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Confinement of a Z-pinch plasma with cold gas end plugs Milne, Andrew F. 1984

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Confinement With  of a  Cold  Z-Pinch  Plasma  Gas End P l u g s by  Andrew  B.A.Sc,  University  F.  Milne  of B r i t i s h  Columbia,  A THESIS THE  1980  SUBMITTED IN PARTIAL FULFILLMENT R E Q U I R E M E N T S FOR T H E D E G R E E OF MASTER OF A P P L I E D S C I E N C E in T H E F A C U L T Y OF GRADUATE S T U D I E S (Department of P h y s i c s )  We  accept  THE  this thesis required  as conforming standard  U N I V E R S I T Y OF B R I T I S H A u g u s t 1984  ©  Andrew  F.  Milne,  to the  COLUMBIA  1984  OF  In p r e s e n t i n g  this thesis  r e q u i r e m e n t s f o r an of  British  it  freely available  agree that for  that  Library  s h a l l make  for reference  and  study.  I  f o r extensive copying of  h i s or  be  her  copying or  f i n a n c i a l gain  shall  g r a n t e d by  ^ ^ Department o f  publication  not  be  22 August  1984  of  further this  Columbia  thesis  head o f  this  my  It is thesis  a l l o w e d w i t h o u t my  Physics  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  the  representatives.  permission.  Date  University  the  s c h o l a r l y p u r p o s e s may  understood  the  the  I agree that  permission by  f u l f i l m e n t of  advanced degree a t  Columbia,  department or for  in partial  written  i i  ABSTRACT Plasma a  plug  the  escaping  of cold  plug  greater  show  heat  temperature measured pascals  flux  of four  and  of  the total  temperatures plasma/solid plug.  solid  could  i s  gained  at  cost  plasma  motion  used of  2  has a  m" .  2 2  The  3  a n d 525  of  the  plasma  adds  a  density  by  flux  the plug  t o 2 0 0 MW.rn ,  barrier.  Linear  but  -2  The c o r r e s p o n d i n g  the "wall  i n t e r a c t i o n by r e p l a c i n g  8X10  work  a t 300K  approximately  the  in this  of  plug  lost,  avoid  the  end  Increasing  t o 420 MW.rn" .  energy  increasing although  the mechanical  i s  that  motion,  helium  2  electrode  a  a  Outward  flux  c a n be s l o w e d by  plasma  density  o f 8 3 0 MW.rn" .  t h e heat  as  a  into  reduces  Z-pinch  the  effect  The helium  flux  to a solid  effective  end  this  2  increases  terms  that  of a  calculations predict  reduce  i s 130 MW.rn" .  factor  loss  will  35000K  heat  t h e ends  Model  loss.  of  mechanical a  gas.  density  experiments  from  400  heat  MW.rn" .  In  2  of gas" i s nearly systems  impurities the solid  at  higher  contributed with  as  a cold  by gas  iii  TABLE  OF  CONTENTS  ABSTRACT  i i  LIST  OF T A B L E S  LIST  OF F I G U R E S  v v i  ACKNOWLEDGEMENTS I.  viii  INTRODUCTION  1  1.1  The L i n e a r  1.2  End Confinement  1.3  Outline  II.  THEORETICAL  Magnetic  Fusion  Concept  A s An I n i t i a l  Value  3 Problem  5  Of The E x p e r i m e n t a l Program  7  DISCUSSION  9  II. 1  The Role  11.2  Definition  11.3  O b s e r v a t i o n Of S p e c t r a l  Lines  19  11.4  Calculation  Shapes  24  11.5  Testing  11.6  Temperature  And D e n s i t y  Measurement  32  11.7  Formalizing  The I n i t i a l  Value  35  11.8  The Shock  11.9  Derivation  Of T h e U n i f o r m  11.10  Prediction  Of Improved  11.11  Summary  III.  EXPERIMENTAL  Of F o r m a l  Models  Of The Plasma  Of The L i n e  The A d i a b a t i c  Tube  10 State  12  Limit  28  Problem  Model  43 Flow  Model  End Confinement  46 50 51  SETUP  54  111.1  The Complete  111.2  The Z-Pinch D i s c h a r g e  56  111.3  The Gas P u f f  60  System  Valve  55  iv  111.4 The S t r e a k Camera  63  111.5  The O p t i c a l M u l t i c h a n n e l A n a l y z e r  65  111.6  Other Experimental  67  111.7  Timing  Appliances  And S y n c h r o n i z a t i o n  71  I I I .8 Summary IV.  V.  VI.  74  DATA AND OBSERVATIONS  79  IV. 1  Comparison With  P r e v i o u s Work  IV.2  S t r e a k P h o t o g r a p h s Of The E s c a p i n g  IV.3  Helium  IV.4  I n t e r a c t i o n With  IV. 5  P r e p a r a t i o n F o r Computer A n a l y s i s  80 Plasma  Line Spectra A Higher  82 85  D e n s i t y Gas P l u g  ANALYSIS  90 .94 96  V. 1  Plasma Temperature  V.2  Plasma D e n s i t y  103  V.3  Comparison With Model P r e d i c t i o n s  110  V.4  C a l c u l a t i o n Of H e a t T r a n s f e r  111  V. 5  Summary  115  CONCLUSIONS  117  REFERENCES  97  120  V  LIST  II-1  Model  II- 2  Summary  OF  TABLES  Nomenclature Of N o m i n a l  41 Parameters  42  111 — 1 E x p e r i m e n t a l  Equipment  75  III- 2 Experimental  Conditions  78  V-1  Summary  Of E x p e r i m e n t a l  Results  116  vi  LIST  OF F I G U R E S  I- 1  Plasma  And Gas I n i t i a l  I I -1  Uniform  II- 2  The Simple  II-3  Energy  II- 4  The Shock  I I I -1  Z-Pinch,  III- 2  Photograph  111-3  Discharge  III-4  Puff  III-5  Gas V a l v e  III-6  Streak  111-7  R o t a t i n g The S l i t  III-8  OMA  111-9  Vacuum  A n d HV S y s t e m s  69  111-10  Timing  Circuit  I  72  111 — 11  Timing  Circuit  II  73  I I I - 12  Common T i m i n g  Sequence  74  IV- 1  Z-pinch  Fired  79  IV-2  Radial  IV-3  Discharge  Current  82  IV-4  25mm  - 120mm S e c t i o n  84  IV-5  25mm T u b e  - 40mm  84  IV-7  OMA  Gain  Profile  86  IV-6  OMA  Dark  Current  86  Flow  State  Structure  Shock  Balance  Valve  38  Wave  43  I n The Shock  Wave W i t h  Region  Heat  Flux  And Shock  Tube  Of The A p p a r a t u s Circuit  Present  48 50 54 55 56  Valve  61 Firing  Camera  Circuit  And O p t i c s Image  And C o l l e c t i o n  Being  Optics  C o l l a p s e Of Plasma  Tube  5  Section  62 63 64 66  81  vii  IV-8  Raw  And  Processed  IV-9  Evolution  IV-10  Gas  IV-11  I n t e r a c t i o n With  I V - 12  A  V- 1  Solid  V-2  Intensity Cross-Correlations  V-3  Open-End  Midpoint  V-4  Open-End  Quarterpoint  V-5  Solid-End  V-6  Temperatures  V-7  Midpoint  Density  V-8  Open-End  Midpoint  V-9  Plasma  V-10  C r o s s - C o r r e l a t i o n Of  V-11  Combined  V-12  Heat  Puff  Step  Of  Data  Vectors  88  Spectral Lines  Pressure  Closer  89  Profile The  91  Density  Step  92  In  End L i n e  93  Intensities  Line  Midpoint  97 99  Ratios Line  Line  100  Ratios  ..101  Ratios  102  Compared  102  For Both And  Electrode  Quarterpoint  Types Densities  Pressures  Flux  105 106  Temperature, Versus  105  Plug  Open-End Density Density  Pressures  107  And  108  Current  113  vi i i  ACKNOWLEDGEMENTS My Peter a  interest  Martin,  dreary  work  on  whose  lectures  f o u r t h year the  Ahlborn. the  i n contemporary  Z-pinch  Mark  spectroscopy,  photographs.  Mair  Fletcher  and  graphics  software.  were  made  by  Walker  particular Z-pinch  me  valve,  My  of  o f h i s many  streak  helped  the  years  Boye  Nogami d i d  on t h e  Curzon,  by  the  Centre  up  subsequent  Ross  many  comments  Frank  the benefit  brightened  supervised  Computing  Useful  and  s t i m u l a t e d by  with  manuscript latter  experience  in in  research.  My not  giving  and  took  o f t h e UBC  first  mechanics  the gas puff  APL  Ross  was  engineering.  suggested  built  a n d Ron  Susan  on quantum  in electrical was  Davis  physics  understanding  f o r Tony  Science  Arrot  for  student.  I  and  Peace am  of physics Luis  who  de  set a  indebted  to  would  n o t be c o m p l e t e  Sobrino,  fine them  active  example for  members  f o r t h e new  their  were i t of  physics  criticism  and  encouragement. Most encouraged words  of me  o f T.S.  a l l , I am  grateful  t o my  to follow the standards  wife, I  Brenda,  had  chosen.  who  always In  Eliot:  We And  shall  from  exploration  the end of a l l our e x p l o r i n g  Shall And  not cease  be t o r e t u r n  know t h e p l a c e  t o where  we  f o r the f i r s t  started time.  August,  1984  the  1  I.INTRODUCTION  I.  The  goal  interaction  Ahlborn  plasma w i l l solid  principle The an  gas  be  gas  that  end  of  from  t h e end  heat  losses by  that  confinement  and  and  than  o f a gas  thesis  an  problem  of  behavior  of  into contact.  it  would  reactor  to  a  could in  plug.  four  theory  empirical  [ A H L B 7 7 ,  c o n d i t i o n s the  end  covers  of a u n i f o r m  S i n n o t , and  the  fusion  spectroscopic  density,  is  suddenly  t o t h e gas  of a l i n e a r  plasma/gas  Sinnot  under c e r t a i n  the presence  the  the  and  i s s u e a t hand  plugs, derivation  of A h l b o r n  test  Ahlborn  work d e s c r i b e d i n t h i s  plasma temperature and  less  end  reduced  examination  to  by  believe  transfer The  The  was  when t h e y a r e b r o u g h t  Sinnot  wall.  arose  fusion.  cold  and  work  proposed  in turn  magnetic  p l a s m a and  this  model  which  S I N N 7 7 ] ,  linear  of  INTRODUCTION  main  used  t o measure  comparison  f l o w model  experimental tests  areas:  of  solid  similar  of the  to  model  predictions. The  spectroscopic  "adiabatic  assumption",  mathematics  if  arise  same  i f the  temperature the  and  "rules  cannot  be  of  He  which  stated  line  to  often  is  buried  As  used  rely  to  thumb" u s e d  to j u s t i f y  simultaneous  Accepted  been t o c a l c u l a t e line,  and  temperature  I I 469nm t o He  I 588nm.  this  can  without  done  density  The  shown  both that  (in  this  the broadening  the  intensity  circumstances  contradiction  the  measurement  practice  from  from  be  the  problems  calculate  II i t w i l l  consistently.  on in  a result,  i n Chapter  o f He  be  was  found  and  applied  I I 588nm  were  explicitly.  spectral  density,  l a b o r a t o r y ) has the  not  theories  are a l s o  under  of  ratio which  examined i n  2  I.INTRODUCTION  Chapter  II.  The  current  literature,  Similarly, which  need  to  essentially  valid  in a  the  heat The  at  tested  In  Chapter  context.  first  It the  and In  a  compared  looking  and  the  subsequent  the  ends  of  the  plasma.  the  measureable  turned  out  plasma/gas model  to  be  remain  model later  to of  gas  much  to  be  will  not  the  by  than  without  i t s proper  to  calculate  carried  a  Z-pinch helium  the  radial  evidence the the  shown  line energy  that  gas  future  the  needed  and  directly  line  spectra  were  found,  closer  to  expansion of  of the  confinement. spectra balance  also at  the  Ahlborn-Sinnot  flows, although work.  to  and  taken of  out  solid  investigation  in  of  the  in  those  photographs  with  types  V  is  remain  and  differences  by  clear  be  uniform  assessment,  such  differences  answered  latter  i n the  streak  It will  model,  p l u g g i n g was  on  hampered  showed  scheme  tube  lower  mounted  to continue  the  gas. end  No  assumptions  shock  i n Chapter  the  on  i s rederived  empirical  were  for certain  the  the  further. rests  regions are  consistent  interface.  is valid  questions  plasma  Nonetheless,  The  of  the  i s used  p i n c h were  interaction  lack  II  flow  appreciated in  Although  well-known  pinch center.  plasma/gas  be  proposal  for differences  attempts  to  examined  to derive  straight  electrodes  at  be  densities  open-ended by  the  the  investigation  fusion.  measured  used  where  from  to  seem  for consistency.  e x t e n s i o n of  temperatures  attain  needs  system  flux  not  Ahlborn-Sinnot  equations  gradients. algebraic  does  and  the  be  an  differential  problem  several  3  I.INTRODUCTION  The  A h l b o r n - S i n n o t model  material  end  advantages  confinement,  not  implications Chapter Chapters  for  II.  The  IV  Conclusions this  seen  chapter  interpreted,  equipment V  presenting  which  models  can  be  these  models  are  briefly  variety  material the  plasma  the  Lorentz  direct  Linear  of  elements  ionized  force,  their lines.  these  particles  goal  of  long  magnetic  or  a  based linear  the  on  enough fusion  that  either  system  the a  known  presence  field  into  used  are  a for  test  can  but  greater the  be  than  field around of  reaction  i s the  device machine.  a  up  t i l l  a  by  will the  holding  reactor  called  a in  influenced  capable  for  the  atoms  orbits  Experience  the mirror  to  for fusion,  research.  shaped  as  Concept  spiral  candidates  be  section.  and  best  of  should  first  a magnetic  arrangement  and  value problem  because  of  in  III,  work  for heating  doughnut as  the  to plasma  motion  examined  problem  suitable  their  The  remaining parts  final  Fusion  practical  i t s analysis.  experiments  i s only  motion  Producing a  [BAKE81] s u g g e s t s those  where  It  are  initial  i n the  are  that  transverse  field  The  Magnetic  sustain.  The  to  field.  and  i n which  an  t o c o n v e r t them  can  are  as  outlined  The  offers  Chapter  data  confinement  approach  this  in  VI.  context  formulated.  needed  vessel  the  then  too  in  described  end  research,  I.1  temperatures  the  fresh  measurement  with  the  of  Z-pinch  i n Chapter  introduce  a  workers  and  is  deal  advanced  fusion  the  previous  part  A  and  modelling  and are  by  represents  main now are  tokamak,  4  I.INTRODUCTION  The  linear  actually was  the  an  early  offers  hope  use  i s as  From  A  of  type  streaming  the  reactor  show  that  an  time  One ends  of  possible  plasma  long  enough  to  material  barriers  plasma tube offers  erodes  Z-pinch  i t s poor  linear like  was  itself  stability)  Otherwise  important  i t s main  experiments.  the  Z-pinch  The  L/a,  from  where  L  gives  and  ten  over  the  easier,  and  disadvantage  is limited  the  i s the  ion thermal  one  is  main  confinement  particles  as  advantages  maintenance  cost.  energy  of  open half  velocity.  by  of the  ends.  The  length  of  Calculations  kilometers are  be  to  attached to  solid  the  possibilities  certain  obtain by In  formed  i t , the  Numerical  that  valid.  the  i s to place  vessel.  temperatures  to  the  i s the  show  concept  contrast  has  stable,  solution  reactor  [MAL077]  lower  The  and  needed  in  system.  Morse  at  a  tokamak,  designs.  l e n g t h s between  the  machine  i s that  and  open-ended  simple  reduces  scales  the  [HAIN78]. pulsed  system  escape  (despite  for  i s more  geometry  confinement  plasma  linear  now  reactor  a  than  considered.  even  complex  plasma  simpler  be  a  work  construction  linear  to  that  of  of  more  The  is  becoming  practical  modular  type  favorite  into  tokamak:  free  first  source  this  insight  the  a  system  studies  by  reactions. Commisso  this  plug,  gas  end  end  of  not  barriers  elements  thesis,  which  plug the  obvious  can  can  the a  "wall  remains be  withstand  the  confinement  carried  out  shown  the  i s extended  to  of  In  gas".  stationary  thought  the and  have  study  at  Malone  Experiments  [COMM77]  d y n a m i c a l l y by  end  material  of  vessel.  as  a  This  in i t s solid counterpart.  as  the  shock model  I.INTRODUCTION  1.2  Figure the  5  End Conf inement  1-1  reaction  a s an  i s a simplified  vessel,  just  picture  after  gas i n t h e shock  tube.  plasma  constrained  a  motion  can at  amplitude forms  an  least  axial  by  be  initial  state  then  as  V  •  £  A  A  A  MAGNETIC  T  PLASMA^  A  A  field,  the  system  motion  of  shown  COLD  CONFINEMENT  that  the  surface" further  step  plasma  between  them  assumption  Plasma  i n the analysis and  gas  radial  the  small  i n Figure  1-1  problem.  GAS  do  not  there  mix,  II i s  so that  as a massless  i s no h e a t  SIZE)  and Gas I n i t i a l  of Chapter  c a n be m o d e l l e d  that  the  9  1-1  first  of  or i f the  (ACTUAL  The  with the  BRASS ELECTRODE  3  AA  A  inside  1  V  •  HOT  i n contact  f o r a one d i m e n s i o n a l f l o w  V  •  of the hot plasma  independent  IP  V  Problem  I f the radial  magnetic  taken  motion,  Value  i t h a s come  undisturbed i s  Initial  flow across  to  State  assume  the "contact barrier.  A  the barrier  I.INTRODUCTION  will  separate  right  is  the  for  referred  driven  two  of  as  the  shock  mix,  but  the  gas  flux  is  heat  being  (e.g.  shock  tube  assumed  allowed to  to  transport  shock would  tube  be  equations  The  electrode  the  at  model  experiments  presented  the  end 1-1).  gave  a  is  given  in Chapters  the  left  is  an  with  to  the  matching  In  is  this  both  the work  at  starting it  will  be  across  the  interface,  shock  velocity.  the  (so  that  the  because equations  "massless  form, is  the  and  the  tested  by  Z-pinch  The d a t a  next  IV.  a not  large  then  shock  heat  expansion  with  In  this  case  conservation a hierarchy  of  this  the  the  plasma/gas  (hence the  A general Full  of  thesis.  model and  that  section.  The  consistent  observing  showed  to  would  tube  discharge  not  flux  derive scope  of  raising  plasma  underlying  description.  i n the  assumed  barrier".  beyond the  both  still  extension  flow  and  a  link  condition  are  a  as  only  fluids  better  III  the  straightforward  re-express  of  on  two  its  of  model were  in Figure  a  diffusion  Such work  predictions  interaction  is  adiabatic)  in characteristic  system  model.  small  to  The  appears  system"  WHIT74).  be  necessary  Ahlborn-Sinnot  surface  a pressure  increasing  and  on  force,  and  model and  wave v e l o c i t i e s .  Sinnot  The  approximately  introduce  it  is  model.  pressure  remains  the  tube  system  contact  The A h l b o r n - S i n n o t m o d e l the  the  i d e a l i z e d "dual  many a n a l y s e s  to  two h a l v e s :  exerting  systems  This  into  shock;  The  capable  interface.  point  problem  cylinder.  piston  between the  the  a piston  expanding solid  6  the  brass  Ahlbornoutline  details  of are  I.INTRODUCTION  7  I.3  The of  by  main  plasma  was  Outline of the Experimental  and a tube  produced 150mm  2x1 0  i n a small, high  and  n r  3  .  of  The  voltage  other  end  plasma/gas to  permit  The  to  test  the  temperature  midpoint.  were  also  the  at  moving  t h e g a s were  flux plugs  calculated were  spectroscopically..  to  plasma  600mm  that  so that  i n which  arrangement  over  a range of  measured  case by  and  the  centers tubes.  the plug i s injecting i t possible densities.  atthe  i n t h e open (half  Shock  with  end  pinch  way b e t w e e n t h e  wave.  photographed  The  spectroscopically  t h e shock  t h e shock  and  ends,  because  photographed  of  open  the quarterpoint  from  of  shock  of plug  solid  and d e n s i t y  expansion  vacuum  made  a  by P r e s t o n  measurement  or glass  525  with  electrode.  gas, or " p r e - f i l l e d "  comparison  of  e l e c t r o d e s h a d open  plugs  This  i n length  density  used  a t t h e same  clear,  model  Temperature  measured  into  heat  density  f i l l  d e n s i t y were  an inward  The  electron  simplify  e l e c t r o d e and the midpoint),  predicts outward  to  valve.  empirical  pinch  ground  puff  and  source  c r e a t e s a plasma  but modified  left  the Ahlborn-Sinnot  In  are a  to a pressure  peak  The p i n c h  either  a fast  a  similar  of metal  t o the Z-pinch  with  test  Z-pinch,  helium  a r e made  free  t h e attachment  identical  and  [PACH71],  left  were  with  i s  interaction.  tubes  gas  40000K  connections  was  pressure  a t 12kV, t h e p i n c h  device  [PRES74] a n d Pachner high  Filled  fired  temperature 23  o f an e x p e r i m e n t a l  of gas t o a c t as the end plug.  i n diameter.  pascals, peak  requirements  Program  tube  waves  model moving  a streak  camera, and  velocities.  The higher  but  not  measured  I.INTRODUCTION  A  number  Chapter plasma  of  The was  interactive then  difficult  to  measure  studied  the  correct. and  V.  Chapter  The d e t a i l s  VI.  these  full  itself and  along  I 588nm  in  a n d He  latter  shift  of t h i s  results  directly.  analysis  and t h e i r  emission  the axis time  In  used  in  asymptotic  ( i n t h e form  of  line  into  an  of the  series  Z-pinch  taken  at  i n the plasma  made  intensities  used  Line  for relaxation I I 469nm  calculations  work  work.  assembled  advocated  that  this  single  oscillations  were c h e c k e d  time  temperatures  The  radial  of these  three microsecond  that  as  t h e He  result  a  by c r o s s - c o r r e l a t i n g  to observe  cross-correlating  of photon with  data  Waves  temperature  important  tested  digitally  base.  positions,  it  be  recorded  i n t r o d u c e d by  the models  spectroscopic  data be  different  the  how  spectroscopy can  profiles)  An  i n n o v a t i o n s were  I I i t i s shown  parameter.  could  8  time was  i n PRES74,  should are given  implications  effects  by  series.  