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Measurements of the Stark widths of N II and N III spectral lines at variable electron densities Purcell, Stephen T. 1982

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MEASUREMENTS OF THE STARK WIDTHS OF N II AND N I I I SPECTRAL LINES AT VARIABLE ELECTRON DENSITIES by Stephen T. P u r c e l l B.Sc,  Dalhousie U n i v e r s i t y ,  1978  THESIS SUBMITTED IN PARTIAL FULFILMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of P h y s i c s  We accept t h i s t h e s i s as conforming to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA July  1982  c) Stephen Thomas P u r c e l l , 1982  In p r e s e n t i n g  t h i s t h e s i s 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 the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree t h a t p e r m i s s i o n 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  be granted by  department or by h i s or her  the head o f  representatives.  my  It is  understood t h a t 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 o r f i n a n c i a l gain  s h a l l not be allowed without my  permission.  Department o f  VriYSl  CS  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date  DE-6  (3/81)  ZTVL. V  2.3  ,  1^32. .  written  i i  ABSTRACT The Stark spectral  widths  lines,  densities  seventeen  emitted  of  2.9 ± .4- x 1 0  of  by  N II  plasmas  .9 ± .1 x 1 0 , cm" ,  1 7  were  3  with 2.2  1 7  and  ten  free  Nine  l i n e w i d t h s and four of the N I I I l i n e w i d t h s  filled  with  50%  helium  and  the  N II  have  not  been  pressure  temperature was several  N II  and  charging  determined  from  to  N III  The  conditions electron  varying The  intensity  electron ratio  of  He I  5876  n i t r o g e n l i n e s were measured at d i f f e r e n t to  check  density  on  linear the  scaling  same  about  half  of  of  of  Stark  and  plasma  width  vs  d e v i c e . However, the l a r g e  e r r o r s i n both the Stark widths measurements,  the  l i n e s . The e l e c t r o n d e n s i t i e s were  estimated by measuring the Stark widths 6678.  by  voltage. the  stabilized  50% n i t r o g e n . The  d i f f e r e n t e l e c t r o n d e n s i t i e s were produced filling  and  1 7  of  p r e v i o u s l y measured. The plasma source was a w a l l discharge  electron  ± .3 x 1 0  measured.  N III  and which  o p t i c a l depths, made i t d i f f i c u l t  the  electron  density  came from a p p r e c i a b l e  t o check the s c a l i n g  over the l i m i t e d range of t h i s experiment.  even  iii  TABLE OF CONTENTS  Page ABSTRACT  i i  TABLE OF CONTENTS  i i i  LIST OF TABLES  iv  LIST OF FIGURES  v  ACKNOWLEDGEMENTS  vi  CHAPTER 1  INTRODUCTION  1  CHAPTER 2  THEORY OF LINE BROADENING  4  CHAPTER 3  EXPERIMENTAL APPARATUS AND TECHNIQUE  15  3-1 3-2 3-3 3-4 3-5 3- 6  15 19 21 24 27 28  CHAPTER 4  CHAPTER 5  The Plasma Source The O p t i c a l S p e c t r o s c o p i c The Timing System Calibration F i r i n g Procedure Data Handling  System  PLASMA DIAGNOSTICS  29  4- 1 4-2 4-3 4-4 4-5 4-6 4-7 4- 8  L o c a l Thermodynamic E q u i l i b r i u m Plasma Homogeneity Reproducibility Time Dependence O p t i c a l Depth LTE Computations Temperature Measurements E l e c t r o n D e n s i t y Measurements  29 34 36 37 37 45 46 49  LINEWIDTH MEASUREMENTS AND CONCLUSIONS  54  5- 1 P r e l i m i n a r y Work 5-2 Stark Widths And C o n c l u s i o n s 5-3 Improvements And Further Work  54 56 62  BIBLIOGRAPHY  67  i v  LIST  OF  TABLES Page  TABLE  (3-1)  Experimental  Conditions  Table  (4-1)  I o n i c D e n s i t i e s At  Table  (4-2)  Equilibration  T  Times  e  =  From  .18 3.1  ev  31  Resonance  Excitation  Rates  34  Table  (4-3)  Error  In  T  42  Table  (4-4)  Plasma  Densities  Table  (4-5)  Widths  Of  Table  (5-1)  N  II And  N  III Stark  Widths  F o r Run  1  56  Table  (5-2)  N  II And  N  III Stark  Widths  F o r Run  2  57  Table  (5-3)  N  I I And  N  III Stark  Widths  F o r Run  3  58  Table  (5-4)  Optical  0  He  I Lines  Depths  From  46 And  Corresponding  Intensity  Ratios  N 's e  .52  62  V  LIST  OF  FIGURES Page  Figure  (3-1)  Layout  Of  Experiment  Figure  (3-2)  Quartz  Discharge  Figure  (3-3)  Arc  Figure  (3-4)  Timing  Figure  (4-1)  C o r r e c t e d S t a r k W i d t h To (w /w ) vs O p t i c a l Depth  Figure  (4-2)  N  Current  II  Without  Timing  .16  Tube  Trace  And  17 Timing  19  System  To  N  III  23  Intensity  Measured  Ratios  Figure  (4-3)  He  5876  Figure  (5-1)  Stark  Figure  (5-2)  Measured  Width  From  Equation I  System  The  Ratio 41 Saha 48  For  Widths  Runs Vs  1,  2  Electron  Profiles  and  3  53  Density  61 63  vi  Acknowledgements Without  the  help  of many of the other members of the  plasma p h y s i c s  group  completed  i t would be i n g r a c i o u s not to g i v e s p e c i f i c  and  this  project  might  not  have  been  thanks where due. First direction  and  foremost,  and  support  I  received  Dr. A. J . Barnard, throughout steered  me  research  into grants,  theoretical  gratefully  the  conceived  obstacles  who designed and b u i l t  helped  me  f i x inumerable of  project.  my He  the  the  originally  experiment,  child  computer  the e l e c t r o n i c g a t i n g system,  equipment pyschcology,  failures  programs  and,  prevented  other  with from  Barnard  used to t r a n s f o r m the raw a  l o t of  and Dr. F. L. Curzon a c t e d as my s u p e r v i s o r while  Dr. Barnard was on s a b a t i c a l l e a v e . Many, i n f a c t the  me  John  data from the OMA to f i n i s h e d p l o t s and answered questions  cleared  I am a l s o indebted to A l  d e s t r o y i n g the d e l i c a t e , expensive apparatus. provided  supervisor,  from my path and used h i s b a t t e r y of  Cheuck  use  from  the  the plasma p h y s i c s f o l d , p r o v i d e d me with  computer programs to my advantage.  extensive  acknowledge  members  of  the  group  most,  of  had a hand i n the f i n a l  product but s h a l l remain anonymous, u n l e s s they  complain.  1  CHAPTER 1  When an e l e c t r i c eigenstates  and  INTRODUCTION  field  energy  i s applied  levels  to, an  a r e p e r t u r b e d . In a plasma  each atom e x p e r i e n c e s a time v a r y i n g e l e c t r i c r e s t of  medium  broadening field  of  and the  produced  perturber,  at  the  combined  emitted an  of  the  atom  p e r t u r b a t i o n s cause  by  another  the  spectral  perturber's  ensemble  Stark  line  particle,  in  a  by  broadening  a  the  i s the  the monopole term (or  multipole  expansion,  averaged  of p e r t u r b e r s . Since the monopole  has the l o n g e s t range, n e u t r a l ignored  from the  can be d e s c r i b e d by a m u l t i p o l e expansion of the  charge) of the over  field  s p e c t r a l l i n e s . The p e r t u r b i n g  p e r t u r b e r ' s charge d i s t r i b u t i o n . widening  atom, i t s  interactions  can  field  often  be  hot dense plasma and Stark broadening i s the  dominant broadening mechanism. The broadening of a l i n e temperature,  electron  will  density,  depend  composition,  homogeneity and the s t a t e s i n v o l v e d i n matching  theory  to  experiment,  powerful d i a g n o s t i c t o o l t o state  of  on  the  the  plasma  opacity  transition.  and By  l i n e broadening p r o v i d e s a  study  both  the  thermodynamic  the plasma and the b a s i c atomic parameters  of the  emitter. Due t o the  complexity  of  the  phenomenom  a  unified  theory i s not p o s s i b l e . However, s e m i e m p i r i c a l formulae have been  developed,  valid  formulae a r e i n f a i r l y  over  l i m i t e d regimes. Though these  good agreement with  experiments  for  2  neutral  and  singly  i o n i z e d l i g h t e r elements  (see H.R.Griem  (1974)) and allow us to use some hydrogen and as  lines  s p e c t r o s c o p i c standards, t h i s i s not t r u e f o r l i n e s  m u l t i p l y charged, to  helium  help  h e a v i e r i o n s . More experiments  elucidate  further  regimes.  For example, present theory p r e d i c t s that of many nonhydrogenic  maximum s c a l e s approximately density,  N ,  needed  which components of the theory  apply i n which density-temperature  broadening  are  from  f o r the Stark  l i n e s the l i n e w i d t h at h a l f  linearly  with  free  electron  (H.R.Griem  (1974) page 2) and i s only weakly  dependent on temperature.  Thus the l i n e w i d t h i s an e x c e l l e n t  e  means of measuring parameters. broadening the  In  a  N , one e  of  the  recent  study  on  by E . K a l l n e , L.A.Jones  authors  suggest  that  most  important  N II  and simple  linear  N  e  = 1.4 x 1 0  1 8  cm"  and  3  (1979),  scaling  linewidths  e  with  N III line  A.J.Barnard  i n a p p r o p r i a t e at higher N . They measured plasma  and  plasma  compared  in a  them with  e a r l i e r measurements made at lower N . The  twofold  this  measurements  e  experiment  was  to  make  extensive  e l e c t r o n d e n s i t i e s between that most  of  of  E.Kallne,  provide  comparison  a  broader  to t h e o r e t i c a l  To minimize  base  of  et.al.,  at  scaling  experimental  at and  data  and for  predictions.  the e f f e c t of inhomogeneities, measurements  were made at three d i f f e r e n t e l e c t r o n d e n s i t i e s . measured  aim of  the e a r l i e r measurements (see review a r t i c l e by N.  Konjevic and W.L.wiese (1976)) t o check l i n e a r to  is  different  c o u l d then be compared  N 's, e  to  Linewidths  from the same plasma source,  study  linear  scaling.  I f the  3  diagnostics  were  a l l measurements  not exact the e r r o r would at l e a s t similarly.  The t h e s i s i s d i v i d e d i n t o f i v e two  we  outline  semiclassical result  showing  the  presented. apparatus chapter  quantum  mechanical  dependence  chapter  three  on  electron  we  discuss  line, is  the  procedures.  thermodynamic  lengthy  In  s t a t e of the and e l e c t r o n  discussion  on  depths made necessary by the p a r t i a l o p a c i t y of our  plasma. In chapter twenty-seven  errors.  A  we d e s c r i b e the experimental  d e n s i t y measurements. Included i s a  different  paralleling  density,  plasma, v a r i o u s d i a g n o s t i c s and the temperature  optical  chapter  interpretations.  and technique and data c o l l e c t i o n four  In  f o r the p r e d i c t e d width of an i s o l a t e d  linear In  chapters.  the theory of l i n e broadening,  and  general  affect  N II  electron  five and  we  present N III  densities  the  lines  along  Stark  measured  with'  their  widths at  of  three  estimated  F o l l o w i n g t h i s i s a d i s c u s s i o n of the r e s u l t s . A l s o  in t h i s chapter we f u t u r e work.  give  suggestion  for  improvements  and  4  CHAPTER 2  An  ideal  THEORY OF  spectrometer  T.TNE  acts  BROADENING  as a f o u r i e r a n a l y s e r of  e l e c t r o m a g n e t i c r a d i a t i o n . I t s output i s p r o p o r t i o n a l power spectrum of energy  level  the  incident  system  of  an  radiation.  atom  or  spectrum of l i g h t emitted from atomic the  relation  emitters  E = -fiu.  undergoing  monochromatic, exactly  or  transitions  the  possible  energies  spectrum  so  would  the  broadening.  The  parameter  i s never  the  line  at  consideration An  half  broadening  description  complex  arguments, by  semiclassical First dipole  perfectly a  finite  is  called  accessible  to  fullwidth  of  i s the  maximum, 2w, so we w i l l g i v e i t c a r e f u l  quantum  of  i t is  paralleling  line  mechanical  f o r m u l a t i o n of quantum mechanics classical  delta  throughout.  adequate  extremely  a  had  spectrum peaks have  most  measurement i n l i n e broadening s t u d i e s  perfectly  be  f i n i t e widths. T h i s widening of the i d e a l s p e c t r a line  use  photons  monochromatic and the emitted photons always have in  and  were  i f a l l the  peaked at u. However, the f i e l d  spread  the  from an ensemble of  transition  equivalently  the same energy,  function  same  study  i o n , we examine the  I f the r a d i a t i o n the  To  t o the  broadening problem.  was i n i t i a l l y  instructive the  quantum  i s an As  modelled  to  the on  discuss line  picture  with  models.  consider  radiation  an  isolated,  as i t undergoes a  excited transition  atom  emitting  between  two  5  s t a t e s . C l a s s i c a l l y we p i c t u r e the atom as a l i g h t l y oscillating  dipole  with angular frequency u  the energy  initially  energy).  An  stored  in  oscillating  the  r a d i a t i o n at i t s c h a r a c t e r i s t i c The  lineshape  emits  (transition  of  oscillation.  (essentially  the frequency  dependence of the power spectrum) can be shown to be and E.Wolf  AE i s  electromagnetic  frequency  of t h i s r a d i a t i o n  = AE/n.  oscillator  dipole  damped,  (M.Born  (1975)) :  LU)  = limd/T)|f  f(t)  i s the complex g e n e r a l i z a t i o n of the time dependence of  the o s c i l l a t o r ,  f (t)exp(-iot)dt |  (2-1)  2  or e q u i v a l e n t l y the f i e l d  f(t) = e x p ( i o t ) ) .  From  0  J.Cooper  (e.g.  i t produces  (1969)  t h i s can be more  c o n v e n i e n t l y w r i t t e n as : L(u) = ( l / j r j R e J * ( s ) e x p ( - i o s ) d s +(s)  i s the a u t o c o r r e l a t i o n  (2-2)  f u n c t i o n given by :  *(s) = <Cf*(0)f(sj> The  average  ensemble  (2-3)  i s over an ensemble of e m i t t e r s . We  average  r a t h e r than a time average  can  use  an  by i n v o k i n g the  ergodic hypothesis. Because a d i p o l e o s c i l l a t o r  emits r a d i a t i o n at  p r o p o r t i o n a l to i t s p h y s i c a l amplitude, exponentially (H.R.Griem  in  time.  This  is  i t s amplitude  called  a  rate decays  r a d i a t i o n damping  (1964) pgs.8-10)). Hence i t has a time dependence  given by f(t) = e x p ( - y t + i o t ) . T h i s 0  g i v e s L(o)  (normalized)  6  from (2-1) or (2-2) and  LU) =  (2-3) as :  U/r) (U-u ) + r ) 2  (2-4)  2  0  L(u) i s a L o r e n t z i a n with  halfwidth  r  (r  is  defined  as  1 / l i f e t i m e of the o s c i l l a t o r ) . C l a s s i c a l l y f o r v i s i b l e l i g h t y ~ 10  sec"  8  o  and  1  ~ 2 x 10 * s e c " , 1  0  1  broadening produces a very narrow Another e f f e c t motion  of  so  natural  line  peak.  that broadens the atomic  lines  is  the  atoms r e l a t i v e t o the spectrometer which Doppler  s h i f t s the emitted distribution  radiation.  For  a  Maxwellian  velocity  the l i n e s are Gaussian with 1/e h a l f w i d t h given  by : w  = 4.6  d  T  is  e  x lO"U (T 0  the  emitters.  ion For  e  temperature nitrogen  approximately  the  t h i s gives w  (ev) / M ( a m u ) ) and  M the atomic mass of the  helium  temperature  ~ .1 A and  d  and  of  .2 A  (2-5)  1/2  at  3  ev,  which  the plasmas we  respectively,  in  is  studied,  wavelength  u n i t s . T h i s width a f f e c t e d only the narrowest l i n e s measured i n t h i s experiment Broadening interact broadening  with  (see s e c t i o n also  and  (3-4)).  occurs  perturb  the  because  nearby  oscillators.  particles In  Stark  the p e r t u r b e r s ' e f f e c t s depend on t h e i r charges,  impact parameters and r e l a t i v e v e l o c i t i e s and p o s i t i o n s . o s c i l l a t o r ' s energy V = -£(t)«d(t)  (and  hence  frequency)  is  where £(t) i s the time dependent  shifted  The by  f i e l d at the  e m i t t e r from the p e r t u r b e r s and d ( t ) i s the d i p o l e moment of the  emitter.  7  From  the p r o p e r t i e s of the F o u r i e r transform,  the time  a s i g n a l must be observed to give a p r o f i l e a c c u r a t e l y at frequency  separation  Experimentally At ~ 1/w.  we measure  following  the  classical  the o s c i l l a t o r  t ~ f>/v.  p  paths.  so  we  need  v i s the average  and  v  are  Since  point  distance  i s the  particles  the c l o s e r the p a r t i c l e  the p e r t u r b a t i o n  i s perturbed  i s the  parameter)  we  may  only during a c o l l i s i o n  time  of  i t causes,  c l o s e s t approach  velocity  at  closest  (impact approach  velocity for neutrals).  The  calculation  can  be  greatly  s p e c i a l l i m i t s of the average c o l l i s i o n For p e r t u r b e r s calculate  their  appropriate move  (w)  where  perturbers  approaches the stronger  (thermal  halfwidth  i s At ~ 1/Au.  frequency.  Classically  say  the  w ~ 1/lifetime ~ v  Note  collision  Au from the l i n e center  little  function  that  effect  move  f o r two  time r = <t>. slowly  we  may  as i f they are s t a t i o n a r y . T h i s i s the  perturbers  must  d u r i n g the l i f e t i m e of the d i p o l e . The p r o f i l e by  calculating  of a p p l i e d e l e c t r i c  statistical  simplified  relatively  i f T >> 1/Au or i f Ao = w  i s then found  the  frequency  shift  f i e l d , then averaging  d i s t r i b u t i o n of f i e l d s t r e n g t h s  to  as  find * ( s ) .  i s called  valid  f o r the r e l a t i v e l y slow moving ions of the plasma.  will  hold  separation  the q u a s i s t a t i c approximation and i s o f t e n  f o r the  line  from l i n e c e n t e r  distribution  difficult  a  over the  This  field  a  (called  wings  to  depending the  p a r t and the r e f e r e n c e s  a  smallest  on  Holt'smark  frequency  T . Finding field)  are H.R.Griem  It  the  i s the  (1974)  and  8  C.F.Hooper, which of  depends  a  (1966)  on  the  particular  field  as  a  The  phase  second  of the  theory  is a  theory  is a  disturb  the  independent  but  with  d  =  total  is  valid  in  In  the  analysed  impact  much T(ions)  the  of >>  of  It  1/w  of  of  a  the  i n which  abruptly,  e  the  gives  of  are a  and  r  real  the  need  be  and  is  line.  The  and  destroy  The  v.  the  collision,  completely  halfwidth  N <v>«  These  disturbing  Fourier  The the  Lindholm collisions  adiabatic  and  Lorentzian  profile  frequency  shift  imaginary  impact profile  parts  of  approximation to  ( T ~" 1/Au)  dependence detail.  of  the  a  frequency  theory  the  Fortunately,  q u a s i s t a t i c approximation  line >>  1/Au.  exp( i o t - i / t ) .  also  range  time in  the  «  by T .  approximation the  but  are  T  strength  approximation  much  derivation  =  certain  field, number  interaction,  collisions  central part  intermediate  applicability  over  c r o s s - s e c t i o n s . The  the  because  be  *j  determined  the  complex  w  the  a  effect  the  impact  with  time.  and  r  optical  separation  must  tf  e  the  in  gives  abruptly  net of  f(t) =  slightly  halfwidth  N <v>tfj .  the  these  careful  phase  are  the  dependence  Lorentzian  for  quickly,  Only  Then  more  feeling  applies  assumes  Holtsmark  strength.  electrons  wavetrain.  transform  field  The  density,  species  is called  for  (1968).  charge  emitter  time  This  valid  the  the  actual  simplest  of  oscillator.  considered. often  ionic  limit  pass  the  and  emitter  function  perturbers  not  Jr.  for  profile.  T(electrons).  electrons That Accurate  perturbations the  ranges  for  ions  often is,  i s more  overlap we  p r e d i c t i o n of  of and for  have the  9  linewidth  i s o f t e n p o s s i b l e using  Now  we  quantum  these two  formulate the above ideas  mechanics.  The  lineshape  state  m  to  n,  summing  over  in  the  for  spontaneous d i p o l e r a d i a t i o n when an  approximations. language  an  atom  electron  a l l the  emitting  decays  states  of  from  i s (J.Cooper  (1969),H.R.Griem(1964)) : LU) where  -  2 8(»-» n  ^u  m n  )|<m|d|n>|^  (2-6)  m  =energy d i f f e r e n c e between s t a t e s m and  m n  d  n  =dipole operator  p  =probability  m  s t a t e m i s occupied  (given  by  Saha Boltzmann equation when the plasma i s  the in  equilibrium) This function  may  be w r i t t e n  using  i n the same form as  the quantum a u t o c o r r e l a t i o n  (2-2)  and  d i f f e r e n c e between the c l a s s i c a l and that  we  replace  the  (2-3). The  quantum d e s c r i p t i o n s i s  c l a s s i c a l d i p o l e o s c i l l a t o r with  matrix element of d between s t a t e s m and The  decay law  probability, f o r an  r,  ensemble  which leads of  emitters.  analog of c l a s s i c a l  r a d i a t i o n damping. The  not  have  discrete  but  uncertainty  p r i n c i p l e and  s t a t e s . The  line profile  Lorentzian density,  a  finite the  the  n.  e x c i t e d s t a t e s of i s o l a t e d atoms  transition  essential  width  have to the This  a  constant exponential  is  quantum  energy l e v e l s are because  nonstationarity  of  of  the  excited  f o r spontaneous emission i s again a  with width r . r i s n e g l i g i b l e except f o r very  low  c o l d plasmas or s p e c i a l t r a n s i t i o n s .  Interactions  also  broaden  the  l i n e by adding a time  10  v a r y i n g p o t e n t i a l to the e m i t t e r ' s vectors  of  unperturbed and  (2-6)  are  Hamiltonian  surrounding  no  eigenfunctions  f i n d the  Hamiltonian  state of  the  emitter  lineshape  s o l v e the time dependent Shrodinger  (1974), J.Cooper  =  The  but are e i g e n f u n c t i o n s of an  with t h i s more complicated  i*a^  longer  p e r t u r b e r system. To  must set up and  The  Hamiltonian.  we  equation  (H.R.Griem (1964) and  (1969)).  t o t a l wavefunction ty obeys : (2-7)  (H.+Hp+V)^  dt where  H  and  = the unperturbed  A  emitter  Hamiltonian  Hp = the p e r t u r b e r s '  Hamiltonian  V  term  The  = the i n t e r a c t i o n problem  can  be  greatly  s i m p l i f i e d by using  c l a s s i c a l path assumption that almost a l l based  upon.  The  assumption  classical  particles  dependent  only  ( i . e . charge  the  will  be  not  i t s state  valid  to  the  broadening.  that  if  the  (no back r e a c t i o n ) . The  i f the average in  a  change  collision  in  contribute  A l s o the c o l l i s i o n s  independent of changes caused i n the  perturber  perturbers  are  trajectories  e m i t t e r ' s charge and This  are  perturbers  classical  impact parameters of a l l c o l l i s i o n s  considered  ignored  calculations  average de B r o g l i e wavelength i s small compared  significantly  the  the  that  along  distribution).  perturbers' to the  on  moving  is  the  are  emitter  by  back r e a c t i o n can  kinetic  energy  of  be the  (~'n'w) i s small compared to the  average p e r t u r b e r k i n e t i c energy  (kT).  This  implies  that  11  broadening or  collisions  a r e much more frequent than e x c i t i n g  d e - e x c i t i n g c o l l i s i o n s . T h i s i s almost  l i n e s i n the o p t i c a l Using  the  always  true  for  range.  classical  path  assumption  the  problem  s i m p l i f i e s to solving :  itfaX  = (H +V . ( t ) ) X A  (2-8)  r  X d e s c r i b e s the s t a t e of the e m i t t i n g system and the  potential  the  emitter  feels  lineshape  we  V _(t) i s c(  from a p e r t u r b e r with a  c l a s s i c a l path. To  find  substitute  the the  solutions  . into  s o l u t i o n s f o r (2-8) do not e x i s t have  been  calculated,  quasistatic For  solutions  can  field  shifts  of  the  from by  the  =  J  w  <£> £  be o b t a i n e d f o r the  £  is  the  perturber  time  at the  the  static  (E.Merzbacher  (1970)),  d i s t r i b u t i o n W ( £ ) . We get :  2 |<m|d[n> |  d  widths  energy l e v e l s of the upper and lower  then average over the f i e l d U )  general  actual  calculating  s t a t e s as a f u n c t i o n of a p p l i e d f i e l d  QS  and  ( T << 1/w) approximations.  CL  monopole  (2-8)  Though  which  the q u a s i s t a t i c case V ( t ) = - £ « d .  e m i t t e r . We o b t a i n the p r o f i l e  L  solve  (2-6).  from  ( T >> 1/w) and impact  independent  Stark  must  2 /5m  S(u-u -(AE (£)-AE (e))/K) mn  fn  n  (2-9) where A E ( £ ) , A E ( £ ) a r e the energy s h i f t s of the upper m  lower s t a t e s Standard  n  and  respectively. perturbation  theory  technique to determine the l e v e l  provides  shifts  in  an terms  expansion of the  12  p e r t u r b a t i o n p o t e n t i a l ' s matrix elements between unperturbed states  (V 's).  Note  m n  that  V  hydrogenic e m i t t e r s the f i r s t the  strong l i n e a r Stark e f f e c t  states  of  nonhydrogenic  they a r e nondegenerate means  V  i s zero  n n  i s an  term of  odd the  o p e r a t o r . For  expansion  (energy s h i f t « | V  | ) . Most 2  n n  ions have d e f i n i t e p a r i t y  i n the o r b i t a l quantum because  gives  because  number.  This  V i s odd. The energy s h i f t of  these s t a t e s i s thus approximated by the second term i n the expansion  (^^| V m*n  Stark e f f e c t In  | ).  This  2  m n  (E.Merzbacher  weak  so  many  (t)  in  (2-8) can to  H  be As  A <  of c o l l i s i o n s  in  the  dependence of a c o l l i s i o n  small T .  Only  the  c o n s i d e r e d . Thus V"  general i t  possible  matters  effect  of  a  and  independent  picture,  the  can be ignored f o r collision  need  be  can be expressed i n terms of S-matrices  scattering  l e v e l s . The p r o f i l e  approach.  CL  net  that  classical  time  over  in  c o n s i d e r e d as a time  detailed  the  is  of these weak c o l l i s i o n s to d i s t u r b the atom i t  perturbation  for  interaction  order each c o l l i s i o n may be  independent. Since  i s only the average e f f e c t C L  (1970)).  