UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Diagnostics in a high density Z pinch plasma Hilko, Brian Kent 1981

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

Item Metadata

Download

Media
831-UBC_1982_A1 H55.pdf [ 6.71MB ]
Metadata
JSON: 831-1.0095270.json
JSON-LD: 831-1.0095270-ld.json
RDF/XML (Pretty): 831-1.0095270-rdf.xml
RDF/JSON: 831-1.0095270-rdf.json
Turtle: 831-1.0095270-turtle.txt
N-Triples: 831-1.0095270-rdf-ntriples.txt
Original Record: 831-1.0095270-source.json
Full Text
831-1.0095270-fulltext.txt
Citation
831-1.0095270.ris

Full Text

DIAGNOSTICS IN A HIGH DENSITY Z PINCH PLASMA  by B r i a n K. H i l k o B.Sc, U n i v e r s i t y .of Waterloo, 1974 M.Sc, U n i v e r s i t y o f B r i t i s h Columbia, 1977  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE  FACULTY OF GRADUATE STUDIES (Department o f P h y s i c s )  We a c c e p t t h i s t h e s i s as conforming t o the r e q u i r e d standards  THE  UNIVERSITY OF BRITISH COLUMBIA  ©  B r i a n H i l k o , 1981 May 1981  In p r e s e n t i n g  this  thesis  i npartial  fulfilment of the  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y of B r i t i s h Columbia, I agree that it  freely  a v a i l a b l e f o r r e f e r e n c e and study.  agree t h a t p e r m i s s i o n for  theLibrary shall  f o r extensive  financial  copying o r p u b l i c a t i o n of this  gain  shall  BRIAN HILKO  Department  of  PHYSICS  The U n i v e r s i t y o f B r i t i s h 2075 W e s b r o o k P l a c e V a n c o u v e r , Canada V6T 1W5 ^  DE-6  (2/79)  I t i s thesis  n o t b e a l l o w e d w i t h o u t my w r i t t e n  permission.  Date  thesis  s c h o l a r l y p u r p o s e s may be g r a n t e d b y t h e h e a d o f my  understood that  ^  I further  copying o f t h i s  department o r by h i s o r h e r r e p r e s e n t a t i v e s . for  make  Columbia  NOVEMBER 27, 1981.  ABSTRACT  A Z-pinch plasma, action  mechanisims,  s u i t a b l e f o r the study of C 0  i s thoroughly  n o n - p e r t u r b i n g , o p t i c a l probe Simple  diagnosed  2  laser-plasma i n t e r -  using  a  number  techniques.  s t r e a k and shadow methods g i v e an  important  preliminary  view o f the s p a t i a l d i s t r i b u t i o n and r a d i a l dynamics o f p l a s m a d u r i n g h i g h compression  phase.  mined as a f u n c t i o n o f  The e l e c t r o n d e n s i t y time  Thomson s c a t t e r e d ruby l a s e r of  1 x 10  1 9  cm -* -  the s c a t t e r i n g  a n  d  by  spectrally  light.  temperatures  temperature  resolving  the  the  are d e t e r -  ion f e a t u r e of  Peak e l e c t r o n d e n s i t i e s w e l l i n excess  near 50 eV a r e observed.  s p a t i a l v a r i a t i o n of e l e c t r o n  The d i a g n o s t i c s used are w e l l s u i t e d a t e l y dense,  and  Complementing  r e s u l t s , h o l o g r a p h i c i n t e r f e r o m e t r y i s performed  both the temporal and  of  - ii  studies.  -  density.  to the examination  hot plasma and have been developed  t i o n i n our l a s e r - p l a s m a i n t e r a c t i o n  t o examine  specifically  for  of  moder-  applica-  TABLE OF CONTENTS Page  ABSTRACT  i i  TABLE OF CONTENTS  i i i  LIST OF TABLES  v  LIST OF FIGURES  vi  ACKNOWLEDGEMENTS  viii  CHAPTER 1  INTRODUCTION  1  CHAPTER 2  THE Z-PINCH APPARATUS  5  CHAPTER 3  STREAK AND SHADOWGRAM PHOTOGRAPHY  12  3.1 3.2 3.3 3.4 3.5 3.6  12 14 16 23 26 33  CHAPTER 4  CHAPTER 7  35  Introduction D i s t i n c t i o n Between E l e c t r o n and Ion Features Advantage o f the Ion Feature  .  DESCRIPTION OF THE SCATTERING EXPERIMENTS 5.1 5.2 5.3 5.4  CHAPTER 6  . ^ . . .  ELEMENTS OF THOMSON SCATTERING 4.1 4.2 4.3  CHAPTER 5  Introduction E x p e r i m e n t a l Method Streak and Shadowgram P i c t u r e s The Plasma Diameter vs Time E l e c t r o n D e n s i t y from Ray R e f r a c t i o n C o n c l u s i o n t o the Photographic Study  Introduction Arrangement o f the S c a t t e r i n g Geometry O v e r a l l Layout o f Experiment C a l i b r a t i o n o f the O p t i c a l System  35 36 46 51  . . . .  51 54 59 65  SCATTERING OBSERVATIONS AND RESULTS  70  6.1 6.2 6.3  70 70 79  Introduction D i s c u s s i o n o f the S p e c t r a Plasma Parameters f o r the Z-Pinch  INTERFEROMETRIC DETERMINATION OF ELECTRON DENSITY 7.1 7.2 7.3 7.'4 7.5  Introduction Double Exposure H o l o g r a p h i c Method The Plasma R e f r a c t i v e Index Formation o f the F r i n g e P a t t e r n The Problem o f Imaging  - iii  -  .  86 86 87 91 92 97  T A B L E OF CONTENTS  (Cont'd)  Page CHAPTER 8  LAYOUT OF THE INTERFEROMETRIC EXPERIMENT 8.1 8.2 8.3 8.4  CHAPTER' 9  G e n e r a l F e a t u r e s o f the I n t e r f e r o g r a m s Data P r o c e s s i n g P l o t s o f the E l e c t r o n D e n s i t y P r o f i l e  CONCLUSION AND SUGGESTIONS  REFERENCES APPENDIX A  . . . .  RESULTS FOR THE Z-PINCH PLASMA 9.1 9.2 9.3  CHAPTER 10  Introduction C a v i t y Dumping o f the L a s e r O s c i l l a t o r O p t i c s o f the Beam Paths Recording and P o s t Exposure P r o c e s s i n g  106 106 106 109 Ill 113 . . . .  113 118 120 126 130  T r i g g e r i n g o f the D i s c h a r g e  - iv-  133  LIST OF TABLES  Table  page  I  B a s i c Parameters  o f the Z-Pinch D i s c h a r g e  II  Numerical E s t i m a t e s f o r the Thomson S c a t t e r i n g  III  R a d i a l Speeds from the S c a t t e r i n g  - v -  Spectra  6 System  .  57 74  LIST OF FIGURES  Figure  Page  1(A)  Photograph o f the Z-Pinch Apparatus  7  1(B)  A C r o s s - S e c t i o n a l View o f the P o r t s  7  2  V o l t a g e and C u r r e n t T r a c e s f o r the D i s c h a r g e C i r c u i t  3  Schematic o f the Shadowgram Experiment  15  4  S t r e a k Photographs o f the P i n c h Phase  18  5  Shadowgram P i c t u r e s  19  6  Formation o f C o n t r a s t i n On-Axis Images  22  7(A)  Plasma Diameter vs Time from S t r e a k Photographs  7(B)  Shadowgram R e s u l t s f o r the Plasma Diameter  25  8  Ray Path i n an Axisymmetric Plasma  28  9  D e f l e c t i o n Curve f o r the Plasma a t Maximum Compression.  32  10  A ' T y p i c a l ' S c a t t e r e d Spectrum  40  11  Comparative S p e c t r a l B r i g h t n e s s o f  .  . . . .  E l e c t r o n and Ion F e a t u r e s  10  25  49  12  Geometry f o r the Thomson S c a t t e r i n g  Measurements  . . .  13  Layout o f the S c a t t e r i n g  14  D e t a i l s of the S c a t t e r i n g  15  Examples  16  R e f r a c t i o n E f f e c t s i n the B a c k s c a t t e r C o l l e c t i o n O p t i c s  77  17  Plasma Temperature R e s u l t s  80  18  Electron Density Results  82  19  I l l u s t r a t i o n o f the Double Exposure Method  88  20  The Plasma R e f r a c t i v e Index v s . E l e c t r o n D e n s i t y  21  A Ray Path Without R e f r a c t i o n  22  Imaging  23  E r r o r s I n t r o d u c e d i n an I n t e r f e r o g r a m by  Experiment  60  Volume  69  o f Observed S p e c t r a  i n a Strongly Refracting  S t r a i g h t L i n e Paths  55  71  . . . . .  . . .  93 95  Plasma  ,99 Assuming 104  - vi -  LIST OF FIGURES (Cont'd)  Fig ure  24  Page  Oscillator  and A m p l i f i e r S e c t i o n s  Dumped Laser  of the C a v i t y  . .  107  25  O p t i c s of the I n t e r f e r o m e t r y  Experiment . . . . . . . .  26  Samples o f the I n t e r f e r c g rams Obtained Near Peak Compression  27  110  114  I l l u s t r a t i o n o f the Region f o r which I n t e r f e r o g r a m s were Analyzed  116  28  The Plasma D i s t r i b u t i o n During  29  Comparison o f the I n t e r f e r o m e t r i c Measurements  . . . .  122  . . . . . . . . . . . . . . . . . . . . .  124  A-1  Biasing  A-2  D e t a i l s o f the P r e - I o n i z a t i o n  the P i n c h Phase and S c a t t e r i n g  and Main Gap T r i g g e r C i r c u i t s  - vii -  133 134  ACKNOWLEDGEMENTS  As p a r t o f a l a r g e pleasure  o f working a l o n g s i d e  my s i n c e r e a p p r e c i a t i o n  experimental  project,  I have  a number o f f i n e p e o p l e .  and t h a n k s  I wish  t o D r . J o c h e n Meyer  s u p e r v i s i o n throughout t h i s p r o j e c t .  had t h e g r e a t to express  for his aid  Dr. G. A l b r e c h t , H. Houtman, D r .  Walsh and A. Cheuck have been u n s e l f i s h and c o n t i n u a l  sources  and C.J.  o f h e l p and  encouragement. My s t a y a t U.B.C. would n o t have been p o s s i b l e without c i a l a s s i s t a n c e o f the Plasma P h y s i c s Group. by a g r a n t  from the N a t i o n a l S c i e n c e  T h i s work has been  and E n g i n e e r i n g  Canada.  - viii  -  Research  the f i n a n supported Council of  CHAPTER 1  This t h e s i s reports  INTRODUCTION  a s e r i e s of d i a g n o s t i c e x p e r i m e n t s  been s p e c i f i c a l l y developed i n c o n j u n c t i o n i n v e s t i g a t i o n of laser-plasma  with,  order  to p l a c e  as p a r t o f , an  i n t e r a c t i o n mechanisms.  i n t r o d u c t i o n , some c o n s i d e r a t i o n w i l l be g i v e n in  and  the o b j e c t i v e s  of  this  that  Therefore,  have  ongoing in  this  to the experiment as a whole  t h e s i s work i n t o  full  perspec-  tive. The  peak compression phase of a Z-pinch d i s c h a r g e  t a r g e t plasma, i n t o which a h i g h power CO2 i n t e n s i t y l a s e r l i g h t can  l a s e r beam  i n Helium i s the  i s focussed.  couple to the p l a s m a v i a a number  High  of d i f f e r e n t  Vnon-linear l a s e r on  processes  (Siebe,  1974;  Milroy et.al.,  the plasma depend s t r o n g l y on  d i s t r i b u t i o n o f the  target.  the  local  As w e l l , many o f  occur s i m u l t a n e o u s l y .  (and  o f t e n do)  this  l a b o r a t o r y w i l l attempt to i s o l a t e and  ent p r o c e s s e s of l a s e r - p l a s m a indicate  The  coupling  and  1976;  Milroy e t . a l . ,  1979).  study the The  following  discussion  (Grek e t . a l . ,  In these cases,  been pre-formed, and  can be e s t a b l i s h e d i n d e p e n d e n t l y of the In a Z-pinch d i s c h a r g e ,  laser  at  endeavour.  1978;  however, i t i s  and  will  laser-plasma  during Jackel diffiinter-  the p r o g r e s s i o n  temperature, and of r a d i u s and  whose i n i t i a l  of  plasma  The  As  - 1 -  well,  the  collapse  plasma  corresponding g r a d i e n t s ,  time.  conditions  pulse.  make a v a i l a b l e a wide range of plasma c o n d i t i o n s .  functions  can  i t seems more d e s i r a b l e to study the i n t e r a c t i o n s using  a t a r g e t plasma, which has  such as d e n s i t y ,  density  fundamentally d i f f e r -  t a r g e t plasma i s c r e a t e d  the p r o c e s s e s of plasma formation  Therefore,  the  processes  t h a t the Z-pinch plasma i s v e r y w e l l s u i t e d to such an  c u l t to d i v o r c e  i b l y as  temperature  the  the e a r l y p o r t i o n s of the i n c i d e n t l a s e r pulse  action.  e f f e c t s of  experiments t h a t are underway  interactions.  In many s i m i l a r experiments, the  et.al.  1979). The  plasma  will  parameters,  vary  reproduc-  conditions  in  the  Z-pinch change on a time s c a l e which i s long  laser pulse.  Hence, the Z-pinch plasma may  but c o n t r o l l e d and w e l l known b e f o r e  p r e d i c t a b l e parameters. hand, one  process i n d e t a i l . initial  conditions  the r e s u l t s of evaluation CO2  can  be  compared  I f the  very  the  incident  used as a t a r g e t o f  hope to study the  It i s , therefore,  to  plasma  conditions  laser-plasma  important  f o r the i n t e r a c t i o n s t u d i e s .  This  t h i s t h e s i s c o n s t i t u t e a thorough and  to  has  varying  interaction  establish  the  been d o n e ,  and  detailed  experimental  of the Z-pinch plasma parameters, p r i o r to i r r a d i a t i o n  with  using  ruby  primary s u b j e c t h e r e laser  light,  but,  methods t h a t are d i r e c t l y result,  is optical  the  brief.  applicable  to  i t w i l l not be p o s s i b l e to avoid  density,  Since n  c  the c o u p l i n g  diagnostics  underlying the  emphasis  i s on  Z-pinch  diagnostic  (n  near  = 1 x 10  c  1 9  the  critical  an  presentation,  the  actual definition  the  particular diagnostic  d e n s i t y plasma depends a g r e a t considered. fication  What may  be  the  deal  on  experiment can  a  high being justi-  f o r another. Four s e p a r a t e experiments have been performed:  streak  The  holographic  remainder of t h i s i n t r o d u c t i o n o u t l i n e s the  t h e s i s and  previews the experiments to be  Chapter 2 g i v e s  the pre  c a r e f u l l y measured  interfero-  subject material  and  post  The  p i n c h phases o f  (Houtman, 1977)  using  - 2 -  of  presented.  a d e s c r i p t i o n of the Z-pinch apparatus and  e s t a b l i s h e d c h a r a c t e r i s t i c s o f the d i s c h a r g e . d e n s i t y during  be  of  this  the  shadowgram photography, Thomson s c a t t e r i n g , and  metry.  -3  In the course of  c  l i m i t a t i o n of one  cm )  electron  below n .  that  kept  electrons  s u i t e d to plasma having  a  inter-  and  d e n s i t y which covers the range above and i t w i l l become c l e a r  As  of the  have been m i n i m i z e d  laser l i g h t  the d i a g n o s t i c s must, i n p a r t i c u l a r , be  the  interaction studies.  mechanisms of i n t e r e s t o c c u r  f o r the i n c i d e n t CO2  of  periodic discussions  a c t i o n experiments, though such o c c u r r e n c e s  this  the  laser. The  and  are  plasma  the  spectroscopic  reviews  temperature  discharge methods.  have  and been  However,  during  peak c o m p r e s s i o n ,  spectroscopy nostics are  during  plasma  presented, the  high  streak  and  only  continuum  two  radiation  r e l a t i v e l y simple  shadowgram p h o t o g r a p h y ,  plasma d e n s i t y .  The  resulting  both  collapse.  The  Thomson s c a t t e r i n g o f r u b y  diagtaking an  dynamics  remainder of t h i s t h e s i s i s  to d e t a i l e d measurement of the plasma temperature and  the methods of  and  pictures give  p r e l i m i n a r y view of d e t a i l s of the plasma s t r u c t u r e and  a l l stages of the o n - a x i s  devoted  emits  In Chapter 3,  c o u l d not be used.  advantage o f important  the  laser  light  d e n s i t y using  and  holographic  interferometry. Thomson s c a t t e r i n g examines the plasma a t the m i c r o s c o p i c looking ly,  level  a t f l u c t u a t i o n s i n the p a r t i c l e d e n s i t y , i . e . plasma waves.  s c a t t e r i n g from e l e c t r o n plasma waves i s observed.  Usual-  However, C h a p t e r  shows t h a t w i t h s c a t t e r i n g methods, a h i g h d e n s i t y p l a s m a  i s most  as a d i a g n o s t i c t o o l .  of the s c a t t e r i n g geometry and geometry has ment o f  d e n s i t y , and,  fluctuation  C0 6.  2  d e s c r i b e s the  experiment  levels giving  l a s e r . The  expected  to occur  scattering observations  Complications  are a l s o p o i n t e d  and  i n the technique, a r i s i n g  with  in  plasma  the  from  the  induced  i n t r o d u c t i o n of  high  and  enhanced the  i n Chapter  plasma  density,  i n t e r f e r o m e t r y measures i n a simple  be  f o r the  t h r o u g h c a v i t y dumping  of  the  the way  are g i v e n  effects  f i r s t p o r t i o n of Chapter 8 d e s c r i b e s the g e n e r a t i o n  diagnostic pulses  oscillator.  or  Some b a s i c p r i n c i p l e s of t h i s technique  i n Chapter 7, but the main c o n s i d e r a t i o n w i l l  duration  measure-  out.  to the e l e c t r o n d e n s i t y .  The  The  temperature  of r e f r a c t i o n , a bulk plasma p r o p e r t y t h a t i s r e l a t e d  fraction.  detail.  r e s u l t s are presented  A t the macroscopic l e v e l , h o l o g r a p h i c index  the  e x t e n s i o n of the experiment t o examine  fluctuations which are  not  Chapter 5 d i s c u s s e s the arrangement  been chosen to serve a two-fold purpose, namely, the  thermal  4  easily  i n v e s t i g a t e d by s c a t t e r i n g from i o n a c o u s t i c f l u c t u a t i o n s , a t e c h n i q u e often considered  by  of  re-  of s h o r t  ruby  laser  T h i s e f f o r t advances the d i a g n o s t i c s towards time s c a l e s more  -  3  -  a p p r o p r i a t e t o the i n t e r a c t i o n s t u d i e s .  The  remainder  p l e t e s the p r e s e n t a t i o n o f the e x p e r i m e n t a l arrangement  of Chapter  8 com-  for interferometry.  A few i n t e r f e r eg rams are shown i n Chapter 9 along w i t h the f i n a l d a t a . i n t e r f e r o m e t r y has g i v e n a f u l l  view, both t e m p o r a l l y and  e l e c t r o n d e n s i t y d i s t r i b u t i o n i n the pinched plasma  s p a t i a l l y , o f the  column.  I n d i v i d u a l l y , each of the d i a g n o s t i c e x p e r i m e n t s to g i v e a complete  well-suited  Together  to p r o v i d i n g  the plasma p r o p e r t i e s .  eV, and  to n  -3  e  though,  I t has  = 6 x 10^  been  which cm , -3  corroborative  found  that  phase has  of  of  this  ( i ) v a r i e s i n e l e c t r o n d e n s i t y from n ( i i ) reaches a maximum temperature  of  been  measurements  the p i n c h p h a s e  T  e  <<  =  50  ( i i i ) i s c o n t a i n e d i n a c y l i n d r i c a l volume t h a t ranges i n d i a m e t e r  from a few m i l l i m e t e r s to l e s s than one m i l l i m e t e r . do not change s i g n i f i c a n t l y  on  a time  scale  w i t h i n 40% typically  while shot-to-shot v a r i a t i o n s l e s s than 2 0 % .  very s u i t a b l e  s i n c e the C O 2 l a s e r  for C 0  2  parameters  nanoseconds.  of o v e r l a p , to  The  typically  i n the e x p e r i m e n t a l d a t a  Hence, t h i s t h e s i s  t a r g e t plasma  The plasma  o f a few  d i f f e r e n t d i a g n o s t i c methods agree, i n the c a s e  blished  insufficient  t h i s s e r i e s of experiments  complementary and  d i s c h a r g e produces a plasma 1 0 ^ 8 cm  is  p i c t u r e of the h i g h temperature, h i g h d e n s i t y  t h i s Z-pinch plasma.  The  shows t h a t  laser-plasma  the  interaction  f i n d s a l r e a d y a f u l l y i o n i z e d plasma  with  Z-pinch  are is a  experiments well  esta-  characteristics. The  f i n a l chapter of t h i s t h e s i s p r e s e n t s a b r i e f  i m p o r t a n t f e a t u r e s o f both the plasma,  and  summary o f  the  the d i a g n o s t i c e x p e r i m e n t s .  As  w e l l , some c o n s i d e r a t i o n w i l l be g i v e n t o the a p p l i c a t i o n o f t h e s e methods i n the i n t e r a c t i o n  studies.  - 4 -  CHAPTER 2  THE Z-PINCH APPARATUS  The Z-pinch d i s c h a r g e used  throughout the i n v e s t i g a t i o n s presented  i n t h i s r e p o r t i s a c o n s t a n t and major component o f the i n t e r a c t i o n  experi-  ments. T h i s chapter i s not intended to p r o v i d e a complete  analysis  o f the  Z-pinch, but rather  (Houtman, 1977)  to review e s t a b l i s h e d  and p r o v i d e a b a c k g r o u n d supplement  characteristics  f o r the remainder  of t h i s  work.  In o r d e r t o  the f o l l o w i n g d i s c u s s i o n s , T a b l e I g i v e s t h e b a s i c  and o p e r a t i n g c o n d i t i o n s o f the d i s c h a r g e w h i l e the photograph shows the apparatus which has been assembled  parameters of Figure 1  f o r i n t e r a c t i o n and d i a g n o s t i c  experiments. The d i s c h a r g e chamber i s c o n s t r u c t e d i n a c y l i n d r i c a l l y manner using a pyrex vacuum v e s s e l 10.2 cm i n s i d e d i a m e t e r .  symmetric  E l e c t r o d e s are  made from copper d i s c s o f the same diameter and have an a x i a l s e p a r a t i o n o f 35.6  cm.  Brass wire mesh i s wrapped about  co-axial return  conductor.  the v e s s e l  exterior  The d i s c h a r g e i s formed  t o form  a  i n a continuously  f l u s h e d helium atmosphere t h a t i s maintained a t 1.2 t o r r p r e s s u r e . The energy s t o r a g e bank c o n s i s t s of s i x 14 uF c a p a c i t o r s which are charged i n p a r a l l e l gap  switch.  to 11.5 kV.  When these s o - c a l l e d  D i r e c t l y atop each  ported  being  Tn o r d e r  to minimize the  the c u r r e n t from each c a p a c i t o r  t o the Z-pinch anode through 5, e l e c t r i c a l l y p a r a l l e l ,  voltage transmission cables.  i s a spark  'main gaps' a r e t r i g g e r e d , the c a p a c i t o r s  are d i s c h a r g e d i n p a r a l l e l through the Z-pinch. t o t a l i n d u c t a n c e o f the c i r c u i t ,  capacitor  i s trans-  16 ohm  high  There i s a t o t a l o f 30 such c a b l e s , a l l these  of equal length. The d i s c h a r g e i s i n i t i a t e d  i n the f o l l o w i n g  spark g a p i s used as the common e l e m e n t cuits.  S i x o f the c i r c u i t s  are i d e n t i c a l  p u l s e s f o r the s i x main spark g a p s . eously.  f o r seven  manner.  A  'master'  separate trigger  and t h e s e  supply the t r i g g e r  The main gaps are t r i g g e r e d  The Z-pinch anode r e c e i v e s the seventh t r i g g e r  cir-  simultan-  p u l s e , such  that,  a t the same time the main gaps a r e t r i g g e r e d , a low d e n s i t y glow d i s c h a r g e  - 5 -  TABLE I BASIC PARAMETERS OF THE Z-PINCH DISCHARGE  Vacuum v e s s e l  pyrex g l a s s , 10.2 cm I.D. 11.4 cm O.D.  Electrode separation  35.6 cm  F i l l i n g gas  1.2 t o r r  Helium,  3.9 x 1 0 per cm  3  C a p a c i t o r bank  84 uF  Charging  11.5 kV  Ringing  voltage  frequency  86 kHZ  A v a i l a b l e energy  5.6 k J  Time o f maximum  compression  1.9 us  Bank energy remaining  @ 1.9 vs  2.7 k J  - 6 -  1 6  atoms  @ 24°C  ARM  Fig ure 1 (A) Photograph of the Z-pinch a p p a r a t u s . (B) A c r o s s - s e c t i o n a l view of the p o r t s .  fills  the chamber.  This provides  f o r pulsed  p r e - i o n i z a t i o n of the plasma.  Appendix A c o n t a i n s  some a d d i t i o n a l d e t a i l s c o n c e r n i n g  the t r i g g e r  c u i t r y and t i m i n g .  With p r e - i o n i z a t i o n , t h e d i s c h a r g e  c a n be  with a j i t t e r  o f l e s s than 10 n s .  The important p o i n t  cir-  initiated  t o be made h e r e i s  t h a t p r e - i o n i z a t i o n o f the plasma has been e s s e n t i a l f o r t h e c o o r d i n a t i o n of plasma and d i a g n o s t i c All  the d i a g n o s t i c  the r a d i a l d i r e c t i o n w i t h Figures  events. s t u d i e s o f t h i s r e p o r t have been p e r f o r m e d i n the c y l i n d e r  axis  oriented  1 and 3 ) . Midway between the e l e c t r o d e s  another are two d i a g n o s t i c p o r t s .  h o r i z o n t a l l y (see  and d i a g o n a l l y opposing one  These p o r t s were made by d r i l l i n g  holes  i n both the pyrex v e s s e l and r e t u r n c o n d u c t o r . Two more i d e n t i c a l holes are drilled  i n the v e r t i c a l d i r e c t i o n f o r i n c i d e n t and  light.  The C 0  direction, other  2  l a s e r beam i s a l s o focused  and, l i k e  i n t o the plasma i n  o f the d i s c h a r g e  a v e r t i c a l diagonal The respectively,  holes  such h o l e s  o f the v e s s e l . that  These two d i a g o n a l s  were d r i l l e d  10% o f the t o t a l  represent  the  radial  through  are c o p l a n a r .  the v e s s e l  The h o l e s  t r a v e l along  and mesh a r e , mesh  l e n g t h o f the plasma c o l u m n whereas  four  about 40% o f the c i r c u m f e r e n c e o f t h e r e t u r n  Therefore,  In  i n the brass  Note here t h a t the access p o r t s  plasma c o l u m n .  laser  ports i s a horizontal  v e s s e l while the CO^ l a s e r beam w i l l  1.9 cm and 3.7 cm i n d i a m e t e r .  c o n s t i t u t e only  CO2  the d i a g n o s t i c p o r t s , midway between e l e c t r o d e s .  words, the l i n e - o f - s i g h t through the d i a g n o s t i c  diagonal  tor.  transmitted  will  introduce  i n the v i c i n i t y  perturbations  o f these  holes,  conduci n the  rotational  symmetry o f the plasma column i s not g u a r a n t e e d . Two side-arms are h o r i z o n t a l l y mounted a t the d i a g n o s t i c p o r t s and sealed  t o the v e s s e l with o - r i n g s  (Figures  1 and 3 ) .  e t c . , a r e mounted on the side-arm end p l a t e s . The C 0  - 8 -  2  Windows and  lenses,  l a s e r beam e n t e r s the  discharge  chamber  v i a an L - s h a p e d  mounted on t h e d i s c h a r g e  focussing  channel.  v e s s e l a t the top v e r t i c a l  This hole,  Figure  1.  face.  A copper m i r r o r , mounted i n s i d e the vacuum channel,  verging)  as shown i n  A 50 cm f o c a l l e n g t h s a l t l e n s i s used as the a i r - v a c u u m  C O 2 l a s e r beam i n t o the d i s c h a r g e  removed from the immediate d i s c h a r g e due  channel i s  to the d e p o s i t i o n  chamber.  inter-  s t e e r s the (con-  O p t i c a l components are  v i c i n i t y and s u f f e r o n l y minor damage  o f the d e b r i s  that  i s generated  during  the d i s -  a small  Rogowski  charg e. The c o i l pick-up  discharge  c u r r e n t , I ( t ) was measured  l o c a t e d i n a r e g i o n near the anode where m a g n e t i c  t o the d i s c h a r g e  c u r r e n t c o u l d be sampled.  a changing magnetic f l u x i n d u c i n g Passive  using  a coil  f i e l d s due  The p r i m a r y measurement here i s current  proportional  to d l / d t .  i n t e g r a t i o n p r o v i d e s d i r e c t o s c i l l o s c o p e d i s p l a y o f t h e main  charge c u r r e n t .  A sample o f t h e c o m p l e t e  p o r t i o n o f d l / d t a r e shown i n F i g u r e 2 .  current  t r a c e and an e x p a n d e d  Also, Figure 2 g i v e s  the c a p a c i t o r  v o l t a g e V ( t ) as measured a t one o f the spark g a p s . The v o l t a g e drop c  the plasma column i t s e l f was n o t measured.  dis-  Therefore,  o n l y charge  across  drainage  from the c a p a c i t o r bank was determined. P a s s i v e elements i n the d i s c h a r g e the r i s i n g  current pulse.  plasma column i t s e l f meters.  c i r c u i t control early stages  As compression proceeds, t h e i n d u c t a n c e  i n c r e a s e s and b e g i n s  to dominate  The r e d u c t i o n or d i p i n c u r r e n t approximately  initiation,  occurs  a t maximum compression.  o f the  the c i r c u i t 2 us a f t e r  I n t h e expanded  of  para-  discharge  dl/dt  trace,  the c u r r e n t d i p , and hence, the maximum compression or p i n c h p h a s e , c a n be easily identified.  Since  t h i s moment o f maximum  e v i d e n t i n the d l / d t s i g n a l , as the time r e f e r e n c e  compression  the time a t which d l / d t i s z e r o  f o r a l l d i a g n o s t i c s presented  - 9 -  i n this  i s clearly  will thesis.  be used  Vc  15 4.  Figure 2 V o l t a g e and c u r r e n t t r a c e s f o r the discharge c i r c u i t .  -  10  -  C h a r a c t e r i z a t i o n o f the d i s c h a r g e dymanics began w i t h the measurements o f Houtman (1977).  and  plasma  conditions  The e x p e r i m e n t s  described  t h e r i n i n c l u d e d end-on framing camera s t u d i e s and e l e c t r o n t e m p e r a t u r e  and  d e n s i t y d e t e r m i n a t i o n s from s p e c t r a l l i n e broadening m e a s u r e m e n t s .  These  experiments g i v e a complete and d e t a i l e d d e s c r i p t i o n o f the c o l l a p s e  phase,  i . e . times p r i o r  plasma  to the d i p i n c u r r e n t .  parameters and r a d i a l  dynamics  u n f o r t u n a t e l y , not p o s s i b l e . e l e c t r o n temperatures and cm  -3  respectively,  with a  during  A c c u r a t e measurement o f the h i g h  compression  phase  were,  I n d i c a t i o n s were t h a t the pinched p l a s m a  d e n s i t i e s i n the minimum luminous  These e s t i m a t e s r e p r e s e n t a s t a r t i n g  range of  40 eV and 8.0 x  r a d i u s of the  o r d e r of 5  had 10 8 1  mm.  p o i n t f o r the p r e s e n t work i n which i t  i s i n t e n d e d to extend measurements to time and s i z e s c a l e s r e l e v a n t p i n c h phase of the d i s c h a r g e .  - 11 -  to the  CHAPTER 3  3.1  STREAK AND  SHADOWGRAM PHOTOGRAPHY  In t r e d u c t i o n The  experiments  described  examine, i n as simple a way  in this  chapter  were  intended  as p o s s i b l e , b a s i c f e a t u r e s of the p l a s m a  to  dis-  t r i b u t i o n d u r i n g the time of maximum o n - a x i s compression. T h i s phase of the p i n c h has not been i n v e s t i g a t e d with s u f f i c i e n t t i o n to observe d e t a i l s of e i t h e r  the plasma  s p a t i a l or temporal  s t r u c t u r e or motion.  r e s p e c t , the p r e s e n t experiments are a s i g n i f i c a n t i m p r o v e m e n t s i o n of e a r l i e r The  important parameter  determined  subsequent  here i s the plasma  expansion.  v = dr/dt  associated  1964),  Because z-pinch plasmas  the p i n c h phase can be expected  seen i n these measurements. the plasma  for i n t e r a c t i o n Two  exten-  the  a  plasma  are n o t o r i o u s l y see  Artsimohighly  column has been  This observation e s t a b l i s h e s  as  Changes i n  t o t e r m i n a t e i n some  u n s t a b l e manner. I r r e g u l a r d i s r u p t i o n of the plasma  which  this  radius  with  u n s t a b l e to s e v e r a l magnetohydrodynamic p e r t u r b a t i o n s (e.g.: vich,  and  near the time o f maximum c o m p r e s s i o n .  r a d i u s g i v e the v e l o c i t i e s  c o l l a p s e and  In  work.  f u n c t i o n of time, r ( t ) , the  resolu-  the  clearly  time d u r i n g  i s s u f f i c i e n t l y w e l l behaved t o s e r v e as a t a r g e t  plasma  studies.  r e l a t i v e l y simple techniques are employed, s t r e a k and  gram photography.  