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Investigations on plasmas produced in electromagnetic shock tubes. Cormack, George Douglas 1962

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INVESTIGATIONS ON PLASMAS PRODUCED IN ELECTROMAGNETIC SHOCK TUBES *y GEORGE DOUGLAS CORMACK B . A . S c , U n i v e r s i t y o f B r i t i s h Columbia, 1955 M.Sc, U n i v e r s i t y o f B r i t i s h Columbia, 1960  A THESIS SUBMITTED IN PARTIAL FULFILMENT OP THE  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  . i n the Department of PHYSICS  We a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d standard  THE  UNIVERSITY OF BRITISH COLUMBIA November, 1962  In presenting  t h i s thesis i n p a r t i a l f u l f i l m e n t of  the r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y  of  B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and for extensive  study.  I f u r t h e r agree t h a t p e r m i s s i o n  c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may  g r a n t e d by the Head o f my Department o r by h i s  be  representatives.  I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a U ^ e d w i t h o u t my w r i t t e n  Department o f  Physics  The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada. Date  November 23,  Columbia,  1962  permission.  k'l' The U n i v e r s i t y o f B r i t i s h  Columbia  FACULTY OF GRADUATE STUDIES  PROGRAMME OF THE f.  FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  of  GEORGE DOUGLAS CORMACK  B . A . S c , The U n i v e r s i t y o f B r i t i s h Columbia, 1955 PUBLICATIONS  )- -  M.Sc,  The U n i v e r s i t y o f B r i t i s h Columbia, 1960  FRIDAY, NOVEMBER 23, Problems  i n Plasma P h y s i c s . G.D. Cormack. UBC E n g i n e e r I, 17, 1960.  S p e c t r o s c o p i c S t u d i e s o f Helium and Argon Plasmas Produced by E l e c t r o m a g n e t i c a l l y D r i v e n Shock Waves. A . J . Barnard, G.D.Cormack and W.V. Simpkinson. Can. J . P h y s i c s 40, 531, 1962. Low  Inductance Low Pressure Spark Gap Switch. G.D. Cormack and A . J . Barnard. Rev. S c i . I n s t r . 33, 606, 1962.  A Low Inductance H i g h Current Vacuum Switch. G.D. Cormack. B u l l . Am. Phys. Soc. ]_, S e r . I I , 156, 1962.  1962, AT'3:30 P.M.  IN ROOM 223, BUCHANAN BUILDING  COMMITTEE IN CHARGE Chairman: F.H. Soward  [. ; ' \- ' ['4^ .' . ,  A . J . Barnard F.L. Curzon R.J. C h u r c h i l l P.R. Smy A.M. Crooker W.A.G. Voss G.B. Walker E x t e r n a l Examiner: J.H. de Leeuw,  jfT'  I n s t i t u t e of Aerophysics,  • .  U n i v e r s i t y o f Toronto  INVESTIGATIONS ON PLASMAS PRODUCED IN ELECTROMAGNETIC SHOCK.TUBES ABSTRACT The shape of the l u m i n o s i t y f r o n t , the homog e n i t y o f the plasma and the s h o t - t o - s h o t r e p r o d u c i b i l i t y o f the s t r u c t u r e of the plasma were found to be dependent upon the c h a r a c t e r i s t i c s o f the d r i v i n g d i s c h a r g e , even a t a time long a f t e r the d r i v i n g c u r r e n t had ceased to flow. In p a r t i c u l a r , m a t e r i a l from the w a l l s of the d r i v e r assemb l y was found to a f f e c t the p r o p e r t i e s o f the plasma. The plasma was used to i n v e s t i g a t e the e l e c t r o dynamical response of an i n d u c t i v e magnetohydrodynamic power g e n e r a t o r . E x p r e s s i o n s f o r the output power were d e r i v e d and compared w i t h the e x p e r i mental r e s u l t s . The e l e c t r o d y n a m i c a l response of a n o v e l e l e c t rodetype B^. magnetohydrodynamic power g e n e r a t o r was c a l c u l a t e d . In an experiment performed w i t h t h i s g e n e r a t o r a magnetohydrodynamic i n t e r a c t i o n was observed i n d i c a t i n g t h a t the plasma was t r a n s p o r t i n g an a z i m u t h a l magnetic f i e l d . No output power was o b t a i n e d . The probable cause f o r t h i s was t h a t the a p p l i e d magnetic f i e l d was i n s u f f i c i e n t to break down the sheath on the e l e c t r o d e s . A low p r e s s u r e spark gap s w i t c h s u i t a b l e f o r use as a main s w i t c h and as a "crowbar" s w i t c h on a c a p a c i t o r bank was developed. The s w i t c h was o p e r a t e d over a v o l t a g e range of 0.5 to 25 kV, at e n e r g i e s up to 4 k J and c u r r e n t s up to 500 kA. Under normal o p e r a t i n g c o n d i t i o n s the t r i g g e r i n g time was 40 nsec and the j i t t e r a p p r o x i m a t e l y 10 nsec. The i n d u c t a n c e of the main s w i t c h was 4nH and the i n d u c t a n c e o f the crowbar s w i t c h was about 1 nH.  Other c o n t r i b u t i o n s are on a wide-voltage-range o p e n - a i r spark gap s w i t c h , h i g h v o l t a g e t r i g g e r c i r c u i t s and on the dynamics of the plasma i n an e l e c t r o m a g n e t i c shock tube. The l a t t e r c o n s i s t s of an elementary treatment o f the e l e c t r o m a g n e t i c a c c e l e r a t i o n p r o c e s s e s and a p r o p o s a l o f a model f o r the d e c e l e r a t i n g plasma.  GRADUATE STUDIES  F i e l d of Study:  Plasma P h y s i c s  Waves  . ...  Spectroscopy Physical Electronics  ........  Advanced Plasma P h y s i c s  J.C.  Savage  A.M.  Crooker  R.E.  Burgess  ......  F.L.  Curzon  Related Studies: Transients  i n L i n e a r Systems ...  Analogue Computors  E.V.  Bohn  E.V.  Bohn  ABSTRACT  E l e c t r o m a g n e t i c shock tubes were used to generate 17 plasmas h a v i n g a number d e n s i t y o f the order o f 10 and an  energy per p a r t i c l e  employed,\the  o f 1-3 ev.  d r i v i n g c u r r e n t was  3 per cm  I n the shock tubes  passed v i a e l e c t r o d e s through  a d i s c h a r g e a t one end o f the tube.  The d i s c h a r g e gases t h a t  were d r i v e n down the shock tube p l u s the ambient gas t h a t p i c k e d up and heated c o n s t i t u t e d the plasma t h a t was  was  studied.  Many workers have assumed t h a t shock e q u a t i o n s can d e s c r i b e the d i s c o n t i n u i t y a t the f r o n t o f the plasma.  An  i n v e s t i g a t i o n i n t o ' t h e e f f e c t s o f changes i n the geometry the d r i v e r mechanism has d i s c l o s e d t h a t the l u m i n o s i t y  of  struct-  ure t h a t can be a t t r i b u t e d to the d i s c h a r g e gases s t a y s v e r y c l o s e to the l u m i n o s i t y f r o n t .  The amount o f ambient  gas  t h a t i s e n t r a i n e d i n f r o n t of the d i s c h a r g e gases i s thus small.  T h e r e f o r e , some doubt e x i s t s about the a p p l i c a b i l i t y  of the shock e q u a t i o n s both i n the p r e s e n t shock tube and i n the e l e c t r o m a g n e t i c shock tubes of other workers. The shape of the l u m i n o s i t y f r o n t o f the plasma was  found to be a f f e c t e d by the p r o p e r t i e s o f the d r i v i n g  d i s c h a r g e , even a t a time l o n g a f t e r the d r i v i n g c u r r e n t had ceased to f l o w .  Instabilities  of the d i s c h a r g e and contamin-  a t i o n by e l e c t r o d e m a t e r i a l were found to d r a s t i c a l l y the homogeneity ducibility  of the plasma..  The homogeneity  affect  and r e p r o -  of the plasma produced by a s m a l l - c a t h o d e d r i v e r  were found to be f a i r l y good.  However, t h e r e was  a large  - i i i amount of c o n t a m i n a t i o n The  plasma was  dynamic response generator.  i n the plasma. used  to i n v e s t i g a t e the  of an i n d u c t i v e magnetohydrodynamic power  E x p r e s s i o n s f o r the output power were d e r i v e d and  compared w i t h the .experimental The  results.  e l e c t r o d y n a m i c a l response  of a n o v e l e l e c t r o d e -  type B^. magnetohydrodynamic power g e n e r a t o r was In  an experiment  performed  calculated.  w i t h t h i s g e n e r a t o r a magneto-  hydrodynamic i n t e r a c t i o n , w a s observed plasma was  electro-  i n d i c a t i n g t h a t the  t r a n s p o r t i n g an a z i m u t h a l magnetic f i e l d .  put power was  obtained.  The  the a p p l i e d magnetic f i e l d  probable  was  No  out-  cause f o r t h i s was  that  insufficient  to break down the  sheath on the e l e c t r o d e s . A low p r e s s u r e spark gap  s w i t c h .suitable f o r use  main s w i t c h and  as a "crowbar" s w i t c h on a c a p a c i t o r bank  developed.  s w i t c h was  0.5  The  to 25 kV,  operated  a t e n e r g i e s up  the j i t t e r  to 4 k J and  the main s w i t c h was s w i t c h was  approximately 4 nH and  c u r r e n t s up to 500  10 nsec.  The  the inductance>of  inductance  kA.  40 of  the crowbar  about 1 nH. Other  c o n t r i b u t i o n s are p r e s e n t e d  range o p e n - a i r spark gap and  was  over a v o l t a g e range of  Under normal o p e r a t i n g c o n d i t i o n s the t r i g g e r i n g time was nsec and  as a  on a  wide-voltage-  switch, high voltage t r i g g e r  circuits  on the dynamics of the plasma i n an e l e c t r o m a g n e t i c shock  tube.  The  latter  c o n s i s t s of an elementary  treatment  of the  e l e c t r o m a g n e t i c a c c e l e r a t i o n p r o c e s s e s and a p r o p o s a l of a model f o r the d e c e l e r a t i n g plasma.  -  X  ACKN0WLEDG1  The  encouragement, guidance and i n t e r e s t t h a t have  been g i v e n by JJr. A . J . Barnard  have been o f i n v a l u a b l e h e l p  to me. The  author  i s a l s o g r a t e f u l to many other members o f  the Plasma P h y s i c s group both f o r t h e i r s u g g e s t i o n s  and t h e i r  assistance. The  r e s e a r c h upon which t h i s t h e s i s i s based was  g r e a t l y f a c i l i t a t e d by the t e c h n i c a l a s s i s t a n c e t h a t was p r o v i d e d by the s t a f f o f the P h y s i c s Workshop.  Other v a l u a b l e  a d v i c e and a s s i s t a n c e has been p r o v i d e d by J . Turner, i n electronics, The  and by J . Lees, financial  i n glass  support  blowing.  f o r t h i s r e s e a r c h p r o j e c t was  p r o v i d e d by the Atomic Energy C o n t r o l Board.  The author i s  g r a t e f u l f o r r e c e i v i n g a s c h o l a r s h i p from the B r i t i s h  Columbia  Telephone Company (1960-1961), an award from the A s s o c i a t i o n of P r o f e s s i o n a l E n g i n e e r s  o f the P r o v i n c e  of Ontario  1961), and a N a t i o n a l R e s e a r c h C o u n c i l S t u d e n t s h i p  (1960-  (1961-1962).  - iv -  TABLE OP CONTENTS Page CHAPTER  I  CHAPTER  II  INTRODUCTION  1  APPARATUS  ."  5  1 . C a p a c i t o r Bank  7  2. Switches  12  3. Shock Tube  19  4. A u x i l i a r y Equipment  20  i.Luminosity  Detector  20  ii  Camera  21  iii  Kerr C e l l Circuit  for Firing  Crowbar S w i t c h . .  i v Magnetic Probes  23 25  CHAPTER I I I PROPERTIES OP THE PLASMA GENERATED IN AN  CHAPTER  IV  ELECTROMAGNETIC SHOCK TUBE  27  1. D i s t o r t i o n o f the L u m i n o s i t y S t r u c t u r e by D r i v e r D i s c h a r g e Phenomena..  27  2. E f f e c t o f the Geometry o f the D r i v e r on the L u m i n o s i t y S t r u c t u r e i n the Plasma.  37  3. Magnetic F i e l d s i n the Plasma  48  4. I n i t i a l Breakdown Phenomena  50  5. Dynamics o f E l e c t r o m a g n e t i c a l l y A c c e l e r a t e d Plasma  52  6. Dynamics o f the D e c e l e r a t i n g Plasma....  68  MAGNETOHYDRODYNAMIC POWER GENERATION  77  1. Some P r o p e r t i e s o f an E l e c t r o d e - T y p e B^. Magnetohydrodynamic Power Generator  77  2. E l e c t r i c a l C h a r a c t e r i s t i c s o f an Electrodeless MHD Generator  97  -  V  -  3. C h a r a c t e r i s t i c s o f a Magnetohydrodynamic Power Generator Employing I n d u c t i v e Power T r a n s f e r CHAPTER  APPENDIX APPENDIX APPENDIX  V  A B C  101  CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK  115  C h a r a c t e r i s t i c s o f V a r i o u s Spark Gap Trigger Circuits  119  P r o p e r t i e s o f a Wide V o l t a g e Range,' Open-Air Spark Gap Switch  126  Low Inductance Low P r e s s u r e Spark Gap Switch  131  APPENDIX . D  P r o p e r t i e s o f a Low Inductance Low P r e s sure Spark Gap S w i t c h 137  APPENDIX  E  Theory f o r the E r u p t i v e I n s t a b i l i t y  154  APPENDIX  F  A n a l y s i s . o f the E x p e r i m e n t a l Data Obt a i n e d w i t h the MHD Generator Employing I n d u c t i v e Power T r a n s f e r  158  BIBLIOGRAPHY  161  - vi -  LIST OF  ILLUSTRATIONS  Figure  Page  1  Capacitor Discharge  Circuit  2  Capacitor Connections.  3  I n t e r c o n n e c t i o n s Between Each Set o f Three Capacitors  Exploded  6 View  7 8  4  Circuits  f o r C o n t r o l of Bank  12  5  Low P r e s s u r e Spark Gap Switches I n s t a l l e d tween C a p a c i t o r Bank and Shock Tube  6  Layout  7  C o n s t r u c t i o n of L u m i n o s i t y D e t e c t o r  20  8  Circuit  21  9  Kerr C e l l Trigger C i r c u i t  23  10  Crowbar Switch T r i g g e r C i r c u i t  24  11  Coplanar D r i v e r f o r E l e c t r o m a g n e t i c Shock Tube.  28  12  Photographs o f Plasma Generated Drivers  29  13  T-Tube D r i v e r s  14  The Protuberances  15  A P o s s i b l e E x p l a n a t i o n f o r the on the Shock F r o n t  Be-  o f Shock Tube  17 19  of L u m i n o s i t y D e t e c t o r  by V a r i o u s  ' 30 on the Shock F r o n t  31  Protuberances 32  16  Proposed Mechanism f o r F i n a l Breakup o f D i s charge Column  35  17  Coaxial Electromagnetic Driver with Electrodes  38  18  C o a x i a l E l e c t r o m a g n e t i c D r i v e r w i t h Short E l e c t r o d e s and a S t a t i c Magnetic F i e l d  39  19  Configurations of Axially-Symmetric D r i v e r s That Were T e s t e d  41  E f f e c t s o f D r i v e r Geometry and Gas P r e s s u r e on L u m i n o s i t y o f Plasma. . ..  43  20  Short  - vii Figure  Page  21  S t r u c t u r e o f L u m i n o s i t y o f Plasma  46  22  B_ T r a n s p o r t e d i n Plasma  49  23  Breakdown Time o f t h e D r i v e r  51  24  Time When Maximum V e l o c i t y Occurs i f t h e D r i v i n g C u r r e n t i s O b t a i n e d f r o m a Damped O s c i l l a tory Circuit  57  Time When Maximum V e l o c i t y Occurs i f t h e D r i v i n g C u r r e n t i s O b t a i n e d from a C r i t i c a l l y Damped C i r c u i t  60  26  V e l o c i t y o f Plasma D u r i n g A c c e l e r a t i o n by V a r i o u s Waveforms o f D r i v i n g C u r r e n t  63  27  T y p i c a l Oscillograms of Current i n D r i v e r of Shock Tube  67  28  x ( t ) Data f o r D e c e l e r a t i n g Plasma  70  29  G r a p h i c a l D e t e r m i n a t i o n o f Parameters i n Propag a t i o n E q u a t i o n f o r D e c e l e r a t i n g Plasma  71  30  P r o p o s e d Model f o r D e c e l e r a t i n g Plasma i n Shock Front  74v  31  The C o n v e n t i o n a l C a r t e s i a n MHD G e n e r a t o r  77  32  The D i s c and t h e C o a x i a l MHD G e n e r a t o r  78  33  The B^. MHD G e n e r a t o r  79  34  The E q u i v a l e n t C i r c u i t f o r t h e S i m p l i f i e d t e s i a n MHD G e n e r a t o r  35  A Low I n d u c t a n c e B_  36  The B  37  A H i g h V o l t a g e B_  38  E x t r a c t i o n o f MHD H a l l C u r r e n t  89  39  A method f o r L e s s e n i n g I n s u l a t o r D e p o s i t i o n Problems  90  40  Construction of B  91  41  T y p i c a l S i g n a l Induced i n Probe a t Base o f B MHD G e n e r a t o r  25  Car-  81  MHD G e n e r a t o r  84  MHD G e n e r a t o r E q u i v a l e n t C i r c u i t  87  MHD G e n e r a t o r  MHD G e n e r a t o r  80  , 0  92  - viii  -  Figure  Page  42  A Magnetohydrodynamic I n t e r a c t i o n t h a t A l t e r the V e l o c i t y of the Plasma  43  Electrodeless B  44  Equivalent C i r c u i t MHD Generator  r  MHD  Gould  Generator  94 98  f o r the E l e c t r o d e l e s s B 99  45  MHD Generator Employing fer  46  The  I n d u c t i v e Power T r a n s -  C o n d u c t i v i t y and V e l o c i t i e s  102  B e i n g Considf-  ered i n the A n a l y s i s  105  47  Power i n Load R e s i s t a n c e as a F u n c t i o n of Time  108  48 49  I n d u c t i v e MHD Generator E x p e r i m e n t a l Apparatus E q u i v a l e n t C i r c u i t f o r I n d u c t i v e MHD Generator Output C o i l .  109  50  V a r i a t i o n of Output tance  51  Output Power as a F u n c t i o n of Load R e s i s t a n c e , Experimental  112  52  Trigger Circuits Cable  119  53  D e r i v a t i v e of T r i g g e r Spark C u r r e n t  121  54  Trigger Circuit  122  55  V o l t a g e Quadrupler T r i g g e r C i r c u i t  124  56  V o l t a g e Doubler T r i g g e r C i r c u i t s  125  57  Open-Air  58  Plasma J e t , T r i g g e r e d Open-Air  59  Circuit  60  T r i g g e r i n g Time of Plasma J e t T r i g g e r e d Switch  128  61  C i r c u i t f o r Simultaneous C u r r e n t and L u m i n o s i t y  138  62  Method of Measuring Pressure Switch  V o l t a g e w i t h Load R e s i s -  Employing  the D i s c h a r g e of a  for Parallel  Gaps..  Three E l e c t r o d e Spark Gap  f o r T e s t i n g Open-Air  Switches...  Spark Gap Spark Gap  111  126  Switch  127  Switches  127  O b s e r v a t i o n of T r i g g e r  T r i g g e r i n g Time of  110  Low 139  - ix Figure  Page  63  Vacuum System  64  T r i g g e r i n g Time of the 4 k J S w i t c h as a F u n c t i o n of P r e s s u r e  65  f o r Switches on C a p a c i t o r Bank.  Motion o f Charged P a r t i c l e s i n T r i g g e r charge  141 Dis-  (  66  140  142  S u b d i v i s i o n o f -the Main Switch i n t o Regions f o r the Purpose of C a l c u l a t i n g the Inductance  151  67  Inductance o f Crowbar S w i t c h  151  68  Suggested Plasmoid Motion t h a t R e s u l t s i n E r u p t i v e I n s t a b i l i t y o f D i s c h a r g e Column  154  V o l t a g e Waveforms C a l c u l a t e d f o r the i v i t y Function  1 60  69  Conduct-  TABLES Table 1.  R e s u l t s o f A n a l y z i n g D e c e l e r a t i o n Data....  74  Table 2.  Comparison of dc E l e c t r i c a l Formulae f o r the C a r t e s i a n and the B MHD G e n e r a t o r s . .  87  P r e d i c t e d Shock Tube dc B^, MHD Characteristics  Generator 88  P r e d i c t e d High Power dc B ^ Characteristics  Generator  Q  Table 3. Table 4.  MHD  88  - 1 -  CHAPTER  I  INTRODUCTION  Electromagnetic  shock tubes have "been adopted i n many  l a b o r a t o r i e s f o r the g e n e r a t i o n o f plasmas h a v i n g a number 17 3 d e n s i t y of the o r d e r of 10 of 1 to 10 ev.  Although  per cm  and an energy per  particle  a l a r g e amount o f i n f o r m a t i o n has  been  p u b l i s h e d about such plasmas, t h e r e i s much r e s e a r c h work t h a t i s y e t to be  done.  The  r e s u l t s o f two  major i n v e s t i g a t i o n s on  such plasmas are r e p o r t e d i n t h i s t h e s i s .  