UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Study of a perturbation in a glow discharge Baldis, Hector Alberto 1968

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1968 A67 B34.pdf [ 2.27MB ]
Metadata
JSON: 831-1.0085106.json
JSON-LD: 831-1.0085106-ld.json
RDF/XML (Pretty): 831-1.0085106-rdf.xml
RDF/JSON: 831-1.0085106-rdf.json
Turtle: 831-1.0085106-turtle.txt
N-Triples: 831-1.0085106-rdf-ntriples.txt
Original Record: 831-1.0085106-source.json
Full Text
831-1.0085106-fulltext.txt
Citation
831-1.0085106.ris

Full Text

A STUDY OF A PERTURBATION IN A GLOW DISCHARGE  by Hector Lie.,Universidad A THESIS  Baldis  A.  Nacional  de C o r d o b a ,  1964  SUBMITTED I N P A R T I A L F U L F I L M E N T OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF in  the  SCIENCE  Department of  PHYSICS  We a c c e p t required  this  thesis  as  conforming  to  standard  THE U N I V E R S I T Y  OF B R I T I S H COLUMBIA  December,  1967  the  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 f u l f i l m e n t o f the  advanced d e g r e e at the U n i v e r s i t y  Library  I agree that  the  study,  I further  permission f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y  p u r p o s e s may  be g r a n t e d by the Head o f my  It i s understood  that  Department o r by h i s r e p r e s e n -  copying or p u b l i c a t i o n of t h i s t h e s i s  f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my  Department nf The U n i v e r s i t y of B r i t i s h Vancouver 8, Canada Date  f o r an  s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and  agree that  tatives.  of B r i t i s h Columbia,  requirements  X><roe \M\OQ:V  Columbia  V\ <ol  written  permission.  for  ABSTRACT  The p e r t u r b a t i o n i n a g l o w d i s c h a r g e studied  theoretically  glow d i s c h a r g e  and e x p e r i m e n t a l l y .  a p e r t u r b a t i o n has  a small s i n u s o i d a l high frequency modulates of  atoms  tude  of  series Bates  the e l e c t r o n in excited  light have  et  is  give  developed better  lished  recently.  the  discharge  behaviour  of  assumptions suggested.  is the  are  The s e l f  discussed  lines  This  and of  density ampli-  the  Balmer  on t h e work and the  w i t h the  applying  number  phase  based  of  results  experimental  w h i c h have  absorption of  The  field.  the  thesis  theories  shown t o h a v e plasma.  four  A theory  agreement  t h a n do a l t e r n a t i v e  electric  first  is  I n an o r d i n a r y  p r o d u c e d by  and hence  in this  values  been  The r e l a t i v e  i n the  been measured.  al,  predicted  energy  states;  emitted  i n hydrogen  been  pub-  l i n e r a d i a t i o n by  a critical  effect  on  the  l i m i t a t i o n s and v a l i d i t y  and a m o d i f i e d e x p e r i m e n t  is  of  - i i i -  T A B L E OF CONTENTS Page ABSTRACT  i i  T A B L E OF CONTENTS  i i i  L I S T OF I L L U S T R A T I O N S  iv  ACKNOWLEDGEMENTS  v  Chapter  I  INTRODUCTION  1  Chapter  II  THEORY  3  Chapter  Chapter  III  IV  Chapter V  See.l  Elementary processes  Sec.2  Steady s t a t e  Sec.3  Solution  DESCRIPTION  solution  with  i n the .  plasma  .  .  .  a perturbation  .  7 .  OF EXPERIMENT  Sec.l  General  Sec. 2  Discharge  Sec.3  Optical  Sec.4  Phase s e n s i t i v e  3  8 12 12  tube  15  system.  15 detector  .  .  .  16  RESULTS  18  Sec.l  Theoretical  solution.  Sec.2  Experimental  .  .  .  .  18  values  20  CONCLUSIONS  24  Sec.l  Discussion  of  results  .  .  .  .  24  Sec.2  Comparison  with  other work.  .  .  25  Sec.3  Suggestions for  f u t u r e work  .  .  26  Appendix  I  E S T I M A T I O N OF ELECTRON ENERGY AND D E N S I T Y  28  Appendix  II  SOLUTION OF ELECTRON ENERGY MODULATION .  30  Appendix  III  COMPUTER PROGRAM  34  BIBLIOGRAPHY  42  -iv-  L I S T OF  ILLUSTRATIONS  Figure  Page  1  Modulation  2  Experimental  3  Results at  4 MHz  21  4  Results at  8 MHz  22  5  R e s u l t s a t 15 MHz  23  6  E l e c t r o n energy a t d i f f e r e n t degrees of modulation  of Balwer l i g h t arrangement  12 -  14  33  -v-  ACKNOWLEDGEMENT S  I would like Dr. J.H.Y/illiamson, tience this  throughout  thesis.  the  technical  for  their  help  to  sincerely  for this  I am a l s o staff, and  t h a n k my  his helpful work and the grateful  to  in particular advice.  supervisor  guidance  and  pa-  preparation  of  the  of  members  to Mr.J.Dooywerd,  CHAPTER  When  I -  INTRODUCTION  a plasma i s n o t f u l l y i o n i z e d t h e r e e x i s t i n i t  n e u t r a l atoms a t d i f f e r e n t l e v e l s o f e x c i t a t i o n . of  I f t h e degree  i o n i z a t i o n o f t h e plasma i s l o w , o r i f t h e plasma i s d e c a y i n g  from a g i v e n degree o f i o n i z a t i o n , t h e s e e x c i t e d atoms a r e an i m p o r t a n t c o n s t i t u e n t o f t h e plasma. The p o p u l a t i o n o f t h e s e atoms a t t h e d i f f e r e n t e x c i t e d l e v e l s a r e i n g e n e r a l o b t a i n e d from t h e b a l a n c e c o n d i t i o n s f o r a l l t h e e l e m e n t a r y p r o c e s s e s t h a t l e a d t o p o p u l a t i o n and d e p o p u l a t i o n o f t h e d i f f e r e n t A statistical  levels.  a p p r o a c h has been u s e d by B a t e s e t a l . ( 1 9 6 2 a )  t o s o l v e t h i s p r o b l e m and t o d e s c r i b e t h e g e n e r a l decay mechanism i n a plasma. D e t a i l e d c a l c u l a t i o n s have been c a r r i e d o u t for  a h y d r o g e n plasma and r e s u l t s have been s u c c e s s f u l l y  to r e l a t e d problems  applied  ( B a t e s and K i n g s t o n 1963,1964).  O t h e r a p p r o a c h e s have been g i v e n by D ' A n g e l o ( 1 9 6 1 ) , by Hinnov and H i r s h b e r g ( 1 9 6 2 ) and by B y r o n e t a l . ( 1 9 6 2 ) . These a r e u s e f u l a p p r o x i m a t e t h e o r i e s and s i m p l i f i c a t i o n s have been made i n t h e t r e a t m e n t o f t h e p r o c e s s o f decay. The t h e o r y o f B a t e s e t a l . i s i n r e a s o n a b l e agreement  with  e x p e r i m e n t a l v a l u e s , b u t i t c a n be a p p l i e d o n l y t o a d e c a y i n g plasma. F u r t h e r m o r e , t h e e f f e c t s o f b o u n d a r i e s have been i g n o r e d so r e s u l t s c a n be a p p l i e d o n l y t o l a r g e p l a s m a s . In o r d e r t o t e s t t h e model f u r t h e r , a s m a l l  perturbation  can be a p p l i e d t o t h e plasma and t h e r e s p o n s e o b s e r v e d . I n t h i s t h e s i s , t h e t h e o r y i s e x t e n d e d t o a l l o w p r e d i c t i o n s t o be made for  such a plasma. E x p e r i m e n t a l d a t a a r e t h e n o b t a i n e d by -1-  -2-  applying a small sinusoidal voltage in  a hydrogen  glow  discharge.  