d  k  v  energy  =  h  frequency,  V  a L  are  m J ly  d L t J l  volume w h i c h the  b y them by E q u a t i o n ( A l l ) I s  N ^ , d  B-^  .  (  A 1 2  )  The  2.  equation  of  Consider length  ds  radiation the in  s  normal of  the  same  energy  to  angle  d w  small d cr  s  is  time  Iv dt  is  I of  crossection the  .  i n  the  intensity  face  emergent  der  and  of  the  of  the  cylinder  from  the  second  The  amount  direction  of  of  i n face  radiant  the  solid  d do d cr dt, v  v  this  absorbed  by  the  hence  i n d  the I v>  i . e .  steady dv  6u)  d l ^ _  ds  is  the  terms  of  I the  dejder-dt  amount  j  der  d V  v  radiated  d CJ d e r  v  i s  dt  state do  dt  -  =  d(  j  - k \> I ^ )  v  <r  d v d t  ds  =  ds This  ds  cylinder; d  i n  be  v  dly  +  and  k ^ d is  I  intensity  direction  about  Let  of  i n c i d e n t on o n e  The  i n  cylinder  ,  frequency  crossing  -  transfer. a  direction.  57  "  equation Einstein's  of  Transfer.  We  coefficients  can  using  write  this  equations  equation  (A9)  and  (A12) . d  I  ^  uL  =  N  ^ u L ^ L + S u L  Iv L u  ) h V  uL  - N  L  U  L  B  L  u  h^  u  L  Iy L u  (A14)  o  Appendix  II  DISCHARGE MODEL A model f o r is  the e l e c t r i c  c i r c u i t of  the f l a s h u n i t  shown b e l o w .  J  B  -4JL8JL  RB Rf  B R  It is  d e r i v e d f r o m an o b v i o u s  elements  of  correspondence  The i n d u c t a n c e Lf  R^ assume  represents  the v a l u e s  respectively.  of  Rg t h e c h a r g i n g r e s i s t a n c e  B from the condenser  discharge  period i s  the c i r c u i t to t h a t  about  triggered  R f and  charging  the c h a r g i n g u n i t  disconnect  three microseconds.  - 58 -  condenser  resistances  as RgC ~ 3 « 2 s e c o n d s  shown b e l o w  capacitor.  the c h a r g i n g u n i t w i t h  r e s i s t o r R g and i n d u c t a n c e L g e s s e n t i a l l y battery  a  The r e s i s t a n c e s  200 K ohms and L g t h e  When t h e d i s c h a r g e i s  C is  the u n i t  t h e l e a d and d i s c h a r g e  The B a t t e r y B r e p r e s e n t s  physical  the f l a s h u n i t  the i n d u c t a n c e of  a b o u t 37 m i l l ! m i c r o h e n r i e s .  inductance.  between  t h e u n i t and common c i r c u i t e l e m e n t s .  c a p a c i t o r o f 1.6 m i c r o f a r a d s o r t h a t o f  and l e a d s ,  d  the  while  the  Thus we s i m p l i f y  -  59  a.  <R f  < i  iH'l-B-'! The e q u a t i o n f o r t h i s c i r c u i t i s R d i  R  2  t  dt  +  t  di  i  +  "dt  2  where R^ = R^+R^.  0  c  The a p p r o p r i a t e s o l u t i o n when t h e s w i t c h s  i s moved from c o n t a c t a t o c o n t a c t b a t time t = 0 i s -  1  _  -D  ~  \L  rr  1  where  V  (ic™  e  - RT VT, ./R! \2L)  sin^t 2  ?;  i  'Z  (A16)  j  The s w i t c h i n g c o r r e s p o n d s to t r i g g e r i n g the d i s c h a r g e . equation  (Ai5)  From  ( A l ) the time d e r i v a t i v e o f the c u r r e n t i s di dt  - B ~^TL  e  -Rt 2L  ( ^ \ c o s ^ t - IL. s i n ^ t )  or Rt  where @  = a r c t a n __R_  2L/>]  co s  (Al?)  -  59  -  a.  O r> o ~>  .3* '•'r d R  "i""!'!