Both of these depend on a h i g h plasma d e n s i t y  shadow-  for  their  from  self-  application. The s t r e a k photographs emitted r a d i a t i o n . temperature  ionized gas  ( Z e l ' d o v i c h , 1966) plasma  Throughout  temperature.  give  an  image o f t h e p l a s m a  the v i s i b l e r e g i o n of the  produces  electron-ion  bremsstrahlung  w i t h an i n t e n s i t y t h a t i s o n l y weakly However, because  spectrum,  the i n t e n s i t y o f  radiation  dependent  the  on  the  bremsstrahlung  r a d i a t i o n depends on the f r e q u e n c y o f e l e c t r o n - i o n c o l l i s i o n s  , the  e m i s s i o n c o e f f i c i e n t w i l l be p r o p o r t i o n a l  the  ~ 12 "  a high  to the p r o d u c t of  plasma  electron  and  i o n number d e n s i t i e s , o r , simply,  n ^, n e  being  e  the  I n t e n s i t y v a r i a t i o n s i n the s t r e a k photographs w i l l  electron  therefore  density.  reflect  the  d i s t r i b u t i o n of electron density. For transparent  the shadow method, t h e p l a s m a o b j e c t with  a spatially  an  the v a r i a t i o n i n e l e c t r o n d e n s i t y  e q u i v a l e n t r e f r a c t i v e index d i s t r i b u t i o n . with  i s considered  uniform  essentially  replaced  The plasma i s t h e n  and c o l l i m a t e d  beam  of l i g h t .  illuminated Upon  passage  through the plasma, p o r t i o n s of the beam are d e f l e c t e d from t h e i r path, the d e f l e c t i o n angle being  p r o p o r t i o n a l to the g r a d i e n t s  t i v e index t h a t must be t r a v e r s e d has an i n i t i a l l y  uniform  (Barnard,  intensity distribution,  t h a t are d e f l e c t i n g i n c i d e n t l i g h t w i l l mitted  beam i n t e n s i t y .  beam r e p r e s e n t s the  1975).  Since  show up a r e d u c t i o n  the plasma's shadow.  From a more g e n e r a l  i n the t r a n s -  point  o f view,  The method small  the s i m p l i c i t y of these techniques,  b r i e f d e s c r i p t i o n o f the methods has been g i v e n . the e x p e r i m e n t a l  arrangement  pertaining  (Section  i s of  b u b b l e s or  techniques.  here  c o l l a p s e i n order  With these d e s c r i p t i o n s ,  pictures  to estimate  to g i v e  t h i s , numerical  i n d i c a t i o n of  study.  In p a r t i c u l a r ,  S e c t i o n 3.5  plasma  considers  some s t r u c t u r e  shadow images are the r e s u l t o f i n t e r f e r e n c e e f f e c t s p r o d u c e d  13 -  Section  snow-plow m o d e l o f  the e l e c t r o n d e n s i t y .  -  refraction  r e s u l t s are given  from t h i s p h o t o g r a p h i c  and a s i m p l e  the shadowgrams i n more d e t a i l .  a better  r e l a t e s t o more g e n e r a l  Following  f o r the plasma parameters obtained the s t r e a k  the above  3.2) c a n be shown, and t h e b a s i c  Then, i t w i l l be worthwhile  c o n t r a s t imaging  only  to the s i z e and s t r u c t u r e of the p i n c h phase can be  how the shadowgram method used  3.4 u s e s  o f the plasma  embedded i n o r d i n a r y window panes.  In keeping with  interpreted.  in refrac-  In t h i s sense then, a photograph of the t r a n s m i t t e d  course q u i t e s i m i l a r to the way i n which one can o b s e r v e  observations  original  the i n c i d e n t beam  those r e g i o n s  technique may be termed r e f r a c t i o n c o n t r a s t imaging.  imperfections  by i t s  i n the  t h r o u g h the  use o f a c o h e r e n t p r o b e second,  independent  beam.  Such  interference  e s t i m a t e of the e l e c t r o n  during  As  well,  they  3.2  are  quite motion  indication  of  Though the i n f o r m a t i o n i n  i s more q u a l i t a t i v e i n n a t u r e , these experiments  r e a s o n a b l e e s t i m a t e s of the e l e c t r o n  l e d to a  look at plasma  b o t h g i v e an  s p a t i a l d i s t r i b u t i o n of e l e c t r o n d e n s i t y . regard  shadow t e c h n i q u e s  Each can p r o v i d e a c l o s e  the p i n c h p h a s e .  have  density.  I t w i l l be seen t h a t the s t r e a k and complementary i n n a t u r e .  effects  have g i v e n  the this  fairly  density.  E x p e r i m e n t a l Method The e x p e r i m e n t a l arrangement f o r both techniques can be d e s c r i b e d  with the a i d o f F i g u r e 3.  For shadowgrams, the beam o f a Q - s w i t c h e d  ruby  i laser  (500 mJ i n 20 ns) i s passed  combination  to produce  through a x10 expander and  a c o l l i m a t e d beam a p p r o x i m a t e l y  Only the c e n t r a l 2 cm p o r t i o n of the expanded the plasma,  thus p r o v i d i n g  the i n c i d e n t beam. located  beam i s used  t r a n s m i t t e d beam i s o b s e r v e d the plasma,  e.g.,  f i l m using lens L.  from ambient exposure.  b l e l e v e l s by imaging  in to  diameter. illuminate  through a  i n a plane  i n the  The plasma shadow, as i t appears  then imaged onto p o l a r o i d  the f i l m  8 cm  filter  f o r a s t r i c t l y uniform i n t e n s i t y d i s t r i b u t i o n i n  some d i s t a n c e beyond  cated i n F i g u r e 3. is  The  spatial  o b j e c t plane  i n the  A cardboard  filter  indi-  object plane, box  D i r e c t plasma l i g h t i s reduced Kodak g e l a t i n  which i s  protects  to n e g l i g i -  (#92) which  cuts  out  o  all  light  with wavelengths  below about  n e u t r a l d e n s i t y f i l t e r s were used  6400 A.  to a d j u s t ' the  Additionally,  exposure  due  gelatin  to the  ruby  laser. In o b t a i n i n g  the shadow p i c t u r e s ,  a x i s to the image plane was  held  fixed.  the d i s t a n c e from  (Figure 3).  14 -  the  the p o s i t i o n of lens  By observing the plasma shadow i n d i f f e r e n t  -  plasma  However, the d i s t a n c e from  plasma to the o b j e c t plane could be v a r i e d by changing L  the  object planes,  r  1  image plane  gelatin filters  ,  feE3 object plane  -7polaroid vacuum side-arm with entrance window  plasma  ruby laser or  Figure 3 Schematic o f the shadowgram experiment, object planes l e s s than 43 cm from t h e p l a s m a a r e c o n t a i n e d w i t h i n the vaccun v e s s e l . The d i s t a n c e f r o m p l a s m a t o image p l a n e i s a p p r o x i m a t e l y 350 cm.  - 15 -  some d i s c r i m i n a t i o n can be made between those r e g i o n s of the plasma t h a t are responsible for either when the o b j e c t plane  l a r g e or s m a l l a n g u l a r i s located c l o s e to  deflections.  the  plasma  axis,  For  example,  the  incident  r a y s t h a t s u f f e r o n l y s m a l l d e f l e c t i o n s w i l l not have d i v e r g e d  sufficiently  to  size  of  the  regions  of  the  c o n t r i b u t e to the image c o n t r a s t .  In t h i s  case  then,  the  shadow w i l l r e f l e c t the e x t e n t of the s t r o n g l y r e f r a c t i n g plasma. On  the other hand, i f the shadow i s observed  p l a n e s , the weakly r e f r a c t i n g of  the plasma shadow s e e n  i n very d i s t a n t object  r e g i o n s w i l l a l s o become a p p a r e n t .  in different  object planes  will  be  Samples presented  shortly. S t r e a k photographs have been obtained manner.  Returning  to F i g u r e 3, i n order  l a s e r i s not used, g e l a t i n  filters  slit  film.  r e p l a c e s the p o l a r o i d  system o f imaging  image  to take s t r e a k p i c t u r e s ,  are removed, and The  straight  schematic  a 4 mm  wide  l e n s L (now  the  vertical  a four  element  plasma a x i s h o r i z o n t a l l y a c r o s s the s l i t w i t h a t o t a l m a g n i f i c a t i o n o f  x7.  t r a n s m i t t e d through  image c o n v e r t e r camera.  the plasma  3.3  film.  The  The  the s l i t  i s arranged  ruby  the  on p o l a r o i d  transport lenses)  forward  t o image  Plasma l i g h t  and  i n a more  i s viewed  using  camera r e c o r d s a streaked  a TRW  model  image of the  1D  plasma  p i c t u r e thus obtained g i v e s a r a d i u s vs time p l o t of  self-luminosity.  Streak and  Shadowgram P i c t u r e s  T h i s s e c t i o n g i v e s a f u l l view of the p i n c h phase from photographs o b t a i n e d with both s t r e a k and  shadow t e c h n i q u e s .  The  description  q u a l i t a t i v e , but serves to i l l u s t r a t e b a s i c f e a t u r e s o f as the correspondence  between the two methods.  ments of the plasma d i a m e t e r  and  shows t h a t  q u i t e good.  - 16 -  the  pinch  S e c t i o n 3.4 g i v e s this  correspondence  here as  is  well  measurecan  be  Figure 4 presents  a composite of the observed  Each o f the three frames shown were obtained discharge.  Between s h o t s , the e x p o s u r e  referenced  from s e p a r a t e  window o f  t r a n s l a t e d w i t h r e s p e c t to the p i n c h time.  streak p h o t o g r a p h s .  the  streak  frame i s an overexposed  The  bright vertical  image o f  the image c o n v e r t e r  tube.)  A t e a r l y times  the  slit.  Based  on  t < -100  a x i s i s compressed, and beginning  ns a d i f f u s e  slit  ns.  The  the surrounding  and  on-axis  shell.  The  t = +100  the plasma boundary d e t e r i o r a t e s .  This  d i s r u p t i o n of the plasma column due The time, by  ns,  to  a low  shell,  plates  luminous  plasma  the  to  plasma  converging  plasma  clarity  i s presumed  on  significant-  high i n t e n s i t y as  a  5 ns.  increases  a much  ( i . e . high  accumulates and  symmetry  to c o r r e s p o n d  to  on of a  instabilities.  f e a t u r e s of the p i n c h phase m e n t i o n e d incoming  from  plasma t h e r e f o r e has  d e n s i t y ) region continuously grows i n d i a m e t e r L a t e r than approximately  of each  deflection  weakly  emission  so t h a t  image, i t i s e a s y  Incoming  the bremsstrahlung  a t about t = -80  higher d e n s i t y than  surrounded  was  ( T h i s image r e s u l t s  the  s h e l l can be seen moving r a d i a l l y inwards.  early  camera  l i n e a t the beginning  determine t h a t the temporal r e s o l u t i o n i s approximately  axis.  the  As a reminder, the time a x i s i s  ' h e s i t a t i o n ' i n the ramp v o l t a g e t h a t i s a p p l i e d to t h e  ly,  of  to the z e r o - c r o s s i n g of d l / d t , as i n d i c a t e d i n F i g u r e 2,  d l / d t = 0 a t time t = 0.  of  firings  ( i i ) a high  density region,  and,  above, namely,  density (iii)  plasma  core  break-up of  ( i ) an  on  the  axis, plasma  column, can a l s o be c l e a r l y seen i n the shadowgram p i c t u r e s . Figure 5 presents t h a t were r e c o r d e d . vessel holes.  The  a sampling  of some t y p i c a l  c i r c l e of exposure  shadowgram p i c t u r e s  i s a p r o j e c t i o n of  These h o l e s have a diameter of 1.9  charge chamber i s shown.  the plasma can be viewed i n both  axial directions,  and,  i n a l l the  appears w e l l a l i g n e d on the g e o m e t r i c a l  "  the  serve as  Also  and  5,  and  ence f o r image m a g n i f i c a t i o n . Now,  i n Figure  cm  p i c t u r e s of  the  Z-axis  Figure  5,  of  a  pinch refer-  the  the  radial  the  plasma  a x i s of the d i s c h a r g e v e s s e l .  17 ~  dis-  -300  -200  -100  0  +100  +200  Time [ns]  Figure 4 S t r e a k p h o t o g r a p h s o f the p i n c h spans a 200 ns time i n t e r v a l .  - 18 -  phase.  Each  frame  Fig ure 5 Shadowgram p i c t u r e s . The e x p o s u r e t i m e and d i s t a n c e from plasma to o b j e c t p l a n e a r e : (A) -70 n s , 32 cm; (B) +110 ns, 7 cm; (C) -20 ns, 32 cm; and (D) -30 ns, 7 cm. The outer boundary of the plasma i s , f o r e x a m p l e , i n d i c a t e d by the arrow i n p i c t u r e ( A ) .  The exposure of F i g u r e 5(A) was  taken a t time t = -70 ns, j u s t as  the incoming plasma reaches the a x i s (see F i g u r e 4 ) .  since  the plasma  o n l y weakly r e f r a c t i n g a t these times, a l a r g e plasma to o b j e c t p l a n e tance o f 32  cm  was  usea  structure.  While t e s t i n g  t i o n s were photographed,  i n o r d e r to o b t a i n  good c o n t r a s t  i n the  the o p t i c s , v a r i o u s index of r e f r a c t i o n including  a g l a s s rod or tube, a gas  is  disimage  distribu-  stream, e t c .  The b r i g h t o n - a x i s exposure of F i g u r e 5(A) i s i n d i c a t i v e of an o b j e c t whose refractive on-axis  index decreases with increasing  plasma  surroundings. be seen. diffuse  must have As w e l l ,  a lower  radius.  electron  density  the outermost boundary  shell  than  the  of the r e f r a c t i n g  F i g u r e 5(A) t h e r e f o r e does c o n f i r m t h a t though d e f i n i t e  Consequently,  incoming  immediate region  plasma  axis.  taken a t t = +110  ns  and  the o b j e c t  plane  the p i n c h column has broken  Development o f the h i g h d e n s i t y plasma shadowgrams o f F i g u r e s 5(C) and identical  (D).  These p i c t u r e s were  o b j e c t p l a n e s (32 cm and 7 cm r e s p e c t i v e l y ) . by r a y s d e f l e c t e d  from  The  though  dark  the c e n t r a l  taken a t  column o f  dense  plasma  F i g u r e 5(C) where the shadow diameter corresponds i n s i z e to the low d e n s i t y Having it  plasma  i n the almost  Figure core. plane,  surround-  plasma. had a look a t the plasma  i s worthwhile here to i n d i c a t e how  axis i t s e l f  5(B).  in different  Small r a y d e f l e c t i o n s become apparent i n a much more d i s t a n t o b j e c t  ing  a  up.  core i s i l l u s t r a t e d  times ( t = -20 ns and -30 ns r e s p e c t i v e l y ) ,  5(D) i s produced  has  i s 7 cm o f f  T h i s photograph d i s t i n g u i s h e s q u i t e d r a m a t i c a l l y between t h e  s t r u c t u r e b e f o r e and a f t e r  can  structure.  Late times are shown i n a somewhat l u c k y photograph, F i g u r e The exposure was  the  i s imaged.  Doing  the p i c t u r e s appear  this w i l l  the shadow method used here and nique o f S c h l i e r e n photography.  shadow i n o f f - a x i s  lead  image p l a n e s ,  when the  plasma  to a b a s i c d i s t i n c t i o n between  the u s u a l , and p o s s i b l y more f a m i l i a r  tech-  However, the f o l l o w i n g d i s c u s s i o n does not  - 20 -  presume t o r e p l a c e the  expert  c o n t r a s t imaging, i . e . :  analysis  o b j e c t p l a n e are c o i n c i d e n t  the shadowgrams show a n o t i c e a b l e  6(A)),  exposure due  to r a y s missing  the p i n c h a x i s w i t h an F/# 2.2°.  When i m a g i n g  the  of refraction  1963.  Holder,  I f the plasma a x i s and  o f the s u b t l e t i e s  though very  the f i r s t c o l l e c t i o n  of 14  implying  3 or  weak v a r i a t i o n i n  lens.  This  lens  views  a maximum d e f l e c t i o n a n g l e  plasma a x i s , exposure  w i t h i n 50 ns of maximum compression and  (see F i g u r e  v a r i a t i o n s occur  mainly  appear j u s t i n s i d e the b o u n d a r y  the h i g h d e n s i t y core where d e n s i t y g r a d i e n t s ,  and  of  of  hence r a y d e f l e c t i o n s ,  are l a r g e s t . Now,  when plasma i s not p r e s e n t ,  o f course be u n i f o r m l y  exposed  i l l u m i n a t i o n i s uniform. cides with This  for a l l object  planes  I f plasma i s p r e s e n t ,  the plasma a x i s ,  latter  the photographs of F i g u r e 5 would  case r e q u i r e s  the  film  that  two  would  and  imaging o p t i c s must have a s u f f i c i e n t l y s m a l l F/# light,  and,  distances  ( i i ) the  comparable  r e f r a c t e d rays to  the  plasma  d i s c u s s i o n w i l l h e l p to i l l u s t r a t e and  not  be be  uniformly  coin-  exposed.  fulfilled.  (i)  The  to c o l l e c t a l l r e f r a c t e d  diverge  radius.  incident  Figure  appreciably 6 and  the  within  following  the d i f f e r e n c e between c o n d i t i o n s  (i)  ( i ) o n l y i s not s a t i s f i e d , exposure v a r i a t i o n s  are  (ii). When c o n d i t i o n  due  do  the  the o b j e c t p l a n e  again  conditions  since  p r i m a r i l y to v i g n e t t i n g  Figure 6 ( A )  lost  at  S c h l i e r e n photography where the replaces  s p e c i f i c angular mined by  some  aperture  i n the  shows such a s i t u a t i o n where a l l r a y s  some minimum angle a r e  viewing  by  the  imaging  object  the r o l e of a k n i f e deflections.  This  i s imaged  edge or g r i d ,  etc.,  by  that  Vu, U  s e n s i t i v e to  ~  21  "  are  being  system.  more  than  corresponds and  limited  to F/#  in eliminating  In t u r n , /the d e f l e c t i o n a n g l e s  the r e f r a c t i v e index g r a d i e n t s  S c h l i e r e n systems are  deflected  lens  itself  imaging  traversed. the r e f r a c t i v e  are  deter-  Therefore, index.  object plane  imagei plane  object plane  Fig ure 6 Formation o f c o n t r a s t i n o n - a x i s i m a g e s . Refracted rays can be (A) v i g n e t t e d and/or (B) d i v e r g e n t .  - 22 -  In c o n t r a s t , when a l l r e f r a c t e d l i g h t i s c o l l e c t e d , but ( i i ) above i s n o t  satisfied,  then  r e f r a c t i o n produces a l o c a l spreading F i g u r e 6(B) d e p i c t s a uniform spaced r a y p a t h s . spaced.  exposure  or d i v e r g e n c e  then,  the  rays  occur  of the i n c i d e n t  i n t e n s i t y i n c i d e n t beam as  In the o b j e c t p l a n e ,  In t h i s case  variations will  condition  are  a s e t of  clearly  a non-uniform d e f l e c t i o n angle,  when light.  equally  not  equally  that i s ,  Vy 2  determines the image s t r u c t u r e . The refracting defined  shadow method i s not r e s t r i c t e d  object.  In f a c t ,  i n the shadow when o f f - a x i s  planes  are  imaged.  are The  more  (as  intend-  the p i n c h phase.  to q u a n t i f y the o b s e r v a t i o n s of t h i s p h o t o g r a p h i c  study,  two  p l o t s of the plasma diameter D(t) are g i v e n i n t h i s s e c t i o n . The  and  shadowgram p i c t u r e s have been analyzed  with e i t h e r  well  Plasma Diameter vs Time  In order  results will  the  shadow  been a p p r o p r i a t e here s i n c e i t was  ed to e s t a b l i s h the plasma dimensions during  The  containing  the o b j e c t (plasma) b o u n d a r i e s  opposed to S c h l i e r e n ) method has  3.4  to image planes  separately.  Comparison  show the c l o s e correspondence between the i n f o r m a t i o n technique.  As w e l l , based on  these p l o t s , a simple  streak of  the  obtained  estimate  of  the e l e c t r o n d e n s i t y a t maximum compression i s g i v e n . F i g u r e 7(A) g i v e s  the d a t a obtained  from e i g h t s t r e a k frames.  diameter of the h i g h d e n s i t y c o r e , denoted by c r o s s e s , was i n the photographs.  The  not so w e l l d e f i n e d and weakly luminous r e g i o n s . were determined  outer boundary o f was  estimated  Velocities  the  shell,  The  was  to be j u s t a t the outer edges o f  the  associated  f o r each frame, independent o f  solid  marked  shown as d o t s ,  with  the  the  l i n e s i n F i g u r e 7 have s l o p e s g i v e n  - 23 -  shell  diameter  s i n c e measurement of the speed w i l l not depend on l o c a t i n g precisely.  clearly  The  core  measurements  the by:  and  boundaries  and  dD/dt ( s h e l l ) = -1.97  ±  0.27  x 10  6  cm  s  _ 1  dD/dt (core)  + 0.11  x 10  6  cm  s  _ 1  were p o s i t i o n e d on  = +2.14  the p l o t t o g i v e  the  best  visual  f i t to  the  data  points. Measurements made on a p p r o x i m a t e l y t h i r t y shadowgrams r e s u l t e d the p l o t of F i g u r e 5(D)),  7(B).  indicated previously  shadow p i c t u r e s taken with  highly r e f r a c t i n g core region occupied ( r a d i a l ) extent slightly  by  while  low  z-dependent,  0.3  + 0.5  MI  lines.  p o s i t i o n and  cm  Diameters  regions,  though,  averaging  was  Figures  5(C)  and  off-axis isolate  the  plane d e l i n e a t e  the  are  the  taken  since  the  done.  t o be  diameter  Because  is  of  this  to be u n c e r t a i n  t o +_  respectively. . p l o t s i s t o be  Those drawn on F i g u r e 7(A) slope,  32  s h e l l d i a m e t e r s are estimated  Comparison of these two solid  i n the  plasma.  some v i s u a l  the core and  and  density  (see  the image plane 7 cm  pictures  of the unexposed  averaging, mm  As  in  to F i g u r e  7(B).  made on  the  basis  of  the  have been t r a n s f e r r e d e x a c t l y ,  The  lines  s t r e a k measurements o n l y , but are judged  were d e t e r m i n e d  to f i t both s e t s  from  of data  in the  equally  well. Given the s i z e of the plasma, the mated using  a 'snow-plow' model o f  assumption of t h i s model i s t h a t v e s s e l i s s w e p t - u p and  confined  the  i s q u i t e good and  has  z-pinch  a l l gas  The  to the v o l u m e t r i c  can  (Leontovich,  contained  within  to a c y l i n d e r having  d e c r e a s e s as c o n s t r i c t i o n p r o c e e d s . in d i r e c t proportion  electron density  the  This  One  discharge  a radius  compression r a t i o .  esti-  1957).  plasma d e n s i t y t h e r e f o r e  o f t e n been used as a c r o s s - c h e c k  be  r  which  increases  assumption  for other  density  diagnostics. With t o t a l sweep-up, the maximum d e n s i t y achieved the plasma r a d i u s i s minimum.  Figure  -  7 indicates that  24  "  the  will  occur  minimum  when  radius  -200  -100  0  *100  time (ns) F i g u r e 7(A) Plasma diameter vs time from s t r e a k  - 200  -100  photographs.  0  -100  time  (ns)  F i g u r e 7(B) Shadowgram r e s u l t s f o r the plasma d i a m e t e r .  - 25 -  r  m  i s , a t most, a p p r o x i m a t e l y 2.5 mm.  w i l l be assumed u n i f o r m . density  i s given  simply by  The i n i t i a l c o n d i t i o n s o f the  atoms per cm  3  m  I f the average i o n i z a t i o n i s Z, then the e l e c t r o n  n  radius  The d i s t r i b u t i o n o f plasma f o r r < r  = Zn (R/r ) . D  m  p r i o r to f i r i n g  v e s s e l , R = 5.08 cm and f i l l (see T a b l e I ) .  complete, so Z = 2.  [1]  2  e  the d i s c h a r g e are the i n n e r  density  n  Q  = 3.90 x 1 0  1 6  helium  A t the minimum r a d i u s , i o n i z a t i o n i s assumed  With these numbers, e q u a t i o n  [1] p r e d i c t s  an  average  electron density of:  n  at r . m  This density  e  = 3.2 x 1 0  i s considerably  1 9  cm  - 3  h i g h e r than the o r i g i n a l e s t i m a t e s of  Houtman, b u t the minimum plasma r a d i u s  was  not well  established  at  that  time. The h i g h d e n s i t y  predicted  by e q u a t i o n  [1] i s f u l l y  supported i n  the next s e c t i o n where e l e c t r o n d e n s i t y e s t i m a t e s are made by an e n t i r e l y d i f f e r e n t method.  3.5  E l e c t r o n D e n s i t y from Ray Here, the shadowgrams  deflections.  Refraction  are re-examined through an a n a l y s i s  of r a y  The r e s u l t w i l l be an e s t i m a t e f o r the e l e c t r o n d e n s i t i e s i n  - 26 -  both the core plasma and surrounding order  to define  First  though, i n  from  t h e shadow  the q u a n t i t i e s t h a t need to be d e t e r m i n e d  p i c t u r e s , r a y bending bution  low d e n s i t y r e g i o n .  in a cylindrically  symmetric r e f r a c t i v e  index  distri-  i s considered. The  electron density  distribution  i n the plasma  i s assumed t o  (.  depend o n l y on the r a d i a l c o o r d i n a t e equivalent r e f r a c t i v e  r and i s r e p l a c e d  (r)  =  (1  - n  e  / n  C  ) V 2 .  The  r e f r a c t i v e index depends on the w a v e l e n g t h  n ,  the c r i t i c a l  lO^  cm~3.  or c u t - o f f d e n s i t y .  The plasma i s c o n f i n e d  o u t s i d e o f which, The Figure In  [ 2 ]  R  o f the probe  to be w i t h i n a  c y l i n d e r of  through c  = 2.3 x  radius r  Q  ,  V = u =1 . o to the x - a x i s .  8 d e p i c t s the path of one r a y , i n c i d e n t on the p l a s m a coordinates,  Bouguer's formula  beam  At ruby l a s e r wavelengths n  probe beam i s c o l l i m a t e d and t r a v e l s p a r a l l e l  cylindrical  by i t s  index:  y  c  everywhere  (Born,  the r a y t r a j e c t o r y w i l l  1975)  where the s o - c a l l e d impact parameter i s p = u y = y .  - 27 -  at height  y.  be g o v e r n e d  by  fy  Figure 8 Ray p a t h i n an axisymmetric  - 28 -  plasma.  When r > r , the Q  ray will  r e f r a c t i v e index i s c o n s t a n t . deflected  ray  a s t r a i g h t l i n e path s i n c e the  Within the o b j e c t (plasma) t h e r a y w i l l  from i t s o r i g i n a l path.  the path w i l l be as i n d i c a t e d  travel  If n  e  d e c r e a s e s with i n c r e a s i n g  i n F i g u r e 8.  Upon e x i t i n g  w i l l have s u f f e r e d a n e t angular d e v i a t i o n ty. Using  i s easy  be  r , then  the plasma, the equation  [3],  i t  t o see t h a t :  00  aKy) = TT-2/(d8/dr)dr ,  [4]  T S  where r  g  i s the  s t a t i o n a r y p o i n t , determined  r a d i u s f o r w h i c h d r / d t = 0. equation  s  or  Parenthetically,  [3] should b e g i n w i t h a +/- s i g n  changes s i g n a t r .  from  Bouger's formula as the i t should  to c l a r i f y  the f a c t  Given an o b j e c t w i t h a s p e c i f i e d  refractive  Conversely,  specifying  corresponding  by knowing  t o each v a l u e  than  crude d e f l e c t i o n The  ty(y)  ,  o f ty be m e a s u r e d .  extraction  distribution,  u ( r ) c a n be  found.  parameter (s)  Experimentally,  arrangement  t h e c u r r e n t shadowgram e x p e r i m e n t s .  p i c t u r e s a v a i l a b l e have allowed  by e q u a t i o n [ 4 ] .  index  u ( r ) r e q u i r e s t h a t the impact  demands a c o n s i d e r a b l y more s o p h i s t i c a t e d 1972)  t h a t dr/d6  ijj(y) t h a t w i l l c h a r a c t e r i z e  enables one t o c a l c u l a t e a d e f l e c t i o n c u r v e  Completely  that  The q u a n t i t y t h a t can be d i r e c t l y measured with shadow  S c h l i e r e n methods i s the angular d e f l e c t i o n determined  the d i s t r i b u t i o n .  be n o t e d  (e.g.: However,  of a useful,  y  this  Kogelschatz, t h e shadow  though  somewhat  curve.  important  i n f o r m a t i o n t o be o b t a i n e d from  i s the maximum d e v i a t i o n angle  \b  the d e f l e c t i o n  as shown i n t h e c u r v e  - 29 -  curve  of Figure  8.  Shmoys (1961) and i|;(y) using n (r). e  The  Keilmann  a v a r i e t y of  (1972) have performed d e t a i l e d c a l c u l a t i o n s o f f u n c t i o n a l forms  for  the  plasma  distribution  f u n c t i o n s chosen f o r n ( r ) are a l l w e l l behaved. The  maximum on a x i s and  decays m o n o t o n i c a l l y  to zero a t r .  e  though d i f f e r e n t i n d e t a i l , c o u l d be a p p r o x i m a t e d The  by  results  a s i n g l e curve, of  Shmoys and  mann s c a l c u l a t i o n s are t h a t , to w i t h i n an u n c e r t a i n t y of about 1  *max "  The  U 0  n  /n  f o l l o w i n g c o n s i d e r a t i o n s i l l u s t r a t e how  [5]  the shadowgrams were  estimates. analyzed.  C e r t a i n l y some bounds can be put on the d e f l e c t i o n angle a knowledge of the shadow r a d i u s i n a g i v e n o b j e c t p l a n e .  o b j e c t plane  ns, 7 cm  the h i g h d e n s i t y core has  parameter no g r e a t e r and  32 cm  plane  than 1.6  place  bounds on  through the low d e n s i t y s h e l l A second way  i t should  i s a t l e a s t 23 mrad and mm.  be  mm  f o r an  that  impact  i n both the 7 for rays  at  i n an  s a f e to say  occurs  d e f l e c t i o n angle  from  For e x a m p l e ,  S i m i l a r l y , observations the  just  a shadow r a d i u s of 1.6  from the plasma. T h e r e f o r e ,  the maximum d e f l e c t i o n angle  Keil-  e °) c ' Cr=  the  35%,  [5] w i l l be used to o b t a i n the d e s i r e d e l e c t r o n d e n s i t y  about t = +30  sharp  A l l of t h e i r d e f l e c t i o n c u r v e s ,  e  form o f which i s i n d i c a t e d i n F i g u r e 8.  There were no  Q  d i s c o n t i n u i t i e s i n e i t h e r n ( r ) or d n / d r .  Equation  density i s  e  cm  passing  region.  used to o b t a i n d e f l e c t i o n angle  f a c t t h a t the probe beam i s c o h e r e n t .  Returning  data  d e p e n d s on  the  to the shadow p h o t o g r a p h s  themselves, p a r t i c u l a r l y F i g u r e 5 ( C ) , i t i s c l e a r t h a t the image s t r u c t u r e near the plasma boundary i s dominated by a number of w e l l d e f i n e d These f r i n g e s r e s u l t from the i n t e r f e r e n c e between undeviated  - 30  -  rays  fringes. passing  o u t s i d e the plasma b o u n d a r y , edges o f the plasma.  and  refracted  N o t i c e a l s o t h a t the  rays  fringe  i n c r e a s i n g d i s t a n c e from the a x i s i n d i c a t i n g  which pass spacing  t h a t the  thorugh  the  decreases  refracted  with  rays  are  Given, as i n F i g u r e 8, the t y p i c a l form of a d e f l e c t i o n c u r v e ,  the  being d e f l e c t e d by u n i f o r m l y i n c r e a s i n g a n g l e s .  above i n t e r p r e t a t i o n of f r i n g e s i s c o n s i d e r e d  substantially  order to o b t a i n data p o i n t s f o r the d e f l e c t i o n curve, ween a d j a c e n t i n t e r f e r e n c e minima i s measured.  the  correct.  In  distance d  This g i v e s  the  bet-  deflection  angle:  ty = s i n "  (X/d) a  1  a s s o c i a t e d w i t h the r a y producing c o o r d i n a t e system of F i g u r e 8, tance x = 1 from the plasma. h e i g h t y'.  With t h i s  X/d  a particular  fringe.  Referring  the o b j e c t plane w i l l be In the o b j e c t p l a n e ,  the  located at a  the  fringe  dis-  appears  (measured) i n f o r m a t i o n , e x t r a p o l a t i o n b a c k  y - a x i s g i v e s the impact  to  to  at the  parameter:  y = y'  o f the r a y d e f l e c t e d by ty . Using analyzed.  The  the above arguments, shadowgrams t a k e n time chosen f o r t h i s  r a d i u s of c o l l a p s e .  