approximation,  the  s m a l l compared  w i t h the  say,  we h a v e t o  resultant  elastic)  in the of  the  to use  frequency. are  on t h e  (elastic,  i n each  of  of  is  and  to  energy. super-  electron  excited  the  be  spectral  atoms. line  s i n u s o i d a l components  The r e l a t i v e  measured  to  average  mean  plasma  order  that  inelastic  number d e n s i t y  t h e n have  a first  energy,  modulation i n the  will  the  p e r t u r b a t i o n has  a ripple  radiated  to  amplitudes  and  and compared v/ith t h e  at  phases theore-  predictions. the  conditions  of  our d i s c h a r g e ,  diffusion  to  the  to e l e c t r o n taken  i n t o account  elementary atomic tant. of  light  components  Under  be  of  perturbation  tical  due  this  Balmer s e r i e s  these  merely  i m p r e s s e d upon the  The i n t e n s i t y  energy  collisions  w i t h atoms,  energy'is  In order  average e l e c t r o n  impress  Due t o e l e c t r o n  perturbation  processes.  diffusion These  Bates  et  to  equations  is  the  walls,  although  processes are  not  recombination  important  relating  In a d d i t i o n there  diffusion  is  and has  the  different  deexcitation  this  is  not  considered  to  so  by impor-  i n the  work  al.  A comparison and D a v y ( 1 9 6 7 b ) charge  i n the  walls  the  is  made w i t h t h e  who s t u d i e d  i n hydrogen  work o f  respectively  and a p e r t u r b e d  Hamberger(1963)  a high frequency  glow d i s c h a r g e  dis-  i n helium.'  CHAPTER I I - THEORY  1)- E l e m e n t a r y p r o c e s s e s The levels  total  of  rate  of  excitation  p l a s m a c a n be  change  plasma.  of  processes  a)  the  a h y d r o g e n atom w i t h  number d e n s i t i e s  respectively. the  Due t o  The e l e m e n t a r y  the  the  number d e n s i t y o f  with  their rate  of a)  to  of  is  in state  the  processes  for  atoms  the  i  W r i t e n ^ and and  for  +  n  e  electrons the  the  i n t o account  p a r t i c u l a r decay equation expressed change  by  q u a n t u m number i ,  n e u t r a l i t y of  same a s  taken  caused  The s y m b o l s H ^ , H  respectively.  macroscopic  ions  g).  principal  atoms  different  a decaying hydrogen  obtained considering transitions  a h y d r o g e n i o n and an e l e c t r o n for  p o p u l a t i o n i n the  and i o n i z a t i o n of  f o l l o w i n g elementary and e denote  i n the  plasma,  electrons. are  shown  i n terms  of  in level i :  downward r a d i a t i v e  cascading:  —  t —  with  The c o e f f i c i e n t  A-y are  neous  e m i s s i o n of  gives  the  level  i . The s e c o n d  tion  the  Einstein coefficient  r a d i a t i o n of  d e p o p u l a t i o n of  level  term g i v e s  towards l e v e l i ;  -3-  frequency i the  due t o  V>ij • The  for  sponta-  first  transitions  p o p u l a t i o n due t o  term  from transi-  _4-  b'  inelastic  Hi  and s u p e r e l a s t i c  e  t-  c o l l i s i o n s with  electrons:  Hi  with  =-7 n ; n  dC J  of  the  have  (Bates the  et  C..  if  i < j  (and a l s o  electron  atom-atom,  These  c  inelastic  The c o e f f i c i e n t s  to  Gj -t* I r>j n Cjt J  A collision is  tions  Q  J  energy  and s u p e r e l a s t i c those  T  defined  if  below)  al.  1962a,  degenerate  s i o n s m u s t be  compared w i t h e l e c t r o n  states  of  a level  is  r a p i d to  body r e c o m b i n a t i o n :  collisions  assumed. ensure  Elastic  such  colli-  a distribution; ^NJ&J^^  with  d)  3  the  r- C  inverse  )  t  of  c),  collisional ionization:  \ H;  +  e  H  +  + e  +  with  = — H e f l i Cic cJ-t  due  neglected.  Wt. + e + e  an;  func-  page 2 9 8 ) . A u n i f o r m d i s t r i b u t i o n amongst  sufficiently  c) t h r e e  are  . Electronic transitions  a t o m - i o n and i o n - i o n c o l l i s i o n s are  a small effect  i > j .  ;  e  - 5 -  e)  radiative  H4. -f-  recombination: *=~  e  Hi  I taP  <-  J  l  }  with  .  a  absorption  fj thick, tion  = 0<? Act  m  occur.  then balanced  a)  The  by the  correspond  and e)  t o be  must  not  exist.  dividing  each  The  This  of  discharge  the g)  account  is  electrons tion  to  to the  effective  of  processes  arc  radiative  depends line  by.  on the shape  the  is  that  has  atomic the  The r a t e  the to  spectrum,  conditions  radiation; taken  into  diffusion  gives  a  change  is  due t o  a  excited  i n c l u d e d but  c o n t r i b u t i o n due t o of  of  contribu-  d i f f u s i o n of  diffusion is  by  (Holstein,  I n a s i m i l a r way t h e r e due t o  found  obtained  be  by a m b i p o l a r  part  transitions  boundary  of  recombination  ground s t a t e  electrons.  decay  of  by a t r a p p i n g f a c t o r  atoms.  compared w i t h  given  p l a s m a was  main s e r i e s  process  walls. This  walls. This  diffusion  the  upwards and downwards  atoms  important  In our c a s e ,  summation i n  between  to  not  i n the  the  ground s t a t e  the  absorp-  and the  towards  contribution to  transitions  and upon the  the  i o n i z a t i o n by l i n e  upward t r a n s i t i o n ,  d e i o n i z a t i o n caused  the  optically  terms  important  the  is  reverse  trapping factor  another  plasma  are  A coefficient  1947).  the  c o r r e s p o n d i n g downward t r a n s i t i o n s  be e x c l u d e d .  balance  If  and photo  these  partially thick  so a c o m p l e t e does  to  —  radiation.  upward t r a n s i t i o n s  will  that  of  ;  is  ambipolar  these  -6-  ine.^  tzAOS?^  dnc  „  ^2.4Q5^  where D  &  ficients of  the  ered  and D a r e  n  D  the  respectively  discharge  (-Df- = |.26  n c  .  3.7?  a m b i p o l a r and atomic and r  is  the  sec")  diffusion  r a d i u s of  the  coef-  capillary  tube.  into  all  the  elementary  processes  consid-  above,  we c a n w r i t e f o r  the  total  of  of  of  4-  account  atoms  in level  OJ A l f  JL  -n.niCic  - Z nc n C«j  state  performed  of  radiation  is  p o p u l a t i o n s have allow for into  Cji  Dane"  transition  c a n be c o m p a c t e d  L nj nc  +  radiative  to  change  _(*^esf Dni ^ H H W  the  absorption  steady  +  c  e  where A ^ j a r e  rate  i :  + n S C J + n o A ci  is  x 10*  Taking  population  self  lO%Te(^)scc-)  X  the  taken  been  changes form:  probabilities  into account.  