to rule  out  suggesting  n o t be  taken  i n Chapters  as IV  are discussed in  9  II.THEORY  II. This work:  chapter  calculation  derivation needed  of  for  Z-pinches. the  In  the  two  purpose  objective  i s to  confinement In  formal  of  collision simple  in  how  two  Section  II.7  the  II.6  scaling  law  that  higher  d e n s i t y end  density,  and  cold  i s to  and  of  overall  first  need  state also  photon  cannot  in  to  be  be  and  resolved  this from  is  emission  deep  use  The  that  roots  the  calculated  relate  shown  illustrate  be  the  variables  in  also  to  plugs.  d e n s i t y measurements  will  later  experience.  gas  up  applied  examined  i t will  theory  The  end  the  be  set  in the  as  gas  also  open-ended  view.  direct  plasma  will  and  model  is  of  introduce  models  stage  and  in  any  sections of  the  theory  in  the  intensity  lines.  will  the  can  this  chapter  world  with  There  the  in  measurements  equilibrium  of  areas  former  specifically  adiabatic  temperature  derive  set  II.2.  main  solid  this  problem  further  spectral  Section  plasma  the  local  will  theory.  explaining  to  an  of  that  world  of  Discussion II.5  adiabatic  needed  the  section  of  Ahlborn-Sinnot  the  to  The  coherent  in general,  dominated  to  will  II.1,  so  a  Z-pinch  between  way.  of  the  definition  conflict  ratio  a  manipulation  explored  II.3  of  modelling  necessary then  assess  section  context  into  four  model.  comparison the  fitted  the  temperature  flow  e p i s t e m o l o g i c a l framework, be  DISCUSSION  of  plasma  uniform  general,  can  the  of  empirical  chapters  the  covers  the  the  THEORETICAL  for  suggests plugs.  of the  the  s e c t i o n s I I . 8 and derivation  improved It  remaining  i s shown  energy here  of  assumptions  I I . 9 , and section  11.10:  confinement and  in  the  these a  with  previous  II.THEORY  section  10  how  velocity gas  end  model of  can  to  summary  setup  II.1  The  scaling of  section  will  to  model  logical  as  an  law  measurements  of  calculate  heat  of  experimental  thought  in  A  used  i t s measurement  The  used  be  plug.  and  the  experimental  a l l the  i s given  Role  Formal  of  be  building.  the  existing It will  also  can  affect  consistency  be  of  of of  a  cold  for  the  III.  11.10  formal  logic  physics  as  that  choice  can  model.  formal  shown the  the  Discussion  in Chapter  in section  product  concepts  needed  escape  Models  derived  concepts  into  11.11.  section  immediately  i n f e r e n c e , the  strengthen  in  plasma  flux  assumptions  follows  to  e x p l a i n how  the  the  the of  This  can  an  be  be  exercise need  for  experimental  technique. A set  complete of  initial  inferences, in  the  into  and  a  may  be  assumptions,  a  set  model  of  external world. facts  and  established. The  formal  frame  of  The  Ahlborn-Sinnot The of  the  As  fluids,  latter  specific  model  macroscopic consistently  to  be  nature  can  state (e.g.  will  of  to be  part  may  an  the  plasma  be  formalized  described  at  and the  those  be  to  be  will  gas  in a a  the  conjecture. allow  some  simple  way.  this  formal  as  tests.  enable  small  provided same  taken  will  rather  making  further  experimental work  a  inferences  divided may  and  with  parts: for  experimental  of  materials  rules  former  subject  t e s t e d as  variables,  three  for testing  The be  into  established in this  statements both  first  conjectures.  model  set  procedures The  reference  broken  number is  of done  temperature  II.THEORY  should  have  no  manipulation  can  net be  transformations. both  intuitive  rules  of  always  meet  set  the  points  often on  model  set  can  of  be  of  themselves  for  consistency  There  is  in  plasma  be  a  aspects  of  the  the  model  numbers  internal  under  building by  chain  The  requires  which  cannot  atoms likely  makes  on  in to  a  have  the  the  the  relate digital  procedures be  atoms  rules,  about  physical  the  be  mathematics.  should  at  denseness  testing  the  not  calculus,  designed to  The  from  b i t integers  multichannel analyzer. i f the  are  logic  describing  inferences  sixteen  i t  may  inference  appearing  instruments.  model of  predictions  of  of  their  a i d to  form  the  i s less  and  algebraic  Furthermore,  about  i n the  formal  great  theorems  number  Experiments  whose  chain  remainder  verification and  to  model  The  the  the  of  is a  something  finite  assumptions  by  to  with  space,  assumptions  experience.  models,  meaningless the  the  tested  long  optical  with  hidden  the measuring  are  the  by  inferences  readouts  but  The  assumptions  algebraic  forth  direct  model  the  An  introduced  Having  the  number  large  the  in differential  for consistency.  real  f o r the  number  simplicity  down  deep  the  small  them),  experimental design.  embody  system.  problems  world  need  between  to a  resulting  manipulation  of  the  The  flow  down  and  example,  physical  pared  judgement  for  guaranteed  energy  checked process.  and  output  photons port  experimental data  assumptions  of will-  inconsistent  test. of  this  a model,  experiment.  i t s spectroscopic  chapter always  w i t h an  Statements  measurement  deals  are  with  eye  about  to  the  advanced  the i t s  practical ultimate  Z-pinch  plasma  in sections  II.2  II.THEORY  to  12  II.6.  Additional  dimensional allowed  initial  value  inference  co-ordinate) their  are  formal  presented  rules  sections  the  model  II.2  At in  a  fluid  first  opposite  is true.  the  bring common  section such  a  out  way  The  of  define  that  no of  a  ideal  gas  in  a  given  volume,  by  the  microscopic 300  An  somewhat  and  a l l of  the more  of  this  neutral  plasma  per  temperature  energy  will  helium  density,  but  the the  knowledge  out  in  this  that  the  construction assumptions  state  amount  helium  II.11  measurement.  is defined  of  An  turn  plug  In  are  tests.  said  model  density  force  and  section  be  by  i s the  the  etc.)  existing  arise.  definition  care.  that  i t will  of  of  State  will  i s the  distribution.  energy  with  end  Density  pressure  equivalent  difficulty  gas  i t s container,  energy  kinetic  meaning  one  symbols  inconsistent  and  the  position  experimental  could  fact  problem:  the  The  final  Plasma  appear  single  equations  the  imposed  temperature  theory.  k e l v i n , almost  motion  need  on  In  paradigm  cold  the  The  that  inconsistency  of  gas  anything  important  methods  state  i t would  a  II.7.  11.10.  elementary. The  on  conservation  the  construct  restriction  depending  a n t i c i p a t i o n of  makes  an  will  to  to  (i.e. a  section  D e f i n i t i o n of  dynamics rather  those  in  II.8  glance,  section  will  to  (through  in  needed  problem  advanced  relation  in  summarizes  statements  of  in  mass  unit  is a  This  variables  easily  525  be  found  area  terms  exerted of  pascals in  in  present  measure  at  in  the  the and free  atoms. plasma pressure  operational  state and  has  no  temperature  definition  that  13  II.THEORY  requires that  the plasma  force  magnetic  c a n be e x e r t e d  confinement  chamber! makes  to  equate  pressures.  their  observable In  described system  electrons  Z-pinch ionized  plasma atoms  interact  therefore of  be  particles It  will  weakly  be  made  terms. be  be a r g u e d to  from  In t h i s  done,  most  an  the free so that the  section  because  later  and bound energy  i twill  bound  any o f In  the  singly enough  It  the  will  collection  subspaces  are separate  as a whole  kinetic  s i m p l y be a s s u m e d  the  moving  slowly  states  irithe system  be  states.  II.3 that  here  of  are either  as a  an  then  atoms.  potential.  atomic  of i n t e r e s t  would  move  large  through  whenever  of the system  in section  of a  states  appear  a l l of which  and i n t e r n a l  to  state.  particles  of the p a r t i c l e s  sum o f i n d i v i d u a l  the issue  Free  form  electrostatic  motion  consist  the  to  the  used  t h e plasma  interacting  would  to  be  of the system  combined  electrons,  free  coupled, up  states  gas end plug  The mechanism f o r  would  a l l of  solid  the p r e s s u r e and t h e  the Hamiltonian. to  what  a  temperature  define  nucleii  convenient to think  corresponding and  the plasma  The p h y s i c s  however,  with  will  in  the cold  plasma  relation  nucleii  through  with  put  between  down  or free  be  of  be a n e e d f o r  A  and t h e bound and  hardly  t o the gas can  correspond  independently,  question  the plasma  and helium  by w r i t i n g  would  could  the  and d e n s i t y  field.  would  There  the  gas thermometer.  analysis,  of electrons  electromagnetic  to  from  temperature  a general  begs  interaction  s t a n d a r d o f an i d e a l energy  the  on.  compare  transferring  number  force  i f t h e plasma  Fortunately,  i tpossible  common  to exert  and that  can  potential this  can  i s the distribution  II.THEORY  of  energy  plasma  within  particles  practical  each  to  be  found  application  transferred  between  mechanism  will  at  comes  the  affects  spectroscopy  subspace,  the  depend  on  states.  The  critical  importance  each  the  and  free  way  states,  defining  and  The  energy  The  whereas  is  dominant  measurement  from  two  of  therein.  gas.  these  number  i n which  emitted  between  the  level  the  photons  relationship in  energy  from  plasma  only  specifically  the  bound  subsystems  measuring  by  i s of  the  plasma  energy  transfer  temperature. Analysis mechanism restate  at  the  pressure  the  the  plasma/gas  balance  is  of  the  gas.  defined  by  the  same  the  number  no  net  of  their  and  momentum  velocity  number  that  to  the  distributions  density  f o r the  same.  is The  mix,  applies and  to  ions  to  that  i s the can  the  to a A  same  also  cold  be  gas.  i s such  interface,  sufficient  so  collision.  pressure  a c r o s s the  that  knowledge  determine  their  distribution is directly  electrons  In  can  "ion  conditions  not  temperature  electrons  ( e . g . an but  do  temperature.  and  i t i s necessary  particle  plasma that  the  Here  plasma  velocity  gas  ions  temperature"), the  of  is transferred  "electron  them  the  theory  velocity  ideal  with  fluids  through  that  kinetic  temperatures  make  two  Furthermore,  different  to  the  means  distribution.  related  starts  interface.  achieved  interface  that  When  temperature  assumption  stationary as  of  be  some  characterized  temperature"  i n the  plasmas,  Z-pinch  and will  by an tend  15  II.THEORY  Although  a  transferred, the  slower  expense the  of  form  plug.  In  means  of  absorbed (In  pressure balance  collisions  gas  atoms  the  former.  of  heat)  the  Z-pinch  energy  The  sufficient  II.3  i t  will  c o m p l i c a t e the  radiation  in this  state The  depend  subsystem  information on  the  to  coupling  Although  only  i t exists  because  photons.  The  of  the  in as  found  temperature.  net is  has  optically extra  states density  of  the by  i n the be  comes  so  photons  emitters. plasma  bound  atoms  calculated  thin,  must  escaping  states,  the  two  gas  end only  emitted  nor  change.  only  could role  from  radiation  state  will  the  in  and  to be  be  of the  If  continually  The  measurement rests  but  without  the  to  the  emit  energy  the  same  state  whether  the  i s that  i f the  no  plasma  reabsorption,  supplied  on  i t is  free  knowing  of  weak,  distribution  usual c r i t e r i o n  escape  state  to  the  subsystems,  will  free  excited  energy  from  be  spectroscopy  (in  the  messenger  corresponds  between  energy  be  The  states  flows  energy  a  i s assumed  A  the  absorption  equilibrium:  established.  that  that  and  at  cold  will  of  free  difficulty  been  the  i s one  the  is  world.  the  a l l that  latter  meaningful  serve as  coupling  bound  can  The  energy  then  the  photons  equilibrium  this at  by  of  process.)  outside  between  q u e s t i o n now  distribution temperature  the  particles  i s neither a  shown  i s to  carried  subsystems.  to cause  momentum  transfer  collisions  measurement  experiment  i s to  radiation  net  the  temperature  be  no  plasma  accelerate  these as  that  fast  effect  the  plasma,  the  to  net  raise  seriously  bound  tend  transfer,  i n amounts  section  between  will  and  ensures  to  the  bound  temperature  and  assumption  that  II.THEORY  energy will  16  given be  to the emitting  transferred  measurements  will  equilibrium  between  photon-emitting It  out  depend  by  on  the  bound  from  spectral  by c o l l i s i o n a l  equilibrium  clearly  bound  transitions instance, should direct the  that  the  emission  with  technique  net test an  their  The  emission  conflict  researchers  mainly was  that  put  t h e same  way,  and atomic  more  states i s  frequent  used  buried  otherwise i s to rule  Griem, f o r  [GRIE64].  the spectral  shows  than  depopulation  assumption  authors  have  This  shapes),  the  denied  (e.g. out  i sin  in describing  line in  rate  quantum making i t  SMIT69). any  a  The  priori  a r e t o be o b s e r v e d  A possible  an  with  a posteriori test i s  V.  between, t h e s e because  that  state  energy  themselves.  certain  model.  i s  t r a n s i t i o n s between t h e  rate  profiles  bound  the  released  much  deeply  i f the line  i n Chapter  past,  so  contradiction  of e q u i l i b r i u m adiabatic  be  with  collisional  (and hence  mathematics  effect of this  discussed  the  can  be  states  the radiation  of photons  mechanical  and t h e  temperature  of  motion  be  the adiabatic  that  states  the  most  words,  should  has argued times  that  other  bound  conflict  of the  thermodynamic  kinetic  associated  the free  the  ten  local  when  excitation  between  be  when  In  states  assumption  even  that  require  between  established.  and  excitation  The v a l i d i t y  being  motion  lines  into  that  collisional  states.  some m o d e l s  free  there  free  transitions, an atom  by  radiation.  i s i n t e r e s t i n g t o note  measured  so  atoms  plasma  the  theories point  temperature  has n o t been of  view  existed  held  studied by  in  most  independently  of  17  11.THEORY  the  means  problem  chosen when  assumptions, assign when of  set  The plasma  bound  to  set  advanced  must  be  and  that  reference  the  following  a  temperature  used  enough  S  as  tests  temperature  f o r each  within  a  the  The  can  number  they  difficulty  comes  imply  type  of  certain  no  inconsistent  the  existence  particle,  energy  one  distance  this  t o happen  thermodynamic  model  with  a  a  in this  be  of  a  thesis  i s that  precisely  in  s h o u l d be  predicted  statement  of  make  small  set  of  temperature  in  a  can  be  tested.  In  and  i s that  "under  to  assumes knowing the  of a  There  temperature"  this  directly  algorithm  test  show  T  i s therefore  that  the  will whose  be  this  certain  a  way  frame  of  conditions plasma  an  attempt be  that  to  done, no  S."  but  test  best  that  p r o c e s s model  that  predicted  be no  model used  need  existence  to as  can  the  can be  be done  T.  If  be  valid,  the  formal  a  basis  for  other  t o make cannot  The invert  The  particular can  such  observation  can  means  valid.  what  preparation,  spectroscopic  T  of in  will  lead  terms  expressed  experimental  i t contains  calculations. "plasma  is  on  is  allow  to calculate  to prove  use  one  specific  One  impossibility  to  end  distribution  theories  prime  T  logic.  applied  i n the  rely  there  T h e o r i e s which  defined  o b s e r v a t i o n s can  algorithm  view  temperature.  states  up  this  parameters.  view  measured,  is  independent  of  In  observation  matters  other, etc. etc.  consistent  the  what  of  "temperatures":  difficult  that  means  i t .  m i c r o s c o p i c energy  each  each it  the  several  for  observe  the since  to  the  to  be  statements proved.  about  a  18  II.THEORY  The is  model  based  the  on  the  plasma  charged  states  as  of  the  distribution  which  is  presence  to  then  of  an  is  to  whose  observed  distribution  In  to  gas  reservoir  temperature  particles  then  summary,  the  assigned  plasma  state  the  ideal  gas  state,  generally  of  an  ideal  gas  thermometer,  because  the main  objective  between  a  and  plasma  the  calculation  kinetic can free  is  be  to of  an  find  motion  adiabatic (otherwise  a  t o be  and  in local  states.  A  requirement the quantum  the  as  states,  be  an  i n the  ideal  gas  to  the  hypothetical  an  extension  be  too  for  rates  and  which  transfer  experimental which in  allows  terms  of  i s known  (or  equilibrium struck  basis  experiment  energy  subsystem  transition  gets  in  expressing  in this  problem  density,  the  This  epistemological  thermodynamic  mechanics  Its  defined  the  must  of  the  plasma.  be  The  of  the  to  correspond  transition  balance that  the  emitting  and  plasma  would  measure  gas.  photon  population  temperature tested)  existence  by  free  i t would  practically  i s to  ideal  i n the  the  energy  states.  way  of  formed  related  bound  into  electric  i s formally  energies.  on  and  applied  same a s  may  states  The  the  to  Z-pinch  coming  subsystem  Another  photon  of  modelling  the  postulate  be  the  the  emission.  macroscopic properties  can  motion  distribution  reservoir.  of  free  i n the  be  with  energy  output  photons  used  the  to  photon  the v e l o c i t y  ideal  relation  i n the  i s an  in  assumed  of  respond  emitted  of  t o be  most  first  these  involved  i s related  this  appear  that  "thermometer"  distribution  turn  temperature  assumption  will  The  number  plasma  particles,  field. bound  of  with  between  rates  difficult)  be and  the the  small the  19  II.THEORY  equilibrium  requirement  (otherwise  the  enough  follow  to  detailed the  bound  that state  the  analysis  the  population  changes  of  this  transition  in  latter  will  not  kinetic problem  rates  be  change  fast  quickly  temperature).  has  yet  to  A  appear  in  literature.  II.3  Observation  Spectroscopic subdivided  into  individual  The  addition  to  be  The  explored  in  The between  two  atoms,  observer.  made.  measurement  and  two  are  but  conditions present  dynamical  not  induce  words,  the  p r o b a b i l i t y of  stronger only  a  atoms  by  are  Statistical  much  the  i s to  number  of  larger  encompassing  than  the  more  which  of  light  light  the a  density  from  emitters  strict  this  may  can by  be the  emitter  to  absorb  in  separation  can  be  are  valid  condition and  one  emitting  state  of  that in  that  coupling  free  space  radiation  emitting  atom  state  the  is  In  photon  must  another  photon  such  a  atoms.  a  way  atom.  emission that  A  other not  be  slightly  must  involve  the  emitting  independent. has  independence which  cases  states  atoms,  statement  emission,  that  when  between  internal  statistically  This  photon  coupling  condition  small  i n many  important  states  affected  of  and  section.  most  plasma  emission  linked  under  Lines  temperature  topics:  parts  single  of  Spectral  propagation  emitting,  the  the  major  of  extremely  justifies  depends  emitter than  one  on  scale  the the  deep  implications.  semiclassical classical  length,  emitter.  In  and  theory  wavelength hence  very  conjunction  of being  likely  with  the  20  II.THEORY  ergodic  hypothesis  emitters  to  be  properties  can  be  atom. next  Without to  number  the  by  optical have  present  interact  a  of  the  .it  an  complete  allows  ensemble  behaviour  depth been  no  of  formal  a  theory  the whose  single would  be  both  and  the  addition  propagate, system  of  that an  charged  resulting  index  so  by  over  is  i s the  on  path  lengths  cases  showing  the  that  that  they  rest  of  the  do  coefficient  require  Z-pinch  longer  the  of that  optical  and  Bernard  than  those  plasma  of  to  be  e m i t t e r s do  not  not  interact  plasma  as  at  i f there  present. absorption, waves  particles  interacting  refraction  the  1 - CJ§AJ  frequency  dispersion  for a  "i 2  there may  by  plasma  the  i f the  predicted  of  will  [PRES74]  Preston  field  direct  n =  0  bounds  assumed  atoms  absorption  independence  Upper  r  w h e r e CJ  dimensionless  absorption coefficient  electromagnetic  effect  a  An  experience  to  depth",  light.  