These i n v e s t i g a t i o n s  were on the p r o p e r t i e s of the plasma generated magnetic shock tube and  age range o p e n - a i r spark gap spark gap  electro-  on magnetohydrodynamic power g e n e r a t i o n .  Other c o n t r i b u t i o n s p r e s e n t e d  pressure  i n an  i n t h i s t h e s i s are on a wide v o l t s w i t c h , on a low  s w i t c h and  inductance  low  on the p r o p e r t i e s of v a r i o u s  cir-  c u i t s s u i t a b l e f o r g e n e r a t i n g the h i g h v o l t a g e p u l s e needed to t r i g g e r a spark gap The  switch.  plasma t h a t i s generated  i n an  electromagnetic  shock tube i s not homogeneous, o f t e n has  poor s h o t - t o - s h o t r e p r o -  d u c i b i l i t y , and u s u a l l y has  front.  a non-planar  Many workers  have taken photographs t h a t show the l a c k of homogeneity of the plasma and  the n o n - p l a n a r i t y of the f r o n t .  p i c t u r e s of the plasma generated shock tubes (1961).  are those by Kolb  Kolb  (1959) has  i n various  Representative  of the  electromagnetic  (1959)? Komelkov (1959)?  a n (  i  Chang  s t a t e d " f u r t h e r work on the mechanisms  r e s p o n s i b l e f o r the f o r m a t i o n of shock f r o n t s i n h i g h speed  gas  -  flows  i s needed".  bility  i n the  configuration T-tube. all  He c o u l d n o t  structure of  2  obtain shot-to-shot  of the plasma generated  electromagnetic  shock tube  He e m p l o y e d a c o n s i d e r a b l e  the  diagnostic  d a t a w i t h one f i r i n g  equipment,has n o t been a v a i l a b l e here been n e c e s s a r y  to  and to a t t e m p t  to l e s s e n  shock tube  The l a r g e via  The d i s c h a r g e  plasma that of  the  generated 1962)  is  Since  the  is  is  are  therefore,  i n an  at  one end o f  effects  the geometry  shock  tube.  constitute  the  shock tube.  on the p r o p e r t i e s  of  the  the  the  the plasma i s field  geometry  of the  dependent  driver  structure  assembly of  the  This i n v e s t i g a t i o n into  d r i v e r on the  structure  discussed i n Chapter I I I ,  was  plasma  Section 1.  t h e p l a s m a was o b s e r v e d ~ t o be  of  The  ( B a r n a r d , Cormack and S i m p k i n s o n  the plasma s t u d i e d .  A t o r o i d a l magnetic  the  passed  p i c k e d up a n d h e a t e d  was a l t e r e d a n d t h e r e s u l t i n g c h a n g e i n t h e of  capacitor,bank.  c a p a c i t o r bank i s  i n some d e t a i l i n C h a p t e r I I I ,  luminosity  electromag-  plus  d r i v i n g discharge  of  exist  shock tube  driving discharge,  of  Such  and i t h a s ,  p r o d u c e d i n an e l e c t r o m a g n e t i c  structure  luminosity  shock tube.  d r i v e n down t h e  by a c o p l a n a r d r i v e r  of  obtain  derived from a low inductance  that  presented  upon the  equipment to  of the  of the plasma generated  gases t h a t  detected  of  the the  Section 2 .  i n the plasma produced  b y a c o a x i a l d r i v e r a n d was a t t r i b u t e d t o a t r a p p i n g i n  the  plasma of  The  the magnetic  field  a  degree of i r r e p r o d u c i b i l i t y .  through a discharge  the a m b i e n t gas  effect  is  the  c u r r e n t obtained from the  electrodes  i s known a s  e s t a b l i s h why i r r e p r o d u c i b i l i t y d o e s  The e n e r g y netic  in a particular  that  amount o f  reproduci-  of  the d r i v i n g d i s c h a r g e .  -  detection of this f i e l d  3 -  i s d i s c u s s e d i n Chapter  S e c t i o n 3.  An i n v e s t i g a t i o n i n t o the s u p p r e s s i o n by a magnetic f i e l d o f the e f f e c t s o f a t r i g g e r spark i n the d r i v e r i s p r e s e n t e d i n Chapter  I I I , S e c t i o n 4. The  equations  c l o s e d form i n Chapter  o f motion f o r the plasma a r e d e r i v e d i n I I I , S e c t i o n s 5 and 6.  an a n a l y s i s i s p r e s e n t e d equations  t h a t i s based  to those employed by H a r t  I n S e c t i o n 5-,  on s i m i l a r  differential  (1962) f o r the dynamics o f  a s l u g o f plasma a c c e l e r a t e d by e l e c t r o m a g n e t i c f o r c e s . (1962) s o l v e d the coupled d i f f e r e n t i a l  equations w i t h an analog  computer and p r e s e n t e d h i s r e s u l t s i n g r a p h i c a l form. f y i n g assumptions t h a t a r e p h y s i c a l l y r e a l i s t i c S e c t i o n 5 i n order t h a t s o l u t i o n s i n c l o s e d form The  e x p r e s s i o n s thus o b t a i n e d a r e v a l i d  Hart  Simpli-  a r e made i n can be o b t a i n e d .  f o r both the e l e c t r o -  magnetic a c c e l e r a t i o n o f a s l u g o f c o n s t a n t mass and o f a s l u g g a i n i n g mass by a snow-plow a c t i o n .  Of p a r t i c u l a r i n t e r e s t i s  an e q u a t i o n t h a t p r e d i c t s the maximum v e l o c i t y o f the plasma. The  fitting  o f an e m p i r i c a l r e l a t i o n to the e x p e r i m e n t a l  data  f o r the d e c e l e r a t i o n o f the plasma i s d e s c r i b e d i n S e c t i o n 6. A model i s proposed  t h a t i s based  on t h i s r e l a t i o n .  The model  can e x p l a i n why v a r i o u s workers have o b t a i n e d d i f f e r e n t f o r the parameter 0  values  i n the o f t e n - q u o t e d r e l a t i o n f o r the  motion of the d e c e l e r a t i n g plasma i n an e l e c t r o m a g n e t i c shock tube,  n x o* t "  where x i s the d i s t a n c e t r a v e l l e d by the s l u g i n time t . The  f u n c t i o n o f an e l e c t r o m a g n e t i c shock tube, the con-  v e r s i o n of e l e c t r i c a l  energy  i n t o k i n e t i c and thermal  energy o f  -  a plasma i s  the  inverse  power g e n e r a t o r . generation,  the  novel  direct  are  1,  energy,  the  extract  been encountered  extraction is  electrodes  the  considered  the  behaviour  dynamical behaviour  of a ' p h y s i c a l l y  electrodeless  an e x p e r i m e n t a l this  MHD p o w e r g e n e r a t o r determination of  generator  are  also  the  presented  i n Chapter  electrodes  the  One o f  i n the  in  pro-  field  cleanliness  realizable  of  Section  electrodeless electro-  configuration  studied.  The r e s u l t s  electrodynamic in this  studied.  the major  Therefore,  IV.  a  with  I n S e c t i o n 3 the  is  of  is  o f an i d e a l i z e d  considered.  energy  behaviour  by o t h e r w o r k e r s  plasma.  power  generator  concerned w i t h the  which contact  electrodynamical  power.  is  of  are  f l o w and h e a t  i n contact  MHD p o w e r g e n e r a t o r  of  the  electrodynamical  the plasma i s  employed to  o f MHD p o w e r  2 the  Section  magnetohydrodynamic  of magnetohydrodynamic  conversion of  electrical  generator  blems t h a t has  the  f u n c t i o n of a  c o n f i g u r a t i o n of magnetohydrodynamic  In this that  the  Certain aspects  of a plasma i n t o In Chapter IV,  of  4 -  properties  Section.  of  -  5 -  CHAPTER  II  APPARATUS  The p r o p e r t i e s magnetic the of  shock tube  capacitor energy  highest  of  d e p e n d m a r k e d l y on t h e  discharge  circuit.  considerations,  when t h e  circuit  that  driving  current is  R  employed f o r  are  electromagnetic resistance  R  s o  cuit are  the g e n e r a t i o n of  c,  tory  In this  is  and an i n d u c t a n c e I shock tube  are  s  •  is  d r i v e r of  represented .  When a l l  and the  charged to a v o l t a g e  the main switches  c u r r e n t through the d r i v e r of  0  and i n t e r n a l  the  produces  shock  e  -it  an  each h a v i n g a  accurately  w i t h an i n d u c t a n c e  of  capacitors  The i m p e d a n c e o f t h e  c o n s i d e r e d t o be p a s s i v e  c l o s i n g of  discharge  such a pulse  circuit n  s h o c k tube by s m a i n s w i t c h e s  V where  basis  the plasma  capacitor  i n p a r a l l e l w i t h the  c o n s i d e r e d t o be i n i t i a l l y  simultaneous  of  of  on the  i n t e r n a l inductance I  connected  R^ i n s e r i e s  elements  c a n be s h o w n ,  temperature  shown i n P i g 1.  of an e l e c t r o m a g n e t i c resistance  the  electro-  characteristics  The u s u a l c o n f i g u r a t i o n o f  each h a v i n g a c a p a c i t a n c e resistance  that  It  i n an  d r i v i n g c u r r e n t has b o t h a s h o r t r i s e - t i m e and  a h i g h peak v a l u e . is  the plasma generated  driver by a cir-  capacitors V , then  the  an o s c i l l a -  tube  S i n ujt  - 6 It  is  evident  from equation  1 that  a driving current  b o t h a s h o r t r i s e - t i m e and a h i g h peak v a l u e discharge  c i r c u i t t h a t has  low inductance bank t h a t has  low inductance  connections  The p r o p e r t i e s  s p a r k gap  s w i t c h t h a t has  a crowbar  s w i t c h are  then described  of  described i n Section the  discussed  the  low inductance,  i n S e c t i o n 2.  1.  the  capacitor  1 of  low  this  pressure  The s h o c k t u b e  I n S e c t i o n 4 the  operation of  the  shock .  Pig  of  The  been employed as a m a i n s w i t c h and  i n S e c t i o n 3.  ment r e q u i r e d f o r  produced i n a  and r e s i s t a n c e .  and p h y s i c a l l a y o u t  been b u i l t are  Chapter.  is  having  Capacitor Discharge  auxiliary  tube . s  Circuit.  is  as is  equip-  discussed.  switches  1. CAPACITOR  BANK  The low i n d u c t a n c e c a p a c i t o r s  t h a t were i n s t a l l e d i n  the c a p a c i t o r bank a r e r a t e d a t 1.6y*F, 25 kV, 25 nH. nections  ,The con-  between and on each c a p a c i t o r were made as i l l u s t r a t e d  i n P i g 2. p a r t s ABCD:  Pig The from  2.  Capacitor  C o n n e c t i o n s . Exploded  c o n n e c t i o n s shown i n P i g 2 permit the c u r r e n t  1/16 i n .  view. to be taken  each c a p a c i t o r v i a two paths t h a t a r e on d i a m e t r i c a l l y  opposite  s i d e s o f the c a p a c i t o r .  T h i s p a r t i c u l a r type o f con-  n e c t i o n r e s u l t e d i n a measured r i n g i n g f r e q u e n c y f o r one capacitor  o f 900 kc o r a c i r c u i t i n d u c t a n c e o f 19-5 nH, a c t u a l l y  lower than the r a t e d v a l u e ,  25 nH, g i v e n by the manufacturer  - 8 for  a completely  electric  short-circuited capacitor.  f i e l d i n these  capacitors  is  Since  to  Such connectors  w o u l d be . d i f f i c u l t t o  The c o n n e c t o r s  of  the  this  length of  the  in a radial d e s i g n and  direction.  flow  The  and i n s u l a t e d f r o m each o t h e r by t e n Arc-over across  connectors  construct.  i n a current  ideal a l l - r a d i a l flow.  .001 i n . insulation (Mylar).  t h e M y l a r was  current  shown i n P i g 2 r e s u l t e d  an a p p r o x i m a t i o n to were s e p a r a t e d  extract  the  conductors  at  different  that  is  capacitors thicknesses surface  a v o i d e d by m a i n t a i n i n g a minimum s u r f a c e  4 i n . between  internal  i n the r a d i a l d i r e c t i o n ,  minimum c i r c u i t i n d u c t a n c e w o u l d he o b t a i n e d i f w e r e made so as  the  of  path  potentials.  s  Pig  3.  I n t e r c o n n e c t i o n s Between Each Set of Three Capa c i t o r s . On t h e a c t u a l b a n k a. s e c o n d s e t o f 9 c a p a c i t o r s i s mounted i m m e d i a t e l y b e h i n d the 9 c a p a c i t o r s shown i n t h i s f i g u r e . The c o l l e c t o r p l a t e i s t h e common c o n n e c t i o n f o r t h e two s e t s of 9 c a p a c i t o r s .  -  The  9 -  i n t e r c o n n e c t i o n s between each s e t o f t h r e e  a c i t o r s are. shown i n P i g 3. 28.8^<F o r any o f 24.0, by r e p l a c i n g o r  cap-  The e n t i r e bank c a p a c i t a n c e o f  19.2, 14.4, 9.6 o r 4 . 8 ^ ? was o b t a i n e d  removing the i n t e r c o n n e c t i n g p l a t e s . A l l  j o i n s between c u r r e n t c a r r y i n g c o n d u c t o r s  were s o l d e r e d ,  with  the e x c e p t i o n o f t h e i n t e r c o n n e c t i n g p l a t e s and t h e s w i t c h e s , i n order to l e s s e n c i r c u i t  inductance.  Some c a r e has been e x e r c i s e d i n t h e c h o i c e o f c o n d u c t o r t h i c k n e s s and t h e method o f c l a m p i n g t h e c o n d u c t o r s . pulses of current that flow during the discharge cause t h e c o n d u c t o r s  The l a r g e  o f t h e bank  t o be r e p e l l e d from each o t h e r .  the mass o f t h e c o n d u c t o r s  Should  be t o o s m a l l , t h e n t h e m o t i o n w i l l  g e n e r a t e a time dependent i n d u c t a n c e  i n the c i r c u i t  a f f e c t t h e wave shape o f t h e c u r r e n t .  that  will  The f o l l o w i n g a n a l y s i s  i n d i c a t e s t h e o r d e r o f magnitude o f t h e q u a n t i t i e s i n v o l v e d . The  m o t i o n o f one c o n d u c t o r r e l a t i v e t o i t s r e s t p o s i t i o n w i l l  be c o n s i d e r e d  and i t w i l l be assumed t h a t t h e c u r r e n t f l o w s on  the f a c i n g s u r f a c e s o f t h e c o n d u c t o r s . meters wide and have a s e p a r a t i o n ment o f a c o n d u c t o r x(t).  When  equation  The c o n d u c t o r s  of b meters.  are a  The d i s p l a c e -  r e l a t i v e to i t s r e s t p o s i t i o n i s designated  damping and n o n - l i n e a r f o r c e s a r e n e g l e c t e d , t h e  of motion f o r the conductor i s  MX  +  K  x  =  I*  2  where M i s t h e mass o f t h e c o n d u c t o r p e r u n i t l e n g t h , K i s t h e r e s t o r i n g f o r c e p e r u n i t l e n g t h e x e r t e d by e x t e r n a l clamps, and I i s the current i n the conductor. that the motion of the conductors  I t i s assumed t h a t b « does n o t a p p r e c i a b l y  a,  affect  I(t),  and t h a t  I(t)  has  I  the *  I  form  e ~ ^ 5 i n cut  0  e q u a t i o n 2 when  The s o l u t i o n t o  3  «  St  K/M«  <5<< *0 a n d J  I S  {I i4 . *  ft) ? 1  The r e s i s t a n c e  « a M  ;  Sin  -_  2  UJ X  [  per u n i t l e n g t h of  the  conductors  that  is  due  to  t h e m o t i o n d e s c r i b e d by e q u a t i o n 4 i s  "  '  l  a  dt  A specific kA,  4a \A\  to  4  case w i l l  a = 0 . 1 5 m, t h i c k n e s s  of  2 . 1 2 K g / m , CO = J 2 T T / 2 } x 1 0 '  then x ( t  Since  the non-time-dependent  circuit  is  of  the  order  the m o t i o n of  the  conductors  the  current  for  the  One o t h e r above a n a l y s i s together  sented the  of  clamps  .001 to has  example  6  = 4.2 x  sec)  resistance  . 0 1 ohms,  little  just  it  effect  i n order that  the  separation  caused  p u l s e was  a magnitude on t h e  deflection.  apparent  that  waveform  the  depends upon the  of  clamped  deflection  rigidly  at is  later  the not  pre-  end  i n time  do s u f f e r  of  of  the  characteristics  conductors  the  example  considerably  the  is  I n the  which occurs  If  typical  pulses  This d e f l e c t i o n  conductors.  a  by the  calculated.  that  ohms/  of  d o e s come o u t  s h o u l d be  preceding paragraph,  6  sec)  6  cited.  important point that  n o t be a p e r m a n e n t  10"  on t h e  conductors  maximum d e f l e c t i o n , is  10"  the  i n the  first  = 2 x  = 2 x 10"  that  current w i l l  is  = 500  I  rad/sec,  meter.  of  If  c o n d u c t o r = 1/16 i n . , M =  1 0 ~ cms,  of  considered.  ^  a copper  = 4.9 x  5  and R ( t  6  now be  J  of a  and the  per-  - 11 manent d e f l e c t i o n ,  then the i n d u c t a n c e  o f the c i r c u i t  is in-  c r e a s e d and the peak c u r r e n t c a p a b i l i t y of the c i r c u i t pondingly  corres-  decreased. The  c h a r g i n g and d i s c h a r g i n g o f the bank a r e con-  t r o l l e d by e l e c t r i c a l r e l a y s . shown i n F i g 4.  The switches  2. Bank, open c i r c u i t / s h o r t , 4. T r i g g e r H.V. AND FIRE.  The bank c o n t r o l c i r c u i t s are are designated: 3. H.V.  o n / o f f , 5. H.V.  1. A . C ,  t o Bank,  to T r i g g e r ,  on/off,  connect/disconnect,  connect/disconnect  The grounds and the h i g h t e n s i o n l e a d s o f the two  h i g h v o l t a g e power s u p p l i e s are i s o l a t e d from the bank a discharge.  To f u r t h e r a v o i d the p o s s i b i l i t y  occurring during a discharge,  during  o f a ground  the f o l l o w i n g l o g i c  loop  c i r c u i t r y has  been i n c l u d e d i n the bank c o n t r o l u n i t .  The numbers r e f e r to  the switches  i f 1 i s on, 3 operates  i f both and  just described:  1 and 2 are on, 4 operates  4 a r e on and 3 i s o f f .  operate switches  2 operates  the switches  The normal f i r i n g  i n the order 12345.  3 and 5 p r o v i d e automatic  the f i r i n g  i f 1 i s on, 5 operates  S p r i n g r e t u r n s on  order.  high voltage trigger c i r c u i t s  described i n d e t a i l i n  Appendix A.  sequence i s to  adherence to the l o g i c i f  sequence i s performed i n t h i s The  i f 1  shown i n F i g 4 are  S e v e r a l minor i n v e s t i g a -  t i o n s on the p r o p e r t i e s o f s i m i l a r t r i g g e r c i r c u i t s are i n c l u d e d i n t h i s Appendix.  - 12 -  S3"  charging relay-  S4j^ S5 0  © j  firing relay  c a p a c i t o r bank  S1 F i g 4.  C i r c u i t s f o r C o n t r o l o f Bank.  2.  SWITCHES  An e l e c t r o m a g n e t i c shock tube r e q u i r e s one or more switches between a c a p a c i t o r bank and the d r i v e r assembly shock tube  ( F i g 1).  i n the  The c a p a c i t o r bank t y p i c a l l y i s charged  s l o w l y from a h i g h v o l t a g e dc s u p p l y to some p o t e n t i a l i n the range o f 2 to 100 kV.  On c l o s i n g the main s w i t c h , the bank d i s -  charges and a l a r g e c u r r e n t d r i v e r assembly  ( o f o r d e r 0.5 MA) f l o w s through the  f o r a time o f the o r d e r o f a few jUaec.  The  switches t h a t pass t h i s c u r r e n t must c l o s e q u i c k l y , say i n a. time much l e s s than one yUsec,  they must have n e g l i g i b l e impedance  - 13 d u r i n g c o n d u c t i o n and t h e y must n o t Also, set  the  of  triggering time,  the  trigger  m u s t be s m a l l . depends l o w as of  pulse  upon the 5 nsec.  therefore  when t h e y  Also,  the  inter-electrode  adjusted  whenever  range  t o be  where  al  is  triggered  the  the  a voltage  t h e gap open-air  triggering  The  often  of  gap i s  s p a r k gap  time  and  all they  objectionable.  the w o r k i n g  be  voltage  range  reported  from approximately  is  as  explosive-like  at which spontaneous It  on-  current,  o f a n o p e n - a i r gap m u s t  outside  occurs.  the  c a n be  adjusted  The w o r k i n g v & l t a g e  the v o l t a g e  triggered.  s p a r k gaps can p o s s e s s  however,  an o p e n - a i r  switch  s w i t c h but  carefully  spacing  switched.  