calculated, i n A ^ j , The  an last  v/hen  When  the  the  iteration equation  -7-  for  i  and j  account.  running from 1 to N i f  This is  a system of  c a n be s o l v e d t o g i v e  the  N levels  N equations  decay of  the  are  with  taken  into  N unknowns  plasma.  that  The v e c t o r  Rj_  is:  fK  2  Equation  (1) g i v e s  i n each  one o f  of  (or  ions  vation  -j- A c i  ^ ( ~ — ) D o . 0*  of  the  the  levels.  number o f  the  total  rate  of  of  of  electrons)  number o f  Y_r>i -v- lie =  change  The r a t e  free  - 1 - C a De  Oc  the  change is  •  CO  number o f of  the  atoms  number  g i v e n by the  conser-  particles  O4o4al  ^  L  which  yields a rate  cine _ „ y  2)-  Steady  state  In order  to  of  change  Mi  solution. find  a p e r t u r b a t i o n i n the  a s o l u t i o n of electron  t i o n m u s t be f o u n d f i r s t . (1) r e d u c e s  to  For  equation  energy, this  the  (1) a f t e r  steady  state  p a r t i c u l a r case,  applying solu-  equation  -swhere the of  this  to  fulfil  3 )-  m a t r i x Qj_j a n d t h e  system of  equations  equation  Solution with  Rl  (4j i s  computed  ficients  state  above,  C-•,  do we h a v e  no  to  solution  a  are  valid.  the  to  The  functions  S T  g  to  the  We h a v e  now  +  S  order  but  T  e  of  n?  energy,  and the  vector  through  coef-  n . e  So n o t  a n d R^ f r o m we must  c a n be d o n e  by  electron  replaced  energy the  by  6Qij  corresponding  nf  in  the  allow  only steady  for  linearising  s m a l l changes i n n^.  i n the  o f Q . . a n d R^ a r e  This  of  function  g  e  electron  P.; + S Ri with  solution  normalized  m a t r i x Qj_j  a Change i n T ,  a n d R..- w i t h r e s p e c t  the  change of Q j j  changes i n n .  F o r a change  t o be  to  The  and an e x p l i c i t  Qi  Q «j +  applied  implicit  effect  values  is  longer  consider due  have  known.  perturbat,ion.  the A  of  etc.  will  Rj_ a r e  (3).  When a p e r t u r b a t i o n equation  vector  change  i n atom  populations  steady  state  -9-  Using expression  (3) and r e t a i n i n g o n l y t h e f i r s t  J  cit  o r d e r t e r ms •  j"  As  Ri ( )e  y  He)  we have  SQij =  SR;  5n  + §CL0'  c  = ?_Ei §n -;- a£i e  ST, §T<  then  (5)  The m a t r i x o f t h e f i r s t  term i s o f o r d e r N and has a l r e a d y  been c a l c u l a t e d f o r the v a l u e T  g  i n the s t e a d y s t a t e s o l u t i o n ,  The p o p u l a t i o n of i o n s ( o r of f r e e e l e c t r o n s ) S e n  c o n s i d e r e d as the p o p u l a t i o n o f a f i c t i t i o u s  c a n  (N+l)th  ^  e  level  to  be i n c l u d e d a f t e r the N r e a l l e v e l s . Thus the c o e f f i c i e n t s  of  ^ e ^ n  n  equation  (5) can be w r i t t e n as the (N+l) column  e l e m e n t s o f a new m a t r i x Q j j o f o r d e r  (N+l) :  -10-  This  term g i v e s  in  any  in  ion population  added  level  the  to  the  Equation  due  contributions  to  the  is  the  change  in  change i n i o n p o p u l a t i o n .  obtained  N equations  (5) c a n be  to  in  from e q u a t i o n  (5) a s  compacted  population This  change  (3) a n d c a n  a N + 1 row i n the  be  new  as:  ^r(on;) = Z Q i j o p j + ?; where P.  is  Take of  the  only  the  form e x p ( j w t ) order  components then  be  The at  (see  terms  we c a n a s s u m e t h e dependance.  (fo)  perturbation:  a small perturbation  first  matrix  neglected  the  e  appendix  i n the  solution  ^T  of  I I ) . A s we  derivation £n^  second  perturbation  w i t h a time  of  considered  equation  to have the  order  terms  frequency.  dependence  same  (5), time  would have  Equation  no  (6) c a n  written:  juoSo;  «^Q\j&Dj  + Pi  (8)  -11-  Q ! . a n d R. t h e n be  are  solved  known a n d r e a l .  The  for  quant5.ties  S i« The  i n appendix  III  the  program used  for  obtained  listed  are  this  complex is  given  i n chapter  the  populations  of  equations  can  computer  n  and t h e  results  IV.  The m o d u l a t i o n i n i n t e n s i t y modulation of  system  of  line  i n both  V'IJ d e p e n d s  levels  i  on  the  a n d j . To  first  order  - W q A S U n i - T ^ n . - ^ )  Sly where  w is  the  of  level  lation  m a t r i x Q! . . radiative  These  product  the  penetration  i . A similar correction  The e f f e c t  of  this  is  depth  m u s t be  times  the  a p p l i e d to  t o add an e f f e c t i v e  for  our  made v e r y discharge.  little  difference  to  the  poputhe  reverse  transition  corrections  results  of  final  CHAPTER I I I  - D E S C R I P T I O N OF EXPERIMENT  1 ) - General The electric tion  plasma field  i n the  studied  i n a hydrogen  electron  small A.C. electric was  observed,  relative  energy field  and the  phase  were measured. four  These  He(4101.74 A ) .  was  produced  discharge was  amplitude  different  lines were  A ) , Hg(4861.33 output  by  discharge.  measurements  A typical  by a p p l y i n g a D . C .  tube  produced  on the  relative  among t h e  l i n e s H (6562.79  shown i n  here  and the  superimposing The e m i t t e d  of  modulation  of  the Balraer  taken  for  the  from the  PON  M  H  Fig.l T he  - M o d u l a t i o n of  amplitude  scales -12-  Balmer are  light and series  and  photomultiplier  Fig.l.  light  arbitrary,  a  first  A ) , 11^(4340.47 A)  D.C  COM  perturba-  is  -13-  Th3 at  least  lines is  r e l a t i v e m o d u l a t i o n were  t e n p i c t u r e s . The v e r t i c a l s c a l e s  i n these p i c t u r e s are  different  sity  o b t a i n e d by a v e r a g i n g  for  each  line.  of  the  different  arbitrary since  the  For each  the z e r o  trace,  was o b t a i n e d b y b l o c k i n g t h e e n t r a n c e  slit  over  light  of  intensity of  inten-  t h e mono-  chromator. To o b t a i n t h e p h a s e was u s e d . Due t o direct  s t a t i s t i c a l noise  measurement  A phase  measurement,  of  detector  is  sensitive  been  a non-linear device,  i n some way m i x e d w i t h  signal  of  In t h i s experiment,  signal  c o u l d have  that  feeds  was a l a r g e straight phase  increase  of  to  the discharge  Instead of  this,  the r e f e r e n c e  from a second p h o t o m u l t i p l i e r l o o k i n g at the d i s c h a r g e .  