The  resulting  The d a t a p o i n t s were determined i n o b j e c t p l a n e s 32 cm  should be c o n t a i n e d regions. the two  t =  exercise corresponds  +30  ns  to the  were  minimum  d e f l e c t i o n curve i s shown i n F i g u r e  by f r i n g e a n a l y s i s of shadowgrams  ( c i r c l e s ) and  maximum d e f l e c t i o n angle  at  7 cm  f o r the core and  respectively within  These bounds were determined  shell the  the  components  upper  and  recorded  plasma. of  lower  the  -  The  plasma  rectangular  simply from the shadow d i a m e t e r s  object planes.  - 31  (squares) f r o m  9.  in  30  0  1  2  3 y (mm)  Figure 9 D e f l e c t i o n curve f o r the plasma a t maximum  - 32 -  compression.  Because the d a t a i s r a t h e r s k e t c h y , shape o f the d e f l e c t i o n  curve  would  be  critical  examination  unjustified.  The  solid  of  the  line  in  F i g u r e 9 has been i n c l u d e d o n l y t o r e p r e s e n t a p l a u s i b l e f i t to the d a t a . Since i t i s c l e a r  t h a t the pinched plasma has a d e f i n i t e  ponent s t r u c t u r e , i t i s not hard by the s u p e r p o s i t i o n o f two  to imagine  that Figure 9 can  two  be  composed  s i m i l a r d e f l e c t i o n c u r v e s , each s c a l i n g  e n t l y i n r a d i u s and h e i g h t .  Both c u r v e s , and  the plasma, can be c h a r a c t e r i z e d  by  t h e r e f o r e both  equation  [5],  com-  differ-  components of  Taking  i  for  the  max s h e l l and laser  core plasmas as 5 mrad and  25 mrad r e s p e c t i v e l y ,  and  n  c  f o r ruby  light, gives: n  ( s h e l l ) = 1.1  x 10  1 9  cm  -3  e  n  (core)  x 10  1 9  cm  -3  e  = 6.0  Even w i t h the p e s s i m i s t i c view o f an u n c e r t a i n t y o f a f a c t o r o f two, f i g u r e s agree w e l l w i t h the average d e n s i t y e s t i m a t e d based  3.6  on a snow plow model of plasma  tended  equation  [1],  compression.  C o n c l u s i o n t o the P h o t o g r a p h i c The experiments  from  these  Study  t h a t have been presented i n t h i s chapter  were i n -  to g i v e a c l o s e r view o f the plasma p i n c h phase than had p r e v i o u s l y  been o b t a i n e d by Houtman.  T h i s has been done using photographic  techniques  t h a t have been ( i ) r e l a t i v e l y simple to implement, ( i i ) p a r t i c u l a r l y c a b l e t o plasmas o f h i g h e l e c t r o n d e n s i t y , and adequate s p a t i a l and  temporal  (iii)  capable  of p r o v i d i n g  resolution.  Primary a s p e c t s o f the plasma dynamics and e v o l u t i o n o f t h e t r o n d e n s i t y s t r u c t u r e have been determined meter as a f u n c t i o n o f  time.  appli-  Estimates  - 33 -  by  measuring  f o r the  electron  the  plasma  elecdia-  d e n s i t y during  maximum compression  have been made w i t h  reasonable  plasma d e n s i t i e s achieved a r e w e l l i n e x c e s s C0  2  l a s e r l i g h t , namely, 1.0 x 1 0  1 9  cm .  accuracy.  of the c r i t i c a l  The peak  density for  i n t h i s r e s p e c t then, the  - 3  phase i s q u i t e s u i t a b l e f o r l a s e r - p l a s m a i n t e r a c t i o n experiments. tively,  the d e n s i t y s t r u c t u r e d u r i n g c o l l a p s e  i s smooth and w e l l  f o r a p p r o x i m a t e l y 200 n s , a f t e r which, the pinched  column b r e a k s  pinch  Qualitabehaved up i n an  i r r e g u l a r and u n p r e d i c t a b l e manner. T h i s concludes the i n i t i a l o b s e r v a t i o n s o f t h e p i n c h p h a s e . photographic  study r e p r e s e n t s an important  w i l l prove v i t a l following  to t h e i n t e r p r e t a t i o n  extension of e a r l i e r  of subsequent  few c h a p t e r s c o n s t i t u t e the second  a c c u r a t e d e t e r m i n a t i o n o f the p l a s m a d e n s i t y and t e m p e r a t u r e p i n c h phase using Thomson s c a t t e r i n g  o f ruby l a s e r  - 34 -  work and  experiments.  p o r t i o n o f t h i s work,  light.  The  The  namely,  during the  CHAPTER 4  4.1  ELEMENTS OF THOMSON SCATTERING  Introduction Thomson s c a t t e r i n g by plasma f l u c t u a t i o n s i s a v e r y common method  f o r measuring  temperature and d e n s i t y .  have been p u b l i s h e d give  a complete  S e v e r a l good reviews o f the s u b j e c t  (Kunze, 1968; E v a n s ,  description  1969; D e S i l v a ,  o f the theory  1970) and t h e s e  and t e c h n i q u e s  o f Thomson  s c a t t e r i n g . The a n a l y s i s p r e s e n t e d i n these reviews has remained unchanged to the p r e s e n t derivations pertaining  time.  This  chapter  the theory w i l l be used  a s p e c t s and parameters o f Thomson s c a t t e r i n g  that  detailed  to define  the b a s i c  are important  for  the  Z-pinch d i a g n o s t i c s . In plasmas, the Coulomb f o r c e s a c t i n g  a wide v a r i e t y o f wave phenomenon.  r i c h i n structure significant,  and d e t a i l .  strong  scattering  i s dominated  the f r e q u e n c y or  from plasma p a r t i c l e  Although o n l y  Coulomb c o u p l i n g  which  between p a r t i c l e s a l l o w f o r  As a c o n s e q u e n c e ,  wavelength spectrum o f l i g h t s c a t t e r e d  in  not attempt  to the t h e o r y o f e l e c t r o m a g n e t i c wave s c a t t e r i n g i n  plasmas. However, r e s u l t s o f  current  will  relatively  scattering  between e l e c t r o n s  fluctuations i s  from  electrons i s  and i o n s  can r e s u l t  by, and c h a r a c t e r i s t i c o f , t h e  ion  distribution. The  first  s e c t i o n o f t h i s chapter d i s c u s s e s  ween the s o - c a l l e d e l e c t r o n and i o n f e a t u r e s light.  Separation  from the two b a s i c  o f the s p e c t r u m  bet-  of scattered  o f the t o t a l spectrum i n t o two d i s t i n c t components stems types o f f l u c t u a t i o n s  that  e l e c t r o n plasma waves and i o n a c o u s t i c waves. method examines the e l e c t r o n f e a t u r e . presented, only  the d i s t i n c t i o n  occur  i n plasmas,  The u s u a l Thomson s c a t t e r i n g  However, i n t h e e x p e r i m e n t s  the i o n component o f the spectrum i s observed.  o f Thomson s c a t t e r i n g  to the c u r r e n t  -  namely,  Application  investigation i s therefore,  35  -  t o be  quite  unconventional normally  sense  that d e t a i l s  observed or even c o n s i d e r e d The  feature  i n the  useful  brightness ability  of  bremsstrahlung  n . e  ion  scattered  emmission.  such  the  features.  light  over  Background  i n t e n s i t y of  as  from a comparison  e l e c t r o n and  to d e t e c t  whereas t h e  result  ion  feature  w i l l demonstrate  for determining  moderately hot, dense e n v i r o n m e n t s This conclusion w i l l  the  scattered  current of  The and  light light  plasma  the  that  represent  an  the i o n f e a t u r e may  important e x t e n s i o n  not  Z-pinch  relative  emphasis w i l l  above  the  the  level  only  be e a s i l y d e t e c t a b l e ,  spectral be  on  of  plasma  linearly  of the u s e f u l n e s s  of  and  in  plasma.  l e v e l s w i l l i n c r e a s e with increases  ion  parameters  At plasma d e n s i t i e s where the e l e c t r o n f e a t u r e i s c o m p l e t e l y  background l i g h t ,  are  f o r r o u t i n e d i a g n o s t i c purposes.  second p o r t i o n of t h i s chapter  is particularly  of  the  n2 g  with  masked i n therefore  Thomson s c a t t e r i n g  diagnostics.  4.2  D i s t i n c t i o n Between E l e c t r o n and  Ion  The  i s , the  spectral distribution,  dependence of l i g h t s c a t t e r e d f a c t o r S(k, u ) .  that  Features i n t e n s i t y vs  from a plasma i s g i v e n  This function i s defined  by the  frequency  s o - c a l l e d shape  through the d i f f e r e n t i a l  cross-  s e c t i o n per u n i t volume:  &  Here, n  e  i s the average  "  Ve  S ( k  »  electron density.  -  36  -  a )  '  The  s c a t t e r i n g p r o p e r t i e s of a  a  s i n g l e e l e c t r o n are c o n t a i n e d i n the Thomson c r o s s - s e c t i o n , not e x p l i c i t l y shown,  0  also  e l e c t r i c dipole radiation. from i o n s  i s neglected).  interacting  c o n t a i n s the u s u a l  The  scattering  determines the wavevector TT = k  The  frequencies  (e.g. has  Q  complete frequency and  cross-section  f o r plasmas has  Salpeter,  shown t h a t  1960; the  k  a  being  s  of  selects  written  the  scattered  energy).  i n d e t a i l by  be  momentum  to the  scattering  several  or Rosenbluth, 1962).  S(k,to) may  of  wavevectors  wavevector dependence of the  1963  shape f a c t o r  of  the  Wavevector k  - C0 | ( c o n s e r v a t i o n  been c a l c u l a t e d  Salpeter,  scattering  fa  f l u c t u a t i o n s which c o n t r i b u t e  co = + | C0  of  of the whole s y s t e m  Conservation  light respectively.  s p a t i a l component of d e n s i t y s i g n a l of the  S(k,oj).  by  - k , with k,-. and s °  o scattered  properties  Though  dependence  (By v i r t u e of i t s much l a r g e r mass,  particles i s described  f o r i n c i d e n t and  angular  .  authors,  Salpeter  as  the  sum  (1960) of  two  s e p a r a t e components, S(k,aO = S (k,a>) + S ( k , c o ) e  where the This be  subscripts  separation  investigated  isolate  emphasizes the by  components of the  waves.  scattering  These are  the r e s t o r i n g r a p i d l y to  6E  e l e c t r o n and  two  [ 6 ]  ion features  feature  techniques.  The  between e l e c t r o n s  following  i n the  description  for o s c i l l a t i o n .  field  Electrons  fiU  and  the  in  the  will two  Langmuir density  which produce  this f i e l d  of course, can  compared with the r e l a t i v e l y massive i o n s .  c o n s i d e r e d immobile and  may  inertia.  off electron  electron density  w i l l set-up an e l e c t r i c  force  profile.  which s c a t t e r i n t o these  r e s u l t s from s c a t t e r i n g  Perturbations  of the  d i f f e r e n t types of plasma waves t h a t  longitudinal, electrostatic fluctuations  only.  charge s e p a r a t i o n  ,  spectrum, namely, the apparent e l e c t r o n  electron  of e l e c t r o n s  f o r e be  r e f e r to the  the b a s i c d i f f e r e n c e  The  i  provides  respond  Ions can  a  very  there-  e l e c t r o n motion i s c o m p l e t e l y decoupled  - 37  -  from the background of p o s i t i v e i o n s e l e c t r i c a l n e u t r a l i t y over  the  Langmuir  of  f l u c t u a t i o n s are  f e a t u r e cannot be expected The are t i e d  (except  plasma the  f a r as  volume).  high  to g i v e  i n so  on  type  and  e l e c t r o n s w i l l now frequencies  be determined  the by  ion motions. the  ion  ensure  electron  the  electron  the i o n motions.  i o n f e a t u r e i s the r e s u l t of s c a t t e r i n g from  ( v i a Coulomb f o r c e s ) t o  ions  Consequently,  frequency  information  the  The  mass so  electrons inertia  that  i n the i o n f e a t u r e are much lower than t h o s e  which  of  these  characteristic  for  the  electron  more  familiar  feature. Ion a c o u s t i c f l u c t u a t i o n s , though analogous to low  frequency  1974).  sound  waves, a r e  also  In response to p e r t u r b a t i o n s  to p r e s e r v e  electrostatic  the  oscillations  i n the i o n d e n s i t y , e l e c t r o n s  l o c a l e l e c t r i c a l n e u t r a l i t y by moving  together  However, not a l l e l e c t r o n s c o n t r i b u t e to n e u t r a l i z i n g the produced by  the  ion disturbance.  I t i s the  m a i n t a i n s the i o n o s c i l l a t i o n . on  The  cities.  the  ions. fields  field  magnitude of the r e s i d u a l f i e l d not p a r t i c i p a t e i n  that  depends shield-  t h i s i n turn i s determined by the d i s t r i b u t i o n of e l e c t r o n Therefore,  a full  d e s c r i p t i o n of  parameters of both e l e c t r o n and The  b a s i s of e q u a t i o n  l i g h t i n t o e l e c t r o n and frequency  be c o n s i d e r e d  the  ion  [6] f o r s e p a r a t i n g  uncorrelated.  c o r r e l a t i o n s are r e q u i r e d  the  the  d i f f e r e n c e i n the  electron's  view o f the e l e c t r o n term, the e l e c t r o n s  ( C l e a r l y , t h i s i s not the g e n e r a l of  p l a s m a waves.  t i o n s under which c o r r e l a t i o n e f f e c t s can  be  ignored  s p e c t r a are d e s c r i b e d  i n more d e t a i l ) .  are a l s o randomly d i s t r i b u t e d i n s p a c e , f l u c t u a t i o n s that  contain  large d i s p a r i t y i n  f o r the e x i s t e n c e  s h o r t l y , when the  will  the spectrum of s c a t t e r e d  i o n f e a t u r e s i s , of course,  In a simple  feature  velo-  ion d i s t r i b u t i o n s .  s c a l e s w h i c h r e s u l t s from  apparent i n e r t i a .  spatial  attempt  electric  residual electric  the number of h i g h energy' e l e c t r o n s which do  ing , and,  with  (Chen,  are  the  -  The  since condi-  be  presented  I f the  electrons  electron density  statistically  - 38  will  case  can  independent.  will Then,  have the  scattered  i n t e n s i t y , at a given  the number of e l e c t r o n s shifted  frequency.  frequency s h i f t ,  the  electron  Maxwellian d i s t r i b u t i o n ,  the  scattered  p r o f i l e w i t h a width determined by  one  s i m i l a r way,  another.  the  proportional  velocities spectrum  are  will  to t h i s  Doppler  described  j u s t be  a  to  by  a  Gaussian  the mean thermal speed of e l e c t r o n s .  i o n s can be  Those e l e c t r o n s  produce a s c a t t e r e d  be  t h a t have a v e l o c i t y corresponding  If  a very  will  considered  that  to behave i n d e p e n d e n t l y  closely follow  spectrum t h a t r e f l e c t s  In  the  ion  motions  of  will  the v e l o c i t y d i s t r i b u t i o n of  the  ions. Based on e l e c t r o n and  ion  the  simple d e s c r i p t i o n above, i t i s easy to see  features  r e s p e c t i v e e l e c t r o n and  will  have  s p e c t r a l widths determined  i o n thermal v e l o c i t i e s .  feature w i l l  t h e r e f o r e be  o f the order  of:  that  The  width of the  by  l a r g e r than t h a t of the i o n component by a f a c t o r  v  e  a large discrepency  = 86  the  electron  ve / v .1 = (m./m i ' e ~)h •  For example, v / v i  the  J  [7]  2  i n a f u l l y i o n i z e d e q u i l i b r i u m helium plasma. Such  i n frequency s c a l i n g has  of experimental a p p l i c a t i o n .  This w i l l  be  s e r i o u s consequences i n  discussed  terms  further  in  Section  possibility  of  density  4.3. The fluctuations waves.  simple e s t i m a t e above p r e c l u d e s that  are  produced  by  collective  e x c i t a t i o n of  N o n e t h e l e s s , i n s p i t e of such c o m p l i c a t i o n s ,  very reasonable r e p r e s e n t a t i o n  of  r e l a t i v e widths of e l e c t r o n and  ion  Figure like.  the  the  both  the  equation  source  and  spectrum  [7] remains a  magnitude of  the  features.  10 shows what a more t y p i c a l s c a t t e r e d  Certainly this  plasma  c a n n o t be  described  appearance of r e s o n a n t s t r u c t u r e i s q u i t e e v i d e n t .  - 39  -  spectrum m i g h t by  The  a Gaussian. remainder  of  look The this  -4 2 -4—»  "E  > t-» O c lo *_ a  H 1  x  FIGURE 10 A ' t y p i c a l ' s c a t t e r e d spectrum. Frequency s c a l e s are normalized t o e i t h e r the e l e c t r o n or i o n thermal v e l o c i t i e s , x = » / k v ^ . Note the r e l a t i v e i n tensity scales.  - 40 -  section  will  initiate  this discussion,  light  that  written  discuss  will  down.  this  appear  'typical'  the f r a c t i o n o f in either  The d i s t r i b u t i o n o f  frequency i n t e g r a t e d  shape f a c t o r s  S (k) e  spectrum  the  the  in detail.  total  electron  scattered (Evans,  = /S (k,£o)dco =  to  scattered  ion feature  will  i s determined  be  by  the  1969)  Oa )" 2  e  amount o f  or  light  In o r d e r  1  [8]  s, oo (l+a )[l+a (l+ZT /T.)] 2  2  e  These  are  calculated  assuming  the  electron  Maxwellian, but a t d i f f e r e n t temperatures. The most important parameter scattered  spectrum observed  and  ion d i s t r i b u t i o n s  The degree  here, which  are  of i o n i z a t i o n i s Z.  determines  i s the c o r r e l a t i o n or s c a t t e r i n g  the  type  of  parameter,  a = CkA )->  [ 9 ]  D  This  i s the r a t i o of two c h a r a c t e r i s t i c l e n g t h s .  The  density  which s c a t t e r s i n c i d e n t l i g h t has a wavelength X = 2ir/k and the d i s t a n c e turn,  over which p a r t i c l e c o r r e l a t i o n s  X i s determined  wavelength  e n t i r e l y by the experimenter  of i n c i d e n t l i g h t , and arrangement  The Debye s h i e l d i n g  length X  is  f i x e d by the  will  this  determines  investigated.  through  c h o i c e of  of the s c a t t e r i n g  In the  geometry".  for electrons,  D ^o^/^V 1 " 2  plasma  be  fluctuation  Cmks)  =  conditions,  i . e . the e l e c t r o n  - 41  -  temperature  T , e  and  density n .  The  e  Debye l e n g t h r e p r e s e n t s  p e r t u r b a t i o n i n the charge d e n s i t y rest  of  charges.  the  p l a s m a by  In order  the  to g e t  can  The  be  effectively  some i d e a of how  l i g h t , consider  illustration  of  local  from  neighbouring  f i r s t o n l y the e l e c t r o n  determined by  i s found  i n the  alpha.  limit  a <<  1 where  i n c i d e n t l i g h t i s s c a t t e r e d from d e n s i t y f l u c t u a t i o n s whose s c a l e l e n g t h i s much l e s s than the Debye l e n g t h . Coulomb f i e l d  i s not apparent.  their electric  fields.  Here,  Of c o u r s e ,  the  correlation effects influence  s p e c t r a l shape i s completely  simplest  a  shielded  a t t r a c t i o n (or r e p u l s i o n )  the frequency spectrum of s c a t t e r e d f e a t u r e where the  the d i s t a n c e over which  the the  long  range  particles  However, over d i s t a n c e s  nature  do  of  k  - 1  the  interact via  s m a l l compared to the Debye  l e n g t h , the net e f f e c t of i n t e r a c t i o n s i s to produce a l o c a l l y random  dis-  t r i b u t i o n of charges .  from  The  s c a t t e r i n g i s the  t o t a l l y independent e l e c t r o n s . in this  limit,  zero, w h i l e  the  e  independently  t o t a l s c a t t e r e d i n t e n s i t y i n the i o n f e a t u r e  s e c t i o n becomes  da/dfi = n a  i n shape corresponding T h i s s i t u a t i o n was [7].  Only T ,  order  to o b t a i n n ,  e  Because the e l e c t r o n s behave  -»- 1 (see e q u a t i o n s  S (k)  same as would be obtained  [8]).  . The  total  scattering  frequency spectrum w i l l be  crossGaussian  to a Maxwellian d i s t r i b u t i o n of e l e c t r o n v e l o c i t i e s .  described  earlier  i n the d i s c u s s i o n leading  the e l e c t r o n temperature may e  The  approaches  the  t o t a l i n t e n s i t y of  d e t e c t i o n system must be d e t e r m i n e d .  to  be measured from the radiation  scattered  ( C a l i b r a t i n g the  equation shape.  In  into  the  scattered  signal  d i r e c t l y i n terms of e l e c t r o n d e n s i t y i s e a s i l y done by R a y l e i g h s c a t t e r i n g from n e u t r a l g a s e s .  T h i s procedure i s d e s c r i b e d  -  42  -  i n the next  chapter).  The alpha  long  range n a t u r e  approaches and  of  the  exceeds u n i t y .  Coulomb  Then,  force  the  becomes a p p a r e n t  f l u c t u a t i o n s that  scattering  have wavelengths the order  Scattering  from these f l u c t u a t i o n s w i l l e x h i b i t the c o o p e r a t i v e  of e l e c t r o n s and  of or g r e a t e r  the s p e c t r a w i l l be d e t e r m i n e d  by  than  the  as  produce  a Debye  length.  behaviour  properties  of  the  plasma waves. The >>  Xp.  The  centered  most d r a m a t i c example i s found i n the e l e c t r o n f e a t u r e c o n s i s t s of two  about the i o n l i n e and  shifted  l i m i t of  narrow  spikes  a >> or  1 or  k  - 1  satellites  by a frequency a p p r o x i m a t e l y  equal  t o the e l e c t r o n plasma frequency,  w  p  =  (  e  2  n  /  e  e  m 0  e ^  •  ( F i g u r e 10 shows the e l e c t r o n s a t e l l i t e s a t modest values  of alpha)-.  These long  w i t h a l a r g e phase v e l o c i t y .  The  (  6E  as a h i g h f r e q u e n c y f i e l d  and  with  field  w e l l developed  6E  even  t associated  plasma.  Slow moving  do not have  the  w i l l r e a d i l y p a r t i c i p a t e i n the o s c i l l a t i o n . t i o n s w i l l r e s u l t i n Doppler s h i f t s  [10]  wavelength f l u c t u a t i o n s p r o p a g a t e  perturbation  However, e l e c t r o n s which are moving  )  are r e a s o n a b l y  these f l u c t u a t i o n s , moves r a p i d l y through the t r o n s see  m k s  phase  time  to  v e l o c i t y of  with elec-  respond. the  wave  S c a t t e r i n g o f f these f l u c t u a -  corresponding  to the phase v e l o c i t y o f  the wave. Thus, a t l a r g e a l p h a ,  the f l u c t u a t i o n t h a t produces s c a t t e r i n g i s  a normal mode of e l e c t r o s t a t i c plasma o s c i l l a t i o n . tron s a t e l l i t e s istic  i s s m a l l compared to t h e i r  of a n a t u r a l o s c i l l a t i o n  experiencing  these s p i k e s w i l l g i v e an a c c u r a t e information  on  measure  feature  for  large  alpha  - 43  -  width of  frequency, a f e a t u r e only of  the e l e c t r o n temperature i s l o s t .  o f the e l e c t r o n  The  weak damping .  the  the  elec-  characterLocating  electron density,  However, the  i s somewhat  limited  but  usefulness since,  as  equations  [8] show v e r y  resonance  lines. The  s c a t t e r e d l i g h t w i l l be c o n t a i n e d  i n c r e a s i n g alpha  can be u n d e r s t o o d  as f o l l o w s .  the phase v e l o c i t y o f e l e c t r o n p l a s m a waves g r e a t l y  the mean thermal speed o f the e l e c t r o n s . Because o f the n e a r l y nature o f the e l e c t r o n f l u i d , by o n l y those e l e c t r o n s with the wave.  i n these  r e a s o n t h a t the c r o s s - s e c t i o n f o r s c a t t e r i n g i n t o the e l e c t r o n  feature decreases with large alpha,  little  As alpha  At  exceeds  frictionless  the f l u c t u a t i o n amplitude w i l l be d e t e r m i n e d v e l o c i t i e s comparable to the phase v e l o c i t y o f  i n c r e a s e s , the phase v e l o c i t y moves f a r t h e r and f a r t h e r  i n t o the wings o f the e l e c t r o n v e l o c i t y d i s t r i b u t i o n ,  so t h a t  fewer and  fewer e l e c t r o n s a r e a b l e t o p a r t i c i p a t e i n the o s c i l l a t i o n . An values  example o f the s p e c t r a l shape  of alpha,  i.e.  corresponding  a ^ 1 i s shown i n F i g u r e  10.  to  intermediate  The i m p o r t a n t  aspect  to note i s t h a t the e l e c t r o n f e a t u r e depends o n l y on the parameters o f t h e electron distribution, n  and T  e  through a •  e  The.shape o f the i o n f e a t u r e  i s a l s o e n t i r e l y determined by a s i n g l e parameter  3  --S£_CZT  2  1-HX  2  /T.)  B , d e f i n e d by:  .  M i ]  6  Parameters o f both e l e c t r o n and i o n d i s t r i b u t i o n s are now p r e s e n t . i t y with  the e l e c t r o n f e a t u r e  c a n be e m p h a s i z e d  Similar-  i f t h e Debye s h i e l d i n g  length f o r ions i s defined,  X  This allows and  D.  a distinction  the corresponding  =  (e KT./Ze n )32  (inks). .  2  o  e  to be made between a  parameter,  - 44 -  e  = a * given  i n equation [ 9 ] ,  a.  Then, the shape parameter  $  =  a(ZT /T.)% e  f o r the i o n l i n e becomes,  B = a.(l+ct )" 2  3 =  When a l p h a i s s m a l l , a s p e c t r a l shape which  Maxwellian d i s t r i b u t i o n  ponent  satellites  so t h e  large a  s p e c t r a l width  of i o n v e l o c i t i e s .  as alpha  has  i o n s behave n e a r l y  i s characterized  Of c o u r s e ,  e l e c t r o n s and  exceeds  , the l i m i t i n g  t h a t appear  a  the  a v a l u e of about  value of  = o  by  a  corresponds  ion feature dis-  e  1 (making  t i o n s are n o r m a l l y h e a v i l y  damped  broad s c a t t e r e d  corresponding  spectrum,  F i g u r e 10, f o r example).  1  e  a »  B large).  oscillations  and  The  and  sharp  1 only develop i n  Ion a c o u s t i c  fluctua-  t h e r e f o r e produce  t o modest v a l u e s o f b e t a  Under n o n - e q u i l i b r i u m plasma c o n d i t i o n s ( T  i o n waves are o n l y w e a k l y damped s h i f t s determined  0.2.  8 i s (Z T / T i ) / 2 .  i n the e l e c t r o n f e a t u r e f o r  the i o n f e a t u r e when Z T / T i >>  Doppler  The  the i o n l i n e  However, the i o n l i n e begins to be a s i g n i f i c a n t com-  o f the spectrum At  i s a l s o s m a l l and  from t o t a l l y independent  appears, S^(k) = 0.  .  i s a p p r o x i m a t e l y Gaussian.  independent o f one a n o t h e r  to s c a t t e r i n g  %  distinct  by the i o n a c o u s t i c  e  a  (see  >>  i o n s a t e l l i t e s appear  T^) at  speed,  [12] C  s  -  (ZKT/m.)!* .  - 45 -  When the  ion feature  does d e v e l o p  waves t h a t produce the  a sharp resonance  s c a t t e r i n g have a phase v e l o c i t y  exceeds the average thermal v e l o c i t y of the moves f a r t h e r i n t o the wings of the fewer and  to the  electron  s e c t i o n S j j k ) decreases with increasing large alpha,  but  also Z T / T i e  electron-ion thermalization extremely large d e v i a t i o n s will  only  Barnard,  approximately  ions.  As  the  >>  feature,  beta when  1.  velocity  the 3  >>  from e q u i l i b r i u m . the  scattering 1.  ion  are  one  If Z T / T i e  resonance  cross-  This implies  However, i n high d e n s i t y  above d i s t i n c t i o n between e l e c t r o n and  necessarily brief. scattering  would < 20,  not  plasmas,  not  expect  equation  (Rosenbluth,  and  A detailed d e s c r i p t i o n  of  the  ion  features  [12]  1 962;  been  Thomson  plasma wave t h e o r y i s w e l l beyond the scope of t h i s  thesis.  important p o i n t  from the p r e v i o u s d i s c u s s i o n  i n equation  i s contained  [12], where the e l e c t r o n and  T h i s d i f f e r e n c e i s examined f u r t h e r i n the  4.3  Advantage o f the  Ion  Since s c a t t e r e d  light  extracted [10]  relative spectral  following  section.  Feature must be  detected  e m i s s i o n o f the plasma, the major advantage of the spectral brightness.  t o be  [7] or e q u a t i o n s  i o n mass determine the  widths.  To  has  s u b t l e t i e s of  In terms of e x p e r i m e n t a l a p p l i c a t i o n , one  interval.  phase  greatly  1980). The  and  which  s  ion  f l u c t u a t i o n a m p l i t u d e . Hence,  i s r a p i d and g e n e r a l l y ,  locate  C  the  ion v e l o c i t y d i s t r i b u t i o n , there  fewer p a r t i c l e s c o n t r i b u t i n g  i n complete s i m i l a r i t y with the  only  structure,  That i s , the h i g h  over  s c a t t e r e d power per  -  thermal  ion feature  compare the r e l a t i v e i n t e n s i t i e s of the  - 46  the  two  is its  unit  selfhigh  frequency  spectral  compon-  e n t s , the p o r t i o n ion feature  of scattered  light  appearing  may be c o n s i d e r e d u n i f o r m l y  in either  distributed  t h e e l e c t r o n or  over  the r e s p e c t i v e  frequency i n t e r v a l s ,  Aco  = g(ct)kv [13]  6  AO). = g ( B ) k v . .  The  f a c t o r s g i n equations  that for g  scattered  light  [13] have been i n t r o d u c e d  may be q u i t e  l a r g e a l p h a or b e t a , s h a r p l y  specify  a Gaussian  defined  function,  the h a l f width a t h a l f maximum.  common s c a t t e r i n g  v e c t o r k so t h a t  though a r b i t r a r y , s c a t t e r i n g The tron  feature  resonance s t r u c t u r e  equations  g ( 0 ) = l n 2, and e q u a t i o n s [13] As w e l l , e q u a t i o n s  comparison  will  [13] s p e c i f y  a  be made f o r a g i v e n ,  r e l a t i v e to the e l e c -  be d e f i n e d a s :  =  S.OOAu l e S (k)Ao>. e i  [8] and the frequency i n t e r v a l s from equations  T  the s p e c t r a l  geometry.  1  Using  can appear and  parameter,  s p e c t r a l i n t e n s i t y o f the i o n f e a t u r e , can t h e r e f o r e  the f a c t  non-uniformly d i s t r i b u t e d . In p a r t i c u l a r ,  << 1 . At v e r y s m a l l values o f t h e s c a t t e r i n g  shape a p p r o a c h e s  to allow for  _ g(oO j V i f  *< > I Vet B  [13]  gives  Za" i a (i ZT e  - 47 -  2  +  +  n.) I  [ 1 4 ]  Equation plasma has T^.  [14]  i s presented g r a p h i c a l l y  been assumed to be  As a l p h a i n c r e a s e s  times b r i g h t e r  with  ( I = 1)  comparable b r i g h t n e s s  an e q u i l i b r i u m helium  from z e r o ,  i n the i o n l i n e i n c r e a s e s  than the  the  alpha  electron  determined by  increases.  The  two  = 0.28.  At  a = 1,  the  feature.  At  larger  alpha,  The  the amount of damping  To e v a l u a t e e q u a t i o n Landau damping  and  [14]  light  .  1  width  of  the  the  ion  alpha,  c o l l i s i o n a l damping  contributions  =  e  contained  line  have is  the  43  narrow  s p e c t r a l i n t e n s i t y of  electron  account  the T  features  e x p e r i e n c e d by e l e c t r o n  for large  where  Z = 2,  a*  at a  like  11  plasma:  f r a c t i o n of s c a t t e r e d  e l e c t r o n resonance s t r u c t u r e begins to appear and the e l e c t r o n f e a t u r e  in Figure  resonance plasma  must be to the  is  waves.  