for  conduction of  are  of large  for  being  time between  b e e n u s e d b y many w o r k e r s .  o f a n o p e n - a i r gap i s ,  most w o r k e r s  value  open-air  noise  is  start  exact a p p l i c a t i o n of Triggered  before  i n t e r v a l of  and the  An a c c e p t a b l e  these p r o p e r t i e s  have  the  close  apparent  to  breakdown  that  a  by  or  convention^  s w i t c h i s n o t an i d e a l  main  switch. An i n v e s t i g a t i o n i n t o the s p a r k gap h a v i n g a w o r k i n g v o l t a g e to this  is  reported  gap i s  i n Appendix B.  extended  by a n o v e l  shown i n t h i s A p p e n d i x t h a t zero is, have  voltage however, the  reasons  between  this  capacitor  open-air  bank.  range  system of  of greater  open-air than  triggering.  gap was n o t  of  is  at  even  The t r i g g e r i n g  time  low voltages  excessive  range It  t r i g g e r i n g c a n be e f f e c t e d  the main e l e c t r o d e s .  of  o f an  The w o r k i n g v o l t a g e  undesirably long at  disadvantage  properties  acoustical employed as  and the  gap  does  noise.  For  these  a s w i t c h on  the  - 14 A u n i d i r e c t i o n a l p u l s e of c u r r e n t through the d r i v e r assembly o f the shock tube i s o f t e n d e s i r e d , r a t h e r than  the  more  For  e a s i l y obtained  damped o s c i l l a t o r y c u r r e n t p u l s e .  example, a damped o s c i l l a t o r y c u r r e n t p u l s e produces, i n q u i c k succession, multiple regions shock tube (Kolb 1957). o n l y one  of plasma t h a t propagate down the  Experimental  work i s f a c i l i t a t e d i f  r e g i o n o f plasma i s produced.  s i s t a n c e i s i n s e r t e d i n the c i r c u i t  for c r i t i c a l  peak c u r r e n t i s reduced e x c e s s i v e l y . p u l s e i n the l o a d can be o b t a i n e d c i r c u i t i n g the l o a d w i t h a low  A  damping,  unidirectional  -more e f f i c i e n t l y by  The  open-air  g e n e r a l be used as a l o a d s h o r t - c i r c u i t i n g s w i t c h  bly  too s m a l l .  the  current short-  spark gap  of  cannot  (a "crowbar"  switch) on a c a p a c i t o r bank because the working v o l t a g e is  re-  impedance s w i t c h at the end  the f i r s t h a l f c y c l e of c u r r e n t . in  When s u f f i c i e n t  range  F o r example, when the l o a d i s the d r i v e r assem-  of an e l e c t r o m a g n e t i c  shock tube and when the impedance of  the d r i v e r i s l e s s than t h a t of the remainder o f the  circuit,  then the crowbar s w i t c h must not break down when the bank v o l t age  V  Q  appears a c r o s s i t but must be  when a v o l t a g e ments are not  of l e s s than V /2 0  compatible  for  most o p e n - a i r  air  spark gap  with  capable  i s applied.  i n g e n e r a l , not  s w i t c h on an e l e c t r o m a g n e t i c employed f o r c r o w b a r r i n g  These two  the known working v o l t a g e  gaps of a p p r o x i m a t e l y  i s thus,  of being t r i g g e r e d  to V^.  range open-  s u i t a b l e as a crowbar  shock tube.  a load  An  require-  I g n i t r o n s have been  (Hughes 1961).  An  ignitron,  however, w i l l not pass c u r r e n t s r e p e a t e d l y  of more than about  50 kA.  of about 100  An  i g n i t r o n a l s o has  an inductance  nH,  - 15 c o n s i d e r a b l y l a r g e r than the i n d u c t a n c e of a t y p i c a l d r i v e r an e l e c t r o m a g n e t i c shock tube.  An i g n i t r o n i s thus not  as the crowbar s w i t c h on an e l e c t r o m a g n e t i c shock A low p r e s s u r e spark gap efficient  suitable  tube.  s w i t c h c o u l d be used  as  crowbar s w i t c h on an e l e c t r o m a g n e t i c shock tube  as a main s w i t c h . q u i r e mechanical  Low  p r e s s u r e spark gap  adjustments  an and  switches do not r e -  i n order to operate over a wide  range o f v o l t a g e and v a r i o u s workers have c o n s t r u c t e d low sure switches h a v i n g i n d u c t a n c e s o f from these switches has proven  on  5 to 30 nH.  pres-  None of  to be c o m p l e t e l y s u i t a b l e f o r crow-  b a r r i n g an e l e c t r o m a g n e t i c shock tube, p r i m a r i l y because  the  i n d u c t a n c e was  effi-  cient.  The  too h i g h f o r the c r o w b a r r i n g a c t i o n to be  inductance  p r e s e n t work was  about 1 nH,  low p r e s s u r e spark gap o t h e r workers.  of the crowbar s w i t c h developed  i n the  c o n s i d e r a b l y l e s s than t h a t o f the  switches t h a t have been developed  T h i s s w i t c h has proven  to be s u i t a b l e as  by the  main s w i t c h on the c a p a c i t o r bank and as the crowbar s w i t c h on the e l e c t r o m a g n e t i c shock  tube.  A c o n s i d e r a b l e number o f d e s i g n s of low spark gap  switches  (LPS) have been developed  Hagerman and W i l l i a m s develop a LPS  /csec,  to  successfully Hg.  the s i m i l a r s w i t c h by Baker (1959) c o u l d d i s -  c u r r e n t s of the order of MA.  about 1.5  by o t h e r workers.  t h a t operated a t a p r e s s u r e of a few microns  T h e i r s w i t c h and charge  (1959) were the f i r s t  pressure  The  t r i g g e r i n g time  the v o l t a g e range 30 to 75 kV,  s t a t e i n d u c t a n c e d u r i n g c o n d u c t i o n was  and  about 30 nH.  geometry of t h e i r switches i t can be i n f e r r e d  the  was steady  From the  that a large  - 16 expansion  of the d i s c h a r g e must have taken p l a c e and  f o r e the impedance of the s w i t c h v a r i e d w i t h time. t i o n i n impedance would have caused form of the c u r r e n t . (1959),  a deformation  Williams  such d e f o r m a t i o n must a l s o have e x i s t e d , but to a l e s s e r of the d i s c h a r g e was  s m a l l e r s i z e of the d i s c h a r g e chamber. t h e i r s w i t c h was V to 20 kV and  a l s o about 10 nsec,  about 5 nH.  Rogers (1960). than 1 yt&aec,  Mather and W i l l i a m s Another LPS was  The  (1959) used  developed  Tsukerman (1960) a l s o developed t h e i r s w i t c h was  of the o r d e r of .01  5 to 10 kV and  d u c t i o n was  by B r u c k e r  and  to 0.1  greater steady  Lobov  and  t r i g g e r i n g time jusec,  during  not g i v e n but c o u l d be e s t i m a t e d to be about 10  LPS  developed  had  a t r i g g e r i n g time of the order of 10 y U s e c ,  by S o k o l ' s k i i , Nastyukha and L o b i k o v  of  0.3  to 12 kV and  an i n d u c t a n c e  of  the order of 100 nH.  The  nH.  (1960)  a v o l t a g e range  Johannson and Smars (1961) have p r e The  triggering  j i t t e r l e s s than 20 nsec, and  a few hundred v o l t s to a t l e a s t 50 kV.  state inductance  con-  t h a t c o u l d be e s t i m a t e d to be  sented c o n s i d e r a b l e data on another LPS. l e s s than 50 nsec,  of  the v o l t a g e  the steady s t a t e i n d u c t a n c e  The  range was  the  about 20 nH. The  100  t h e i r s w i t c h as  4 to 30 kV and  a LPS.  of  conduction  t r i g g e r i n g time of t h e i r s w i t c h was  the v o l t a g e range was  the  t r i g g e r i n g time  the v o l t a g e range was  s t a t e i n d u c t a n c e d u r i n g c o n d u c t i o n was  range was  The  l i m i t e d by  the steady s t a t e i n d u c t a n c e d u r i n g  a crowbar s w i t c h .  was  This v a r i a of the wave-  In the s w i t c h of Mather and  e x t e n t , s i n c e the expansion  was  that there-  d u r i n g c o n d u c t i o n was  s p e c i f i c requirements  20 to 25  The  time  the v o l t a g e steady  nH.  t h a t were d e s i r e d to be  met  - 17 by the main and nH,  crowbar s w i t c h were:  inductance  l e s s than 5  t r i g g e r i n g time s m a l l w i t h s m a l l j i t t e r - so t h a t s h o t - t o -  shot r e l i a b i l i t y might be o b t a i n e d ,  a v o l t a g e range as wide as  p o s s i b l e , a maximum working v o l t a g e of a t l e a s t 25 kV, to  pass a c u r r e n t of the order of 1 MA  low n o i s e l e v e l d u r i n g f i r i n g . by any  o f the switches  by the low  inductance  f o r a few / i s e c ,  These requirements  developed  ability and  a  were not  met  by o t h e r workers, but were  met  low p r e s s u r e  spark gap  s w i t c h used i n the  p r e s e n t work. A d e s c r i p t i o n and  a d i s c u s s i o n of the o p e r a t i n g  a c t e r i s t i c s of the s w i t c h f i n a l l y Appendix C. (Fig  The  adopted are p r e s e n t e d  char-  in  main s w i t c h i n s t a l l e d on the c a p a c i t o r bank  5) i s i d e n t i c a l  bar s w i t c h i n s t a l l e d  to t h a t d e s c r i b e d i n Appendix C; on the c a p a c i t o r bank ( F i g 5)  the  crow-  differs  s l i g h t l y i n c o n s t r u c t i o n from the crowbar s w i t c h d e s c r i b e d i n Appendix  D. r  Fig  5.  crowbar  switch  low P r e s s u r e Spark Gap Switches I n s t a l l e d Between C a p a c i t o r Bank and Shock Tube,  -  -  18  s w i t c h shown i n P i g 5 was  The c r o w b a r  down when b a n k p o t e n t i a l a p p e a r e d constructed when  the  arity  to  firing  the  this  the  it  initial crowbar  i n the  applied  shock  tube  crowbar  range  t/4  of  performed  at  satisfactory acoustical  energy  compared to  that  are  every  300  switches  crowbar w i t h the  period  the  switches  described  switch  load  described  d r i v e r of  the  dependable  shown i n P i g 5 w e r e  up t o  3 kJ.  by a d i s c h a r g e  accumulated u n t i l  operated  O p e r a t i o n was  was  epoxy  The  insignificant  s p a r k gap  discharging  encountered w i t h the  Lucite.  a p r e - f i r i n g breakdown  The s w i t c h t h e n h a d t o be  the  fairly  switches.  bond.  i n t h e L u c i t e h a d become  After about  dis-  compound  No c o m p o n e n t s h a v e b e e n c h a n g e d  exception of  the h o l e  was  the  w i t h an i n d u c t i v e  safer  Some d i f f i c u l t y was  firings.  for  electrical  and the L u c i t e c l e a n e d w i t h an a b r a s i v e  s w i t c h w i t h the discharges  the  of  for  argon or n i t r o g e n i n the  the main s w i t c h o c c u r r e d .  assembled  for  p r o d u c e d by an o p e n - a i r  energy.  pol-  5'-  levels  generated  A conducting deposit of  f o r reasons  experiments,  that  with either  noise  time  opposite  w h e r e x was  The v a c u u m l i n e s  w i t h the  s w i t c h shown i n . P i g  same  3x/4  to  safe,  Subsequent  The s w i t c h e s  the  of  a s a l o a d , w e r e p e r f o r m e d w i t h t h e more  2,000 t i m e s  was  The o p t i m u m t i m e  P r e l i m i n a r y experiments  i n A p p e n d i x C.  This switch  p o t e n t i a l was  as were t h e vacuum l i n e s  were t h e r e f o r e  break  s w i t c h , when a n i n d u c t i v e l o a d was u s e d ,  shown i n P i g 5 w e r e n o t a s  i n A p p e n d i x C.  it.  applied potential.  o s c i l l a t o r y discharge.  isolation,  across  to not  c o u l d be f i r e d o p t i m u m l y d u r i n g t h e  instantaneous  therefore of  so t h a t  designed  in  the  about 1/32  once  in.  1,500  - 19 l a r g e r i n d i a m e t e r t h a n t h a t i n t h e dummy c a t h o d e .  A careful  enlargement o f t h e h o l e i n t h e dummy cathode and an a d d i n g o f a s m a l l amount o f epoxy r e s i n on t h e i n s i d e o f t h e h o l e r e s t o r e d normal  operation.  3. SHOCK TUBE A p i c t o r i a l d i a g r a m o f t h e l a y o u t o f t h e shock tube and a s s o c i a t e d vacuum system i s g i v e n i n F i g 6.  The l a r g e  m e c h a n i c a l pump c o u l d q u i c k l y , e v a c u a t e t h e shock tube t o a p r e s s u r e o f l e s s t h a n 0.5 m i c r o n s Hg. tions of  The j o i n s between t h e s e c -  t h e shock tube were s e a l e d w i t h O - r i n g s mounted i n  s u c h a manner t h a t t h e shock tube c o u l d be r a p i d l y d i s a s s e m b l e d and c l e a n e d .  The w o r k i n g s e c t i J n o f t h e shock tube was con-  s t r u c t e d o f q u a r t z t u b i n g 31/32 i n . i n s i d e d i a m e t e r , 1 9/64 i n . o u t s i d e d i a m e t e r and 2 f t i n l e n g t h . to c a p a c i t o r bank  F i g 6.  l a y o u t o f Shock Tube.  -  20  -  4. A U X I L I A R Y EQUIPMENT i.  Luminosity  Detector.  The p l a s m a g e n e r a t e d line  i n a n em s h o c k  emits  r a d i a t i o n and c o n t i n u u m r a d i a t i o n i n t h e v i s i b l e  A u n i t was ipliers.  pulse  constructed  to  T h i s u n i t has  velocity  of  that  the  signifies  been used  to  Kerr  camera.  cell  detect  the  trigger  this  been used  luminous front  c u l a r l o c a t i o n along the  extensively  and t o p r o v i d e  passage of shock  radiation with  the  tube.  equipment .such  apertures slits  l i m i t e d the  dimension perpendicular  of view  x 2.5 cm.  to  plasma f o r  The c o n s t r u c t i o n o f  electrical  Pig.  i n the  of  5 cms. the  axis  the  electrical  shock  f i e l d of view i n the  h a v i n g an a x i a l • s e p a r a t i o n  greater field  that  an  any  parti-  pulse  oscilloscopes  the  region. photomult-  The e l e c t r i c a l as  both  to measure  plasma past  The two p h o t o m u l t i p l i e r s v i e w e d  the  tube  and a  tube  through  plasma to  two  Each s l i t had  its  of  The  the  tube.  e a c h p h o t o m u l t i p l i e r was the u n i t i s  has  0.1  cm  shown i n P i g 7 a n d  c i r c u i t i n P i g 8.  7« C o n s t r u c t i o n o f L u m i n o s i t y D e t e c t o r . The u n i t i s e n c l o s e d by a box t h a t i s l i g h t - t i g h t w i t h e x c e p t i o n of the entrance s l i t s .  shown the  - 21 When the output was l o a d e d w i t h 8 f t o f unterminated RG-58/U c a b l e , the cathode to ground c a p a c i t a n c e was 230 pF. —12 The  rise  time o f the output  = 0.16/isec. isolated  s i g n a l was then  (680)(230 x 10  The two p h o t o m u l t i p l i e r c i r c u i t s were  )  electrically  ( s e p a r a t e ' b a t t e r y s u p p l i e s and ground c i r c u i t s ) i n  order that appreciable spurious e l e c t r i c a l  s i g n a l s generated  the d i s c h a r g e o f the main c a p a c i t o r bank would n o t be  by  generated  i n the p h o t o m u l t i p l i e r c i r c u i t s . 100pP  Pig ii.  Kerr C e l l  8. C i r c u i t  of Luminosity  Detector,  Camera.  An Avco Type 060 K e r r c e l l w i t h an exposure time o f 0.1 ^ s e c and a m o d i f i e d Dumont P o l a r o i d o s c i l l o s c o p e camera were employed to take photographs o f the plasma.  The p u l s e needed to  t r i g g e r the spark g&p,switch i n the h i g h v o l t a g e c i r c u i t o f the  -  Kerr  c e l l was g e n e r a t e d  circuit  c a n be o p e r a t e d  single pulse when t h e  by t h e in  and b i n a r y .  trigger  22  -  c i r c u i t shown i n P i g 9-  two modes w h i c h a r e The b i n a r y mode o f  the main bank t r i g g e r e d  In  t h e b i n a r y mode o f o p e r a t i o n t h i s  the  subsequently  greater at  the  o p e r a t i o n the  output of the  of the  fires  this  tube  is  discharge  generator  I n the  of  independent  for  generated  firing  the pulse  controls  over-  p u l s e mode o f  the p u l s e  shape  operation,  appearing  firing  at  after  c a p a c i t o r C*  VI  acts  a p p e a r i n g o n Sg2 o f V3 t h a t  of t h y r a t r o n V2.  first  of  o p e r a t i o n the . p o t e n t i a l  is  The p o t e n t i a l o n Sg2  S i n c e V3 w i l l  t h e p o t e n t i a l o n b o t h G l a n d SG2 o f V3 on t h e  by V I ,  s i n g l e p u l s e mode  the pulse  a b o u t 7 yttsec •,&£ter. V I h a s f i r e d .  not f i r e  integrated  generated  V3 i n t h e b i n a r y mode o f o p e r a t i o n d o e s n o t become  will  the  t h y r a t r o n V3, o r t h e  c i r c u i t i n the  single  as a n i n t e g r a t o r  unless  pulse  of  The o u t p u t o f V I t h e n i s  t h e b i n a r y mode o f  until  single  the  has  of  only  amplitude  b r o u g h t p o s i t i v e w i t h i n a b o u t 0.1 ^ i s e c  by t h e  been  I n the  The w a v e f o r m o f  essentially  the d u r a t i o n of  and s w i t c h S i c  In  VI.  c i r c u i t receptive  o n Sg2 o f V3 i s fired.  detector.  s p u r i o u s s i g n a l has  time of  used  c i r c u i t , c a n t h u s be c o n t r o l l e d b y v a r y i n g R .  s w i t c h S i b adds R t o t h e  Sg2 o f V3.  pulse  input pulse  tube V I .  The f i r i n g  Switch Sla controls  operation,  first  input pulse.  b y t h e RC c i r c u i t . delay  by the  appearing luminosity s i g n a l .  than 2 v o l t s  waveform o f  all  the b o o t - s t r a p  as a p r i m i n g s i g n a l t o make t h e  p u l s e mode o f  o p e r a t i o n was  a spurious s i g n a l generated  of  to  designated  p u l s e was o b t a i n e d f r o m t h e l u m i n o s i t y  I t was f o u n d t h a t  utilized  This  is  o f V I , when t h e  positive not  fire  positive, circuit is  V3 in  - 23 the b i n a r y mode o f o p e r a t i o n . will,  The second p u l s e coming i n t o V I  however, f i r e V I and V3 i f t h e second p u l s e a r r i v e s be-  tween 7 and 300 / t s e c a f t e r t h e f i r s t p u l s e has f i r e d V I .  P i g 9. K e r r C e l l T r i g g e r C i r c u i t . iii.  C i r c u i t f o r F i r i n g Crowbar Swit.ch. The crowbar s w i t c h was t r i g g e r e d  a t a time measured  w i t h r e s p e c t t o t h e s t a r t o f f l o w o f t h e bank c u r r e n t . o f f l o w o f bank c u r r e n t was a more j i t t e r - f r e e r e f e r e n c e  The s t f e r t time  t h a n t h e s t a r t o f f l o w o f main s w i t c h t r i g g e r c u r r e n t because the breakdown t i m e s o f t h e main s w i t c h and t h e d r i v e r d i d n o t then introduce a d d i t i o n a l delays  (see F i g s 2-3 and 6.4-).  I t was  magnetic  o o rv>  47-n.  i — w - —  short  -0 H-  O 4 O Ss o &  8  to o o  fire  22 o  \6 .  -n  i  input  vro'be  470K  K  -AAA-, 47K  VSA-  •MM  10K  1  .1  • Q 0 1 A F T " ^rv>Q  IV)  V\A-  1  o o  4  02  o  w  IV)  Hc+ O  AAA-  tr  I I  fV)  4  H-  Ot) 0*3 CD  IV)  o o  VTI  o  IV)  o  4  O H4 O  w  |—V\A-  e  (V)  t  IV)  —AAA-  i§5£., VJIO  o  - t3 -  found t h a t the t h y r a t r o n c i r c u i t  of P i g 52a was  f a c t o r y as a crowbar t r i g g e r c i r c u i t would f i r e anode due ated by  not  because the  thyratron  on what seemed to be a ".signal a p p e a r i n g to the h i g h frequency,  finally  on  high p o t e n t i a l pulse  the main s w i t c h t r i g g e r c i r c u i t .  trigger circuit  satis-  adopted and  The  gener-  crowbar  shown i n P i g 10  e s s e n t i a l l y f r e e of t h i s u n d e s i r a b l e  the  switch  was  triggering.  