T h i s arragement  phases  c o u l d be  observed with is  reference reference  oscillator  but  there  n o i s e when a  had the  Fig.2.  s i g n a l was  obtain  a particular line  disadvantage  detector  was  an o s c i l l o s c o p e . The g e n e r a l  shown i n  the  that  of  only  measured.  The o u t p u t f r o m t h e phase  iment  in  c o n n e c t i o n was made f r o m t h e H . F . o s c i l l a t o r t o  detector.  relative  tube,  e l e c t r i c a l p i c k up of  a  the  been taken from the h i g h f r e q u e n c y  the A , C . v o l t a g e  any  inaccurate.  which the modulated s i g n a l i s t h e same f r e q u e n c y .  device  from the D . C . d i s c h a r g e ,  phase would have  sensitive  a phase  i n t e g r a t e d and set  up of  the  exper-  -14-  OB L A V U M I T  F - o p t i c a l -f i\-l*c*" P.M.- phoTornoH'tpUer  PHASE s e w s m v e OSTECTOR  tNT£6f*ATOft  oscauoscope  Fig.  2  - Experimental  o v - r a n c j m e n T  -15-  2 )- Discharge  tube.  A standard hydrogen G e i s s l e r Two e x t e r n a l of  the  D.C.  tube  electrodes i n order  electric  were  to  tube  located  a p p l y the  f i e l d was a p p l i e d t o  was v i s e d a s  on the  way e l e c t r i c  i s o l a t i o n was o b t a i n e d  llator  and D . C . power s u p p l y w i t h o u t use  The  electrodes.  between  of  region  field.  internal  In t h i s  source.  capillary  H.F. electric the  a  H.F.osci-  capacitors  and  chokes. The  steady  and under the  this  positive  (appendix density lator D.C.  T  e  voltage.  3)-  Optical  c o n d i t i o n the  This  was s e t  10 % i n t h e  was s e t  up w i t h  gives  estimates  °K a n d n  of  = 3xl0  4  up t o  g i v e a peak v a l u e  This gives  electron  g  = 10  monochromator,  be  35  cm" . 3  of  10 mA,  field  volts  electron  1 2  and  The H . F . of  oscil-  the  slightly less II).  was o b s e r v e d  with  in  cm~^torr~^  energy  a tenth  (appendix  model 82-010, of  f/10.  with  a linear  A/mm  and a speed  1P21  photomultiplier tube.  with  a s i m i l a r p h o t o m u l t i p l i e r and the  r e f e r e n c e was i s o l a t e d  strong  of  applied  than  system.  The m o d u l a t e d l i g h t  as  to  a perturbation  energy  a current  a x i a l reduced e l e c t r i c  c o l u m n X / p was e s t i m a t e d  I).  of  discharge  enough  a Jarrel-Ash d i s p e r s i o n of  The s i g n a l was o b t a i n e d The r e f e r e n c e  with  t o be u s e d a s  filters.  reference  Ebcrt  with  s i g n a l was  particular Only H signals.  Q  16  a RCA  obtained  line  and H  used g  were  -16-  In o r d e r essary  t o measure  the  depth of  modulation, i t  to  o b t a i n the D . C .  s i g n a l from the  addition,  a 50 XI l o a d was  necessary  ance of  the  phase  sensitive  c o u l d n o t be u s e d the  phototube.  without tors  in the  saturation,  output  up c a p a c i t o r s  zero  vertical  4)-  Phase  the  large  anced  device.  diodes  500 M H z . I t  i n the  possible the  dynode  (10  roA).  is  (model  taken with a  1 0 5 1 A ) was u s e d a s a  This mixer c o n s i s t s 1959)  designed  of  a r i n g of  and o p e r a t e s between  for  use  t o pay interest  for  clean  between  sensitive  ( F a u l k n e r and H a r d i n g , 1966;  four  phase bal-  0 . 2 MHz a n d  w i t h 50 11 s y s t e m s a n d t h i s  price  phase  Fig.l  detector.  worthwile  Different  speed  1 mV/cm.  implies a small signal operation.  of  shown i n  f o r IIg , w h i c h was  impedance  frequencies  increase  stages.  p i c k up n o i s e  trace  A further  a n o d e was o b t a i n e d by u s i n g  five  electric  (Wilcox, is  of  resis-  last  sensitive  anode  biasing  i n the  of  the  current  at  sensitivity  to  follower  output  A Hewlett-Packard mixer sensitive  an e m i t t e r  imped-  voltage  as  reference  input  In  to a l l o w a reasonable  current  The amount o f in the  to match the So,  nec-  photomultiplier.  a n d 50 Si h a d t o be c o n n e c t e d  In order  was made a s  device.  was  noiseless  But t h i s  was  o p e r a t i o n at  low  a the  4 MHz a n d 15 M H z . detector  c i r c u i t s wore  Scantlebury,  1961)  but  it  tried was  not  -17-  possible small  to get  p i c k up n o i s e A s B.C.  may be u s e d , input to  was  at  the  but  A.C.  the  A large  the  output  observed  sensitivity  possible  to  detect  signals  of  The phase the  signals  a zero ture.  output So t h e  independent In order delayed  of  a tenth  i n phase  signal  is  input  to get  i n steps  and a c a l i b r a t e d  of  the  sufficiently  mixer a high  l o a d s h o u l d be capacitor  signal.  was  501L o r  impedance  less  t h e n u s e d as  T h i s gave a s t e a d y  1 mV/cm. W i t h  of  shift a  of  set  at  the  l o a d and D.C.  up i t  at  signal a  was  to a delay  be-  nanosecond.  o r 180°  gave a maximun o u t p u t out  of  phase.  o b t a i n e d when s i g n a l s  when  Furthermore, are  a null-detector  in  with  quadraoutput  amplitude. a null  0.1  box.  this  corresponding  detector  m i x e r was u s e d a s of  with,  frequencies.  output  a phase  sensitive  are  perfomance  w i t h a T e k t r o n i x 585A o s c i l l o s c o p e  vertical  tween  that  load at  frequency.  integrate  that  a satisfactory  reading,  nsec,using  the  extra  reference  signal  pieces  50 i l c a b l e  of  was  CHAPTER  IV - RESULTS  1 ) - The o r e t i c a 1 _J s o 1 u t i o n . To f i n d tures  of  energy  is  a p p l i e d , the to  first.  do s o ,  (1962a).  in  not  the  energy  of  p o p u l a t i o n s , and the  of  equations  of  the  Regarding the  same s o u r c e s  e  and so t h e  An e s t i m a t i o n  Once t h e used to  values  obtained  of the  as  c o l l i s i o n a l processes, coefficients  et  al,  of T  this  energy  and n  e  are  e  are  is  solved.  m u s t be  com-  are  well  i n Bates et  precise  have been  u s i n g the  These c o l l i s i o n a l c o e f f i c i e n t s T .  (7))  deparelectron  m u s t be  Einstein A coefficients  o b t a i n e d from the  available  (8)  m a t r i x Qj • (equation  a s i m i l a r way t o B a t e s  (1959).  