that to f i r s t  considered s t a t i s t i c a l l y  V  i s c a l l e d the q u a d r a t i c  the impact approximation the average  assumed  takes  shift  of  p e r t u r b e r s o f f the upper and lower  i s found by averaging  impact  parameters,  the  perturbation  v e l o c i t i e s and times of  13  Cooper  (1969)  gives  an  expression  f o r L(o) v a l i d  t r a n s i t i o n s between two w e l l separated  for  l e v e l s , a and b as :  L U ) = 1 Re 2 d < f m n | ( i u - i ( H -H. ) . ) " | m' n ' ^ d*,, I r mm'- N S v - a b ab / / -mn' 1  T  m n mn  1  1  (2-10) where  d — mn  = d i p o l e matrix  HgjHjj  = the e m i t t e r Hamiltonians  c  element that  act  on  the  substates m and n r e s p e c t i v e l y 4>  = the i n t e r a c t i o n operator  Qb  scattering In  plasmas  quasistatically approximation.  matrices  the and To  w r i t t e n i n terms of  ions the  obtain  can  usually  be  electrons  in  the  profile  final  the  c a l c u l a t e the impact broadening by e l e c t r o n s of of  the  field  Hamiltonian  profile LU)  impact we  the  first states  H ( £ ) , which now depends on the s t a t i c Q  s t r e n g t h produced by the i o n p e r t u r b e r s ,  average  treated  over the ion e l e c t r i c  £.  Then  we  f i e l d d i s t r i b u t i o n . The f i n a l  i s given by :  - l j w ( £ ) d £ R e ^ d  m  n  ^  d *  v  (2-11) (2-11) w i l l neglecting  be  valid  i f the  uncertainty  introduced  by  the i o n motion i s small compared to the e l e c t r o n  impact width or d i s t a n c e  from  line  center,  whichever  is  greater. For nitrogen,  i s o l a t e d l i n e s from nonhydrogenic e m i t t e r s , such as quasistatic  to the q u a d r a t i c  i o n broadening w i l l cause s h i f t s due  Stark e f f e c t . Often  this  field  dependence  1 4  is  a  relatively  weak  calculated directly a  Lorentzian  determined (1969))  from  profile  by  effect  # .  ( 2 - 1 0 ) . To f i r s t with  e  f f m +  <r  n +  m  upper and  2  small  cutoffs  is  for  introduced  scattering  matrices  small c u t o f f w i l l  the  impact  because  It  low c u t o f f  crossections  in  f ( n ) and f ( n ) m  n  by  imposing  Debye  sphere  breakdown f o r small impact be v a l i d  large large  shields  i s i n t r o d u c e d because  the  parameters.  i f strong c o - l l i s i o n s  do  not  the p r o f i l e .  i s important to note that the width i s p r o p o r t i o n a l  and only weakly dependent on  average).  (2-12)  v e |  parameters. The  the  occur f r e q u e n t l y enough to a f f e c t  e  shift  s c a t t e r i n g amplitudes.  d i s t a n t p e r t u r b e r s . The  to N  frequency  optical  C r o s s e c t i o n s are u s u a l l y e v a l u a t e d  The  be  order (2-10) g i v e s  lower s t a t e s r e s p e c t i v e l y and  are the e l a s t i c  cutoff  can  impact width i s (J.Cooper  n  inelastic  n  and  profile  and  Jdn|f (n)-f (o)| )>  <r and <r are the t o t a l the  width  The e l e c t r o n  ab  the  :  W = N <(v/2)(  m  and  We  hope  to  temperature.  at  e  (from  support the l i n e a r  with f r e e e l e c t r o n d e n s i t y measurements  T  different  in  this  electron  the  velocity  s c a l i n g of width  experiment densities  by but  taking fixed  15  CHAPTER  The source,  III  experimental an  optical  calibration minus  3-1  Source  The  plasma  studied  capacitor inch  long  was  formed  bank quartz  This  portion  produces  either  i s shown  was  tube  shape  was  helium  flared  The  discharge  large  ends  current  1/2  as  (1970).  inch  shown  from  a  bore, in  4.5  figure  because  the c o n s t r i c t e d  center  a h o t , dense  plasma.  The e l e c t r o d e s ,  placed  observe  were h o l l o w the plasma  of the plasma materials.  simple  1 n  it  produced  i s shown  RC  they The  with  along  .78  inch  i t smain  w i n d o w s away  suffered tube  of research  discharge  in figure  a damped  c y c l e . The plasma  interval  experiment  less  was grade  bore  axis. from  By the  contamination  filled  with  at pressures  50% of  3,  torr.  R ~  half  a  and  chosen  a n d 50% n i t r o g e n  6 a n d 9.5  system  stabilized  sealed,  the p o s i t i o n of the quartz  electrode  plasma  (1970) and R . N e l s o n  extending  from  a timing  (3-1).  us  part  of a pulsed  in figure  allowing  hottest  TECHNIQUE  of the  wall  a vacuum  with  AND  layout  by d i s c h a r g i n g  end of the tube, to  a  by H.James  through  (3-2).  at  used  system,  The o v e r a l l  system  Plasma  plasma  consists  spectroscopic  The  to that  APPARATUS  apparatus  equipment.  the timing  similar The  EXPERIMENTAL  circuit  (3-1).  oscillating  When  with  observed  by e l e c t r o n i c a l l y  switching  = 20.4  t h e bank  current  was  C  with  for  a  was 30  usee  1  usee  the detector  uF a n d dumped first time  system a t  16  20.4 fiF  D  ALIGNMENT LASER  1  O  MR SPARK SWITCH  DISCHARGE TUBE  30  AM-  MM  in  19 MM  IM SPECTROMETER  <  1205 D GATE POWER SUPPLY  SCOPE  CHART RECORDER  COMPUTER TERMINAL  Figure  (3-1) : Layout  I205A OMA CONSOLE  MINI COMPUTER  of experiment  without  .»  TO MAIN COMPUTER  timing  system.  17  # m  m  OPTICAL CONE  FLAT  Figure  (3-2)  : Quartz d i s c h a r g e tube.  18  the  first The  current electron  changing  density  the f i l l i n g  temperature in  maximum.  varied  the experiment  only  a  they  (3-1)  1  3.0 6.0  2 3  9.5  The shown  dl/dt  in figure  placed  along  measures function  of  cycle,  =  0).  plasma  to  assume  The  traces  had  t h e same  the  The  discharge signal  at almost  e  and T  for dl/dt time  time  and  dependence  as  run  approximately  the  pin  is  diode  diode  plasma  the  The was  slowly  as  a  approximately first  gate  1/3  signal  activated at that  constant  intensity  coil,  a  about  independent  3.1 3.1 3.1  from  c u r r e n t was  detector  light  ev  a Rowgowski  time.  e  7  3  1  the c u r r e n t v a r i e s  e  T 1  2.2 2.9  from  relatively  used  (3-1).  e  1 1  The  for  t h e same the  N  X10"  cm"  signal  intensity  c o n d i t i o n s were N  v o l t a g e . The  .36  with  path.  by  Conditions  kj  light  when  varied  c o n d i t i o n s were  FIRING ENERGY  as measured  optical  Because  the  MAX  7  ( 3 - 3 ) shows  was  charging  Three  kamps  t o the l i g h t  peaking  figure  I  11 11  time.  proportional  bank  Experimental  6  the  plasma  are tabulated in table  (3-3) w i t h  the t o t a l  and  10 10  trace,  the  little.  TUBE CHARGING PRESSURE VOLTAGE kv torr  RUN  dl/dt  pressure  and  TABLE  of  f o r runs  1 but higher  (at time,  allowing  (see s e c t i o n 2  in  us  (4-4)). and  3  amplitudes.  19  2 MSEC DIV 6KV CHARGING VOLTAGE 3TORR TUBE PRESSURE  Figure  3-2  The  (3-3)  : Arc c u r r e n t t r a c e and  O p t i c a l Spectroscopic  The  optical  system  is  timing.  System shown in f i g u r e (3-1)  and  the  o p t i c a l cone or observed plasma region i n f i g u r e (3-2). plasma  was  observed  along  The  i t s main a x i s f o r almost a l l of  the measurements. T h i s was  done to allow the c o l l e c t i o n of a  s u f f i c i e n t amount of l i g h t  to study  lines.  As  a  consistency  s t u d i e d side-on central  axis  entrance  slit  He-Ne  laser.  with a 19 mm  as w e l l . For the of  the  tube was  of a SPEX 1 The  two  meter  N II end-on  4614  as  and  strong  4643 were  measurements,  point  spectrometer  by  cone  had  a  before  diameter  the — 1/4  vessel the  resolution  —  .1 A.  optical  diameter of  d i s p e r s i o n of the spectrometer i s 8.0  A/mm  a  along  widens,  v e s s e l . The  the  using  lenses shown i n f i g u r e (3-1),  just  the  a c c u r a t e l y a l i g n e d with  diameter stop between them, d e f i n e d the  cone. At the optical  check  weak as w e l l  the the with  Because l i n e s of v a r y i n g s t r e n g t h s were  20  studied,  a  step  spectrometer the  filter  to  allow  positioned  at  the  entrance  c o n t r o l l e d amounts  of  of  light  the  through  slit. The  device  used  Optical  Multichannel  1205D  vidicon  console. single  This  OMA  This  rectangle  divided  unit  separate  the  an  line It  and  profiles  was  consists  1205A  an  of  memory  individual  reduces  the  spectrum sweeps  500  the  storage  profile  current  to  channel on  the  OMA gated  resolved amplifying  the  in  1205A  stage  by  a  of be  which  and  bandwidth across  to  the  first  the The  of  the  high  by  the stage  charged detectors  light  incident  1205D  This  the  micron  500  electron  the  25  these  stored of  a  mm  amplifying  of  i n an  10  produced  array  each  of  sensitive  by  each  the  linear  reads  beam  as  data  is  digitally spectrum 12.5  the i t then  in  a  recorded mm  wide  1205D.  used  in  give  either time  r e s p e c t i v e l y . In is  strips,  detectors.  console  dispersion  modes  a  of  light  current  current  array  could  spectra  The  portion  wide  photodetector.  the  surface  mm  proportional  memory. The  photosensitive The  the  12.5  striking  charge  measuring  1205D's  vertical  upon  corresponding by  a  selected  is amplified  focused  stored  transmitted  or  into  A  the  is  electrons  across  depends  upon  photodetector.  The  the  follows.  surface  1205D a n d  detectors.  as  incident  photodetached  time)  the  (OMA).  records  works  surface.  500  Analyser  device  is  upon  record  detector  spectrum  wide,  to  shot.  The  of  was  defocused  gated by  continuous  integrated mode  the  operating  (= or  real time  detector's i t  at  a  21  reduced v o l t a g e . Then at the d e s i r e d time i t i s turned on by applying  a  large  v o l t a g e f o r 1 ^sec. In t h i s mode the  has a machine width of — 7 c h a n n e l s . During we  observed  the  OMA  experiment  N II and N I I I l i n e s which had widths of ~ 1 A  as w e l l as HE I 5876 and 6678 which had  widths  ~ 10 A.  To  observe n i t r o g e n l i n e s much wider then the machine width yet small  compared to the width of the d e t e c t o r s u r f a c e , i t was  necessary t o p l a c e a magnifying l e n s a t the e x i t hole of the spectrometer. T h i s e n l a r g e d the  image  linewidths  ( c a l - ,03A/ch).  of  20-40  channels  — 6.5  times The  giving helium  l i n e s were recorded without the l e n s  ( c a l - .2A/ch). The  v i d i c o n u n i t was  which  p l a c e d on a  r o t a t i o n a l and v e r t i c a l The OMA  mount  allowed  OMA  careful  alignment.  console c o u l d produce  p l o t s on a c h a r t r e c o r d e r  or  o s c i l l o s c o p e . A f t e r each shot the data was  a  minicomputer  and then to a f i l e  t r a n s f e r r e d to  i n the u n i v e r s i t y ' s main  computer f o r l a t e r m a n i p u l a t i o n .  3-3  The Timing System The t i m i n g system  figure  (3-4).  After  f o r gated mode o p e r a t i o n i s shown  in  the d i s c h a r g e tube has been f i l l e d  to  the d e s i r e d p r e s s u r e and the c a p a c i t o r bank charged  to  desired  iniates  v o l t a g e , a manual s w i t c h i s t r i g g e r e d which  the  the d i s c h a r g e procedure. To know how the  internal  to time our d i s c h a r g e  timing  of  the OMA.  The OMA  from the channels s e q u e n t i a l l y i n 38.4 beam  sweeps  we  must  understand  reads the s i g n a l  msec as the  electron  a c r o s s the d e t e c t o r s (the read c y c l e ) . I t then  22  resets  .6  msec  (the  repeats.  To  time  resolve  discharge  and  record  is  in  done  until is  by a  dead  the  turned  on  time by  (at  our  spectrum  d i s a b l i n g the  set  time)  and  plasma  we  during  the  amplifier  the  applying  the  of  read  must dead  the  fire  the  time.  This  photodetectors  discharge  current  a  volt,  1  the  manual  -1300  cycle  maximum) when i t  usee  duration  pulse. The allows The  the  then  timing  100  and  pressurized  The DI/Dt  s i g n a l as  signal  reaches  a  after  a  This  immediately  provide hence trace  -1300  I  after  oscilloscope, the  of  from  by  a  variable  the  a  The  the  by  a  a  (or  1 »»sec  timing  delay  of  of the  the  to  The a  trigger  By  the  unit  be to  of  power  the  coil's when  trigger  the  unit, switch.  supply 1205D the  trace adjusted any  a  trigger  The  the  gate  a  ionizes  edge  observing  could  of  krytron  to  by  commence.  switches  pulse  gate  to  coil.  gate  i n t e g r a t i o n ) and  kv  pin  leading  the  spectrum.  20  spark  bank  which  signal  long  air  time).  allowing  the  the  rising,  unit  to  The  produces  i t produces  Rowgowski  level  sends  of  of  unit.  center  spark  i t s dead  which  i s boosted  which  console.  reaches  unit  capacitor  fast  OMA  timing  SCR  to  trigger  fires volt  to  the  pulse  the  the  preset  measurement (or  to  switch  the  vidicon  electrodes  variable delay,  the  back  This  measured  is received  signal  the  signal  main  s i g n a l to  until  switch.  