i v . Magnetic Probes. • The  bank c u r r e n t arid the c u r r e n t i n t o the d r i v e r  were observed w i t h s m a l l c o i l s i n s e r t e d through the sheets  of"the coplanar  t u r n s of AWG form 1 mm end  conductors.  Each c o i l  Each c o i l was  were t w i s t e d , then connected to a BNC tubing with  RG-58/U c a b l e was ment. nAB,  The  epoxy r e s i n .  tubing.  then used to connect the c o i l  voltage  s i g n a l appearing  across  closed leads  s e a l e d to  terminated to other  equip-  the t e r m i n a t i o n i s  where n i s the number of t u r n s o f wire  area e n c l o s e d  The  j a c k which was A l e n g t h of  20  l o n g on a  i n s e r t e d i n t o the  of a 2 i n . l e n g t h o f s m a l l bore q u a r t z  the q u a r t z  c o n s i s t e d of  45 wire wound as a s i n g l e l a y e r 1 mm  i n diameter.  ground  on the c o i l , A  the  by a s i n g l e t u r n and B the r a t e of change o f  magnetic i n d u c t i o n through the c o i l . o r i e n t e d to p i c k up c u r r e n t t h a t was  this current. g r a t o r i n order  The  use  the c o i l  the magnetic i n d u c t i o n generated by  to be measured.  the t e r m i n a t i o n was  During  The  voltage appearing  was  the across  then p r o p o r t i o n a l to the r a t e of change of coil  s i g n a l was  o f t e n f e d i n t o an RC  t h a t the c u r r e n t c o u l d be observed on an  inte•  -  oscilloscope. to "be 70 Mc  The  -  26  r i n g i n g frequency  when coupled  cathode f o l l o w e r h a v i n g  without a low  measured  termination d i r e c t l y into a  input capacitance.  quency l i m i t a t i o n of the probes was the o s c i l l o s c o p e s employed  of the c o i l was  The  high  fre-  thus comparable to t h a t o f  ( T e k t r o n i x 535  and  551).  -  27 -  CHAPTER  III  PROPERTIES OF THE PLASMA  GENERATED  IN AN ELECTROMAGNETIC SHOCK TUBE  1. DISTORTION OF THE LUMINOSITY STRUCTURE BY DRIVER DISCHARGE PHENOMENA Some i n f o r m a t i o n p r e s e n t e d by o t h e r workers that  the d r i v i n g d i s c h a r g e a f f e c t s the p r o p e r t i e s  o f the plasma.  Burkhardt and Lovberg (1960) found t h a t under c e r t a i n tions  of i n i t i a l  gas d i s t r i b u t i o n and a p p l i e d  current d i s t r i b u t i o n i n a coaxial  indicates  condi-  v o l t a g e the  d r i v e r would l o s e  its azi-  muthal symmetry and g a t h e r i n t o a p i n c h e d d i s c h a r g e a t one s i d e of the tube. mobility  Fowler, Paxton and Hughes (1961) found t h a t the  o f the i o n s i n the d r i v i n g d i s c h a r g e a f f e c t e d the  v e l o c i t y o f the plasma. The  plasma generated i n an e l e c t r o m a g n e t i c shock tube  w i t h c o p l a n a r d r i v e r , F i g 11, has been s p e c t r o s c o p i c a l l y  anal-  yzed by Barnard, Cormack and Simpkinson (1962) and Simpkinson (1961).  The s p e c t r o s c o p i c v a l u e s f o r e l e c t r o n  temperature were compared w i t h the p r e d i c t i o n s f o r a p l a n e shock wave. work a K e r r c e l l planarity  o f the t h e o r y  Subsequent to the c o m p l e t i o n o f t h i s  camera was c o n s t r u c t e d and used to check the  o f the l u m i n o s i t y f r o n t  of t h i s i n v e s t i g a t i o n presented i n t h i s  d e n s i t y and  o f the plasma.  i n t o the p l a n a r i t y  section.  The r e s u l t s  o f the f r o n t a r e  scale a)  2 in. = 1 in.  Cross-sectional  Fig  View  b)  P i c t o r i a l View  11. C o p l a n a r D r i v e r f o r E l e c t r o m a g n e t i c The K e r r c e l l p h o t o g r a p h s  indicate  that  shape  the  of  inosity  of  the  the  of  of  greater  to  the  (1961). surface  i s not  of  the  the  lum-  drivers  These d r i v e r s , area  of  the plasma are  re-  reproduc-  photographs  s u r p r i s i n g as  had p r e v i o u s l y  the  been  observed  r e p r o d u c i b i l i t y ( B a r n a r d , Cormack  In this respect  T-tube  of  c a n be s e e n f r o m  intensities  shot-to-shot  S i m p k i n s o n 1962). superior  both  The g o o d s h o t - t o - s h o t  This feature  the l i n e  to have good  Linke  important properties  the plasma s t r u c t u r e  m t o o i n F i g 12. histories  and the h o m o g e n e i t y  clearly  plasma.  by t h e s e p h o t o g r a p h s .  ibility  Tube.  shown i n F i g 12  i n the d r i v e r a f f e c t s  luminosity front  Several vealed  discharge  Shock  the  coplanar  described  driver  is  by Kolb(l957) and  i l l u s t r a t e d i n F i g 13, h a d a  electrodes  exposed  to  the  discharge.  and  - 29 -  d)  r) u) v)  r  s) w)  >  t)  4  y)  4  *  ^  P i g 12. Photographs of Plasma Generated by Various D r i v e r s . a) to p ) : Coplanar d r i v e r , 4/*F c a p a c i t o r bank, 12.5 kV, period 4.5 /*sec, argon a t 1 mm Hg. q) to t ) : D r i v e r of P i g 17, 19.2/tP c a p a c i t o r bank, 8 kV, peri o d 4.5/«sec, argon a t 160 microns Hg. Pressure i n main switch'*'1.5 microns Hg. u) to z ) : D r i v e r of P i g 18, c o n d i t i o n s same as f o r p i c t u r e s a) to t ) . P o l lowing displacements measured i n cm from base of d r i v e r to l u m i n o s i t y f r o n t and times i n ^ s e c from onset of current flow. a ) x < 0 . 7 . b)x = 1.4,t= 0.7, c)x=3.7,t=1.1, d)x=4.4,t=1.3, e)x=5.3,t=1.7, f)x=5.8, t=1.9, g)x=7.0,t=2.2, h)x=8/7, i ) x = l 6 . 1 . I n a) to i ) the upper electrode was p o s i t i v e ; i n j ) to p) the lower electrode was p o s i t i v e . j)x=3.7, t=1.1, k)x= 4.4,t=1.3, l)x=5.3,t=1.7, m)to o)x=7.0, t=2.2,V p)x=16.1, q)x=10.5, r ) to t)x=48, u) to z) x=53.5. I = current i n f i e l d c o i l , A . u) I = .2, v) I = .5, w) 1= 1, x) I = 2, y) I = 5, z) I = 17. S i n g l e p i c tures are side views. Double p i c t u r e s are top and side views. D r i v i n g currents not crowbarred.  - 30 The  e x p e r i m e n t a l work on the low p r e s s u r e s w i t c h d e s c r i b e d i n  Appendix C i n d i c a t e s t h a t an o s c i l l a t o r y d i s c h a r g e o f 100 peak v a l u e and channel  frequency  about 200 kc has a  a r e a of about 1 cm  d r i v e r was  p  .  The  kA  cross-sectional  d i s c h a r g e i n the  coplanar  thus f o r c e d to cover the e l e c t r o d e s (the a r e a o f p  the e l e c t r o d e s was  about 0.25  c u r r e n t about 70 kA).  cm  and  I t i s suggested  t h a t the i r r e p r o d u c i b i l i t y observed Kolb  the peak v a l u e of the by the p r e s e n t  by both l i n k e  (1961) and  (1959) can be a t t r i b u t e d to the l a r g e a r e a of the  rodes i n t h e i r T-tubes.  author  elect-  I f the e l e c t r o d e s i z e i s comparable  to or l a r g e r than the s i z e of the d i s c h a r g e channel, then l o c a t i o n of c o n t a c t of the d i s c h a r g e onto  the  each e l e c t r o d e i s  u n p r e d i c t a b l e . - The  d i s c h a r g e w i l l move r a p i d l y over the s u r -  f a c e of the cathode  s e e k i n g always a l o c a t i o n o f f e r i n g more  efficient  e l e c t r o n e m i s s i o n (Seeker  1959).  t a) Used by Kolb  (1957) Fig  b) Used by L i n k e  13. T-Tube D r i v e r s .  (1961)  - 31 One  undesirable  characteristic  of the plasma r e v e a l e d  i n the photographs i n P i g 12 was  the n o n - p l a n a r i t y o f the lum-  inosity front.  cms,  p l a n a r i t y was is  Even a t x = 16.1 evident.  The  the departure  amount of departure  s i m i l a r to t h a t o b t a i n e d  from p l a n a r i t y  by McLean e t a l .(1960) but  s i d e r a b l y l e s s than the worst r e p o r t e d by Kolb The  The  adjacent  photographs i n P i g 12 i n d i c a t e t h a t the  luminosity  I t i s suggested by the author t h a t  the e r u p t i v e i n s t a b i l i t y , K e r v a l i d z e and  observed i n a p i n c h d i s c h a r g e  i n o s i t y s t r u c t u r e that i s f a i n t l y v i s i b l e i n P i g 12 i s drawn more c l e a r l y i n P i g  a) t = 0.7>*sec 14.  The  by  Gvaladze (1959), i s r e s p o n s i b l e f o r  the protuberances on the l u m i n o s i t y f r o n t .  Pig  polarity  l e a d i n g p o r t i o n of the l u m i n o s i t y f r o n t i s always  to the anode.  Kvartzhava,  i s con-  (1959).  a p p l i e d to the e l e c t r o d e s a f f e c t s the shape of the front.  from  b)  The  i n t e r n a l lum-  i n the  photographs  14.  t = 1 . ly^sec  c) t = 1.3/»sec  P r o t u b e r a n c e s on the Shock F r o n t .  - 32 The double-pronged  front  shown i n F i g s 12b to p i s  a c h a r a c t e r i s t i c o f n o t o n l y the plasma produced by a c o p l a n a r d r i v e r but a l s o o f the plasma produced by a T-tube (Kolb 1957).  The double-pronged  driver  f r o n t evident i n F i g H a  c o u l d be caused by the JXB f o r c e s a c t i n g on the d i s c h a r g e channel.  The magnetic  field  i n t e n s i t y i n the c o r n e r s o f the  d i s c h a r g e i s g r e a t e r than a t the c e n t e r o f the shock tube as can be shown by a c a l c u l a t i o n employing B i o t and S a v a r t ' s law. The f a c t t h a t the protuberance n e a r e s t the anode, as shown i n F i g H a , i s the more prominent  i s p r o b a b l y caused by the i o n s  i n the d i s c h a r g e i m p a r t i n g some o f t h e i r momentum to the d i s charge as a whole.  T h i s momentum e f f e c t has been observed  by Fowler, Paxton and Hughes (1961) i n an e l e c t r o m a g n e t i c shock tube o f q u i t e d i f f e r e n t d e s i g n from t h a t b e i n g c o n s i d e r e d h e r e . Very c l o s e examination o f photographs d i s c l o s e s the c r a t e r - l i k e  shape  c, d and e i n P i g 12  shown near the top of F i g H e  A mechanism t h a t c o u l d be r e s p o n s i b l e f o r the p r o t u b e r a n c e s shown i n F i g 14 i s drawn i n more d e t a i l i n F i g 15.  Fig  15. A P o s s i b l e E x p l a n a t i o n f o r the Protuberances on the Shock F r o n t .  It acting  is  on the  region of As t h i s  the  inside  starts  to  diffuse  current  I is  immediately  discharge  set  intensity  but  corner  current  force.  to  force  between  in  the  ejected.  plasmoid.  discharge  mechanism i s anism based  on the  energy  of  region  a  loop between  r e g i o n and  current  directed  the  the  effects  p l a s m o i d has the  current  i n a depression  operative  that  of  studied  by  magnetic  its of  passed  The  to  the  kinetic  IXB de-  out of  I and the  is  evident  of  that  this  the  arc,  discharge the  i n P i g s 12c column b e h i n d  crater-like  an e r u p t i v e  pro-  plasmoid  initial  i n the main d i s c h a r g e  The p r e s e n c e  field  i n the r e g i o n where  This depression shape  if  is  away  discharge  plasmoid.  discharge the  been  w i t h the  i n the  that  The r e g i o n  the r e g i o n i s  I interacts  column i n d i c a t e s  probably  the  inside  difference  the  a  discharge.  diffusing,  e n t i t y .that has  overcome  Once t h e  a crater-like  ejected  inside  discharge.  kinetic  against  across  current would r e s u l t p l a s m o i d was  by the  force  sufficient  the r e p u l s i v e  the  i n the  the  away f r o m t h e  inside  The s t r u c t u r e  The c u r r e n t  can pass c o m p l e t e l y  celerating  still  a plasma-magnetic  (1956).  is  accelerates  into  field is  JXB f o r c e  and by b o t h a t r a p p e d m a g n e t i c  I.  a decelerating  e as  corner  field  by a l a r g e  i n t e n s i t y B generated  to  discharge  While i t  the magnetic  outside  a plasmoid,  the  up a r o u n d t h e r e g i o n by t h e  of  inside  and a l o o p  energy  the  the magnetic  outwards.  characterized  from the  duce  of  that  c y l i n d r i c a l l y - s h a p e d r e g i o n moves the  Bostick  corner  author  p l a s m a away f r o m t h e  of  thus  -  s u g g e s t e d by the  corner  the  33  shape  instability  rather  t h a n an e j e c t i o n  mech-  i o n momentum e f f e c t  n o t e d by F o w l e r ,  Paxton  - 34 and  Hughes (1961).  Further  -  s u b s t a n t i a t i o n of the e x i s t e n c e  an e r u p t i v e i n s t a b i l i t y mechanism i s p r o v i d e d a p r o t u b e r a n c e appears at each corner order  of the d i s c h a r g e .  that An  of magnitude c a l c u l a t i o n of the dynamics of a .plasmoid  moving a c c o r d i n g ity  by the f a c t  of  theory  t h a t the  to the p r e c e d i n g  i s presented  suggested e r u p t i v e  i n Appendix E .  eruptive i n s t a b i l i t y  The  instabil-  c a l c u l a t i o n shows  c o u l d account f o r the  protuber-  ances . A second breakup of evidence  i n photographs e and  1.7>t*sec  a f t e r the d i s c h a r g e  luminous gas  appears to be  the d i s c h a r g e f " i n F i g 12. c u r r e n t has  At a time of about  s t a r t e d to  The  p e r i o d o f the  4.5_^sec, so t h a t t h i s breakup o c c u r r e d  t h a t the plasma a t t a i n e d a maximum v e l o c i t y t h i s Chapter). to  In the t r a n s i t i o n shown  a t the c e n t e r o f the d i s c h a r g e ,  compression.  T h i s r e g i o n has  magnetic f i e l d  p i c t u r e d i n F i g 16c  and  particle  due .to l a t e r a l  a h i g h c o n d u c t i v i t y and r e t a i n s  for a sufficient d to occur.  charge c u r r e n t i s d e c r e a s i n g  and  the magnetic f i e l d  time f o r the motion  In F i g 16c  i n F i g 16d trapped  I6e the l o o p c u r r e n t s combine and B o s t i c k (1956) has  the t o t a l  the l o o p  dis-  currents  i n the plasma become  comparable i n magnitude to the t o t a l d i s c h a r g e  the d r i v e r .  time  (see S e c t i o n 5 of  energy occurs  Fig  discharge  a t about the  i n F i g 16 a to b, a r e g i o n of h i g h l u m i n o s i t y and  generated by  dis-  F i g 16 p i c t u r e s the sequence t h a t c o u l d l e a d  the observed l u m i n o s i t y p a t t e r n s .  a trapped  flow,  e j e c t e d from the c e n t e r of the  charge back towards the d r i v e r . was  column i s i n  current.  In  are e j e c t e d back toward  established that a  plasmoid  -  35  -  F i g 16. P r o p o s e d Mechanism f o r F i n a l Breakup o f D i s charge Column. The p e r i o d o f t h e d i s c h a r g e  was 45 jmaec.  i s e l o n g a t e d when i t p a s s e s t h r o u g h a m a g n e t i c f i e l d perpendicular moid.  oriented  to the plane c o n t a i n i n g the current i n the p l a s -  The same phenomenon i s a p p a r e n t i n F i g I6e i n w h i c h a  t h i n wedge o f plasma i s shown "being e j e c t e d backwards from t h e discharge.  The c o a l e s c i n g o f t h e p l a s m o i d w i t h t h e d i s c h a r g e  formed by t h e second p u l s e o f c u r r e n t i s due t o t h e f o r c e o f a t t r a c t i o n between t h e c u r r e n t i n t h e p l a s m o i d and t h e d i s charge c u r r e n t  (Fig 16f).  I t i s of i n t e r e s t that the i n t e r n a l  s t r u c t u r e o f t h e plasma g e n e r a t e d by t h i s second p u l s e o f c u r r e n t i s q u i t e s i m i l a r t o t h a t g e n e r a t e d by t h e f i r s t as i s i n d i c a t e d i n F i g 1 2 i and p. The  l u m i n o s i t y p a t t e r n t h a t can be d i r e c t l y  to t h e d r i v i n g d i s c h a r g e  stays very  attributed  close to the f r o n t of the  - 36 plasma even a f t e r tance  down t h e  shock  uncontaminated, (1961) h a s preciable layer This  tered  of  amount o f the  theory  the  light.  pattern  tube  of  the  discharge is  applied  the  to  ed t o  electric  this  the  conductivity w i l l cms.  pinching of  w o u l d be t h a t  flows  to  extend  the  author  gas  The p e r s i s t e n c e  interest.  toward the particles  E i t h e r there  luminosity pattern do n o t l e a v e  the  caused  that  the  i n the  side"  created of  tube  scat-  luminosity of  contube  of  subject-  rising  a distance  The p i n c h  "Y on i t s  the  propagate  gas  pinched  tube.  is the  region rises,  result.  the  between  the  for  in this  and the  of  by  shock  The r e g i o n  shock  early  As soon as v o l t a g e  field is  density  the l u m i n o s i t y p a t t e r n does n o t  boundary-  d u r i n g the  an i n d i r e c t r e s u l t  rise.  center  ap-  tubes.  carriers will  down t h e  an  shock  down t h e  o f a "V on i t s  tube  electromagnetic  The c o n d u c t i v i t y  current  Hooker  tube.  of  field will  of  shock  luminosity front  volume  dis-  the  c o u l d be -due t o a n i n s t a b i l i t y o f  theory.  thin.  through the  c o u l d n o t p l a u s i b l y be  driver.  current  forcing particles  quite  and the w a l l o f  s u g g e s t e d by t h e  As t h e the  thus  gas  d r i v e r an e l e c t r i c  of  of  is  stages of breakdown.  electrodes  is  The r e g i o n  shown i n F i g 12a a n d b i s  initial  utihis  12i a n d p ) .  shock-heated  d r i v e r gas  d u r i n g the  shape  a considerable  gas  should apply  It  travelled  i n a diaphragm d r i v e n shock  duction through a large  several  (Figs  shock-heated  The s h a p e stages  plasma has  shown t h a t  between same  the  pattern for  a shape,  side" column  The f a c t  down t h e  of  tube  of  the  some  is  a steady  flow  of  during this  time  or the  that supports  1 >tsec  particles  pinched region during t h i s  radiating time.  I t has discharge  has  a pronounced  the  of  the  of  the  on t h e  shown t h a t  under the  driver  stays very  that  even at  shock  tube.  close  to  It  has  conditions  the  front  of  driving of  the  In  parti-  affect  a considerable  ceased to f l o w .  experimental  the  properties  d r i v i n g discharge  plasma,  d r i v i n g c u r r e n t has  gas  effect  Section  an e l e c t r o m a g n e t i c  instabilities  homogeneity  -  b e e n shown i n t h i s  plasma g e n e r a t e d ' i n cular,  37  the  time  also  been  studied, the  after  the  plasma.  2. E F F E C T OF THE GEOMETRY OF THE DRIVER ON THE LUMINOSITY STRUCTURE I N THE PLASMA Introduction The that  the homogeneity  erated  of  reached  of  the  the  geometry  scribed  in this  generating  shock  of  the  a reproducible was  facilitated.  A course  The o b j e c t  amenable  studies  of research generation  d u c i b l e .properties;" or that m i g h t be a c h a r a c t e r i s t i c  indicate  that  gen-  the  of  on  the  the  struc-  by  chang-  the work  de-  possibility  produced behind a plane  spectroscopic  the  plasma  of  p l a s m a t h a t was b o t h f a i r l y f r e e  time-resolved  to  the  Section,  depend m a r k e d l y  to a s c e r t a i n  S u c h a p l a s m a w o u l d be r e a d i l y  either  preceding  p l a s m a c a n be a l t e r e d  driver.  