is  values  system  The v a l u e s  known a n d a r e  are  expected  t h e s e f r o m e q u i l i b r i u m when a p e r t u r b a t i o n i n  In order pute  the  formulae  al.  results  computed of  functions  of  Gryzinski electron  made i n a p p e n d i x  estimated,  the  I.  program  e q u i l i b r i u m p o p u l a t i o n s and hence  the 17  total but  number o f  its  particles  exact value  s o c i a t i o n of  not  t  o  t  a  l  .  T h i s s h o u l d be a r o u n d 10  v / e l l known s i n c e  hydrogen molecules  The c h a n g e we c a n  is  n  in populations  is &n  not ±  are  the  degree  Replacing  this  XI  complex  for -18-  dis-  quantities,so  + j vfi  expressions  'cm  known.  write  «  of  6 n^^ i n e q u a t i o n  (8):  —"3  -19-  k Separating  real  part  and i m a g i n a r y  part  we  have  the 2(N +  1)  equations:  (°0  (i,W=| N + l) y  with  2 ( N + 1) unknowns x ^ a n d y ^ . E l i m i n a t i n g x ^  The.vector electron in the  energy  the e l e c t r i c system The  is  ST .  This  field  i n appendix  e  of equations  i s given  ( 9 ) c a n be  s o l u t i o n f o r the f i r s t  the p e r t u r b a t i o n  with  represent series.  respect  II.  When Q J ^ a n d  four  The r e l a t i v e  considered  expresed  lines  of the Baimer  n a m e l y 4,  with  respect  f o r three  8 a n d 15  state  of each  t o the phase  delay  thus  these line  i n these  of l e v e l  i n nanoseconds.  different  series  amplitudes are  emitted  p h a s e s a r e a-lso g i v e n  as an e q u i v a l e n t  were p e r f o r m e d  The  of modulation  a r e known,  solved.  to the e q u i l i b r i u m  the depth  i n the  i n terms o f the m o d u l a t i o n  shown i n f i g u r e s 3, 4 a n d 5. T h e r e l a t i v e  given  are  i s c a l c u l a t e d by u s i n g  gives:  perturbation  n  figures i n the  f i g u r e s and 3  and a r e  Calculations frequencies,  MHz.  c a l c u l a t i o n of s e l f  absorption  i n the plasma  and t h e  -20-  evaluation  of  the  transition probabilities  collisions  were p e r f o r m e d n u m e r i c a l l y u s i n g  by D r . J . H . W i l l i a m s o n .  that  These  model of  the  completely  Lyman l i n e s  model,  w h i c h were o b t a i n e d  given  for  are  are  series  not  absorbed  comparison  2)- E x p e r i m e n t a l  quencies  of  figures  4,  the  and the  values  t o do t h i s of  since  of  the  to  detector  Considering for  the is  example  values a  of  also  are  as  fre-  are  an  given  equiva-  amplitudes  obtained  trace.  have  theoretically.  only relative  Due t o  measurements  values.  0.5  nsec  at  at  4 MHz, T h i s b r i n g s  5.  have an  the  the  signal  signal,  a frequency  errors for  from fluc-  accuracy sensitivity  amplitude.  a difference of  15 M H z , a n d  a maximum e r r o r o f  The c o r r e s p o n d i n g 3, 4 a n d  statistical  measurements,  t h e w e a k He  was e a s y d e t e c t a b l e  in figures  are  obtained  expressed  a f u n c t i o n of  nsec  given  this  5.  values  these  phase  0.1  line.  for  the  a m p l i t u d e m o d u l a t i o n were t a k e n  discharge,these  5%. W i t h r e s p e c t  particular  of H  oscilloscope  of  phase  assumes  taken with perturbation  8 a n d 15 M H z , a n d t h e  photographs of the i n the  plasma  by z e r o ,  A-y  3, 4 a n d  have been  The measurements  tuation  i n appendix I I I .  a l l . The r e s u l t s  by r e p l a c i n g  i n nanoseconds,  is possible  written  values.  been n o r m a l i z e d to It  electron  t r a p p e d whereas a l l  3, 4 a n d 5. The p h a s e s a r e  delay  to  subprograms  a hydrogen  at  in figures  The measurements  lent  included  A common s i m p l i f i e d  higher  in  are  due  10% f o r  each l i n e are  of of this also  F; . 3 9  Results at  4 MHz .  O - P r o p e r s e l f a b s o r p t i o n ; A -Lyman t h i c k ; • - D a v y ' s approach; J - E x p e r i m e n t a l v a l u e s .  Ff . 4 9  - Re so! i s  S T  8  MHz.  O - P r o p e r s e l f s b s o r p t i o n ; A -Lyman t h i c k ; 0 - D a v y ' s approach; J - E x p e r i m e n t a l v a l u e s .  Ff . 5 9  © -Proper s e l f absorption;A  -  Resells sf  15  MHz..  -Lyman t h i c k ; Q - D a v y ' s approach; £ - E x p e r i m e n t a l v a l u e s .  CHAPTER V - CONCLUSIONS  1)-  D i s c u s s i o n of Figures  expected levels  3,  4 and 5 shows r e a s o n a b l e  and observed  i n most c a s e s .  caused by e r r o r s Gryzinski's 3 of  results.  of  theory.  between  the modulation i n the  The d i s c r e p a n c i e s  i n the c o l l i s i o n  the  excited  i n some c a s e s may be  coefficients  F u r t h e r experments,  this chapter,  tively,  values  agreement  predicted  as suggested  c o u l d be c a r r i e d o u t  to check  in  by section  this. Alterna-  t h e a s s u m p t i o n s made i n t h e m o d e l s h o u l d b e r e v i s e d a n d  reconsidered. The e l e c t r o n e n e r g y Maxwellian, electric is  and t h i s  field  a weak p o i n t i n t h e  a p p l i e d and so the  n o t M a x w e l l i a n any l o n g e r .  distribution, transitions have ate  been state  have  of  electrons  due t o a t o m - a t o m ,  levels  last  of  molecules  discharge the  one,  constituent  to the  the degree of  and the e f f e c t s  the  shown by t h e d a t a  these  collisions the of  degenermolecules  assumptions  to estimate  the  effect  d i s s o c i a t i o n was u n k n o w n . The  the ends of  which i n d i c a t e s of  radial  the w a l l s . E l e c t r o n i c  atom-ion or i o n - i o n  showed s t r i a t i o n s a t  discharge,  to  The m o s t i m p o r t a n t o f  that  the  capillary region  molecules are  an i m p o r -  plasma.  The i m p o r t a n t r o l e o f is  diffuse  a n d i t was n o t p o s s i b l e  since  an  a x i a l energy d i s t r i b u t i o n  The same a p p l i e s  was a s s u m e d ,  be  theory since  a u n i f o r m d i s t r i b u t i o n amongst  been n e g l e c t e d .  the  tant  since  ignored,  is  of  is  is  d i s t r i b u t i o n was a s s u m e d t o  self  in figures -24-  a b s o r p t i o n i n the 3,  4 a n d 5 . The  discharge  corrected  -25-  c a l c u l a t i o n of s e l f a b s o r p t i o n showed that the plasma i n our experiment was o p t i c a l l y t h i c k towards Balmer l i n e s and, l e s s e r degree, towards the remaining  '".o a  series. This indicates  that a c o r r e c t c a l c u l a t i o n of s e l f a b s o r p t i o n i s important, and inaccuracy i n the p r e d i c t e d values could a l s o be due  to  inaccuracy i n the e v a l u a t i o n of the t r a p p i n g f a c t o r since the r a d i a l d i s t r i b u t i o n of ground s t a t e and e x c i t e d atoms i s not known.  