made o f  both  spectral  width  (Evans, 1969). Landau or c o l l i s i o n l e s s damping d e c r e a s e s e x p o n e n t i a l l y creasing  a l p h a and  the  pondingly increases. itely  with  s p e c t r a l i n t e n s i t y of the e l e c t r o n resonance However, the  s i n c e , u l t i m a t e l y , the  s p e c t r a l width cannot d e c r e a s e  corres-  indefin-  frequency of e l e c t r o n - e l e c t r o n c o l l i s i o n s  determine the r a t e of energy d i s s i p a t i o n from the wave. C o l l i s i o n a l b u t i o n s to the  s p e c t r a l width can  be  expressed i n terms of  N  number of p a r t i c l e s i n a Debye cube.  i l l u s t r a t e s how The indeed  N  D  D  a f f e c t s the r e l a t i v e  conclusion  the most i n t e n s e  the e n t i r e range of the  infinity.  D e  of the  However, F i g u r e  11 i s t h a t the  scattered  s c a t t e r i n g parameter  Because of the ease of d e t e c t i o n ,  spectrum  also  -  ion  over  line  is  virtually  alpha.  the  ion f e a t u r e  i m p o r t a n t a p p l i c a t i o n i n plasmas of r e l a t i v e l y high  - 48  11  colli-  brightness.  to be drawn from F i g u r e feature  > the  s  Equation 14 c o r r e s p o n d s to the  approaching  will  contri-  = X n  D  s i o n l e s s case, t h a t i s , N  in-  finds  i t s most  electron density  where  100  i  -  i  —i  i  i  r  e bright  :ness  10  Ion /  Feature  i  ^—  >  *-> a  /  i Electron  0.1 .1  i  i  Feature  i  i  2  1  \  4  1  6 alpha  F i g u r e 11 Comparative s p e c t r a l b r i g h t n e s s o f e l e c t r o n and i o n features. A r e l a t i v e b r i g h t n e s s g r e a t e r than u n i t y i n d i c a t e s t h a t the s p e c t r a l b r i g h t n e s s o f t h e i o n f e a t u r e exceeds t h a t o f the e l e c t r o n f e a t u r e ( s e e e q u a t i o n 14).  - 49 -  bremsstrahlung  emmission i s l a r g e .  1966)  s p e c t r a l brightness  f o r the  The  classical expression  of e l e c t r o n - i o n  (Zel'dovich,  bremsstrahlung, J  B  has  the dependence:  n J  At o p t i c a l frequencies  « —  D  The  > the  and  i s contained  i n the  T  1  dependence i n J  s m a l l k w i l l lead  s  kT  Aw  brightness  of the  to b r i g h t s c a t t e r e d  proportional  « k(KT) .  The  2  corres-  from slow f l u c t u a t i o n s  spectra.  s B "  <V  / J  k  Forming  the  temperature, the  feature.  -  50  with  ratio:  _1  with  higher  -  the  scattering  a t h i g h plasma d e n s i t i e s , advantage must be ion  few  •  the more d i f f i c u l t i t i s to i n t e r r o g a t e  ques. T h e r e f o r e ,  = T) more than a  2  shows t h a t , r o u g h l y independent of the density,  = T^  virtually  l i g h t , Jg w i l l behave l i k e ,  shows t h a t s c a t t e r i n g  J  e  is  e  « — r 5  k~  interval  s p e c t r a l b r i g h t n e ss of s c a t t e r e d  J  (T  factor  l i g h t however, i s l i n e a r l y  n  The  exponental  temperatures  t o t a l amount of s c a t t e r e d  t o the d e n s i t y ponding  exp(-hv/KT) .  hv » 2 eV  c o n s t a n t f o r a l l plasmas having eV.  2  taken  plasma techniof  the  CHAPTER 5  5.1  DESCRIPTION OF THE SCATTERING  EXPERIMENTS  Introduction T h i s chapter d e s c r i b e s i n d e t a i l  t h a t were used mentioning  here  the s c a t t e r i n g ture.  f o r Thomson s c a t t e r i n g  the e x p e r i m e n t a l  i n the Z-pinch  plasma.  t h a t , i n s p i t e of the d i s c u s s i o n s f r o m experiments  f i r s t attempted  I f i t c o u l d be d e t e c t e d ,  the e l e c t r o n  the l a s t  f e a t u r e would  from  the i o n f e a t u r e d i d not s u f f e r first  section  m e t r i e s t h a t were used tions.  of t h i s  chapter  this  shows  to examine s c a t t e r i n g  An a n a l y s i s o f t h e g e o m e t r i e s  scattering  from  will  from  serve  as a  low.  As w i l l  be  limitation. t h e two s e p a r a t e ion acoustic  distinguish  geo-  fluctua-  between t h e two  systems while a few n u m e r i c a l e s t i m a t e s w i l l h e l p to i l l u s t r a t e  some o f the c h a r a c t e r i s t i c s and p a r a m e t e r s mentioned i n the p r e v i o u s c h a p t e r .  o f the i o n f e a t u r e t h a t were  The f o l l o w i n g c o n s i d e r a t i o n s i n d i c a t e  why two separate s c a t t e r i n g  systems were chosen and t h a t , i n f a c t ,  sent d i a g n o s t i c experiments  are i n t i m a t e l y  interaction  fea-  e m i s s i o n , s i g n a l to  n o i s e r a t i o s i n the e l e c t r o n f e a t u r e were p r o h i b i t i v e l y  The  chapter,  t h e i o n f e a t u r e . How-  e v e r , because of the v e r y h i g h l e v e l s o f bremsstrahlung  later,  I t i s worth  to i n v e s t i g a t e the e l e c t r o n  c r o s s - c h e c k on the plasma parameters o b t a i n e d  seen  arrangements  related  the p r e -  to the C O 2 l a s e r - p l a s m a  experiments.  One o f the primary i n t e r e s t s i n l a s e r - p l a s m a  interaction  experi-  ments i s the study o f n o n - l i n e a r p a r a m e t r i c p r o c e s s e s which, among  others,  i n c l u d e s s t i m u l a t e d Raman or B r i l l o u i n of  these p r o c e s s e s can be found  These p r o c e s s e s are s c a t t e r i n g  scattering.  elsewhere  (e.g.:  A complete  Chen, 1974; Siebe,  i n s t a b i l i t i e s which a r e p r o d u c e d  high i n c i d e n t laser i n t e n s i t i e s .  The e a s i e s t  - 51 -  description  instability  1974).  with  to e x c i t e ,  very and  therefore  most important, i s the  scattered  by  scattering  involves  At can  be  and  the  excited  enhances the  an  B r i l l o u i n mode, whereby the CO2 ion  acoustic  wave.  expense of some of the  incident  to amplitudes which are  are  (Stimulated  is  Raman  e l e c t r o n Langmuir wave).  those which s c a t t e r  l a s e r energy, p l a s m a  many o r d e r s of  normal thermal l e v e l of plasma f l u c t u a t i o n s . fluctuations  laser  the CO  As  magnitude  well,  the  waves  above  most  the  unstable  l a s e r beam d i r e c t l y back  onto  2 itself ^  so  that  the  12.  =  enhanced  The  CO2  generate s p e c i f i c , the plasma  plasma  of  long wavelength, and h i g h l y  the  Thomson  of ruby l a s e r  Thomson s c a t t e r i n g wavevector of  quires  scattering  angles. Also,  light.  must be the  that scattered  a  wavelength therefore  non-thermal f l u c t u a t i o n s  In order  density  been  to do  this,  the  matched, i n both magnitude and  i n order to c o r r e l a t e  temperature and  has  in  arranged  to  through  the  wavevector  for  of such enhanced f l u c t u a t i o n s  ruby l a s e r l i g h t be  would l i k e  the  geometries  f l u c t u a t i o n induced by CO2  parameters, one  measuring  have  l a s e r - p l a s m a i n t e r a c t i o n experiments w i l l  d i r e c t l y examine the p r o p e r t i e s  the  will  density.  One  scattering  fluctuations  the  laser.  observed  stimulated  at  direction, This  very  in  turn  small  spectrum of the  interaction  volume.  This  thermal l e v e l of d e n s i t y  can  plasma  the be  re-  forward  p r o c e s s e s with the  to have a simultaneous measurement of  i n the  with  plasma  done  fluctuations.  by  There-  r  f o r e , a second Thomson s c a t t e r i n g density the  fluctuations  plasma and  processes  are  geometry  i s arranged  t h a t are determined o n l y by  totally  uncorrelated  (except i n as much as  the C 0  -  2  52  with  the the  l a s e r may  -  to  scatter  thermal p r o p e r t i e s stimulated  change the  from of  scattering  local  thermal  properties).  The second Thomson s c a t t e r i n g g e o m e t r y  s h o r t wavelength f l u c t u a t i o n s i n the extreme For prior  the p r e s e n t  to introducing  purpose  the C 0  2  both  from s c a t t e r e d  scattered  light,  the plasma  s c a t t e r i n g systems  observe the thermal l e v e l o f i o n f l u c t u a t i o n s . sured  looks a t  back s c a t t e r d i r e c t i o n .  of establishing  laser,  therefore  a r e used to  The plasma p a r a m e t e r s  s p e c t r a a r e the e l e c t r o n d e n s i t y  and the i o n temperature f r o m  conditions  mea-  from the i n t e n s i t y o f  the s p e c t r a l  distribution.  Even though i t w i l l be assumed throughout t h a t the e l e c t r o n and i o n temperatures  are equal,  the i o n f e a t u r e result of t h i s ,  i t i s i m p o r t a n t to r e i t e r a t e t h a t t h e s p e c t r a l w i d t h o f  i s determined by the d i s t r i b u t i o n o f i o n v e l o c i t i e s . many d e t a i l s o f t h e s c a t t e r i n g g e o m e t r y  systems w i l l be dominated needed  by the r e l a t i v e l y  t o examine the i o n f e a t u r e .  back-scatter angstroms)  high  t o be r e s o l v e d  The f i n a l  resolution  capabilities  that  o n l y the  i s wide enough  (a few  easily.  section of t h i s  chapter describes  s e n s i t i v i t y o f the d e t e c t i o n systems by R a y l e i g h gases. C a l i b r a t i o n i s required  i n order  When s c a t t e r i n g i n t o t h e e l e c t r o n  c a l i b r a t i o n o f the  scattering  from  to determine the e l e c t r o n  feature,  this  procedure  n e c e s s a r y s i n c e the s p e c t r a l shape, determined by a l p h a , t o both the e l e c t r o n temperature and d e n s i t y . width and shape can be used t o determine n the i o n f e a t u r e , determined by t h e b e t a , e i t h e r plasma parameter  and d e t e c t i o n  I t w i l l be seen s h o r t l y t h a t  spectrum has a wavelength s p r e a d  As a  e  Then,  and T.  i s often not  measurement o f t h e  However, the  Therefore,  - 53 -  shape o f  i n s e n s i t i v e to  c a l i b r a t i o n o f the  d e t e c t i o n systems w i l l be n e c e s s a r y f o r d e n s i t y measurements which the i o n f e a t u r e .  density.  i s quite sensitive  i s particularly  (see e q u a t i o n [ 1 1 ] ) .  neutral  utilize  5.2  Arrangement o f the S c a t t e r i n g Orientation  Thomson s c a t t e r i n g following involved  o f the plasma w i t h  i s shown i n F i g u r e  description  and h e l p  Geometry  w i l l give  respect  12.  to the wavevectors f o r  With r e f e r e n c e  to Figure  12, the  an i n d i c a t i o n o f some o f t h e numbers  to c l a r i f y how the s c a t t e r i n g  systems are a r r a n g e d .  What  can be expected i n terms o f the s p e c t r a l d i s t r i b u t i o n o f s c a t t e r e d w i l l a l s o be g i v e n .  When plasma parameters are r e q u i r e d  in calculations,  the i n i t i a l e s t i m a t e o f Houtman i s used f o r the maximum plasma w h i l e the maximum d e n s i t y  i s taken from the e s t i m a t e s  light  temperature  made i n C h a p t e r  3,  i.e.:  n  = 4 x 10  e  T  The ^x  =  - 3  = 40 eV.  wavevector o f the d e n s i t y  ^o ~ ^ x s * ' ^ double s u b s c r i p t i n g J  cm  1 9  ie  f l u c t u a t i o n producing here and i n F i g u r e  between forward, x = f and b a c k w a r d , x = b s c a t t e r i n g i n c i d e n t ruby l a s e r beam has k Because s c a t t e r e d wavelength k  Q  l i g h t i s only  = k  x s  For the forward  plasma a x i s and  12, d i s t i n g u i s h e s directions.  = |k |= 2 IT/6943 A or kg =  9.05 x 1 0  0  slightly shifted  from  the i n c i d e n t  t o a very good approximation so t h a t k  i s determined s o l e l y by the directions.  Q  angle e  x  between  scattering  system, k f l i e s  t h a t the B r i l l o u i n p r o c e s s be i n t e r r o g a t e d :  -  54 -  = 2k  x  i n c i d e n t and  0^ = 7.5°. T h i s angle i s d e t e r m i n e d k  f  = 2 k  scattering i s  Q  The 4  cm . - 1  laser  s i n (6 /2) x  scattered  parallel  beam  t o the  by t h e r e q u i r e m e n t  C 0 : )  = 1.19 x 1 0  4  cm . - 1  FIGURE 12 Geometry f o r the Thomson S c a t t e r i n g  - 55 -  Measurements  Backscattered  l i g h t i s detected  172.5° w i t h k^ = 1.81  x 10  i n the a n t i p a r a l l e l d i r e c t i o n h a v i n g  cm .  5  The  -1  f l u c t u a t i o n s observed  w i l l propagate i n the r a d i a l d i r e c t i o n , a x i s and  perpendicular  6^  =  i n backscatter  to both  the  plasma  k f . As mentioned i n the i n t r o d u c t i o n , the k - v e c t o r arrangement  has  been chosen with the i n t e r a c t i o n experiments i n mind. Refering Atol  a kv.i  back  to  can be estimated  p e r a t u r e of 40 eV.  to. = co - to i o s  to = k c ° o being  previous  using  chapter,  The  = dto  spectral  and  are s m a l l , and  the widths w i l l  , , w i l l appear s h i f t e d  according  the speed of l i g h t i n vacuum.)  the i o n f e a t u r e can be expected  incident  to:  light,  dto = cdk  For the backward  be  temexpres-  frequency  at  frequency  = to dX/X o o  scattering  »  c  system,  to have a FWHM o f a p p r o x i m a t e l y  w h i l e the spectrum i n forward  width  a plasma  c o n v e r s i o n i s e a s i l y done s i n c e the  o  maximum plasma compression,  the  the above k - v e c t o r s  (As a matter of convenience,  sed i n wavelength u n i t s . shifts  the  6.0  A  at  direction will  be  o  narrower by the f a c t o r k f / k b , making s  The l e n g t h and  the width  s  above c a l c u l a t i o n s , along  relevant s c a t t e r i n g  parameters used to d e s c r i b e  the  A.  with o t h e r s such as the plasma Debye  parameters,  Table I I g i v e s a summary of n u m e r i c a l  o n l y about 0.4  are  estimates  p l a s m a and  quite  straightforward .  f o r a few of the  the  two  important  scattering  systems.  Though these e s t i m a t e s are o n l y r e p r e s e n t a t i v e of peak compression, serve to p o i n t out p a r t i c u l a r l y large while N  D  i s small.  t h a t , i n high d e n s i t y plasma,  Comparing  alpha  is  detectable  experiments.  S i n c e the o b j e c t i v e of these experiments i s to determine what plasma parameters are during therefore establish i n i t i a l  do  the r e l e v a n t numbers from T a b l e I I w i t h  F i g u r e 11 r e i n f o r c e s the f a c t t h a t o n l y the i o n f e a t u r e w i l l be i n the c u r r e n t s c a t t e r i n g  they  a l l stages of the h i g h c o m p r e s s i o n c o n d i t i o n s f o r the  - 56  -  interaction  phase  studies,  the and both  TABLE I I Numerical E s t i m a t e s f o r the Thomson S c a t t e r i n g  Z - p i n c h plasma parameters: ( a t peak  Systems  helium, Z = 2  compression) n  e  = 4.0  T  e  = T i = T = 40 eV = 4.3  x  10  X  = 7.4  x  10~  = 2.72  x  10  1 5  = 9.05  x  10  4  D  D  0)  o  k  Q  o  7.5  k  1.2 x 1 0  3.  7  sec  - 1  cm  sec cm  - 1  -1  = 6943 A  6  a  cm  6  - 3  = 16  Forward  X A  cm  1 9  parameters:  X  FWHM  10  Vj_  N  Ruby l a s e r s c a t t e r i n g  x  Backward 172.5 4  1.8 x 1 0  0 , 4 0  6 , 0  112  7.5  1.4  1.4  - 57 -  (deg. 5  (cm (A)  -1  scattering  systems are used o n l y  p e r t i e s of the Z - p i n c h . has  not  the  unperturbed  I t i s u n f o r t u n a t e t h a t the  been used to make  plasma. The  to measure  scattering  measurements with the C0  reasons f o r t h i s stem from the  two  thermal  pro-  diagnostics  l a s e r i n c i d e n t i n the  2  p r i n c i p l e f a c t o r s , the  first  o f which i s a c i r c u m s t a n c e e s s e n t i a l l y h i s t o r i c a l i n n a t u r e . Originally, ments ( A l b r e c h t , plasma.  the  1979)  set-up f o r these l a s e r / p l a s m a had  could  arrangement shown i n F i g u r e  be  12.  interrogated  with the  forward  A l t h o u g h many f o c u s s i n g  h a l f the  schemes a t t e m p t e d  v i r t u a l l y impossible  s u f f i c i e n t overlap without d r a m a t i c a l l y a l t e r i n g  istics.  The  i n t e r a c t i o n geometry has  second, and  of the CO2  perimental detection  to  described  diagnostic  the  the  CO2  volume  i n Chapter  the  CO2  2. intro-  l a s e r l i g h t i s a d i r e c t r e s u l t of the q u i t e g e n e r a l s c a t t e r i n g experiment.  that  character-  main r e a s o n f o r Thomson s c a t t e r i n g w i t h o u t  d i f f i c u l t i e s of any  in  eliminate  s i n c e been changed to have  l a s e r i n c i d e n t r a d i a l l y i n t o the plasma as was The  l e n g t h of  the plasma  the  scattering  to i n t r o d u c e  l i g h t a x i a l l y so t h a t the i n t e r a c t i o n volume and  duction  axially into  Such a c o n f i g u r a t i o n , however r e q u i r e d  severe r e f r a c t i o n e f f e c t s , i t was  had  beam i n t r o d u c e d  l a s e r beam propagate almost p a r a l l e l t o , and  plasma column.  laser  laser  P a r a m e t r i c a l l y enhanced f l u c t u a t i o n s would t h e r e f o r e p r o p a g a t e  the a x i a l d i r e c t i o n and  the CO2  the CO2  interaction experi-  ex-  In p a r t i c u l a r , the  system must have s u f f i c i e n t r e s o l u t i o n c a p a b i l i t i e s  to  see  the  to  the  o  shape o f the i o n f e a t u r e . expected b a c k s c a t t e r  A s p e c t r a l width of 6.0  spectrum i s of course  not  the r e s o l u t i o n range of t y p i c a l monochromators.  - 58  -  A corresponding  l a r g e , but The  i s well  forward  within  scatter  ion  f e a t u r e i s c o n s i d e r a b l y narrower making r e s o l u t i o n o f conventional  techniques  a much more d i f f i c u l t  problem.  s p e c t r a l r e s o l u t i o n i s t h e r e f o r e o n l y attempted where the proposed d e t e c t i o n s y s t e m c a n extending  the method to higher  easier  backscatter  measurements.  to perform  valuable cross-check scattered  used  and  with  Scattering  with  backscatter the  Data  the  can  be  obtained  forward done  difficulties  of  examined.  scatter intensity  are  s i m i l t a n e o u s l y with  the  i n forward  obtained  system  from  the  scatter will  be  a n a l y s i s of  a  back-  light.  their geometrical  ment w i l l now  5.3  and  of the r e s u l t s  Having d i s c u s s e d and  i n the  spectrum  r e s o l u t i o n experiments can be  Non-resolved measurements o f relatively  be  this  be  the s a l i e n t f e a t u r e s  of  Figure  13.  viewing  s c a t t e r i n g systems i s shown i n the The  o r i e n t a t i o n of  ports, e t c . , w i l l  e a r l i e r d e s c r i p t i o n s of Chapters 2 and  oscillator  vectors  Experiment  f u l l arrangement of the two  s i d e arms and  The  scattering  described.  semi-schematic d i a g r a m v e s s e l with  the  arrangement, the remainder of the s c a t t e r i n g e x p e r i -  O v e r a l l Layout o f The  of  i n c i d e n t l i g h t source  be  the  recalled  rather  from  the  3.  i s a conventional  Q-switched r u b y  i n combination w i t h a s i n g l e a m p l i f i c a t i o n s t a g e .  scattered spectra are  discharge  narrow,  i t i s of  interest  laser  Because  the  to c o n s i d e r  the  s p e c t r a l d i s t r i b u t i o n of i n c i d e n t l i g h t . The coupler  oscillator  c a v i t y has  i s a 66% r e f l e c t i n g ,  etalon provides  a  100%  multiple  rear  surface  reflector  and  Fabry-Perot  f o r some l o n g i t u d i n a l l a s e r mode s e l e c t i o n .  the  etalon. The  width.  The  mode s p a c i n g ,  of  0.37  has o  A,  e a c h mode b e i n g  less  than  however, i s somewhat l e s s than the g a i n  width o f the l a s e r f l o u r e s c e n c e  The  etalon  o  a measured mode s p a c i n g  output  line.  - 59  Consequently, the  -  0.06  A in  narrowed  l a s e r output  has  a  b  FIGURE 13 Layout o f the s c a t t e r i n g  - 60 -  experiment.  wavelength d i s t r i b u t i o n c o n s i s t i n g o f s e v e r a l n a r r o w s p i k e s the e t a l o n mode s p a c i n g . the e t a l o n a r e p r e s e n t , appear i n the output  separated  by  U s u a l l y , o n l y one or two l o n g i t u d i n a l modes o f b u t o f t e n , one or two s l i g h t l y o f f - a x i s modes  spectrum.  This  s t r u c t u r e i n the l a s e r  also  spectrum i s  o  always contained  w i t h i n l e s s than a 0.6 A i n t e r v a l .  However, the s c a t t e r e d o  spectrum i n the forward (see Table  II).  d i r e c t i o n i s expected to be much l e s s t h a n  Therefore,  s p e c t r a l l y r e s o l v e d measurements o f the forward  scatter ion feature w i l l require consistent i s o l a t i o n mode.  In b a c k s c a t t e r ,  the w a v e l e n g t h d i s t r i b u t i o n  s u f f i c i e n t l y s m a l l and can be i g n o r e d to  1A wide  as being  of a s i n g l e  etalon  of i n c i d e n t l i g h t i s  a significant  contribution  the width o f the s c a t t e r e d spectrum. Power l e v e l s i n the i n c i d e n t beam are t y p i c a l l y about 300 MW,  j o u l e s i n a 20 ns FWHM p u l s e . laser  l i g h t entering  beam path  In o r d e r  to minimize  t h e amount o f s t r a y  the d e t e c t i o n o p t i c s , t h e e n t i r e l a s e r  and i n c i d e n t  i s housed i n a l i g h t t i g h t arrangement o f boxes and tubes.  immediately  prior  through a helium  to introducing  flushed s p a t i a l  Filtering  filtering  the beam helped  pinhole.  approximately  0.25 mm.  plasma i s c o l l e c t e d  Incident  Helium g a s i s used t o  a t the p i n h o l e  eliminate spurious  which were found t o c o n t r i b u t e s i g n i f i c a n t l y 'cleaned' beam i s then focussed  Also,  t h e beam i n t o vacuum, i t i s f o c u s s e d  reduce the p o s s i b i l i t y o f l a s e r breakdown s p a r k s 1975).  or 6  off-axis  to s t r a y  light  onto the p i n c h a x i s t o a s p o t light  which  i s transmitted  i n a R a y l e i g h horn beam dump, i n t e n d e d  (Morgan,  lasing  modes  levels.  The  diameter of through the  to absorb  com-  p l e t e l y a l l unscattered r a d i a t i o n . The  forward  s c a t t e r beam path c o n s i s t s o f a s e r i e s of m i r r o r s and  l e n s e s which t r a n s p o r t the s c a t t e r e d beam and image t h e s c a t t e r i n g onto the entrance ion  s l i t o f a Spex 3/4 meter f o c a l l e n g t h monochromator.  f e a t u r e though i s n o t s p e c t r a l l y  only to f i l t e r  volume  o u t background  resolved  so t h e monochromator  l i g h t from the plasma.  Exit s l i t s  The acts  are s e t to  o  t r a n s m i t o n l y a 7 A wide band, c e n t e r e d  on t h e l a s e r  - 61 -  wavelength.  Beyond  the e x i t s l i t ,  a low  loss optical  l i g h t to a p h o t o m u l t i p l i e r . output  are  bundle  Oscilloscope  photographed g i v i n g  collected.  fiber  traces  a temporal  d u r a t i o n o f the l a s e r  pulse.  On  light  this  of  record  S u c h power m e a s u r e m e n t s p r o v i d e  a g a i n s t plasma l i g h t s i n c e s c a t t e r e d  collects the of  signal.  appears  (The  as  an a d d i t i o n a l b i a s  l i m i t a t i o n here i s due  only  s c a l e , the  or  the plasma.  Scattered  that i s  must s t i l l  on  the  ns  level  of  light  scattered  baseline  i n the  be  the 20  background  to f l u c t u a t i o n s i n t h e  light  for  average  baseline  r e s u l t from shot n o i s e i n both the p h o t o m u l t i p l i e r and photons by  light  additional discrimination  plasma background l i g h t does not change s i g n i f i c a n t l y and essentially  transports  photomultiplier  the  i s present  time  and  that  emission  detected  of  over  and  to r e c o r d  the  above such s t a t i s t i c a l f l u c t u a t i o n s . ) In b a c k s c a t t e r , full  the d e t e c t i o n  system  s p e c t r a l d i s t r i b u t i o n of s c a t t e r e d l i g h t  laser.  Much of the c o m p l e x i t y  on matching istics.  the c o l l e c t i o n and  The  detector  on  s i n g l e shot  of the b a c k s c a t t e r  optical  i s an O p t i c a l M u l t i c h a n n e l Corp.  Analyser  (model  A electronic control console).  The  extremely s o p h i s t i c a t e d e l e c t r o n i c image c o n v e r t e r model having  two  stages  o p e r a t i o n of the OMA PAR  Corp.  of image a m p l i f i c a t i o n .  can be  of  system  d i s p e r s i o n o p t i c s to the d e t e c t o r  produced by P r i n c e t o n A p p l i e d R e s e a r c h with model 1204  i s designed  OMA  the  ruby  i s based character-  (abbreviated  1 2051  detector  OMA) head  is essentially  camera, t h i s  an  particular  D e t a i l s of the d e s i g n  and  found i n the i n s t r u c t i o n manuals a v a i l a b l e from  For a d i s c u s s i o n of the b a c k s c a t t e r  optics, only  the  following  is  segmented  brief description i s given. An  o p t i c a l image on the d e t e c t o r  into a linear by 5.0  mm  a r r a y of 500  channels,  head  each corresponding  h i g h p o r t i o n of the photocathode.  t a r g e t area i s 12.5 c o l l e c t e d during  mm  a 768  by ys  each channel i s d i g i t i z e d  5.0 "on" and  mm.  photocathode  The  Amplified  to a 0.025 mm  f u l l a c t i v e p o r t i o n of photoelectron  signals  time, a f t e r which, the accumulated s t o r e d i n memory.  ~ 62  "  wide the are  signal in  For any g i v e n channel,  one  d i g i t a l count c o r r e s p o n d s t o the a c c u m u l a t e d  effect  v i s i b l e photons i n c i d e n t on the photocathode. the  photocathode i s 6 0 % ) .  here. F i r s t ,  (The quantum  Two a s p e c t s o f t h e d e t e c t o r  the f i n i t e width o f each d e t e c t o r  OMA  s p a t i a l r e s o l u t i o n be matched w i t h t h a t  for  optimum s p e c t r a l r e s o l u t i o n .  is  o f a p p r o x i m a t e l y 20  are o f importance  channel requires  o f the d i s p e r s i o n  t h a t the  instrument  Secondly, s i n c e o p t i c a l i n p u t t o t h e OMA  accumulated, i . e . : time i n t e g r a t e d , d i s c r i m i n a t i o n  l i g h t and plasma background  e f f i c i e n c y of  between  scattered  must be made on the b a s i s o f energy r a t h e r  than  power. D i s p e r s i o n o f the spectrum i s p r o v i d e d using  a second  Spex 3/4 m  f o c a l l e n g t h monochromator equipped w i t h a 1200 line/mm g r a t i n g , 1st  blazed i n  o  o r d e r f o r 7000 A. The monochromator has a c o l l e c t i o n r a t i o o f F/7.5 and o  a r e c i p r o c a l d i s p e r s i o n o f 10 A/mm. wide by 0.350 mm h i g h .  Imaging  The e n t r a n c e s l i t  1:1 a t t h e e x i t  was s e t a t 0.012 mm  plane g i v e s  a spectral  o  r e s o l u t i o n i n t e r v a l o f 0.12 A FWHM. of  Additional external optics,  a x5 microscope o b j e c t i v e and a beam t r a n s p o r t  lens,  consisting  images  t h e mono-  chromator e x i t p l a n e onto the OMA head w i t h a t o t a l m a g n i f i c a t i o n o f x10.5. The monochromator e n t r a n c e s l i t channels.  t h e r e f o r e c o v e r s 75% o f the h e i g h t o f 5 OMA  The maximum r e s o l u t i o n w i t h t h i s  o  A/channel).  This matching  i snotquite  monochromator e n t r a n c e s l i t tion limited  arrangement  optimal since  o  i s 0.12 A (0.024 the width o f the  used i s s l i g h t l y more than t w i c e t h e  c a p a b i l i t i e s o f the i n s t r u m e n t .  r e s o l u t i o n o f 3 c h a n n e l s FWHM, t h i s  A l s o , t h e OMA h a s a s p a t i a l  limitation  being due t o e l e c t r i c a l  c r o s s - t a l k between a d j a c e n t OMA c h a n n e l s .  For the backscatter  a t t e n t i o n t o f i n e d e t a i l s o f the m a t c h i n g  i s unimportant  i n d i c a t e s t h a t the system d e s c r i b e d tion. the  above h a s more  arrangement detection  o f forward  attempts  scattered  light.  to provide a t least  system.  "  63 "  Table I I  than adequate  Therefore,  a near  spectrum,  since  However, t h i s system may not have s u f f i c i e n t r e s o l u t i o n  spectrum  diffrac-  resolu-  t o examine  the b a c k s c a t t e r  limitation  test  o f the  D i s c r i m i n a t i o n a g a i n s t plasma l i g h t i s v i t a l  since bremsstrahlung  i s emitted  over the s e v e r a l microsecond  pared w i t h  the 20 ns d u r a t i o n o f s c a t t e r e d l i g h t .  The OMA  c a l gating  mode which p e r m i t s l i g h t to be d e t e c t e d  o n l y f o r the d u r a t i o n o f  a user  supplied voltage pulse.  time i n t e r v a l of the d i s c h a r g e  However, f o r s h o r t g a t i n g  d i s t o r t i o n s i n the e l e c t r o n i c i m a g i n g  stages  r e s o l u t i o n c a p a b i l i t i e s o f the i n s t r u m e n t  which  and  an e l e c t r o - o p t i c s h u t t e r p e r f o r m s  Backscattered p o l a r i z e r , pockels  and c r o s s e d  double c r y s t a l , KD*P u n i t having  there are  degrade the  the g a t i n g  1978).  (or ' r e a l time') mode  function.  The  shutter  way.  l i g h t i s passed  cell,  electri-  (Simpson, 1977; A l b r e c h t ,  OMA i s t h e r e f o r e used i n the continuous r e c o r d i n g  simple  pulses  severely  The  o p e r a t e s i n the f o l l o w i n g  has an  com-  through  the s e r i e s combination o f  polarizer.  The p o c k e l s  a half-wave v o l t a g e  cell  is a  o f 2.2 kV and p o l a r -  i z e r s are o f the Glan-Thomson type.  The f i r s t p o l a r i z e r takes advantage of  the  l a s e r beam by p a s s i n g  l i n e a r p o l a r i z a t i o n o f the r u b y  l i g h t and r e j e c t i n g o n e - h a l f  of the plasma e m i s s i o n .  a l l scattered  Now, when the p o c k e l s  cell  i s not a c t i v a t e d , the p o l a r i z a t i o n of l i g h t  transmitted  cell  i s n o t a l t e r e d and t h e r e f o r e w i l l be blocked  by the second p o l a r i z e r .  I f the p o c k e l s the c e l l w i l l  cell  i s s u p p l i e d with  e x i t with  the plane of p o l a r i z a t i o n r o t a t e d  the second p o l a r i z e r w i l l t r i g g e r e d , cable discharge wave v o l t a g e  i t s half-wave v o l t a g e ,  be t r a n s m i t t i n g . circuit  i s used  p u l s e o f 100 ns d u r a t i o n .  