S e c t i o n was  c o n t a m i n a t i o n and t h a t  would l e a d  tube  driving discharge,  l u m i n o s i t y i n the  i n g the  i n the  and r e p r o d u c i b i l i t y o f  i n an e l e c t r o m a g n e t i c  properties ture  conclusions  of  front.  to a n a l y s i s .  Also,  on s u c h a p l a s m a w o u l d was of  therefore  adopted  a, p l a s m a w i t h  be that  repro-  w o u l d c l a r i f y why i r r e p r o d u c i b i l i t y property  of  the  plasma generated  in  -  an e l e c t r o m a g n e t i c  38  shock tube.  -  In t h i s s e c t i o n K e r r  photographs of the plasma generated "by s e v e r a l of d r i v e r are p r e s e n t e d and Experimental  first  p i c t u r e d i n P i g 17.  L i k e the  t h i s d r i v e r has  17-  discussed.  c o n f i g u r a t i o n of d r i v e r t h a t was other  cylindrical  a) P i c t o r i a l View Pig  configurations  Results  The  Section,  cell  drivers described  The  of the  d i d not  to t .  r e s u l t i n good s h o t - t o - s h o t  s t r u c t u r e of the l u m i n o s i t y  i r r e p r o d u c i b i l i t y evident  to p.  Electrodes  photographs of the plasma produced by  i n the  the  This reproduc-  plasma.  from these photographs i s con-  s i d e r a b l y worse than t h a t i n d i c a t e d by 12a  i n this  View,  D r i v e r w i t h Short  d r i v e r shown i n P i g 17 are p r e s e n t e d i n P i g 12q driver obviously  tested i s  symmetry.  b) G r o s s - S e c t i o n a l Pull size.  Coaxial Electromagnetic Kerr  ibility  cell  the photographs i n P i g  That i s , the i r r e p r o d u c i b i l i t y was  dependent upon  - 39 the geometry of the d r i v e r . Al-fven, L i n d b e r g luminosity  and M i t l i d  (1959) observed t h a t  the  f r o n t of the plasma generated by a c o a x i a l e l e c t r o -  magnetic d r i v e r c o u l d be made more plane by a p p l y i n g a r a d i a l magnetic f i e l d was  still  a t the  e x i t of the d r i v e r .  f l o w i n g through the plasma w h i l e  through the r a d i a l magnetic f i e l d . /6sec 0.09 0.3  to about 100 Wb/m  (300  2  - 0.95  kA,  - 900  The  and  d r i v i n g current  the plasma passed  c u r r e n t rose w i t h  the magnetic f i e l d G)  The  i n t e n s i t y was  the c o r r e s p o n d i n g  static  0.03  at  mWb.  tested.  described  Pig  18.  18  A s m a l l t r i g g e r spark promoted breakdown i n i t i a l l y  the base of the d r i v e r .  d r i v e r was  -  flux  A s i m i l a r c o n f i g u r a t i o n of d r i v e r shown i n P i g was  3  T h i s method of t r i g g e r i n g the  employed i n a l l of the d r i v e r s t h a t are in this  subsequently  Section.  C o a x i a l E l e c t r o m a g n e t i c D r i v e r w i t h Short E l e c t r o d e s and a S t a t i c Magnetic P i e l d . The magnetic f i e l d i n t e n s i t i e s shown were measured when a 5A c o i l c u r r e n t was f l o w i n g i n the f i e l d c o i l .  - 40  -  T y p i c a l p h o t o g r a p h s o f the plasma g e n e r a t e d by d r i v e r shown i n P i g 18 are p r e s e n t e d i n P i g 12u  to z.  the  It  found t h a t the s t r u c t u r e o f the l u m i n o s i t y i n the plasma  was was  not r e p r o d u c i b l e , r e g a r d l e s s  of the magnitude o f the m a g n e t i c  field  A t low v a l u e s  (coil  c u r r e n t £ 20A).  of c o i l  the l u m i n o s i t y f r o n t tended t o be composed o f one large protuberances.  At h i g h v a l u e s ,  current?  1^  or more  5 t o 20 amperes, the  f r o n t tended to be composed o f many s m a l l e r p r o t u b e r a n c e s . an i n t e r m e d i a t e  value  b i l i z i n g value,  the shock f r o n t o f t e n tended t o be p l a n e .  value  of f i e l d , w h i c h w i l l be c a l l e d the  o f the s t a b i l i z i n g f i e l d  low p r e s s u r e  i n A p p e n d i x C, a d e c r e a s e i n gas r a t e of r i s e of bank c u r r e n t .  sta-  depended on the p r e s s u r e  main s w i t c h on the c a p a c i t o r bank. pressure  An i n c r e a s e  As  of a p p l i e d f i e l d  mentioned  d e c r e a s e d the  initial  i n the i n i t i a l  increase  T h i s e f f e c t was  t r a p p e d i n the plasma was  The  i n the  o f r i s e o f bank c u r r e n t t h u s d e c r e a s e d the magnitude of s t a b i l i z i n g f i e l d required.  rate the  as i f the amount  increased  i n the i n i t i a l r a t e of r i s e o f c u r r e n t .  by  an  A larger  i n i t i a l r a t e o f r i s e of c u r r e n t , w h i c h would r e s u l t i n a i n i t i a l v e l o c i t y o f the l u m i n o s i t y f r o n t and  cause more  s i o n of the l i n e s o f f o r c e t r a p p e d i n the a d v a n c i n g p o s s i b l y r e s u l t s i n a "breaking" and  J a c o b s e n 1960)  Lindberg  amount of the a p p l i e d  t r a p p e d i n the plasma t h u s s h o u l d have been i n c r e a s e d increase  discharge,  (the term employed by  The  higher exten-  o f more l i n e s o f f o r c e t h a n a s m a l l e r  r a t e of r i s e of c u r r e n t w o u l d .  At  by  initial field an  i n the i n i t i a l r a t e o f r i s e of c u r r e n t , a r e s u l t t h a t  i s c o n f i r m e d by the e x p e r i m e n t a l  data.  a)  e)  D r i v e r with, downstream B  Driver with d i s c anode  Fig  19.  f)  b)  Driver with  Driver with small area cathode  g)  short  anode  Driver with p i n cathode  Configurations of Axially-Symmetric T h a t Were T e s t e d .  Drivers  - 42 In properties, tested.  an attempt to o b t a i n a plasma h a v i n g r e p r o d u c i b l e the c o n f i g u r a t i o n s o f d r i v e r shown i n P i g 19 were  Most of the t e s t s were conducted w i t h a 19.2/iP bank  charged to 8 kV and w i t h argon a t a p r e s s u r e o f 160 microns Hg in  the shock tube.  The l e n g t h of the c e n t e r p i n i n the d r i v e r s  shown i n P i g 19a to d was  g r e a t e r than the d i s t a n c e over which  a c c e l e r a t i o n o f the plasma o c c u r r e d . ment i n r e p r o d u c i b i l i t y was  Wo  significant  o b t a i n e d w i t h the c o n f i g u r a t i o n s  shown i n P i g 19a and b over t h a t shown i n P i g 18. crease i n v e l o c i t y and l u m i n o s i t y was Pig  19c, h a v i n g a l a r g e a r e a anode.  i n l u m i n o s i t y and the the  improve-  effect  Some i n -  obtained with a d r i v e r , The  e x t e n t of the i n c r e a s e  of the a p p l i e d magnetic f i e l d  on  l u m i n o s i t y o f the plasma i s i n d i c a t e d by the photographs  i n P i g 20 a and b.  A g a i n a v a l u e o f a p p l i e d magnetic  t h a t tended to s t a b i l i z e  the plasma c o u l d be n o t e d .  A time i n t e g r a t e d spectrum of the v i s i b l e  radiation  from the plasma generated by the d r i v e r o f P i g 19c was The spectrum was  field  taken a t a d i s t a n c e o f 50 cms  taken.  from the T e f l o n  at  the base o f the d r i v e r , and the i n i t i a l p r e s s u r e o f argon  in  the shock  bank was  tube was  160 microns Hg.  19.2/<P c a p a c i t o r  d i s c h a r g e d from 8 kV and the d r i v e r was  The waveform o f the d r i v i n g c u r r e n t was the  The  f i r s t p u l s e of a s i n e wave.  crowbarred.  therefore  essentially  No s t a t i c magnetic f i e l d  a p p l i e d to the d r i v e r and the v e l o c i t y o f the l u m i n o s i t y where the spectrum was  taken was  2.3  cm^wsec.  The  was front  spectrum  c o n t a i n e d l i n e s of A H ,  G a l , CI, weak C u l and a- narrow H o r l i n e .  I t was  t h a t no S i l i n e s were observed and  o f some i n t e r e s t  that  a)  ID)  C)  d)  e)  P i g 20. E f f e c t s o f D r i v e r Geometry and Gas P r e s s u r e on L u m i n o s i t y o f Plasma. a ) D r i v e r o f P i g 19b. 19.2 M R c a p a c i t o r bank, 8kV, u n c r o w b a r r e d , 160 m i c r o n s Hg a r g o n i n shock t u b e , 20 m i c r o n s Hg a r g o n i n s w i t c h e s . F i d u c i a l marks a t 45 and 50 cms. b) D r i v e r o f F i g 19c. C o n d i t i o n s same as f o r case a ) . Lens o p e n i n g unchanged f o r c a s e s a) and b ) . c) t o e) D r i v e r o f F i g 19d. F i d u c i a l marks a t 30 and 35 cm. 19.2/fF c a p a c i t o r bank, 8 kV, crowbarr e d , 20 m i c r o n s Hg a r g o n i n s w i t c h e s . Shock tube p r e s s u r e s i n m i c r o n s Hg o f a r g o n : c) 160, d) 600, e) 1000. F i e l d c o i l c u r r e n t s i n A, r e a d i n g down: a) and b ) : 0, .033, .1, .3, 1, 3, 10, 15. c): 0, 1, 3, 3.4, 4, 5, 7.5, 10. d) and e): 0, 2, 4, 6, 9, 12, 15, 0. Two v i e w s c o n s t i t u t e one p h o t o g r a p h . The upper p i c t u r e i s a t o p v i e w o f t h e plasma, the l o w e r i s a s i d e v i e w .  -  44  -  the o v e r a l l number o f i m p u r i t y l i n e s was v e r y l o w . The e f f e c t o f t h e i n i t i a l p r e s s u r e  i n t h e shock tube  on t h e s t r u c t u r e o f t h e l u m i n o s i t y o f t h e plasma i s shown i n Fig  20c t o e.  The d r i v e r employed i s shown i n F i g 19d.  The  s t a b i l i z i n g e f f e c t on t h e plasma o f a h i g h i n i t i a l p r e s s u r e i n the shock tube i s e v i d e n t .  This d r i v e r , i n c i d e n t a l l y ,  produced  a plasma h a v i n g a g r e a t e r v e l o c i t y t h a n t h e plasma produced by any  other d r i v e r tested. I t was found t h a t t h e magnitude o f t h e a p p l i e d mag-  n e t i c f i e l d a f f e c t e d the pressure  r i s e i n t h e system due t o 3  firing.  F o r example, t h e p r e s s u r e  i n t h e 1200 cm  shock tube  vacuum system r o s e from 160 m i c r o n s Hg t o 185 m i c r o n s Hg f o r a c r o w b a r r e d 8 kV d i s c h a r g e  i n t o a r g o n when no m a g n e t i c  was a p p l i e d t o t h e d r i v e r . field  c o i l , the pressure  field  W i t h a 10 A c u r r e n t i n t h e m a g n e t i c  r o s e o n l y t o 175 m i c r o n s Hg.  The d r i v e r i n F i g 19e was d e v e l o p e d w i t h t h e o b j e c t of d e c r e a s i n g  the area of the e l e c t r o d e s .  I t was b e l i e v e d  that  i r r e p r o d u c i b i l i t y o f t h e l u m i n o s i t y s t r u c t u r e o f t h e plasma m i g h t be due t o movement o f t h e a r c over t h e s u r f a c e electrodes.  Photographs r e v e a l e d  that the l u m i n o s i t y s t r u c t u r e ,  i n p a r t i c u l a r t h e p l a n a r i t y o f t h e f r o n t , was more for  of the  reproducible  t h i s d r i v e r t h a n f o r any o f t h o s e p r e v i o u s l y t e s t e d .  time-integrated contained  A  s p e c t r o g r a m o f t h e l u m i n o s i t y f r o m t h i s plasma  a l a r g e number o f G r I I l i n e s .  the s t a i n l e s s s t e e l anode was i n s p e c t e d ed a c l e a n roughened a p p e a r a n c e .  The i n n e r s u r f a c e o f and found t o have assum-  I t was c o n c l u d e d t h a t t h e  l a r g e amount o f e l e c t r o d e m a t e r i a l i n t h e plasma was p r o b a b l y  - 45 due to the s m a l l i n t e r - e l e c t r o d e s p a c i n g .  The e l e c t r o n s i n  the d i s c h a r g e were p r o b a b l y a b l e to pass from cathode to anode w i t h low c o l l i s i o n a l  energy l o s s e s , then impart  to the anode, which was heated  their  energy  and l o s t i o n s and atoms to the  plasma. The d r i v e r shown i n F i g 19f produced a plasma h a v i n g a f a i r l y r e p r o d u c i b l e l u m i n o s i t y s t r u c t u r e , as p i c t u r e d i n F i g 21a to h. the f i r s t  A l l f i r i n g s w i t h t h i s d r i v e r were crowbarred  zero o f the c u r r e n t .  The prominent l i n e s  appearing  i n a time i n t e g r a t e d spectrum taken a t x = 50 cms, x = 2.0 /isec, were o f A l l . were a l s o noted.  No S i l l  l i n e s appeared.  to a monochromator.  The h i s t o r y of the  with a photomultiplier  The s h o t - t o - s h o t  d u c i b i l i t y o f the peak i n t e n s i t y of each s p e c t r a l l i n e was o n l y f a i r .  cm/  Weak l i n e s o f C u l , Z n l , and the H»rlines  i n t e n s i t y o f c e r t a i n l i n e s was observed t h a t was f i t t e d  at  reproobserved  The r e p r o d u c i b i l i t y was, however, b e t t e r than  o b t a i n e d w i t h the other d r i v e r s , w i t h the e x c e p t i o n o f the coplanar  driver. Another i n d i c a t i o n o f the r e p r o d u c i b i l i t y of the  plasma produced by the small-cathode  d r i v e r i s r e v e a l e d by  the o s c i l l o g r a m s o f the s i g n a l s observed detector  ( F i g 2 1 i to p0 .  w i t h the l u m i n o s i t y  S e v e r a l crowbarred  f i r i n g s a t an  energy o f 3 k J were attemped w i t h t h i s d r i v e r .  The h o l e i n  the T e f l o n was i n s u f f i c i e n t l y l a r g e to pass the h i g h e r c u r r e n t and  the T e f l o n was c o n s i d e r a b l y decomposed by these  firings.  One u n d e s i r a b l e f e a t u r e o f t h i s d r i v e r was t h a t i t produced a lower v e l o c i t y than the d r i v e r i n F i g 19d.  -  46  -  P i g 21. S t r u c t u r e o f L u m i n o s i t y o f Plasma. 19.2,aF c a p a c i t o r "bank, 8 kV. c r o w b a r r e d . a) t o o) D r i v e r o f P i g 1 9 f . p) t o w) D r i v e r o f P i g 19g. Shock tube p r e s s u r e : a) t o f ) , and i ) t o v) 160 m i c r o n s Hg o f a r g o n , g) 600 m i c r o n s Hg o f a r g o n , h) and w) 1000 m i c r o n s Hg o f a r g o n . F i d u c i a l mark a t 40 cm. P h o t o g r a p h s i ) and o) are s i g n a l s from p h o t o m u l t i p l i e r ( l u m i n o s i t y d e t e c t o r ) a t 40 cm. S c a l e s : 5 V / d i v and .4 ><* s e c / d i v .  -  47  A c o n f i g u r a t i o n of tween t h o s e luminosity pictured was  structure  of  but  with a thin layer  anode  cathode  shown i n P i g 1 9 g .  the  cathode  same a s  p r o d u c e d by the  of  this  o f what a p p e a r e d  The b r a s s  luminosity  quite  front  driver  irreproduc-  d r i v e r was f o u n d t o be t o be b r a s s  is  by t h e  plated  crowbar-  must have been b o i l e d o r s p u t t e r e d  by e l e c t r o n bombardment.  resulted  driver  of  that  the  beThe  The v e l o c i t y  t h e l u m i n o s i t y s t r u c t u r e was  The c o p p e r  red f i r i n g s .  is  the plasma produced by t h i s  i n P i g 21 cp t o isr.  i n P i g 19d,  the  d r i v e r t h a t was a c o m p r o m i s e  shown i n P i g 19d a n d f  quite high, nearly  ible.  -  The i o n bombardment  i n deposition rather  than l o s s  of  off  of  the  cathode  material. Discussion The d r i v e r shown i n P i g 19d p r o d u c e d t h e p l a s m a i n g the  least  to-shot  r e p r o d u c i b i l i t y of  of  the  dable  c o n t a m i n a t i o n and the h i g h e s t  p l a n a r i t y of time-resolved  the  the  structure  to a l l o w  spectroscopic  measurements  t o be  f i e l d to  the  area  anode and t h i s electrode  anode r e s u l t e d lessened  materials.  shot-to-shot the  s t a b i l i z e d by  generated  the  v a r i a t i o n i n the  driving discharge.  made. applying  t h e most repro-r Apparently  i n a low current d e n s i t y  contamination of  Also,  depen-  driver.  plasma and the b e s t p l a n a r i t y o f f r o n t .  the l a r g e  shqfcfc-  the l u m i n o s i t y and  insufficient  The d r i v e r shown i n P i g 1 9 f ducible  of  The  f r o n t was  The p l a s m a c o u l d n o t be s a t i s f a c t o r i l y a r a d i a l magnetic  velocity.  hav-  the  small area  l o c a t i o n of  The s m a l l a r e a  plasma by  cathode the  cathode  the  the,  anode  reduced  cathode was  at  end  the of  major  - 48 cause of the good s h o t - t o - s h o t  reproducibility.  3. MAGNETIC FIELDS IN THE Marshall  PLASMA  (1960) d e t e c t e d an a z i m u t h a l  i n the plasma e j e c t e d by a c o a x i a l d r i v e r .  magnetic  field  H i s measurements  were made on a plasma moving i n t o a vacuum.  S i m i l a r measure-  ments were made i n the p r e s e n t work on the plasma produced i n an e l e c t r o m a g n e t i c Fig  19c.  shock tube powered by the d r i v e r shown i n  Measurements were made w i t h a magnetic probe,  v i o u s l y d e s c r i b e d , o r i e n t e d to p i c k up of magnetic f i e l d  the a z i m u t h a l  a t a d i s t a n c e of 1 mm  of the shock tube.  The  observed  t o r o i d a l magnetic f i e l d  component  i n from the i n s i d e  waH  waveshape i s shown i n F i g 22  a l o n g w i t h an e x p l a n a t i o n f o r the e x i s t e n c e of t h i s The  pre-  field.  i n this explanation i s attributed  to a t r a p p i n g of the d r i v i n g f i e l d .  A quantitative interpre-  t a t i o n of the probe s i g n a l s would be i n e r r o r because i t was b e l i e v e d t h a t the probe d i s t u r b e d the plasma. a c a l c u l a t i o n based on the observed adoption J-3  of a simple model, was  A/cm  ducibility was  .  The  the s i g n a l was  t h a t B , „ « 4 G, max Ty  generated  was  n  The  of  the  o n  A,  reprosignal  indicating  that  by a r a t e of change of f l u x l i n k a g e The  shot-to-shot  i n the shape of the s i g n a l d i s a p p e a r e d  p l a c e d 5 mm  on  I. , - 20 xo xa_L  shot-to-shot  r o t a t e d 180°,  r a t h e r than by e l e c t r o s t a t i c e f f e c t s . ducibility  v  d i d v a r y somewhat.  i n v e r t e d when the c o i l was  results  probe s i g n a l , and  shape of the s i g n a l had  but the amplitude  The  i n from the w a l l .  The  a l o n g the l e n g t h of the shock tube was  repro-  when the  v a r i a t i o n o f the not i n v e s t i g a t e d .  coil  signal  - 49 ,03V  a) t= Fig  b) t= 4>tsec  c) t= 35 /(sec, x= 87 cm  22. B^. T r a n s p o r t e d i n Plasma. The d r i v i n g c u r r e n t J ceased to f l o w when t * 2 . 3 / < s e c . I n i t i a l p r e s sure 160 microns Hg, l u m i n o s i t y f r o n t v e l o c i t y at x = 87 cm was 2.0 cm/a sec. F u r t h e r v e r i f i c a t i o n t h a t a c u r r e n t d i p o l e was p r o -  pagating w i t h the  down the tube was o b t a i n e d MHD g e n e r a t o r .  These experiments a r e d e s c r i b e d i n  d e t a i l i n Chapter IV, S e c t i o n 1. these  d u r i n g experiments conducted  The r e l e v a n t r e s u l t  from  experiments t h a t o f f e r e d f u r t h e r c o n f i r m a t i o n o f the  e x i s t e n c e o f a c u r r e n t d i p o l e was t h a t the v e l o c i t y o f the plasma c o u l d be a l t e r e d by a p p l y i n g a s t a t i c field  i n f r o n t o f the plasma.  plasma was e i t h e r decreased  azimuthal  magnetic  The normal d e c e l e r a t i o n o f the  or i n c r e a s e d by an a p p l i e d  t h a t r e s p e c t i v e l y a i d e d or opposed the trapped  magnetic  field field.  - 50 4. INITIAL BREAKDOWN PHENOMENA The magnitude o f the magnetic  field  (see F i g 18  F i g s 19a to d) a p p l i e d to the c o a x i a l d r i v e r was affect  the breakdown time o f the d r i v e r .  found to  T h i s dependency i s  g i v e n i n F i g 23 f o r the d r i v e r shown i n F i g 19d. the coil  The break i n  curve o c c u r s a t a v a l u e o f c u r r e n t through the dc t h a t produced  a magnetic  the  t r i g g e r i n g plasma  The  electric  field  i n the r a d i a l  field  that s a t i s f i e d  and  field  a t the i n j e c t i o n p o i n t o f the r e l a t i o n E/B  = C.  a t the t r i g g e r i n j e c t i o n p o i n t was  d i r e c t i o n and the a p p l i e d magnetic  primarily  field  i n the  axial direction.  The p r o b a b l e e x p l a n a t i o n f o r the dependence  of magnetic  on the breakdown time i s t h a t charged  field  parti-  c l e s o r i g i n a t i n g i n the t r i g g e r spark move i n an a z i m u t h a l d i r e c t i o n i n the c r o s s e d E and B f i e l d s and are r e t u r n e d to the  cathode.  They thus cannot l e a v e the cathode.  There are  two major i n t e r e s t i n g p o i n t s about t h i s phenomenon.  The  first  i s t h a t the i n j e c t i o n o f charged p a r t i c l e s , v e r y p r o b a b l y e l e c t r o n s by the t r i g g e r spark, i s the primary mechanism t h a t l e a d s to breakdown.  The  initiating  second p o i n t i s t h a t  e i t h e r f r e e e l e c t r o n s come from the t r i g g e r spark or t h a t the plasma  i n the t r i g g e r spark can be stopped by c r o s s e d E and B  fields. The initiated B<E/C.  curve i n F i g 23 i n d i c a t e s t h a t breakdown  was  a t the base o f the d r i v e r by the t r i g g e r spark, when The phenomenon noted by H a r t (1959), t h a t breakdown  o c c u r r e d i n i t i a l l y a t the open end o f the d r i v e r , was observed i n the p r e s e n t experiments.  There are two  thus not  possible  - 51  2 Field  -  4 coil  6 c u r r e n t i n A.  10  8  F i g 23. Breakdown Time of the D r i v e r shown i n F i g 19d. Argon i n shock tube a t p r e s s u r e of 160 microns Hg, 19.2^3? bank d i s c h a r g i n g from 8 kV. Breakdown time of u n t r i g g e r e d d r i v e r was 2.2./asec. explanations f o r t h i s discrepancy. was  A negative  center electrode  employed i n the p r e s e n t work; Hart used a p o s i t i v e  electrode.  A l s o a t r i g g e r spark was  shock tube.  When B> E/C,  the t r i g g e r spark has no  employed i n the  center  present  the p r e c e d i n g curve i n d i c a t e s t h a t e f f e c t on the breakdown time.  Possibly  i n t h i s r e g i o n of o p e r a t i o n , breakdown does occur i n i t i a l l y the open end  of the d r i v e r , as,noted  A t r i g g e r was  The  i s g i v e n i n F i g 4. i n the 1200  cm  circuit  The  de-  w i t h the e x c e p t i o n of t h a t  f o r the t r i g g e r p u l s e  t r i g g e r d i s c h a r g e r a i s e d the  shock tube by 0.02  the c o n t a m i n a t i o n  (1959).  i n s t a l l e d i n each o f the d r i v e r s  s c r i b e d i n S e c t i o n 2 of t h i s Chapter shown i n F i g 17.  by H a r t  at  microns Hg.  The  generator pressure amount of  i n the plasma t h a t c o u l d be d i r e c t l y  ed to the d i s c h a r g e of the t r i g g e r p u l s e was  attribut-  thus s m a l l .  - 52 5. DYNAMICS OP  -  ELECTROMAGNETICALIY ACCELERATED PLASMA  Introduction In t h i s S e c t i o n  e x p r e s s i o n s are  motion of a plasma a c c e l e r a t e d  by  Mostov, N e u r i n g e r and  problem.  The  published  s o l u t i o n to two of H a r t , as Neither  the  forces.  (1959), H a r t  (1962),  Rigney (1961), have c o n s i d e r e d  r e s u l t s are  often given  coupled d i f f e r e n t i a l  form of p r e s e n t a t i o n  mensions of the  as a s e r i e s  e q u a t i o n s or, i n the  provides a c l e a r p i c t u r e of  case  the  dynamics of the plasma of a change i n the d i d r i v e r , the k i n d or p r e s s u r e of gas  employed,  e f f e c t of a gross change i n the waveform of the  current.  this  curves o b t a i n e d w i t h the a i d of an a n a l o g computer.  e f f e c t s on the  or the  for  electromagnetic  Numerous a u t h o r s , f o r example D a t t n e r and  derived  A c l o s e d form f o r x ( t ) , the  displacement of  driving the  plasma as a f u n c t i o n of time, c o u l d be used to p r e d i c t  the  e f f e c t s of such changes.  closed  forms f o r x ( t ) , x ( t ) and  In the a n a l y s i s t h a t f o l l o w s , x ( t ) are  derived.  The  analysis i s  v a l i d f o r b o t h the a c c e l e r a t i o n of a s l u g of plasma and  the  a c c e l e r a t i o n of a plasma g a i n i n g mass by a snowplow a c t i o n . The  closed  forms f o r x ( t ) , x ( t ) and  i n g 'that l ( t ) ,  the  d r i v i n g current  x ( t ) are  o b t a i n e d by  assum-  as a f u n c t i o n of time, i s  known. Theory Kirchhoffs initially  law  f o r the  charged to v o l t a g e  V, Q  current  discharging  i n d u c t a n c e L ,. s e r i e s r e s i s t a n c e R Q  resistance R(I,t)  and  I from a c a p a c i t o r  Q  and  into a series  a d r i v i n g assembly  i n d u c t a n c e per u n i t l e n g t h  of  is  of  C,  - 53 -  ^((L .L,x)l] 0  +  |R.  +  R,(i^]l+^jl(f)«ie  = V  6  0  o where x ( t ) i s the displacement the d r i v i n g assembly.  of the plasma from the  base of  I t i s assumed t h a t the d r i v i n g  assembly  has a c o n s t a n t i n d u c t a n c e per u n i t d i s t a n c e t r a v e l l e d by plasma.  The  c o a x i a l d r i v e r shown i n P i g 19d possesses  i n d u c t a n c e as do a l s o to a c l o s e a p p r o x i m a t i o n shown i n P i g s 19 and  those shown i n P i g s 11,  When i t i s assumed t h a t energy  13,  17 and  an  drivers 18.  expended i n i o n i z i n g term,  e q u a t i o n f o r the system i s  where Y i s the v o l t a g e a c r o s s the c a p a c i t o r , m s l u g mass and m^  Q  i s the  initial  i s the mass i n c r e a s e of the plasma per  a x i a l l e n g t h of the -electrode assembly. advancing  such  the o t h e r  and h e a t i n g the plasma can be i n c l u d e d as a J o u l e heat the energy  the  plasma entraps the gas  unit  I t i s assumed t h a t the  i t encounters;  plow model i s c o n s i d e r e d to be a p p l i c a b l e .  thus the snow-  The K e r r  cell  photographs shown i n P i g 12 i n d i c a t e t h a t t h e r e i s v i r t u a l l y no shock-heated  plasma i n f r o n t of the d i s c h a r g e d u r i n g the  acceleration period. not a p p l i c a b l e .  The  s t a n d a r d shock e q u a t i o n s are t h e r e f o r e  A permeable snowplow a c t i o n can be i n c l u d e d  i n the model by s u i t a b l y c h o o s i n g m^. of c o n t a m i n a t i o n  S i m i l a r l y the  effect  of the plasma by e l e c t r o d e m a t e r i a l can  i n c l u d e d by s u i t a b l y c h o o s i n g m  Q  and m^.  be  I t i s f u r t h e r assumed  t h a t the plasma i s t h i n i n the d i r e c t i o n of motion, t h a t c u r r e n t  - 54 flow i n the plasma i s p e r p e n d i c u l a r to both the d r i v i n g magnetic f i e l d  and  the d i r e c t i o n of plasma motion, and  t h a t no  e x t e r n a l magnetic f i e l d s are a p p l i e d . T a k i n g the time d e r i v a t i v e of e q u a t i o n  7, , n o t i n g  t h a t CV = - I , d i v i d i n g by I, s u b t r a c t i n g e q u a t i o n 6,  then i n -  t e g r a t i n g y i e l d s the momentum c o n s e r v a t i o n e q u a t i o n f o r the plasma  [m. + m , x ( i ) ] x ( t ) -  g(t)  8  .  where  §(t) The (1962) and  L, [i{t)f  = |  9  a n a l y s i s thus f a r i s s i m i l a r to t h a t of H a r t  of D a t t n e r  u a t i o n 8 d e p a r t s from  (1959).  The method of s o l u t i o n of eq-  t h a t of other workers from  t h i s point;  onwards. I t i s of i n t e r e s t  to s o l v e e q u a t i o n 8 f i r s t  s p e c i f y i n g the form of the f u n c t i o n g ( t ) .  The  without  s o l u t i o n when  x(t=0) = 0 i s :  „/.x  2m,g(t)  /m, + 2  -  x(t) =  *(t)«  or  '~  m  Q  10  9  /m  [m.  + 2m,g(t)  2 e  J  +  2m,g(t)]Va  11  - 55 D e f i n i n g t * as the time when maximum v e l o c i t y  occurs  14  X (t'j = 0 therefore  [m.» 2 , ( f ) ] § ( f ) +  W  = m.fjftfjj  g  2 .... .15  or  §(t*) Prom e q u a t i o n s  =  ^.[xft*)]*  .....16  10 and 11, /^.*\ _ i / n O o * 2 n o , q ( t * ) 2  x  '  1  Equation  y  M  , «  •  - mn  Q  1  2 m , g ( f )  ?  18  18 i s e q u i v a l e n t to  * { t >  i g l  , m,-o  2  0  The maximum v e l o c i t y i s a f i g u r e o f m e r i t f o r an e l e c t r o m a g n e t i c a l l y a c c e l e r a t e d plasma.  Therefore,  equations  19 and 20 a r e of v a l u e f o r p r e d i c t i n g the maximum v e l o c i t y t h a t can be o b t a i n e d i n any p a r t i c u l a r c o n s t a n t c r o s s - s e c t i o n e l e c t romagnetic shock tube. velocities equations  I t i s of i n t e r e s t  to compare the  o b t a i n e d by o t h e r authors w i t h those p r e d i c t e d by 19 and 20.  F o r example, the computer s o l u t i o n s  i n Hart's P i g 4 are e s s e n t i a l l y i d e n t i c a l d i c t e d by e q u a t i o n 19.  given  to the v a l u e s p r e -  I t i s also of i n t e r e s t  to compare  e q u a t i o n 19 w i t h the e q u a t i o n o b t a i n e d by assuming t h a t a shock model i s a p p l i c a b l e r a t h e r than a snowplow model. example, the r e l a t i o n x = 1.1 A ^ L v rn,  Por  I can be o b t a i n e d from the  - 56 a n a l y s i s o f Chang  (1961).  Several s p e c i f i c ered,.  forms f o r g ( t ) w i l l now "be c o n s i d -  A l t h o u g h o n l y one c u r r e n t waveform, a s i n u s o i d , i s o f  immediate importance,  i t i s of interest  to determine  a l s o the  e f f e c t o f o t h e r waveforms o f d r i v i n g c u r r e n t on the dynamics of the a c c e l e r a t i n g  plasma.  In many plasma a c c e l e r a t i o n experiments R » Q  L  Q  R ( l , t ) , where d i s the d i s t a n c e t h a t the plasma  d u r i n g the f i r s t  current pulse.  Under these  » L^d and travels  assumptions,  e q u a t i o n 6 can be l i n e a r i z e d and the o s c i l l a t o r y  solution i s  then  i(t) = i  e~  0  4t  S i n to't  21  where  & = R /2L o  0  ,  -  =/l7c  6J  ?  ,  *  0  =V./cJL.  The v a l u e s o f g ( t ) , g ( t ) and g ( t ) f o r s u b s t i t u t i o n i n t o e q u a t i o n s 10 to 12 a r e then •• /1 \  cj(t)  I | i-2  = j L, I  r  0  -2i"t . 2  e  CO  i[»sr]  i  wt I  [e-  ; l 4 t  ] 23  -ait' r -  24 The maximum v e l o c i t y and p o s i t i o n where the maximum v e l o c i t y o c c u r s can be found from equations 17 and 18 a f t e r t * has been determined.  A g r a p h i c a l s o l u t i o n o f e q u a t i o n 15 f o r  - 57 t * i s g i v e n i n P i g 24 when the c u r r e n t e q u a t i o n 21.  The e q u a t i o n t h a t  waveform i s t h a t o f  i s solved  graphically i s  P i g 24. Time When Maximum V e l o c i t y Occurs i f the D r i v i n g C u r r e n t i s Obtained from a Damped O s c i l l a t o r y C i r c u i t . Lot*(<* = o, * = o ) io8-9°. =  It  i s to be noted  58 t h a t wt* does not v a r y g r e a t l y  w i t h changes i n <* when «*<!, assumed t h a t only the f i r s t a c c e l e r a t i n g the plasma.  I n the graph o f P i g 24 i t i s  current pulse i s operative i n  T h i s assumption has been v e r i f i e d  e x p e r i m e n t a l l y by s h o r t - c i r c u i t i n g the c o a x i a l d r i v e r o f a shock tube a t the end o f the f i r s t  c u r r e n t p u l s e and s t u d y i n g  the x ( t ) c h a r a c t e r i s t i c s o f the shock f r o n t .  They were  e s s e n t i a l l y i d e n t i c a l to the x ( t ) c h a r a c t e r i s t i c s  obtained  when the d i s c h a r g e was not crowbarred, thus c o n f i r m i n g , a t l e a s t under the c o n d i t i o n s s t u d i e d , ' t h a t o n l y the f i r s t p u l s e was o p e r a t i v e i n g e n e r a t i n g Quite  simple  the f i r s t  expressions  current  shock.  are o b t a i n e d  f o r x ( t ) and  ±(t) when damping i s assumed to be n e g l i g i b l e d u r i n g the f i r s t current pulse.  Thus, assuming lit)  - I„  s i n 6ot  .... .26  results i n cj(t)  = —• L, I  0  2  sin  2  601  2  q M - ^ L . I ^ V - s i n ' w t ]  , .2 m  +  L,I. m, r , , , * - s i n c o t ] 2  L|Ip x(t)  =  4 lo  2  \ j)j:. f  2  2  _  m  ?  .....29  <  s i ncut cosa)"t]  1  J  31 And  t * i s d e f i n e d by the e q u a t i o n  - 59 tan  •&•  -  32 wheree-and JT a r e the v a r i a b l e s t h a t were p r e v i o u s l y d e f i n e d .  In  t h i s case, however, to i s d e f i n e d by the r e l a t i o n t 0 L C = 1 . 2  o  The s o l u t i o n to e q u a t i o n 32 i s p r e s e n t e d as the <* = 0 curve i n P i g 24. Another c u r r e n t waveform t h a t i s of i n t e r e s t as a p o s s i b l e s h o c k - g e n e r a t i n g waveform i s t h a t generated ically  damped c i r c u i t .  in a  crit-  ,2  Then  o = 1/1 C and  lit) « & t  -St e  33 -2<£t  34  -24f 35  9  (  t  ALU'  "  )  4  2  I2  41  36  The time when maximum v e l o c i t y o c c u r s , t * , can be determined  from  the e q u a t i o n t h a t i s o b t a i n e d by s e t t i n g x ( t )  equal to z e r o : y f e a  ?  = e"  where € = 2 d t  2 f  {. 2f-f-f -f A}+ e J  4  +  and V =  ° ,V , .  f  { - 2 - 2 f  .. occurs when  <St* =  2 f . f ] i +  37  The s o l u t i o n to e q u a t i o n 37  i s g i v e n i n g r a p h i c a l form i n P i g 25. ocity  +  When f = 0, maximum v e l -  1.29 or l ( t * ) = 0.355 V  .  - 60 -  fo  4  1  F i g 25. Time When Maximum V e l o c i t y Occurs i f the D r i v i n g C u r r e n t i s Obtained from a C r i t i c a l l y Damped C i r c u i t . Equation  8, the momentum c o n s e r v a t i o n e q u a t i o n f o r  the plasma, i s v a l i d n o t o n l y f o r a d r i v i n g c u r r e n t by the d i s c h a r g e i s also v a l i d  o f a c a p a c i t o r (see equations  f o r d r i v i n g c u r r e n t s o f unusual  ated by other c i r c u i t s .  F o r example, Hart  6 and 7 ) , but waveshape gener-  (1962) has suggested  that a ramp waveshape o f c u r r e n t may produce a h i g h shock wave.  Applying  generated  velocity  the above methods t o a ramp waveform  I(t)=  ,38  results i n  g(t) = L , I g(t) 9  (t)«  2 0  t /2t 2  2  L.lIt'At*  , 59 ,40  iXt'A^x' 41  x(t) *  /m  a g  + m,L,I  2 0  tyi2r 42  - 61 -  »  ( t )  _  [L,I  2 0  t /2t ][m a  4  |W x(t)  a 0  + m,L I t  a 0  ty36T ] 2  m.L.IoHVlZT*]*  +  possesses no maximum v a l u e  •••••44  4  s i n c e x ( 0 £ t £ T ) 4 0.  As i t i s probable  t h a t a sawtooth c u r r e n t waveform would  i n the g e n e r a t i o n  o f one shock f r o n t f o r each c u r r e n t  i t w i l l be assumed t h a t the maximum v e l o c i t y occurs end  o f the f i r s t  current pulse.  x(t-f-t) =  result  pulse,  a t the  Then  °  L |I  X  /  b  / V + m L I. rVl2 45 d r i v i n g c u r r e n t waveform w i l l be considered; ,  1  One l a s t  I(t)  ={  Then  *  1 °  x  (t) =  1  46  >  t  <  0  +rn,L,I t /2 rr), rr), a  - ™<  a  0  .47  L,I t/2 a  0  /m. It  8  i s of i n t e r e s t  + m L,I t /2 a  (  a  48  e  to note t h a t when m  Q  = 0, the  v e l o c i t y o f the plasma i s a constant  x ( t , «.-o) = x ( t * / 3 £ m « , « v o , w . > o ) - ^ I .  49  - 62 A step waveform o f c u r r e n t of 1/0.946  thus r e s u l t s i n a plasma v e l o c i t y  (see F i g 24) t h a t o f a plasma a c c e l e r a t e d by a s i n e  waveform o f c u r r e n t , when m The  Q  = 0.  equations o f motion f o r a plasma s l u g moving i n t o  a vacuum w i l l now be c o n s i d e r e d . obtained  The e q u a t i o n s o f motion a r e  from e q u a t i o n 8 by p u t t i n g m^ = 0.  x(t) = g(t)/no  50  0  i(t)=  5c(t). The the  .....51  cj(t)/m  4  .52  maximum v e l o c i t y o f such a s l u g i s a t t a i n e d a t  time when g ( t ) = 0, or l ( t ) =0.  F o r the o s c i l l a t o r y  cur-  r e n t waveform the maximum s l u g v e l o c i t y i s a t t a i n e d when out* = TT , when we once more assume t h a t o n l y the f i r s t is  operative  i n a c c e l e r a t i n g the plasma.  current  pulse  F o r the c r i t i c a l l y -  damped c i r c u i t , maximum s l u g v e l o c i t y i s approached as t-*"°°. Artsimovich slug being form.  T h e i r a n a l y t i c s o l u t i o n , which i s v a l i d f o r s m a l l to t h a t which can be r e a d i l y o b t a i n e d  wavetime,  from e q u a t i o n  They a l s o s o l v e d , w i t h the a i d o f an a n a l o g computer, two  e q u a t i o n s s i m i l a r to e q u a t i o n s 6 and 8. utions 21,  an e q u a t i o n f o r a  a c c e l e r a t e d by an o s c i l l a t o r y undamped c u r r e n t  is identical 50.  et a l (1958) d e r i v e d  sol-  i n d i c a t e t h a t the assumption made j u s t p r i o r to e q u a t i o n  namely t h a t L d<^L  m. = 0 , 1  T h e i r computer  , can be s t a t e d more r i g o r o u s l y when  1  as * *-i » m to x  0  a  « L  e0  -  F i g 26. V e l o c i t y of Plasma D u r i n g A c c e l e r a t i o n "by V a r i o u s Waveforms of D r i v i n g C u r r e n t .  - 64 A comparison o f the e f f e c t s o f the shape o f the current  waveform on ±(t) i s p r e s e n t e d i n P i g 26. In the p r e c e d i n g a n a l y s i s  the  e f f e c t s o f d i s c h a r g e contaminants ( m a t e r i a l  d i s c h a r g e from the e l e c t r o d e s can he i n c l u d e d  consisted  the  Q  and m^.  the t o t a l mass i n a plasma  d i s c h a r g e gases was p r o p o r t i o n a l  time i n t e g r a l o f the square o f the c u r r e n t . that  eroded "by the  i n the a n a l y s i s by s u i t a b l y c h o o s i n g m  o f only  that  and i n s u l a t i o n i n the d r i v e r )  S t a r r and N a f f (1960) found t h a t that  i t has "been assumed  They  to the  indicated  the i n s t a n t a n e o u s mass i n the plasma was p r o p o r t i o n a l to time i n t e g r a l o f the square o f the c u r r e n t  of measurement.  up to the time  Thus under t h i s assumption the momentum equa-  t i o n f o r the a c c e l e r a t i n g plasma can be expressed as  > x 2  J 53  where K = f j _ ] _ / J I d t , f^ i m  = "the f i n a l mass of the plasma  m  n a  na  X - the time a t which  at the end o f the a c c e l e r a t i o n p e r i o d , acceleration  ceases.  d r i v i n g current 26)  The s o l u t i o n to e q u a t i o n 53 when the  i s the f i r s t h a l f c y c l e o f a s i n e wave  is  (equation  a  X Experimental The  =  L, I * TT  Results motion of the plasma d u r i n g  a c c e l e r a t i o n i n the  c o a x i a l d r i v e r s shown i n P i g s 19c to g c o u l d  not be observed  d i r e c t l y because the metal o u t e r c y l i n d e r p r e v e n t e d d i r e c t  - 65 -  d e t e c t i o n of the plasma w i t h the l u m i n o s i t y d e t e c t o r .  