photon  emitting  traditionally  the  in both It  is  of  the  cases  atoms  integral  calculated  will  possibility  "optical  small.  "thin".  other  the  by  be  work,  Each  emitting  transparency,  through  In  The  from  of  the  taken  in  optically  were  as  indicates  all.  mechanics,  members  assumption  calculating  path  [BERN79], the  as  calculated  this  defined  the  depth  treated  independence  analyzed  zero  statistical  impossible.  The  over  in  1  2  ,  not  of  also be  relation  through  wave  /  is  a  the  able  to  for  a  potential.  frequency  CJ i s  II.THEORY  21  OJ  and  m  and  electric number will be  M  are  charge,  density  be  the  much  Z  of  Ne_^  a  and  the  large  semiclassical  model  of  photon  being  than  the  to  include  with  for the  vector  an  potential  H  and the  weak  =  Z-pinch  -  where  very  high  comes  from  assuming  -  2  Ze r  means  strong  a  a  where  |kj  +  2  that  are  that  A  +  must  only  significantly function. exponential  over It  as  unit is  term  effect  will  unity.  because  the  the  wavelength  this  model  potential  the  first  is  the  modified  electromagnetic  the  e A 2mc 2  be  occurs  present). field  The  is  field  co/c. the  would demanded  not by  of  small in  (which  laser  i t is  for  experiments  wavelength  restriction  sinusoidal,  implies  v_ i m p o r t a n t  then the  2  Aoe  co  Large range  - e<t>,  2  - j (k • r-<jt) +  0  -  on  N  to  however,  In  Coulomb  eA'p mc  A e  2ir/\  =  the  close  relies  classical  coupling  fields  =  n  the  and  absorption  large  j (k • r_-o;t) A  ion,  general  radius.  in  is  A(r,t),  p 2m  coupling  In  emission  e  the  The  co t o o  atomic  of  of  co m a k e s  of  have  electron  momentum  ions.  value  2  masses,  number  second.  to  Hamiltonian  ion  atomic  /  -I  0  and  1  2  eM  possible  greater  NZe  0  electrons than  +  em  electron  larger  i s not  i  L  i s the  n e g l i g i b l e when It  r =  0  be  model.  ,  that to  possible  k«jr  the to  will  change  atomic expand  wave the  22  II.THEORY  The  Z-pinch  limits.  The  plasma  Bohr  falls  radius  approximately  5 x 1 0 " m,  parameter  the  in  a  so  11  classical  The s e m i c l a s s i c a l  the  band  optical A  have  further  only  will  coupling  states.  It will  operator  into  factoring way  that  of emitted  translational think by  a  of  each  moving  system).  Summing  correction  must  to  Doppler  effect.  An  emitter  a  frequency  independently the  frequency  emitter  (always  moving given  and have shift  are  for their  along  way  distribution  L(ACJ)dAw  =  will  density  ideal  at this  If  velocity be  dAo>.  and i s to  surrounded  non-relativistic means  velocities  will  gas  f o r the  internal  emitters  of sight  F(CACO/CJ)C/O)  internal  i n t h e same  object  a  atoms  ( i . e . by  an  on b o t h  different  a normalized  in  in  ACJ/CO = v / c .  by  parts  fixed  frequencies  and  distribution  different  the line  absorption.  the emitter  of looking  as a  small:  and frequencies i n  factored  possible  from  i s also  product),  depend  i s The  i f the emitting  a tensor  then  The p h o t o n  k«r_^0.00l.  internal  A different  b e made  shift  into  extreme  helium  without  to factor  and  two  translational  will  light  the observer.  their  probability  independent  plasma  b e made  The  photons  effects.  implies  classically  may  components  distribution.  ionized  is valid,  translational  velocity  singly  model  between  space  these  of r e f r a c t i o n  be p o s s i b l e  the Hilbert  velocity energy  then  between  index  propagate  simplification  weak  of  0  X=469nm  o> /o=*0.01 . 0  nicely  relative  be s h i f t e d  at velocity  the  that  by t h e  v has  emitters  move  distribution  F(v),  23  II.THEORY  If  the  the of  line  profile  Doppler L(Aco)  plasma  Pico).  assuming  equilibrium  i n the  width  energy  distribution  F(v)  takes  whose  a  good The  that  measure  =  weak  coupling  excited  velocities  atoms  lead  to  effects  are  plasma  however,  total  experimental  Doppler  coupling  practical  theory,  calculated practice  from  however,  larger  by  broadening  neglect  completely  the  not  of  i t s  over The  a  to  extra  calculated  form,  spectrum of  radius,  adds  only  nearly  by  Gaussian  and  that  which For  the  fact faster  include Z-pinch to  the  suggesting  that  contribution  The  line  profile  by  the  interaction  a  single  independent  spectrum  f o r the  0.015nm  4nm,  little  i t .  of  account  [BERM75].  dominated  ensemble line  goes  Theories  Berman  so  an  one  domain.  entropy  collisions.  line  for a  as  domain  Bohr  makes  the  operator  i s normally  does  exists  perturbers.  space  broadening.  of  emitters  Hilbert  M  width  is  and  L  line  experiment  The  a  o b s e r v a t i o n s can  the c o n v o l u t i o n  the  F(v)  then  I kT  assumption  reviewed  by  P(co),  deviation  CJ.  have  is  density  time  action  Doppler  more  these  whatever  the  the  i t s maximum  standard  of  with  include  the  this  c  is  given  ( i . e . frequency)  on  ACJ  be  that  will  in  i n t r o d u c e d by  that  will  emitters  connection  Multiplication  convolution  assuming  profile  from  i n thermal  line  independent  The  comes  factors.  the  broadened  and  separation  of  is  emitter  emitting  obtained  by  in  may  atoms.  that this of  be In  sampling  II.THEORY  24  photons  from  from  same e m i t t i n g  the  these  a  atoms  in this  plasma  would i f the  metastable In  this  may  be  plasma states  work  have  there are  "folded  in"  as  of  function  11. 4  Theories  would  when be  of  modern  technique radiation  power  spectral  Pico)  and  the  sum  field quantum  states  broadening  the  out  where  pumping).  Doppler  effect  has  that  been  profile  Shapes  date  back  that  atomic  other  has  advanced  as  particles  weakly  the  be  density.  with  i s to write  thin  (e.g.  spectrum  and  Line  system  of  used.  optically  to calculating  the  be  optical  so  independent  pointed  collisions  for a  far  as  vibrations [MICH95].  substantially. coupled  emission  to  spectrum  The  the  free  as  the  density  =  4CJ*  Z  3  i s over  perturbers.  principle  line  i s to  prepared  conditions,  of  independence  an  through  temperature  photons  a l t h o u g h c a r e must  specially  i s reduced  plasma  the  3c  where  the  Michelson  by  time  space  after  spectral  altered  that  such  Calculation  Albert  Since  no  the  that  attained  several  model  independence,  been  problem  ensemble  shown  been  even  statistical  i f the  this  has  possibly  The  i t was  guarantee  The  1895,  atom.  section  calculated. a  interval,  is essential  Earlier  taken  finite  contain  The  8(  oi-cj  a/3  a l l states density  everything  )  <a\p\a>  |a>  and  </3|d|a>  a/3  |0>  operator  p and  that  be  may  of  a l l the  dipole  known  emitters  operator d  about  the  in  system.  25  II.THEORY  Similar  expressions  [PEAC81], The Fourier  have  been  Smith  [SMIT69],  power  spectral  used  as a  and Griem  s t a r t i n g point  by  Peach  [GRIE64].  density  P(co) i s i n t u r n  given  by t h e  transform  3cos = J _ C(s)e 2TT-  Pico)  of  the autocorrelation  C(s)  ds,  function  <a|d|0>><0|U* ( s , 0 ) d u ( s , 0 )  = I  | a>  <a|p|a>,  aj3  where  <a|d|/3>  moment.  i s the expectation  The  equivalent  Lindholm-Foley Since the  \a>  problem  requires  impact and  independence expected time  average  number  is  of a  of a  mean  single  leads  p.  and  that  the  and  the plasma.  atom  appropriate  of  statistical  may  affected  space  The l i n e the  time  turn  i t s  a l l of the  The p r o b l e m  system, in  properties  c a n be c a l c u l a t e d  emitter  single  from  to  This  and  from  the  therefore by  with a corresponding Hilbert  are calculated  dipole  of the f u l l  assumptions  emitter.  product of a  states.  states  space  of emitters  single  to describe  spectroscopy  statement  U  Hilbert  ergodicity  classical  model.  earlier  of perturbers,  needed  shift  finding  a  The  as that  the tensor  atomic  of  f o r an ensemble  re-expressed  by  and  phase  one o f  choice  of the  classical  |/3> a r e s t a t i o n a r y  becomes  representation.  value  be  a  large  space  formed  whatever  profiles  else  needed f o r  evolution  of  the  26  II.THEORY  The time  time  dependent  dependent  formally  with  interaction  a  Dyson  The  end  the  perturbation  and  so  the  result  on.  series  due  to  with  where The  they  impact  collisions  a l l act model  between and  collision  perturbed  impact  transition  theory. scattering before limit  the on  next  the  The  producing state at  a  of  the  A l l an  "electric  energies rate  of  and  three,  perturbers quasistatic  that  This  the  power  the  distribution  of  series  then  not is  scattering  assume  goes  assumption  do  interaction  from to  of  sampled  impacts the  have  to  that  the  completion  will  also  set  a  rate.  act  time at  once,  alters  Transitions  from  of  are  each  which  dipole  sequence  time  derived  perturbers  emitter. by  a  (i.e.  always so  A  eliminates  is calculated  subspace,  that  be  microfield"  determined  microfield  perturber  the  the  i t s assumed  which  interaction  the  describes  motivates  where  and  generates  can  model  of  which  series  model  emitters.  assumed  occurs.  quasistatic  altogether.  from  and  almost  and  calculated  perturbers, this  time,  levels,  isolated,  event  density  a  i t s name  models  are  impact  probabilities  however  events  with  the  once.  sometimes  other  These  at  energy  alter  but  the  parameters  It  adiabatic),  at  gets  uniformly. the  one  two  be  by  representation.  expansion)  working  perturbers  velocities  is  of  can  interaction  cluster  limits:  emitter  the  i s determined and  perturber,  difficulty  the  in  (a  one  operator  potential,  series  approximate  interact model  is a  The  two  evolution  spectral  take  stationary  place The  density  density  collectively  the  operator. the  dependence  uniformly  distribution  operator  P(CJ)  comes  on  the  from  a  27  II.THEORY  uniform  sampling  area  of  plasma  Mozer  [BARA59, The  deals  theory  either  or  from  the  Time  operator  t  at  time  Eliminating which  commutes must  this  vanishes at  requirement  with of  Relaxing intermediate the  range  really  the  static. are  given  An  the  i n the  hidden  emitter the  is time  (Such  a  commute  finite  within  to  the  unchanged  is  is  made  aware  the  of  in its  potential  choosing  at  a  interval,  t>t . 0  potential and  Such  Hamiltonian,  by  operator  operator  interval.  is the  by two  broadening the  spectral  this  where  be  if  impact  formalism,  ordering  to  i t  a  which  potential  precisely  the  theory.  between line  of  true  left  the  time  that  is  i n the  seem  with  is equivalent  some  since  deletion  needed  not  nature,  assumption,  is  even  next  be  ordering  power  of  same  not  however,  plasma, outline  the  assumption  current  from  can  HOOP68].  by  collision"  adiabatic  is adiabatic  The  unperturbed  situation  of  calculated inside  the  this  [HOOP66,  do  times  the  Baranger,  authors  operator  outside  energies.  adiabatic  this  of  does  0  a l l  commute  is  series.  the  implications.)  s t u d i e d e x t e n s i v e l y by  s u b t l y ) when  Dyson  although  separate  states.  number  (more  This  Hooper  "elastic  quantum  collision,  SMIT69,  model  sometimes  the  atomic  been  and  stationary  as  principal  has  MOZE60],  although  deleted  perturbed  quasistatic  with  models,  of  when  easy,  still  theories.  of  i s not  and  test  a  system can  electric  field  of  the  beyond  the  P(a>)  the  and  lies  When  spectrum  density the  means  limits  line  technique  section.  no  assumed  be field  to  be  its validity  II.THEORY  28  11.5  The  adiabatic  assumption, the  which  probability  requirements  c a n be  MERZ70)  reduced  theory  is  of  of  is  the Adiabat i c  c a n be  perturbation  MESS 5 8 ,  Test ing  calculation  found  i n almost  line  that  function  the atomic  H(t)  where  H  represents  0  unperturbed  the  (A  and t h e i r  particles.  measure  of  interaction  the  structure  jhdU(t,t ) dt 0  is  then  used  is  k n o w n , U may  independent  The s m a l l and  H(t)U(t,t ), 0  t o d e f i n e the time be  jfcdU, dt  factored  =  into  XU V(t)U U 0  0  e.g.  reduced energy  in the to  a  levels.  form  + XV(t),  0  of the system.  =  of  forP(CJ)  involved  i s of the  the  set  textbook,  is  that  on  formal  of the s t a t e s problem  simple  requirement depend  Hamiltonian  e m i t t e r , and V ( t ) i s the p o t e n t i a l  of other  quite  i n the expression  states  time  presence  asymptotic  as a  not  Hamiltonian  = H  a  any s t a n d a r d  operator  atomic  on  levels.  broadening  of the l o c a l  Suppose  emission  energy  The d i p o l e  The  informally  the  to a constant  transition.  dependent  stated  photon  Limit  a  energy  parameter means  X  =  1,  operator  U.  0  a  0  equation  Since  11=11011, , a n d t h e e q u a t i o n  U, ( t ) =  both  f o r developing the  U(t ,t )  evolution  due t o t h e is  The S c h r o d i n g e r  0  of the  1 ,  H  0  f o r U,  29  II.THEORY  may  be  rewritten  U,(t)  which  may  then  Higher V(t) with  U  that  be  a n d U,.  0  no  0  solved terms  by  eigenstates  transitions  occur,  i s that  allowing  0  0  although  H  0  i s formally  ordering  line bound  U  state  ii  identical  =  from  going  broadening  exp  into  mechanism  energy  to the  in strict  of  assuming  terms  the only  due t o X V ( t )  i s then  given  V(s) will  -jh" e  i  t  series  the the f u l l a  long  c a n be  i n the diagonal  2  L  effect  be  by  commute  with  0  i s removed  Without  commute  expression  U  which  and can t h e r e f o r e  f o r a l l s, then  the simpler  i n X. unless  of t r a n s i t i o n series  series  to calculate,  mathematical  The power  with  f o r a power  as H ,  probabilities  small.  equation,  Uo(s)V(s)U (s)U,(s),  in X are d i f f i c u l t  i s the  V ( s ) commutes  ds  iteration  This  asymptotically  V(s'),  as the i n t e g r a l  o  1 -  t h e same  requirement  If  =  order  has  t =0  for  obtained  when  time  expansion.  d i s c u s s i o n o f t h e method, t h e illustrated elements  by  o f U,  the  changing  II.THEORY  The  30  first  function,  exponential  i s  but the second  perturbation.  simply  depends  Fluctuations  on  in  Fourier  transform of the product.  states  in a  light  distribution the  final  expansion, precise instead  form  interaction  the  can  electric  distribution Holtsmark referred  The of  implies  of  on a c r u d e  of  the  the state  is  t h e He  I I n=4  made  fields.  the ratio the was  of P(CJ).  about  the  details,  and  assuming  that  The s m a l l  parameter  The  field  to  probability  calculated parameter  the  i n 1919 b y i s  usually  microfield,  quantum  number  using  t h e Bohr  radius  n,  . Ze 0  t o n=3  a j  n (n+1/2)(n+1) z  transition  5.3.10" 'm.  of the Z-pinch  be s a i d  plasma.  i s estimated c l a s s i c a l l y  47re  two  of the asymptotic  o f t h e Coulomb  first  the  the energy  density  to avoid  by  of  magnitude  spectral  i t i s best  delta  out" the  determine  must  a  energies of  square  and the standard s c a l e  1  approximately  density  latter  with p r i n c i p a l  C  The  something  by  "spread  the v a l i d i t y  by e l e c t r i c  t o as the Holtsmark  field  will  of  history  The c h a n g i n g  estimate  imposed  E  For  that  be e s t i m a t e d f r o m field  will  t o t h e power  V ( t ) . Again  [HOLT19],  Coulomb  time  V(t)  i s t o check  i s governed  then  the  transition  directly  task  which  rely  transform  of the emitted photons.  transform leads The  X  emitting  the  1  give  a t 469nm, t h e B o h r  The  nominal  radius  temperature  a  0  and  II.THEORY  31  X  =  E  /  E  H  Although from  zero  enough  to  A  to  of  the  of  X  stopping  are  beyond  well  this limit  correct.  a  be  scope  nothing There  done  one  of with  field  the  line  section  just  .  small  has  been  the  also  term.  this the  not  said  assumption  close  at  enough these  Everything that  about  series.  small  the  is  a l l about  questions  Nonetheless,  thesis.  lies  mechanism  asymptotic  is really  extends  number.  broadening  are  of  strengths  distribution  reasonably  the and  of  of  convergence!)  with  the  section will is  of  in this  justify  as  perturbers.  (and  given  most  X  complicated,  accuracy  value  leave  description  quite  0.01  distribution  infinity,  zero  motion  the  Holtsmark to  full  still the  the  * C  The to  topics beyond  adiabatic  II.THEORY  32  II.6  Given adiabatic are  that  best  formulas case  where  practice  effects  can  relied 469nm  MEWE67 a n d A  here. the  and  II.3  He  The  I I . 5 , so  +  of  a  way  of  of  represent  the  that  their In  limiting are  respective  the  case  Z-pinch  of  plasmas  ratio  Approximate  measurement  further  reiteration  of  section  plasma  a  between  forms  of  experiment.  density  this  density,  broadening  intensity  [MEWE67].  of  semi-empirical  similar  the  the  will  was not  i s devoted  temperature  from  given be  in  needed  entirely  spectral  to line  ratios. MEWE67,  wavelength  weight  absorption),  the and  be  level g (r) +  I  that  the  X can  i n i t s upper  statistical  provided  the  convolution.  in this  of  remaining part  Following  n (r)  used  use  to  measurement  case  quasistatic  i n such  588nm  according  the  These  observations  I  In  to  and  through  were  calculation  of  use.  is  light  spectroscopic  [GRIE74].  impact,  outline  to  emit  of  Mewe's c a l c u l a t i o n  GRIE74  intensity  line  Griem  previous  general  sections  technique  added  on  will  methods  independent  be  temperature,  II  by  be  D e n s i t y Measurement  experimental  Doppler,  to  and  plasma  several  for  given  assumed  have  the  theory,  available  current  He  Temperature  = C  plasma that  the  total related  (with  intensity to  the  principal  I  a  spectral  population  density  quantum  of  number  r)  and  by  . n«(r)  ? t T H  is lower  . gf  ,  X*  optically state  of  thin the  ( i . e . no  transition  self i s not  33  II.THEORY  the  ground  state.  statistical  The  weight  constants  of  oscillator  strength"  structure  components.  geometry  and  statistical of  the  weight  are  level  constant  C  respectively  and  averaging  identical  g+(r)  this  the  over  arises  from  the  the  "absorption  a l l  from  the  the  for a l l spectral  i s known  thermal  referred  by  be  The  value  name  will  equation  modified  which  fine  optical  lines.  quantum  Saha-Boltzmann  n.(r,Z) g (r,Z)  =  be  The  mechanics  so  its  The  temperature  equation  to  their  operator, the  maximum  is  usually  equivalent:  and  density  calculated  name, a l t h o u g h  b(r,Z) from  be  by  obtained  classical  to  temperature  density  given  of  +  plasma  system  +  same  far  the  n (r)  of  are  the  of  n (r)  the  to  will  allow  correction factors  densities  from  +  population.  Z-pinch  classical  n (r)  the  Saha-Boltzmann  intensity  equilibrium  principle.  the  line  calculating  in  entropy  will  The  by  f  atom.  involves  for  '  and  lower  determined  is therefore  Relating  which  the  g  expected from  in general  account  for  i n MEWE67  the there  population  equilibrium values.  i s given  the  This  as  b(r,Z)  +  where  n (r,Z) +  principal the  i s the  quantum  emitting  atom  population  of to  number  r,  and  Z  refers  (Z=0,  1  or  2  for  respectively).  The  other  the  and  the  electrons  density  densities next  N  and  He  the the I,  level net  charge  II,  or  n,(r,Z+1)  ionized species.  The  with  refer  on III to  statistical  II.THEORY  weights  34  g  and  +  subscripts E(r,Z)  g,  have  and arguments  i s the  continuum.  energy For  hydrogenic  upper  remaining  the  symbols  into  intensities 588nm  line  have  ion  equation  E(r,Z)  inverse  form  The  inverse  know  the  compare  their  usual  meaning.  f o r I , and taking  and  temperature system.  