on the i n c i d e n t l a s e r p u l s e .  For g a t i n g  Plasma emission  occurring  light  entering  by 9 0 ° .  purposes,  to g e n e r a t e  The g a t e p u l s e  through the  a krytron  a 2.2 kV,  i s centered outside  Then,  square i n time  this  time  i n t e r v a l i s suppressed. In order gating  to o b t a i n a good o n - o f f  method, l i g h t passing  c o n t r a s t r a t i o with  through the p o l a r i z e r / p o c k e l s c e l l  must be a c c u r a t e l y c o l l i m a t e d .  A 50 cm f o c a l  scattered  c o n e ) and images  light  onto a f i e l d  (F/16 c o l l e c t i o n  limiting  this  pinhole.  Scattered  " 64 "  length  lens  arrangement  c o l l e c t s the  the s c a t t e r i n g  l i g h t i s transmitted  optical  volume  through the  pinhole  and then c o l l i m a t e d .  shutter  and then r e f o c u s s e d  the e n t r a n c e s l i t  This collimated  beam i s p a s s e d  through the  onto the monochromator entrance s l i t .  i s imaged  onto  the plasma  axis  (Overall,  with  X0.71  magnifica-  contrast  ratio  can exceed  t i o n ). With p e r f e c t c o l l i m a t i o n , t h e o n - o f f 1000:1 , b u t the observed c o n t r a s t The  i s about  e f f e c t o f poor c o n t r a s t has been very  time s c a l e s  involved.  observations. during  This  o f magnitude  by making  the f o l l o w i n g  l i g h t w i l l o f course be c o l l e c t e d  100 ns on time. A l s o , because the OMA  time i n t e g r a t e s ,  plasma e m i s s i o n w i l l r e g i s t e r (as leakage l i g h t ) f o r t h e f u l l the d i s c h a r g e ,  namely, a few microseconds.  experiments i s t h a t , by using  the  scattered  5.4  of  the o p t i c a l s h u t t e r , plasma background l e v e l s  to g i v e  However, i t w i l l be seen  very good s i g n a l t o n o i s e  ratios in  spectra.  C a l i b r a t i o n o f the O p t i c a l Systems A c a l i b r a t i o n o f the d e t e c t i o n  order  duration  The o v e r a l l e f f e c t f o r t h e s e  are reduced o n l y by a p p r o x i m a t e l y a f a c t o r o f 10. t h a t t h i s has been s u f f i c i e n t  lower.  important because o f the r e l a t i v e  c a n be u n d e r s t o o d  Plasma l i g h t and s c a t t e r e d  the s h u t t e r ' s  an o r d e r  sensitivity  must be p e r f o r m e d i n  t o determine e l e c t r o n d e n s i t i e s from observed s c a t t e r e d  Therefore,  before  t i o n by R a y l e i g h  showing some o f the plasma s c a t t e r i n g scattering i s d i s c u s s e d .  intensities.  spectra,  In t h e p r o c e s s ,  an  calibraimportant  l i m i t a t i o n o f the c u r r e n t geometry w i l l be pointed o u t . The related  frequency i n t e g r a t e d d i f f e r e n t i a l  scattering c r o s s - s e c t i o n i s  to the e l e c t r o n d e n s i t y ng by:  da/dfi = n a S.fk) . e e  I  V  J  r  \  -  65 -  D i r e c t a p p l i c a t i o n of t h i s r e l a t i o n s h i p r e q u i r e s the complete imaging and  detection  system, a v e r y d i f f i c u l t  i b l e procedure to implement with r e l i a b i l i t y . perform a r e l a t i v e c a l i b r a t i o n by R a y l e i g h T h i s form of c a l i b r a t i o n can  be done as  Given the p r e s e n t s c a t t e r i n g ed  to a number d e n s i t y ,  Oft .  Scattering  n  o f f t h i s gas  be  A l l molecules c o n t r i b u t i n g  contained  unspecified  identical  for  are  R  factor f contains both  example, f a c t o r s such as:  solid  expressed  Rayleigh  Using e x a c t l y  s i m i l a r expression  the  R  which,  is  to  gases.  cross-section  when  normalized  s c a t t e r i n g volume  of the  system t h a t  f o r s c a t t e r i n t o the  for  ion  e t c . , would a l l be  Thomson s c a t t e r i n g  V . R  remain  experiments.  angle of c o l l e c t i o n , throughput of  same s y s t e m  fill-  as  scattering  components, d i s p e r s i o n i n s t r u m e n t s or d e t e c t o r s , ed i n f .  off neutral  Rayleigh  i n the  a l l properties  Thomson and  practice  system, the d i s c h a r g e v e s s e l i s  produces a s i g n a l P  to P  imposs-  follows.  o f molecules with known  Q  c a l i b r a t i o n of i f not  The g e n e r a l  scattering  t o the i n c i d e n t l a s e r i n t e n s i t y , can  The  an a b s o l u t e  For  imaging includgives  feature,  n o S.(k)V^f . e  Forming  the r a t i o  P-P/PR  and  n  solving  e  i  T  J  f o r the e l e c t r o n d e n s i t y ,  n  e  gives:  [15]  e  - 66  -  a  where the f a c t o r i n square  brackets i s j u s t  the c a l i b r a t i o n  constant for  the d e t e c t i o n system. Given S ^ ( k ) , the e l e c t r o n d e n s i t y may be determined paring  the plasma s c a t t e r i n g  s i g n a l s with those obtained  simply by com-  by s c a t t e r i n g  from  a known p r e s s u r e o f c a l i b r a t i o n g a s . Many g a s e s can be used f o r c a l i b r a t i o n purposes  ( G e o r g e , e t . a l . , 1965; D e S i l v a ,  n i t r o g e n where V  T  a /a R e  and S i ( k ) = 1 then  = 3.65 x 102. scattering  t o t a l s i g n a l as a plasma w i t h n I t should be noted  g  from  l a s e r wavelength. ally  Assuming  from Doppler  to the R a y l e i g h  ation of scattered i n t e n s i t y  Z/(1+ZT /T£) = 2/3.  A p a r t from the  by  molecules a t the  l i g h t can be a c c i d e n t level  of stray  When s t r a y l i g h t i s  by examing  the l i n e a r  vari-  E x t r a p o l a t i o n to zero  level.  q u i r e a knowledge o f S^(k) and hence o f a l p h a .  e  broadening  signal.  Measurement o f the e l e c t r o n d e n s i t y using  therefore  has a b a n d w i d t h  a constant  with gas pressure.  p r e s s u r e w i l l r e v e a l the s t r a y l i g h t  g i v e the same  m e a s u r e m e n t s must be made  p r e s e n t , the t r u e R a y l e i g h s i g n a l i s determined  a >>1 and  will  =  - 3  Even a t zero g a s p r e s s u r e s , l a s e r  l i g h t which w i l l be added  2  R  cm .  1 6  s c a t t e r e d i n t o the d e t e c t i o n system g i v i n g  Table I I shows  N  that Rayleigh scattered l i g h t  Therefore,  being  f o r the moment t h a t V  110 t o r r o f  = 1.0 x 1 0  which i s v e r y s m a l l , being determined i n a room temperature g a s .  1970) t h e most common  S^(k)  equation  For both  [15] i s e s s e n t i a l l y independent o f a l p h a , g i v i n g t i o n of n . e  - 67 -  scattering  approaches the  discrepancy i n  [15] d o e s r e systems,  constant  volume then,  a q u i t e simple  value  equation  determina-  In many c i r c u m s t a n c e s , s i n c e the  two  volumes V  and  R  the c a n c e l l e d f a c t o r f . the c a s e .  Figure  V  equation  l i g h t w i l l be c o l l e c t e d . volume i s determined mm.  to a d i a m e t e r entrance  equation  slits  0.25  mm  on  13,  T  not  12.  plasma  7.5°  The axis.  angle  r e g i o n o f o v e r l a p from which Figure  is  This figure i s  the  at a shallow  smaller  important  aspects  with  scattered  the s c a t t e r i n g  than  the  of  the  scattering  and  of the s c a t t e r i n g system should analyzing  scattered s i g n a l s .  1.9 high  volume  must be estimated  f i x e d a t 1.9  and  Firstly,  inm.  As  long  The  L^/Liji.  Using  volumes  F i g u r e 14,  the  1^ i s LJJ =  as the plasma diameter i s l a r g e r than t h i s , s t r e a k photographs as the  be  when  t h i s i s taken to be d i r e c t l y p r o p o r t i o n a l to  Otherwise, Lrp i s measured from  diameter.  therefore  [15] i s used to c a l c u l a t e e l e c t r o n d e n s i t i e s , the r e l a t i v e  r e s p e c t i v e l e n g t h s of the s c a t t e r i n g volumes,  T  this  to have a l e n g t h , normal to the plasma a x i s of L =  k e p t i n mind when viewing  L .  experiment  into  p o r t i o n s of the p i n c h phase. Two  R  d =  With the geometry o f  d e n s i t y plasma core i s s i g n i f i c a n t l y  V /v  can be i n c o r p o r a t e d  R e c a l l i n g the s t r e a k or shadow photographs, the d i a m e t e r  during  simplified  the wavevector diagram of F i g u r e  produces a r a t h e r long  Q  further  14 shows the s c a t t e r i n g volume i n d e t a i l .  monochromator  r e s p e c t to k  be  However, f o r the c u r r e n t  i n c i d e n t beam i s focussed the  can  a r e i d e n t i c a l and  T  t o be viewed i n c o n j u n c t i o n w i t h  Imaging  [15]  b r i g h t core  second, now  obvious p o i n t , i s t h a t along  the viewing  direc-  t i o n there i s c o n s i d e r a b l e  l a c k of s p a t i a l r e s o l u t i o n .  Parameters  deter-  mined from s c a t t e r e d l i g h t w i l l  t h e r e f o r e be  d e n s i t y plasma c o r e .  "  68  "  average values  f o r the  high  FIGURE 14 D e t a i l s of the  scattering  - 69 -  volume  CHAPTER 6  6.1  SCATTERING OBSERVATIONS AND  RESULTS  In t r e d u c t i o n Some a s p e c t s of the s c a t t e r i n g experiments were not q u i t e  and  l e a d to a few q u e s t i o n s  The  first  data  about the i n t e r p r e t a t i o n o f  s e c t i o n of t h i s chapter  presents  to show the type of i n f o r m a t i o n  questions  a sampling  t h a t was  observed  of  the  obtained.  expected signals.  raw  spectral  Answers  to  the  t h a t arose w i l l g i v e b e t t e r i n s i g h t i n t o the shock wave nature  the plasma s t r u c t u r e a t p i n c h  time.  As  well, i t will  be  seen  that  the  e f f e c t s o f r e f r a c t i o n can e n t e r i n t o c o n s i d e r a t i o n i n r a t h e r a s u b t l e A complete i n t e r p r e t a t i o n of the d a t a w i l l be seen to r e l y earlier  s t r e a k and The  final  extend  way.  h e a v i l y on  the  shadowgram o b s e r v a t i o n s . s e c t i o n of t h i s chapter  ments by p r e s e n t i n g obtained  of  the  concludes  e l e c t r o n temperature  f o r the f u l l d u r a t i o n of the p i n c h  phase.  the r e s u l t s of p r e v i o u s experiments on  measurements are compared with  the  and  estimates  this  the s c a t t e r i n g e x p e r i density The  measurements  data  confirm  Z-pinch.  The  made i n C h a p t e r  3,  and  density and,  in  Each  of  p a r t i c u l a r , w i t h the snow-plow model of plasma c o l l a p s e .  6.2  D i s c u s s i o n o f the  Spectra  A few b a c k s c a t t e r s p e c t r a are r e p r o d u c e d the s p e c t r a was  recorded  d i s p l a y the f u l l 500  on a s i n g l e shot of the ruby l a s e r .  channel  OMA  records.  t o t a l wavelength i n t e r v a l of 12 A,  The  These  traces  h o r i z o n t a l s c a l e spans  The  top spectrum, F i g u r e  a c a l i b r a t i o n shot showing R a y l e i g h s c a t t e r i n g from  nitrogen gas.  15.  a  though note t h a t the s c a l e i s i n v e r t e d ,  wavelength i n c r e a s i n g l i n e a r l y to the l e f t . is  i n Figure  Laser mode s t r u c t u r e due  - 70  1/2  atmosphere  to the o s c i l l a t o r output  -  15(A) of  etalon i s  (A)  1/2  IB)  n = 0.6 x 1 0  1 8  p  T = 22 t =-160  1.6 x 1 0  T=  28 eV  1 9  cm'  3  t = • 40 ns  (D)  n=  3.3 x 1 0  T =  6.3  e  e  t  = *310  1 8  cm"  eV ns  FIGURE 15 observed spectra. The f u l l i n t e r v a l d i s p l a y e d h, with wavelength i n c r e a s i n g to the l e f t . o  - 71 -  3  ns  n~ = e  cm*  eV  e  (C)  N2  atmosphere  3  evident.  For  t h i s shot, there were o n l y two  w i t h the modes separated  by 0.37  scattering  events, each  labelled  computed temperature and  density.  Spectra  15(A)  and  A.  15(B)  The  remaining  according  are  shows s t a t i s t i c a l f l u c t u a t i o n s o f  severe  s p e c t r a l shape. bottom two strong  baseline  present,  observation  with  time  approximately  Compared to the c a l i b r a t i o n the  b a s e l i n e which are  shot,  now  As w e l l the  to i l l u s t r a t e  one  of the n o i s e  complication  Thomson s c a t t e r i n g from h i g h d e n s i t y plasma, d i s c u s s e d i s concerned  with  the  level  of  the  plasma  ill-defined  b r a t i o n s h o t s , R a y l e i g h s c a t t e r i n g was  levels  stray l i g h t .  quite  For  arise  observation appearing  to  in  pres-  s t r a y l i g h t was  along  there  with  was  no  p r e s e n t , and  d e n s i t y of 7 x 1 0 ^  f o r i n the a n a l y s i s , i t was  plasma s c a t t e r i n g s i g n a l s during However, a r o u n d  scattering fixed  the  1  the  stray  measurable  o n l y amounted cm .  This  -3  most of the p i n c h phase.  time  o f maximum c o m p r e s s i o n  s i g n a l s would show u n p r e d i c t a b l e  levels.  Large  and,  not a s i g n i f i c a n t c o n t r i b u t i o n  shot  to shot  the  amounts o f  stray light  - 72 -  forward  variations (for  t i m i n g ) of as much as s i x o r d e r s of magnitude above expected  scattering  both  measured as a f u n c t i o n of f i l l  l e v e l o f s t r a y l i g h t i s w e l l below the e l e c t r o n d e n s i t i e s of i n t e r e s t  to  be  cali-  s c a t t e r i n g from an e q u i v a l e n t e l e c t r o n  though accounted  when  the s e r i e s of  In b a c k s c a t t e r ,  In f o r w a r d s e a t t e r ,  t h a t can  stray light  to a s c e r t a i n the d e t e c t i o n s e n s i t i v i t y (see S e c t i o n 5.4).  The  levels.  first  backward s c a t t e r i n g d e t e c t i o n systems.  sure i n order  more  However, Thomson s c a t t e r e d l i g h t i s c l e a r l y p r e s e n t .  order  and  and  equal  s p e c t r a i n F i g u r e 15 show t h a t h i g h e r d e n s i t y plasma g i v e  In  to  the  f l u c t u a t i o n s make f o r a r a t h e r  s c a t t e r e d s i g n a l s , w e l l i n excess  forward  modes  three s p e c t r a are plasma  s i n c e plasma background l i g h t i s a l s o r e c o r d e d .  d e n s i t y i s low and  light  to  displayed  s e n s i t i v i t i e s i n the v e r t i c a l d i r e c t i o n . 15(B)  longitudinal  a l s o appear  thermal i n back-  scattered  spectra,  enhanced.  Figure  spike  though o n l y when the forward s c a t t e r 15(C) g i v e s  an example o f t h i s c i r c u m s t a n c e .  superimposed on top o f the s c a t t e r e d  Rayleigh scattered  s i g n a l i n Figure  appears a t the l a s e r wavelength. consistent  w i t h the N  2  15(A), s t r a y l i g h t  Figure  be  l i g h t can be d e f l e c t e d  15(B) and (D) show no s t r a y  explained  do i n d i c a t e  by  noting  beam power i s a t the megawatt l e v e l  can lead  to serious  therefore  that  light  slightly  s t r a y l i g h t problems.  t h a t the  the i n c i d e n t  Considering  even  l i g h t and c o r r e l a t e d  back s c a t t e r spectrum have  that  while s c a t t e r e d  i t i s easy t o s e e t h a t  o f forward s c a t t e r e d  light,  The a n g u -  to such an e x t e n t t h a t t r a n s m i t t e d  i n a d e q u a t e l y absorbed by the beam dump.  dumping  i s u n b r o a d e n e d and  o f a shadowgram technique depends on r a y bending.  the photon l e v e l ,  L i k e the  calibration.  l a r d e f l e c t i o n e s t i m a t e s made e a r l i e r laser  The n a r r o w  signal i s stray l i g h t .  These o b s e r v a t i o n s a r e o f c o u r s e applicability  s i g n a l s are g r e a t l y  light  will  the i n c i d e n t  i s measured a t  inefficient  The l a r g e  beam  enhancements  appearance o f s t r a y l i g h t  been a t t r i b u t e d  ruby  to high  i n the  l e v e l s of  s t r a y l i g h t brought about by r e f r a c t i o n o f the i n c i d e n t l a s e r beam. A second a s p e c t o f the s p e c t r a spectra incident  of Figure  l a s e r wavelength.  metry o f F i g u r e density  15 a p p e a r  to n o t i c e  noticably  12, t h a t the backward  speed o f plasma c o n t a i n e d w i t h i n  a r e not v e r y a c c u r a t e s i n c e  the middle respect  scattering  direction.  a r e much  and, p r i m a r i l y because the s h i f t s  (For some s p e c t r a  like  73  -  radial  o f the  than the  observed a r e o f the  15(C), s t r a y l i g h t has aided  -  shift  smaller  same magnitude as s h o t - t o - s h o t f l u c t u a t i o n s i n the w a v e l e n g t h light.  from  volume.  on a n e t D o p p l e r  the s h i f t s  geo-  Therefore, a  an i n d i c a t i o n o f the a v e r a g e  based  two  to the  the wavevector  d i r e c t i o n detects  the s c a t t e r i n g  velocity estimates  width o f the s p e c t r a ,  with  I t w i l l be r e c a l l e d , from  net d i s p l a c e m e n t o f the spectrum g i v e s  spectra  red shifted  f l u c t u a t i o n s which propagate i n the r a d i a l  Radial  i s that  of i n c i d e n t  as a wavelength  reference).  As w e l l , o n l y a l i m i t e d  number  times when the red s h i f t s were s i g n i f i c a n t . s i g n i f i c a n t and  of  shots  were made a t  Nonetheless,  the  early  shifts  are  T a b l e I I I p r e s e n t s the r a d i a l v e l o c i t y measurements, d r / d t ,  as they c o u l d be e x t r a c t e d from  the a v a i l a b l e s c a t t e r i n g  data.  TABLE I I I  R a d i a l Speeds from the S c a t t e r i n g  Time (ns)  -50  - 1  < t < 0  -0.9+0.4  > 0  0  above measurements can be c o n s i d e r e d along with the s t r e a k and i n Chapter  e n t r i e s i n T a b l e I I I show t h a t t h e plasma a x i s , sees r a d i a l the plasma  sec )  -3.2+1.6  shadowgram r e s u l t s presented  of  cm  6  -150  t  The  d r / d t (x 1 0  Spectra  3.  Most  scattering  notably,  volume,  speeds t h a t d i f f e r with time.  (see F i g u r e s 7(A)  and  7(B))  first  two  l o c a t e d near  the  The  moves i n w a r d  the  outer  with  an  boundary approxi-  mately  uniform speed, which i s r o u g h l y equal to the s e c o n d  entry in  III.  At  is  somewhat e a r l i e r  significantly faster.  times,  plasma  near  the  axis  T h i s d i f f e r e n c e i n plasma speed  near  Table  travelling  the a x i s i s a t  l e a s t q u a l i t a t i v e l y c o n s i s t e n t with a d e s c r i p t i o n of the p i n c h e f f e c t i n c l u d e s the f o r m a t i o n of shock waves speed  can be understood The  moving  inward  travelling  filled  tube.  plasma inward  Compressed  with t h i s magnetic p i s t o n , c a n  inward  1957).  The  difference  in  as f o l l o w s .  magnetic f o r c e s d r i v i n g  d r i v e n i n t o a gas  (Allen,  that  faster  than  the  -  bulk  74  -  of  a c t much l i k e  plasma, be  collected  preceded  the p l a s m a  by  up  a  piston by,  a shock  l o c a t e d near  and wave the  p i s t o n . The shock f r o n t t h e r e f o r e reaches the a x i s sooner than t h e b u l k o f the  plasma.  the  net D o p p l e r  appearance  S i n c e the s c a t t e r i n g shift  times  i s interpreted  of the shock f r o n t , w h i l e , s h o r t l y  accumulated  a t the p i s t o n , would  d i r e c t e d motions would would  at early  volume i s l o c a t e d n e a r  the plasma as  indicating  a f t e r w a r d s , slower  e n t e r the s c a t t e r i n g  e v e n t u a l l y be t h e r m a l i z e d and  no  axis,  volume.  the  plasma, Radially  net Doppler  shift  be e v i d e n t , as the f i n a l e n t r y i n T a b l e I I I i n d i c a t e s . T h i s view o f the p i n c h phase c o u l d have been a l l u d e d  3 when the s t r e a k p i c t u r e s  ( F i g u r e s 4 or 7) were d i s c u s s e d .  a two component s t r u c t u r e i n the plasma column shock wave nature o f plasma c o l l a p s e . converging core.  on a x i s i s what i n i t i a t e s  However,  i s also  In p a r t i c u l a r ,  Development o f  indicative  the p r e c u r s o r  f o r m a t i o n o f the h i g h d e n s i t y  the p h o t o g r a p h i c e x p e r i m e n t s  velocities directly.  to i n Chapter  do  n o t measure  of  the  shock plasma  particle  In combination w i t h Chapter 3, the Doppler s h i f t d a t a  can be e x p l a i n e d q u a l i t a t i v e l y , but, the s c a t t e r i n g s p a t i a l r e s o l u t i o n required  experiments  to make q u a n t i t a t i v e e v a l u a t i o n s  lack  o f the  the  shock  structure. The  f i n a l p o i n t of d i s c u s s i o n i n t h i s s e c t i o n  concerns again  net  wavelength  the  average Doppler s h i f t a r i s e s , not from the presence of a red s h i f t ,  s h i f t appearing i n the b a c k s c a t t e r s p e c t r a . A q u e s t i o n about  from the absence o f a b l u e s h i f t .  Presumably,  i f the s c a t t e r i n g  s y m m e t r i c a l l y l o c a t e d on the plasma a x i s , s c a t t e r e d ed from both ' s i d e s ' o f the plasma.  to the o b s e r v e d  radially one would  red  shift.  Beyond  inward w i l l i n f a c t be moving expect not o n l y red s h i f t e d  blue s h i f t e d  one, the t o t a l  light  but  volume i s  should be observ-  The r e g i o n of plasma n e a r e s t the l a s e r  and b a c k s c a t t e r o p t i c s w i l l be moving away f r o m rise  the  the a x i s ,  towards  - 75 -  plasma  the i n c i d e n t  spectrum,  spectrum showing  the i n c i d e n t  but a l s o  beam g i v i n g collapsing  beam. a  Hence,  similtaneous  symmetry about the r u b y  wave-  length.  One  p l a u s i b l e explanation  ponent w i l l be it  put  f o r the  absence of  forward i n terms of r e f r a c t i o n .  i s worth i n d i c a t i n g why  a blue  shifted  Before doing  r e f r a c t i o n e f f e c t s were c o n s i d e r e d  so  a  com-  though,  plausible  explanation. As  has  already  been shown by  o f s t r a y l i g h t there can the  plasma.  Figure  be r a t h e r  interferometric gradients, o f 3.5°. 1.3°,  e x i s t i n g near the  angular In  i t was  backscattered  verified  cone has  negligible  angle  the c a s e .  that  of  the  Recalling  volume w i t h an F/#  a half-angle  of 1.8°.  i l l u s t r a t e s how  can  the  the  o f 16.  course  the  sharp  the  density  in  excess  is  is  small  collection optics.  discussion  other  of  maximum d e f l e c t i o n  focal length  In  by  exceed  the  i f this deflection  in Section lens  words,  which  the  5.3, views  collection  T h e r e f o r e , the minimum d e f l e c t i o n a n g l e  q u i t e comparable w i t h the maximum a c c e p t a n c e cussion  that  backscatter  l i g h t i s c o l l e c t e d by a 50 cm  scattering  discussion  core boundary, produce d e f l e c t i o n s  r e f r a c t i o n e f f e c t s w i l l be  However, t h i s i s not  deflections  f a c t , during  Nonetheless, i f i t i s a c c e p t e d  compared to the a c c e p t a n c e  the  the  degrees.  measurements,  from the  l a r g e d e f l e c t i o n s of ruby l a s e r l i g h t  9 shows t h a t  a p p r o x i m a t e l y 23 mrad or 1.3  shadowgrams and,  such a c i r c u m s t a n c e  angle.  can  The  lead  to  following  only  is  dis-  red-shifted  spectra. C o n s i d e r then t h a t the on-axis scattered  and  represents  l i g h t c o l l e c t e d by  over a l l the  of  the  symmetrically located Also,  source  the  portions  larger  16,  volume i s s y m m e t r i c a l l y  of  light.  the b a c k s c a t t e r  high density  i n Figure  comparable to or On  line  elemental c o n t r i b u t i o n s  cross-section  signal.  a  scattering  of the  the  than the  along core  the  line.  plasma  and  be  amount  Figure  16  indicates  a  of  some i n t e g r a l  contribute  volume has  to  shows how  the  length  a  two total  which  is  core d i a m e t e r .  l e f t of the plasma a x i s , s c a t t e r e d  plasma moving towards the  total  optics w i l l  l i n e would  scattering  The  located  light, originating  i n c i d e n t beam, must r e - t r a v e r s e  "  76  "  the  plasma  from and  FIGURE 16 Refraction  e f f e c t s i n the b a c k s c a t t e r  - 77  -  collection  optics.  t h e r e f o r e be r e f r a c t e d away from the c o l l e c t i o n solid  l i n e i n Figure  i n Figure  6.  The  16 and  dotted  can  lens.  be compared with the  l i n e i n Figure  16,  T h i s i s shown by ray  trajectory  the  given  o r i g i n a t i n g from the  same p o i n t  i n the plasma, shows the path o f the same r a y i f r e f r a c t i o n were  neglected.  The  r e s u l t of r e f r a c t i o n then i s to d e c r e a s e the e f f e c t i v e c o l l e c t i o n  for  this region On  of the  the other  s c a t t e r i n g volume. hand, the  corresponding  element of  volume which i s c l o s e r to the  l e n s produces the red  ponent and  s i g n a l with  creased  contributes  to the  as a r e s u l t of r e f r a c t i o n .  l i g h t l o s t from the  it  t o t a l amount of s c a t t e r e d  the c h a r a c t e r i s t i c s of the plasma n e a r e s t  explanation observing  e f f e c t s of for  not  r e f r a c t i o n are  seeing  only r e d - s h i f t e d the  ment of the  spectra  i n length,  so accomodating as  can  s i g n a l that  at  least  The  most l i k e l y  i s that  there  i s simply  about the  plasma  accomplished by p l a c i n g axis  of  the  a  However, c o n s i d e r i n g  a  an  error  axis.  Align-  discharge  vessel.  c o n s t i t u t e o n l y 25% o f the  from  the  total signal.  -  78  -  i f the  exactly  far  side  plasma  to  the  of  the  not  the  geo-  a x i s was  dis-  f o c a l volume, i n the d i r e c t i o n o f  scattering  on  i t s e l f was  placed  o f the  in  pinhole  For  from the c e n t e r  for  t h a t the s c a t t e r i n g volume i s  to have the plasma a x i s correspond  mm,  partial  reason  m e t r i c a l a x i s of the v e s s e l .  d e n t beam, by 0.5  lens.  small  i t i s q u i t e p o s s i b l e t h a t the d i s c h a r g e  instance,  that  i s domin-  the c o l l e c t i o n  shift.  l o c a t i o n of the  from  see  monochromator entrance s l i t s were then imaged  of t h i s p i n h o l e .  o n l y 2 mm  a blue  s c a t t e r i n g system was  i n c i d e n t beam and  center  is in-  l i g h t c o l l e c t e d remains  considered  s c a t t e r i n g volume s y m m e t r i c a l l y  a t the p r e c i s e g e o m e t r i c a l The  that  However, with the i n c l u s i o n of r e f r a c t i o n e f f e c t s , one  The  imaging  cone  approximation, the amount of  i s p o s s i b l e f o r the plasma to produce a s c a t t e r e d  ated by  scattering  s h i f t e d s p e c t r a l com-  a collection  In a f i r s t  the  ' f a r ' s i d e of the s c a t t e r i n g volume w i l l be g a i n e d  the near s i d e so t h a t the fixed.  cone  the  inci-  plasma  would  Apart scattering  from  some o f t h e u n c e r t a i n t i e s  in fully  o b s e r v a t i o n s , and, to the e x t e n t t h a t the s c a t t e r i n g  r e p r e s e n t a r a d i a l l y averaged i n v e s t i g a t i o n o f the p l a s m a be seen i n the f o l l o w i n g scattering  6.3  explaining  experiments  column,  i t will  s e c t i o n t h a t the plasma parameters determined from  agree v e r y w e l l w i t h p r e v i o u s independent measurements.  Plasma Parameters f o r the Z-Pinch Results  scattering  f o r the plasma  experiments are  parameters  shown i n F i g u r e s  o b t a i n e d from 17 and  18.  the  temperature and e l e c t r o n d e n s i t y r e s p e c t i v e l y as a f u n c t i o n  during  the p i n c h phase.  A g a i n , the time a x i s i s r e f e r e n c e d  The smooth c u r v e s drawn on each p l o t r e p r e s e n t the  a visual  Thomson  These g i v e  plasma  of  to d l / d t  the time =  0.  a p p r o x i m a t i o n to  data points. Ion  temperatures, F i g u r e  aided v i s u a l  fitting  calculated ionized  using  e  electron-ion c o l l i s i o n quite valid of  were d e t e r m i n e d  The t h e o r e t i c a l  Salpeter's  helium and T  17,  using  a  computer  r o u t i n e to compare the o b s e r v e d b a c k s c a t t e r  with t h e o r e t i c a l p r o f i l e s .  = T^.  shape  f o r the i o n f e a t u r e i s  (1963) a p p r o x i m a t i o n w i t h Z = Over  spectra  2 for  fully  the range of plasma parameters measured,  times are i n the sub-nanosecond  regime  to assume e q u a l e l e c t r o n and i o n temperatures.  so i t i s  When t h e  shape  the b a c k s c a t t e r spectrum i s w e l l d e f i n e d , as i n F i g u r e 15(C) or (D), the  fitting  procedure a l l o w s the average i o n temperature to be determined to an  u n c e r t a i n t y of 10 - 20%. 10  the  1 8  (see  cm , -3  the b a c k s c a t t e r  Below an e l e c t r o n d e n s i t y of a p p r o x i m a t e l y s p e c t r a show r a t h e r poor s i g n a l to n o i s e  F i g u r e 15(B) f o r example).  In these i n s t a n c e s ,  ments become l e s s a c c u r a t e and are good  temperature  t o , a t worst, about  - 79 -  40%.  1 x  ratios  measure-  FIGURE 17 Plasma temperature r e s u l t s . Measurements are from Thomson s c a t t e r i n g i n the backward d i r e c t i o n (open c i r c l e s ) and l i n e t o continuum r a t i o s ( c r o s s e s ) .  - 80 -  For comparison, the d a t a p o i n t s drawn as c r o s s e s g i v e measurements f r o m e a r l i e r et.al.,  1980).  work,  (Houtman, 1977; A l b r e c h t ,  These e s t i m a t e s were based on the l i n e  temperature 1979; H i l k o  to continuum  ratio  o  f o r the H e l l 4686 A emmission  line.  Above  25 eV, t h i s  spectral  e s s e n t i a l l y n o n - e x i s t e n t s i n c e the plasma i s f u l l y i o n i z e d . s p e c t r o s c o p i c d a t a below 25 eV i s r e l i a b l e and agrees Thomson s c a t t e r i n g  results.  Typical  error  line i s  However, t h e  favourably  b a r s have been  w i t h the  indicated i n  F i g u r e 17. E l e c t r o n d e n s i t y d a t a , F i g u r e 18, i s o b t a i n e d from (open squares) and backward the R a y l e i g h  scattering  (open c i r c l e s ) s c a t t e r i n g  calibrations, n  e  was  the plasma d i a m e t e r .  When comparing  forward  experiments.  