An  experimental value f o r the peak v e l o c i t y could, however, be c a l c u l a t e d by e x t r a p o l a t i n g the x ( t ) c h a r a c t e r i s t i c for  observed  the d e c e l e r a t i n g plasma back to a p o s i t i o n of x = 10 cms  (the  approximate p o s i t i o n of maximum v e l o c i t y ) and then c a l c u -  l a t i n g the v e l o c i t y a t t h i s l o c a t i o n .  When t h i s procedure was  a p p l i e d to the data presented as curve b i n P i g 28, the value '  E x p e r i m e n t a l = 3.5 cm/usec was obtained.  The current  waveform was the f i r s t h a l f - c y c l e of a s i n e wave i n which I = 200,000 A and£o= 1.34 x 10  rad/sec.  An estimate of the amount  of e l e c t r o d e m a t e r i a l and other contaminants  i n the plasma was  obtained from the pressure r i s e i n the system caused by a f i r ing.  The pressure i n c r e a s e d i n the 1200 cm  shock tube from  160 - 5 to 195 - 5 microns Hg f o r a f i r i n g t h a t was crowbarred at the f i r s t zero of the c u r r e n t .  T h i s pressure r i s e was t h a t  due to non-condensable vapors r e l e a s e d by the f i r i n g , s i n c e a l i q u i d a i r t r a p removed the condensable vapors.  The mass  corresponding to t h i s pressure r i s e and an assumed mean mole c u l a r weight of 40 was 104 /tg. gas encountered  When complete t r a p p i n g of the  by the advancing current sheet was assumed to  occur and when the mass c o n t r i b u t e d by the discharge, 104/*g, was considered to be deposited i n the plasma a t a r a t e proport i o n a l to the d i s t a n c e that the discharge had t r a v e l l e d , then m  Q  = 0 and m  1  = (0.213 + 1.04) x 1 0 "  8  the maximum v e l o c i t y occurred when u)t* 19 n o t i n g t h a t L = 4.7  cm/ttsec.  kg/cm.  Prom P i g 24,  = 108.9°.  Prom  equation  = 1.4 x 1 0 " H/m, i t f o l l o w s t h a t x(t*)^ 7  1  licQr  The discrepancy between the experimental and  „  - 66 t h e o r e t i c a l values of x ( t * ) could be r e s o l v e d by c o n s i d e r i n g a higher r a t e of contamination of the plasma by discharge materials.  When the l i q u i d a i r t r a p was not on the shock tube,  the pressure r i s e was higher than that obtained w i t h the t r a p on.  A l s o , a t h i n l a y e r of m a t e r i a l was appearing on the w a l l s  of the shock tube near the d r i v e r .  The amount of e l e c t r o d e  m a t e r i a l i n the plasma at the time t h a t maximum v e l o c i t y  was  achieved was thus l a r g e r than 104Ag. The v e l o c i t y of the plasma at x = 10 cms f o r the case presented as curve c i n P i g 28 i s 6.9 sure i n c r e a s e d i n the 1200 cm to 30 - 5 microns Hg.  cm/asec.  The p r e s -  shock tube from 0.1 microns  Hg  The mass of gases causing t h i s r i s e i n  pressure, assuming a mean molecular weight f o r the gases of 40, was 89/*g.  The maximum v e l o c i t y as p r e d i c t e d from equation  54 under the c o n d i t i o n s o f ^ = 1.4 i 10 H/m, I = .2 MA, 6 —R 1.34 x 10 rad/sec and m„. , = 8.9 x 10 kg was x,, „ ' final ° theory = 3.7 cm/// sec. I t i s apparent t h a t the l a r g e amount of e l e c t r o d e m a t e r i a l i n the plasma renders comparison  of the experimental  r e s u l t s With the t h e o r e t i c a l p r e d i c t i o n s q u i t e d i f f i c u l t .  The  o s c i l l o g r a m s shown i n P i g 27 o f f e r i n d i r e c t c o n f i r m a t i o n of the l a r g e amount of contamination i n the plasma.  The d i s t a n c e over  which a c c e l e r a t i o n should have occurred, a c c o r d i n g to the above theory, f o r a f i r i n g i n which P = 160 microns Hg, no e l e c t r o d e contamination present,co = 1.34 x 10 rad/sec, = 1.4 x 1 0 -7 Q  H/m,  L  Q  = 2-9 nH, I = 200 kA, no damping, was  of L,|d was t h e r e f o r e 14 nH.  10 cms.,  The value  Thus f o r t h i s case the c r i t e r i o n  -67  -  zoo loo a)  Pig  for  27.  T y p i c a l O s c i l l o g r a m s of C u r r e n t i n D r i v e r of Shock Tube, a) I n i t i a l p r e s s u r e = 1000 microns Hg. h) I n i t i a l p r e s s u r e = 160 microns Hg. c) I n i t i a l p r e s sure = 0.1 microns Hg. The 19.2//P hank was d i s charged from a p o t e n t i a l of 8 kV, the d r i v e r was the s m a l l cathode d r i v e r shown i n P i g 19f, the gas i n the shock tube was argon, the switches c o n t a i n e d n i t r o g e n a t a p r e s s u r e of 20 microns Hg and the d r i v e r was crowharred a t a time t h a t r e s u l t e d i n the u n i d i r e c t i o n a l c u r r e n t p u l s e t h a t i s shown.  the a p p l i c a b i l i t y of the above theory, I ^ d «  have been s a t i s f i e d .  The  L , Q  inductance  of the c i r c u i t .  show t h a t t h e r e was  The  time-vary-  o s c i l l o g r a m s i n P i g 27  no d i f f e r e n c e i n the c u r r e n t waveform when  the p r e s s u r e  i n the shock tube was  microns Hg.  A l a r g e amount of c o n t a m i n a t i o n  would account  not  c u r r e n t waveform s h o u l d , t h e r e f o r e ,  have been a p p r e c i a b l y d i s t o r t e d by the e f f e c t s of the ing  should  f o r the observed  the shock tube on l ( t ) .  v a r i e d from 0.1  to  1000  i n the plasma  independence of the p r e s s u r e i n  - 68  -  Discussion • I t has  been assumed throughout the p r e s e n t  Section  t h a t the d r i v i n g f o r c e s on the plasma are p r i m a r i l y e l e c t r o magnetic f o r c e s r a t h e r than f o r c e s caused by a J o u l e - h e a t e d gas.  have a l s o been n e g l e c t e d . t h e o r e t i c a l and  1962)  The  thermal c o n d u c t i o n l o s s e s  experimental v e l o c i t i e s  j u s t i f i e d because the  (see a l s o Hart  of these a d d i t i o n a l energy  t r a n s f e r mechanisms i s j u s t i f i e d , studied.  energy  approximate agreement between  i n d i c a t e s t h a t the n e g l e c t  mental c o n d i t i o n s  expansion of  Mechanisms such as f r i c t i o n a l  l o s s e s , r a d i a t i v e energy l o s s e s and  the  the  at l e a s t .under the  experi-  A more complete a n a l y s i s i s not  e f f e c t s of the l a r g e amount of contamin-  a t i o n i n the plasma are i n s u f f i c i e n t l y known. A major c o n c l u s i o n the  small  i s t h a t the plasma generated  cathode d r i v E r shown i n P i g 19f  electrode material.  The  considerable  t h e o r e t i c a l analysis' i n d i c a t e s that  the amount of t h i s m a t e r i a l the .period of the  contains  by  c o u l d be l e s s e n e d  by  decreasing  d r i v i n g current.  6. DYNAMICS OP  THE  DECELERATING PLASMA  Introduction Various  workers have observed t h a t the  of the plasma a f t e r the be r e p r e s e n t e d  d r i v i n g c u r r e n t has  by  deceleration  ceased f l o w i n g  can  fi  x oc t  .... .55  p  D i f f e r e n t workers have a s s i g n e d which are independent of x or t .  values One  to the parameter of the  objects  of  {3 the  - 69 p r e s e n t S e c t i o n i s to show t h a t such an assignment i s v a l i d o n l y over a l i m i t e d a value and  range of x or to  0.667 a t an i n i t i a l  |3= 0.4-17 a t an i n i t i a l  Kash et a l (1958) o b t a i n e d  p r e s s u r e of under 100 microns  p r e s s u r e of 10 mm  (1960) s t a t e s t h a t the former  figure  Hg.  the b a s i s of hydrodynamic t h e o r y .  Bershader  have o b t a i n e d  under 100 microns  i n a x i a l d i s c h a r g e tubes  6 in.  Cormack (1960) o b t a i n e d  @=  0.48  jS = 0.61  at  Hg p r e s s u r e .  1000  of diameter  microns  a t 500  microns  Hg  pressure,  microns  f o r a c o p l a n a r d r i v e n shock i n argon I t i s apparent  of ^ on v a r i o u s parameters s h o u l d be Experimental  3 to  f o r a T-tube d r i v e n  f o r a c o p l a n a r d r i v e n shock i n h e l i u m a t 300  Hg p r e s s u r e and  data  ( 3 - 1 a t p r e s s u r e s i n a i r of  shock p a s s i n g through argon i n i t i a l l y P - 0.79  blast  f? = 0.667 on  (1960) c i t e s  of o t h e r workers who Hg  Bershader  i s i n agreement w i t h  wave t h e o r y and H a r r i s (1960) d e r i v e s the v a l u e  Hg  t h a t the dependence  clarified.  data i s p r e s e n t e d i n t h i s S e c t i o n t h a t  shows t h a t the v a l u e of the parameter (3 d e c r e s e s as the plasma travels  down the tube.  depend on the i n i t i a l observation. is  The  e x p e r i m e n t a l v a l u e of (S i s shown to  p r e s s u r e i n the tube and  An e m p i r i c a l r e l a t i o n i s f i t t e d  d i s c u s s e d i n terms of a proposed  model, (9  depends upon the i n i t i a l  model.  plasma and  momentum of the plasma.  The  data.and  p r e s s u r e i n the tube,  of o b s e r v a t i o n , energy  Experimental  to the  of  A c c o r d i n g to t h i s  d r i v i n g mass, the time the i n i t i a l  the time  the  l o s s e s from  the  Data data p r e s e n t e d  i n P i g s 28 and  29 were o b t a i n e d  w i t h the l u m i n o s i t y d e t e c t o r t h a t has been d e s c r i b e d i n Chapter  - 70 II,  S e c t i o n 4,  i . The  time  tectable luminosity front  -  of the a r r i v a l  (but not t h a t due  r a d i a t i o n ) measured r e l a t i v e to the onset t.  The  of the f i r s t  arrival  time was  de-  to p r e c u r s o r  of d r i v e r c u r r e n t ,  is  designated  measured as a f u n c t i o n  of  the d i s t a n c e x down the shock tube from the base of the  driver.  of (3 from  The  experimental  .44  to .86.  v a l u e of {3 decreases cm to x = 80  cm.  v a l u e of 3 due  curves  shown i n P i g 28 have v a l u e s  In p a r t i c u l a r , from .81  The  to .53  curve b) shows t h a t the over the range of x =  i n c r e a s e a t constant  to a decrease  i n the i n i t i a l  time  30  t i n the  p r e s s u r e i n the  tube i s a l s o e v i d e n t .  80 70  5  60 50 x cm  b)  40  a)  30 >  e)  _  20 t, Pig  /jl  sec  28. x ( t ) Data f o r D e c e l e r a t i n g Plasma, a ) S m a l l cathode d r i v e r , P i g 1°,f, i n i t i a l p r e s s u r e 1 mm Hg, b ) S m a l l cathode d r i v e r , P i g 19f, i n i t i a l p r e s s u r e .16 Hg, c ) S m a l l cathode d r i v e r ^ P i g 19f> i n i t i a l p r e s s u r e .1 micron Hg, d ) C o a x i a l d r i v e r w i t h non-smooth anode, P i g 19c, i n i t i a l p r e s s u r e .16 mm-Hg, e) D r i v e r w i t h disc--anode,, P i g 19e, i n i t i a l p r e s s u r e .16 mm H g . - A l l d r i v i n g c u r r e n t s were crowbarred -at the end of the f i r s t c u r r e n t p u l s e .  The s t r a i g h t l i n e s F i g 29 s a t i s f y the  71  -  t h a t are f i t t e d  to the data i n  equation t/x = Rx/2P + S/P  56  where P, R and S are parameters t h a t w i l l following section.  The v a l u e s  he d i s c u s s e d i n the  o f P, R and S do not depend  on  x or t . t/x  1 .2  ^sec/cm a)  /  1 .0  ,8  -^^^^^^i  ^^^^^  ^-**e)  *~ c) "**  0  0  20  40 x,  Fig  60  80  cm  29. G r a p h i c a l D e t e r m i n a t i o n o f Parameters i n Propagat i o n E q u a t i o n f o r D e c e l e r a t i n g Plasma.a) to e) d e s i g n a t i o n s are e x p l a i n e d i n F i g 28.  - 72 TheoryEquation  56 i s e q u i v a l e n t to the d i f f e r e n t i a l  equa-  tion (S + Rx)x = P In a simple tum  .... .57  i n t e r p r e t a t i o n , P can he c o n s i d e r e d  to be the momen-  o f the plasma when x = 0 and S the mass o f the plasma when  x = 0.  T h i s mass, which w i l l be d e s i g n a t e d  m , i s not the  t r u e mass a t x = 0 but r a t h e r i s the mass t h a t the plasma would have possessed  a t x = 0 i f i t had been d e c e l e r a t i n g over the  range 0 £ x $ 30 cms a c c o r d i n g  to the same equations  over the range 30 cmsS x S 80 cms.  Again,  that applied  i n a simple  inter-  p r e t a t i o n , R would be the mass i n f l u x to the plasma per u n i t of d i s t a n c e t r a v e l l e d . l i n e with tation.  Curve c i n P i g 29 s h o u l d be a s t r a i g h t  e s s e n t i a l l y zero Since  slope according  to t h i s i n t e r p r e -  the s l o p e i s a p p r e c i a b l e , the above i n t e r p r e -  t a t i o n f o r R i s not s t r i c t l y v a l i d .  A more r e a l i s t i c  inter-  p r e t a t i o n f o r R i s t h a t i t i s the mass i n f l u x to the plasma per u n i t o f d i s t a n c e t r a v e l l e d p l u s the drag u n i t of d(xx)/dt.  on the plasma per  D e n o t i n g the l a t t e r q u n a t i t y as m^ and the  former as m^ l e a d s t o :  {n0 + [nr>, +nn ]x]x = P  58  d  o  The  parameter m^ i s r e l a t e d to energy l o s s e s from the plasma.  The  q u a n t i t y m^ i s assumed to be the mass o f the gas i n i t i a l l y  filling  the, tube per u n i t l e n g t h o f the shock tube.  snowplow a c t i o n i s thus assumed to take , The s o l u t i o n t o the p r e c e d i n g  X  Jm*  place. equation i s  + 2p*> tm j]Pt t  c  - rY)o  — — — — — — _ M _ mj + m,!  A complete  59  - 73 or i n a form t h a t i s u s e f u l f o r data r e d u c t i o n  t/x  = {nn, + m ] x / 2 P  +  ( 1  w /P  .....60  0  E q u a t i o n 59 can he approximated by  x ^y2Pt/m,i-mj|  1  2P(m,+ m } t > > ™ d  2  .„.„ 1 6  ooooe O2  The proposed model thus p r e d i c t s t h a t the v a l u e o f |S i n equat i o n 55 can be between 0.5 and 1 depending upon the time o f o b s e r v a t i o n , the mass per u n i t l e n g t h o f the gas i n i t i a l l y i n the shock tube, the d r i v i n g mass a t x = 0, the momentum o f the plasma a t x = 0 and the energy l o s s parameter  m^.  The proposed model f o r the d e c e l e r a t i n g plasma i s p i c t u r e d i n P i g 30.  The energy l o s s parameter m^ i s i n t e r p r e t -  ed i n t h i s f i g u r e as b e i n g due to l o s s o f p a r t i c l e s v i a the boundary  l a y e r and l o s s o f i n t e r n a l energy o f the plasma by  both heat c o n d u c t i o n to the w a l l s and r a d i a t i o n l o s s e s the plasma.  from  A mechanism t h a t i s n o t shown i n P i g 30, but t h a t  might be o p e r a t i v e , i s d i f f u s i o n o f the shock-heated gas through the d r i v i n g gas.  The r e s u l t s t h a t have been d i s c u s s e d i n  Chapter I I I , S e c t i o n 1 i n d i c a t e t h a t the s t r u c t u r e o f the l u m i n o s i t y o f the plasma  t h a t can be d i r e c t l y a t t r i b u t e d to  the d r i v i n g d i s c h a r g e s t a y s extremely c l o s e to the shock  front.  A l a r g e f l o w o f the shock-heated gas p a s t the d r i v i n g gas must thus o c c u r .  T h i s f l o w c o u l d occur both through the boundary  l a y e r between the d r i v i n g gases and the w a l l s o f the shock tube, and through the body o f the d r i v i n g gas. the boundary  The f l o w through  l a y e r has been c o n s i d e r e d by Hooker (1961).  - 74  ©< v e l o c i t y < x  v e l o c i t y ?0  radiation 3|gS£_..g&SeS _ ~. mp y^g-rw i t h 'n^63^3City !  i .  >  n e a r - e q ugas i l i b r i u m shockheated  Pig  j ^J-sj non-equilibrium shock-heated gas 30. Proposed Model f o r D e c e l e r a t i n g Plasma i n Shock Pront-Pixed Coordinates.  A n a l y s i s of E x p e r i m e n t a l The  v a l u e s of the v a r i a b l e s g i v e n i n Table  o b t a i n e d by f i t t i n g the data i n P i g m. + Case  Data  equations  of the form of equation 60  a)  -  b)  .0056  c)  .0018  a)  .0058  e)  .0050  V/ /tsec/cm P  2  Table  to  29.  m, d  P /csec/cm  1 were  .230  .127  1.  m  o  / m  1 d cm + m  -  Driver  Initial Pressure microns Hg  small area cathode,Pig crowbarred  19f,  41 .1  s m a l l area cathode,Pig crowbarred  t9t,  70.6  small area cathode,Pig crowbarred  19f,  .133  22.9  coaxial,Pig crowbarred  .223  44.6  d i s c , P i g 19e crowbarred  19c, >  1000  160  0.1  160 160  R e s u l t s of A n a l y z i n g D e c e l e r a t i o n Data.  - 75 The  e x p e r i m e n t a l data f o r case a)  hot he f i t t e d  (see F i g 29) c o u l d  to a f u n c t i o n of the form of e q u a t i o n 60.  The  i n c r e a s i n g s l o p e of curve a) i n F i g 29 w i t h i n c r e a s i n g x i n d i c a t e s t h a t m^  + m^  i n c r e a s e d w i t h x.  t i o n f o r t h i s anomalous b e h a v i o u r was  A possible  suggested by the shape  of the s i g n a l observed w i t h the l u m i n o s i t y d e t e c t o r . 80 cm,  a pronounced  s i g n a l by  ~4  mm.  s p i k e of l u m i n o s i t y preceded  p r o b a b l y due  cms,  later.  The  the main  T h i s s p i k e of  to r a d i a t i o n from i m p u r i t i e s a t  the boundary between the w a l l of the shock front.  At x =  A l s o , the main s i g n a l r o s e to a peak v a l u e  at a c o n s i d e r a b l e d i s t a n c e , ~ 5 l u m i n o s i t y was  explana-  tube and the  shock  important p o i n t i s t h a t the r e g i o n of n o n - e q u i l i -  brium shock-heated  gas  ( F i g 50) was  n e a r - e q u i l i b r i u m shock-heated  ^4  gas was  mm  i n , l e n g t h . a n d the  very probably several  cms  i n length.  was  never observed a t e i t h e r lower p r e s s u r e s or a t h i g h e r  velocities. to e ) .  A s p i k e of l u m i n o s i t y p r e c e d i n g the main s i g n a l  A l s o m^+  m^ was  independent  of x f o r cases  I t i s thus i n d i c a t e d t h a t case a) d i f f e r e d  from the o t h e r s .  fundamentally  The p r o b a b l e cause f o r the d i f f e r e n c e  t h a t i n case a) a t r u e shock f r o n t formed  gas  the dominant energy i n the plasma r a t h e r than the energy  The  was of  The model shown i n F i g 50 would thus not  'be a p p l i c a b l e f o r case a) s i n c e i t was t h a t the energy  was  i n f r o n t of the  d r i v e r gases and t h a t the energy of the shock-heated  the d r i v e r gases.  b)  of the d r i v e r gases  assumed i n t h i s model  predominated.  i m p u r i t y s p e c t r a l l i n e s observed i n the r a d i a t i o n  emitted by the plasma c o n f i r m t h a t d r i v e r gases are p r e s e n t .  - 76 This 30,  -  evidence supports the v a l i d i t y  of the model drawn i n F i g  i n which o n l y a s m a l l r e g i o n of shock-heated plasma i s  shown.  Further  evidence f o r the  drawn i n F i g 30 i s p r o v i d e d  by  " s l u g " s t r u c t u r e of plasma  the  oscillograms  i n F i g 21 i to' a.  Rockman (1961) found t h a t the v e l o c i t y of the o s i t y f r o n t was (P=  0.667) i f a f i c t i t i o u s  employed an was  p r e d i c t e d f a i r l y a c c u r a t e l y by b l a s t  theory  chosen.  