tables  by  o f two  I I 469nm  in this  ended of  to simplify  replacing  a  by t h e p r e v i o u s  and  given  line  t o He I  with  already  known  deviation  will  for  series  t o occur give  to  second  to  It  i s  in  GRIE74  close  tothe  in the solid  notice  to  first  wave.  calculations  Taylor  V.  wanting  and  expansion  An  ultimately  the Z-pinch:  pinch vessels, plasma  i n MEWE67.  because  experiment inside  equation  i n Chapter  however,  the exact  them  g  be u s e d  approximate  existence  large  b  and density  and density  Any  of  expression will  a n d open  possible  MEWE67  a ratio  densities  • e x p J" E_p_ 1 .  /  are determined  two r e a s o n s  the  population  t h e c o n s t a n t C, t h e He  i s only  the solid  therefore  0  temperature  determine  quasi-  Kl"  and E  0  of this  are only  the  the  c a n be p u t i n t h e f o r m  and  there  and  to  2  I 588  for  r  term  i s g i v e n by  2  0  constants K  their  13.6'(Z+1) .r" .  Iq.s<> = K - [ k T J  The  to  t h e energy  level  He I I  expression f o rthe  to eliminate ratio  from  o f He I , t h i s  this  the earlier  ionization  =  attached  Finally,  t  hydrogenic  levels  Substituting  as N and n .  of  E(r,Z)  The  t h e same m e a n i n g  that  a  end fresh  II.THEORY  35  calculation  should  unnecessary. A the  Chapter  final  point  adiabatic  theories  justify  the  itself  will  Chapter  V.  be  of  that  practical  that  are  needed  can  first  the  along  exerted  on  radial  over an  the  components.  a  magnetic therefore  be  instead  entire plasma  field.  of  Value  and  exerted into  as  the  to  with  the  same  with major  to matters the  assumptions  in  This  the  state that  produce  wave  parallel  the  be  forces  a x i a l and in  PRES74  ( l e s s than current  a uniform  and  first  variables  into  i n that  on t h e p l a s m a  Z-pinch  requires  conclusively  follows  models  section.  plasma  shock  data  Problem  be done  second  on  calculations in  be s e p a r a b l e  i s shown  The l a t t e r  much  a r e reduced  t h e plasma  distribution will  separable  the other  system.  particles  relies  Any a t t e m p t t o  i n the present  of the pinching  Forces  MEWE67  equilibrium  The three  i s that  axis,  The former  length).  uniform  be  them.  dependence  detail.  to the spectroscopic  with  be c o v e r e d  i n more  subject  and density  assumption  curvature  600mm  equally  will  a s a one d i m e n s i o n a l  the  the small  predict  will  major  radial  uniform  by  to  o u t t o be  as  thermodynamic  c a l c u l a t i o n , t h e same m u s t  used  turns  o r i n GRIE74.  the I n i t i a l  the temperature  be t r e a t e d  that  just  along  Formalizing  t o do t h i s  The  emission,  local  discussed  topic  i s that  earlier  applied  this  this  b e made  calculations Tests  II.7  Now  of photon  necessary  inconsistency.  examine  should  outlined  rate  but i n p r a c t i c e  V will  that  theory  density  collision  be d o n e ,  3mm with  circular  particles  will  perpendicular  II.THEORY  36  components,  with  the a x i a l  and  perpendicular.  The a s s u m p t i o n  therefore  t o be  The  likely second  major  assumption  are  roughly  action.  This  assumption  because  pinching  shock  end  may  plug In  those  surface  in  postulating  well  i s slower,  a heat  shock  this  theory  i s that  over  a period  t h e peak  duration  of  contact  and the f i r s t  consistent suggesting can  with that  be a v e r a g e d  a  dynamics i s  i t  given  appearance camera.  uniform  from  The  period the  time.  strong against constant the  four  i s also  plasma wave  by  i s that  than  There  the strong  interaction  model.  t o be  longer  first  in  the than  argument  peak.  long  gas  higher,  initial  are observed  pressure  the e n t i r e  an  of t h e shock  This  that  hypothesis  The  the  by t h e  discrepancy  valid  density  l a g between  shown  shock  this  ten microseconds,  justify,  balance.  pressure  plasma.  velocities  to  to the c o l d  be  after  and  dynamical  created  energy  will  explains  the  peak  pressure  expanding  of gas  difficult  density  and the shock  any c o n t r i b u t i o n over  more  the o v e r a l l  density  of at least  of the streak  being  temperature  the period  but an e q u a l l y  shock  two m i c r o s e c o n d  view  both  axial  plasma  impetus  constant  is  further  of  initial  example,  II.9  region by  microsecond  a  flux,  compression  over  distort  section  i s that  initial  for  by  independent  i s somewhat  The  V,  predicted  argument  the  wave.  Chapter  contact  constant  of the large  very  of  directions  justified.  density  mainly  radial  to  i n the  a  gas field  stability  i s  driving  plasma,  initial  thrust  37  II.THEORY  Given  these  conservation one  of  dimensional  flow  can. be  region  material  major  mass,  The  up  position  are  the  internal  s t a t e s of  across  algebraic in  the  at  system.  any  one  The  one  from  derived  uniform  regions  subdivision model are  needed The  initial the wave be  to  of  have not  in  existing  s t r u c t u r e , and two  regions  to  predict a  having  and  knowledge  about  fluid  i s already 1-1  regardless enough  undisturbed.  shown  the  of  Past these  will of  the  away studies  evolve  in  from of  undisturbed  size to  the  of  flow  is a  set  of  regions  internal  states  entire  later  model  equations  and  is  that  ( i . e . further  In  a  more  uniform  for  also with  take large  example,  there  will  systems will  that  sort  interface  regions  than  study.  some  similar  flow  regions  will  into  the  its  equations)  systems  dynamics  that  a l l the  II.9  known,  so  of  c u r r e n t l y under  II.8  the  volume  flow  accuracy). by  that  a  a  their  uniform  for  at  result  gradients  processes  Figure  and  the  conditions  Changes  differential  gained  It  is  and  sections  far  edges  be  the  considered that  to  the  is  jump  net  volumes  internal  improve  jumps.  s t a t e of  of  written  conservation  The  for  regions,  p r o p e r t i e s of  their  set  no  describe  pressure  initial  full  to  regions  d i f f e r e n c e between a  uniform  state.  surface. the  be  region  the  sufficient  i s nothing  models  advantage  is  will  there  of  neighboring  of  equations  assumption  elemental  (through  Knowledge  development.  number  connecting  time  major  f u r t h e r reduced  contact  equations  basic  momentum may  some d e f i n i t e  related  the  a  Each  at  and  energy  are  interfaces.  and  third  into  equations  existing  assumptions,  energy,  flow.  broken  conservation the  two  be  of  always to  be  have formed  38  II.THEORY  by  a shock  A model  wave  i n t h e gas and an e x p a n s i o n  of the system  developed thesis,  between  t o whatever  level  investigation  scheme  makes  of  i t adequate the  these  and  heat  parameters  i s t h e minimum  flux  can  plasma. then  seems n e c e s s a r y . end  the motion  across  needed  i n the  waves  Ahlborn-Sinnot  to predict  interface  two  of d e t a i l  the  wave  i t .  to describe  plasma/gas  relevant  these  this  confinement  of the  The  In  be  s e t of  effects.  4  EXPANSION  FAN  CONTACT  SHOCK  FRONT  SURFACE  11 — 1  The a  four  Figure  formal version region  II-l.  flow  Regions  plasma.  Region  rightward  moving  the  expanded  two  Flow  o f t h e A h l b o r n - S i n n o t model system:  a  one a n d f o u r i s  contact  plasma  Uniform  structure  forms  starts  of t h e form  are the undisturbed  the shock  surface.  Structure  compressed  Behind  region  the  three,  shown i n gas  gas ahead contact  and  the  with  and  of the surface  pressure  39  II.THEORY  gradient region of  between  four  its  i s normally  fan  transfer  heat  flux  require that  from  q,  that  the  heat  and  existence  of  low  Ahlborn-Sinnot  model  Calculation conditions:  predicted the  this  frame  a  gas  G.  false  this  process between  gas  leading  edge  of  the  to  the  flux  i s to the  unify  form:  course  of  observe  i n the  in  of  the  set  general  the  tube.  model  two  variables that  the  within  measurement  i s brought S  means The  clear  on  objective  interaction  a  The  means c o n s i s t e n t  and  are  so  makes  second  through  in practice  allow  of  and  system.  also  to  depend  assumptions  fact  zero  will  P  a  q  q  "Plasma  formal  such  and  S  restrict  shock  process  their  will  classical  observable  by  throughout.  to  system,  The  for  instantaneous,  will  q  the  Finally,  includes q  be  i t s corresponding the  velocity.  uniform  Setting  equivalent  to  shape  that  regions  heat  the  regions  flow  of  (from  i s accounted  uniform  i s that  models,  the  assumptions.  assumption  experiment  the  plasma  fan  sound  stay  of  Failure  The  plasma  to  undisturbed  expansion  derivation  states are  the  the  temperature  reference  In  any  describe  model  of  the  within  that  statement  observed." a  to  other  single  with  of  model  with  at  values.  first  adequate  the  plasma  flow  and  traces).  although  comparatively  is  called  travels  pressure  assumed  region  characteristic  expansion heat  this  in  contact  should  that  basic  into  be  there  is  premise  of  confined  to  the  choice  be  made  thesis  was  shock  tube  to  them.  Finally,  much  obtained  from  prior  model  taken  from  was  information  work an  in  existing  used  related version  in  this  fields.  The  presented  by  Whitham  40  II.THEORY  [WHIT74], appears  in this  analysis Sinnot was  subject  was  PRES74, valid the  and  summarized  are  this  gas  state  presented  flow  model.  Systeme  plasma  Emmons II-l,  variables  assumptions  of was  the  two  Other  The  nominal  in Table  following  of  units  Ahlborn  II-2.  model values The  sections.  and  checking  throughout. in part  useful  from  z  Whitham's  measurement  available  [LICK62].  and  $.  i s a l r e a d y known  data.  strength  Dimensional  selecting  range  shock  of  International  plasma in  the  name  uniform  helium  i n the  new the  helped  in Table  the  that  with  Z-pinch  and  change  joined  expected  Lick  minor  under  using  the  equilibrium of  the  by  f o r the  tables  and  then  simplified  the  thesis  to derive  Furthermore,  to  the  from  procedures material  published  nomenclature of  models  on  the  is  plasma  themselves  .THEORY  11 — 1  Model  Nomenclature  Variables A  cross  sectional  a  sound  velocity  c  specific  E  energy  h  specific  M  mass  N  number  P  pressure  q  heat  R  helium  T  temperature  t  time  (seconds)  U  shock  front  V  contact  z  axial  7  enthalpy  P  mass  heat  (m.s  of shock - 1  tube  (m ) 2  )  at constant  volume  (J.kg  _ 1  .K"  (joules) enthalpy  present  (J.kg~ ) 1  (m~ ) 3  (pascals  flux  2 (kg)  in region  density  from  =  N.nr ) 2  3 to 2  region  gas constant  1  (m.s~ ) 1  velocity  density  (dimensionless)  flux  expanded  4  undisturbed  (W.nr )  $=(p ~Pi)/pi 2  Subscripts  3  (m)  3  strength  shock  1  (kg.nr )  energy  2  (m.s~ )  co-ordinate  coefficient  undisturbed  2  ( J . k g " • .K~ )  velocity  position  1  (W.irr )  (kelvin)  surface  mechanical shock  area  cold  gas  compressed  gas  plasma plasma  2  (dimensionless)  1  II.THEORY  II-2  Cold  Gas  Summary  of Nominal  Parameters  Ahead o f Shock  Composition  Helium  Enthalpy  7i  =  1.667  Temperature  T,  =  300K  Pressure  p,  =  525  Mass  Density  p,  =  8.44x10-"  Speed  a,  =  1018  Sound  Plasma  Coefficient  Driver  (from  (99.995%  pascals  m.s"  He He He e-  + +  1.18  Temperature  T,  =  35000K  Pressure  p„  =  101300  Mass  p«  =  6.98x10-"  N«  = 8X10  a„  =  Density  Sound  Density  Speed  Variation  Scaled  Coefficient  Number  i n N„  1  and  T  a  2 2  13090  +10%,  pascals  m'  kg.m" 3  m.s"  1  -30%  Variables  Temperature  T =  T/T,  Number  n  N/N,  Density  =  General Ideal  Gas  3  0.28% 49.68% 0.12% 49.92%  +  7a =  Electron  kg.m"  t=15/us t o t = 4 8 u s )  Composition: equilibrium mole f r a c t i o n s [LICK62]  Enthalpy  pure)  Constant  i n p=pRT  R = 2073 specific  J.kg- .K" to helium 1  1  3  43  II.THEORY  If the  there  system  II.8  The  no  heat  is  shown  in Figure  Shock  Tube  transfer  Model  across  11 — 1 w i l l  the  evolve  contact  as  surface,  shown  below.  i  /  CONTACT SURFACE *  EXPANSION  FAN /  I  PLASMA !§fm J&m  HOT  SHOCK FRONT  COLD  GAS  Z=o  II-2  Once is  again,  the  region  undisturbed  is  given  U.  Each  by  V,  region  i s the  plasma. the  p  given  i t s specific  The  the  velocity  corresponding  density  p.  The  coefficient  gas  of  shock  internal  Simple  Shock  plug;  the  i t s state energy  region  contact  velocity  of  Wave  four  surface  i s given  defined each  by  by  a  region  is  enthalpy,  h  where  undisturbed  i s in equilibrium with  pressure by  and  and  one  The  y  may  =  _x_  £,  7-1  p  also  depend  on  p  and  p,  but  in a l l  II.THEORY  cases to  will  the  where the  44  l i e between  ideal  pressure free  extra  The quote  kinetic  stored  enthalpy shock  states.  means  model  the governing  o f 1.67  of specific  Smaller  in  for  atoms.  7  will  and  i t  a smaller  stored  account  states of excited  that  the  The  increase the  pressure.  i swell  equation  values  applies  heats, and  p r o p o r t i o n a l t o t h e energy  a t any given  tube  The value  7 i s the ratio  i n t h e bound  7/(7-1)  of  specific  where  i sdirectly  motion  energy  factor  gas  1.1 a n d 1 . 6 7 .  known,  from  suffices  to  WHIT74,  2 • an 7«-1 a .  where  the  iteration. the and  shock  The e n t h a l p y  tables of Lick a  f t  are calculated values  LICK62)  of approximately  Its the  in  from  7,  one atmosphere:  to error  also  A  p,, the  t o an i n f l u e n c e s t i f l i n g  108 c a n t h e r e f o r e b e u s e d A  shock  asymptotic  of  relations  this  thirty  power  with  strength  f o rlarge  The  a,  nominal from  pascals.  by v a r y i n g  then  $=108.  T„, arguably  change  and although  in  this  factor  o f 0.08.  from  (again  values,  pressure  by  velocities  pressure 101300  found taken  2  percent  two p e r c e n t ,  changes  are  a =7p/p.  nominal  c a n be c h e c k e d  parameter.  be  The sound  plasma  their  can  a n d 7,  the relation  an e s t i m a t e d  and $ by o n l y  temperature  7,  [LICK62].  a, p, and 7 a r e g i v e n  least-known  raised of  give  sensitivity  changes  coefficients  a n d Emmons  initial  If  S=(p2~Pi)/Pi  strength  A shock  T  a  change  in  $  i s  strength  confidence. can  $ (also  be  from  analyzed WHIT74).  with If  the U  i s  45  II.THEORY  the  observed  and  shock  shock  velocity,  pressure p  are  2  V  then  given  contact  surface  velocity  V  by  o(rM,  2 U +  =  the  7+1  p  2 u  =  2  + o(r ).  2  1  P l  7+1  the  When  the  shock  tube  which shock  nominal model,  reduces  the  fifty-six  or  percent  will  detectable means  with  that  regions.  streak  clear  I f no  expansion  are  underlying  premises  first  surface. where  this  not  those must  assumption The  assumption  wave  be  by  false. no  section  i s relaxed  The  or  model,  most  transfer  will  p r e s e n t an heat  flux  the  to  the the  then  one  a  test in  the  light  of  i f  likely  the  event  emit  between  found, the  i n any  to  wave  either  temperature  seen  into  (to  temperature  heat  and  in  enough  plasma  is  percent  difficult  i s that  s h o u l d be  predicted  of  following  A  be  inserted  expansion  b o t h ) , but  hot  camera.  differences  conditions  the  14500K,  i s an  appear  not  prediction  roughly a  may  should  are  fifty-six  (or p o s s i b l y  Another  be  prediction  p r e s s u r e by  change  II-2  Table  reduction  density  experimentally. shock  This  2  from  i t s chief  plasma  pressure p ) .  temperature  values  35000K various shock of  the  candidate i s  a c r o s s the  contact  alternate i s allowed.  model  II.THEORY  46  11.9  An  intuitive  plasma  to  velocity heat and  of  flux the  the  shock  and  be  the V  the  mass  rate  at  a  Initial mass  to  mass shock  density  of  p,UA.  The  volume  which  also Note  implies that  piston,  and  in  shock  the  that  i f the  must  mass  p  also  =  The  ratio  that  energy  velocities.  The  shock  gas  hence  the  that  shock the  a  wave shock  plasma.  The  of  U,  V  and  constant,  upstream  so of  the the  if  density  region at  and  a  sweeps  rate  ratio rates,  will  p  2  up  (U-V)A. of  shock  namely  p,U, U-V  p  be  is  the  measurements  expands  zero,  is  2  i s fixed  2  the  the  shock  i s conserved  implication  and  of  the  volume  the  pressure  i f density  then  both  2  both  increasing  i s uniform  shock  i s just  and  from  i t i s shown  of  as  shock.  are  flowing  q.  time,  p  section  experimental  gas  the  Model  pressure  expansion  calculate  with  heat  gas  well  how  i n the  volume  this  Flow  velocities  the  shows  change  and  In  as  reducing  not  determine  wave.  to  that  i n c r e a s e the  surface,  used  Uni form  suggests  the  pressure  do  the  affect  derivation  can If  will  will  contact  following  and  gas  and  of  argument  the  q  pressure  U  Derivation  as  at  the  fixed  by  above,  then  constant. from  cannot  be  is related  to  q  interface. the  The must  heated  driving  temperature experimental  show  without  up  in  changing  the U  V. The  momentum.  pressure In  an  p  2  infinitesimal  time  p, 6t,  by the  the shock  c o n s e r v a t i o n of gas  receives  47  II.THEORY  new  momentum  new  mass  p A6t  from  2  p,UA5t  velocity  V .  supplied  by  i s  the plasma added  It therefore the d r i v i n g  comes over  conservation from  the heat  distance  V5t.  piston.  energy P l  the  flux  UA5t,  heating  as  temperature  and  5t t h e s e  A l l of  +  density  8E  energy  needed  6t,  and a c c e l e r a t e d  p,UA6tV, e x a c t l y  picture.  to that  leaving  of  The energy the  contribute  piston  input acting  energy  qASt.  temperature  kinetic  and compression  the  2  gas  same  PTUV.  = p AV5t  +  unchanged.  partly  t h e shock  q and the force  In time  shock  stays  =  2  In the  The A5t c a n c e l s ,  finishes  6E  Because  to  g a i n s momentum  p  Energy  piston.  i s constant, goes  +  into  (p!UA6t)V /2, 2  to bring  the  of the shock.  new  i t sinternal  the  new  but a l s o mass  The p r o c e s s  mass i n the  to  the  i s shown i n  Figure I I - 3 . The on  state  t h e amount  change  energy  o f mass  M  and  6E  The  specific  mass  of gas  p /p 2  2  state.  heat  c  ideal  i t schange  =  Mc6T  =  _M_6(p/p). 7-1  i s taken  i s externally I t does  SE o f a n  driven  n o t do work  gas  depends  i n temperature  a t c o n s t a n t volume, from on  the i t s  P 1 / P 1  solely  6T,  because  state  surroundings.  to  the the  48  II.THEORY  3  [  HEAT  1  2  |  NEW at time t  N x  x  v\  v \  MASS':  X  V  \  V  pv^  2 mmm  1  !  WORK  mmm  J i  at time  t+5t  II-3  The  8(p/p)  term  can  6E  Energy  then  be  = _1_ 7-1  L  Balance  expanded  factor  can  P1UV 2  The  conservation  2  be  +  cancelled  1  j £iP  7-1L  P  " Pi  p V + _1_| 2 7-1 2  L  £JJ?2 P 2  2  UA6t. -I  and  - p,  6E e q u a t e d  to the  |U  q.  = p V 2  +  input  6E : +  J  2  o f momentum  give  p 2  A8t  Region  p_2_ - p_L p,UA5t p, J 2  = _JL_ £JLP2 7-1 L p  The  to  i n t h e Shock  equation  " Pi  simplifies  |U » P J  2  V +  q,  the  first  term:  49  II.THEORY  which  gives  q as a  function  q  I £_LP  1  =  7-1  For  q=0,  relations shown the and  this  V,  changing  something this  like  section  describe real  region  the that  and  the  the  system  i n temperature,  gradient-free.  intensity  changes  boundaries  between  calculations  in this  this  thus  experimental  on  the  uniform section  test.  i s as  of  implicitly  one  negating Later  of the system pressure  in  assume  a  long  region  with  regions.  and the next  can  The be  a  flux steady  that  IV i t w i l l  photographs  with  heat  assumption  in  U and V  regions  large  streak flow  that  separating  i n Chapter  into  derivations  Too  the  of U  II-2  Figure  Nonetheless,  interfaces  into  shock  increased  diagram  in their properties.  change  that  11.10  strong  the c h a r a c t e r i s t i c traces  II-4.  of r e a l  smooth  is  "spread"  of Figure  would  flow  i s small,  evolution  motion  to the asymptotic  The e v o l u t i o n q  in section  differences  " P  2  reduces  When  will  quantities:  92  earlier.  II-2.  