2)-  Comparison w i t h other work. Hamberger(1963) using a s i m i l a r c a p i l l a r y discharge w i t h  a pure A.C.  e l e c t r i c f i e l d , c a l c u l a t e d the r e c i p r o c a l of the  time constant f o r the decay of e l e c t r o n d e n s i t y , and even f o r pressures as low as 0.2  t o r r , he found i t to be of the order  5 —1 of 10 sec . On t h i s ground, he concluded that there w i l l be no change i n e l e c t r o n d e n s i t y when the frequency of a p p l i e d 7 -1  e l e c t r i c f i e l d i s of the order of 10  sec  , due to the long  d i f f u s i o n decay constant. The t h e o r e t i c a l r e s u l t s obtained here disagree with h i s c o n c l u s i o n s and show that n  e  varies  j u s t as do the populations i n the e x c i t e d l e v e l s . As the r e c i p r o c a l mean l i f e - of l e v e l 5 i s comparable with a discharge frequency  of 10 MHz,  Bamberger expected to f i n d  a p p r e c i a b l y l e s s modulation of H^.. able decrease of modulation. crease of modulation of H  In f a c t he found no n o t i c e -  In our experiment, a s l i g h t i n -  i s found e x p e r i m e n t a l l y , i n agree-  ment with the t h e o r e t i c a l p r e d i c t i o n s .  -26-  A modulated glow discharge Davy(1967b),  a l t h o u g h h i s measuiements  1 MHz. H i s t h e o r e t i c a l polar  d i f f u s i o n to  ground s t a t e . density gy,  the  a frequency  of  the  only for  modulation of  of  the 0  electron  0.51,  0.73  than these values.  show t h a t  8n  e  phase  and 0 . 8 4 nsec  and $ T  the  ener-  excited  a n d T T / 2 . When a p p l i e d t o  4 M H z . Our m e a s u r e m e n t s  results  ambi-  electron  l i g h t r a d i a t e d from  predicts  by  below  and i o n i z a t i o n d i r e c t l y from  h i s formulae  of  larger  theoretical  the  shifts  for  respectively  show p h a s e  shifts  In a d d i t i o n ,  our  e  are  not  10  necessarily  quadrature.  Suggestions  for  For future be u s e d ,  future  work,  operated  would decrease the  (1967a) accounts  that  between  lines  times  3)-  phase  studied here,  t h e Hg t o H g  in  the w a l l s  He p r e d i c t s  should l i e  discharge  at  model  w e r e a l l made  s h o u l d l a g -ir/2 b e h i n d t h e m o d u l a t i o n o f  and t h a t  states  i n h e l i u m has been s t u d i e d  at  the  a discharge a lower gas  d i f f u s i o n to  c o n d i t i o n s towards  Lower gas  work.  densities  with a large pressure.  the w a l l s  a M a x w e l l i z a t i o n of  will  decrease  the  self  A larger  tube  In order governing  will  also  t o get  electron  the discharge,  insight  i n t o the  a perturbation of  improve energy.  a b s o r p t i o n of i n the  a l l o w a d i r e c t measurement  a better  should  diameter  and s h o u l d  a t i o n w h i c h was f o u n d t o p l a y a n i m p o r t a n t r o l e A larger  diameter  of T  radidischarge  e  mechanisms  different  kind  and n . e  -27-  should be used. Instead of producing the p e r t u r b a t i o n through a modulation of the e l e c t r o n energy, an a b s o r p t i o n experiment c o u l d be performed, u s i n g a modulated source of l i g h t  (similar  t o that d e s c r i b e d by Hamberger) w i t h the same gas as i n the discharge under study. The l i g h t from such a source could be modulated up to 100% and used to produce a d i r e c t p e r t u r b a t i o n t o a p a r t i c u l a r atomic l e v e l , by pumping between two given l e v e l s . In our experiment, the e l e c t r o n i c pumping was done mainly from ground s t a t e t o a l l the upper l e v e l s . -  A P P E N D I X I - E S T I M A T I O N OF ELECTRON ENERGY AND D E N S I T Y  These  quantities  and e s t i m a t e d  values  have not been measured were u s e d .  g i v e n by von Engel(1965) r a d i u s cpR, where of  the gas,  positive  p is  is  the  gas  the  assumed  pressure discharge  the reduced  o n l y on the  and R i s  the r a d i u s of  tube used i n the  10 t o r r .  we o b t a i n f o r  p a g e 243) T e = 3 x 1 0  the  cm a n d t h e  U s i n g c - l . 0 5 x 10  e l e c t r o n energy  the  impedance  of  field is  the p o s i t i v e  was p e r f o r m e d b y m e a s u r i n g t h e quency  at  the  external  given  over  real). was cm" is  and p o s i t i v e  where  reactance  The D . C . component  1  torr" . 1  p  c  of  of  = 35 k i l / c m  1965  drift velocity  g i v e n by the m o b i l i t y  equation:  -28-  a  value  In order  to  of  This fre-  the A . C . e l e c t r i c the g l a s s at  field  between frequencies  The  (assumed  the- t o t a l c u r r e n t  a x i a l reduced e l e c t r i c  Now, t h e  if  as a f u n c t i o n of  c o l u m n was n e g l i g i b l e  i n t h i s way was Z  10 mA, s o t h e  With  c o l u m n was m e a s u r e d .  5 MHz, compared w i t h the column impedance.  measured  ,  (von E n g e l ,  obtained.  impedance  electrodes  was a p p l i e d . T h e c a p a c i t i v e electrodes  pres-  °K.  4  the a x i a l reduced e l e c t r i c  do s o ,  the  gas  as  T h e e l e c t r o n number d e n s i t y c a n be e s t i m a t e d of  nature  experiment,  by v o n E n g e l f o r h y d r o g e n , we h a v e c p R = 0.525 x 10 this value,  are  discharge  dependent  c a p i l l a r y r e g i o n i s 0.05  t o be  experiment  e l e c t r o n energy  as a f u n c t i o n of  a constant  column. In the  the r a d i u s of sure  c is  Values of  in this  impedance  t o be  i n the  purely  discharge  f i e l d i s X / p = 35 electrons  in  volt  hydrogen  -29-  Ve  =  3 J  x  |0  5  X  (cm sec"')  ;  and the c u r r e n t d e n s i t y i s :  j a  e  He Ve  2 So then, i f we w r i t e f o r the t o t a l current I = n R j , we have: n«  «•  3.7 x  -I a 10= -rr R  =(0.54  e  X/p  ^  *io'*)  1 a  R *X/p  Using the value of X/p obtained above we get f o r the e l e c t r o n 12 —3 number d e n s i t y n = 10 cm e  APPENDIX I I  Ii t,  the  SOLUTION FOR ELECTRON ENERGY  is  t h e mean e n e r g y  cnange  between field,  T  -  d(T )  of  an e l e c t r o n  d u r i n g a time dt  e  the energy  is  at  instant  g i v e n by t h e  g a i n due t o a d i s p l a c e m e n t  a n d \,he l o s s  some  difference  dx i n t h e  due t o c o l l i s i o n s w i t h t h e  gas  electric  atoms  (Harris  and v o n E n g e l , page 4 9 6 ) :  dlTa) = e E dx where  - IC P T e c i t  e is  the  electron charge,p  q u e n c y , IC  the  average  s i o n and E the case  modulation.  