—B~""" /»—  '  ,  The e q u a t i o n f o r  this  circuit + Rt di  R t f i dt  _  c  -D  e  ^ L  where  - RT  i R j  The s w i t c h i n g  corresponds  equation  (Al)  the  di dt  — B ~/iVL  to  ? 1 V  I  time t = 0  is (A15)  $ (A16)  triggering  time d e r i v a t i v e —Ht 2L  b at  switch  siri/>it  TT  1 Lc  e  s o l u t i o n when t h e  a to c o n t a c t  ~~r  x  = 0  i  The a p p r o p r i a t e  i s moved f r o m c o n t a c t .:  +  dt  2  w h e r e R^ = R^+R^.  is  of  ( ^cos^t  the discharge.  the  current  From  is  - R__ s i n ^ t ) 2L  or •|where  0  = arctan  2 R  c  e  -Rt  cos  (^t  + © )  (A17)  s  - 60 -  The l o g a r i t h a m i c d e c r i m e n t LD d e f i n e d (LD)=  log  e  d  is  given  2JI sty  With the e x p r e s s i o n . R  f  t  / 1/  u  7  T + 2T  by (LD) =  b;-.  by  and L„ f o r  2L  (A18)  f  A3 and A*f i t a discharge  is  possible  by o b s e r v i n g 2  LD and P t h e p e r i o d we h a v e L = P c  to di . dt  1 1+TT + ( L D ) 2  2  calculate Measuring and R = L ( L D ) p  BIBLIOGRAPHY  P r o c e e d i n g s o f t h e 4th I n t e r n a t i o n a l C o n f e r e n c e o f I o n i z a t i o n Phenomena i n Gases, I 9 6 0 , IID 518.  1.  Garton,  W.R.S.,  2.  Garton,  W.R.S., of  3.  Ladenberg,  4.  Korff,  theRoyal R„,  Reviews  S.A., a n d B r e i t , 4  Ladenberg,  G.,  1957 >  A.,  A70  Society,  1934,  Physics, 5.  and Rajaratnama,  8l5.  o f Modern 1932,  Proceedings  Physics,  Reviews  5 243,  o f Modern  4-71.  R „ , and Levy,  S„,  1930,  Zeitschrift  Fur Physik,  65 189. 6.  Francis,  7.  Anderson,  8.  Kofoid,  9.  Spitzer,  10. D i e k e ,  G.,  I o n i z a t i o n Phenomena  J.A.,  J.M.,  i960,  L„,  Physics  Power  25,  J 75  Apparatus  of Fully  Page  394.  and Systems,  Ionized  90.  Gases,  51 999=  P. 81.  1954,  Journal  o f Applied  1952,  Journal  of  196.  G.H., a n d C u n n i n g h a m , Optical  12. R i e s z ,  Astrophysics,  G.H., a n d C r o s s w h i t e , H.M., Physics,  11. D i e k e ,  1932,  i n Gases,  Society  R., a n d D i e k e ,  S.P.,  o f America, G.H.,  1954,  42  the  187.  Journal  of Applied  Physics,  25, 196. 13.  Theophanis,  G.A.,  i960,  Review  31, 4.  - 61 -  of Scientific  Instruments,  FIGURE 1 - NEON LEVELS  <  FIGURE 2 - A P P A R A T U S  r^^^Insulating Plate iP  Copper Collar C  0  Wire Gauge  Kl r\ \  \ \ x  \A////// v\ v \\\\\\z  ///////  Window Wo  Quartz Flash Tube , Insulating Cylinder I  r  •/////////////////////  Plane Lead L_  St VT777~777  Insulating Plate I  (  I  4 cm-  <7-  Windows Electrode  \  Tube / /  /  /  \ \  \  Y  Tube  3  /~i  •S3  2. 5 cm  1 mm_ 3:  171  Z_Z  / / / / / / / /  V/J///A  r  z /  I  Deflection Plate D  PI / / / / / / / /  1  Z  2  Z  /  _  Extension Tube  F I G U R E 4 - WINDOW  KV V / *  IS S  GEOMETRIES  Z  Z  S N N I  W  Z  3  Reflection Plate D  Negative Electrode -  Trigger  FIGURE 5 - TRIGGERING  Electrodes  GEOMETRIES  FIGURE 6 - UAVI3 FORMS  Electrode - N  Electrode - P  Sidearm A  Resevoir a - Absorbtion Tube  >  Pump  Absorption Tube Pirani Gauge  McLeod Ga  Impurity Gas S u p p l y ^  \,\,  ^)  Needle Valve  b - Flow Scheme  FIGURE 7 - P L A S M A UNIT  1 Flash Tube  Input B Oscilloscope b - Synchronization  FIGURE 8 - S H U T T E R UNIT  FIGURE  9 -HIGH  VOLTAGE PULSE  GENERATOR  

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