discharge  i s timed  a  applied  a i r spark  the  gate  a  pulse.  the  with  send  signal  i s then  a i r between  allowing  to  sends  volt  starts  waits  a  then  transformer  the  unit  then  sends  unit  short  firing  timing  console  time,  a  actual  time  to and  DI/Dt on  an  using during  23  I205A OMA CONSOLE  — f A I205D ^ I V:>DETECTORyy  TIMING UNIT  GATE POWER SUPPLY  SCR UNIT  KRYTRON SWITCH  TRIGGER UNIT  mm  I^NAIR S P A R K \J  TRIGGER  Figure  ->  vcr ROGOWSKL COIL  (3-4) : Timing  system  24  the  d i s c h a r g e . Timing j i t t e r  from shot to shot was l e s s then  .1 (isec by the above method.  3-4  Calibration To measure the Stark widths of  first  the  had t o c a l i b r a t e the wavelength  line  profiles  we  accurately.  The recorded p r o f i l e s a r e the c o n v o l u t i o n of the a c t u a l emitted  profile  with  the  broadening  function  measurement system. To determine the Stark widths total  widths  we  had  to  neon  laser  at  from  6328.2 A.  The  profile  laser  width was — 7 channels at halfmaximum 1/10  maximum.  To  find  the  assumes the machine p r o f i l e convolution  of  to  can  easily  be  using the  deconvolution  H. van de  Hulst  and  at  a  Voigt  profile  the  because  and  tables  1/10  maximum  provided  J.Reesnick  most  20%  the  (1947).  in a  the  1/10  maximum  the  by  A n a l y s i s by t h i s usually lines.  is difficult  to  apparatus p r o v i d e s such few p o i n t s on n o i s e i s s i g n i f i c a n t a t that  l e v e l s i g n a l . A l s o the a p p r e c i a b l e asymetry makes  Stark  paper  f o r some of the narrowest  machine p r o f i l e and because  profile  (the  found from the measured p r o f i l e s by  U n f o r t u n a t e l y the width a t measure  machine  widths one u s u a l l y  method gave the machine broadening c o r r e c t i o n to be ~ 10%  has a  a Gaussian and L o r e n t z i a n ) . Then, using the  machine widths a t 1/2 maximum and widths  a  and — 14 channels wide  Stark  be  of  light  n e g l i g i b l e width compared t o the machine width. The  at  the  determine the machine broadening  f u n c t i o n . T h i s was measured by r e c o r d i n g the helium  of our  analysis  of  the  machine  q u e s t i o n a b l e . Thus i n s t e a d of  25  using the  the  deconvolution tables,  machine  Run  2  conditions  different two  with  linewidths 2.2,  N  and  if  3995 the  simply  were  He  subtract  I  machine  broadening to  channel  channels.  Though  iron  5876  at  the  OMA  were exit  1.8  machine obtain  width  of  To  calibrate  arc  placed  in  strong  in  lines  the  (150  at  two  surface.  The  measuring  the  lens  in place  for N are  That  channels  widths. the  II  and 3919,  consistent  Lorentzian. 7  at  channels)  These  lowering  i s , we  from  This  the  should  error  for  be the  ±10%. whether the  of  50  channel  the  machine  He-Ne channels  slightly  wider  150)  the  OMA  at  this  channels  front iron the  of  arc  broadening  laser  profile  was  across  the  500  the  full  lower  d i d not  channels  affect  over  whole  the  calibration the  wavelength was  found  the  to  spectrometer).  differ Since  of  an the  (C.Hodgman  (1957))  significant  interest by  slit  used  narrow  three of  we  well-identified  range  range  to  entrance  many  optical  accurate calibration  to wavelength  the  has  permitting  to  A  Stark  3995  profiles.  The  (due  With  by  channels)  a  number,  i t was  spectrometer.  The  4.3 (29  the  and  1 conditions,  possible  like  before  below  at  A  3919  detector  respectively.  intervals  8 channels  II  lens.  and  5.4  determine  at  measured  the  carefully  measured  (FWHM ~  Run  5876  to  more  with  I  and  the  checked  varied  He  broadens  widths  Also,  N  1.0,  3.0  machine  measured  recording  across  without  experimentally determined  by  dispersions  and  without, II  and  dispersions  different  lines the  broadening  we  ~  this  3%  (3800-6800  over  was  figures  this  much  less  A).  range then  26  other  errors  calibration channels  the was  also  to within  a  the  iron  mode  and c o u l d only  time.  arc  The  amplifier scale gated  shift  number  was  specific  rechecking  500  channels  channel  the  number  from  channel  source  To  straight  was  obtained.  observed  gated  without  measure  we  function  across  no  after  vs  a  exit  each lens  channel  this  this  graph  linear  number  channels  vs  response  to  and we  Because  place.  of The later  same,  below  that  a  light  produce  pure  helium  the  constant  needed  To  with  continuum  limit,  i s fairly  above  the  for shift  i s not the  response  lines.  was  across  up t o a c e r t a i n  realignment in  laser  channel  mode  line  a t 5300 A where  affected  time  The  switching t o gated  discharge  spectral  signal.  on a  t h e 500 c h a n n e l s .  the  wavelength  line  The r e s p o n s e  the r e l a t i v e  fired  and  the  mode.  real  o f t h e 1205D's  of real  150 t o 4 5 0 b u t i s w e a k e r  detector  measured  receive,  that  in  of the  By d o i n g  give  of d i f f e r e n t  the spectrum  continuum  channels  t h e 500  i n gated  OMA  of the l i g h t  then  almost  continuous  continuum  time,  an  sensitivity  the  t h e He-Ne  number.  they  t o be o b s e r v e d  function  the channel  signal  range.  the  in real  light  in  as a  The  c o m p l i c a t i o n was  a widening  number  used.  across  defocusing  by p o s i t i o n i n g  individual  especially  and  was  linear  to calibrate  causes  shift  Though  relative  be  t o o weak  i n channel  channel  and  were  be u s e d  obtained  4500 A  f e w % . One a d d e d  mode  time  at to  focusing  i n gated  to real  found  lines  rapid  or  calibration  helium  has  a  the optics, measured used  and  strong  the alignment  response,  the  i t  of was  with and response  to correct  the  27  measured  spectra.  fullwidths OMA  and  less  thus  response  when  corrected. Usually  be  done  a  the  just  3-5  Firing  this  be  sure.  exit when  the  lense, taking  be  However  the  OMA  range.  We  lines  region  the  look  response  two  The  linear  plots  of  we  had  had to  to  of  lines  the  effects  of  a  lot  the  are  lines  this  affected  the  better  OMA  vs  has  to  compared  for  used  were  not  vary  we  response  had  of  necessary. This  tested  be  follow  The  steps  helium  and  nitrogen  Align  (3)  Measure  gated  to  and  machine  width  u s i n g he  OMA  (4)  Measure  pure  helium. Record  N  system  does with  a  tungsten  using  iron  continuum  II  and  N  continuums  for  each  graph  and  stored  paper  and  and  without  complicated  in mixing exit  time ne  calibrations  the  procedure  :  with  real  with  rather  were  (2)  optical  made a  data.  Mix  (5)  the  would  (1)  of  the  to minimize  the  alignment  measurements  scale  a l l measured  Procedure  Because because  A.  over  to  of  light  measurements.  appreciably  of  However,  magnitudes  2-30  that  positioned  incident  by  lamp  be  out  spread  calibration  when  separated  the  function.  of  temperature  than  could  the  wavelength  It turned  chamber.  lens  channel laser.  in  place.  number  Determine  correction wavelength  arc. response  III line.  by  spectra The  digitally  firing  as  profiles in  the  discharge  well were main  as  into  nearby  plotted  on  computer  28  after  each  refilled (6)  shot.  with  Remove  The  clean  exit  discharge  gas  before  lens  and  was  each  pumped  out  and  directly  on  shot.  realign  OMA  spectrometer. (7)  Redo  step  (4).  (8)  Fire  discharge  This  procedure  3-6  Data  Handling  Each  profile  element  array  intensities  was  of  project  (Msc.  raw  into  data  was  that  programs  that  represented  fell  upon  John  finished  subtracted  normalized  the  were  measured  (1979)),  the the  center  scale From a  the  Bernard,  plots.  of  line  with  runs.  numbers  of  paper.  a l l three  6678.  digit  profiles,  graph  and  computer  response  ruled  5876  in a  thesis  wavelength  for  I  stored  continuum  the  r e c o r d He  performed  6  computer  and  were  produced final  for  to  the  a  corrected  one,  finished plots  for  this the the  continuums, calibrated  plots  the  The  similar  smoothed  background to  a  500  light  transform  slightly  intensities  these  used  programs  OMA,  as  photodetectors.  developed  determined  and  ruler.  The  500  file  on  fine  fullwidths  29  CHAPTER  In impact T  e  Chapter halfwidth  through  test  our  the  ratios  the  both  of  We  local  discuss  electron  4-1  e  In  T  of  He N  . The  e  I  II  line  diagnostic  in  detail  recombination  plasma  collisions.  densities equat ion.  in  The  condition  electron  weakly  we was  to  depended  N  well  dependence  and  the  to  had  to  estimated from  the  III the  on  as  giving  on  Therefore  temperature  line plasma  as  plasma  opacity.  temperature  (LTE). of  an  A  ion  different  excitation, are  between  plasma  (H.Griem  and  atomic  given  LTE by  ch.6)  de-excitation,  can  states  called in  (1964)  controlled primarily  collisions  temperature  states  and  density  equilibrium  Equilibrium  and  electron  the  theory  intensities  before  ionization  equilibrium  e  (2-12)).  the  methods  dense  quantum  and  N  for  measurements.  Thermodynamic  equilibrium  (see  r e p r o d u c i b i l i t y , time each  on  against  5876  hot  the  expression  electron  a  electron  DIAGNOSTICS  linearly  thermodynamic  density  Local  an  depends  and  These  homogeneity,  give  measurements  several  in  PLASMA  v e l o c i t y average  width  intensities. being  N  we  that  width  determine from  I  IV  create and  local has  the  i o n i z a t i o n stages  given  an  species  at  thermodynamic  densities  Boltzmann  by  in  various  equation by  the  and Saha  30  The  Boltzmann  equation  for  the  density  of  ions i n the  excited state n i s : N  in  N,  =  where  N  g  /kT )  in  (4-1)  fi  = the d e n s i t y i n the e x c i t e d  ) n  Ej  exp(-E  ln  = the e x c i t a t i o n  n  Nj  state  energy  = the t o t a l d e n s i t y of the ion  Z , ( T ) = the p a r t i t i o n f u n c t i o n e  and  gj The  = the degeneracy of the e x c i t e d  n  Saha equation  f o r the r a t i o of t o t a l  state. densities  in  two c o n s e c u t i v e i o n i z a t i o n stages i s : N Nj = 6 x Nj  10- Z j ( T ) ( k T ) Z j (T ) 21  e  The  e  3 / 2  P  exp(-E; /kT ) r o  (4-2)  e  e  higher  ionization  stage i s l a b e l l e d by i and the lower  by j . m  i s the e l e c t r o n mass. We ignore the s m a l l  of  ionization  the  .1 ev i n t h i s  potential  lowering  by the Debye sphere which i s  experiment.  To s o l v e f o r the i o n i c d e n s i t i e s at a p a r t i c u l a r N T  e  we use (4-2)  and  the  n e u t r a l i t y . The l a t t e r N  e  Zj  equation  of  macroscopic  the  (4-1) (4-3)  us  charge  an  number of the i  t h  ion stage. The sum i s  i n the plasma. Using  (4-2) with  (4-3)  equal number of equations and unknowns. Table  shows the i o n i c d e n s i t i e s c a l c u l a t e d by  charge  (4-3)  over a l l ions present gives  and  is :  = ZzjNj i is  e  Dr.A.J.Barnard's  computer  from  (4-2) and  programs,  at  the  31  estimated  temperature  studied singly ~  (see  of  sections  ionised  90-80% the  and  doubly  TABLE  See  The  (4-8)). ~  0.9  X10  I II III IV  electron  velocity  distribution  required  to  given  by  t  10 (kT /ev)  ~  t  H.Griem  5  T  e  3  tjj  ~  (mj/m )  to  equalise  our is  1  /  2  helium  we  safe  get  to  ~  in Table  =  e  3.1  2.9  1 7  e  varied assume  =  For  and  (4-1).  ev  X10  1 7  3  15.09 17.01 14.28 12.87 16.25 16.93 14.44  definable is  temperature  Maxwellian.  i f the  The  velocity distribution is  (4-4)  2  x  10  ions  the  x  1.3 10"  1 0  little that  10" sec  in  .1  both  cm" ,  1 7  of  time  x  time  :  1 0  mass  is  t |  sec  and  and  usee  (4-4)  3  m.  for both  temperatures  t j j " .7  e  and  . cm" ))  Maxwellian  N  99%  description  3  their  tjj  plasmas  e  is ~  Ne'cm" sec  and  t  a  (1964))  sec.  1 2  e  nitrogen for  10"  ev  3  e  x  =  ~  e  3 / 2  e  Using  have  establish a  T  plasmas  ionised  for a  14.85 16.88 14.28 12.52 16.02 16.82 14.57  16.48 14.26 1 1 .38 1 5.26 1 6.45 14.59  will  e  X10  0  1 4.06  singly  At  2.2  1 7  the  helium  values  Densities  electrons  e  the  of  The  (4-5)  Log, (N  I II III  (see  7-20%  section  Ion He He He N N N N  densities  calculate  Ionic  3  and  nitrogen  to  (4-1)  cm"  e  the  used  electron  (4-7)  ionised.  