f r a c t i o n of  (external)  the e l e c t r i c  field  electric  E has  where X i s  a. s\n  T-  modulation at  A t h i g h gas  pressure  electron drift velocity field,  is  i n each  energy  lost  field.  In our p a r t i c u l a r  J  the  (A-2) electric  field  frequency w ( a «  (10  torr  and a  i n our experiment)  i n phase  w i t h the  the  oscillating  elec-  so  (A-2>)  1  z is  the a x i a l coordinate  the m o b i l i t y of  i n our case frequency  is  1).  M  is  colli-  )  u) c  •^5- = l ( | fQsinco-t) 4* P -. ' where  fre-  as:  t h e D . C . component o f  the f r a c t i o n of  electron collision  a D . C . component p l u s a s m a l l A . C .  So E c a n be e x p r e s e d  gr - )( (i  tric  the  (A-0  is  since p ^  the at  i n the  electrons.  t h i s pressure  11 10  sec  discharge  This expression the  electron  1 and the h i g h e s t -30-  tube is  a n d \i justified  collision  angular  frequency  -31-  applied of C  i s <J^ 1 0 °  sec  - J  and u d e r i v e d  ,P  \  This also  justified  from e x p e r i m e n t a l  the use  data  of  obtained  values i n D.C.  discharges. Under t h i s field  X / p > 15  approximation  conditions volt  cm  for  torr  1  \  values of  reduced  Hamberger(1963)  electric  uses  the  KV/p:  3.23  =  and f o r  l 0  x  ( e  7  ,  3  ,  T  U-4)  -])  a  P Since  i n our d i s c h a r g e  (appendix  I),  this  X/p i s  approximation  Using expressions c a n be  found  (A-2),  is  (A-3)  t o be 35 v o l t  cm  torr"  1  1  justified. and  (A-4),  equation(A-l)  written:  -dls..^ ep-^-O+a Using numerical values for  sir?co-tI"-3.23  xio (e° ~l)pTe Te 31  7  u and X / p :  eUf = A ( l + a sinco-tf - B ( e  0 , 3 , T e  -i)Tc  CA-S)  d -t where  A = 4.53  (A-5)  is  solved  degrees of plot  has  electron  9  eV s e c "  b e e n made f o r energy  increased  is  applied,  the the  1  and B = 3 . 2 3  x 10  numerically using Runga-Kutta  modulation.  is  frequency  x 10  is  Solutions  are  shown i n F i g . 6 . An  f o u n d t o be s i n u s o i d a l .  2w a n d i t s  pattern  electron is  also  variation  If  becomes d i s t o r t e d .  v a r i a t i o n of  1  energy plotted  Equation  method f o r  10% m o d u l a t i o n a n d t h e  pattern  sec" .  8  the  If  different enlarged in  modulation  a pure A . C .  is for  field  found to have comparison  in  a  -32-  F i g . 3 . T h i s p a r t i c u l a r r e s u l t has been obtained p r e v i o u s l y by Hamberger  (1963).  -33-  Te  Fiq.6 - electron degrees  energy at different of m o do I s i too .  APPENDIX I I I - COMPUTER PROGRAM  -34-  s ^FORTRAN C COMPUTE _C_ C C  EQUILIBRIUM  POPULATIONS  AND  A PERTURBATION IN ELECTRON ENERGY UNITS ARE DEGREES» "NANOSEC, CUBIC  . THEIR  CHANGE  WITH  RESPECT  9 c  TO  '  3  MICRONS  c  . D I M E N S I O N QM_( 2 0 »_20J_»_P0P ( 20 ) * R E C O M B J _ 2 0 _ ) » R E C 0 P J 2 O J »_TR ( 5 0 _ _ 1 " v ( p o ) , X ( 7 0 > , A V 3 ( ? 0 > , A \ G ( 2 0 ) , A R ( 2 0 , 2 0 ! , Q v o ("Q , 70) , Q O M v ( 2 0 , 2 0 ) ,  [ "  v  2  QQOM(20,20),F(20,20),A(20,20),POPST(20), COMMON COMMON  WWH(20>,  Z  j  PERT(20>  .  / Q A / A A ( 20 • 2 0J_ /TP/ SH(20>, C(20,20),  CC(20),  CIC(20),  AC(20),  ACE(20 )  N = 10 N P = N + 1__  ,  PI=3.1 A 159265 D I FF = . 2 2 E-3 READ I N E I N S T E I N A C O E F F I C I E N T S READ (5,101") ( ( A ( I , J ) ,1 = 1 , 1 0 ) CALL DO  COPY  11  ( A , AA,  ,J=l , 1 0  1 0 , 20)  I=1»N  A; = 1 * 1  11 C C  C 18 19 C  „  DO  11  AJ  = J*J  J  -  1»I  0 1  "W = T . / A J - l . / A I F ( L , J ) = 2.3386 * AU,J> * AI R E A D ( 5 , 1 0 1 ) ( TR ( K ) , K = 1 , 2 5 ) SOLVE  FOR  EQUILIBRIUM  POPULATIONS  READ( 5,101 )TE,DE DE= D E * 1 . E - 1 2 CALL TRPROB(TE,N) INITIAL ESTIMATES OF E Q U I L I B R I U M READ ( 5 , 1 0 1 ) ( P O P ( I ) , I=1,N)  _  AT  .  /  —  (A J * ;  ENERGY  TE  POPULATIONS  COEFFICIENTS  ARE M U L T I P L I E D  DO 4 1 I = 2 , N IA = I - l DO 3 3 J = ! , I A " ~ ~ WW=F(I,J)*POP(J)*0.0029 IF (J.EQ.2) W W H ( I ) = WW_  WL = A'LOG (WW*160Vr/ArOGT2V) WL = A M A X 1 ( 2 . , A M I N 1 KWL = I N T ( W L + 0 . 5 )  (WL,  B  -  ' 2 4 . ) )  v  T  -  AND  ARE  DENSITY  FED IN  R A P P I N G "FACTOR'S"  -  —  •  W*W*W)  DO 1 9 1 = 1 , N POPST(I)=POP(I) RADIATIVE  ~l  -  -  -  DE  — — — — —  X W L = WL AA<I*J) 1  AB i I, J )  33 41 C  -__  FLOAT(KWL) 2. * (TR(KWL+l)*XWL*(l.+XWL)/2. TR_( KWL - 1 _ ) * X W L * U . ._-XWU / 2  =' A A ( F, J ) * WW  AA(I»1)=AA(I,1)+DIFF EQ_UIL I B R I U M _ P O P U L A T I O N S CALL  20  =  *  ARE  POP ( I ) ?  _)_ *  A  +  ( ( 1 . + WW ) * P O P ( J ) ) '  REEVALUATED  Q M A T R ( QM » R E C O M B",T E"» D E V N )  C A L L C O P Y ( Q M » QMOMM » N P • 2 0 ) DO 2 0 J = 1 » N POP(J)=-RECOMB(J) . CALL SOLTN(QMOMM,POP,N»20»DET)  .  SUM=DE 1 POP(NP)=DE POPCON = 0. DO 1 5 1 = 1 , N IF ( A B S ( P O P ( I ) - P O P S T ( I ) ) . G T . . 0 1 * P O P S T ( I ) ) 15 C  SUM=SUM+POP(I) I F ( P O P C O N . G T . 0 . 0 1 ) G O TO 1 8 I T E R A T I O N I S C O M P L E T E D WHEN P O P . A R E U N C H A N G E D  C C  ~ ENERGY  C  TEP=TE*1.1 CALL TRPROB(TEP,N) C A L L QMATR. ( Q M P ,_R E C O P , T E P , D E , N ) C A L C U L A T E A P P L I E D P E R T U R B A T I O N TO P O P U L A T I O N S  60 C  61  C C 10  TR(KWD*(1.-XWL*XWL)  (I• _ J . ) _ / _ L i ^ t _ _  POPCON  =  1  "  WITHIN  1  PERCENT  ^  f PERTURBATION  DO 6 0 I = 1 , N P _PERT( I)=RECOP( I) DO 6 0 J = 1 » N PERT(I)=PERT(I) + ALLOW FOR MODULATION DO 6 1 I = 2 , N I A = 1-1 DO 6 1 J = 1 » I A Q M ( J , J ) = QM ( J , J QM(I,J) = QM(I»J) WWH ( 1 ) __= 0 . WWH ! ?.) = 0. WWH(NP) = 0.  (10 PERCENT?  ,  ; QMP(I,J)#POP(J) C A U S E D BY V A R Y I N G  OPTICAL  _ ) - A B U ,J) + AB(I,J)  S O L V E FOR R E S P O N S E AT F R E Q U E N C Y READ(5,101) OM WRITE(6»lll)TE»DE»OM  OM  THICKNESS  ,  '_  22  WRITE(6»135)SUM WRITE(6»119)(POP(I)» 1=1,N) 0 MM = 0 M * l . . E - 9 DO 2 2 J = 1 , N P DO 2 2 1 = 1 , N P QMOMMJI,J)=QM(I,J)/OMM C A L L MULT'( QMOMM ,QMOMM , Q Q O M , N P , 2 0 )  DO 7 0 1 = 1 , N P Y ( I ) = - P E R T ( I ) /OMM 70 QQOM(I,I)=QQOM(I,I)+l. C S O L V E FOR I M A G I N A R Y PART OF R E S P O N S E C A L L S O L T N ( QQOM , Y , N P , 2 0 , _ D E J ) C SOLVE O R REAL PART OF RESPONSE CALL MATVEC(QMOMM,Y,X,NP,20) DO 8 0 I = 1 , N P , " X ! I )= X(I)*100./POP(I) Y(I) = Y(I)*100./POP(I) CORRECT FOR T R A P P I N G OF BALMER SERIES X ( I T= X ( I ) - X ( 2 r * W W H ( I ) / ( 1 . +WWH ( I ) ) Y(I)=Y(I)-Y(2 )*WWH( I ) / ( 1 . + W W H ( I ) ) A M P ( I ) = S Q R T ( X ( I ) * X ( I ) + Y ( I )_*Y ( I )_) 80 A N G ( I ) = A T A N 2 ( Y ( I ) , X ( I ) !