computed from  w i t h S^(k) = 2/3. As shown i n F i g u r e 14, the s c a t t e r i n g mated l e n g t h o f 1.9 mm which, a t times d u r i n g  both  Using  e q u a t i o n [15]  volume had an e s t i -  maximum compression,  R a y l e i g h and plasma  exceeded  scattering  signals  t h i s d i s c r e p a n c y i n c o l l e c t i o n volumes was accounted f o r . C o l l e c t i v e s c a t t e r i n g , i . e . : an i o n f e a t u r e i n the backward t i o n was n o t observed f o r d e n s i t i e s below 2 x 1 0  1 7  ments a t e a r l y times could be extended  cm"  i n forward d i r e c t i o n light. spurious  During  still  scatter data.  1 7  n  e  > 10  2 0  phase, cm  - 3  D e n s i t y measure-  - 3  3  contained s i g n i f i c a n t  the h i g h compression  data points with  to < 1 0  cm .  Figure  s i n c e the  i o n feature  amounts o f s c a t t e r e d 18 shows a p p a r e n t l y  which o r i g i n a t e  from the forward  These and o t h e r o f f s c a l e p o i n t s are due t o the l a r g e  l i g h t enhancements d i s c u s s e d e a r l i e r .  stray  A c c o r d i n g l y , t h o s e measurements i n  the forward d i r e c t i o n t h a t i n d i c a t e e l e c t r o n  0  direc-  - 81 -  densities  well  i n excess of  FIGURE 1 8 Electron d e n s i t y r e s u l t s . M e a s u r e m e n t s a r e f r o m Thomson s c a t t e r i n g i n backward d i r e c t i o n (open c i r c l e s ) and f o r w a r d d i r e c t i o n (open s q u a r e s ) , and S t a r k brodening ( c r o s s e s ) . The d o t t e d l i n e shows the snow-plow model p r e d i c t i o n f o r Z = 2.  - 82 -  i  10^  cm  u  ments on Figure  are not p l o t t e d i n F i g u r e  -3  t h i s Z-pinch were o b t a i n e d  18 as c r o s s e s .  experiments had tion).  The  ( L i k e the  been arranged  18.  Again, the  f i r s t d e n s i t y measure-  s p e c t r o s c o p i c a l l y and  s c a t t e r i n g geometry,  to view the on-axis  agreement between a l l t h r e e  are  the  included  in  spectroscopic  plasma i n a r a d i a l d i r e c -  density  determinations  is  quite  good. I t i s i n t e r e s t i n g to compare d e n s i t y scattering 3.4.  with  Equation  of equation  from  the snowplow model of plasma c o l l a p s e d e s c r i b e d  f i l l gas.  The  the column r a d i u s and  dotted  l i n e i n Figure  [1] f o r f u l l y i o n i z e d helium w i t h  t i o n of time taken from the s t r e a k  and  Thomson  in  [1] s p e c i f i e s t h a t the average e l e c t r o n d e n s i t y  plasma column i s determined by o f the i n i t i a l  measurements  Section  within  the  assumes t o t a l sweep-up  18 shows the p r e d i c t i o n s  the o u t e r  radius  as  a  shadowgram p l o t s , F i g u r e  func-  7(A)  or  7(B). A t peak compression, the s c a t t e r i n g measurements and from t o t a l sweep-up correspond c o m p l e t e l y o f the s c a t t e r i n g system and correspond.  However, p r i o r  i s considerably The the  the averaging  predictions  because the averaging  properties  p r o p e r t i e s of e q u a t i o n  [1]  to peak compression, the plasma d e n s i t y  lower than an i n t e r n a l l y  uniform  distribution  also  on-axis  predicts.  r a d i a l d i s t r i b u t i o n of e l e c t r o n d e n s i t y i s of course not u n i f o r m . streak  swept-up by  and  shawdowgram  the magnetic f i e l d  s h e l l up u n t i l about t = -50 i n s i d e the s h e l l scattering this  studies  show t h a t  remains c o n f i n e d  ns.  P r i o r to  this  most o f within time,  The  average e l e c t r o n d e n s i t y  of  l i n e s i n c e a t these times,  small  size  compared  the  plasma  with  the  of  the  - 83  vessel  -  so  shell  the  the  low  is thin  density and  r e s o l u t i o n to  the  c l o s e l y f o l l o w the d o t t e d  that  a relatively  ( t h a t i s , near the a x i s ) w i l l be c o m p a r a t i v e l y  experiments have more than adequate s p a t i a l  clearly.  the g a s  Both  itself  the show will  plasma r a d i u s  amount o f g a s  is  that  remains to be o f the s h e l l  c o l l e c t e d up w i l l c o n t r i b u t e l i t t l e  electron  density  plasma.  T h i s concludes p r e s e n t a t i o n and  to the  o f the Thomson s c a t t e r i n g d i a g n o s t i c s  the Z-pinch plasma parameters o b t a i n e d  d i s c u s s i o n provides  by  t h i s method.  The  a b r i e f r e v i e w of some of the i m p o r t a n t  following  aspects  of  he  c u r r e n t s c a t t e r i n g experiments. The  s c a t t e r i n g r e s u l t s have v e r i f i e d  surements of the p l a s m a p a r a m e t e r s phases of  the  discharge.  Where  obtained  temperature,  density gradients  high  density  the  pre  (and  and  other)  diagnostics  measurement  phase.  The  capabilities  plasma d e n s i t y  T h i s has  introduced  some p r o b l e m s  a i d i n d i s c r i m i n a t i n g a g a i n s t s t r a y l i g h t . However, i n order  dumping w i l l be Two  i n the  forward  direction,  with  system,  to r e s o l v e  more e f f i c i e n t  beam  required.  v i t a l aspects  of the s c a t t e r i n g e x p e r i m e n t s have  limited  d e t a i l w i t h which the h i g h compression phase c o u l d be i n v e s t i g a t e d . ly,  and  refrac-  S p e c t r a l l y r e s o l v e d d e t e c t i o n , as i n the b a c k s c a t t e r  the thermal i o n s p e c t r u m  mea-  post-pinch  are s u f f i c i e n t l y l a r g e to r e s u l t i n s i g n i f i c a n t  t i o n a t the ruby l a s e r wavelength. stray light.  spectroscopic  s c a t t e r i n g from i o n a c o u s t i c f l u c t u a t i o n s  proved to be a v a l u a b l e method f o r extending  i n t o the h i g h  can  for  spectroscopic  attempted p r e v i o u s l y have f a i l e d , has  previous  the c u r r e n t arrangement of the  l a c k of h i g h s p a t i a l r e s o l u t i o n .  scattering  s y s t e m s has  the  First-  resulted  in  a  Consequently, the measurements have g i v e n  o n l y the average l i n e - o f - s i g h t plasma c o n d i t i o n s whereas the plasma temperature, d e n s i t y  and  radial  velocity distribution  volume can be q u i t e non-uniform. Secondly, the by the q-switching  process  is insufficient  r a p i d changes t h a t occur during t i o n s are p r e s e n t , shadowgram z-pinch  study,  the  the on-axis  within  the  temporal r e s o l u t i o n a f f o r d e d  to  isolate  collapse.  some o f  contributed  g r e a t l y to diagnosing  plasma.  -  84 "  the  Though these  s c a t t e r i n g experiments, combined with  have  scattering  limita-  the s t r e a k the  more  and  current  The f i n a l experiment of t h i s t h e s i s work attempts to g i v e a second independent measurement o f the e l e c t r o n d e n s i t y g o a l o f overcoming  w i t h , as w e l l ,  the temporal and s p a t i a l l i m i t a t i o n s  experiments, thus p r o v i d i n g  a more d e t a i l e d  phase.  " 85 ~  view  of the  o f the peak  the s p e c i f i c scattering compression  CHAPTER 7  7.1  INTERFEROMETRIC DETERMINATION OF ELECTRON DENSITY  In t r e d u c t i o n With s c a t t e r i n g  methods, the plasma i s i n t e r r o g a t e d a t t h e m i c r o -  scopic l e v e l v i a p a r t i c l e fluctuations.  Such a technique i s i m p o r t a n t f o r  the i n t e r a c t i o n experiments s i n c e the C 0 d i r e c t l y to s p e c i f i c  fluctuations.  2  l a s e r can be absorbed by c o u p l i n g  E f f e c t s of  the C 0  l a s e r can  2  observed a t the macroscopic l e v e l s i n c e l o c a l i z e d d i s t u r b a n c e s t u a l l y decay i n some hydrcdymanic  a l s o be  will  even-  f a s h i o n . T h e r e f o r e , i n the n e x t s t a g e o f  d i a g n o s t i c i n v e s t i g a t i o n , the Z - p i n c h i s examined  by m e a s u r i n g  s c o p i c plasma parameter, namely, the index o f r e f r a c t i o n . done using double exposure h o l o g r a p h i c i n t e r f e r o m e t r y .  a macro-  This  The  has  interferometric  measurements have g i v e n a complete two d i m e n s i o n a l view o f the plasma tron density d i s t r i b u t i o n . scattering  elec-  These experiments then not o n l y complement  the  r e s u l t s w i t h an independent measurement of n , but a l s o d r a m a t i e  c a l l y improve  spatial  The f i r s t  resolution.  section  describes  exposure h o l o g r a p h i c technique and why  t h e major  advantage  t h i s method was  of the  selected  c o n v e n t i o n a l ones. Next, a simple approach to the f o r m a t i o n and t i o n o f the i n t e r f e r e n c e p a t t e r n w i l l be g i v e n .  of  t e c h n i q u e s to h i g h d e n s i t y plasma, or i n g e n e r a l , h i g h l y  over  presented w i l l  of  interferometric refracting  Though t h e  phase intro-  calculations  show t h a t r e f r a c t i o n e f f e c t s are not o f p r i m a r y  - 86 -  more  interpreta-  The problem r e s u l t s from the a d d i t i o n a l phase d i s t o r t i o n s  duced as a r e s u l t of c u r v a t u r e i n the r a y p a t h s .  double  However, the r e m a i n d e r  t h i s c h a p t e r e x p r e s s e s a concern f o r the a p p l i c a b i l i t y  objects.  been  importance  f o r the c u r r e n t verify  this.  used imaging  Z - p i n c h d i a g n o s t i c s , i t has  In p a r t i c u l a r , arrangment may  i t is vital  in fact  to p o i n t  not be adequate  for  out  the  been that  important the  proposed  to  currently  interaction  experiments.  7.2  Double Exposure H o l o g r a p h i c Holographic  and  photographic  i n t e r f e r o m e t r y covers  processing  (e.g. C o l l i e r  complete treatment of the theory, i n t e r f e r o m e t r y can be No  Method a wide range of t o p i c s i n o p t i c s et.al.,  p r a c t i c e , and  1971).  a p p l i c a t i o n of  found i n the t e x t w r i t t e n by C h a r l e s M.  attempt w i l l be made here to d e s c r i b e a l l aspects  r e l e v a n t f e a t u r e s of the techniques experiments w i l l be p o i n t e d This f i r s t sure procedure and  the most important  nothing  current  a l s o be  holographic  expo-  discussed  technique  i n time.  methods The  conseen  and  i t will  be  offers  a great  deal  of  i n the study of t r a n s i e n t events. double exposure method i s i l l u s t r a t e d  i n Figure  more than a schematic arrangement f o r r e c o r d i n g  l a s e r beam i s s p l i t  i n t o two  recombined, and  graphic  to the  method, namely, t h a t the  o f f - a x i s holograms of a t r a n s p a r e n t o b j e c t .  being  though  d i f f e r e n c e between conven-  i n space or, d i f f e r e n t i a l  sequences of t h i s d i f f e r e n c e w i l l  The  (1979).  the b a s i c i d e a of the d o u b l e  the h o l o g r a p h i c  are r e s p e c t i v e l y d i f f e r e n t i a l  flexibility  Vest  out where a p p r o p r i a t e .  p o i n t s out  exposure  and  holographic  of the method,  i n v o l v e d , as they apply  section i l l u s t r a t e s  t i o n a l i n t e r f e r o m e t r y and  t h a t the d o u b l e  A very recent  plate.  One  the  beams w h i c h  travel  wavefront, designated  the  s p a t i a l l y uniform  (or a t l e a s t simple) a m p l i t u d e  T h i s beam i s used  h o l o g r a p h i c a l l y to r e c o r d  -  reconstructing  In F i g u r e 19(a),  interference pattern  - 87  and  19 which shows  different i s recorded reference and  phase  the amplitude and  the  incident  paths on  a  beam,  before photohas  a  distribution. phase  distri-  (A)  Recording  laser  beam  object  splitter  ( B)  relay optics  Reconstruction  FIGURE 19 Illustration  o f the double exposure  -  88 -  method.  b u t i o n o f the second wavefront, t h e s c e n e  beam.  c o n s i d e r a t i o n i s t r a n s p a r e n t , upon t r a n s m i s s i o n  S i n c e the o b j e c t through  the phase d i s t r i b u t i o n o f the scene wavefront i s a l t e r e d  under  the o b j e c t ,  only  while the a m p l i -  tude d i s t r i b u t i o n remains unchanged. The scene beam a l s o c o n t a i n s some u n s p e c i f i e d r e l a y o p t i c s . c o u l d be a simple o p t i c a l d e l a y f o r matching  the beam p a t h s  This  to the coher-  ence l e n g t h o f the l a s e r s o u r c e , and/or a more c o m p l i c a t e d imaging a r r a n g e ment a l l o w i n g plate.  f o r say, m a g n i f i c a t i o n  o f the o b j e c t  wavefront onto the  Though n o t shown, the r e f e r e n c e beam as w e l l could c o n t a i n  beam h a n d l i n g  or m a g n i f i c a t i o n matching  components.  T h i s system then i s used to r e c o r d the same p h o t o g r a p h i c p l a t e .  similar  two d i f f e r e n t  The f i r s t exposure r e c o r d s  scene  beams on  the wavefront o f  the scene beam when the o b j e c t i s n o t p r e s e n t , w h i l e the second exposure i s made w i t h t h e o b j e c t  i n place.  r e c o r d e d a t d i f f e r e n t times.  The two s c e n e  beams must t h e r e f o r e  However, a f t e r development  and p r o c e s s i n g  the p l a t e , a s i n g l e r e f e r e n c e beam i s used t o r e c o n s t r u c t both s c e n e s i m u l t a n e o u s l y , as i l l u s t r a t e d  i n F i g u r e 19(B).  Now, i n t e r f e r e n c e  the two r e c o n s t r u c t e d wavefronts can be observed and r e c o r d e d .  be of  beams  between  The d i f f e r -  ence between the ( r e c o n s t r u c t e d ) scene beams i s due o n l y to the presence of the o b j e c t s i n c e a l l e l s e i n the s c e n e  beam p a t h was i d e n t i c a l  f o r both  exposures. Examination o f the two scene beams o f F i g u r e 19(B), from the p o i n t o f view o f the p o l a r o i d  f i l m , would lead  ference pattern o r i g i n a t e d  to the c o n c l u s i o n t h a t t h e i n t e r -  from a c o n v e n t i o n a l  M i c h e l s o n or Mach-Zender  i n t e r f e r o m e t e r w i t h a t r a n s p a r e n t , phase d i s t o r t i n g  o b j e c t i n one arm.  t h i s sense then, the double exposure h o l o g r a p h i c t e c h n i q u e j u s t merely mimics a l l the u s u a l i n t e r f e r o m e t r i c  In  described  methods e x c e p t t h a t  t h e two  wavefronts o f i n t e r e s t a r e permanently r e c o r d e d through h o l o g r a p h y and c a n be viewed a t l e i s u r e . interfering  The most i m p o r t a n t d i f f e r e n c e  wavefronts i n the double e x p o s u r e  - 89 -  method  though  i s t h a t the  originate,  n o t from  d i f f e r e n t r e g i o n s of space, but ferometry  i s j u s t the o p p o s i t e  sent s i m u l t a n e o u s l y following  from d i f f e r e n t times.  but t r a v e l through d i f f e r e n t r e g i o n s of s p a c e .  b r i e f d i s c u s s i o n , the f l e x i b i l i t y allowed  o f the c u r r e n t l a s e r / p l a s m a In the p r e s e n t  The  second exposure can  which must of course ary object.  The  to t h a t obtained one  arm  and  then be  taken  at  various  l a s t only f o r the  low  be  the  example  made  pressure  times during  duration  of  the  before helium.  the  pinch  laser  i n t e r f e r e n c e p a t t e r n produced w i l l be e n t i r e l y  pulse,  station-  equivalent  i n say a Mach-Zender c o n f i g u r a t i o n where the p l a s m a  arm.  there i s a uniform  In t h i s i n s t a n c e then,  the wavefronts might o n l y be c o n s i d e r e d  is in  refractive index a holographic  dis-  record  of  an advantage because i t a l l o w s some  f o r subsequent image p r o c e s s i n g .  Using  a short pulse  laser for holographic  f o r another p o s s i b l e exposure sequence.  during  which o c c u r r e d reconstructed  interferometry  I f i t i s arranged  i n t e r v a l between exposures a l s o very s h o r t ,  then  both  allows  to have the  exposures  could  time be  the p i n c h phase. Then, o n l y the change i n plasma c o n d i t i o n s i n the time i n t e r v a l between exposures would be s e e n  interference pattern.  One  r a p i d plasma motions f r o m more s l o w l y (Armstrong, 1977). be of  through the  be s h o r t enough t h a t the plasma appears as a  t r i b u t i o n i n the other  obtained  out  the v e s s e l c o n t a i n s  o f the i n t e r f e r o m e t e r and  flexibility  In  by the i n t e r f e r o m e t r i c  experiment, the f i r s t exposure can  Each exposure w i l l  pre-  i n t e r a c t i o n experiments.  the Z-pinch d i s c h a r g e  phase.  inter-  s i n c e the beams t h a t i n t e r f e r e must be  s t u d i e s which are d i f f e r e n t i a l i n time are p o i n t e d  firing  Conventional  particular  could therefore completely varying  'ambient'  in  isolate  configurations  As an example, a p p l i c a t i o n of such an arrangement importance i n i s o l a t i n g  proposed  i n t e r a c t i o n experiments  the order  of  a nanosecond  or  s i n c e the  less,  plasma i s e s s e n t i a l l y s t a t i o n a r y .  e f f e c t s of the  a time  which  However, the most o f t e n c i t e d  - 90  -  will  CO2 l a s e r i n the  CO2 l a s e r p u l s e w i l l s c a l e over  the  the  l a s t for target  example of  the  temporal i s o l a t i o n advantage o f double exposure h o l o g r a p h i c  metry  i s when t h e a m b i e n t  optics,  a circumstance  configuration  which cannot  contains  be t o l e r a t e d  rather with  interfero-  poor  quality  conventional  methods. In any event, the above p o s s i b i l i t i e s a r i s e from the f a c t t h a t the double exposure method i s d i f f e r e n t i a l  i n time.  For the p r e s e n t  the  f i r s t i n t e r f e r o m e t r i c measurements were intended  ing  r e s u l t s by examining  t o extend the s c a t t e r -  the plasma c o n f i g u r a t i o n d u r i n g  maximum  s i o n , t h a t i s , when the f i r s t exposure i s made b e f o r e f i r i n g For  t h i s case, S e c t i o n  7.4 g i v e s  a simple  analysis  i n t e r p r e t a t i o n o f the i n t e r f e r e n c e p a t t e r n . following  short section e s t a b l i s h e s  index as a f u n c t i o n o f e l e c t r o n  7.3  Plasma R e f r a c t i v e The  in  the d i s c h a r g e .  this though, the  f o r the plasma r e f r a c t i v e  density.  Index  b a s i c plasma p r o p e r t y  that i s of i n t e r e s t f o r i n t e r f e r o m e t r y  the index o f r e f r a c t i o n which, i n i t s s i m p l e s t  related  compres-  o f t h e f o r m a t i o n and  B e f o r e doing  some d a t a  purposes,  t o the e l e c t r o n d e n s i t y  form  (Jahoda,  1971) i s  through e q u a t i o n [ 2 ] .  y ( r ) = (1 - n / n ) V 2 c  e  The  index o f r e f r a c t i o n depends on the wavelength a t which i t i s m e a s u r e d ,  through the c r i t i c a l  density,  n  c  n , where: c  = 1.12 x 1 0  2 1  X"  2  cm" , 3  if 10  the wavelength i s g i v e n 21  i n microns.  Using  ruby l a s e r l i g h t , n  =2.33 x  cm . -3  In terms of i n t e r f e r o m e t r i c m e a s u r e m e n t s , differs order  c  significantly  o f 1% n .  from  unity  when the  the  refractive  electron density  becomes  For comparison, the plasma r e f r a c t i v e index i s s m a l l e r  c  u n i t y by about the same amount t h a t o r d i n a r y a i r i s l a r g e r n .  d i s t i n c t i o n between h i g h and  low d e n s i t y plasma, the c u r r e n t Z - p i n c h  former In  interest,  This provides  c  a more or  the than  than u n i t y ,  an e l e c t r o n d e n s i t y o f 0.05%  i n the  index  at  less quantitative being  category.  what f o l l o w s so,  as  later,  a matter  of  the  actual  convenience  numbers and  involved  reference,  may  be  of  Figure  20  is  i n c l u d e d here to show the plasma r e f r a c t i v e index a t the wavelength of ruby laser  7.4  light.  Formation o f the F r i n g e  Pattern  T h i s s e c t i o n g i v e s a simple  a n a l y s i s of the g e n e r a t i o n  and  inter-  p r e t a t i o n of the i n t e r f e r e n c e p a t t e r n produced when the e f f e c t s o f r e f r a c t i o n are not i m p o r t a n t . as g e n e r a t i n g  As w i l l be  seen l a t e r , r e f r a c t i o n e f f e c t s , as  a good d e a l more mathematical c o m p l i c a t i o n ,  duce a more s e r i o u s problem.  The  basic ideas  presented  will also here  well  intro-  though  will  remain unchanged when r e f r a c t i o n i s i n c l u d e d . The  p i n c h plasma i s assumed to have a symmetric  distribution, n  e  = n ( r ) which does not vary along e  - 92  -  electron  density  the plasma column, i . e . :  FIGURE 20 The  plasma r e f r a c t i v e index v s . e l e c t r o n  - 93  -  density.  i n the z d i r e c t i o n .  The plasma can t h e r e f o r e be r e p l a c e d by i t s e q u i v a l e n t  r e f r a c t i v e index d i s t r i b u t i o n a c c o r d i n g cross-section  o f the plasma  maximum r a d i u s o f r The  path.  .  [2].  i s shown where  For r > r , u = u o Q  In F i g u r e  V = u (r)  Consider  2 1 ,a  inside  a  =1.  plasma i s i l l u m i n a t e d by a c o l l i m a t e d beam, e n t e r i n g  t o the x - a x i s . h e i g h t y.  Q  column  to e q u a t i o n  parallel  then the o p t i c a l p a t h l e n g t h o f a r a y i n c i d e n t a t  The l i g h t r a y i s assumed n o t t o d e v i a t e  from  a straight  line  Ray c u r v a t u r e due to r e f r a c t i o n e f f e c t s i s t h e r e f o r e i g n o r e d . As a f i r s t or r e f e r e n c e exposure,  r a y t r a v e l s an o p t i c a l path  1  = u (x -x.) n  O  the second  exposure,  plasma  O  B  i s not present  i n going  and t h e  from A t o B.  For  A  the plasma i s i n p l a c e and the o p t i c a l path  from  A to  B i s now 1-| , where l  evaluated  over  the l i m i t s  ween r e f e r e n c e and s c e n e difference  A<f> = 2irAl/X  wavelengths  P = Al/X  t  =  Ju(rjdx  t o X-Q. The path d i f f e r e n c e r a y c a n be e x p r e s s e d  .  alternatively  (Lambda w i l l be c o n s i s t e n t l y taken  interfere.  are p r e s e n t  integer while  pattern, desired fringes.  as the vacuum  simultaneously  The i n t e r f e r e n c e p a t t e r n t h a t i s t h e n  w i l l d i s p l a y contours o f c o n s t a n t P, i n t e r f e r e n c e maxima is  as a phase  N  Upon r e c o n s t r u c t i o n , the two wavefronts they w i l l  - 1^, b e t -  q  o r , more a p p r o p r i a t e l y , i n terms o f t h e number o f  waveleng th.)  and  Al = 1  half-integer  P correspond  produced  o c c u r r i n g when P  to minima.  In t h e f r i n g e  the o n l y d i r e c t l y measurable q u a n t i t y i s the f r i n g e number P. pathlength information i s t h e r e f o r e o b t a i n e d  by s i m p l y  The  counting  Each f r i n g e i s l o c a t e d i n the i n t e r f e r e n c e p a t t e r n and i d e n t i f i e d  by i t s corresponding  v a l u e o f P.  - 94 -  >v-  1  FIGURE 21 r a y path w i t h o u t  - 95 -  refraction.  With the axisymmetric c o n f i g u r a t i o n of F i g u r e the  21 , i t i s c l e a r  f r i n g e number depends o n l y on y  l - X (y -y(r))dx r  P(y)  whereas the r e f r a c t i v e i n d e x Equation  B  ,  o  X  r  u(r).  i s a function  o f the r a d i a l  [16] can be shown to be the Abel t r a n s f o r m  Standard n u m e r i c a l r o u t i n e s  coordinate  be used  radial  strictly  valid  assumes  straight  lines.  this  explicitly  inversion  d a t a becomes an extremely lengthy  that  In the f o l l o w i n g  and-complex  s e c t i o n , the problem  i n an axisymmetric o b j e c t i s o u t l i n e d and the assumption  when performing  i n order  to i l l u s t r a t e  interferometry  fringes  the  care  of  are  inter-  procedure,  and,  an u n s u i t -  of r a y r e f r a c t i o n of s t r a i g h t  w h i c h must  on h i g h l y r e f r a c t i n g o b j e c t s .  - 96 -  longer  the r a y p a t h s  the d a t a can be ambiguous enough to make i n t e r f e r o m e t r y  paths i s c o n s i d e r e d  distribu-  i s no  However, w i t h o u t t h i s assumption the u n f o l d i n g  able d i a g n o s t i c .  to  i s not so s t r a i g h t forward i f r a y r e f r a c -  In p a r t i c u l a r , A b e l  in fact,  r.  function  to the d i s t r i b u t i o n o f  t i o n i s taken i n t o account.  ferometric  ]  ng(r).  i n the i n t e r f e r e n c e p a t t e r n  since  can then  the complete  The a n a l y s i s and e q u a t i o n s l e a d i n g P(y)  6  r e l a t i o n s h i p between  ( e . g . F a n , 1975)  A b e l i n v e r t the i n t e r f e r o m e t r i c d a t a to g i v e u ( r ) and t h e r e f o r e  1  A  the o b s e r v a b l e f u n c t i o n , P(y) and the l i n e i n t e g r a l of the d e s i r e d  tion  that  be  line taken  7.5  The  Problem o f Imaging  In order  to h e l p reduce the e f f e c t s of r e f r a c t i o n , w a v e f r o n t s  recorded  by using  a l e n s or system of l e n s e s  directly  on  the  photographic  plate.  This  to form an image of the i s of  course  obvious approach to the problem of r e f r a c t i o n , depending imaging process  i s viewed.  the o b j e c t , i s of i n t e r e s t .  directions can  the  then see  cannot be  two  as f o l l o w s .  By producing  original  r a y s may  and  phase  the  image o f  object  some i m a g i n g  basic question  to be c o n s i d e r e d  the  point  only  point i n  object,  a  lens  of  in question.  the One  e l e m e n t when r e f r a c t i o n  i n t h i s s e c t i o n can  to the o b j e c t , must the image plane be  considerably  be  stated  Given an axisymmetric r e f r a c t i v e index d i s t r i b u t i o n , where, i n  t i o n i s c l e a r l y r e l a t e d to the p r e s e n t more g e n e r a l  plasma experiments the plasma contained  interest.  i n the  has  shown t h a t r a y c u r v a t u r e (the plane x=0  to This  Z-pinch i n v e s t i g a t i o n , b u t  For  neglect ques-  i t is  of  example, i n v i r t u a l l y a l l l a s e r /  f o c a l volume  l a s e r i s c y l i n d r i c a l or c o n i c a l . can  t h e r e f o r e be d e s c r i b e d  i n an  system. E q u a l l y important i s t h a t such plasmas have  h i g h e l e c t r o n d e n s i t i e s and This question  l o c a t e d i n order  i n t e r f e r o m e t r i c data?  f o c a l volume of the  axisymmetric c o o r d i n a t e  axis  scene r a y , a t a g i v e n  r e l a t i o n s h i p , independently  have l e f t  the n e c e s s i t y of using  an  the e f f e c t s of r e f r a c t i o n when a n a l y z i n g  The  actual  neglected. The  relation  the  the  less  From the p o i n t of view of i n t e r f e r o m e t r y ,  the phase r e l a t i o n s h i p between r e f e r e n c e  a c t s to r e s t o r e  object  a more or  on how  are  are  therefore strongly refracting objects.  been addressed, i n p a r t , by V e s t  e f f e c t s can  plasma  the assumption of s t r a i g h t l i n e paths, w i l l y i e l d  the  correct distribution  u(r) to w i t h i n a few  percent.  t o be v a l i d  very  of  extreme  cases  Then, A b e l  i f the  f r i n g e d a t a , based on  objects.  i s imaged.  neglected  the  for  21)  be  has  i n v e r s i o n of  even  of Figure  in fact  (1975) who  r e f r a c t i o n by  However, o n l y the image plane l o c a t e d  symmetry was  examined.  In  order  to o b t a i n  - 97  -  T h i s r e s u l t was  p r e c i s e l y on  a more c o m p l e t e  shown  axisymmetric the  axis  picture  of and  therefore gain a better understanding r e s u l t s , i t was f e l t planes,  that  o f the t r u e  consideration  should  l i m i t a t i o n s of  be g i v e n  to other  the e a r l i e r d i s c u s s i o n s o f the Thomson s c a t t e r i n g r e s u l t s , t h i s indeed  ments. ) planes  shown i t s e l f  have been  u =  i s unity.  be shown how  on  possibility experi-  various  image  analyzed. 22 d e p i c t s a g a i n  an axisymmetric r e f r a c t i v e index d i s t r i b u -  t o a r a d i u s R Q , beyond which the r e f r a c t i v e index  u ( r ) extending  The probe beam i s c o l l i m a t e d and e n t e r s  to the x - a x i s .  (Based  to be q u i t e r e a l i n the p r e s e n t d i a g n o s t i c  In the f o l l o w i n g d e s c r i p t i o n i t w i l l  Figure tion  image  p a r t i c u l a r l y i n view o f the f a c t t h a t i t may n o t always be p o s s i b l e  t o know b e f o r e hand where p r e c i s e l y the plasma w i l l be l o c a t e d .  has  Vest's  A p h o t o g r a p h i c p l a t e , used  imaged i n t o the o b j e c t a t the plane x =  from the l e f t ,  to record  parallel  the w a v e f r o n t s , i s  X£ -j . m a  e  In the presence o f the o b j e c t , one r a y o f the probe beam i s shown entering path CD. x-axis.  the d i s t r i b u t i o n a t a h e i g h t y = B and t r a v e l l i n g This r a y leaves  the o b j e c t  In the d i s c u s s i o n o f r e f r a c t i o n angles  t i a l r a y path was g i v e n  the angular  =  |  (  u  2  r  2 .  B  ^ with  respect  to the  i n Chapter 3, the d i f f e r e n -  i n c y l i n d r i c a l coordinates  iX  and  a t an a n g l e  the r e f r a c t e d  by Bouguer's  formula:  2 ^ ,  [  d e v i a t i o n can then be determined  3  ]  ( S c h r e i b e r , e t a l . , 1 973)  as:  R  o  iKB) = 2cos (B/R ) - 2  (dr/d0)- dr  _ 1  1  o  r The  .  m  lower i n t e g r a t i o n l i m i t i s the i n f l e c t i o n p o i n t o f equation  the d e r i v a t i v e i s z e r o .  To avoid a d d i t i o n a l c o m p l i c a t i o n s  [ 3 ] , where  to t h i s d e s c r i p -  t i o n , i t w i l l be assumed t h a t there i s o n l y one such s t a t i o n a r y p o i n t  - 98 -  with-  FIGURE 22 Imaging  i n a strongly refracting  - 99 -  plasma.  in  the d i s t r i b u t i o n .  