programs  N  and  tj  the  ions m  ~  t  j  e  ~  .025  (see  electrons  time  and  ~ ( \/  e  m  is  electrons ^ ee * t  e  .1  F  »isec  >.sec.  section and  gives  o  r  and  Since  (4-4)) i t ions  have  32  Maxwellian v e l o c i t y d i s t r i b u t i o n s at the same temperature. For  a  electron  Boltzmann  density  excitations  distribution  must  be  high  completely  to  exist  enough  dominate  at  so  T , the e  collisional  over  radiative  d e - e x c i t a t i o n s . Estimates of the minimum neccessary e l e c t r o n d e n s i t y are o f t e n made by r e q u i r i n g the average excitation  of a l e v e l t o be 10 times g r e a t e r  than the  average r a d i a t i v e d e - e x c i t a t i o n r a t e . The d e n s i t i e s  i n the  various  10%. In  states  general  this  because lower  rate  collisional  will  i s more e a s i l y  they  have  radiative  separations  then  follow  s a t i s f i e d by the  larger  decay  (4-1) t o w i t h i n  collisional  rates  due  higher  c r o s s - s e c t i o n s and  to  smaller  e x c i t e d s t a t e s are o f t e n governed by  if  lower  r a d i a t i v e decay  states  are  relatively  reabsorption  emitted  (4-1)  overpopulated  during  of  resonance  transitions  line  to  the  radiation ground  state  hence  the minimum neccessary N  e  (radiation  state).  reduces the r a d i a t i v e decay r a t e to  the  a N II and N I I I plasma at 3  (1975),  consider  collisional  ev,  and  They give the minimum neccessary N  e  as 3 x 1 0  cm" . Since  the  electron  3  densities  this  found  is in  well this  cm" ) equations (4-1) and (4-2) should 3  below  experiment  et.al.  resonance  absorption. 1 6  ground  criteria  W.A.Cilliers,  processes  This  f o r a Boltzmann  d i s t r i b u t i o n . In a paper on the thermal e q u i l i b r i u m for  by  the plasma r e a l i z e f u l l LTE  effectively and  even  ( p a r t i a l LTE).  A process which o f t e n helps is  energy  between l e v e l s . Thus the r a t i o s of d e n s i t i e s i n  the higher the  states  f o r f u l l LTE estimated  (~ 2 x 1 0  be accurate  1 7  to w i t h i n  33  a  few % f o r t h e n i t r o g e n Papers  b y R.Mewe  we c a n e x p e c t papers from  the  (4-1)  full  Table  II  reabsorbs  were  full  of  for  Mewe  (optically  state  optically quantum states of  density  density  even  nitrogen  This  transition  to  state  less  (~ 2/3  the  f o rthe  (triplet  3  because  they  free  state we  f o r an principal  The  higher  t h e ground  Because our  not  decrease  come  o f t h e He I with  from levels  (4-1) and  state the  calculate  the  the electron  electrons  of  state  stage,  and  of t h e ground  when  (4-1)).  see that the  LTE.  may b e p r e d i c t e d  lower  2 P°)  we  will  the densities  population  Our  He I I  appreciably of  state  line.  difference.  o f t h e He I g r o u n d  ( s e es e c t i o n  Besides  close  be i n L T E w i t h  He I I  strongly  overpopulated  the  the  that  b u t by t h e s e c o n d  energy  decay  (see table  in  i s important  depths  also  resonance  resonance  times  are  of the small  t h e ground  using  of a plasma  stage  line  densities  interpolating  t o t h e 304 A l i n e  10  i o n i z a t i o n ) . Thus  than  (4-2)  ~  the levels  of  by  that these  radiative  1 and 2 of Drawin  predominantly  overpopulation  other  tables  o f t h e He I w i l l  i s  f o r He I I case  thick  of state  and  t h e 304 A  resonance  He I I b e c a u s e  the  the  o f He I i s  number  plasma  LTE  i n t h e He I I  from  thin  show  by c o n s i d e r i n g  excitation  thick)  optically  Interpolating  the ratio  calculated  conclude  predominantly  ground  calculate  collisional  were  (1964)  L T E f o r He I I b u t n o t f o r He I . I n  to densities  We  plasmas  ( 1 9 6 7 ) a n d H.W.Drawin  authors  absorption, rates.  II and I I I ions.  o f He He I  I I . 5876  the optical  (4-5)).  a minimum  N  e  requirement,  the various  ions  must  34  take s u f f i c i e n t l y plasma  must  short  respond  times  to  reach  equilibrium.  rapidly  to  changes  i n the  p a r a m e t e r s w h i c h i n t h i s e x p e r i m e n t v a r i e d by t h e several  «sec.  slowest  of  reached.  the  This  s t a t e because ground  The  processes is  and  e q u a t i o n 6-65)  the c o l l i s i o n a l  lowest  gives  t i m e w h i c h we and He  Table  e  (4-2) f o r N  y<sec w h i c h i s s t i l l  II.  for  They  longest  significantly  shorter  the the  are  the  ((1964),  collisional equilibration tabulated  i s f o r He than  in  II at  the  .2  plasma  (4-1)  E q u i l i b r a t i o n T i m e s From R e s o n a n c e N  e  I on  = 2 x 10  1 7  He I  Resonance Line (A)  584  Equilibration Times (sec)  1x10-  Plasma To  ground  time. Table  4-2  of  is  between  s t a t e s . H.Griem  . The  1 7  of the  differences  use t o c a l c u l a t e  = 2X10  order  equilibrium  excitation  expression  I and  external  be e s t i m a t e d by t h e  which  excited  an  t i m e s f o r N I-111  variation  through  of t h e l a r g e energy  state  excitation  e q u i l i b r i u m t i m e may  The  cm* He  II  N  304 2 x 1 0"  6  = 3.1  e  ev  I  N II  1 135  1 084  2x10"  6  1 2  Rates  4X10"  N  III 990  9  5x10"  1 1  Homogeneity  interpret  our measured  that c o n t r i b u t i o n s to the l i n e from r e g i o n s of d i f f e r i n g inhomogeneity  T  3  Excitation  arises  N  e  p r o f i l e s we must be  i n t e n s i t i e s were n o t  and T .  because  e  uneven  In  our  plasma  certain received regime  Ohmic h e a t i n g and  heat  35  t r a n s p o r t to c o o l e r r e g i o n s c r e a t e s temperature, d e n s i t y and pressure g r a d i e n t s . By the Saha e q u a t i o n , lower regions  have  lower  electron  density  temperature  because  of  less  ionization. In s e v e r a l p r e v i o u s s t u d i e s performed on s i m i l a r sources, the r a d i a l and a x i a l dependence of the studied. was  R.Nelson  formed  plasma  i n the c o n s t r i c t e d s e c t i o n of the v e s s e l when a 9  showed that N tube w a l l s  e  was  uniform r a d i a l l y t o w i t h i n  .05  gas.  cone  for  the  uniformity  of  N  suggests that T  e  uniform, at l e a s t to w e l l o u t s i d e the o p t i c a l a l s o showed that the temperature was tube  axis  in  outside  the end-on measurements (see f i g u r e  ( 3 - 2 ) ) . Though the r a d i a l temperature d i s t r i b u t i o n measured,  was  not  i s also  e  cone.  Nelson  very constant along the  the c o n s t r i c t e d s e c t i o n of the v e s s e l .  Past the p o i n t where the tube f l a r e s , the temperature rapidly.  As  to  the  e l e c t r o d e s . By assuming a l i n e a r  g r a d i e n t and that N  e  drops by 2/3  we can estimate the amount  from the c o o l e r r e g i o n . We  at  region because with any  for  the  cold  temperature g r a d i e n t the plasma  is solely  N II  He II  stages  predominate tables  from  instead  of  the  i n the c o n s t r i c t e d  widening  temperature  of l i n e r a d i a t i o n coming 1/3  drops  a rough estimate from h i s data the temperature  approximately h a l v e s i n h a l f the d i s t a n c e from the point  He  i n . of the  (10% of the t o t a l d i a m e t e r ) . T h i s i s w e l l  optical  main  was  (1970) e s t a b l i s h e d that a uniform plasma  kamps c u r r e n t was d i s c h a r g e d i n t o a 10 t o r r helium  the  plasma  in  use  N  e  significant  the  He I  and  and N I I I stages that  s e c t i o n of  the  tube.  Using  Dr.Barnard's programs based on equation (4-11)  36  for  line  5876, He  ~  3%  II and  regions. we  intensities, line  III  line  N  These  don't  uniform  side-on widths  4-3  by He  should  comparing  found  come  that  of  from  He I  amounts o f the  cooler  and e l e c t r o n  the axial side-on  the width  5% o f t h e w i d t h  n o t be s e r i o u s l y  5%  inaccurate estimates  temperature  showed  ~  density  end-on  o f He  profile  I 3889  observed  affected  density  electron  and  observed  end-on.  by  since  Thus our  inhomogeneities.  Reproducibility  shot  plasma  minute  t e n warmup  were  taken  intervals).  varied hence  c o n d i t i o n s were  i f about  measurements  by T  firings  to  pitted,  drift  involved  i t took  The  our  i f we  because  of the large  windows  etc.  of  had averaged number  data of  the  of l i n e s  as  taking  between  was  shots  of t h i s  we  irreproducibility  reproducibility several shots  between  electrodes  r u n . Because  plasma  e  15% a n d  operation  data  minutes  N  the system  stained,  Since five  by ~  Also  of  (~ o n e  hence  intervals  hours  shot  i f the  succession  not as good.  several  estimates  effect  reduced  was  full  and  varied  longer  at least  for a  rapid  from  of l i n e w i d t h s and  at  quartz  varied,  s i x hours  raise  somewhat.  over  taken  intensities  However  changed,  timings  about  should  "~ 1%.  line  reproducible  were  in fairly  the reproducibility  alignments  fairly  The  very  shots  Measurements  "~ 5%. by  e  tended  and  very  that  and n e g l i g i b l e  intensities  Nelson  was w i t h i n  The to  intensities  the d e t a i l e d  Finally  measurements.  estimate  are of course  know  profiles. was  N II  we  could  of each  studied  have  been  p r o f i l e but  this  was  not  37  done.  4-4  Time A  study  timing the  Dependence  showed  plasma  at  electron and  the  the  of  the  width  them  to  the  final  density  vary  intensity  ~  5%  over  chosen  varies  temperature  other  and  by  ~  the  during  and  He 1  I  5876  usee  timing.  5%  negligibly.  uncertainties  of  we  This  our  vs  gate  observed  means  our  observation  This  is  small  the  plasma  time  compared  can  to  considered  quasi stat ionary.  4-5  Optical  Depth  Photons  emitted  plasma  may  already  be in  absorption collision  the profile  To  from  of  length  length  volume  Strong  at  of  emission  near  the  then  of line  the  finite plasma  Because  profile  line  reabsorption  is  a  the  transition.  the  photons  plasma  height  the  as  halfwidths  c a l c u l a t e the  plasma  the  of  atoms  within  are  flattens  the  optically  reabsorbed will  a  center  called  center,  in  the  lines,  overestimate  width.  intensity  at  the  transitions  those  same  plasma,  and  the  light  unit  state  reabsorbed.  Profile  Stark  by  i s the  dominated  determined the  lower  profiles  thick.  atomic  reabsorbed  preferentially emitted  from  K(o).  edge element  of  optical  emitted 1 and The the  within  by  thickness, a  constant  homogeneous, absorption  contribution plasma, the  T,  to  I (o), m  plasma  at  the  the  stationary,  LTE  coefficient intensity  from x,  consider  an with  per  measured  infinitesimal emissivity  38  I (o)/l  (emitted  e  dl (u)  =  m  unit  length)  along  U)  e  the  line  of  sight  ( 1-exp(-K(u)l) )  from  = IpU)  T (u ) = An  a  173).  T(U)  =  It  is  0  r  0  f  n  m  n  L(o) We units.  =  2.82  for  state  m  to  a n  :  0  to  1  gives  :  ( l-exp(-rU) )  spectral line i s given  n  the  classical  =  the  absorption  =  the  ion  =  the  normalized  (4-5)  by  emitted  during  H.Griem  ((1964)  the  10-  N  2  1  we  f  =  n  get  (4-6)  radius  oscillator i n the line the  emitted 0  n  electron  in  L(X. )  ))L(o)l  e  density  (4-6)  then for  x  T  =  w  (4-1)  for  N ( l/exp(-WkT  rewrite  halfwidth  0  n m  Assuming  Using  as  :  2  N  T  from  2n r cf  where  written  K(o)1  expression  transition  pg  be  T T O )  K(o)l where  can  e  = I  m  per  dx(I (o)/l)exp(-K(o)x)  Integrating  I U)  power  lower  for  T  more  where at  state  shape practical  profiles 1/irw  strength  are X.  0  line  wavelength  Lorentzian  i s the  line  center.  center:  N g (exp(-E /kT )-exp(-E /kT ))X Z (T )  m  0  n  n  with  B  m  e  2 0  l/w  e  (4-7)  With by  ~  depth  T  T /4 0  below  Initial  0  x  below 100%. .4  by  1 the  total  Usually  one  considering  calculations  on  emitted  intensity  is  reduced  keep  the  optical  parameters  in  (4-7).  attempts the  several  N  II  to  and  N  III  lines  and  39  He  I  5876  were  showed  forced  to  There  were  depths.  (1)  we  had  to  voltages reduced dirty through large did  recheck  stained  amount  of  however  clean  At  the  measurements  of  firing  conditions.  (2)  state  by  varying  Reducing  the  total  electron  density  and  It  is  lower  also filling  reduce of  the  helium  at  the  to  50:50  nitrogen-helium would  have  see  which  all  the  were LTE  us  still  Also  the  obscured  of  another  redo  our  considerations.  just  for  survey  Thus  we  such of  mixture. the  problem We  at  cannot  the  ratio  reabsorption  as  diluted  the  argon.  