* 1 8 0 . / P I WRITE(6»13Q) W R I T E ( 6 , 1 1 9 ) ( X ( I ) , I =1 ,NPJ WRITE(6,129) WRITE(6,119)(Y(I),1=1,NP) WRITE(6,132) _ W R I T E ( 6 , 1 2 0 ) (ANG( I),I = 1,NP) WRITE(6»133) W R I T E ( 6 , 1 2 0 !_( A M P U J , I =J_» N_PJ 6 0 TO 1 0 101 FORMAT (10F8.0) P  111  FORMAT ( 5H1  119  F O R M A T ( IX»lP'll'ETl .2')  120 129 130 132 133  FORMAT(IX,11F11.2) FORMAT ( 3 2 H - I M A G I N A R Y _ P A R T _ O F R E S P O N S E FORMAT(32H-REAL PART OF RESPONSE (X j FORMAT(32H-ANG FORMAT(32H-RELATIVE CHANGE__IN POPUL.  135  TE,F10.0,5H  FORMAT(32H-POPULATIONS END  NE ,  1 P E 1 0 . 2 ,__5 H "~  ~"  OM ,  E10.2)  ~" (_Y)J ") ) )  "SUM =, T P E T O . 2 )  SUBROUTINE COMPUTE DECAY  QMATR(QM,RECOMB>TE,DE,N) • MATRIX Q(I»J> FROM T R A N S I T I O N  D I M E N S I O N _QM ( 2 0_» 2_0 )jRECOMB ( 20) COMMON / O A / A A ( 2 0 , 2 0 ) COMMON / T P / S H ( 2 0 ) , C ( 2 0 , 2 0 > * -CC(20)» AMDIFF = 0.73E-6*TE  51 50  55  NP = N+1 DO 5 0 J = 1 » N S I 6 = C I C ( J )*DE QM(NP*J)=SIG DO 5 1 1 = 1 , N QM ( I , J ) = A A ( J , I )_+DE_*C__J_,_IJ_ SIG=SIG+QM(I,J) QM(J,J)=-SIG QNN = AMD I F F R EN = AMD I F F # D E " DO 5 5 I = 1 , N QM ( I , N P )_= ( 2 v * A _ J J _ + 3 . _ * _ C C J J _ ) *pE_*_D_E R E C O M B ( T ) = ( A C ( I ) + CC~7l ) * D E f * D E * D E ~ Q N N = Q N N + QM ( I ,NP ) R E N = R E N + R E C O M B (_!___ QM(1,NP)=QM(1,NP)+AMDIFF RECOMB(1)=RECOMB(1)+AMDIFF*DE QM(NP,NP)=-QNN R ECOMB(NP)=-REN RETURN END _ _  3  L  PROBABILITIES .  6  CIC(20),  AC ( 2 0 ) , A C E ( 2 0 )  ,  (H u  '  Z i  .  —  .  t — h  .  ^ °°  SUBROUTINE~TRPROB COEFFICIENTS  FOR  PROBABILITIES UNITS  (TE ,N ) SAHA  EQUILIBRIUM  POPULATIONS  B E T W E E N_B0UNJD_ _3T A T E_S_A N D _ T_0_A N D  A R E " " D E G R E E S " >~ N A N S E C  AND  CUBIC  AND  TRANSITION  F R O M_C 0 N T I H _ U U M  MICRONS  D I M E N S I O N X L G ( 6 ) , WLG ( 6 ) » E X ( Z O ) . C O M M O N _ / T P / S H ( 2 0 _ ) , _C( 2 0 , 2 0 )_• C C ( 2 0 ) _ _ C I C ( 2 0 )_, AC___2_0 ) , _ A C E _2 0J XLG(l) = 0.2228466042 ~ " XLG(2) = 1.1889321017 XLG(3)_= 2.992736326 " X L G ( 4 f "="5 . 7 7 5 143^5 6 9 XLG(5) = 9.837467418 XLG(6)_= 15.98287398 W L G d T =' . 4 5 8 9 6 4 6 7 3 9 5 WLG(2) = .41700083077 WLG(3) = .113373382074 WLG(4)  =".010399197453  WLG(5)  =  W L G ( 6 )___=_  .2610172028E-3 .89854790643E-6  TR'"=  157890. / TE  SQTE  =  SQTR  =_SQRT(.TR)  DO PP  SQRT(TE)  I = 1,N 1*1 SH ! I ) = 0.0 EX(I) = EXP(-TR/PP) IF (TR/PP .L E . 8 8 . ) SH(I ) = 30 =>  PP  *  4.136E-4/(TE*SQTE  *  EX( I )  DO 3 1 I = 1 , N P = I PP = P*P TF = TR/PP SUM = 0.0 SUM1 = 0,0 SUM2  =  0.0  DO 3 2 K = 1 , 6 U = X L G ( K ) / TF X = U + 1.0  ,  H  =  ( P * X ) * * ( - 2 . / 3 . 1  G  =  (  SUM1 SUM2  1.0 =  +  SUM1  0 . 1 7 2 8 * ( U - 1 . ) * H +  0.0496*(U*U+4.*U/3.+l.>*H*H)  -  WLG(K)*G  . =' SUM2""+'VLGTKT*G~*  IF  (X.LT.2.)  F  =  IF  (X.GE.2.)  F  =  _  .  :  X L G ( K ) """  2 . * ( U * 2 . 0 / ( X + l . ) 1 * * 1 . 5 ( 5 . * X -  6.)  *  SORT ( X / J  /  X+_._)_#* 3  1  X  32  SUM  =  AC  SUM  +  W L G ( K ) * F  ( I ) =  5 . 1 9 7 E - 1 1 *  SQTR  *  SUM1  /  P  A C E ( I _ _ _=  5 . 1 9 7 E - l l *  SQTR  *  SUM2  *  T E  =Vo  H  CIC( CC  1151 I)  =  (I ) _ =  *  SUM *  EX( I)  H  *  PP  C (TYl ) = 0. I F ( I . E Q . N ) GO JA  =  DO Q QQ A  J  =  =  34  0.0 K =  1,6  X I _ G ( K> / T F A)  H  *  ( U .G E .  SUM  31  TR/(A*PP)  /('(Y+A)**3 IF  (TE*SQTE)  _  Y_ = U + 1.0 IF (U.LT. 1  /  JA,N  Q*Q  =  =  4.136E-4  QQ/(GQ-PP)  SUM„,= DO 34 U  TO  SQTE  J  =  TF  *  /  =  SUM  E  ( 2 . - A + Y * Q . + 4 . * A )  *  (-3.*A  +  SUM  *  PP*PP#A*A  /  f i _*_ E X ( J J _ / _ E _ X U _ ) _ _____  33  C (J» I)  =  H  31  CONTINUE . ..  RETURN END  SENTRY  U  * ( 1 . + A )  Y * ( 3 . + 4 ._* A )_)_* S Q R T_(_Y / (_Y+AJ * * 3  ('< ) * E  =  *  )*SQRT(  A) )  _ A )__ E__ = +" W L G  =.02302  =  C (J » J )  ..  P  +l _ _ _  I  33 =  pp  '*  H  /  P'P  -  /  QQ  (QQ*Q*SQT E)  4.67E-1  "  .49204 .16754_ .07943 30000 42940^ 1 .0E08* 0.5E08 . 25E08_  *"  "  .48725 14JL00_ .07655 1.E12 47.7  5.5^E-7 4.39E-2 "  .48047 1 2 5_14_ .07392 3.55  1 . 7 7 E - 2 4 . 1 0 E - 3 1 . 6 4 E - 3 7 . 5 3 E - 4 3.8 5 E - 4 2 . 1 3 E - 4 1.26F-4 8 . 3 7 E - 3 2 . 5 2 E - 3 9 . 6 8 E - 4 4 . 3 7 E - 4 2..20E-4 1 . 2 1 E - 4 7 . 0 8 F - 5 8 . 9 4 E _ 3 _ 2 . 1 9 E - 3 _ _ 7 _ . _ 7 4 E _ _ 4 _ 3 _ . J 4 E _ - 4 _ 1 _ . 64E_-4__8_. 8 5 E - 5 _ 5 _ n F - 5 2 V 6 8 E - 3 7.67E-4 3.03E-4 1.42E-4 7.43E-5 4.12E-5 1.02E-3 3.24E-4 1.38E-4 6.87E-5 3.78F-5 4.5 0E-4__1. 5 5 E - 4 J 7 . 0 3 E - 5 _ 3 . 6 7 E - 5 2.26E-4 8.15E-5 3.88E-5 1.23E-4 A._5E-5 7.12E-5 .47165 J_1JJ_L_ .07130 .758  .46117 10609_ .0692! .306  .44859 .09965  .47855 )09424  .38606 .08964  .30846 .08600  .7 7 1 4 1 .08757  .188  .158  .161  .182  .713  1  •t  BIBLIOGRAHY  B a t e s D . R . , K i n g s t o n A . E . and McWhirter R . W . P . (1962a)Proc.. R o y . S o c . A 2 6 7 , 297} ( 1 9 6 2 b ) P r o c . R o y . S o c . A 2 7 0 . 1 5 5 . B a t e s D . R . and K i n g s t o n A . E . ( 1 9 6 3 ) P l a n e t . S p a c e S c i . 1 1 , 1 ; (1964a)Proc.Roy.Soc. A279.10; (1964b)Proc.Roy.Soc. A279.32. Byron S.,  S a b l e r R . C . and B o r t z P . I .  D'Angelo N.  (1961 )Phys .Rev  (1962)Phys.Rev.Lett._,376.  505.  Davy P . ( 1 9 6 7 a ) R e v . P h y s . A p p l . _ , 65; ( 1 9 6 7 b ) E i g h t I n t e r n a t i o n a l C o n f e r e n c e on Phenomena i n I o n i z e d G a s e s , V i e n n a . F a u l k n e r E . A . and H a r d i n g D.W. Gryzinski M.  (1966 ) J . S c i . I n s t r . 4 3 , 9 7 .  (1959)Phys.Rev.115,374.  Hamberger S . M . (1963 ) P l a s m a P h y s . H a r r i e s W . L . and von E n g e l A .  5., 7 3 .  (1954)Proc.Roy.Soc.  Hinnov E . and H i r s c h b e r g J . G . (1962)Phys.Rev. H o l s t e i n T.  (1947) P h y s . R e v .  Scantlebury G.S.P. von E n g e l A .  795.  72,1212.  (1961)Electronic  (1965)Ionized  125,  A222.490.  Engineering, Dec.61,803.  Gases.Oxford.  Wilcox R.H. (1959)Rev.Sci.Instr.  -4 2  30,  1009.  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0085106/manifest

Comment

Related Items