in Figure shock  L  equation  introduced  of experimental  be  the shown  mark heat  justified  the flux by  50  II.THEORY  1  i  SLOWER CONTACT SURFACE SMALLER EXPANSION FAN  /  /  / SHOCK REGION HIGHER PRESSURE  / W y  ^FASTER  SHOCK FRONT  Z=  II-4  11.10  heat the  The Shock  Prediction  of Improved  The  total  flux  q and t h e p r e s s u r e - v e l o c i t y  mechanical  energy  Wave w i t h  energy  flux  used  End  a t t h e open  t o "push"  Heat  Flux  Present  Confinement  end.includes  flux  which  the contact  both the  accounts f o r  surface:  $ = pV 2  =  The  total It  p,  will  heat is  i s then  i s clear reduce  flux  whether  minimum  loss  from  given  2  b y t h e sum q + * .  t h e c o n s e r v a t i o n o f mass  * by r e d u c i n g U a n d V.  q will  tend  t o reduce  p, c a n be c h o s e n  will  p,UV .  be l e s s  than  that  It i s also  V a n d i n c r e a s e U.  t o minimize  the heat  loss  q+$,  and  to a solid  increasing  clear  that the  The q u e s t i o n whether  this  electrode.  II.THEORY  If heat The  51  q  i s  small  conduction scaling  compared  relation  for #  i s then  -.1/2  r  7 + 1  p  i s fixed  2  by t h e p l a s m a ,  time  of gas dynamical  four  will  cut $  The  corresponding  found  that  the  V  V ~  U  root  be  be  2 u| 1 - ( x M ) 7+1 2  into  conjecture,  when  q  p,  by  on t h e p l a s m a equation  R T  iU"  during the  a  factor  of  escape for  velocity i s  V.  If  q  i s  a s y m p t o t i c a l l y , so  - (j±±) (7-1 )U" g 1. 2 p, J 3  2  square  root  i s present.  I I . 1 i t was  three formal  main rules  external  procedures  reality.  Sections  basic  a n d V.  o f p,,  then  V  The e x p e r i m e n t a l  (and test  $) will  q and $ as f u n c t i o n s of p,.  section  broken  raising  constant  c a n be expanded  11.11  In  2  by  reduced  to find  by  balance  term  s c a l e s as the inverse  will  given  for p  ignore  3/2 -1/2 Pi •  then  effect  L  If  2  equations  and i s roughly  action,  the energy  square  i s given  P  shock  to  in half.  by s o l v i n g  small,  i t i s convenient  and use the s t r o n g  * ~ LLl_J If  to  statements,  Summary  stated that parts:  basic  f o r working  for  testing  II.2 to II.7 whereas  a  formal  statements  out t h e i r the  have  sections  model  model  largely  could  be  of fact  and  inferences, in dealt  I I . 8 t o 11.10  and  experimental with covered  the the  II.THEORY  formal of  52  rules.  This  the t e s t i n g The  procedures  first  following  section  list  part  t o be  of  of basic  provides  the  a  summary  introduced model  in  anticipation  i n Chapter I I I .  c a n be  summarized  into the  premises:  1.  The plasma c o n d i t i o n s p r e s s u r e peak.  2.  T h e number d i s t r i b u t i o n o f v e l o c i t i e s i n t h e p l a s m a may b e c h a r a c t e r i z e d b y t h e same t e m p e r a t u r e a s t h e number d i s t r i b u t i o n i n t h e b o u n d s t a t e s c o r r e s p o n d i n g t o He I 588nm a n d He I I 469nm ( i . e l o c a l t h e r m o d y n a m i c equilibrium exists).  3.  T h e number d i s t r i b u t i o n i n t h e b o u n d s t a t e s i s a t t a i n e d t h r o u g h a c o l l i s i o n r a t e low enough f o r t h e p h o t o n e m i s s i o n t o be a d i a b a t i c .  4.  The p l a s m a  is optically  5.  The plasma  a n d g a s do  6.  The s o l e energy t r a n s f e r between plasma and gas i s through p a r t i c l e c o l l i s i o n at the i n t e r f a c e .  7.  The f l o w i s one d i m e n s i o n a l , w i t h n e g l i g i b l e of energy between r a d i a l and a x i a l m o t i o n .  transfer  8.  T h e f l o w may b e d i v i d e d i n t o internally in equilibrium.  which a r e  9.  Interfaces externally  10  The h e a t f l u x a c r o s s t h e plasma/gas i n t e r f a c e i s s m a l l enough t o p r e s e r v e both t h e sharp b o u n d a r i e s of t h e u n i f o r m flow r e g i o n s and t h e a d i a b a t i c model of plasma expansion.  The  second  descriptions that  higher  effectively  of  are constant  after  not mix.  of the model  sections  density  gas  i s derived  initial  thin.  uniform  regions  b e t w e e n t h e r e g i o n s may b e as changes i n l u m i n o s i t y .  part  the  i s  embodied  I I . 8 and I I . 9 .  plugs  will  in section  observed  the  The major  confine  11.10.  in  the  formal  prediction  plasma  more  II.THEORY  53  Finally, concisely  the  third  part  i n the f o l l o w i n g  "Helium plasma brought  the  model  The  with cold  shock  tube  helium  model  at  with -3  V=7000m.s" ,  Ahlborn-Sinnot  It  a plasma  pressure  conjecture  l o w e r V, w h i l e  p„  U  keeping p  V  a  i t .  The  empirical  transfer  with  the  Such a comparison  will  comparison  remaining p a r t s of t h i s specific  525  no h e a t t r a n s f e r contact  fifty-six  raising  is  3  and  surface  percent.  flux q w i l l  c l o s e r to i t s nominal  c a l c u l a t e d heat  c a n t h e n be c o m p a r e d PRES74.  300K  p, w i l l  The  raise  U  value.  reduce the net  a r e n o t a s p r e d i c t e d by t h e s h o c k  f l o w model w i t h heat  replace  by  m~  2 2  l o s s q+<i>."  and  uniform  stated  e x p a n s i o n wave w h i c h  i s that heat  i s f u r t h e r expected that  energy If  and  3  reduces the plasma  and  be  way:  p r e d i c t s a shock v e l o c i t y U=9500m.s , a velocity  may  a t 35000K a n d e l e c t r o n d e n s i t y 8 X 1 0  into contact  pascals.  of  flux  solid  can  be  tube model, brought  f o r t h e open end end  value  in  reported  be more s e n s i t i v e t h a n t h e  deal  with  measurements used t o c a r r y out t h i s  the work.  to  Z-pinch  o f m i d p o i n t t e m p e r a t u r e and d e n s i t y . thesis  the  apparatus  in  crude The and  Ill.EXPERIMENT  54  III. The a  experiment  c o n s i s t s of three  Z-pinch t o supply  pre-fill  EXPERIMENTAL SETUP parts: a glass  shock  t h e d r i v i n g p l a s m a , and a g a s p u f f  t h e shock t u b e w i t h  a higher  density  tube,  valve to  gas p l u g :  vac  111-1  The  above  discharge  diagram  takes place  shows  the p o s i t i v e electrode  is  in  of the pinch  valve,  joined  the  glass  to  The i n i t i a l shock t u b e  general  on t h e r i g h t .  connected t o the brass  outside  tubing.  the  between t h e n e g a t i v e  and  turn  Z-Pinch, Valve  vessel. the pinch  a n d Shock Tube  arrangement.  electrode  on t h e l e f t  The p o s i t i v e  electrode  mesh r e t u r n c o n d u c t o r  On t h e f a r r i g h t by a 150mm l e n g t h  s t a t e shown i n F i g u r e  The  i s the  on t h e  gas  puff  o f 25mm ID g l a s s  1-1 i s c r e a t e d  joins the p o s i t i v e electrode.  where  Ill.EXPERIMENT  55  III.1  The context  schematic in  the  The C o m p l e t e  representation  photograph  of  pinch  picture. left  The  hand  itself  shock  end.  analyzer  (OMA) u s e d  between  the  holes the to  for  Photograph  visible  tube and  OMA  to and  capacitor  the at  gas  the  puff  far  gas  upper  record the  valve are  right the  valve. hand  is  an  seen  in  the  lines.  center at  of  the  the  upper  Out of  optical table  bank  the on  The vacuum a n d g a s edge.  Apparatus  optical multichannel  Underneath  The s e c o n d  the  mounted  the  spectral  pinch is  bank.  right  may b e  of  diagonally across  a n c h o r i n g components.  Z-pinch drive  runs  At the  Figure III-1  below:  111-2  The  System  sight  with  larger  tapped  table  the.left  is  is  used  supply are  just  Ill.EXPERIMENT  56  I I I . 2 The Z-Pinch D i s c h a r g e The  Z-pinch  i s driven  microfarad capacitor.  by  t h e energy s t o r e d i n a f i f t y  The d i s c h a r g e c i r c u i t  Main c a p a c i t o r C, i s charged i n i t i a l l y 0.05MF t r i g g e r c a p a c i t o r i s charged 200k°,  resistor.  The  bank  i s as shown below.  t o twelve k i l o v o l t s . in parallel  The  through the  energy of f o u r k i l o j o u l e s i s about  enough t o heat a cup of c o f f e e t h r e e degrees C e l s i u s .  pinch  42 fi  200  HV  +o  V—VvVHVW  1 I 50 uF  C  0.05 F M  10M 190M  tr-  1  UV flash  The d i s c h a r g e b e g i n s w i t h a 9kV which  flashes  a  small  spark  between t h e e l e c t r o d e s of gap photons  travel  AAA/—"  k  through  III-3  Discharge C i r c u i t  pulse  from  a  thyratron,  gap p l a c e d i n s i d e a q u a r t z tube S . . The 3  t h e tube  surfaces, driving o f f electrons.  and The  resulting -ultraviolet strike gap  the electrode  breaks  down, t h e  57  III.EXPERIMENT  trigger load  capacitor  appears The  pin  i s discharged,  across  the  so  that  i s opposite  in polarity  to  the  static  voltage.  gap  electrodes  have  Current 100mm  flows  wide.  ground  electrode The  clamped  Following corners modes  were and  theory  a  the  to  reduced.  In  to  test was  leads  The  coil  output,  change  of  the  current,  a  time  ringing was  constant  period  d i s p l a y e d on  pinch  was  eventually  fired.  is an  of  the  across as  i t s 42J2  ST the  trigger gap.  great  even  The  as  the  when  the  plate  mesh  in  too  of  a  Rogowski  to  maximize  (For  the  should  noise  coil, the  from  a  The  the  passive  be  RC  highly  of  network  the  every  s e v e r a l hundred to  rate  integrated  photographed  pinch  inserted  signal/noise  comparison,  26/zs.)  and the  noise  properly.  i n t e g r a t e d by  oscilloscope  sharp  waveguide  much  i s proportional to  approximately  return  engineering, between  was  the  polyethylene  Electrical  there  with  100MS.  leads  waveguide.  coupling  oriented  showed  brass  wrapped  modes.  concept  was  are  copper  i s made c o a x i a l l y ,  i n microwave  practice  which  flat  the  parallel  space  Comparison  collected  leads  a  measured and  to  minimize  this  ratio.  with  pinch  the  practice  free  be  to  form  common  on  occur  through  attached  radiative  current  between  to  S , .  twice  Z-pinch  current  eliminated  sources The  two  gap  voltage  will  across  eroded.  the  being  together  main  voltage  Breakdown  badly  to  voltage  i s t h e r e f o r e almost  Connection  conductor.  other  been  the  of  i s arranged  voltage  in  pin  circuit  instantaneous  and  trigger  and  ,pinch signal  time  the  photographs reproducible.  58  Ill.EXPERIMENT  There  are  integrate voltage) the  the over  time  sine  as  wave  energy  the  standard  this  current  of  Because after  the  the  first  experiment,  first  cycle,  of  l63kA  smoothly.  integrals 180°  instead  discharge only  of  of  current  discovered  compared  with  discrepancies  of  gives  i n the  to  much  BERN79  and  method The  the  coil  were  error  work  machines current  be  current to  the  treat  the  decaying  The  initial to  squared the  the times  Z-pinch  this  131kA.  accurate.  the  A  peak  work.  not  always  proceed  the  current  performed  over  u n n o t i c e d because calculations.  because the  of  peak  distribution  f o r example,  in later  a  parameters,  mistakenly  s h o u l d be  value  current  more  remained  of  indicated  lower  does  DAUG66,  appears  this  i s to  when  i t s RLC  throughout  Rogowski  rarely  earlier  a  changing  90°.  in  technique  thereby  used  the  equated  equivalent  to  normally  equated  current  i t s internal  be  first  of  changes  the  In  the  first  i s expected  will  begins  signal. be  coil  value.  second  Z-pinch  Calibration this  The  the  be  method  then  are  of  i s to  the  exponentially  infinity  methods  then  measured  can  of  will  ( i . e . 90°)  an  One  current This  second  the  to  i t s model  calculation  current  zero  two to  A  coil.  integral  the  can  that  to  the  voltage.  capacitors  from  163kA.  so  Rogowski  time  current  fitted  i n the  The  the  capacitors.  be  is close  In  from  quarter cycle  circuit,  integral  resistance. current  RLC  a  (itself  capacitor  first  the  can  stored  signal  integrated  on  an  to calibrate  interval  zero  The  charge  Z-pinch  the  to  waveform.  ways  current  of  correspond  total  two  the  Z-pinch  same  seen  with  It had  type. this  the was  to  be  Apparent in  mind.  59  Ill.EXPERIMENT  Prior  to  firing  the  evacuated  and b a c k f i l l e d  discharge  begins  voltage inside  on  path  experiences  i s  shell  initial  breakdown.  first  towards  thereafter,  the wall. will  shock  tube  plasma  be  the the  of  The  when  a  current imploding  and compresses  i s ionized  four  from  one  actual  twenty this  point  the  after  the  and the p i n c h  There  the  the supersonic radial into  contact  plasma/gas  interface  the i n i t i a l  density  flow  system  Only to  to  entire  i s very left  about drive  drift pinch  seen  i s nowhere  energy  needed  through  begins  the  mass d e n s i t y  and  was  passes  on, t h e plasma  the temperature.  kilojoules  dimensional  life.  microseconds  constant.  density),  system  and the plasma  (the nominal  "instantly"  initial  i n the  zeros,  From  to maintain  initial  jolt  full.  f i l l  Furthermore,  The  "shell"  microseconds  the axis  current  i s essentially  initial  plasma  By  t o expand  sufficient  the  on  ten  switches the  and  heats  The  Gas a l o n g t h e  the axis.  which  at the axis  of i t ss e v e r a l  vessel  the  i n towards shock  Gas  g a p S,  ionized,  the  i s  helium.  the electrodes. i s quickly  vessel  i s complete. Shortly  the  a  pinch  grade  at spark  established,  drives  gas, a r r i v i n g  the  onto  a net JxB force  central  the  t h e breakdown C,  the  laboratory  of the pinch vessel  conduction  phase  with  capacitor  wall  current  when  discharge,  by t h e  else f o r close in  to  C, i s  a quarter of the  pinch.  shock  ( i . e . the pinch)  brings  with  gas i n t h e shock  tube.  i s therefore  peak  very  i s not too  of Figure  1-1  sharp.  strong,  If then  i s reproduced i n  60  Ill.EXPERIMENT  III.3  The same  simplest  pressure  needed the  to test  from  a  density  much  of  magnetic  shock  tube  but higher  tube  puff  a thin  the oncoming  was  density  The gas p u f f  with  will  wave  t r a v e l s much  taken  from  a published  resulting  the valve  equally  faster  of  additional  separating  firing  appear  shock  part  the  by  the  are also  For this  created  membrane,  to  plugs  Although  as that  plastic  filled  "pre-filled"  valve.  i s not as sharp  of gas with  than  two i s  static  the speed  sound. The  and  fast  t h e shock  more c o n v e n i e n t .  when  i s a  Valve  the p r e d i c t i o n s of the model.  step  regions  gas end p l u g  as the Z-pinch,  experiment  gas  The Gas P u f f  valve  Stallings  and  the  material  was  [KUSW70].  The body  diaphragm  from  i s stronger  than  7075  was  made  aircraft  t h e 2024 a l l o y  from  by Kuswa, Delrin  aluminum. indicated  The  single  turn  driving  coil  and  fitted  into  grooves  cut i n the D e l r i n p l a s t i c .  its  attached  leads  machined  were  sealed  shows a c r o s s  section  Figure  III-4  inlet  passage  enlarged  was  design  and spring-pushrod  t o show  detail.  in  from  place  6mm  with  of the finished arrangement  have  Stamm  plastic,  This  latter  i n the  plans.  brass  plate,  The c o i l epoxy  resin.  valve. been  and  The  slightly  Ill.EXPERIMENT  6 1  HV  :::::::::::  ** *  i  — 1 i  1 1 1 1  gas  "  1  I ' 1 -i  •  s.  3  r  1  ^1  80 mm The through eddy  currents the  around  the  the  sides  eight  in  diaphragm the  hundred  original by  Another  the  position  shot  flow can  of be  The  out  rising  O-ring  the  valve  Puff  opening the  by  pressure  fired  with  very  of  the  through  little  flowing  field  seat.  induces  than  spring  delay.  flows cut  in  approximately ten.  restored  the  force  Gas  grooves  is  is less is  Valve  resulting  through  diaphragm  coming  the  duration  time  emptied,  f r e s h gas  magnetic  from of  Puff  current  and  its  -4  of  diaphragm,  chamber.  the  in pulse  3 5 k A  away  and  plenum  been  a  coil.  microseconds;  has  the  by  aluminum  diaphragm  of  plenum  aided  i s opened  i t s single turn  drives  the  valve  —  to  When its  and  pushrod,  inlet  passage.  62  Ill.EXPERIMENT  III-5  Figure that  was  (l0.2yF) and  III-5 built  shows for  capacitors  the switching  Capacitor  C  2  use  were  i s charged  C, i s c h a r g e d  thyratron  i s fired,  drop  capacitively  with  were  placed  length  o f RGU-8 c a b l e .  The v a l v e  details  misfiring  of i t s operation  through  t o the S  coupled  i s conducted  Further  voltage  will  on  plane, sheaths. and  When t h e  The  voltage  trigger pin.  The gap  to the  worked  only  2  203  supply,  unit.  R,.  bank  type  ground  inside co-axial  t o -9kV by t h e t h y r a t r o n  down a n d c u r r e n t  experiment,  Two NRG  a copper  t o -5kV by t h e h i g h  C, i s d i s c h a r g e d  Circuit  capacitor  valve.  beneath  breaks  entire  Firing  "low-noise"  the  mounted  circuits  capacitor  i s  the special  Gas V a l v e  valve  reliably very  be g i v e n  by  a  short  throughout the  rare  occasions.  i n Chapter  V.  Ill.EXPERIMENT  63  III.4  The with  outward  a  streak  III-6.  Light  by  a  The  rotating  slit  camera  from  convex  across  motion  the  lens  and  concave the  The  of of  the the  plasma  By  Camera  uniform type and  focussed  mirror  film.  Streak  shown shock  onto  "streaks"  selecting  along  the  can  be  material known marks, the  streak the  angle  of  axis  "smeared  speed,  and  speed  of  the  of  image  a the  the  out"  an  luminous  boundary.  is  gas  camera image from  is  of a  a  motion  front  be  Figure  collected slit.  entrance  horizontal  of  line  and  Optics  the  luminous  image.  measured can  in  the  triangular  scale  recorded  entrance  S t r e a k Camera  tube,  into  distance  heated  light  shock  system  schematically  the  III-6  segment  flow  from  With  a  timing  calculated  from  64  Ill.EXPERIMENT  III-7 The the  arrangement  slit  although  to  observe  there  i s  cylindrical find  photographs  laser  streak  i n front  image.  shock  of both  travelled  the  beam  of the s l i t .  special Polaroid  from  the  side,  this  inside  calibrated slit,  so  the  that  device  cassette),  streak  velocity (two  the  a t t h e same was  as charts attached  to  laser  beam  object to  would speed  mounted the  to  Streak  measured  photodiodes  a  helium-neon  r a y from camera  and  used  Z-pinch.  a  the  The s t r e a k  was  by p l a c i n g  in  rotates  viewing  IV.  mirror  plane  in  i n Chapter  the principal  Image  direction,  technique  as  the film  III-7  vertical  definition  are presented was  the S l i t  Figure  path  across  calibration film  of  velocities  in  the  loss  camera  same  in  some  of the entrance  the  shown  motion  types  The r o t a t i n g  sweep image  object  the radial  The  of mirrors  Rotating  then as the  with  a  on  a  machine  by  Ill.EXPERIMENT  65  previous  researchers  were  found  percent.  Measurements  taken  at  percent  drift  was  III.5  Inside plasma a  the  lens  optical device with line.  five Light  cover  a The  the  were then  of  the  aligned moved  within  of  signal  went  photons  can  OMA. this  the  The  to  from the  to  the  axis  zero.  escape  from  five  axis  of  signal  cylindrical  10mm  at  in a  to  the  plasma  in a the  region.  slit  recorded the  of  a  with  an  exit.  video  This  camera, the  channels  would  slow  at  but  picture by  the  the  exit  checked was  be), The  axis  will  represents  the  the  lenses was  Only  light  from  After  this  the  a l l be  at  G e i s s l e r tube  is optically than  before  placed  and  spiral.  detector.  plasma  therefore  by  collected  is dispersed  OMA  signal.  the  was  o p t i c s was  absorption, of  five  by  "digitize"  G e i s s l e r tube  OMA  a  nanometers.  the  A  reached If  mounted  hundred ten  the the  without  within  I t s output small  maximize  were  monochromator  assembled. (where  axis  lines  anode  fifty  were measured  entrance  used  over  showed  density  the  tube  segment  into  pinch  away  10mm  emitted  pickup  by  Analyzer  pinch  onto  approximately  was  the  (OMA)  d i s c r i m i n a t i n g power  Z-pinch  center  the  be  and  spectral  analyzer  grating. of  from  helium  hundred  range  expected.  focussed  to  coming  diffraction  could  temperature  Light  multichannel  a  times  Optical Multichannel  The  is similar  different  The  and  monochromator.  in error  best  spectroscopy.  convex  be  the  pinch,  that  to  thin, the  picked an  so  that  photons up  average  by  the over  Ill.EXPERIMENT  66  III-8 Time mounted  resolution  in front  intensifier this  case  falling  onto  than  microsecond  possible For  the  final  t o r e c o r d an each  in  of these  were entire  by a t h o u s a n d  was  operated  by  Records  were t a k e n a t t h e p i n c h m i d p o i n t  and  the U n i v e r s i t y  I 588nm and open).  