The e q u a t i o n s  i f d e s i r e d , i n a piecewise  presented  here can be e a s i l y  f a s h i o n , t o i n c l u d e more e l a b o r a t e  extended,  distribution  functions. Now, when the r a y i n q u e s t i o n , distribution, i t travels Extrapolating  a straight  backwards, t h i s s c e n e  namely  line  path  the scene dy/dx  ray intersects  r a y , e x i t s the  = const.  = tan  t h e image p l a n e  h e i g h t y = B^. When the r e f e r e n c e exposure i s taken,  .  at a  the o b j e c t i s n o t p r e -  s e n t and the r a y which w i l l i n t e r f e r e w i t h the above scene r a y i s j u s t  that  r e f e r e n c e r a y which a l s o i n t e r c e p t the image plane  This  r e f e r e n c e r a y i s shown i n F i g u r e 22 t r a v e l l i n g  a t h e i g h t y = B^.  p a r a l l e l t o the x - a x i s  along  the p a t h GEHF. The to  r e f e r e n c e and scene r a y s o f F i g u r e 22 w i l l  according  t h e i r r e l a t i v e phase, or o p t i c a l path d i f f e r e n c e , a t t h e p h o t o g r a p h i c  plate.  To determine  the path  d i f f e r e n c e , consider  which, i n s i d e the d i s t r i b u t i o n , the i n t e g r a l o f tal  interfere  t r a v e l s an o p t i c a l  u ( r ) d s from p o i n t C t o p o i n t D.  a r c segment along  the r e f r a c t e d p a t h .  (ds)  2  2  equation  L g i v e n by  Here, ds i s an i n c r e m e n coordinates  2  = (dr) (l+r (d6/dr) )  Using  the scene r a y  pathlength  In c y l i n d r i c a l  = ( d r ) + (rd9) 2  2  first  2  .  [3] and the assumption t h a t t h e d i s t r i b u t i o n  i s symmetric  about the s t a t i o n a r y p o i n t g i v e s :  R  °  u rdr  .  2  l  1  8  l  r  m The noting  r e f e r e n c e r a y path  t o be compared  with  L i s found  t h a t both r e f e r e n c e and scene r a y s can be c o n s i d e r e d  p o i n t s G and C r e s p e c t i v e l y .  Secondly,  -  by  first  i n phase a t the  on the e x i t s i d e o f t h e d i s t r i b u -  100 -  tion,  the curve through p o i n t s D and H i s a c i r c u l a r  apparent p o i n t o f o r i g i n o f the two r a y s .  a r c c e n t e r e d a t the  Through an i d e a l imaging  system,  both r a y s w i l l t r a v e l the same o p t i c a l p a t h f r o m D o r H t o t h e r e c o r d i n g film.  T h e r e f o r e , the o p t i c a l p a t h d i f f e r e n c e  between t h e r e f e r e n c e and  scene r a y s shown w i l l be:  The i n t e r f e r e n c e p a t t e r n observed  will  display  contours  s t a n t d e l t a , and the i n t e r f e r o g r a m i s analyzed by simply counting  of  con-  fringes.  For the experiment d e p i c t e d i n F i g u r e 22, t h e measured d i s t r i b u t i o n  of  f r i n g e s i n the image plane w i l l be c a l l e d M, where:  M(y) =  A(y)/X  .  [20]  Because the r e f r a c t i v e index d i s t r i b u t i o n i s axisymmetric, M and d e l t a a r e indicated e x p l i c i t l y plane.  to be o n l y a f u n c t i o n o f the y c o o r d i n a t e i n the image  I m p l i c i t l y though, M i s understood  the l o c a t i o n of the image p l a n e .  to be a l s o a f u n c t i o n o f Ximage'  Given a s p e c i f i c  refractive  index  dis-  t r i b u t i o n , e q u a t i o n s [ 3 ] , and [17] t o [20] a l l o w s the f r i n g e f u n c t i o n M t o be c a l c u l a t e d  f o r any d e s i r e d  image p l a n e .  The q u e s t i o n being asked does the observed equation  here can now be r e s t a t e d as f o l l o w s .  f u n c t i o n M(y) d i f f e r  from  the f r i n g e  function  [ 1 6 ] , where P(y) i s c a l c u l a t e d on the assumption  t i o n takes p l a c e ?  I f P and M d i f f e r  the observed d a t a w i l l not y i e l d  significantly,  the c o r r e c t  that  no  How  P(y) i n refrac-  then Abel i n v e r s i o n o f  refractive  index  distribu-  tion. As the e q u a t i o n s i n v o l v e d  a r e n o t v e r y amenable t o a n a l y t i c a l  i n v e s t i g a t i o n , they have been s o l v e d n u m e r i c a l l y , w i t h  the observed  assumed f u n c t i o n s , P and M, being compared i n the f o l l o w i n g  - 101 -  manner.  and  The  image plane i s d i v i d e d  the spacing g i v e n by y  m a x  i n t o N e v e n l y spaced v a l u e s o f y,  / N , where:  (Y >. max> = 0.  M  v  Depending o f course on the image plane chosen, w i l l extend out to a t l e a s t y  m a x  = R.  differ  the observed  fringe pattern  A l s o , f o r each of the N y - c o o r d i n -  D  a t e s i n the observed p a t t e r n , the s t r a i g h t calculated.  with  The measured and assumed  line  fringe  fringe  function,  P(y) i s  p a t t e r n s are determined  to  by an amount:  N P(0)  With  I '{M(y.)-P(y.)} /N i=l  [21]  2  the m a j o r i t y o f the c a l c u l a t i o n s t h a t were performed,  tially  i n v a r i a n t f o r N > 10.  = 50 was  used  However, f o r those r e s u l t s p r e s e n t e d  = 0) , makes sigma  s i z e o f the r e f r a c t i v e index d i s t r i b u t i o n , used as a b a s i s f o r comparing  so  independent that  a l a r g e v a r i e t y of  S e v e r a l f u n c t i o n a l forms  the f o l l o w i n g  essenhere,  N  to ensure a c o m p l e t e l y r e p r e s e n t a t i v e sampling. The n o r m a l i z -  a t i o n f a c t o r P(y = 0) = M(y  were examined.  sigma was  f o r the  of  equation  the [21]  actual can  be  experiments.  refractive  index  distribution  As a t y p i c a l example, e q u a t i o n [21] w i l l be presented using parabolic  function:  y(r) = 1 - e ( l - r ) 2  , r < 1  [ 2 2 ]  , r > 1 .  = 1  F i g u r e 23 d i s p l a y s s e v e r a l curves o f c o n s t a n t s i g m a , f u n c t i o n o f the r e f r a c t i v e  index  on-axis  - 102  -  and  the  location  g i v e n as  o f the  a  image  plane.  The  cated  a x i s of symmetry f o r the o b j e c t i s l o c a t e d  i n Figure  22.  Given the r e f r a c t i v e a t r =  the e r r o r i n t r o d u c e d  by assuming  axis.  As  well,  for  r e f r a c t i v e index begins to d e v i a t e  error  1/10  might be  located within  the diameter of the It will  be  value  of x.  lens  Thus, the  the  (x < 0), or i n f r o n t  (x >  very  allowed  dramatically so  extreme  l e s s than 5%,  i n Figure  image p l a n e s  23,  axis,  being  l e n s and  combined  had  the  at  as  the  example  the  then  average  the  better  a  apparent slightly  considered  image t h a n +_  are  optimum positive  the  image  i n the  present  d i s p l a c e the vacuum image more  towards  e f f e c t of  the  i t will,  'plasma  r e s u l t s i n an image of the a x i s of symmetry.  < 0 i n equation  the  y ( r = 0) = 0.8,  When the o b j e c t i s i n p l a c e ,  the o b j e c t c o n s i d e r e d e  that  j u s t i n f r o n t of the  case, a c t l i k e a d i v e r g i n g the a x i s .  i s to be  that  as  A not  that, i f , at  indi-  shows  increase  the o b j e c t with a p r e c i s i o n o f  also  However, the  l o c a t i o n s i n vacuum.  23  as  object.  noted  image plane i s l o c a t e d  decreases  from u n i t y .  i n the observed f r i n g e p a t t e r n  plane must be  0,  a p a r t i c u l a r maximum e r r o r ,  l a t i t u d e i n l o c a t i n g the image p l a n e  (Sweeney, e t a l . , 1976)  Figure  s t r a i g h t l i n e paths w i l l  image plane i s moved i n c r e a s i n g l y f a r t h e r behind 0) of the  0,  at x =  On  lens' the  and  external  other  hand, i f  a r e f r a c t i v e index always l a r g e r than 1,  that i s ,  [22] , the apparent optimum image plane would be  slightly  negative. There are which should error  i n the observed  ing  the  23 i n d i c a t e s o n l y the  rays.  S p e c i f i c areas o f  t h a t can be  s i g n i f i c a n t l y more  where the g r a d i e n t s  t h a t must be  traversed  Secondly, though the parameter sigma i s a n a t u r a l c h o i c e f r i n g e p a t t e r n s M(y)  and  P(y), c r i t i c a l  However, from an e x p e r i m e n t a l s t a n d p o i n t ,  o n l y M(y).  Since  the Abel i n v e r s i o n p r o c e s s  -  103  -  can  23,  average  a  the  given  severe, are  very  f o r compar-  examination of the s t r a i g h t  l i n e path assumption must u l t i m a t e l y be performed on y(r).  i n Figure  f r i n g e p a t t e r n when i t i s assumed t h a t  show d e v i a t i o n s  p a r t i c u l a r l y i n regions  [21], as presented  Figure  been g e n e r a t e d by u n r e f r a c t e d  fringe pattern w i l l  steep.  a s p e c t s of e q u a t i o n  be k e p t i n mind. F i r s t l y ,  introduced  p a t t e r n has  two  the be  the  desired  basic viewed  function  observable as  a  is  weighted  image plane, x  FIGURE 23 Errors introduced  i n an i n t e r f e r o g r a m  -  104  by assuming  -  straight line  paths.  i n t e g r a t i o n over the  slope of the f r i n g e , f u n c t i o n ,  p r i a t e to make comparisons based on on  the  functions The  t r i v i a l one The  the d e r i v a t i v e s of M and  has  imaging  y e t to be  in highly  solved  more  P,  appro-  rather  than  is a  non-  satisfactory  way.  r e f r a c t i v e objects  i n any  generally  c a l c u l a t i o n s t h a t have been shown here do,  c a t i o n of the  l i m i t a t i o n s of i n t e r f e r o m e t r y  s i t y plasma.  For  the p r e s e n t  index on a x i s w i l l be has  be  themselves.  problem o f and  i t may  a s i z e the order  about t h i s p r e c i s i o n , F i g u r e dominated by imaging  as a d i a g n o s t i c  Z-pinch d i a g n o s t i c s , the  i n the range 0.99 of a few  however, g i v e a b e t t e r  t o 0.98.  m i l l i m e t e r s and  can  Since  for  high  detail  the complete e x p e r i m e n t a l  metric  measurements on  The  the Z - p i n c h  c u r r e n t l y be  following  arrangement used  the Z-pinch plasma.  -  105  -  den-  minimum r e f r a c t i v e  chapter  plasma  located  23 shows t h a t these i n v e s t i g a t i o n s w i l l  considerations.  indi-  not  describes  to p e r f o r m  with be in  i n t e r f ero-  CHAPTER 8  LAYOUT OF THE  INTERFEROMETRIC EXPERIMENT  i  8.1  Introduction The l i g h t s o u r c e f o r p r o d u c i n g i n t e r f e r o g rams i s a g a i n a r u b y  laser. the  O p e r a t i n g the l a s e r i n Q-switched mode produces e x p o s u r e  20 t o 30 ns range.  However, the e l e c t r o n d e n s i t y  c a n t l y over the d u r a t i o n of a Q-switched p u l s e always be c o n s i d e r e d  stationary.  The  effect  so  can change  that  attempted w i t h a Q-switched p u l s e ,  factory.  The  oscillator  first  section  in this  signifi-  the plasma  o f plasma  motion  exposure w i l l be to smear out the i n t e r f e r e n c e p a t t e r n . metry was  times i n  cannot  during  Though i n t e r f e r o-  the r e s u l t s  were n o t  satis-  c h a p t e r shows a s i m p l e r u b y  t h a t uses c a v i t y dumping g e n e r a t i n g  an  much s h o r t e r  light  laser  pulses.  The remainder of the chapter o u t l i n e s many p e r t i n e n t d e t a i l s of the r e s t of the  e x p e r i m e n t a l arrangement  ence beam p a t h s as w e l l  including  the o p t i c s o f t h e s c e n e  as p h o t o g r a p h i c p r o c e s s i n g  and  and  refer-  reconstruction  data.  8.2  C a v i t y Dumping o f the L a s e r O s c i l l a t o r The i d e a and t h e o r y of l a s e r c a v i t y dumping was  A. V u y l s t e k e (1963).  S i n c e t h e n , many d i f f e r e n t  f i r s t p r e s e n t e d by  arrangements  used to e x t r a c t s h o r t d u r a t i o n l i g h t p u l s e s from a l a s e r 1973;  Hamal, 1978).  Here, a v e r y simple scheme i s used  have  cavity and  the  (Siegman, essential  a s p e c t s o f the procedure can be d e s c r i b e d w i t h the a i d o f F i g u r e upper p o r t i o n of t h i s f i g u r e shows the c u r r e n t arrangement the  oscillator  24.  The  of components i n  cavity.  The r e a r m i r r o r i s 100% r e f l e c t i n g e t a l o n remains as a f r o n t m i r r o r . polarizer  been  PC1  and  w h i l e the p r e v i o u s l y PC2  are pockels c e l l s  i s c a l c i t e i n a Glan-Thompson arrangement.  -  106 -  described and  the  Without PC2 p r e s e n t ,  100%  pol.  ruby rod  etalon  FIGURE 24 Oscillator  and a m p l i f i e r  sections  - 107  of the c a v i t y dumped  -  laser.  the c a v i t y appears as a c o n v e n t i o n a l p o l a r i z e r provide and,  with  the Q-switching  no v o l t a g e  transmitting  applied,  Q-switched  action.  PC2 i s p l a c e d  i t behaves merely  the q u a r t e r  the ruby rod i s pumped. t o zero, now r e n d e r i n g  as a p a s s i v e ,  wave r o t a t i o n v o l t a g e  In F i g u r e  Photons which now d o u b l e  pass  time i t t a k e s  This i n i t i a t e s  wave v o l t a g e  t o dump a l l l i g h t  L the d i s t a n c e between  have  i s applied  from  i n s i d e the c a v i t y i s  I f n i s the average r e f r a c -  f r o n t and r e a r  mirrors,  and c i s t h e  the m i r r o r - t o - m i r r o r  transit  time.  improvement over the Q-switched  pulse  duration.  with a voltage pulse  that i s s h o r t e r  o f c a v i t y dumping pulses  In order  the double  makes i t q u i t e  transit  supplied  time.  The  an a t t r a c t i v e method f o r  i n the 1 t o 10 ns range. t o e x t r a c t h i g h energy p u l s e s  consider  replacing  the e t a l o n  m i r r o r . The e t a l o n here p r o v i d e s temporal coherence l e n g t h e t a l o n , though r e p r e s e n t i n g i s simply  than  This i s However,  the c a v i t y l e n g t h need n o t l i m i t the pulse width s i n c e PC2 can be  normally  t o PC2.  their polarization  C u r r e n t l y , nL =75 cm g i v i n g a p u l s e width o f about 5 n s .  generating  density  then the c a v i t y dumped p u l s e w i l l have a t o t a l d u r a t i o n o f  a p p r o x i m a t e l y twice  a considerable  build-  or dumped by the p o l a r i z e r .  determined p u r e l y by the c a v i t y t r a n s i t time.  speed o f l i g h t ,  on PC1 i s dropped  However, when t h e p h o t o n  t h r o u g h PC2 w i l l  r o t a t e d by 90° and be r e f l e c t e d  while  24, the p r e f e r r e d p o l a r i z a t i o n i n s i d e  i n s i d e the c a v i t y i s maximum, the q u a r t e r  simplicity  freely  i s h e l d on PC1  PC1 a l s o f r e e l y t r a n s m i t t i n g .  the c a v i t y i s i n the plane o f the page.  t - 2 nL/c,  i n s i d e the c a v i t y  A t maximum i n v e r s i o n the v o l t a g e  up o f the Q-switched p u l s e .  t i v e index,  PC1 and t h e  component.  Initially,  The  oscillator.  by c a v i t y dumping  with  a second  one would  100% r e f l e c t i n g  l o n g i t u d i n a l mode s e l e c t i o n t o improve the  o f the l a s e r .  Light  coupled  o u t t h r o u g h the  a s i g n i f i c a n t f r a c t i o n o f the a v a i l a b l e energy,  rejected.  - 108 -  The  lower p o r t i o n o f F i g u r e  24 shows t h e r e m a i n d e r  l a s e r system, which i s s i m p l y a double pass a m p l i f e r  stage.  o f the ruby The o n l y odd  component here i s a second c a l c i t e p o l a r i z e r used to s t e e r the beam through the  amplifier.  The  entire  The reason f o r t h i s  optical  Helium-Neon l a s e r . first  system  i s one o f e x p e r i m e n t a l c o n v e n i e n c e .  i s aligned  using  t h e beam  In the c a v i t y dump d i r e c t i o n ,  c a l c i t e p o l a r i z e r normal t o the e x i t f a c e .  ment beam and ruby l a s e r beam e x i t the o s c i l l a t o r erent angles. difference  Dispersion data f o r c a l c i t e  d i s p e r s i o n of c a l c i t e , allowing  the  He-Ne  Consequently, t h e a l i g n cavity at s l i g h t l y  (Machewirth,  diff-  1979) shows  this  the whole experiment to be a l i g n e d  with  O p t i c s o f the Beam Paths leaving  a p p r o x i m a t e l y 2.5 mm.  the a m p l i f i e r ,  pinhole,  i s used  to f i l t e r  F i g u r e 25 shows a p a r t i a l l y interferometer  the ruby l a s e r has a beam diameter o f  Natural d i v e r g e n c e over  beam diameter t o about 6 mm.  and  collimate  simplified  t h e beam  version  plane  for interferometry.  o f the remainder  the beam through a 50% r e f l e c t i n g  i n t o the d i s c h a r g e v e s s e l .  o f the  by l e n s  with a t o t a l  i s housed  by the d o t t e d r e c t a n g l e i n F i g u r e 25. i s limited  provides equal  A system o f t h r e e l e n s e s p r o d u c e s  The p h o t o g r a p h i c p l a t e i t s e l f  optics  mirror  The scene beam i s d i r e c t e d  plasma a x i s on the p h o t o g r a p h i c p l a t e ,  imaging  i n c r e a s e s the  A f i n a l x4 beam expander, w i t h a f o c a l  amplitude r e f e r e n c e and scene beams.  x3.5.  a 9 m path  optics.  Passing  ted  l i g h t does not l e a v e t h e  laser.  After  the  l o w power  to be a p p r o x i m a t e l y 0.05°. The second p o l a r i z e r compensates f o r  the  8.3  of a  radially  an image o f  magnification of  i n a l i g h t t i g h t box i n d i c a -  The a n g u l a r a c c e p t a n c e  L1 t o a f u l l  cone  of the  a n g l e o f 7.2° o r  F/8.0. In  the r e f e r e n c e arm, l e n s L2 f o c u s s e s the r e f e r e n c e beam  a spatial f i l t e r  through  p i n h o l e P1. The beam s u b s e q u e n t l y expands f r e e l y t o s t r i k e  ~ 109 "  FIGURE 25 O p t i c s o f the i n t e r f e r o m e t r y  110  -  experiment.  the p l a t e  a t an a n g l e  o f 5° w i t h  r e s p e c t to the scene  l e n s e s i n the r e f e r e n c e arm s e r v e s i m p l y t o i n v e r t recombined wave f r o n t s have the proper  this  beam. Two  other  beam so t h a t t h e  s p a t i a l o r i e n t a t i o n with r e s p e c t t o  each o t h e r . Even w i t h the p r o v i s i o n s f o r beam f i l t e r i n g , of  the l a s e r was n o t p a r t i c u l a r l y good.  the s p a t i a l  Lense L2 was chosen to expand t h e  r e f e r e n c e beam by e x a c t l y t h e same amount as t h e s c e n e adjusting  beam.  T h e n , by  m i r r o r M1, both beams c o u l d be p r e c i s e l y o v e r l a p e d on t h e p l a t e .  Lack o f s p a t i a l coherence coherence,  was t h e r e f o r e not a problem. C o n s i d e r i n g  both beam paths a r e matched to w i t h i n 5 t o 10 mm over  d i s t a n c e from beam s p l i t t e r duce good q u a l i t y  8.4  coherence  to p l a t e .  temporal  t h e 8.5 m  T h i s matching was s u f f i c i e n t t o p r o -  fringes.  Recording  and P o s t Exposure P r o c e s s i n g  The wave f r o n t s a r e r e c o r d e d on Kodak type 120-02 h i g h holographic p l a t e s .  T h i s 0.006 mm  ween 4 and 6 (depending  t h i c k emulsion  resolution  has a c o n t r a s t index  bet-  on development t i m e ) and r e q u i r e s an e x p o s u r e o f o  about 300 e r g s / c m both  exposures  2  a t 7000 A t o produce a developed  a r e made, t h e p l a t e s  d e n s i t y D = 1.0.  are processed  i n the  recommended f a s h i o n using D-19 f o r 5 minutes as the d e v e l o p e r Many o f the p h o t o g r a p h i c h i g h c o n t r a s t , making  emulsions  them v e r y s e n s i t i v e  available  ensure  shot t o s h o t ,  exposures  f o r holography  to v a r i a t i o n s  are biased  t h a t each shot g e t s f u l l y r e c o r d e d .  have a d e n s i t y u s u a l l y ranging struction  then  vapour method  i s to bleach  from  1 t o 4.  the emulsion  (Graube, 1974).  - 111 -  towards  i n exposure.  using  have Be-  by 50% o r  the heavy  After development, The f i n a l  standard  stage.  cause o f t h i s , and s i n c e the ruby l a s e r I n t e n s i t y can f l u c t u a t e more from  After  side to  the p l a t e s  step before  recon-  a s i m p l e , d r y , bromine  The  procedure o f heavy over exposure and s u b s e q u e n t b l e a c h i n g i s  quite standard interested ity.  i n holographic  i n producing  As w e l l , bleached  (Chang, 1970).  interferometry.  This  i s because  high c o n t r a s t f r i n g e s r a t h e r than r e c o r d i n g holograms have very h i g h d i f f r a c t i o n  one i s linear-  efficiencies  T h i s g r e a t l y f a c i l i t a t e s both alignment o f the r e c o n s t r u c -  t i o n o p t i c s , and photographing When r e c o r d i n g  o f the i n t e r f e r e n c e p a t t e r n .  the holograms, the p l a t e i t s e l f was imaged onto the  plasma a x i s t o e l i m i n a t e r e f r a c t i o n  effects.  In order  to maintain  this  f e a t u r e i n r e c o n s t r u c t i o n , the i n t e r f e r e n c e p a t t e r n must be r e c o r d e d  a t an  image o f the p l a t e .  using  helium-neon l a s e r  Reconstructions  l i g h t and a simple,  o f the wave f r o n t s are o b t a i n e d  s i n g l e l e n s imaging a r r a n g e m e n t . The  helium-neon l a s e r s e r v e s as the o r i g i n a l r e f e r e n c e illuminated cess.  Using  beam and t h e p l a t e i s  from the emulsion s i d e , as was done d u r i n g o n l y the f i r s t order  transmitted  light  the r e c o r d i n g  (corresponding  pro-  to the  o r i g i n a l scene beams), the p l a t e , and t h e r e f o r e plasma a x i s , i s imaged onto ordinary polaroid film.  High r e s o l u t i o n f i l m i s not r e q u i r e d to r e c o r d the  i n t e r f e r e n c e p a t t e r n s i n c e the l e n s a l l o w s as d e s i r e d .  - 112 -  the p l a t e image to be  magnified  CHAPTER 9  9.1  RESULTS FOR THE Z-PINCH PLASMA  General F e a t u r e s o f the I n t e r f e r eg rams T h i s s e c t i o n p r e s e n t s a q u a l i t a t i v e i n t e r p r e t a t i o n and d i s c u s s i o n  of  the f r i n g e p a t t e r n s t h a t were o b s e r v e d .  prior  to f i r i n g  during  the d i s c h a r g e .  The f i r s t  e x p o s u r e was  The second exposure, made a t v a r i o u s  the p i n c h phase, i s a g a i n r e f e r e n c e d i n time  to the d l / d t  few r e c o n s t r u c t e d i n t e r f e r e n c e p a t t e r n s are shown i n F i g u r e cular  field  of view r e p r e s e n t s the h o l e s  The z - a x i s of the d i s c h a r g e v e s s e l corresponds  diameter  o f these  axis.  This  parallel  The  is clearly  not the case  to a l e f t  perturbation  of the access  o f the h o l e s  h o l e s i n the outer r e t u r n The  cir-  to r i g h t  would  stages  w a l l o f the  i s of course  Along  photograph  T h i s l a c k o f symmetry  the i n t e r i o r  i n the v e s s e l .  Each  the f o r m a t i v e  p o r t s , there  complex d i s t o r t i o n o f the magnetic f i e l d  here.  structure.  i n t r o d u c e d i n t o the plasma c o l u m n d u r i n g  the v i c i n i t y  A  t o , and s y m m e t r i c a l l y centered about the  d i s c h a r g e , when c u r r e n t i s flowing along In  26.  the plasma had p e r f e c t c y l i n d r i c a l symmetry, the f r i n g e s  d i s p l a y s q u i t e a complex two d i m e n s i o n a l is  trace.  circles.  be s t r a i g h t l i n e s running discharge  times  (1.9 cm diameter) i n the d i s c h a r g e  vessel.  If  made  with  o f the vessel.  the p h y s i c a l  this,  there  is a  c o n f i g u r a t i o n s i n c e there are a l s o  conductor.  i n t e r f e r o m e t r i c experiments were performed using a v e s s e l with  f o u r h o l e s , two f o r the d i a g n o s t i c s and two f o r the CO2 l a s e r .  In Chapter  2 i t was p o i n t e d o u t t h a t these h o l e s c o n s t i t u t e a s i g n i f i c a n t f r a c t i o n the c i r c u m f e r e n c e  of  of the v e s s e l so t h a t complete r o t a t i o n a l symmetry of the  plasma column was n o t expected.  However, the s e v e r i t y  o f the d i s t o r t i o n s  c o u l d n o t be p r e d i c t e d and there was some hope t h a t the symmetry would n o t  -  113 -  FIGURE  26  Samples of the i n t e r f e r o g r a m s o b t a i n e d near peak compression. t i o n times a r e :  (A) t = -31 ns,  (B) t = -30 n s , (C) t = -90 ns, and (D) t = +85 n s .  - 114 -  The o b s e r v a -  be degraded to the e x t e n t seen i n F i g u r e 26.  For c o m p a r i s o n ,  gram photographs shown i n F i g u r e 5 were obtained having  o n l y the two d i a g n o s t i c p o r t s .  the plasma symmetry i s w e l l Apart  With o n l y two  a discharge  holes  i n the  This i s best i l l u s t r a t e d  vessel,  taken a t i d e n t i c a l  times  spaced. In these r e g i o n s of the plasma, both i n terms of s p a c i n g , number, and  t = -30  ns.  m e t r i c measurement techniques  1 7  cm  i n going  -3  widely  remarkably  sensitivities  plasma d i s t r i b u t i o n  apparent i n the f r i n g e p a t t e r n . As a v e r y rough g u i d e , by about 1 x 1 0  and  low  of the f r i n g e s . I n t e r f e r o -  are c h a r a c t e r i z e d by t h e i r h i g h  so t h a t , r e l a t i v e l y s m a l l v a r i a t i o n s i n the  26(A)  In the  f r i n g e p a t t e r n s are  contour  shot  in Figures  d e n s i t y r e g i o n s , o u t s i d e the plasma c o r e , the f r i n g e s are broad  d e n s i t y changes  vessel  from the l a c k of symmetry, f o r m a t i o n of the plasma from  26(B), which were both  similar  shadow-  preserved.  t o shot i s q u i t e r e p r o d u c i b l e . and  using  the  would  be  the average e l e c t r o n  from a maxima to the  adja-  c e n t f r i n g e minima. S i m i l a r i t i e s between the f r i n g e p a t t e r n s of F i g u r e s 26(A) extend  i n t o the more dense r e g i o n s of the plasma c o r e .  here are c l o s e l y spaced and d i f f i c u l t  there  details  of  interference patterns. Near the time o f maximum c o m p r e s s i o n  ( B ) ) , the i n t e r f e r o g r a m s out the v i c i n i t y of the  plasma a x i s .  Lack  of  t r u e here t h a t r a y bending w i l l be compensated beams are recombined a t an image o f  the  plasma  must be a b l e to c o l l e c t a l l r e f r a c t e d l i g h t . acceptance cone of F/9  (again  o f t e n do not show a c l e a r  p r i m a r i l y the r e s u l t of r e f r a c t i o n of the p r o b e  passing  structural  (B)  fringes  to see i n these r e p r o d u c t i o n s ,  i s a c o n s i d e r a b l e degree of correspondence between the two  Though the  and  which  i s not  small  through the s t r o n g l y r e f r a c t i n g  -  115  f r i n g e s near beam.  the  a x i s , the  enough  the  and  throughaxis i s  Though i t r e m a i n s  for since  The  26(A)  fringe pattern  interfering  imaging  current  core.  system  o p t i c s has  to c o l l e c t  r e g i o n s of the  -  Figures  those  an  rays  FIGURE 27 I l l u s t r a t i o n of the r e g i o n f o r which i n t e r f e r o g r a m s were  -  116  -  analyzed.  Though r e f r a c t i o n i s a t l e a s t p a r t i a l l y f r i n g e s i n the c o r e r e g i o n , m o t i o n a l b l u r r i n g factor.  The f o l l o w i n g e s t i m a t e  indicates  r e s p o n s i b l e f o r missing  may s t i l l  be a c o n t r i b u t i n g  t h a t the f r i n g e s  c a n a l s o be  smeared o u t d u r i n g a 5 ns probe p u l s e . A ray travelling  through  f r i n g e number P g i v e n by e q u a t i o n  the plasma  [16].  c o l u m n c a n be a s s i g n e d  I f the r a y t r a v e l s  meter o f the plasma, and, o n l y the f i r s t order expansion index  where n i s the average and r v a r y  with  f  =  (  n r / n c  o f the r e f r a c t i v e  ) >  time.  Equation  [1] s u g g e s t s  t h i s c a n c e l l a t i o n e f f e c t i s not q u i t e Over an exposure time Assuming  differentiating  of  At, t h e f r i n g e according  c  at  K  3 g i v e s d r / d t = 1 x 10^ cm s e c  maximum average  Negligible  constant,  number  will  to equation  - 1  .  As a worst case  c h a n g e by  [ 1 ] , then,  AP  1 9  cm . - 3  estimate,  Taking  these  motional  blurring  would  require  AP <<  figures  1.  of a  exposure time cannot be n e g l e c t e d as a p o s s i b l e f a c t o r c o n t r i b u t i n g fringes.  -  117 -  This  However,  the above e s t i m a t e shows t h a t the e f f e c t  absence o f w e l l d e f i n e d  the  1.2.  c o n d i t i o n i s w e l l s a t i s f i e d during much o f the p i n c h phase. maximum compression,  though  }  electron density i s 4 x 1 0  At = 5 ns g i v e s  another.  [23] w i t h r e s p e c t to time r e s u l t s i n :  X n  Chapter  to remain  o f one  complete.  n and r a r e r e l a t e d equation  Both  t h a t , i f the p a r t i c l e  independently  When r d e c r e a s e s , n i n c r e a s e s so t h a t P t e n d s  AP.  [23]  e l e c t r o n d e n s i t y w i t h i n the column, r a d i u s r .  i n v e n t o r y i s f i x e d , n and r do n o t c h a n g e  with  a dia-  (equation [2]) i s used, P w i l l be g i v e n by:  P  n  along  a  near  finite to the  A t e a r l y times, as i n F i g u r e 26(C), and  the plasma i s much l e s s dense,  has c o r r e s p o n d i n g l y weak d e n s i t y g r a d i e n t s .  tion  are  therefore completely  throughout the plasma column. ness and  F i g u r e 26(D)  shows an i n t e r f e r o g r a m t h a t was  T h i s photograph c o r r e s p o n d s plasma has  9.2  negligible  to  the  Plasma motion and  and  f r i n g e s can  be  refracobserved  has been i n c l u d e d f o r complete-  taken w e l l a f t e r peak compression.  shadowgram o f  Figure  5(B)  where  the  blown a p a r t i n a r a t h e r t u r b u l e n t f a s h i o n .  Data P r o c e s s i n g Q u a n t i t a t i v e a n a l y s i s of the data r e q u i r e s t h a t  t i o n P(y) i n e q u a t i o n  [16] be d e t e r m i n e d  i n t e r f e r c g r a m corresponding found, P(y) was (1975), and  from  the  fringe  func-  interferograms.  Each  to a d i f f e r e n t time i n the  Abel i n v e r t e d using  the  pinch  phase.  