This  nitrogen  besides passed  the  experiment.  is a  from  in  reduce  this  have  gas  lines  gas  took three  density  or  a we  and  the  changing  suffer  with  acid  (1966)).  could  argon  experiment  would  (C.R.Neufeld  We  gets  the  homogeneity  both  vessel  the  of  pressure  by  and  to c o l l e c t  interest  problem  would  wished  pressure  plasma  we  was  we  number  filling  problem  observations  the  Reduce  a  1.  making  4643  the  reducing  plasma  firings since  optical  observable with  and  by  we  pressures  4614  because  to  various  N  II  the  equipment  hydrofluoric  depth  so  apparatus  with  ratio.  forced  the  were  filling  mixture  at  the  tube  the  range  thus  end  pressures  nitrogen  reduce  very  that  optical  3  the  hence  known  to  changing  repeated  side-on  lower  so  especially  data.  to  r e a b s o r p t i o n was  lines  they  from  .5  side-on  realized  length.  i t difficult  us  restructuring  if  path  to  plasma  a l l the  see  optical  open  experiment  Besides  to  and  the  i n the  experiment.  ways  only  i n the  undesirable. have  three  Observe  late  depths  r e a s s e s s the  Unfortunately fairly  optical  on  lines  to  complicating this  option.  40  (3)  Choose  relatively  strengths. generally  or  Unfortunately more  because  they  difficult have  theoretically.  lines  multiplet  stronger,  more  s t r o n g enough  final  selection  depths check  and on  As  of  one  t o be lines  the  observed  profiles  m  T  0  (N.Konjevic  The  problem  those  to  tried  m  For the  low  new  t o measure  optical  lines. two  depends  plotted on  s  with  accurately.  lines  (4-3).  I and  N  - 1)  depth,  in principle  the o p t i c a l  (4-8)  errors  II and  of  depth width  we  i s known. w  vs  s  the  must  (4-8)  in T  0  1  (4-1) f o r r be  . We  i n 1,  than  5%  f  T  0  n  m  0  t o 4.  i s hard , T , e  N  e  in 1 are less  for N  Since  iteratively. to  III i f  we  The  determine  and  t a b u l a t e the e r r o r s  uncertainties less  from  0  solved  i s that  uncertainties  The  a  multiplet.  i f  in figure  using  The  considerable table  w,  As  (4-8) 0  is  the  i s to choose  with  measured and  and  lines  w„  problem  He  to a  :  0  s  width,  t h e weaker  get f o r the Stark  (r /ln(l/(l+exp(-T ))) w /w  that  yet not absorbed.  picked  also  is  approximation  the o p t i c a l  ( 4 - 7 ) , we w  lines.  experimentally  Stark  cases  are  interest  favor  measuring  close  t h e same  reducing  (4-5) and  by  a  we  we  t h e same  i n unusual  Thus  get  depth  as  width  have  i n our  lines  less  studied,  thing  of p r e v i o u s l y  =  s  and  infrequently  s t r e n g t h from  well  measured  w  a mix  correct  Using  of  optical  differing  can  t o measure  interesting  lines  oscillator  weaker  except  can  low  the  (1981)).  we  with  of  However,  approximation,  M.S.Dimitrijevic a  been  lines  most  i n t h e same m u l t i p l e t  close  in  weak  w  in  than  cause  s  T  0  in  10% f o r  accept  the  41  Figure  (4-1)  : Corrected s/ ) (  w  w  v  m  rough  estimates  oscillator The  within (4-8).  7%  The  estimated from  and  (4-2) and for  w. s  The  width  uncertainties  by W.L.Wiese,  ratio  i n the  et.al.  (1966).  i s estimated in section  (4-7) t o  measurements  e  corresponding  5  (4-3).  are given  measurement  the N  from  chapter  Stark width t o measured optical depth.  of section  strengths  temperature  s  errors  (4-7).  We  to within  ~  30%  these  cause  used  an  in  in T  average  section 0  can  be  error  42  Table  SOURCE ION  1  He I N II N III  5 5 2  The in  T  0  three  OF ERROR T  1 10 12  N e  10 1 2 32  values  i n  a r e large,  excessive.  Also  sets  (4-3)  Error  IN T  e  W  25 25 16  0  s  TOTAL  T =  s  0  ERROR FROM T  m  • 5  1  5 7 7  ( 4 - 3 ) show  errors should  15 21 22  though  i n w /w s  0  1 .5  10 14 15  that  the uncertainties  and thus  0  w /w  50 65 70  ~ 2/3 o f t h e s e  of data,  T  (±%)  7 15 15  table  In  the errors are  m  are systematic not affect  not  t o the the N  e  sealing. Another comparing  equal Thus  Consider  depths  T  transition from  of  determining  the intensities  multiplet. optical  method  0  of  two l i n e s  a n dT  0  lines  from  ' . Thel i n e s  energies,  Stark  T  0  i s possible  within  by  the  same  t h e same m u l t i p l e t ,  with  will  widths  have  and  approximately  optical  paths.  ( 4 - 7 ) we g e t :  T_o_= 9rifnm = BC o' 9p f p q  (4-9)  T  where  B = g /g  From  equation  line  n  center  D = ImUo) ImUo)  p  i s  and C = (4-4)  fm/fpq • n  the ratio  o f measured  intensities at  :  = IeUn)(1-exp(-T ))/T IeUo) (1-exp(-T ' ) ) / T ' 0  0  N  0  (4-10)  43  From H.Griem ( 1 9 6 4 ) ,  page 1 7 5 ,  center  is :  I Uo)  = 4ir hc rog f mN L()\ ) 2  e  and  the emitted  intensity  at  (4-11)  2  n  n  m  0  (4-2)  t h e r e f o r e using  line  the r a t i o of  emitted  intensities  is : IeUp)  iIUo)  n  9ppq f  (4-9)  Substituting T  0  (4-12)  and  (4-13)  is  get : (4-13)  easily  be used to f i n d T  must  measure  the  l i n e s from the same significant  oscillator  The  In t h i s experiment D was  shots, i t  could  percent. (1966),  The  Equation  T , e  / s are  w,  e  (4-13)  or  s  accuracy  can  it the  to  30%  within  or a v e r a g i n g to  within  two give  does not absolute  but  D. by  several a  few  o s c i l l a t o r s t r e n g t h s given by W.L.Wiese, e t . a l  over  the  wavelength  experiments s c a l e . The  i n a c c u r a t e because a b s o l u t e  line  using given  (4-11) absolute  intensities  number d e n s i t i e s i n e x c i t e d s t a t e s are d i f f i c u l t However,  method  i s governed by C and  determined  were measured i n emission  integrated  N,  measured  be  this  because  l i n e s simultaneously easily  To use  which  0  i n t e n s i t i e s of at l e a s t  (4-7)  over  of 1,  strengths.  the two  ' from ( 4 - 9 ) .  relative  improvement  measuring  0  solved numerically for T  multiplet.  depend on the accuracy  n t T  we  0  then can  f  in ( 4 - 1 0 )  = -ln(D(exp(-T /BC)-1)+1)  Equation  we  (4-12)  = g fnm = BC  and  to measure.  r e l a t i v e o s c i l l a t o r s t r e n g t h s for l i n e s w i t h i n the  44  same m u l t i p l e t w i l l obey (4-12). The C's  will  are  no c a l i b r a t i o n  the  the two  problems. Thus the C's  Wiese  are  probably  a p p l i c a b i l i t y of  calculated  accurate  to  from  within a  (4-13) w i l l depend on  few  whether  l i n e s d i f f e r s u f f i c i e n t l y i n s t r e n g t h so t h a t one  preferentially condition errors  the r e l a t i v e  given  nearby l i n e s . T h i s i s very easy to measure because there  percent. The  on  the  two  of  only  of  i n t e n s i t i e s of  tables  depend  accuracy  absorbed.  i s not met  in  D,  Unfortunately  That  (4-13)  i s D/BC  is  i n t h i s experiment  < .8 say. If such a  extremely  v i r t u a l l y r u l i n g out  is  susceptible  to  the use of t h i s method.  we  did  not  measure  the  r e l a t i v e l i n e i n t e n s i t i e s to the degree of accuracy  possible  because  the  was  we  had  collected.  not worked out t h i s theory before  We  must be s a t i s f i e d with D's  ±15%.  T h i s t y p i c a l l y g i v e s an e r r o r of ~ 100  so we  used  future with  (4-7)  use.  i n s t e a d , though we  In chapter  (4-13)  for  comparison  we  since  depends on LTE and  (4-7) An  depths  with  could in p r i n c i p l e  % or more i n T  values (4-7).  for T  check our LTE  0  computed such  a  assumptions  (4-13) does not.  p o i n t t o note i s t h a t though  of  lines  were  0  From  important many  within  note (4-13) f o r p o s s i b l e  5 we present  comparison  good to  data  the  l a r g e enough to a f f e c t  optical end-on  measurements, only the resonance l i n e s were strong enough to a f f e c t population d e n s i t i e s in their t r a n s i t i o n i s because the p r o b a b i l i t y  that a l i n e i s  states. This  absorbed  d i r e c t i o n s depends on the r a d i u s of the c y l i n d e r and l e n g t h of the major a x i s .  in  all  not  the  45  4-6  LTE  Computations  Extensive programs various  quantities programs  densities  of  (50:50)  The  (1966).  ideal  gas  specified  He and  I,  the  N 's  and  oscillator  except  for N  those  two  programs and  that  of  each  output  Q ff  ,  for  0  II  Q ff  and  N  III  used  4641.. T h e  calculated the  Coulomb  line  ranges log(N )  each  e  using and  (4-2),  and  the  were  g 's n  and  et.al.  the  programs  next  by  ions  (N)  from  pressure  the  (P)  from  (4-18). Then,  using  total  intensities  were  calculated  (4-1).  The  (4-1)  came  another  and  s p a c i n g s of ion,  log(relative  of from  energy  levels  from  Wiese  strengths for  of  programs  (4-7)  f o r each  line,  for  Dr.Barnard's  approximation the  the  equation  oscillator  by  using  W.L.Wiese,  lines  in  the  e  from  the  equation  T ,  neutrality  plasma  wavelength,  LTE.  nitrogen  a l l the  defined  e  (1949)). F i n a l l y  programs  0  and  were  specified  log(T /LU )l) •  of  e q u a t i o n , the  assumed  depths  and,  density  and  e  plasma  (1959)  densities,  I I I 4634 a n d  the e  ion  calculated  to  needed  C.Moore  computer  assuming  e  helium  charge  obtained  Boltzmann  lines  For  of  strengths  A.Damgaard,  optical  of  ratio  functions,  over N  the  given  were  law  T  i n the  tables  of mass  and  e  ion species  macroscopic  total  integrated  e  the  the  the  conservation  (4-11)  , for given N  the  N  which  computed  energies  calculated  Dr.A.J.Barnard  s e t of  first  the  Using  integrated  of  partition  ionization  an  function  the  from  of  a  (4-2),  and  estimated  the  made by  as  a l l  equation  (4-3).  was  developed  The  Saha  use  (D.R.Bates  calculated  the  (4-1). N  e  and  T  log(N),  e  values, log(P),  intensity)  and  46  It  i s worth n o t i n g that the programs  constant  density  given by the i n i t i a l  thus allowance made f o r the d r i f t  d i d not  filling  of p a r t i c l e s  assume  a  p r e s s u r e and from the  hot  central  region  of the plasma to lower temperature  regions.  In t a b l e  (4-3) we g i v e the t o t a l d e n s i t y c a l c u l a t e d  assuming  no p a r t i c l e d r i f t  and the d e n s i t i e s given by the  Table  (4-4)  Plasma  Total density without d r i f t Run 1 Run 2 Run 3  4-7  1.1 x 2.3 x 3.6 x  Temperature  10 10 10  programs.  Densities  Total density with drift .63 x 1.6 x 2.0 x  1 7 1 7 1 7  10 10 10  % Drop 40 30 40  1 7 17 17  Measurements  The temperature was determined by measuring the of  the t o t a l l i n e i n t e n s i t i e s  4641  to the i n t e n s i t y  4552 the  to  of N II 4601,  4607, 4614,  of N III 4643 and the  ratio  over  density.  the  Using (4-1),  wavelength  intensities  scale,  (4-2) and  the  of l i n e s from subsequent  ratio  3  3/2  n  e  total  primes  q  p  label  00  2  v  the  (4-11) of  N II  e  J  lower stage l i n e . I  the  on  free  integrated  total  line  stages i s : (4-14)  /  m  3  on  ionization  I j =_§_ = 2fnmq X' A n k T \ exy(-E +E -En\ If a' N f^ g X \2 h ] \ kT The  of  and  N I I I 4515. These r a t i o s are s t r o n g l y dependent  e l e c t r o n temperature and weakly dependent  electron  ratios  T  and I f are the  i n t e n s i t i e s and a and a' are the t o t a l areas under the  p r o f i l e s . For L o r e n t z i a n p r o f i l e s a/a' = wh/w'h' where w and w' are the Stark widths and h and h' are the h e i g h t s at l i n e  47  center. To This  use  is  often  optically this  (4-14)  thin  line  strongly  for  (4-14)  on  N 's  were  final  N  e  The for  a/a' run  advantages.  N  III  used  This  and  the  5876  and  N  T .  which  our  of  and  were  N  e  width  Stark  width  3)  x  10  substituted  determined  at  the  is  with  i s only  from  an  lines  temperature  different  in  first  III  2.5,  e  However  e  the  scaling  N .  which  compared  (1.2,  e  of  for  we  linear  T 's  similarly  1 7  in  weakly  the  above  values at  Figure The the  these  since  the  same to  (4-2) plotted  change  shows p l o t s  temperatures  so  were same  the  a/a'  points  had  neutral  reabsorption  not  are  calibrations  the  mentioned  lines  they  entrance  Also  lines  were  corresponding temperatures  about  meant  and  f o r the  the  Using  had  the  calibrated.  figure  ratios  intensity  at  LTE.  Thus  The  e  I  for  reabsorption  respectively,  T 's.  that  He  by  II  e  appreciably  First,  lines  lines.  N  N 's,  3  estimate  our  estimates.  (4-14).  relative  the  so  e  not  each  from  N  thin  The  2 and  of  (4-14)  assuming  density.  