to a disk  An  He  file  of B r i t i s h  I I 469nm), and additional  of  two  on  lasting out.)  lines  less It  hundred  t h e Amdahl 470 Computing  f o r two  was  OMA system  Centre.  spectral  was  be  shot.  types of e l e c t r o d e  sequence of  light  t i m e " would  five  Columbia  the  pulse, in the  in a single  s h o t s , a r e c o r d of the  transferred  intensifier  volt  filtered  profile  Optics  opaque,  (Fluctuations  channels  (He  All  "exposure  therefore line  image  Normally  duration.  profile.  Collection  b y . an  the d e t e c t o r d u r i n g t h i s  into  and  detector.  " s w i t c h e d on"  microsecond  integrated one  provided  o f t h e main  c o u l d be  o f one  was  OMA  lines (solid  taken at  the  67  Ill.EXPERIMENT  quarterpoint to  of  the  forty-eight  open-end  microseconds  microsecond  from  changes  rapidly),  most  Additional reference. matched of  hundred  shown  number  of  of  There rotary  in  the  data  and  of  one  the  data  (where  b e f o r e and  after.  calibration  and  the  monochromator  was  tube,  different  tube  zero  and  slit  repeated  eventually  the  effects  widths firings  were of  the  o c c u p i e d some  two  these  were  pump,  series  and  a  could  was  are  needed  measure  the  be  f i l l  than  roughing  the  gas,  one  was  measured  which  been  calibrated  in concert to  with  charge  parameters,  accurate,  i n the  100mm d i a m e t e r  pressure had  must  pumps  of  thousand.  less  Z - p i n c h works  reliable,  the  and and  so in  safe.  vacuum  reduce  The  i n twenty  vessel,  voltage, two  the  These  devices  capable  millipascals.  pumping  Experimental Appliances  III-2,  pinch  high  pascals,  part  of  from  for  a Geissler  and  set of  Other  in Figure  A l l of  case  five  of  other machines.  f i l l  forth. the  scale  ran  interval  microseconds  taken  Geissler  complete  record  microseconds  were  filters the  a  sequences  files.  As  bank,  two  density  III.6  a  and  spectrum  The  with  wavelength  both  The  twenty  the  with  Z-pinch.  to  records  against  measured  six  The  neutral  pinch.  system:  the  system  l a b grade  to  Contamination  with  in an  earlier  from  with  was  than  a  pure gas  two  hundred to  one after  The  f i l l  Tru-Torr electronic  guage  a  the  The  left  five MKS  pump.  less  helium,  Duo-Seal  to approximately  o i l diffusion  pressure  part  a Welch  thousand.  manometer  containing  68  Ill.EXPERIMENT  dibutyl than the  ester  half pinch  pthalic  of by  electronic  a  connected  to  high  the  firing  vacuum  system!  tried  mechanical that  finally  its  own:  vacuum  and  closed  the  include  some  but  stress  of  solved  the  the  response  to  these  pressure  power  equipped  with  operated  by  to  the  during  supply  charged  short  the  better  admitted  to  by  use.  a  the  This  error  to  back  arranged  so  the  bank  120VAC  One  solenoid  other  switch  was  solenoid closed  for  the hose  problems  the  valve  opened  successfully percent.  capacitor Each  switch,  from  the  sufficiently  two  when  of  through  banks  bank  solenoid  switch  tubes  new  bus.  two  to  rubber  forth  both  voltage  had  ID  valves  relaxation voltage  The  the  Glass  were  capacitors  inside  25mm  and  than  that  the  withstand  as  line  and  not  some  needle  less  single high  the  The  sequence  few  place  insulation.  oscillations a  single  therefore  could  surging  control.  circuited  extra  f i l l  of  a  voltage,  connection  introduced  same c i r c u i t :  (preventing  bus.  was  from  remote  levels).  the gas  high  firing.  problem in  through  the  joints  repeated  final  the  dangerous  was  was  controlled  a c t u a l l y took  to  first,  in  as  short  reduced  use  here  itself  valve  done  original  addition  in  gas  solenoid  "Z-pinch"  that  switch,  Accuracy  f i l l  were  consistent  be  0«).  The  Fortunately,  could  2 2  same e l e c t r o d e  oscillations  The  H  1 6  The  filling  of  lengthened  hose.  percent.  and  first  were  (C  guage.  Pumping  be  one  acid  was  switches the  they  "dump"  were  not  b u i l d i n g up  connected  charging  and  the  to  bank  opened  I II.EXPERIMENT  69  DUMP j j  HV SUPPLY  ^  + ISOLATE  V\Ar  HV BUS  VALVE BANK  I  ^1  DUMP  X  _L-  ISOLATE  MAIN BANK  0  @( T ^ i ^  HXH OIL  HELIUM ROTARY  GAS  PUMP III-9  Vacuum and HV Systems  Ill.EXPERIMENT  Both mounted three  70  sets  on  top  of  120VAC  solenoids warning  switches  the  a  lamps  for  each  bank:  return.  A  single  whenever efforts  the  rigidly  up  the  equipment,  dangers  were  contact entire  were  to  other  demonstrated  to  any  the  period  of  Voltmeters  meter the  placed  divider  currents  the  faces  on  a  oscilloscope and  digital  base,  and  percent.  time  this x  ±3%  wires  switch  were  for  the  turned  on  active. safety.  were  worker were  The  firing  barriers  were  set  posted,  and  ear  that  no  was  high  Inherent  might  accidents  and  burns  come  in  during  the  accuracy  fashioned  from  percent.  Each  one  resistor,  the  small  from  and  resistor  appearing  out).  The  precision  this of  at  the  r e s i s t a n c e of  ohmmeter.  kilovolts  a  were  The  marked  on  operation. were  calibrated  dual  calibrated  found  large  twelve  555  the  a  a  were  within  voltage  with  bases  to  with  coil  during  Only  was  banks  with  parallel  Tektronix  counter.  The  series  five  use  itself  were  new  accurate  meter  for  equipment  signals  in  for  master  box  There  laboratory workers.  There  measured  predicted  The  in  i f the  was  hot  checklist,  capacitor  (to prevent  terminals  meter  the  nominally  divider  insulated  work.  connected  arrangement voltage  the for  microammeters, was  machine.  two  signs  an  cabinet.  encourage  p r e s c r i b e d by  supplied  with  ammeter  to  warning  from  supply  solenoids  w e r e made  was  defenders  operated  voltage  procedure around  were  high  lines  and  Strong  of  with  upper to  beam  be  a  beam  observing  their  oscilloscope.  The  frequency had  slow  specified  by  in  a  by  generator  functioning  time  approximately  two  the  manufacturer's  Ill.EXPERIMENT  calibration  71  procedure  useful.  Time  be  as having  taken  calibration old  measurements this  devices  age and l a c k  checked  by  cycle  allows  run  these  must  data  cycles time,  supply  system moment  at  fire. work  which  This  immediately thesis  Timing Figure  later,  so  screen. pulse  The  The p i n c h that  T h e OMA  the zero gate  f o r t h e image  only  due t o  standard.  easily.  not used  was c h o s e n  intensifier,  cannot or  be the  i s  sets  pulses the  are given  otherwise  signal fired  pulse  t o be  two  the  still system  in this  specified.  i s shown triggers  in the  microseconds  c a n be v e r i f i e d off  the  i t s command t o  gas i n j e c t i o n  "ready"  which  instead  disrupts  unless  without  reference  interval.  One  electrical  measurements  thyratron  internal  f o r the ultimate  receives  a t which  origin  OMA  i s  signal.  the thytatron  Time  h a s an  f o r a short  thyratron  point  Each  timing  t h e two d e v i c e s  were  origin  signal,  the  h a d t o be  of interest,  not very  devices  f o r the discharge  mainly  instruments  camera.  timing  t o the system  III-10.  oscilloscope.  or a t least  afterwards.  of  Synchronization  t o be t a k e n  from  n o t be  therefore  Some  a useable  are different,  as noise  relative  finding  the Z-pinch  should  errors,  Several  and streak  i s the latest  reliably,  had s e r i o u s  and  The time  thesis  would  allowance.  i s the object  these  reference.  percent  before  the master  Nonetheless,  recalibration  in this  care.  Timing  t h e OMA  a t t h e same  other  three  the Z-pinch  controlled which  given  of proper  for consistency  Although  that  themselves  III.7  Because  showed  high  c a n be s e t t o a n y d e l a y  on  i t s  voltage between  72  Ill.EXPERIMENT  3-CHANNEL SCOPE TRIGGER  O  DELAY  O  O  UNIT  u  O  MONITOR SYSTEM ZERO  SYSTEM ZERO  OMA  THYRATRON READY  HV  ROGOWSKI COIL  I  INT  PINCH  FIRE  PULSER  FIRE  HV TO DETECTOR III-10  zero  and  high can  forty-eight  voltage  be p h o t o g r a p h e d  recording  of a  The  the  mirror  appear Figure found  at  line  camera  and  t o make  beginning  111-11 , a t i m e  delay  t o be a p p r o p r i a t e .  to the oscilloscope,  profile with  a similar a  of  of the film. of eight  where  i t  Successful  pulse  Its  triggers i s fired.  escaping  For the setup  hundred  from t h e  arrangement.  the pinch the  I  the sequence.  "sync"  thereafter  t h e image  current.  terminates  up t o speed,  shortly  Circuit  A monitor .signal  the discharge  works  i s brought  i s chosen the  returns  alongside  oscilloscope, delay  then  spectral  streak  rotating  The  pulser  microseconds.  Timing  plasma shown i n  microseconds  was  73  Ill.EXPERIMENT  3-CHANNEL DELAY UNIT  o  son  SCOPE TRIGGER  o  PRESSURE SYSTEM ZERO  I  ROGOWSKI COIL  STREAK CAMERA  THYRATRON  THYRATRON  I  I  2  1  SYNC  FIRE  FIRE  PINCH  VALVE  111 — 11 T i m i n g Studies injection  of  made  the  higher  use of t h i s  locate  the  puff  "edge"  tube.  For  this  part  of  the  gain  spectroscopy, capacitor camera  banks  to  experiments  so was  eight  a r e shown  with.  the  gas p l u g s  hundred  at different  partially  contend  density  experiment  offset Timing  formed  inside  by h a v i n g sequences  only  puff  gap the  there  caused  II  by  microsecond  positions  i n complexity  Circuit  shock  was  by h a v i n g the  f o r both  i n F i g u r e 1 1 1 — 12 on t h e f o l l o w i n g  to  no two  streak sets page.  of  Ill.EXPERIMENT  74  OMA READY  SYSTEM ZERO  111-12 III.8  The  experimental  designed  to produce  models  of  density  i n the cold  conditions and  of  Table  A  the  full  1 1 1 — 1.  appears BERN79,  in  PRES74,  list  chapter  reproduced  in this  in flow  i s created i s  will  the  and  a n d DAUG66.  experimental  The that  work.  by  the  i n the  work  firing  multichannel i s given i n of be  section  the plasma  and  of the plasma  t a b l e s may first  is  the Z-pinch,  equipment  earlier  similar  confirm  by  found  and o p t i c a l  of the experimental  III-2,  Sequence  chapter  system  Observations  camera  with  this  controlled  valve.  the streak  PACH71,  following  Plasma  gas p u f f  Comparison Table  described  gas end p l u g  g a s a r e made w i t h  analyzer.  setup  II.  Timing  Summary  t h e one d i m e n s i o n a l  Chapter  Common  Preston found of  in the  o f PRES74 i s  Ill.EXPERIMENT  75  111 — 1 E x p e r i m e n t a l  Discharge  Equipment  Vessel  Material  Pyrex  Dimensions  L e n g t h 760mm, OD 170mm  Electrode  Vacuum  Separation  ID  150mm,  600mm  System  Rotary  Welch  Pump  Diffusion  Pump  MKS Gas  Model  C o n s o l i d a t e d Vacuum, M o d e l MC275-01 Varian  Gauges  Filling  Duo-Seal  801,  "Tru-Torr"  t y p e VT-8  Helium ( l a b grade) 99.995% pure  Pressure  less (200  Leak  Rate  a p p r o x 25 P a / h (50 m i l l i t o r r / h o u r )  Circuit  High  Voltage  100mm  thermocouple  Base  Discharge  1402  Supply  t h a n 1OOmPa microtorr)  Universal Voltronics model BAL-22-35 203, 5X10.3MF  Capacitors  NRG  Voltage  Conway m i c r o - a m m e t e r i n s e r i e s w i t h TRW HV "Tiger" resistors  Measurement  Inductance  340  nH,  L=(w C)2  1  76  Ill.EXPERIMENT  (Table  Gas  Puff  III-l  continued.)  Valve  Material  Delrin plastic, 7075 A l u m i n u m  HV  same a s  Supply  Capacitors  NRG  Plenum  Edwards  Diagnostic  Guage  discharge  203, 2X10.2JUF  S p e e d i v a c C.G.3  Equipment  Streak  Camera  Gathering  UBC  Plasma Single  Optics  Physics Convex  Imaging  Optics  Concave  Writing  Speed  1.6±0.1mm/MS  Slit  Optical  Multichannel  Analy  Optics  Monochromator  High Local  Voltage  Supply  Oscilloscope  (nominal)  Princeton Applied Research m o d e l 1205, 500 c h a n n e l s Single  Convex  Lens f/4  F l u k e 412B Hewlett-Packard  7035B  T e l e q u i p m e n t D61  T e k t r o n i x 5 5 5 d u a l beam (1A1 a n d B t y p e plug-ins)  Oscilloscopes  Tektronix Pressure  Lens f / 5  S P E X 1704 • b l a z e d a t 500nm •aperture f/9 • d i s p e r s i o n 0.8nm/mm  Plotter  Display  [HUNI68]  Mirror f/5  70mm b y 0.2mm  Dimension  Gathering  Gas  Brass  Transducer  Celesco  454 d u a l  LD-25  channel  Ill.EXPERIMENT  77  (Table  Calibration  III-1 continued.)  Equipment  Frequency  Digital  Generator  Counter  K r o h n - H i t e model ( 0 . 2 H z - 3MHz) F l u k e model (6 d i g i t s )  1000  1900A  Ohmmeter  K i e t h l e y model (4 d i g i t s )  168  Manometer  dibutyl ester pthalic acid ( C H O , 1047 k g / m ) 3  1 6  2 2  f l  78  Ill.EXPERIMENT  III-2  Experimental  Parameter  Charging F i l l  Voltage  Pressure  D u r a t i o n of half cycle  1/e Best  Period  -12kV  -12kV  533 p a s c a l s (4 t o r r )  525 p a s c a l s (3.94 t o r r ) 1 3MS  1 MS  1 1 MS  9MS not  Time  given  50MS  44kHz  38kHz  l75kA  Current of  Observation  Gas  Valve  Capacitor  Gas  Valve  Plenum  Nominal  Electron  Nominal  Mass  Nominal  Plasma  0  to  1 63kA 13MS  0  Voltage  Electron  Pressure Density  Peak  Plasma  Temperature Density  Temperature  to  48MS  5kV  Density  Peak  Work  (assumed)  F i t Frequency  Maximum  This  0MS  s h o c k wave on a x i s  Relaxation  PRES74  10.5MS  first  Time of breakdown a f t e r system zero Time of arrival  Conditions  20X1 0  2 2  48000K  ur  3  lOlkPa  Oatm)  8X10  nr  2 2  3  5x10-°  kg.nr  3  35000K  (3.0  eV)  30X1 0  2 2  nr  3  ( 3 . 7 5 x nominal)  41000K (1.167  (3.5 eV) x nominal)  Initial  Gas  Plug  Density  8.4x10-*  Initial  Gas  Plug  Pressure  525 p a s c a l s  Gas  Puff  Pressure  kg.nr  2100 p a s c a l s (4 x i n i t i a l )  3  79  IV.DATA  IV. In theory  contrast and  means  things  that  The use  of  this  data  Z-pinch  Figure the  comparison, point puff III-8  near valve has  the  the  the  i s not  dark  is  work  for  described  deals and  with  OMA  assessed  the the  records.  by  comparing  PRES74.  and  visible  better  also  being  in Figure  the  chapter  in  Z-pinch  and  which  photographs  machine  opening  mounted,  removed  this  monochromator  photograph  the  been  similar  chapters,  streak  previous  shows  are  OBSERVATIONS  previous  produced:  the  IV-1  the  AND  production,  from  to  picture  to of  are  DATA  fired. OMA  the  detector  III-2  was  on  far  metal  To  the  screen  visibility.  head.  taken wall.) shown  left  in  of (For  from The  a gas  Figure  IV.DATA  80  IV.1  The  Z-pinch  laboratory. gases  The  is  by  525  used (613mm  Preston  versus  lead  general  comparison  Preston  made  a  microseconds should  form  The the  the  first  slit in  collapse  rotated Figure  as  the  in  IV-2.  so  pinching  Figure  the  from  III-7.  Calculations  A  show  that  after  the  axial  current  causing  the  bright  velocity  was  found  reflected 1 0mm//xs a n d The looks. in and  inward  shock  shock  travelled  1 2 . 5mm//zs  a  percent  Streak  photographs  possible  (i.e. five  versus shape a  III-2. thirteen  he  describes  to  do  this,  the  measure  streak  shock  zero,  is  wave  sharply  be  the  camera shown  hits  the  increasing  flash visible to  lOmm/MS.  was  on  8mm/MS.  Preston's  the The  values  are  respectively.  twenty  interpretation  at  the  although  photograph  the  microseconds  The  being  first  To  typical  eleven  film.  experiment  Table  plasma  with  axis  and  directly  (533  in  machines  side  system  this f i l l  electrode  the  waves.  the  in  experiment.  two  shock  in  given  the  this  this  quantify,  of  and  for  comparing  to  is  differences  to  was  study  work  pressure  easy  devices  state  viewed  main  years  different  past  related  f i l l  of  of  differences  discharge,  in  was  two  thorough  initial task  not  number  this  the  also  are  the  the  v e l o c i t i e s of  radial  of  of  the  Work  made  closely  and  were  a  been  some  600mm),  very  of  have  most  that  Previous  for  [PRES74],  There  attachment  with  studied  and  Z-pinch  pascals).  and  been  pressures,  applicable. that  has  Investigations  and  length  Comparison  difference in  the  percent  this  radial drift  is  not  as  experiment shock in  the  serious have  i s not streak  a  well  as  ±10%  i t  error  defined),  camera.  It  is  IV.DATA  81  0  i  i  i  i  i  i  i  5  10  15  20  25  30  35  1  1  1  1  1  1  40  1  1  1  1  1  1  1  1  1  45 50  T I M E IN M I C R O S E C O N D S IV-2  also  possible  density  front  radial  shock  velocities electron  from  10mm//us  I n PRES74  IV-3.  everywhere PRES74  difference  were  photographs  also  f i t complex  and shock of  the  at  i s  would  peak,  An a d d i t i o n a l c h e c k  calculated using  in  tothe the  a range of  the  include  trailing  t h e 8mm/MS  experiment. discharge  approximately  plasma  Plasma  shows  giving  exponential  velocities  the  PRES74  t o 5mm/MS  The  of  not correspond  wide,  in this  matched.  Collapse  in  fairly  a range  the frequency  currents  else.  be  Such  does  Data  i n t h e shock  had a best  Measurements  percent  to  peak.  variables  front  by P r e s t o n .  structure  experiment  discharge  in  measured  on t h e s t r e a k  Other  38kHz.  the luminous  density  observed  this  that  Radial  current  frequency of 44kHz.  a r e compared  density but  in  showed  The  i n Figure a  thirty  relative  closeness  because  the values  i s made  interferometry  rather  than  line  IV.DATA  82  TIME IN M I C R O S E C O N D S IV-3  broadening. however, be  safe  Both  and to  these  call  IV.2  In could  be  these  II.8  regions  differences section to  and  in  the  i t was  with  could  devices  Photographs  II  a  II.9 be  the  describes  observe  two  Streak  modelled  used  measurements  the  Chapter  sections  studies  how  moving  shown set  MEWE67  tended  of  luminosity  of  regions  of  but  the  camera the  closer. not  would  Plasma  that  flowing  In  existence of  III.4 model.  of  strong  material.  section flow  interaction  regions.  detection  uniform  It  identical.  flow  shown  of  Current  temperature  plasma/gas  the the  the  Escaping  further by  streak  be  uniform  confirmed  the  the  that  for  to  similar  of  i t was  Discharge  is  This used  83  IV.DATA  Although photographs IV-4  by  a factor  of three.  Figure  IV-5  separation seen from  o f t h e shock  several  plasma  contact  two too  experiment  aluminum weak  measured  from  obstacles.  the  Still,  knowing  justify  using  50mm  IV-1  ID t u b e  escaping  that  done  but  out  t h e 50mm  a one d i m e n s i o n a l  a t the beginning  magnified  there  i s not  surface Averaging  a  the The  can  be  the data  shock  and t h i s  of  directly.  of the magnified  with  mounted.  luminous  without  long.  velocity segment h a s  i s taken  t o be t h e  V.  were  turned  IV-4.  gives  analysis  150mm  so photographs  contact  top of Figure  i n Figures  region  plasma  the  streak  t o the Z-pinch),  electrode  the  from  i s  of this  t o develop,  was a l s o  luminous,  These  the  of  shown  (closest  part  a t 8800±400m/s,  blocks  t o be  120mm  segments  velocity  number  studied  wave  A similar  moving  surface  An  the  large  being  to  wave  120mm  U=12700±600m/s. the  Close  show  near  a  the leftmost  t h e shock  type  better  tube  the leftmost  I V - 5 shows  for  quite  a r e o f t h e two t y p e s  The shock  Figure  time  a  most  IV-4 covers  enough  A  were  taken,  and IV-5.  Figure and  there  bow to tube  ID  tube  The outgoing  i t s time  of  shocks be  mounted  chapter.  flight  badly  support  for  in  shock  formed  quite  will  model  the blocks of this  a 50mm  be  a t the metal scattered.  a shock  shown  wave was could  the smaller i s  which  helps t o 25mm  in  tube.  Figure  84  IV.DATA  1  1  4 0 mm  0 IV-5  25mm  Tube  - 40mm  Section  85  IV.DATA  IV.3  The its  streak  film  optical  is  with,  plasma  itself,  forth.  brass  Then  comes  amplify  a l l  pinch  for  Inside the  range  range.)  This  pulsing  the  A  typical  to  drift  rather  time,  standard  in  the  spectrum  into  the  nor  the  leakage  channels or  "dark  Their  four  subtract the  relative to  the  OMA  lower  first  average  signal  flat  region across  i s shown  at the  noise  from  must  be  severe  (An  ironic  their  linear  the  pinch.  currents  channels  by  tend  which  are  is similar.)  The  records in  was  used  as  correcting  a a  signal.  