the n u m e r i c a l r o u t i n e d e s c r i b e d  Once by  Fan  the e l e c t r o n d e n s i t y d i s t r i b u t i o n n ( r ) i s o b t a i n e d . e  C l e a r l y though, complete a n a l y s i s of each i n t e r f e r e n c e p a t t e r n quite a formidable  task s i n c e ( i ) t h e r e are a very l a r g e number of  is  fringes,  ( i i ) the p e r t u r b a t i o n s produced by the access p o r t s have g i v e n an a d d i t i o n al  z-dependence t o the plasma d i s t r i b u t i o n , and  i n t e r v a l observed,  the c o m p l e x i t y  of  the  fringe  ( i i i ) f o r much o f pattern  near  a x i s does not a l l o w f o r an unambiguous assignment o f f r i n g e these r e a s o n s , and  P(y,  z = z ) Q  the p r i m a r y action  the a n a l y s i s has been l i m i t e d i s found  to  a single  laser.  The  z  Q  i s chosen  to correspond  -  for  with  s k e t c h of F i g u r e 27 i s arranged  - 118  plasma For  z coordinate,  as a f u n c t i o n of time i n the p i n c h phase.  s t u d i e s , the c o o r d i n a t e 2  the  time  numbers.  i n t e r e s t i s i n e s t a b l i s h i n g the plasma d i s t r i b u t i o n  p o s i t i o n of the C 0  the  the  z  Q  Since interfocal  to c o r r e s -  pond w i t h  the o r i e n t a t i o n o f the i n t e r f e r o g r a m s  l o c a t e s the r e g i o n of plasma f o r which data l a s e r beam e n t e r s anode and  the  field  of  cathode of the d i s c h a r g e  l e f t of the The  measuring  being  y coordinate  top  of  sketch  The i n t e r a c t i o n  Figure  2 7 with  r e s p e c t i v e l y o f f to the  the  right  minima along  reconstructions  and  scaled  to r e a l The  Though i t may  over  measured,  the  the  two,  are  then  i s very  using  Abel  w i t h i n the  The  region  the  nearly  of  the  axisym-  to make t h i s a s s u m p t i o n ,  the  more important, sources of e r r o r .  plasma  where  in  inverted  region  to s p e c i f y the r a d i a l p o s i t i o n of f r i n g e s , the  of r = y = 0 i s r e q u i r e d .  scan  A l l photo-  coordinates  half-diameter  plasma  not be v e r y s a t i s f y i n g  f o l l o w i n g d i s c u s s i o n p o i n t s out In order  plasma  fringe functions  the assumption t h a t , a t l e a s t  plasma column t h a t i s being  space  the  were made t o a i d  the v e r y c l o s e l y spaced f r i n g e s near the plasma c o r e .  known image m a g n i f i c a t i o n s .  centered  the  of each v i s i b l e maxima and  Highly magnified  g r a p h dimensions are  metric.  is collected.  This  frame.  l i n e i s recorded.  with  view from  of F i g u r e 27.  the  axis, r =  location  0 i s determined  fringe density  i s high.  to  The  be  best  judgement t h a t can be made here i s t h a t the o r i g i n , y = 0, i s u n c e r t a i n  to  no more than + 0.5  of  Figure  26.  The  mm  which corresponds to about + 2 mm  o r i g i n uncertainty enters  i n a r a t h e r complex way.  i n t o the u n f o l d i n g  However, f o r the r e s u l t s t h a t w i l l  net e f f e c t i s p r i m a r i l y an u n c e r t a i n t y , by in  i n the p i c t u r e s  l o c a t i n g the r a d i a l c o o r d i n a t e  computations be  shown,  the same amount as g i v e n  the  above,  a x i s with r e s p e c t to the e l e c t r o n d e n s i t y  d i s t r u b i t i o n , r a t h e r than an e r r o r i n the e l e c t r o n d e n s i t y i t s e l f .  From  q u a l i t a t i v e p o i n t of view, t h i s e f f e c t i s to be e x p e c t e d  inver-  sion i n t e g r a l i s mainly  s e n s i t i v e to  the  since  the  d e r i v a t i v e , dP(y)/dy which  a  is  i n v a r i a n t under t r a n s l a t i o n . The t o the outer  f r i n g e number P must a l s o have a r e f e r e n c e  point  corresponding  boundary y = r  = 0.  Far  D  o f the  plasma where P ( r ) Q  -  119  -  from  the  a x i s , the f r i n g e s are w i d e l y spaced and appear to e x t e n d o f view. The boundary r z o n t a l a x i s being  y.  D  beyond  By e x t r a p o l a t i n g  dure, amounts t o s i m p l y t e r m i n a t i n g  t o l a r g e y, r  and t h e r e f o r e  Q  maximum r a d i u s ,  w h i c h was u s u a l l y  o f the viewing  of r  absolute  was  unimportant- s i n c e  1 0 6 t o 10 1  sities  1  cm  the  and i s q u i t e  - 3  t o be  The p r e c i s e  choice  error introduced  give  This  i s the order o f  to the e l e c t r o n den-  -3  be dominated by the u n c e r t a i n t i e s and assumptions r e q u i r e d  i n h e r e n t l y high  proce-  estimated  the d i s c u s s i o n o f the i n t e r f e r c g r a m s  electron density d i s t r i b u t i o n .  This  cm .  1  this point,  ports.  i n s i g n i f i c a n t compared  o f i n t e r e s t , namely 1 0 8 t o 1020 At  P = 0,  the d i s t r i b u t i o n a t some more o r l e s s  between 1.5 t o 2 times the r a d i u s Q  field  i s o b t a i n e d by p l o t t i n g P ( y ) v s . y, w i t h the h o r i -  i s determined as the p o i n t where P ( y ) becomes h o r i z o n t a l l i n e .  a r b i t r a r y , but large  the  i s , i n part,  s e n s i t i v i t y of interferometry.  may a p p e a r t o to e x t r a c t the  a consequence  o f the  The i n t e r f e r c g r a m s  do indeed  a v e r y d e t a i l e d p i c t u r e o f the plasma, b u t , i n the f o l l o w i n g  section,  a more q u a n t i t a t i v e view i s p r e s e n t e d , and t h i s w i l l t a i n t i e s into better  9.3  density  put the uncer-  perspective.  P l o t s o f the E l e c t r o n D e n s i t y Figure  help  Profile  28 shows t h e i n t e r f e r o m e t r i c  results  f o r the e l e c t r o n  n ( r , t ) over the time i n t e r v a l -90 ns _< t <^ 60 n s . e  A t times  than about t = +50 ns, the plasma has b r o k e n - u p and t h e f r i n g e cannot be a n a l y z e d  (see F i g u r e  26(D)).  Earlier  column has the combination o f l a r g e r a d i u s fringe pattern  t h a t extends w e l l o u t s i d e  -  patterns  than t = -90 ns, the plasma  and low d e n s i t y  the f i e l d  120 -  later  o f view.  and p r o d u c e s a This  makes i t  difficult  to e x t r a p o l a t e  the  fringe pattern  to  large  about the o n - a x i s plasma d e n s i t y i s absent due f r i n g e s near r = 0.  The  p r o f i l e s are extended  p o i n t w i t h a h o r i z o n t a l dashed f r i n g e s could are  l i n e i n order  to  radii.  the  lack  of  the  within  time i n t e r v a l  As w e l l , these dashed  lines  of  the r e s u l t s of the  ments as presented i n F i g u r e  18.  The  density  Thomson  scattering  measure-  o n l y the c e n t r a l 15% o f the  scattering  From t h i s p o i n t of view, i t i s c l e a r  that  the  by  i t is  interfero-  data.  a considerable  electron  the  d a t a of F i g u r e  provided  defined.  somewhat s k e t c h y ,  time span c o v e r e d  metric  system has  28 r e p r e s e n t s  the  be  out.  Though the i n t e r f e r o m e t r i c d a t a a p p e a r s worthwhile here to r e c a l l  data where  shown, b u i l d - u p  the plasma column i s w e l l mapped  first  region  i n d i c a t i v e of the a c c u r a c y with which the plasma a x i s could  However, f o r the  observable  from r = 0 to the  to i n d i c a t e  not be measured with c e r t a i n t y .  Information  c a v i t y dumped  improvement i n the  laser  temporal  resolution  c a p a b i l i t i e s of these e x p e r i m e n t a l i n v e s t i g a t i o n s . Such a l a r g e  discrepancy  i n time s c a l e s makes i t somewhat d i f f i c u l t since, over  the  results yield tion,  the  span  of  the  i n t e r f e r o m e t r i c data,  o n l y a few d a t a p o i n t s .  Also,  s c a t t e r i n g measurements r e p r e s e n t  while the sities.  time  to c o r r e l a t e the  i n t e r f e r o m e t r i c d a t a would be  i n terms of radially  expected  N o n e t h e l e s s , the remainder of t h i s  experiments  the  scattering  spatial  averaged  discussion  will  resolu-  densities,  to show h i g h e r  comparison of the i n t e r f e r o m e t r i c d a t a with p r e v i o u s be  two  peak  den-  provide  r e s u l t s , and  some  i t will  seen t h a t the correspondence i s q u i t e good. A simple judgement of the r e l i a b i l i t y of the d e n s i t y p r o f i l e s  be made on  the b a s i s of an i n v e n t o r y  of e l e c t r o n s .  charge, the  t o t a l number of a v a i l a b l e e l e c t r o n s  0.63  cm ,  x 10  1 9  -1  i s determined by  the i n i t i a l  per fill  e l e c t r o n d e n s i t y p r o f i l e s were i n t e g r a t e d , assuming to f i n d  the  column.  An  total  number  of  electrons  average of ten p r o f i l e s  measured  shows the  -  121  -  Before f i r i n g unit  the  length,  can dis-  namely,  c o n d i t i o n s . Each of cylindrical to be  number  of  within  the  symmetry, the  electrons  pinch to  be  6  electron density  l*10  19  cm" ) 3  FIGURE 28 The plasma d i s t r i b u t i o n during  -  122  -  the p i n c h phase.  0.47  + 0.9  x 10  1 9  cm ,  which accounts  -1  f o r 75% o f the f i l l g a s .  not a l l the gas  w i l l have been swept-up during  the d i s c h a r g e .  I f 25% o f the gas  Of  course,  the e a r l y i m p l o s i o n stage  i s assumed to remain u n i f o r m l y  distribu-  ted w i t h i n the chamber, the background e l e c t r o n d e n s i t y would be 2 x cm . -3  With the o b s e r v a t i o n f i e l d  background e l e c t r o n d e n s i t y Therefore,  limited  to c o m p a r a t i v e l y  i s somewhat b e l o w  a measured c o l l e c t i o n f a c t o r of  75%  the  10 ^ 1  small r a d i i ,  present  represents  of  this  sensitivity.  a  lower  bound.  In view of t h i s , the i n v e n t o r y of e l e c t r o n s i s r a t h e r complete. F i g u r e 29 g i v e s a comparison of the i n t e r f e r o m e t r i c d a t a Thomson s c a t t e r i n g r e s u l t s .  The  open c i r c l e s i n t h i s f i g u r e show the  t r o n d e n s i t y measurements o b t a i n e d s p e c t r o s c o p i c v a l u e a t t = -80  with  the elec-  from the s c a t t e r i n g experiments p l u s  ns.  The  i n t e r f e r o m e t r i c data  i s shown  one as  b a r s , but these bars r e q u i r e some e x p l a n a t i o n . Because the s c a t t e r i n g experiments l a c k s p a t i a l r e s o l u t i o n i n radial direction, averaged over the b a r s  the 2 mm  l e n g t h of the s c a t t e r i n g volume.  i n F i g u r e 29 show the average d e n s i t y assuming  volume was the  the d e n s i t y p r o f i l e s of F i g u r e 28 were t h e r e f o r e  symmetrically  l o c a t e d on the p l a s m a a x i s .  d i s c u s s i o n i n s e c t i o n 6.2  scattered  concerning  s p e c t r a , an attempt was  the  corresponds volume was  to a v e r a g i n g  the  The  red  shift  recalling in  some  i n t e r f e r o m e t r i c data been d i s p l a c e d  lower l i m i t of the bars i n F i g u r e  density profiles  d i s p l a c e d i n the r a d i a l d i r e c t i o n by 1  of  t h a t the s c a t t e r i n g  would be more c o n s i s t e n t w i t h a s c a t t e r i n g volume t h a t had with r e s p e c t to the plasma a x i s .  radially  upper l i m i t  However,  net  made to see i f the  The  the  assuming  29  the s c a t t e r i n g  mm.  Even though there does appear to be a tendency f o r the s c a t t e r i n g experiments to g i v e lower e l e c t r o n d e n s i t i e s , i f e r r o r bars were p l a c e d the s c a t t e r i n g d a t a ,  they would be a p p r o x i m a t e l y  -  123  -  + 30%.  Consequently,  on any  ro  'E o  .4 h  x  c  2  h  -100  time (ns)  •100  FIGURE 29 Comparison o f the i n t e r f e r o m e t r i c and s c a t t e r i n g measurements. Open c i r c l e s show the Thomson s c a t t e r i n g r e s u l t s . The b a r s g i v e t h e c o r r e s p o n d i n g measurements t h a t were e x t r a c t e d from the d e n s i t y p r o f i l e s .  - 124 -  judgement c o n c e r n i n g  imaging  tenuous j u s t i f i c a t i o n .  Nonetheless,  t r a t e s c l e a r l y and most averaged  i n the s c a t t e r i n g this  exercise  importantly, that,  over the s c a t t e r i n g  volume,  experiments  would  i n comparison  i f the d e n s i t y  the i n t e r f e r o m e t r i c  have  illus-  p r o f i l e s are  and s c a t t e r i n g  measurements agree v e r y c l o s e l y . On the other hand, i f the d e n s i t y p r o f i l e s are e x t r a p o l a t e d  to r =  0, the peak e l e c t r o n d e n s i t y on a x i s would be s i g n i f i c a n t l y h i g h e r (about a f a c t o r o f two h i g h e r ) than the s c a t t e r i n g peak d e n s i t y a t maximum compression  d a t a shows.  i s indicated  In p a r t i c u l a r , t h e  to be 7 x 1 0 ^ c m .  i n s e c t i o n 3.5, the shadowgram a n a l y s i s p r o v i d e d an e a r l y 10  1 9  close  cm  - 3  f o r the o n - a x i s  correspondence  d e n s i t y a t maximum compression.  between  these  - 3  Now,  estimate of 6 x Although such a  two v a l u e s may be f o r t u i t o u s , t h e  shadowgram experiment has proven to be a v e r y r e a s o n a b l e e s t i m a t o r .  - 125 -  CHAPTER 10  CONCLUSION AND  T h i s f i n a l chapter w i l l conclude mental i n v e s t i g a t i o n s performed  SUGGESTIONS  the p r e s e n t a t i o n o f  as p a r t of t h i s t h e s i s work.  d i s c u s s i o n s w i l l c o n s i d e r b r i e f l y each of the experiments, providing  the  experi-  The f o l l o w i n g  with  the  ( i ) a review of the s a l i e n t f e a t u r e s of the h i g h d e n s i t y  plasma t h a t have been observed,  ( i i ) a summary o f  ments, with some c o n s i d e r a t i o n g i v e n  to  (iii)  aim  of  Z-pinch  the d i a g n o s t i c e x p e r i -  their  application  to  the  laser/plasma i n t e r a c t i o n studies. The  first  photography,  experiments,  were performed  v i o u s l y unexplored t h i s end,  two  and  intended  h i g h compression  these i n i t i a l  namely, as  an  phase o f  experiments  the  introduction  this  Z-pinch  have been g i v e n  e v o l u t i o n of the on-axis plasma by e s t a b l i s h i n g the b a s i c s t r u c t u r e and dynamics, as phase.  s t r e a k and  having  f u n c t i o n s of  relatively  c o l l a p s e s to a minimum o u t e r shock compressed and  heated  o n - a x i s plasma develops plasma from  from  the  cm.  The  along  the s h e l l c o n t i n u e s to accumulate  and  be  the with  the  pinch  components.  plasma  h i g h d e n s i t y plasma  s u b - m i l l i m e t e r dimensions  To  view of  during  major  pre-  discharge.  a clear  time  the  low e l e c t r o n d e n s i t y (< 1 0  r a d i u s o f 0.25  to form  to  the plasma s i z e ,  The plasma s t r u c t u r e i s c h a r a c t e r i z e d by two  d i f f u s e plasma s h e l l ,  shadowgram  A  cm ),  1 8  - 3  on-axis core.  This  and grows i n s i z e compressed  is  into  as the  core. These i n i t i a l common: to  experiments  they are simple and  experimental d e t a i l s ,  obtained.  a wealth  to do.  one  very i m p o r t a n t  incident  as being  well suited  power d e n s i t i e s ,  of q u a n t i t a t i v e  to the the  interaction  126  -  attention  i n f o r m a t i o n has  laser/plasma  c h a r a c t e r i z e d by s m a l l s c a l e s t r u c t u r e and  -  feature in  Here, with o n l y modest  R e f r a c t i o n methods, such as the shadow p h o t o g r a p h y ,  be o v e r l o o k e d high  easy  have had  been  should  studies.  At  not very  r e g i o n i s known t o  steep d e n s i t y g r a d i e n t s  be  (Milroy,  et.al.,  1978;  Itj, e t . a l . ,  1979).  With a p p r o p r i a t e m o d i f i c a t i o n s ,  ques based on r e f r a c t i o n can be v e r y s e n s i t i v e volume.  probes  of the  interaction  For i n s t a n c e , through a n g u l a r d e c o m p o s i t i o n o f t h e  transmitted  probe beam, one can o b t a i n d i r e c t i n f o r m a t i o n about the p l a s m a and shape w i t h o u t r e q u i r i n g for high s p a t i a l  any s p e c i a l  (and o f t e n expensive) c o n s i d e r a t i o n  experiments,  the plasma  seen to range up to a maximum o f 45 - 50 eV, and  4 x 10  cm ,  1 9  was  -3  closely  temperature  the e l e c t r o n  has been measured over a range o f t h r e e o r d e r s o f magnitude. peak d e n s i t y ,  structure  resolution.  From the Thomson s c a t t e r i n g was  techni-  The  c o r r o b o r a t e d by two  density measured  independent  e s t i m a t e s o b t a i n e d from the s t r e a k and shadowgram o b s e r v a t i o n s . Complex n u m e r i c a l m o d e l l i n g of the p l a s m a discharge plasma.  (Hain, e t . a l . ,  1960)  However, the plasma  parameter  in this  and  p r e d i c t s strong  similar  (Houtman, 1977,  and d e n s i t y .  in a  d i s c h a r g e s (e.g. S t e e l , t o be  A l b r e c h t , 1979)  A l s o , more r e c e n t  inappropriate  this  X-ray measurement t e c h n i q u e s have p r o v e d  inadequate  because  v i t a l for establishing well, i t i s believed one  o f the  few,  routine diagnostic  scattering  experiments  the plasma temperature during  t h a t these Thomson s c a t t e r i n g  i f not  the  first  application  peak  have  Z-pinch  using  the  plasma  therefore  been  the p i n c h phase.  As  experiments r e p r e s e n t  o f the i o n f e a t u r e  as  a  experiments w i l l be of paramount importance f o r the  i n t e r a c t i o n s t u d i e s s i n c e they w i l l i n t e r r o g a t e  al.,  during  tool.  The s c a t t e r i n g  scopic  1978).  because of the h i g h temperature t o examine  The  accessible  et.al.,  attempts  temperature i s too low.  Z-pinch  shock heating o f the o n - a x i s  temperature has not been an e a s i l y  S p e c t r o s c o p i c measurements have p r o v e d compression  collapse  the p l a s m a  a t the  micro-  l e v e l . A l l o f the p a r a m e t r i c p r o c e s s e s expected to occur (Drake, e t .  1974)  have t h e i r s i g n a t u r e s i n the f r e q u e n c y and/or  trum o f the induced plasma  fluctuations.  The s c a t t e r i n g  - 127 -  wavevector experiments  specthat  have been presented were arranged and  s i n g l e shot r e c o r d i n g  to p r o v i d e  of the  entire  f o r high  low  spectral resolution  frequency  f l u c t u a t i o n spec-  trum. In the s t r a y l i g h t can is  introduced  low  frequency regime of s c a t t e r e d  be a very  s t r a y l i g h t can  be  Also,  recently  second d u r a t i o n d i a g n o s t i c p u l s e s .  l i g h t can  should using  further discriminated  with the means made a v a i l a b l e by  not p r e s e n t this  the macroscopic l e v e l ,  a d e t a i l e d p i c t u r e of the  holes  i n the d i s c h a r g e  optical gating  14 show t h a t  on  sub-nano-  method  used  the b a s i s of time o f  in  flight.  these experiments, s t r a y  light  investigations  Consequently,  appear i n an e x t r e m e l y  reproducible  t i o n s i n the be  possible  a cylindrical  to adopt  the  been  shown t h a t ,  manner, any  (Curzon  been the  effort  It i s well established  et.al,  1964).  which e f f e c t i v e l y  to  for p r e c i -  It  methods o f C u r z o n e t . a l . a n d  perturbation  a z i m u t h a l i r r e g u l a r i t y g e n e r a t e d by I t has  has  the plasma column as a r e s u l t of  shape of the v e s s e l w a l l  local  However, b e c a u s e  time w e l l spent i n p r o v i d i n g  s i o n measurements of the d e n s i t y d i s t r i b u t i o n . i n s t a b i l i t i e s d e v e l o p on  the  some u n c e r t a i n t y  fringe patterns.  have  Q u a l i t a t i v e l y , the  r e t u r n conductor have degraded  r e s t o r e the plasma symmetry w i l l be  that  perturbashould, thereby  overwhelms  the  t h o u g h r e f r a c t i o n e f f e c t s on  the  the a c c e s s p o r t s .  even  i n t e r f e r o m e t r i c experiments are not n e g l i g i b l e , p r e c i s e imaging i m p o r t a n t requirement f o r examining for  effi-  the i n t e r f e r o m e t r i c i n v e s t i g a t i o n s  i n t o the a n a l y s i s of the  perturbations  produce  more  light  s c a l e d i n time, s t r a y  plasma d i s t r i b u t i o n .  v e s s e l and  symmetry of the plasma column.  therefore,  for  to p r o d u c e  a s e r i o u s problem f o r f u t u r e s c a t t e r i n g  given  surface  that stray  of  Z-pinch.  At  introduced  against  problem  light via s p e c t r a l r e s o l u t i o n .  been m o d i f i e d  I f the  the  s p e c t r a of F i g u r e  s c a t t e r i n g experiments i s c o r r e s p o n d i n g l y  be  Therefore,  knowing  i n arranging  the b a c k s c a t t e r e d  i s o l a t e d from s c a t t e r e d  the ruby l a s e r has  the p r e s e n t  Firstly,  because of r e f r a c t i o n w i l l a i d  c i e n t beam dumping.  Finally,  important one.  spectra,  the Z - p i n c h p l a s m a  the i n t e r a c t i o n experiments, the plasma r e g i o n  -  128  -  of  itself.  was  not  an  However,  interest will  have  dimensions  the order  o f , and s m a l l e r  T h i s , i n t u r n , w i l l be s i g n i f i c a n t l y plasma column.  Then, i m a g i n g  the CO2 l a s e r f o c a l spot  than, smaller  than  the i n t e r a c t i o n  the dimensions  region  with  i n d i c a t e d by F i g u r e 22 may n o t be p o s s i b l e , p a r t i c u l a r l y p h y s i c a l l i m i t a t i o n s imposed by the s i z e o f the d i s c h a r g e l y , h i g h q u a l i t y imaging  of small  objects  requires  the  be e a s i l y  density  accuracy  v e s s e l . (General-  placing  short  focal  h e r e . ) The  s o l u t i o n would be t o a v o i d r e f r a c t i o n e f f e c t s by using  quency doubled ruby l a s e r can  o f the  i n view o f the  l e n g t h o p t i c s c l o s e t o the o b j e c t - a s i t u a t i o n n o t a c c e p t a b l e most r e a s o n a b l e  size.  light.  tolerated.  fre-  The l o s s i n s e n s i t i v i t y o f a f a c t o r o f 2  The c o r r e s p o n d i n g  increase  i n the c r i t i c a l  (a f a c t o r o f 4) w i l l produce an enormous r e l a x a t i o n o f the imaging  r e q u i r e m e n t s when the e l e c t r o n d e n s i t y i s below about 1 x 1 0 ^ c m . 2  F i n a l l y , by using holography, s h o r t  the time d i f f e r e n t i a l nature  time s c a l e  v a r i a t i o n s i n the  l a s e r i n t e r a c t i o n r e g i o n can be c o m p l e t e l y "background" plasma column. photographing  ns i n t e r - e x p o s u r e  separation.  these  l i n e s without The  filled  isolated  from  p r e l i m i n a r y way b y  the core were completely  Considerable  improvements  i n v e s t i g a t i o n s t h a t were p r e s e n t e d functions.  A thorough  i n this  a 12 this  eliminated  c a n be made  from along  to i r r a d i a t i o n with  t h e s i s have  examination  density  ful-  o f the Z-pinch  compression  g i v e n a complete data base o f i n f o r m a t i o n on the i n i t i a l  be  using  a great deal of d i f f i c u l t y anticipated.  t h e i r intended  ed p r o v i d e  the unperturbed  near peak c o m p r e s s i o n ,  plasma c h a r a c t e r i s t i c s throughout the h i g h  prior  exposure  Though the plasma core does change over  time i n t e r v a l , a l l f r i n g e s o u t s i d e the i n t e r f e r e n c e p a t t e r n .  of double  plasma d e n s i t y i n the CO2  T h i s was t e s t e d i n a v e r y  the plasma column i t s e l f ,  - 3  p h a s e has  target conditions,  the CO2 l a s e r . The experiments t h a t were  present-  a sequence o f micro and macroscopic d i a g n o s t i c methods t h a t c a n  f r u i t f u l l y a p p l i e d t o a d e t a i l e d study  -  of laser/plasma i n t e r a c t i o n s .  129 -  REFERENCES A l b r e c h t , G.F.,  Ph.D.  T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia,  A l b r e c h t , G.F.; K a l l n e , (1978).  E. and Meyer, J . , Rev.  A l l e n , J.E., P r o c . Phys. S o c , Armstrong,  W.T.  B70,  and Forman, P.R.,  24  S c i . Instrum., 4 9 ( 1 2 ) ,  A p p l . O p t i c s 16(1), 229  Barnard, A . J . and A h l b o r n , B.,  Am.  Barnard, A . J . and G u l i z i a , C.,  Can. J . Phys.,  M.  Chen, F.F., Collier,  58, 565  A p p l i e d O p t i c s , 9 ( 3 ) , 713  R . J . , L i n , L.H. (Academic, 1971).  and  Curzon, F.L.; Hodgson, R.T. 281 (1964).  Burchhardt,  and C h u r c h i l l ,  (Gordon  (1975).  5th  Edition,  123  (1970).  (Plenum,  C.B.,  6,  (1980).  of O p t i c s ' ,  In ' I n t r o d u c t i o n to Plasma P h y s i c s ' ,  (1977).  R e a c t i o n s ' Ch.  J . Phys., 4 3 ( 7 ) , 573  and W o l f , E. , i n ' P r i n c i p l e s (Pergamon, 1975).  Chang, M. and George, N.,  1637  (1957).  A r t s i m o v i c h , L.A., i n ' C o n t r o l l e d Thermonuclear and Breach, 1964).  Born,  (1979).  1974).  'Optical  R. J . , J . N u c l e a r  Holography',  Energy  C,  6,  D e s i l v a , A.W. and Goldenbaum, G.C., i n 'Methods o f E x p e r i m e n t a l P h y s i c s ' E d i t e d by R.H. L o v b e r g and H.R. G r i e m , V o l . 9A, C h . 3, 61 (Academic, 1970). Drake,  J.F.; Kaw, P.K.; Lee, Y.C.; Schmidt, G.; L i u , C S . M.N., Phys. F l u i d s , 17 ( 4 ) , 778 (1974).  Evans, D.E.  and K a t z e n s t e i n , J . , Rep.  Fan, L.S. and S q u i r e , W.,  Prog. Phys.,  Graube, A.,  32, 207  Computer Phys. Commun., 10, 98  George, T.V.; G o l d s t e i n , L.; Slama, L. and (2A), 369 (1965). A p p l . O p t i c s , 13  Rosenbluth,  (1969).  (1975).  Yokoyama, M. , P h y s .  Rev.,  137  (12), 2942 (1974).  Grek, B.; M a r t i n , F.; Johnston, T.W.; P e p i n , H.; M i t c h e l , F., Phys. Rev. L e t t . , 41(26), 1811 (1978). Hain, K.;  and  G.  and  Rheault,  Hain, G.; R o b e r t s , K.V.; R o b e r t s , S.J. and K o p p e n d o r f e r , N a t u r f o r s c h g , 15 ( A ) , 1039 (1960).  -  130  -  W. , 7,  REFERENCES H i l k o , B., Meyer, J . , A l b r e c h t , ( 9 ) , 4693 (1980).  G. , and  (Cont'd)  Houtman, H.,  J . A p p l . Phys.,  51  H o l d e r , D.W. No.  and N o r t h , R.J., ' S c h l i e r e n Methods', Notes on A p p l i e d S c i e n c e 31, (HMSO London, 1963).  Houtman, H.,  M.Sc.  J a c k e l , S.; Jahoda,  T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia,  P e r r y , B. and L u b i n , M.,  Phys. Rev.  F., Plasma P h y s i c s 14, 112  K o g e l s c h a t z , U. and S c h n e i d e r , W.R., Kunze, H.J.,  (Pergamon,  i n 'Plasma D i a g n o s t i c s ' , 550  Machewirth,  O p t i c a l S p e c t r a , December  J.M.,  Osovets,  M i l r o y , R.D.; Capjack, C.E.; 57, 514 (1979). Morgan, C.G.,  Rep.  S.M.,  J . Nuclear  38, 621  120  ( 5 ) , 1528  E.E., J . Geophys. Res.,  S c h r e i b e r , P.W.; Hunter 635 (1973).  I I , A.M.  68  32  Siebe, J . , Phys. F l u i d s , 17  ( 4 ) , 765  Siegman, A.E., Simpson, R.W.  Phys. Rev.  ( 5 ) , 1321  ( 4 ) , 689  Rev.  209  Can. J . Phys.,  L e t t . , 43  (20),  1502  Plasma P h y s i c s ,  15,  (1960). (1963).  (1961).  (1974).  IEEE J . Quantum E l e c t r o n . , QE-9, and T a l m i , Y.,  I I , V o l . 4,  (1979).  and Smith J r . , D.R.,  Shmoys, J . , J . A p p l . Phys.,  (1972).  (1975).  Salzmann, D. and O f f e n b e r g e r , A.A., (1979).  Salpeter,  Energy  M c M u l l i n , J.N. and James, C.R.,  Prog. Phys.,  S a l p e t e r , E.E., Phys. Rev.,  ( 8 ) , 1822  ( N o r t h - H o l l a n d , 1968).  and  Steel,  (1976).  1972).  A p p l i e d O p t i c s , 11  L e o n t o v i c h , M.A. (1957).  A.;  L e t t . , 3 7 ( 2 ) , 95  F.C. and Sawyer, G.A., i n 'Methods o f E x p e r i m e n t a l P h y s i c s ' , Plasma P h y s i c s , V o l . 9 ( b ) , 1 (Academic, 1971).  Keilmann,  Ng,  (1977).  247  S c i . Instrum., 48  D.G.; R o c k e t , P.D.; B a c h , D.R. Instrum., 49 ( 4 ) , 456 (1978).  - 131  and  -  (1973). (10), 1295  C o l e s t o c k , P.L.,  (1977). Rev. S c i .  REFERENCES  (Cont'd)  Sweeney, D.W.; Attwood, D.T. and Coleman, L.W., (1976). Rosenbluth,  M.N.  and Rostoker,  V e s t , CM.,  A p p l . Opt., 14 ( 7 ) , 1601  V e s t , CM.,  'Holographic  A p p l . O p t i c s , 15  N., Phys. F l u i d s , 5 ( 7 ) , 776  ( 5 ) , 1126  (1962).  (1975).  I n t e r f e r o m e t r y ' , (John  V u y l s t e k e , A.A., J . A p p l . Phys., 34 ( 6 ) , 1615  Wiley & Sons, 1979). (1963).  Z e l ' d o v i c h , Y.B. and R a i z e r , Y.P., i n ' P h y s i c s o f Shock .Waves and H i g h T e m p e r a t u r e Hydrodynamic Phenomenon', V o l . 1, 258 ( A c a d e m i c , 1966).  - 132 -  APPENDIX A  TRIGGERING OF  D e t a i l s o f the d e s i g n ,  been i n c l u d e d  DISCHARGE  c o n s t r u c t i o n and  c i r c u i t are w e l l documented i n our appendix has  THE  laboratory  here i n order  operation  (e.g.:  discharge  Houtman, 1977).  to e s t a b l i s h the  mentation of those changes to the c i r c u i t r y  of the  necessary  t h a t were made by  the  This docu-  present  author. F i g u r e A-1 master gap  shows one  i s described  diameter h o l e  pre-ionization circuit  v i a F i g u r e A-2.  i n the c e n t e r  With t h i s arrangement, and, i o n i z a t i o n was greater  s i x main g a p  trigger circuits.  i s an e n t i r e l y c o - a x i a l a r r a n g e m e n t , h o u s i n g  t r i g g e r c a p a c i t o r s . The gap  of the  sufficient  than 50 ns  Note t h a t  i n order  the  t h a t was  a t the c u r r e n t o p e r a t i n g  to reduce the j i t t e r  and  main gap  "  a 3  cm  electrode.  main d i s c h a r g e  from  trigger c i r c u i t s .  "  master  pre-  gap  133  trigger  pF  the  FIGURE A-1  Biasing  anode has  conditions,  to z-oinch T T  to l e s s than 5 ns. Master  i n the  s i x 2700  added to the  Z-pinch  to accommodate the  the  The  .nylon 3=  lucite  brass ring  A  •lb optical fiber PM tube  main discharge pref lash -H  h-  50 i 5 ns  FIGURE  A-2  D e s c r i p t i o n o f the p r e - i o n i z a t i o n .  - 134 -  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0095270/manifest

Comment

Related Items