to c a l c u l a t e  dependent e  in  an  independent  somewhat  optically  1,  width  dependent.  use  runs  have  i s almost  experiments  electron  the  widened  of  first  from  plasma  to  previous  3  must  temperature  measurements  cm"  done  is  estimates  with  we  are  were  determined  several  close  important  in wavelength,  necessary. Secondly intensities  density  as  filters  spectrometer  would  measured  and  affect  the  a l l  the N  could  need  II be  not  the  no  be  lines  much. of the 3.06  Ij/If  vs  T  measured ±  .04  e  as  ratios.  ev,  3.09  given From ±  .03  by this ev  48  RUN 3 CURVES FROM SAHABOLTZMANN EQUATION 1 N2 4643/N3 464I 2 N2 4601/N 3 4641 3N2 4607/N3 4641 4N2 4621/N3 4641 5 N2 46I4/N3 4641  < tr.  >-  H  II  PLOTTED POINTS ARE MEASURED RATIOS  CO Ul  I-  3.0  Figure  3.1 T,(ev)  3.2  (4-2) : N II / N I I I i n t e n s i t y Equation  r a t i o s from the Saha  49  and  3.07  errors the to  .02  quoted  error some  lines. of  ±  Added  caused  The  N  3.1  ±  .1  a  only  I  5876  He  I I 4686  Electron As  neutral  and  singly  we  for  by  several  ,lighter  of  the widths  o f many  further  measured  for N . e  check  He  from I  to  the  odd  that  when  of the  such  p r e s s u r e s were  used  processes.  finding  the  done  ratio  because  lines.  50%  In  6678  of  nitrogen  was  agreement  of  weak  these  and  50%  t h e He  measured  I  The  of  strong  dependence  lines,  experiment  exists  broadening  elements.  and  this  the width  good  f o r the Stark  temperature  be  II  i n fnm/^pq •  runs  commonly  introduction,  density  could  seem  by  in  Measurements  experiment  of  N  error  temperature  ionization  i s more  N II  respectively.  error  at a  three  by  electron  in a mixture  3  4%  and  temperatures  error  may  filling  on  formed  50%  arrive  the  and  as  ionized  probes  and  It  dependence  sensitive  2 and  the temperature  i n the and  1,  e  runs.  I I 4686  Density  theory  The  represent  of d i f f e r e n t gave  another  i s absorbed  obscured  mentioned  between  Thus  voltages  t o He  was  add  3  d i d not measure  He  They  i s the systematic  in N  same  energy  ratio  f o r runs  error  the  3 respectively.  reabsorbtion  I I I 4515  ev  a l l  firing  of  4-8  30% errors  is  the extra We  to N  3.06  for  2 and  deviations.  standard deviation  ev  different  1,  the shot-to-shot i r r e p r o d u c i b i l i t y  measurements.  temperature  but  and  these  temperature  runs  the the v a r i e d  3.12  from  However,  by  I I 4552  to the  (4-14)  for  are the standard  extent  3.08,  ev  make  on them  the plasma helium  was  so  N  5876  line.  As  f o r runs  1 and  2  e  a as  50  well,  though  not  for  run  3  because  i t was  too  broad  for  the  OMA. Isolated primarily  lines  by  electron  approximations H.Griem the  = W  s  W  +  lines  1.75  i s the  A  as  (1-.75  this  term  Debye  W  ion  of  R  =  10-*(T (ev))-  plasma  with  and  ~  T  e  F  0  q  f  =  2.61  is  convert  tables only  for W  singly  10,000-40,000  Holtsmark  field  Zq,N?/  the the  for  by  (2-12), the  and  R  and  ion-ion  total  N  is  is  another relative  correlations.  e  f o r He and  A  a  relative  the  halfwidth with  A  I  The  5876  in H^".  with  :  e  gives  effects.  approximately  measures  scales linearly  by  Griem  these  broadening  the  i s given  x  ion  expression  measures  that  R  8.34  an  determined  that  shielding  20%  experiment.  for  crude  (4-15)  parameter  is  allow  of  s  broadened  relatively  gives  w,  width  static  second  to  are  W  impact  importance  of  5876  and  (226)),  R)  parameter  importance  I  :  dimensionless  dimensionless  He  sufficient  halfwidth,  electron  of  as  impacts  equation  Stark  Lorentzian  w  are  ((1974),  full  such  1  /  2  N  1  /  (4-16)  s  e  and  A  f o r He  ionized °K.  strength  A  I  atoms  p e r t u r e r s , at  immersed N  e  is proportional to  given  by  values  10  the  a  cm"  1 6  3  normal  :  (4-17)  3  charge  =  in  and of  A  Nj  the  given  density by  Griem  of  an  ion  to  values  species.  To  appropriate  51  for  a  plasma  (4-17)  and  containing (4-3).  multiply  Griem's  Qeff =  liQiNK  This  After  (4-6).  range  this  of The  knowing  3  directly  W,  assuming  A  into  this  (4-8) The  no N  turns  and  R  along  the  not to  determination.  theory  1,  2 and  2/3  of  density  .3) 3  fullwidths  x  10  we  must  :  mentioned  1.5  for  the  in  N -T e  e  1 7  and  w,  the  5876  said  are  .4)  in  be  after  10  1 7  (4-4)  depth  width  the  from  Stark the  (4-1) width  estimated Griem  and  errors that  (.9  ±  Our  .1)  a l l in cur  machine  the  table  by  shows  using  iterations.  systematic.  are  use  optical  in  ""10%  to  (4-15)  comes  are  widths  had  three e  by  from  e  tabulated  errors  x  widened  the  reproducibility  Table  widths  in N  cause  to  N  the  within  e r r o r s are  ±  (4-15)  measured  correct  measurements (2.9  the  error  these  and  is  a c c u r a t e l y . We  e  width;  they  from  e  calculating  the  these  respectively. s  use  N .  converged  to  ~  ±  then  errors  ~  (2.2  by  as  calculating  errors  homogeneity  estimated  must  find  determined  I  N  first  This  Added  the  About  ~  e  substitute  measured  calibration, 10%.  Q ff  be  with  obtain  of  whose  the  of  programs  that  He  c o n t r i b u t i o n to  depths  accuracy  could  (4-15)  and  with  we  i s given  e  now  since  repeat.  largest  optical  can  reabsorption,  and  out  scale  procedure  e  . Q ff  e  Dr.Barnard's  It  we  iterative  Q ff  algebra  we  (4-18)  electron density how  simple  ions,  experiment.  reabsorbtion,  with  by  charged  ,  Unfortunately,  an  some  values  i s c a l c u l a t e d by  section  multiply  the  3  x for  are  final 10  1 7  ,  runs  measured  c o r r e c t i o n w',  the  52  optical  depths  electron  0  ,  the  densities  5876 a n d  Table  T  final  Stark  predicted  by  Run  Widths  w_ m  O f He  1 2 3  T  w'  5.4 12.3 16.3  1 2  4.1 1 1 15  10.3 21.8  I 6678  it  not  negligible  calculate  three  a  from  optical the  gives  In  figure  ( 4 - 3 ) we  with  response  little  4.0 9.7 12.6  show  e  enr  e  I  (0.9 (2.2 (2.9  3  ±.1)x10 ±.3)X10 t ^ J x l O  1 7  1 7  1  7  6678 9.0 20  1.0 2.3  for N  i t swidth  hard  The  o f He  us g r e a t e r  N 's  5876  a probe  depth.  widths  I 5876  runs  N  s  as  e  fact  I 6678  x x  He  that  the  are close  o f He  I  i s that  confidence i n those  the plots  10 10  1 7  1 7  5876  t o measure. A l s o  documented. In i t s favor  He  intensity and  weak a n d  as w e l l  I  .05 . 1  i s not as good  i t i s quite  w  .2 .5 .6  9.0 20.5  because  from  the  f o r He I  And C o r r e s p o n d i n g  0  He  almost  and  e  the Stark widths  I Lines  He  is  w  6678.  (4-5)  He  widths  I 5876  i t has  N 's e  we  to those values. for  the  background  continuums  subtracted,  channel  corrected,  wavelength  calibration  applied  smoothing  for cosmetic  purposes  only.  53  WAVELENGTH IN ANGSTOMS  Figure  ( 4 - 3 ) : He  I 5876  f o r Runs  1,  2 and  3  54  CHAPTER V  In  this  chapter  linewidths plasmas  5-1  of three  a  x  10  N.Konjevic, (1979).  early the  we  et.al.  achieved  (1976)  of  2 x  vary  N  e  by h i g h e r  lower  nitrogen  e  most  accurately  with  broadening  becomes  To  make  would  by  1  7  too  those  to cm"  be  h a d t o be  made  N  lines. in  e  a  data  E.Kallne, devices  o f 2-10  showed  torr  and  III lines  3 ev and t h e f r e e  of three.  pressures  lines  for were-  system  end-on too  we  this bank Our  showed  electron found  At higher  and c h a r g i n g  by  et.al.  (1965) e . g . ) .  II and N  factor  the  provide  f o r r u n 2 c o n d i t i o n s . We  3  strong  the o p t i c a l  were  i n the review  of  similar  I, N  data  at  listed  pressures  He  filling  was  This  ( s e e H.James,  by a b o u t  reabsorbtion N  emitted  measurable  lines  on  o f some  l O  and  record  and  10 k v  temperature  t o be  observations  measurements  at f i l l i n g  measurements  could,  to  studies  voltages  calibrated  conditions  most  be o b t a i n e d  density  III lines,  measured  densities.  of  range.  - 3  to  plasma  electron  wished  Previous  charging  II and N  sets  firing  cm  1 7  CONCLUSIONS  the experimentally  l o t of p r e l i m i n a r y  we  intermediate  could  final  suitable  Originally  N  AND  Work  the  collected,  (1-5)  present  different  Preliminary  find  we  of twenty-seven  Before  to  L I N E W I D T H MEASUREMENTS  N , e  voltages,  measurements. At  narrow  had chosen  to  measure  and  Doppler  important.  the f i n a l  selection  of lines  t o be  studied,  we  55  f i r s t made a l i t e r a t u r e linewidth  search t o f i n d a l l  predictions  and  the  theoretical  experimental  linewidth  measurements. Next, rough p r o f i l e measurements were taken of all  the N II and  listed  in  the  N III  lines  between  t a b l e s of W.L.Wiese, e t . a l .  run 2 c o n d i t i o n s f o r t h i s study. without  the e x i t  3500 A  The  and  6500 A  (1966). We used  lines  were  recorded  l e n s , a l l o w i n g measurement of many l i n e s i n  a s i n g l e shot. The Stark widths c o u l d not be determined from these  spectra  because  most  of  the  nitrogen  narrower than the machine p r o f i l e . T h i s quick us  which  lines  permit  accurate  where  to  were  sufficiently  Dr.Barnard  the  depths  (see s e c t i o n ( 4 - 6 ) ) . For  our rough estimates  quick  survey  the  for  the  lines  of  accurately  not  using the programs of  these  calculations  e  we  e  and e a r l i e r measurements. The l i n e s were  basis  represented  showed  of N , T , and l i n e w i d t h s from the  sufficient  strength,  o p t i c a l depths. F i n a l l y , we chose a measured  strong and i s o l a t e d to  p r e l i m i n a r y survey,  used  on  showed  the background continuums f o r each l i n e .  Then, we c a l c u l a t e d the o p t i c a l by  survey  r e c o r d i n g of t h e i r p r o f i l e s . A l s o i t  measure  excluded  l i n e s were  list  from the h i g h e s t  i s o l a t i o n and low of  lines  to  r a t e d l i n e s . The  previously  be list  measured  and  new l i n e s . Where p o s s i b l e we t r i e d t o i n c l u d e two l i n e s  from  the  an a p p r o p r i a t e mix of  rated  same m u l t i p l e t so we c o u l d compare t h e i r widths and t r y  the second method of determining (4-5)).  optical  depths (see s e c t i o n  56  Table (5-1) : Stark Widths For Run 1 N ION N N N N N N N N N N N N N N N N N N N N N N N N N N N  5-2  II II II II II II II II II II II II 11 II II II II III III III III III III III III III III  e  =  (.9  ± .1) x 10  LINE  MLT  571 1 5045 3919 4601 4607 4614 4621 4630 4643 5952 5942 5496 5351 5321 3830 4552 3995 4097 41 03 4515 451 1 3771 3755 4867 4874 4634 4641  (3) (4) (17) (5) (5) (5) (5) (5) (5) (28) (28) (29) (69) (69) (30) (58) (12) (1) (1 ) (3) (3) (4) (4) (9) (9) (2) (2)  w  cm"  1 7  3  m  T w  0.58 0.47 0.36 0.47 0.42 0.43 0.43 0.53 0.40 0.78 0.94 0.64 0.65 0.70 0.88 1 .80 0.55 0.43 0.35 0.36 0.33 0.33 0.28 0.42 0.41 0.40 0.48  0.34 0.62 0.36 0.40 0.34 0.19 0.29 1 .45 0.52 0.12 0.61 0.24 0.03 0.01 0.03 0.10 1 .69 1.41 0.74 0.18 0.14 0.04 0.03 0.10 0.01 0.50 0.79  e  - 3.1 ev s  ±%  R  0.44 0.31 0.26 0.35 0.30 0.33 0.32 0.29 0.26. 0.69 0.75 0.53 0.59 0.64 0.87 1 .76 0.30 0.22 0.20 0.25 0.22 0.26 0.20 0.32 0.32 0.26 0.31  18 23 23 20 20 18 19 36 27 17 27 14 14 21 12 12 39 36 28 18 18 18 20 18 20 23 29  1 .0 1 .0 1 .0 1.0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1.0 1 .0 1 .0 1.0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0  d  w  0.12 0.11 0.08 0.10 0.10 0.10 0.10 0.10 0.10 0.13 0.13 0.12 0.12 0.11 0.08 0.10 0.09 0.09 . 0.09 0.10 0.10 0.08 0.08 0.11 0.11 0.10 0.10  Stark Widths And C o n c l u s i o n s In  tables  calibrated  full  (5-1),  (5-2)  and  (5-3)  we  present  the  l i n e w i d t h measurements i n angstroms. In the  t a b l e s MLT i s the m u l t i p l e t number given by C.Moore,  (1959).  w  optical  m  i s the u n c o r r e c t e d width from the OMA.  depth.  w  corrected Doppler  d  is  the  Doppler  width .  f o r machine broadening broadening.  ±%  is  the  w  s  T  0  i s the  i s the Stark width  (-.2 A), o p t i c a l depth estimated  and  e r r o r from a l l  sources f o r the Stark widths. R i s the r a t i o of Stark width of the same l i n e measured i n Run 1.  w  s  to  the  57  Table  N ION N N N N N N N N N N N N N N N N N N N N N N N N N N N  II II II II II II II II II II II II II II II II II III III III III III III III III III III  the  (2.2 ±  LINE  MLT  errors  optical  errors and  depth  due  time  width 1  =  e  571 1 . 