linear,  a m p l i f i c a t i o n was continuum  Dark  step  not  i s measured  firing  gain  so  does  i s so  decade.  IV-6.  third  meaning.  l i e within  selected  were  a  the  and  spectrum  current",  OMA  The  this  channels  is essentially  resulting  randomly  radio  any  without  the  (The  calculations.  i s to  on  vessel,  current  spans  in Figure  anyway.  have  To  from  OMA  raw  the  simple. first  The  i s the  and  With  monochromator  The  to  scale,  so  the  'distortion:  barely  mainly  not  of  tube,  current,  but  of  though  monochromator  The  a l l  large  wavelengths.  walls  magnitude  i s shown  unreliable  spectrum  or  a  detector:  distributed.  observation  example  average  gain.  the  the  equally,  detector  that  on  are  OMA's e l e c t r o n i c s h u t t e r  with  Even  reach  conductor,  equally  leakage  smoothed  raw  to  channels  of  is  things  electrical  OMA  Spectra  a l l visible  through  i t s width  the  consequence  have  mesh  its  current  processed  that  second  the  to  analyzer  photons  Line  r e g i s t e r s motion  sensitive  begin  the  camera  multichannel  through  Helium  each  measured 480nm, lOOnm  in Figure  had  a  by  tuning  where  the  system  IV-7.  different the helium  passband. A  smoothed  86  IV.DATA o m  m  CN  i I i i i i I i i  50  100  i  i I i i i i  150  I  i i i i I i i i i I  200  OMA  250  i i  300  i i I i i i i I i i i i I i i i  350  3 O  450  500  Channel IV-6  c  400  OMA Dark C u r r e n t  o o «o o o in  U  I i i i i | i i i r | i i i i |  50  100  150  200  OMA  I i i i i I i i i i I i i i i I i i i i '[•  250  300  350  400  450  500  Channel IV-7  OMA Gain  Profile  87  IV.DATA  version equal dark  was  normalized  to unity, current)  and each  as  smoothing The  since  this  The  an  falling  operator  can  on t h e  profiles  at  On  this  have  correcting reduced around IV-8  to the  the signal  shows  a  uniform  scaling  there  hand,  OMA  and  applying  discrete matrix  a  space.  from  the  the  diffusion  equation,  while  filtering  out  (less  the  elegantly  OMA  this  high  derived)  was  by  by  also  decided  hundred  and  and then  no  i s normalized  to  first.  even  the data  fifty-six  more  area-preserving  was v e r y  gain,  just  of  after  In the end the  line  n o t t o compensate f o r  left  and i t s processed  was a p p l i e d  already  diffusion  smoothing  the data  and  the  an  not  i n any event  current  were  signal  case  the gain  "unsmoothed"  raw p r o f i l e  Although  In  the issue  peak,  hundred  proportional to the intensity  replaced  (which  dark two  five  c u r r e n t s a r e averaged  It  simply  for  that  detector.  to avoid  broadening  method  made  the other  a l l .  the  on t h e a p p r o p r i a t e  energy  the  gain.  vector",  of  (less  [BEVI69].  be  instrument would  "data  being  and t h e dark  was d e c i d e d  a  similar  be  should  smoothing, it  A  energy,  transformation.  treating  the signal  by B e v i n g t o n  argument  standard  i s t o s e t up a smoothing  "spikes".  represents light  of  a l l the channels  o f t h e raw s p e c t r u m  representation  preserves  discussed  by  defined  technique  difference  frequency is  elements  t h e sum o v e r  b y i t s own  done  operator  favored  finite  was  make  channel  was d i v i d e d  Smoothing channels  to  since  more.  After  vectors  elements  as they  were  centered  were.  Figure  counterpart.  relative  compensate  small),  changes,  for  a  changing  final slit  88  IV.DATA  o  OMA  Channel  IV-8  widths  and n e u t r a l  density  established  with  micrometer  barrel.  scaled  up  so t h a t  they  had  lines  taken  the  no  been  energy  and a  Lines  recorded  taken a  and Processed  filters.  filters  their  through  Raw  integrated  The  area  transmission  density  factor.  when  conditions  changed,  than  one  record  available for a  the  data  showed  Finally, and  the processed  p l o t t e d as  summarize  the Z-pinch  shown  the spectroscopic  slit  filter  and averages given  t o be  highly  lines  were  in Figure  smaller  Extra  taken  was  reading  would  at the reference neutral  reference  + 120/um at a  IV-9.  work.  Data  be  intensity on  slit  shots were line.  was  the  slit  width  were  t h e same a s  width. were  Vectors  Similarly,  scaled were used  i f  up  by  sometimes when  more  Comparison  of  reproducible.  collected These  into  matrices  matrices completely  IV.DATA  89  He I 588nm Open End Quarterpoint  10  ^  2 0  s  ffl  lC  ?  5Q  ^jitl  4) o-  He I I 469nm Open End Quarterpoint  10  30  IV-9  S  co**  5  e  in  4 0  *5Q  20 ; r f 0  rfjtfl  e  E v o l u t i o n of S p e c t r a l L i n e s  90  IV.DATA  IV.4  The puff  Interaction  higher  valve  tube  density  just  ahead  (including  velocity  out from  ahead the  shock  took  place.  by  photographs  down  exiting  past  itself  annular  flow.  length  restriction,  the tube.  tube  the  occurs must  lOlkPa,  travel  the  some  and  conditions  i s  surface the  the  created  bank  to  the  about  slowed  interaction  in  be  reaches  "front  the  streak  enter  charged of  driven  t o 5kV.  approximately  flow  poses  a  In too long t o "bend" effect  shock  wave  uniform.  plenum  These  a s an  a  similar  i t becomes the valve  gas  diffusing  enough  A  t h e plasma  since  which  gradient.  photographs.  good  over  i salso  of  a  t h e tube  uniformity  be n o t be s h a r p  made w i t h  surface"  h a d moved  diameter,  before  n o t be u s e d ,  expected,  transversely  e n d , where  puff  could  the puff  must  tube  will  streak  were  a  step  o f I0l8m/s  shown  out the density  distance  of the shots  standard  of gas flowing  t h e main  150mm  that  diaphragm  change  at the electrode  also All  valve  smoothing  on  i s  and t h e puff The  amount  before  connecting  density  velocity  until  gas d i f f u s i n g  the density  x-t trace  smooth  times  since  The  long,  t h e main  than  showed  This  The f r o n t  longitudinally, a  shorter  photographs  several  by f i r i n g t h e  IV-11 and IV-12.  tubes  the  190mm  sound  The i n t e r a c t i o n  d i d n o t become  distance  produced  A small  percent  streak  puff  edge.  twenty  of Figures  Plug  ( 0 . 46mm//is) .  placed  a t the helium  about  Connecting  the  o f 250MS  Gas  discharge.  was  460m/s  the electrode  of the puff  because  fittings)  Density  were  of the Z-pinch  the  delay  a Higher  gas plugs  was a p p r o x i m a t e l y  valve-to-pinch 70mm  with  filled  to  standard  firing  2100 Pa  in  a  IV.DATA  91  O co  O O CO  <  o o _  U CO  O  IT) CN  / \  / \\  PA  / \  O _  o  CN  z  / / //  O O m  LLi o Q£ o _ o CO CO o LU o Q£  J  \  \V  /  /  ^  —  — ^ .  m  Q. o  1  1 0  1  I  1  I  1  I  1  I  1  I  IN  background  shown  transducer  will of  pressure  mounted  uniform  slow  trajectory,  flow  by a  model  exact  I  predicts  that  IV-12 c l e a r l y although  cycles.  show  the  t o change  particularly Comparison  are successful  Profile  calculations of  with  four. a  higher  factor proportional  even  and  Pressure  The  is puff  piezoelectric  outlet.  surface  and  factor  measured  contact  i s  end p l u g s  in  heat  The  gas  Puff  and that  i t appears  pinching  an  I V - 1 0 was  model  ill-defined, effect  with  Gas  increase,  the  IV-11  Pa, which  at the valve  t h e shock  slow  Figures  step  in Figure  the density  wili  o f 525  as a d e n s i t y  The  I  MICROSECONDS IV-10  pressure  i I  1  I  500 1000 1500 2000 2500 3000 3500 4000 4500 5000 TIME  taken  1  I  strong with  more. a  on  Figure  at blocking  into  root  the  gas  The p h o t o g r a p h s  "bend"  in  surface  than  plugs  to the square  transfer  contact more  density  the the  IV-4  the i s  shock second shows  the plasma.  in  shock  somewhat itself. and  third  that  cold  92  IV.DATA  Puff Edge  20 /*s shock contact surface  pinch  160 mm  40 mm IV-11  Unfortunately, the  shock  nor  valve  took  place The  before  initial  from  IV-4.  The  in  puff.  the  final  contact  the  Figure  This  shock  surface  the  IV-12  to  velocity  gas"  can  of  the  probably  velocity velocity has  edge  some  shows  the  of  sharpen the  system  of  moved  the  was  step  IV-11  is  V=2000±1OOm/s.  a  valve-to-pinch  with  to  in the the  interaction  9600±360m/s, in  is longitudinal  from  bend  moving  shown  what  and  delay the a  of  Figure  diffusion  matters  U'=5440±190m/s,  interaction  by  Step  established.  ignored;  in  the  closer  plasma/gas  of  35mm  Density  detect  12700±600m/s  decline be  the  to  been  in Figure  velocity  cause  had  cases  flow  with  possible  step  both  uniform  IV-11 puff  the  In  shock  "no  not  i t possible  a  likely  Figure places  was  closer.  down  the  was  t r a j e c t o r y once  electrode, puff  i t  Interaction  0  most  the  -250MS,  electrode  puff  injected  is  final  which end. fifty  93  IV.DATA  II]  Puff Edge  z-<—I  1  160 mm  1  0  40 mm IV-12  microseconds will it  a  have mere  earlier. advanced  12mm  into  defined  than  i n the  At  this  point  photography, flux  into  work  needed  as the to  Compared another  the  there  enough gas. prepare  23mm  tube.  previous  Figure towards  The  now  data  more  exists  following  this  flow  IV-11, the  here  Step  the  Closer  puff  electrode,  In  edge  placing  i s even  more  poorly  gained  from  streak  photograph.  is little  data The  to  A  to  be  to  section  f o r machine  calculate outlines  the some  computation.  heat of  the  94  IV.DATA  IV.5 The  experimental  Z-pinch to  Preparation  procedure  t o be f o l l o w e d  called  by a d a t a  t h e main U n i v e r s i t y computer.  disk  file  volumes  of  of  i t s own.  OMA  photographs. high  voltage  and  a  that  plots  Each  the  against  Clerical  e r r o r s were  virtually  without  The  residing  plotted  i n Figure  tape.  When  Use  of  graphs.  Array  series.  correlation, of  an  IV-9.)  a  made  with  line at  files  system to  were of  a paper  current, optical  plot  meant  could  of  out and the r e s u l t i n g  three streak  and  time  a  showing t h e  sequence  the  APL  and n i n e t y  was  functions  which  disk  be  firing.  data  base  set  was  (Two o f t h e s e kept  on  seven  language  were  magnetic occupied  hundred  and  simplified the  towards  f o r i n t e g r a t i o n and width to  produce  then  defined  and the l i k e .  could  spectral  storage.  and o r i e n t e d  were  of  the workspace  pages:  processing  interactive  functions  were  was o v e r ,  three  array  a  workspace.  gathering  APL  was  Backup c o p i e s  interpolation  vectors  file  of  on t h e s p e c t r a l m a t r i c e s Other  these  pressure  of the processing in  the  which  operated  end  k i l o b y t e s of magnetic  analysis,  assigned  to the discharge  f i l l  disk  records  the data  some o n e h u n d r e d seventy-two  the  weeded  was  the  fault.  end r e s u l t  matrices  of  the local  collection  in relation  of  from  shot  large  firing  a l s o had a photograph  A s s o c i a t i n g each at  transfer Each  a  plot  pulse  record  processing  cross-checked  and  Analysis  f o r each  Supplementing  OMA  monitor  written  arrangement.  set  f o r Computer  the  producing measurement  vector  f o r time  time  shifting,  The end product  be p l o t t e d on a p p r o p r i a t e  was  a  display  95  IV.DATA  devices.  Interactive  predictions possible results. in  the  to  against construct This  following  analysis the  actual  functions  strongly chapter.  makes  i t easy  data,  which  computational  and  would  to  test here  give  approach  the again the  will  be  model i t  was  desired evident  96  V.ANALYSIS  V. The  previous  chapter  diagnostic  equipment,  into  and graphs  charts  gathered. analyze  This  empirical  and  testing  I I . 9 . Broader  are  discussed  the  midpoint.  of  whether  model. was  When  the  checked  photographs. the  data  PRES74 the only  more  a vacuum  confine  from  tricks  Z-pinch,  sections  and  II.8  f o r future  energy  could  in  I I was  loss  made from  work  the  relied  on  at the pinch Taylor  models  series  o f GRIE74 and  calculations. b e made  initially  predicted  be f o u n d ,  velocities  flux  Z-pinch  can s t i l l  wave  flow  of heat  more  I I :  A  regardless  i s correct.  of Chapter  the  ended  the accepted  theory  waves  present.  t h e plasma  and suggestions  calculated  successfully.  streaming  and graphs t o  i n Chapter  in  measurements  were  The u n i f o r m  calculation  free  density  expansion  against  information  and open-ended  introduced  of the end plugs  no s u c h  charts  the  transformed  the  not covered  and open  a r e no h i d d e n  t h e models  for  thesis  be  by  VI.  t h e measurement  Testing  i tcould  use of those  implications  produced  represent  the solid  i n turn  comparison  that  of t h e models  derived  There  looking  of this  and  These  approximations  direct  makes  of  the data  better  of the s o l i d  temperature  MEWE67.  which  i n Chapter  Comparison  with  suggesting  comparison  experimental  dealt  chapter  t h e two a r e a s  ANALYSIS  model  t h e shock  heat  The r e s u l t s to a solid expected  The h i g h e r effectively.  from  tube  of tube  model  the streak  transfer  matched  a r e compared  with the  electrode,  f o ra true  density  case  by t h e s h o c k  measured  with  a  and  open  gas plug  with  end with  i s shown t o  V. ANALYSIS  97  V. 1  The ratio  kinetic  of  He  discussed IV-9 of The  temperature  II  469nm  earlier  are  lower  line  to  over  shown i s I  A  Temperature  i s calculated He  9  scaled  from  588nm,  V-1.  intensity  The upper factor  the theory  profiles  t o produce  up by a  the  following  The l i n e  wavelength  in Figure 6  I  II.6.  in section  integrated  intensities  Plasma  of  Figure  the time line  series  i s  I  5  B  .  B  of t e n .  DE  o  z  o -  SOLID ELECTRODE  o in • '•  o  O <  ! ;  o  \  LU o  >  CN -  <  O  LU  \  •  Al  /  He 1 588nm  \i  i  *  He II 469nm (xlO)  * 1  O d  0' T ' f  15» I'T  1 1 1 1  10  1  1  I  15  1  1  1 1  1  20  their For  obvious  sensitivity  this  reason  about  nine  shown  later  1  1 1  25  !  1 1  i iiiiiiiiii  30  35  1 1  1 1  40  problem  with  to error  when  i t i s unwise  microseconds are blank  the  time.  ratio  50  calculations  i s why  i s  are small.  temperatures  which  1 1  Intensities  intensities  calculate  the data,  this  End L i n e  line  the line  to  into  before  Solid  ii  45  TIME IN MICROSECONDS V-1  An  1  until  the graphs  98  V.ANALYSIS  The as  a  discussion  function  expression  of  in section  of  the  temperature  I a6  = K  9  5 88  from  Figure  approximate  4 of  when the  i s accurate the  plasma  ratio  of  0  i  • |^kTj  Iu e 9 = 1 588  density to  = T  =  1 +  used  shown  later Preston  upper the  i s close nominal  in this  that  amount.  for  relaxation  Ifl j 6  will  the  close  -  to  single  construct  the  the  3.0),  to nominal  to N„.  1 +  If  log  T  1  0  l  >  i s then the  f  i  temperature  "relative  defined  as  approximation  1,  9  to  nominal"  temperatures  section. that  the  relaxation  calculated  with  this  experiment  the  e f f e c t s by t o have of  free  show  T«  J- 5 8 8  were  cross-correlation  to  used  time  approximately three microseconds,  In  i s known  from  then  -  calculated  temperatures  energy  kT J  temperatures,  + 0 - 23 J  1  to c a l c u l a t e  l e v e l s was  (which  intensity  s i m p l i f i e d to a  -exp  1.47(kT  region  Ti(  be  be  line  3 / 2  MEWE67 was  i n the  actual  T  may  could  that  relation  logio  which  showed  form  r Data  II.6  a  comparing very  I588  motion up  as  small  and states a  the  6  spectral the  the  spreading  and  the  II  i n PRES74  lines  were  autocorrelation time)  Delays bound and  He  9 values shifted  relaxation  I«6 9 • to  I«  of  by  tested of  with  I  5 8  8  the  in transferring states  shifting  pertinent of  the  99  V.ANALYSIS  CO UJ  -  Q  ZD  He 1 588nm  A  •  / \  z o  <  —  _  —  UJ  >  AUTOCORRELATION  .  He 1 588nm. He II 469nm  /\  CROSSCORRELATION  0  10  -  <  _  l  111 UJ •  11111111  -50  j  1111111111111111111  -40 -30  -20  -10  20  30  40  50  TIME SHIFT IN MICROSECONDS V-2  correlation  peak,  thermodynamic A  slight  the  and t h i s  equilibrium  shift  i s evident  three microseconds  this left  thesis  i s at least  an e s t i m a t e  calculating  the line  where  a sensitive  test  f o r measuring  the  of the local temperature.  i n F i g u r e V-2, b u t i t i s nowhere  advocated  i n PRES74.  be c a l c u l a t e d  the  measurements ratios  microseconds. V-4 a n d V - 5 . the data  temperatures  one u s e f o r t i m e  of the f l u c t u a t i o n s  of  V-3,  needed  therefore  precision  five  offers  Cross-Correlations  near  The temperatures with  the line  shifting  however,  in  ratios  unshifted. There  gives  will  Intensity  Sample  with  (relative  is range  line  a t every  of delays  from  point.) together  zero  by to  in Figures  have  The  i t  relative  checked  a r e shown  intensities  t o T „ ) a r e shown  The  therefore  calculations  (Interpolated  was n o t t a k e n  a  i n the data.  as  been  used  zero-offset  i n F i g u r e V-6.  V.ANALYSIS  100  o o  469nm DELAY  in  OO  CN  0 (HIGHLIGHTED)'  o ° I—  o  <  o m  co 2 Z 6 UJ  i iii Ii iii  10  15  20  25  30  35  40  45  50  TIME IN MICROSECONDS V-3 The twin, three  solid-end  with  a  Z-pinch  slow  rise  kilojoules left  current effect,  in  half-cycle. but  the  strongly. open-end  A  therefore  cannot  must  second  the  of  oscillation.  lessen  the  radial  absence  of  second  explain  why  this  pinch  third so.  It  with  after  the  first  third  cycles  have  little  temperature that  pinch  to  be  the  to  in  the  centers,  and  ends.  induces  Radial  some  i n t e r e s t i n g to  smaller else  peaks.  electrode worth  the  fluctuates  current  electrode  probably  Something  i t s open-end  bank  close  would  than  Ratios  due  is  the  carriers  effects.  and is  tube  most  Line  likely  open-end  from  a  charge  fluctuations in a  and  explanation  form  stable  capacitor  flow  Midpoint  temperature  corresponding  of  these  in  The  acceleration further  i s much more  the  possible  pinch  Open-End  examine  holes  noting  Section  type  V-2  is  to the will  V.ANALYSIS  101  O co  469nm DELAY  m  0 (HIGHLIGHTED)  CO CN  o ° I— o <. o m to Z LU  2 d  ? 6  i i i i i i i 10  i  15  i25i i i i i30i i i i i35i i i i 40 i i i i i i45i i i i 50 i  20  TIME IN MICROSECONDS V-4  The in  fluctuations  calculating  the the  of  quarterpoint  the  nominal  wave  transit  c a n p r o v i d e an e s t i m a t e  temperature,  presence  Open-End Q u a r t e r p o i n t L i n e  but f i r s t  the plasma  expansion  and midpoint  plasma  sound  they  i s I50±2.5mm,  velocity  will  therefore  Comparison  of  the  open-end  midpoint  temperatures  shows t h a t  a n y common  features  speed  be  temperature the  stay  fifty-six  tube  model  all.  Further  dealt  with  very within  small. fifteen  be a b o u t  The  fact  percent  show  up  implications  i n the following  of t h i s  and from  for  Table  The  of  II-2  expansion  microseconds.  and  quarterpoint  travelling  at  fluctuations  predicted  this i n the  implies  that  by t h e  i f i t i s t o show  constant  section.  checked  o f t h e mean  i n the density  made  The s e p a r a t i o n  eleven  that  percent pressure reduction must  be  i s 13090m/s.  time  must  of the error  must  wave.  Ratios  temperature  shock up a t  will  be  V.ANALYSIS 1 02  V-5  Solid-End Midpoint Line Rati.  CN  < z  z  O~ z  O  H  O oo  P u  OH  CONDITIONS  SOLID MIDPOINT OPEN MIDPOINT  o-i  .0?"EN„_QUARTERy6TNT"  d 10  15  20  25  30  35  40  TIME IN MICROSECONDS  45  50  103  V . A N A L Y S I S  V.2  Density, convenient  nominal  showed  that  lines.  This  develop  like  temperature, value.  the  uses  density  N„=8X10  In  GRIE74,  the half  where (in  N  0  , W  and A  0  electrostatic  0  was  nr  2 2  From  the  and  o  nominal width  to the width analysis  valid  Chapter of  of  II  spectral  GRIE74  to  i n the neighborhood  of  at half  given  maximum W  i n GRIE74,  i s given  and  R  0  is  by  defined  t o be  1/6  values N = l 0  2  2  o  N„=8X10  nr  2 2  3  3  o  the nominal  o  n r , T =20000K,  imply  temperature that  He  W =0.0l76nm, o  T„=35000K,  I 588nm  has a  and Griem  o f W=0.159nm. If  the  of  to a  6  R =0.2950,  density  relative  .  