5045 391 9 4601 4607 461 4 4621 4630 4643 5952 5942 5496 5351 5321 3830 4552 3995 4097 4103 4515 451 1 3771 3755 4867 4874 4634 4641  The  correction  measure  the  w  m  == 3.1  e  d  w  ev  s  ±%  R  0.12 0.11 0.08 0.10 0.10 0.10 0.10 0.10 0.10 0.13  1.01 0.71 0.57 0.68 0.62 0.67 0.63 0.95 0.65 1 .23  25 34 26 29 28 20 25 52 33 20  2.3 2.3 2.2 1 .9 2.1 2.0 2.0 3.3 2.5 1.8  (29) (69)  1 .32 1.13  0.77 0.10  0.12 0.12  1 .09 1.10  23 15  2.1 1 .9  (30) (58) (12) (1 ) (1 ) (3) (3) (4) (4) (9) (9) (2) (2)  1 .90 3.40 1 .60 0.80 0.66 0.66 0.63 0.50 0.50 0.85 0.85 0.80 0.80  0.08 0.31 6.49 2.02 0.98 0.23 0.18 0.07 0.05 0.12 0.01 1 .24 0.60  0.08 0.10 0.09 0.09 0.09 0.10 0.10 0.08 0.08 0. 1 1 0.11 0.10 0.10  1 .86 3.15 0.51 0.46 0.48 0.58 0.56 0.45 0.46 0.83 0.85 0.54 0.65  22 19 64 41 28 17 19 17 25 14 22 36 37  2.1 1.8 1 .7 2.1 2.4 2.3 2.5 1 .7 2.3 2.6 2.6 2. 1 2.1  in  w  come  s  which  mainly  total  of ±  from  i s 'tabulated  about±5%.  of  errors  in  The  based  (4-2).  on  error  lines  I I I 4643  height.  the halfwidth  table  the narrowest  t h e weaker  and N  the uncertainty  in The  calibrations, reproducibility  10% a f f e c t s  halfmaximum  because  T  3  1 .02 1 .60 1.12 1 .38 1.14 0.60 0.99 3.30 1 .52 0.41  (N I I 4641  higher  cm"  1 7  2  1 .30 1.11 0.80 1 .00 0.87 0.83 0.86 1 .90 1 .00 1 .36  F o r some  estimate  minimized  w  10  F o r Run  (3) (4) (17) (5) (5) (5) (5) (5) (5) (28)  variations  isolated  .4) x  Widths  to inhomogeneity,  especially.  well  (5-2) : S t a r k  and  in lines  of run  those  n o t so  f o r e x a m p l e ) we  how  accurate  The  effect  occurs  machine  we  also could  i s somewhat  at the steepest  part  58  Table  N  e  =  (5-3) : S t a r k  (2.9  ±  .4)  x  Widths  10  1 7  cnr  ION  LINE  MLT  N II N II N II N II N II N II N II N II N II N II N II N II N II N II N II N II N II N III N III N III N III N III N. I l l N III N III N III N III  571 1 5045 3919 4601 4607 4614 4621 4630 4643 5952 5942 5496 5351 5321 3830 4552 3995 4097 41 03 4515 451 1 3771 3755 4867 4874 4634 4641  (3) (4)  1 .70 1 .45  1 .76 3.26  (5) (5) (5) (5) (5) (5) (28)  1 .40 1 .20 1 .05 1 .20 2.40 1 .40 1 .60  (29) (69)  of  the p r o f i l e  worked that and  ~  out 1/2  As multiplet amounts all  35 51  2.6 2.2  2.25 1 .90 1 .03 1 .53 8.12 2.55 0.72  0.10 0.10 0.10 0.10 0.10 0.10 0.13  0.84 0.77 0.82 0.83 0.69 0.79 1 .34  46 41 25 30 83 54 23  2.4 2.6 2.5 2.6 2.4 3.0 1 .9  1 .60 1 .40  1 .40 0.16  0.12 0.12  1.14 1 .35  32 16  2.2 2.3  (30) (58) (12) (1 ) (1 ) (3) (3) (4) (4) (9)  2.20 4.60 2.60 0.78 0.70 0.80 0.75 0.66 0.54 0.83  0.13 0.45 9.22 3.75 1 .40 0.26 0.21 0.07 0.06 0.16  0.08 0.100.09 0.09 0.09 0.10 0.10 0.08 0.08 0.11  2.13 4.12 0.74 0.29 0.46 0.75 0.67 0.65 0.50 0.76  23 1 7 83 53 29 20 20 19 19 14  2.4 2.3 2.5 1 .3 2.3 3.0 3.1 2.5 2.5 2.4  (2) (2)  0.90 0.95  0.74 1 .54  0.10 0.10  0.71 0.61  29 41  2.7 2.0  =  2  error  m  w  0). With f o r each  errors affect  the  more  d  these line  w  points  in  mind  individually.  a l lthree  We  we note  runs  the  same  within  the  same  t h e R's. w 's  for  s  than  affecting  f o r shot  correction  1.12 0.68  w  run a r e g e n e r a l l y v e r y  to l i t t l e  errors  (except  0.12 0.11  not change  and  ev R  2  expected,  •= 3.1  e  ±%  of these  should  T  3  3  s  (d L/do  the  F o r Run  to shot  lines  close.  a consistency  such  a  s e t of  reproducibilty  for reabsorption).  However,  check  lines and  because  are under  this most  systematic or  over  59  We as  we  see  had  very  hoped,  susceptible The  4643  of  and  3  that  the  R's  particularly  for  run  3,  to  the  run  1  errors and  very  both  tables  were  wider  Because  of  ( T  <  0  because the  measurements  we  These  .05).  A,  .61  A  agreement  of  uniform  they  and  II  are  4614  measured .90  are N  as  N  A  for  not  II  strong  error  estimates  Stark 1,  affected  by  as  side-on  and  runs  4643  between  our  as  widths.  were,  times  not note  side-on  they  2.4  suspect  but  measurements  If  i t is  close  The  .30  are  measurements  favorably.  lines  depth  in  end-on  respectively.  optical been  the  side-on  compare  widths 2  from  would  have  N  4614.  II  and  end-on  are  overly  pessimistic. To  check  ratios  of  linear  the  scaling  electron  ratios  1  : 2.45  ±  .2  : 3.2  ±  .3  1  : 2.2  ±  .4  : 2.5  ±  .3  then  errors  we  the  2/3  ~  the  N  30% give  the  deviations.  our  bars.  error  cannot  conclude  We  to  need  give  and  (5-1) 4552  from  for  w  shows plotted  the  in  in  the  For  the  w  against  Stark N . e  get with  (5-3).  The  subtracting 30%  error  ratio  are  obeyed so  the  in the  within  large  proportional reduce  the get  lines  and  are  to  we  by  s  the  we  e  of  i s almost  and  e  runs  s  estimated  section full  R  (5-2)  i s not N  N w  uncertainties  of  compare  three  computed  scaling  range  this  (5-1),  i s or  s  the  average  are  errors  the  we  s  for  from  Linear  w  widths.  tables  error  the  from  the  ratio  whether  increase  with  e  and  e  Because  suggestions Figure  5496  N  The  standard  Stark  in  systematic  measurement.  e  the  error in  N  densities  average  less  of  of  we  to  N . e  error.  We  (5-3). widths These  of  are  N-II three  4614, of  our  60  more  a c c u r a t e l y measured  were  drawn  without  subtracting  error  theoretical the  lines.  bars  the  represent  p r e d i c t i o n s of  figure,  fairly  The  systematic  with  Those  bars points  measurements  authors.  agreement  error  error.  experimental  other  good  points  As  with  we  can  linear  and  see  from  scaling  is  obeyed. The are  N  only  II  widths  3995,  approxiamately our  run  depths  1  of  four  lines  with  double  lines  what  may  This  table  equation  would the  (5-4) (4-13)  we when  given  in tables  within  error  estimates.  4614,  4621,  4630  the  values  using (and  of  (4-9). hence  N  (5-1),  and  II This  f o r each  4614  gave the  with  III  be  E.Kallne  4103.  scaling  authors  Their  that  the  et.al.,  widths  would  give  calculate  same m u l t i p l e t  the  widths  are  wider  c o n s i s t e n t with  are with  optical of  the  three  optically  out  thick  discrepancy. give  the  optical  feasible.  The  to  N  note  (5-2)  4643  of  the  we the  explain  compare  linear  Though  within  times.  can  4097 a n d  negligible,  and In  III  data.  as  stronger  N  we  T  and 0  ' S  multiplet each us  of  five  other  Agreement  (5-3) for  depths with  i s not N  were  found  lines  II  for  T  through  by  of  0  ' S  are  4607,  averaging  lines, 0  T  but  4601,  other  values  the  good,  the  the  calculated  N  II  (4-9)).  then 4614  FIG (5-1)  STARK WIDTHS  VS ELECTRON DENSITY  ro tr O  I-3H  1.5. Q  _l < X CVJ Q  2d  1  i  r-2-l  T  h3l X  o  1 3d 3e  f  »c  T  h2H  Z>  u. la lb  Id  I  i Id  J- 2a  T  1 N 2 4614 2 N 2 5496 3 N 2 4552  a REF. (10) d REF. (21) b REF. (9) e REF. (16) REF. (6) BARRED POINTS FROM THIS EXPERIMENT 17 I N.XIQ cm - 3  62  Table  (5-4)  : Optical  ION N N N N N N N N N N N N N N  In  II II II II II II II II III III III III III III  with  should have  be  to  measurements could  the  should  be and  constricted  amounts  of  N  II  lot  more  plasma  4643 are  The  best  both  side  depth  which  way  would  and  that  work  is  necessesary  Abel  This  would  tell  density  come  optical  tube  done.  I  measured  the  column.  of  the  along  and  portion  of  the  just  past  us  how  vessel,  from  the  on  the  weak  on  the  axis.  inversions  decrease  end-on. side  feasible while  center  electron  .8 .6  showed  tube  He  2.8 1 .4  the  the  and  2.4 1 .2 1 . 1 1 .9 .83 .61  subtracted.  plasma  lines  measured  3  2.8 2.4 1.2 1.9 8.9 3.0  several  from  and  strong  be  the at  4614  RUN  2.3 1 .9 1.0 1 .6 7.2 2.4  circumvented. the  2  Ratios  Work  came  or  II  a  of  temperature the  of  feel  measurements point  N  still  diagnostics  Further  Intensity  RUN  continuums  observe  with  1  present  error  eliminated  been  We  we  And  From  1.5 1 .3 .68 1.0 4.9 1 .6 .12 .67 1. 1 .54 .49 .87 0.0 0.0  background  biggest  Experience  lines  (5-2)  Improvements The  RUN  4601 4607 4614 4621 4630 4643 5952 5942 4097 4103 4634 4641 451 5 451 1  figure  profiles  5-3  LINE  Depths  with and  and  the  N  widening  the  plasma  distance hence  cooler,  e  if  from large  lower  N  e  £9  64  regions. rapidly,  The making  eliminated could  be  sections  by  do  out  not  spectrometer's  time of  of mode  gated  linear the  N  II  In and  real  OMA.  N  III  time  mode c h a n n e l  of  cases  the  The  second  method  lines.  This  lens  such  we  lens  dispersions the  machine  at  could  the  OMA  could than  mode 500  then  1/2  the  The  wider  OMA  spectrum would  we  could  T  the  , in a  advantages.  of  is easily  eliminating how  accomplished  the  exit  OMA  broadens  the  i t  be  observe  the  same  thus  the  would  more double  in  time the  each of  a  Using  to  gated  continuum  machine  broadening  the  placing  narrowest a  more  spectrometer. line  determine  Lorentzian  much  measured.  by  of  real width  shot.  affects  slit  and  and  the  in  measurement  real  i s unnecessesary  used  observe  single  The  of  a  electronic  a  This  by  First  machine  has  allow  widths  front  be  the  channels.  channels  a c r o s s the profile  be  portion  methods.  replace  precisely  could  adjustable a  500  two  to  hence  calibration  by  slit  this  added  determine  lines'  in  the  two  across  to  narrower  installed  the  and  response  is  easily.  be  less  line,  has  This  could  The  across  several  could  replaced  reduced  in this  band  staining  difficult,  i t removable.  the  be  has  response  wavelength  shot.  in  syetem  mode. A l s o  section  rapidly.  could  which  of  c l e a n e d or  entrance'  the  narrow  measurements  caused  shutter  the  section  and  broadening  gating  a  stain  error  mechanical  with  side-on  making  taken  The machine  problem  lines  at  With  different  precisely of  how  varying  widths. The  shot  to  shot  jitter  in electron  density  could  be  65  bypassed  by o b s e r v i n g  spectrometer This and  would  could  electron  any f e a r s  the  above  be below We  same  wish  could  was d o n e  density that  with  the  a  separate  by J . B e r n a r d  measurements system  with  (1978).  each  changes  fixed,  line  during  To  a  N  we  voltage.  optical  depth  we  could  to  side-on  measurements  to  about  5 x  an  order  of magnitude would  suggested  within  a  (bandwidth intensities  7  causes  c m  -  3  multiplet ~  15 would  A). be  a  .5 x  when  we the  broadened i f  from width  10  1 6  our  tables  be a t  cm  - 3  least  .  pressure  and  accompanying  problem  with  until  the  line  line.  by t h i s  method  f o r some  lines.  end-on Then  We  gating  could  be  observed  The  ratio  very  would  might  their  N  the range  (4-13).  system in  switch  increase  equation  t o t h e OMA  of  we  and hence  to test  measured  Also  by  the f i l l i n g  reabsorbtion.  f o r that  easily  voltage.  are Doppler  =  e  the  the temperature i s  the Stark  the  be i n t e r e s t i n g changes  quite  two l i n e s  increase  observe  density  1  at N  avoid  increased  I 0  that  using  discharge,  since  Only  width  would  To  i n the  However,  criterion  e  firing  It  later  lines  less.  s t i l l  lowered  of the l i n e s  the Doppler  raise  while  be  on most  even  and or f i r i n g  significantly.  f i t the times  pressure  many  error  range  e  can  e  decreased.  i s lowered  would  N  the plasma  has  relatively  the N  source.  observe  the error  10% a n d t h e r e l a t i v e  the f i l l i n g  current  the  as  line  improvements  to extend  plasma  reducing  four  system  I 5876  data run. With  e  give  eliminate  long  N  OMA  t h e He  lines  single  line  accurately.  to  With  many a  e  shot  center To  test  66  (4-13) we would choose plasma c o n d i t i o n s such more  lines  of  that  two  or  v a r y i n g s t r e n g t h were reabsorbed end-on but  not s i d e - o n . Then u s i n g  (4-13),  we  would  calculate  their  o p t i c a l depths, c o r r e c t t h e i r measured widths from (4-8) and compare  with  side-on  measurements.  these o p t i c a l depths to those from assumptions were i n c o r r e c t .  A l s o we c o u l d compare  (4-7) to see i f  our  LTE  67  BIBLIOGRAPHY  ( 1 ) B a t e s , D.R. a n d D a m g a a r d , A., P h i l o s o p h i c a l T r a n s a c t i o n s o f t h e R o y a l S o c i e t y o f L o n d o n , A 2 4 2 , 101 (1949). (2) Bernard, J., Columbia, (1979). ( 3 ) B o r n , M., Press, Oxford  Msc.  (5) Cooper, J., Gordon and Breach,  H.W.,  (8) G r i e m ,  H.R.  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