units)  tabulated  A =0.059,  3  width  1/3 =  II.3 to II.6  related  formula  are also  CGS  c a n be c a l c u l a t e d  the standard  approximate  nominal  Density  Sections  density  section  an  Plasma  n  i s the r a t i o  ratio  formula  can  of  actual  be  shifted  of a c t u a l to to N  t o nominal  nominal A  and  density,  temperature,  T „ , where  n=r=1:  5/12  1/4 W(n)  =  0.141n  1 +  0.173n  -  0.0401n  T  then  and the  r  is  Griem  104  V.ANALYSIS  This the  expression Taylor  can i n p r i n c i p l e  be i n v e r t e d ,  and  expanded  as  series  n  =  1 + dn(W,)•(W-W,)  + 0(  (W-W,)  ),  2  dw where and  the f i r s t  W,=0.159  temperature  derivative  i s now  defined  dependence  to  simple  linear  0.25  n=1,  this  expression  relation  t o look  The  between will  line  line  profiles  will  be more  be l e s s  than  W  Figure  i s  shift  a r e no s i g n i f i c a n t  hypothetical pinch.  expansion  A closer  quarterpoint the the such  speed time  electrodes,  check  densities o f sound  of passage.  features  will  and  region i s given shown  should  by  from  accurate  from  the  none  open-end  V-8.  Waves  features  of the graph small.  the  V-7 shows t h e  microseconds  the  from  slight  d i f f e r e n c e s between t h e  t o common  be v e r y  Figure  certainly  i n Figure lead  calculated  Apart  twenty  Examination  be a l s o  than t h e  of n  ten percent:  IV-9.  timing  open  small  wave.  of the Z-pinch.  and  accurate  In t h e range  at the center  solid  the  0.159).  density  there  If  then  width  of  differentiation  a t n=1.  N a n d W.  f o r the expansion  experimental  spectral  as the width  1 + 6.13( W -  t o 4.00, t h e e r r o r  enough  by i m p l i c i t  i s neglected,  n(W) =  Close  i s found  in  the  after the  midpoint  and  travelling at separated  shows  that  by any  V. ANALYSIS  105  V-7  M i d p o i n t D e n s i t y f o r Both E l e c t r o d e Types  o «© LOCATION MIDPOINT QUARTERPOINT  *3 o Z  9  CO  IH  z O  3 I1 i I  o  u  < 9  >>  o d  i  |  i  10  i  i  l  | i  15  TIME  V-8  i  i  i  | i  20 IN  i  i  i  | i  25  i  l  l  \  i  30  i  i  i  | i  35  i  i  i  | i  40  i  i  i  | i  45  i  i  50  MICROSECONDS  Open-End M i d p o i n t and Q u a r t e r p o i n t D e n s i t i e s  V.ANALYSIS  106  in o  - J  < 9  <  o Z  -y  <  C  O  N  D  I  T  I  O  N  S  SOLID MIDPOINT  10  .°„ .?N.. . P. .P!! i . p  M  l  p  s  T  OPEN QUARTERPOINT  0  o m CN  o  OC —' m  II  CN  ' ' I' '  10 T  15  I  M  20  E  25  I N  M  I  C  30 R  O  S  35 E  C  O  AO N  V-9  A  final  test  quarterpoint  was  plasma  temperature  and  density,  cross-correlation  way  that  motion into plus  positive  between the  pinch  eleven  The  following is  the  correlated  cycle  time  the  time  shift  from  the  the  these  two  are  series  would  quarterpoint  the  upper  ten microseconds,  wave.  of  Plasma  calculating  from  and  S  the  was  of  then  taken  midpoint.  and  nominal  in Figure  r e p r e s e n t the  and  midpoint  product shown  Pressures  IV-9.  i n such  a  delay  i n wave  wave  moving  A  end  electrode  should produce  curve  in Figure  V-10  a  peak  at  microseconds.  Although at  the  by  pressures  The  a  made  D  50  45  the  feature current with of  the  is  real  cause  instead  reversal, very  thirteen  i s probably due  where  strong  shows  to the  first  microseconds  the  not weak  second peak.  i s simply  a  small an  rise  expansion  second  pinch  pressure  peak  The  current  too  close  to  half the  V.ANALYSIS  107  CO LU  OPEN END PRESSURE:  Q 3  MID- AND QUARTERPOINT  < CORRELATION WITH FIRST LU >  PRESSURE PEAKS  REMOVED  LU 11 n 111111'11111 II II 1111111111111111111111111111111111111111 [ 11111 n 111111 II 111111 II 1111111111 u 1111  •50  -40  -30  -20  150mm  transit  with  F i g u r e 11-10  quarterpoint among must  other  10  20  Cross-Correlation  30  40  the  worst  the f i r s t shows  things,  no  that  to that  possible  of  pressures.  be c l o s e  of Open-End  of eleven microseconds.  microseconds  correlation in  time  i s almost  fifteen  0  50  TIME SHIFT IN MICROSECONDS V-10  wave  -10  the peak  choice.  pressure also  goes  correlation Absence pressure  of the  in  an the  separation  When  series away.  between of  plasma.  A probe  Pressures  the  are The  the  of  first  removed,  lower  curve  midpoint  expansion  wave  outgoing  shock  and  means, wave  V.ANALYSIS  108  I*  R A D 1 A L SH  TEMPERATURE  P  CK  —  \  \jy^y ''jr-"" ~^"  '  y  DENSITY  ""'  — kA  i  SOLID MIDPOINT OPEN MIDPOINT  I / \\ \  I 1 1 M  M  0 . 5  OPEN QUARTERPOINT  //Ai \  ;  i i  —  1  I  1 I 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 I I 1 1 1  10  15  20  25  30  1  1 1 1 1 1  35  1  1 1 1 1 1 1 1  40  M  45  50  and  Current  TIME IN MICROSECONDS V-11  For shown a  ease  Combined  of  comparison,  collectively  complete  in Figure  lack  of  even  though  continuously.  This  suggests  the  current  outgoing  in  the  would  tend  little  effect  expansion The  rapid  being  be  seen,  closer  at The to  of  in  the  over  expansion end  the  the  The  most  in  either  pinch plasma  f i l l  time  the  the  streak  plasma  photograph  prevents  times  and  wave  could  only  any  or  ringing  Z-pinch  expands and  a  that  current  while  having  of  this  radial  of  Figure  IV-2.  axial  distances have  is  is  temperature  the  electrodes.  density  Such  evidence  are  feature  entire vessel,  thereafter.  Further  series  striking  current  in  the  plasma  density.  least  the  that  Density  experimental  the  i s uniform  seen  diffusion  experiment. much  the  V-11.  to  maintain  on  can  shock  plasma  to  the  oscillation  temperature,  with  Temperature,  waves used  been  in  from this  detected  V.ANALYSIS  109  Looking  specifically  microseconds, timing  than  be  viewed  V-3  t o V-5.  differences  anything as  a  Of  midpoint  well  time  of  as  the  pinch  shift  the  shock  would  advancing the  same.  (see  the  be  peak  peaks  Conditions  plasma  found  directly  tested  near  Nonetheless,  an  in  optics up  the  not  equivalent,  which  makes  i t an  the  models  two  of  sections.  shock  sections  fifteen  those  temperature visible those  the  in Figures for  the  i n space  as  that  movement  electrodes)  off-axis.  axis  had  i n the curves  have  are no  could  The  been  time  of  should  taken  is possible  endpoints  volume-filling  density  attached  three  more  for accuracy  the  and  radial reached,  series. very  When  much  effect  on  the the  center.  and  the  only  slightly  point  the  pinch  temperature  in  It  before  earlier  the  in the  changing  aligned  at the  III.5).  ten  are  fluctuations  however,  picked  are  the  between  density  series  (e.g.  to  the  of  collection  then  period  Variations  section  vessel OMA  density  product  were  the  in  else.  a l l the  open-end  at  attainable almost  tube.  II.8  and  The II.9  plasma in  ideal  has  a  i t s narrowly "driver"  analysis  of  confined  f o r the  gas  system  with  this  i s developed  uniform  in  the  next  110  V.ANALYSIS  V.3  Since no  other the to  of confinement,  the process  words,  does  correct show  Of the the  The  contact  wave  U=12700±600m/s.  for  5=178,  error  of their The  best  systematic was  whereby  fast,  The b e s t  measured fit,  error.  and the pressure  195000  p a s c a l s , almost  plasma evidence  shock  at  the  points  conduction  strength  a  taken,  wave.  arises  showed as  to  conditions.  In  and Sinnot  make  measurements  seem  found  in  t h e 120mm  the  flow  section  The a v e r a g e d and  that  both  the  shock  within  gave  velocity  of  f i t t o the simple  i s not good  drop  of  at the contact  was  that  not  of  shock  model  was  experimental  expected  shock  surface.  in  slow,  even  the  of wave  detectable.  In  for  pressure  an  and d e n s i t y pressure  face  t h e shock  implies a driving  temperature  higher  enough  s u r f a c e was  5=178  twice  measured to  ends  values.  The c o n t a c t  a  be  a n d V=9080,  however,  fact,  by A h l b o r n  V=8800±400m/s,  U=12200  naturally  different  can  photographs  was  open  end.  of the shock  surface  versus  i f the interior  answer  a t t h e open  picture  under  proposed  p r e d i c t i o n s even  a l l the streak  best  of s o l i d  occur  t h e model  observed  Model P r e d i c t i o n s  the question  could  otherwise?  structure  with  the e m p i r i c a l study  evidence  whether  Comparison  equilibrium  [LICK62].  caused  of  by  The heat  11 1  V.ANALYSIS  Calculation  V.4  The  first  that  applies to  will  be  the  pressure  mere  will  be  was  heat  flux  found  to  by  i n the  the the  ±120%  numbers other.  error are  The  value  limit  solid  electrode.  flux  to  energy  of  p  2  =  of  suitable  addition  of  V,  can  flow  and  Because  U,  p  of  7  of  (I-7)-  1  Fortunately,  consistent with 7 has  where 5/3.  an  changed  Calculations  throughout. be  calculated  model,  and  1 f  i s given  which  in  from  the  section  II.9  from  taking  within  1.3x10  8  as  heat  W/m  the  velocity the  plasma V  shock  will  Table  II-2  and  W/m .  8  2  the  can  2  flux  from  difference  experimental  for comparison  the  P!  by  (1.3±120%)x10  really  mechanical  flux  are  value of  unity.  value  value  the  factor  [LICK62],  gas  uniform  comes  which  pressure  this  the  values heat  upper  In  shock  i t s ideal  using  into  q  The  i n the  find  the  i s close to  14300K  from  i s to  be  Substituting IV,  of  q  Transfer  because  if 7  density  percent  simplified  wave,  error  temperature  balance  Chapter  to  Heat  in calculating  shock  and  two  The energy  the  sensitive  equilibrium a  step  of  best  with  the  however, pushes define  strength  be  the  two  large  error  of  each  interpreted  energy  gas  them  of  plugs away.  lost  will  as  an  to  a  absorb  The  product  mechanical  energy  is large,  p  2  and  V  can  be  V.ANALYSIS  calculated  from  the asymptotic  V  p  =  r e l a t i o n s of sectionI I . 8 ,  2 U 7+1  = _2_p,U  2  0(  +  5" ) , 1  + 0 ( r '),  2  7+1  from  7  which  may  be e l i m i n a t e d ,  $  The  values  of p  In  the total  contrast,  estimated based  flux  the  in  impressive. plasma The  would  free  plasma  conduction  loss  with  gives  a  gas  end plug  W/m ,  8  W/m . 2  to 4x10  given  a t maximum  in  a  solid W/m .  8  PACH71,  no b a r r i e r s a t  escape  from  t h e ends  value look  of 13X10  rather  and  in  good.  W/m . 2  theory  flux  i s more  a l l in  the  system,  by  velocity a  assuming  and the i n d i c a t e d product 8  was  streaming  at the thermal  calculated  work,  i n turn  was  current.  were  i s  electrode This  2  the so-called free  flux  give  2  I f there  mechanical  a,  be o n l y  measurements  8  IV.2 then  by  heat  streaming  does  given  (9.6±2.6)X10  a maximum  Comparison  in sections  4>+q =  to  becomes  2  2  (8.3±1.3)X10  i s then  PRES74  on c u r r e n t  represents  =  p V  PTUV .  =  U and V measured  1f  *  and  so t h a t  Such  a comparison  that  f t  .  the  o f p« a n d makes t h e  V.ANALYSIS  U J  oc o  1— o U J  IT)  !:.JI.....!?I.^AJ.^.„....f:.Lu, R  U J  M  G  x  ,  ,  •  OC  <  R  o  TOTAL  ZD o o _  ooo  MECH  ^  oc  11 1  -  Q . OO  (— 1—  o o ID -  SOLID END HEAT  FLUX  <  HEAT Jt  <  o  O  —  U J  0.0  <  1.0  0.5  1.5  KILOGRAMS  2.0  PER  V-12  The  heat  calculated of used  U'  and  for q  flux  from  into  V  measured  general  Heat  Flu-x  xlO  versus  density  model.  4.0  gas  4.5  3  Plug Density  plug  can  also  S u b s t i t u t i n g the  i n s e c t i o n IV.4  into  the  same  q'  =  (4.2±0.2)x10  $'  =  (2.0±0.1)X10  8  W/m ,  =  (6.2±0.3)X10  8  W/m .  trend  of  8  the measurements  equation  W/m , 2  2  2  i s shown  in Figure  be  values  gives  $'+q'  The  flow  3.5  CUBIC M E T R E  the higher  the uniform  3.0  2.5  V-12.  V.ANALYSIS  A in  final  section  check  I I . 9:  that  "adiabatically". reserve as  much  flux can  of heat  be t a k e n  into  density  then  hundred  joules.  give  a  a A  small  enough  important  to attain  25mm  in  2  flux  allow  uniformity. tube length  area.  Its  of 4x10  transit  s  W/m  time)  2  nominal of  will q  used expand  a  large  t o absorb  constant that  ( i . e .half  acting  that  A  to  that  the shock  suggests  content  The a s s u m p t i o n  justified.  f o r the plasma  in  energy  assumptions  i n the sense  will  ID shock 0.3m  total  wave  joules.  on one o f t h e  i n the plasma  0.0005m  end-to-midpoint  t o be  be  as a column  by  likely  q  as needed  length)  four  b e made  It i s also  energy  flowing  about  must  heat  the plasma the  pinch  temperature  approximately  and one  over  22us  (i.e.  the  deplete  this  region  by  i s small  is  therefore  115  V.ANALYSIS  V. 5  In solid the  the  and  investigation  open  midpoint  shows  a  general much  slow  that  rise a  was  at  flow  less  the  model  than  density  higher  Sinnot),  went  dense  enough  the  Density  no  confinement,  of  by  The  former  fluctuates,  i n the the  two  plasma  significant  the  measuring  plasma.  latter  as  a  The  solid  A  stop  heat  simple the  but  cases i s so  effect  best  The  in is  fast  at  the  for a  over  to  solid-end  distance by  increase  extrapolation surface  predicted  calculated  predicted  tended  contact  shows will  was  heat system.  reduced  Ahlborn as  by  and  mechanical  that  a  absorb  gas  plug  as  much  electrode. of  can  indeed  block  summarized  (as  flux  was  transfer.  acting  plug  result  Z-pinch.  heat  pressure  main  plugs  electrode  reported earlier  gas  the  down. to  with  from  although  loss  a  of  diffusion has  end  compared  The  open-end  that  by  end  density  radial  electrodes  loss  heat  and  dynamic  directly  temperature.  The  Additional a  were  gas  midpoint.  uniform  flux  lower  the  Behaviour the  of  in temperature.  same.  changing  pinch  electrodes temperature  shows  the  Summary  This i n the  and  this  work  the  other  following  and  has  escape more final  been of  to  show  plasma  that the  gas  ends  of  general conclusions will  be  chapter.  from  cold  1 16  V.ANALYSIS  V-1  525  Pa  Plug  (p,=8.4x10""  Directly  kg/m ) 3  =  12700±600  V  =  88001400  q  =  (1 .3±1 . 6 ) x l 0 '  Mechanical Energy Flux (pressure x v e l o c i t y )  $  =  (8.3±1.3)X10  Total  q+$  Heat  Plug  Directly  Surface  Velocity  from Model Flux  into  Energy  and  m/s m/s  Data  Gas  Flux  (p,=33.6x10"•  =  (10±3)X10  2  W/m  2  kg/m ) 3  5440±190  m/s  V  =  20001100  m/s  q'  =  (4.2i0.2)xl0  Mechanical Energy Flux (pressure x v e l o c i t y )  *>'  =  (2.010. 1 ) x l 0  Total  q'+4>' =  Velocity  Contact  Calculated Heat  Comparison  W/m  8  =  Surface  Velocity  from Model Flux  into  Energy  with  Flux  2  b  U'  Comparison  W/m  8  Measured  Shock  Free  Results  U  Calculated  Heat  Experimental  Velocity  Contact  Pa  of  Measured  Shock  2100  Summary  Solid  Flux  Brass  Vacuum  Streaming  Data  Gas  [PRES74]  with  and  Flux  W/m  8  2  End 13x10  s  8  (6.2l0.3)xl0  Electrode 4x10  8  W/m  2  W/m  2  W/m  2  8  W/m  2  V I .CONCLUSIONS  VI. As  suggested  obtained  in  CONCLUSIONS  the  introduction,  most  of  the  results  c a n be g a t h e r e d  into  four  main  areas.  in  this  thesis  First  of a l l ,  the  commonly  shown  to rely  on t h e a d i a b a t i c  create and  a conflict  the c o l l i s i o n  Two  new  tests  expansion  spectral  line  relaxation  Z-pinch.  on  Analysis  any  the  heat  transfer  be  applied  equilibrium.  and  a  new  and c r o s s - c o r r e l a t i o n of calculation  without  showed  the three  were  and d e n s i t y V showed  that  microsecond  a simple  was a l l o w e d . system  directly  radial  from  shock  compared  a t the midpoint  that  differences  and a newly  t o any o t h e r  emission  of the asymptotic  model,  end confinement  o f two a d h o c m o d e l s : transfer,  of photon  i n PRES74.  i n Chapter  prevented  were  T h i s was s h o w n t o  estimate  and gas end plugs  the Ahlborn-Sinnot  particle  an  adiabatic  measured  theories  thermodynamic  The l a t t e r  advocated  model  the auto-  the temperature  plasma  terms  of l o c a l  the  based  the solid  approximation.  proposed:  intensities.  shift  measuring  model  be  spectroscopic  the adiabatic  in  could  Second,  Third,  were  test  temperature  the  rate  parameter  equilibrium  by  between  used  diffusion  being  scheme  of the  observed.  was a s s e s s e d i n  tube  with  no h e a t  derived uniform  flow  model  T h e new m o d e l f o r which  of  can  in  or  where  principle  i t s assumptions  c a n be  satisfied. Fourth,  and f i n a l l y ,  uniform  flow  closely,  and could  into  the  cold  model  with  experimental heat  transfer  t h e r e f o r e be u s e d  gas  end p l u g .  tests  showed  matched  to calculate  Estimates  that  the  the data  more  the heat  i n PRES74  flux  of t h e heat  V I .CONCLUSIONS  lost  to  a  solid  considerably showed to  that  first  general  area  arise  that  Z-pinch  for further  heat  that the  loss  energy  balance.  of further  in this  work:  the  predecessors,  about  of  processes  which  rely  must  be  (to  everything science modify human  to  expand  their  direct on  axioms  so  a  and t h e i r  theory  impose  the  quantum  I t i s then test  inferences  statements makes  evolution.  Its  inferences  of  for their  be  Unlike  mechanics  Models  quantum  can  itself.  f o r making  experience.  that  turn  t o make  quantum  system  models,  in  physics  sought  reality,  contain. these  This  physical  measurement  metaphor  the purpose  on  of n a t u r a l  their  predictions,  stay  consistent  and with  experience. The  as  they  areas  models  observables  consistent)  else  of  to construct  which  i s essentially  world  small  t h e need  o f quantum  e x t e r n a l and independent  about  number  a  i n the  classical  consequence  reference  A  i s only  not  found  its  ultimate  also  c a n be  as a  solely  chapter  research  seen  statements  absorbed  up t h e d e n s i t y ,  a t the ends  c o n s i s t e n t t h e o r i e s of measurement.  about  gas  previous  in scaling  with  logical  the  work.  context  covered  showed  although  would  the fact  open  The  heat,  problems  of the t o t a l  remain  electrode  less  mention  part  118  practical  computers  physical  from  power  of  generation  and symbolic  processes  follow  implications  an  logic  [ALLE83].  inconsistent  "logical  of this  play  a  Given  set of  will  larger that  axioms,  inference engines"  computers)  viewpoint  require  (soon an  role  will in  be  felt  modelling  any c o n c l u s i o n  will  applying  full  the  t o appear  effort  to  in fifth remove  119  V I .CONCLUSIONS  contradictions,  especially  which  formalism  relate  the  consistent  linkage  thesis  step  is a  A  further  model more  in  a  form,  system  and  be  model  validity. would  do  systems  of  A  the  a  mentioned.  The  build  and  comes  i n the The  arrives,  and  very  heat  studies  the  few  remarks in  Z-pinch to  gas the  on  of  multiple  use, of  but  and  the  axis  and the  be  for  an  plasma  the  scales to  of  a  would  its  own  concept flow  device  by  can  system.  plasma/gas  that  already  i s easy  for this  until  of  radial  the  shock  principle  be The  plasma-to-gas  applications. useful  to  work  supersonic  in  Models  very  role  materials etc.).  important be  a  future  models  unchanged  state  observe.  fluid  asymptotic  continuous  advantage  to  interesting  to  the  known  remains  could  this  stated  confinement  observing  i s easy  Z-pinch  be  result  the  i t s main  have  The  made a b o u t  g r a d i e n t s , pure  always  in  estimate  end  testing  well  initial  in  densities.  for  i t s axial  up  equations.  (steep  will  designed this  is a  resulting  clean  method  extension  general  should  set  of  The  Ahlborn-Sinnot  be  should  specifically  the  should  axioms  its  world.  attempted  assumptions  differential of  measurement  goal.  rederive  The  temperatures  afterwards  of  applying  creation  transfer  properly  to  of  human  measurement  ultimate  way.  set  theories  macroscopic  and  be  simplify  reliable  shock.  the  mathematics  clear  Z-pinch, and  process  a  higher  interaction,  made  by  to  Finally, of  the  the  c o n s i s t e n t statement  much at  would  partial  with  this  general  f o r example  full a  step  to  process  towards  more  clearly,  of  from  in  A  further  120  REFERENCES AHLB77  AHLB81  A h l b o r n , B. Confinement o f a F u s i o n Plasma by a C o l d Gas B l a n k e t Canadian J o u r n a l of P h y s i c s v o l 55, pl047 A h l b o r n , B. a n d L i e s e , W. 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