Rockman  e l e c t r o d e l e s s d r i v e r to produce h i s plasma  thus not  as has  o r i g i n f o r x was  concerned w i t h a l a r g e amount of d i s c h a r g e  been the  case w i t h the  In the p r e s e n t the p r o p e r t i e s  plasma t h a t has spectroscopic  and gases,  experiments h e r e .  Chapter s e v e r a l i n v e s t i g a t i o n s i n t o  of the plasma produced i n an  been d e s c r i b e d .  lumin-  em  shock tube have  These i n v e s t i g a t i o n s have i n d i c a t e d t h a t been produced i s not  studies.  The  the  suitable for detailed  plasma i s , however, good enough  to be used f o r t e s t i n g magnetohydrodynamic power  generators.  - 77 -  CHAPTER  IV  MAGNETOHYDRODYNAMIC POWER GENERATION  1. SOME PROPERTIES OF AN ELECTRODE-TYPE B^. MAGNETOHYDRODYNAMIC POWER GENERATOR Introduction The m a j o r i t y o f workers who have i n v e s t i g a t e d the p r o p e r t i e s o f MHD power g e n e r a t o r s have c o n s i d e r e d the Cart e s i a n geometry o f g e n e r a t o r shown i n F i g 31.  In this  con-  f i g u r a t i o n the c u r r e n t i s c o l l e c t e d v i a p a r a l l e l p l a t e s which are i n e l e c t r i c a l  c o n t a c t w i t h the plasma.  h  F i g 31. The C o n v e n t i o n a l C a r t e s i a n MHD Generator. Less commonly c o n s i d e r e d geometries c o a x i a l types shown i n F i g 32. generated by the H a l l  current.  I n the c o a x i a l type power i s ?  Power i s generated  g e n e r a t o r by the c o n d u c t i o n c u r r e n t , geometries  a r e the d i s c and  i n the d i s c  Rosa (1961) d i s c u s s e s the  shown i n F i g s 31 and 32 and concludes t h a t the  F i g 32.  The D i s c and  C a r t e s i a n form has ing reasons.  The  the C o a x i a l MHD  Generators.  the b e t t n r c h a r a c t e r i s t i c s , f o r the first  operate a t any v a l u e  r e a s o n i s t h a t the C a r t e s i a n form w i l l  of cOT(&>= e l e c t r o n c y c l o t r o n r e s o n a n t  f r e q u e n c y , X - average f r e e time of an e l e c t r o n i n the s i n c e , i t can he  conduction  current,  or from hoth  expands and  accounted f o r s i n c e there decoupling  c o o l s , can he r e a d i l y  e x i s t s a r e l a t i v e l y h i g h degree of  between the upstream and  downstream p a r t s of  flow when the C a r t e s i a n form i s operated as a current generator.  conduction-  segmented "electrodes can be used i n t h i s type ,of  of  C a r t e s i a n geometry over the d i s c or c o a x i a l type are i n the B^.  MHD  generator  (flow v e l o c i t y ) and cOZ,  a d v a n t a g e s , d i s c u s s e d by Rosa (1961) i n f a v o u r  inherent  the  Such f e a t u r e s as v a r i a b l e c r o s s - s e c t i o n  to c o n t r o l v a r i a t i o n s i n 0", V two  cur-  Secondly, v a r i a t i o n s i n c o n d u c t i v i t y ((f ) and 60 X,  which occur as the gas  and  gas),  connected to g i v e a power output from e i t h e r  the H a l l c u r r e n t or the rents.  follow-  generator  shown i n P i g 33.  These the also  This  - 79 particular  c o n f i g u r a t i o n has n o t p r e v i o u s l y "been c o n s i d e r e d  by o t h e r workers.  P i g 33. The B^. MHD The electrical  object of t h i s  Generator.  s e c t i o n i s to determine the  c h a r a c t e r i s t i c s o f the B^. MHD  g e n s r a t o r and, to  compare i t s p r o p e r t i e s w i t h those o f the more c o n v e n t i o n a l C a r t e s i a n form. The E l e c t r i c a l E q u a t i o n s As  o f the C a r t e s i a n MHD  Generator  the major i n t e r e s t i s i n the order o f magnitude  of the v a r i a b l e s a p p e a r i n g i n the e l e c t r i c a l  equations, the  f o l l o w i n g s i m p l i f i e d a n a l y s i s should s u f f i c e . that l i t t l e  o f the f l o w energy  I t i s assumed  i s e x t r a c t e d and thus t h a t  the v e l o c i t y o f the plasma i s c o n s t a n t through  the g e n e r a t o r .  Then,.Ohm's Law f o r the c o n d u c t i o n c u r r e n t f l o w i n g through the c o n v e n t i o n a l MHD  generator  J  shown i n P i g 31 i s  , or[E  + U x B ]  _ . .  6  3  When edge e f f e c t s and sheath p o t e n t i a l s are n e g l e c t e d , the e l e c t r i c  f i e l d between the e l e c t r o d e s i s  - 80 -  | and  = ~T 1°  .... 64  the c u r r e n t through the plasma i s  I  uz i  a  .... 65  t  From equations 63 to 65:  I = a-hi, ( v B  or  V = sirB The  equivalent  Fig  8  .. 66  - sl/fl-h-t,  circuit  i s t h e r e f o r e t h a t o f F i g 34.  WV  sv  - v/s}  o  6  34. The E q u i v a l e n t C i r c u i t f o r the S i m p l i f i e d C a r t e s i a n MHD Generator.  The  preceding  more r e a l i s t i c .  o v e r - s i m p l i f i e d a n a l y s i s c o u l d be made  Such c o m p l i c a t i n g  f a c t o r s as a decrease i n  the v e l o c i t y o f the plasma or a v a r i a b l e c r o s s - s e c t i o n a l area (to  o b t a i n a constant  (Harris  1960).  S i m i l a r l y , the e f f e c t o f a t e n s o r  c o u l d be i n c l u d e d has  considered  plasma v e l o c i t y ) c o u l d be i n c l u d e d  (Hurwitz,  K i l b and S u t t o n  the g e n e r a t i o n  1-961).  conductivity Smy  (1961)  o f a l t e r n a t i n g c u r r e n t by such  - 81 a generator,  and  P a i n and  Smy  -  (1960) have c o n s i d e r e d  of m o d i f i c a t i o n of the a p p l i e d magnetic f i e l d to the induced The  E l e c t r i c a l C h a r a c t e r i s t i c s of the B^. MHD  inductance  be determined.  Generator  i s shown i n P i g  35.  to be  low can  A t h i n d i s c of plasma of t h i c k n e s s A moving  generator. considered  due  response of the g e n e r a t o r  with constant v e l o c i t y v i s considered  is  "by the f i e l d  of the l o a d c i r c u i t i s c o n s i d e r e d  i n order t h a t the h i g h frequency  MHD  effect  c u r r e n t i n the plasma.  The model t h a t i s c o n s i d e r e d The  the  to pass through  Plasma i n s t a b i l i t i e s are n e g l e c t e d .  the  The  load  to be a r e s i s t i v e d i s c a t the base of the gen-  erator. X= vt •  \ K  velocity V z P i g 35. A Low  The  electric  field  Generator.  displacement  currents w i l l  i n t e n s i t y and  plasma w i l l be assumed to have o n l y r a d i a l  The  be  c u r r e n t i n the  components.  i m p l i e d by t h i s assumption t h a t H a l l c u r r e n t s and on the f i e l d s are n e g l e c t e d .  * » ' (Re)  z  Inductance B~ MHD  Charge d e n s i t i e s and neglected.  ^  Re s i'S t iVe  It i s  edge e f f e c t s  e x i s t e n c e of n o n - r a d i a l  com-  - 82 ponents o f both the e l e c t r i c f i e l d in  the plasma w i l l  i n t e n s i t y and the c u r r e n t  depend upon the boundary c o n d i t i o n s  e x i s t a t the i n t e r f a c e between  the plasma and the e l e c t r o d e s .  An a n a l y s i s t h a t i n c l u d e s the e f f e c t s o f the a x i a l of e l e c t r i c f i e l d  that  components  i n t e n s i t y and c u r r e n t i n the plasma would  be too i n v o l v e d to be o f immediate i n t e r e s t . The r a d i a l e l e c t r i c  field  be expressed as E ( r , f , t ) = E p  i n the plasma E p ( r , f , t ) can  (jf,t)/r.  S i m i l a r r e l a t i o n s are  v a l i d f o r the r a d i a l c u r r e n t d e n s i t y J p ( r , f , t ) i n the plasma and the azimuthal  magnetic i n d u c t i o n f i e l d B p ( r , ^ , t ) g e n e r a t e d  by plasma c u r r e n t s . magnetic f i e l d of  I t i s assumed t h a t (rv/c A«  I.  0  B ( r , t ) i s thus independent of f .  The a p p l i e d  The  value  , the plasma c o n d u c t i v i t y , i s independent o f the magnetic  induction f i e l d s  s i n c e H a l l c u r r e n t s have been  S p a t i a l coordinates  are d e f i n e d i n P i g 35.  neglected.  Equation  63  67 and Ampere's  Law,  57 Vt.  I f  Prom Faraday's Law  I.R  A  +V  " A> f  68  J  ~  3f  i t follows  9  +  E ( ? t ) U A , = ~itf ^^ p o  69  that B  e  ?  +  d a  a  region PQRS where V current  e  i s the sum  of the sheath p o t e n t i a l s and I. i s the ^ 1  i n t o the l o a d  70 can be e v a l u a t e d  ^  ( i = induced).  The i n t e g r a l i n , e q u a t i o n  by c o n s i d e r i n g the r e g i o n s  PQTU and UTRS  - 83 ( P i g 35) s e p a r a t e l y .  Then  ? PQRS  •••••71 D i f f e r e n t i a t i n g e q u a t i o n 70 w i t h r e s p e c t to j$ and e q u a t i o n 71 w i t h r e s p e c t to t then f  yields O 9  and  s u b s t i t u t i n g t h i s i n t o e q u a t i o n 69 g i v e s 3 Bp.u,t)  _!_  3B ,(g,t)  a  *s*o  de  =  v  P  3B o(tt),  +  9e  z  aa.tt)  P  c2t  3 t  '  • • • • © f .2  N o t i n g t h a t I ( t ) = 2TT / J (f,t)«lf , B pe  and B  ( t ) =/Z  e  p o  (^t) =  VA.T.K-V!, _  J" > ( 2 , t ) c l £ P<  T ( t ) / 2 I T , then e q u a t i o n s 67, 70 and 71 can a  be combined to g i v e  +  •• •72  ^ /4  I„A,A, f i . (t)  r  B  , .,  /• / ?8„fet)  v *i^{L(rr»  74  e  The s t e a d y - s t a t e s o l u t i o n to e q u a t i o n 73 f o r the model shown i n P i g 35 i s ( s i n c e B  2-rr  p Q  ( f = 0) = 0  and B  B .(?)=A„I,{e""-'-,  ( f = A) po T ) Q  75  P  E q u a t i o n 74 now has the s t e a d y - s t a t e s o l u t i o n  TT  * *  which,-isince GVjU A 0  TT  «  I  2TT  e  -1  76  , s i m p l i f i e s to  x^ 1  2TTC"A  .77  84 Potential  \v\A.,/a.  ° ,h *.  Drop =  f  x  2TT  -  W  <rA —  5LTT  .  i  5^ I  "J ' Ibstihelcol  ,  yUXBJ-*- I n d u c t a n c e = M *  '  b  a) Time-Dependent C i r c u i t  opj-v-jp-'  prmr^  I h At/A,  Mutual  -tit)  onofh^A-iAj.  l e| cta« e _ f Vre e g^ i o" n K  u  { t  bouMelecl  1TTCTA  aid  - A V —  a Hoi  X«i ,  K £\i A  t  TT  b) S t e a d y - S t a t e  C i r c u i t , Plasma D i s c T r a v e r s i n g Generator  P i g 36. The B^, MHD Generator  Equivalent C i r c u i t  The s t e a d y - s t a t e s o l u t i o n to e q u a t i o n 73 f o r a steadily-flowing  plasma p a s s i n g through  the g e n e r a t o r i s  • 78 and  e q u a t i o n 74 then has the s t e a d y - s t a t e s o l u t i o n  • 79 An e s t i m a t e o f the response  time o f the g e n e r a t o r  shown i n P i g 35 can be o b t a i n e d by assuming t h a t e q u a t i o n 75 is valid  even when  = I^-(t).  I ( t ) = I and crvu A 0  7T  E  A V  Then e q u a t i o n 74 y i e l d s when  «l 'L *  2TTiT/\ 5  2TT  I  J  3  i • • «  o30  - 85 which has the s o l u t i o n  f TT *•*  v  e  v ao»  3  2TT0-A  +  Thus the c u r r e n t i n t o a s h o r t - c i r c u i t and when V  e  t e r m i n a t i o n when J  •31  »  A/3  i s neglected i s D  X i ( R l V » o , t) = 20-LTAoA  82  B  e  The  s t e a d y - s t a t e c u r r e n t t h a t c o u l d he o b t a i n e d from  a g e n e r a t o r c o n t a i n i n g a s t e a d i l y - f l o w i n g plasma i s found from e q u a t i o n 79 to be air  T.  P. + which f o r the assumptions  Y  Q  = R^ = 0, reduces to the f o l l o w -  ing expression C The 0"U-/4oA «  assumption 1, appears  I ^  about magnetic  ••.••84  Reynold's  number, t h a t  to be the major r e a s o n why the output  c u r r e n t i s p r e d i c t e d to be s m a l l f o r the g e n e r a t o r t e s t e d on the shock  tube  ( e q u a t i o n s 76,77 and 82).  The r e a s o n why t h i s  assumption, was i n t r o d u c e d was to take advantage r e l a t i o n B ( r , t ) = /i I (t)/2TTr. a a compression  When crvjJ. A  0 a  Q  0  when B ( r , t ) V t f l  tor,  <{; 1, f i e l d  ahead o f the plasma and f l u x t r a n s p o r t by the plasma  would a l t e r t h i s simple r e l a t i o n .  plasma d i s c  o f the simple  ( t ) / 2 tt r .  A s i t u a t i o n can be envisaged  F o r example, i n the case o f the  ( w i t h cns/^A > 1) a p p r o a c h i n g the base o f the genera-  e q u a t i o n 76 p r e d i c t s a v a l u e o f 1^ t h a t i s too s m a l l .  Similarly,  e q u a t i o n s 79, 81 and 84 under c e r t a i n c o n d i t i o n s  - 86  -  p r e d i c t v a l u e s of I ^ ( t ) t h a t are too small steady  s t a t e v a l u e of 1^  ( e q u a t i o n 83)  i f R^  > 1.  The  can thus he v e r y l a r g e  when R^ > 1 . The  p o t e n t i a l l y l a r g e output  o b t a i n e d from the B^. MHD  g e n e r a t o r when R^  flux amplification characteristic tude of the induced field until  The  of the g e n e r a t o r .  process  a B^  field  and  a r a d i a l flow  A c c o r d i n g to Rosa (1961), a c c o r d i n g to Smy s i t i e s heats  MHD  (1961),  generator,  Y  &8  MHD  However,  i o n bombardment a t h i g h c u r r e n t den-  e l e c t r o d e p o t e n t i a l drop.  case of v = 10^ m/sec, \r\Kj\=  Experimental e  generator  velocity.  the e l e c t r o d e p o t e n t i a l drop may  the B^. MHD  value f o r V  83  (1961) i n the  volts.  I n the  B^.  impose a i s qu^te  low.  = 10 A,  work c o u l d v e r i f y wnether such a Again,  one way  i f a c u r r e n t supply capable  then  volts  g e n e r a t o r w i l l not f u n c t i o n u n l e s s V  i s obtainable.  this difficulty,  1,1 ,02  2TT  .02 V.  magnetic  by e q u a t i o n  s e r i o u s l i m i t a t i o n s i n c e the v o l t a g e generated  Obviously,  magni-  the cathode to a s u f f i c i e n t l y h i g h temperature to  in a negligible  For a t y p i c a l  to the  of a m p l i f i c a t i o n i s s i m i l a r to t h a t  T h i s d e v i c e d i f f e r s from the B^.  i n t h a t i t has  he  The  c u r r e n t i s i n c r e a s e d by i t s own  been c o n s i d e r e d by Kolm and Mawardi  Hydromagnet.  result  > 1 i s due  the e q u i l i b r i u m c o n d i t i o n expressed  i s reached. which has  c u r r e n t t h a t can  g  <  low  of surmounting of g e n e r a t i n g a  very large I  i s not a v a i l a b l e , c o u l d be to pass the e x c i t i n g cl down m u l t i p l e w i r e s imbedded i n a t u b u l a r c e n t r a l  current I cl conductor  as shown i n P i g 37.  Then f o r n w i r e s , the  generator  - 87 voltage V  i s g i v e n by  Pig  37. A High V o l t a g e B^. MHD Generator.  Comparison o f E l e c t r i c a l  C h a r a c t e r i s t i c s o f the Two Generators  When t r a n s i e n t e f f e c t s and e l e c t r o d e c o n t a c t potential  e f f e c t s a r e n e g l e c t e d , the e l e c t r i c a l  formulae  shown  i n Table 2 a r e a p p l i c a b l e f o r the case o f a s t e a d i l y f l o w i n g plasma. V  g  volts  R  g  ohms  P  m  A  a  ( o c c u r s when H = B ^ )  x  n  g  c  (Y  )  2  = 0.25 ±_j*L_ g Cartesian  SvB  2ir  s/arlnl,  w a t t s  0.25sarhl,{v&}  «r{e"^.}  L  Table 2. Comparison o f dc E l e c t r i c a l Formulae f o r the C a r t e s i a n and the B MHD G e n e r a t o r s . A  For a shock tube a p p l i c a t i o n ' i n which cfxrji £ = 2, 0  J  - 88 h = .02 m, S = 0.02 istics  1=.1  m,  -  B = 1 weber/m , n l  IT= lO^m/sec, \nA /\=  m,  shown i n Table 3 are  R  volts  20  volts  10"  10  x 10~ ohm:s  0.32  5  For a dC'-high power a p p l i c a t i o n 10  nl  = 10 ,  2  mhos/m, S = 0.2 6  &  V=  ^Q^  m,  m/sec,  >  h = 0.2 X  Cartesian  R  g  200  volts  200  volts  i n which C T V / i ^ t 2  electrical  P  g ohms  5  x 10~  4  ohms  max  5  Mw  320  Mw  Generator  o b j e c t of p r e s e n t i n g the above comparisons i s  to show t h a t the B^. g e n e r a t o r does have s i m i l a r c h a r a c t e r i s t i c s to the C a r t e s i a n g e n e r a t o r . are worthy of note. B^.  2,  B = 1 W/m,,  T a b l e 4. P r e d i c t e d High Power dc B^. MHD Characteristics. The  Mw  4.  2 x 10~ .31  Mw  Generator  m, i , = 5 m,  c h a r a c t e r i s t i c s are as shown i n Table  V  MHD  1, then the  \V%A^/A. =  max  ohms  5  .31  P  g  T a b l e 3. P r e d i c t e d Shock Tube dc B Characteristics.  <T=  lO^mhos/m,,  valid.  g 200  C=  4  1, then the dc c h a r a c t e r -  i  Cartesian  = 10 ",  2  The  electrical differences  For example, the lower r e s i s t a n c e of the  g e n e r a t o r p r e s e n t s some d i f f i c u l t y i n the matching of the  - 89 generator  to a l o a d .  -  This d i f f i c u l t y  c o u l d he  employing a s u i t a b l y designed r o t a r y c o n v e r t e r e s s e n t i a l l y as an impedance matching d e v i c e . ance of the B  e  generator  may  surmounted Toy which a c t s The  low  a l s o cause d i f f i c u l t i e s  resistwith  the t r a n s i e n t response i n , f o r example, an ac B.Q.  MHD  A l t e r n a t i n g power c o u l d be  flowing  s t e a d i l y through a B^. with  obtained  generator  by  from a plasma e x c i t i n g the  generator,  generator  a s i n u s o i d a l l y varying I ( t ) . a  Discussion H a l l c u r r e n t has  been n e g l e c t e d .  be p o s s i b l e to e x t r a c t and  use  t h i s c u r r e n t by  segmented e l e c t r o d e s as shown i n F i g 38. be s i m i l a r to t h a t which has to e x t r a c t the H a l l  A c t u a l l y , i t should  The  employing p r i n c i p l e would  been proposed by Rosa (1961)  c u r r e n t from a C a r t e s i a n  generator.  3 -^Cemol.  H W h u 7  t S3  /  7  "sIe««J«t»,  (b)  Fig  38. E x t r a c t i o n of MHD H a l l C u r r e n t . a) C a r t e s i a n MHD Generator w i t h Segmented Electrodes. b) B ^ MHD Generator w i t h Segmented E l e c t r o d e s ,  - 90 Ohm's Law  -  i n the form used "by Rosa (1961) i s : 86  The  last  term i n t h i s e q u a t i o n  f l o w i n g i n the plasma. both the B.Q. nected CJX  and  represents  Cartesian generators  F i g 38b  s i n c e both Can  shows the B^. generator  connection  One  of r o t a r y  major advantage t h a t the B^.  the is  electrodes.  One  shown i n F i g  39.  generator  to  in  freedom the  l a y e r on the i n s u l a t i o n between  geometry t h a t would e x p l o i t t h i s  inlet  advantage  8*.  outlet  r  Fig  has  i s the r e l a t i v e  B MHD generator  cooled region (to l e s s e n deposition)  could  or a f a i r l y  s h o r t i n g between the e l e c t r o d e s due  d e p o s i t i o n of a conducting  that  convertor.  comparison to the C a r t e s i a n g e n e r a t o r from e v e n t u a l  con-  M u l t i p l e segments c o u l d  a l s o be used but would r e q u i r e m u l t i p l e l o a d s , design  be  (which becomes l a r g e when  be used to e x t r a c t the H a l l c u r r e n t .  complicated  current  I t s importance i s about the same i n  to e x t r a c t the H a l l c u r r e n t  > 1).  the H a l l  cooled region to l o a d  39. A Method f o r L e s s e n i n g Problems.  Insulator  <i  Deposition  The  a n a l y s i s t h a t has been p r e s e n t e d has been f o r a  plasma h a v i n g a c o n s t a n t f l o w v e l o c i t y through The  the B^. g e n e r a t o r .  amount of the power e x t r a c t e d t h a t i s shown i n Tables 3  and 4 c o u l d be l a r g e enough to a p p r e c i a b l y a l t e r t h i s velocity.  flow  These v a l u e s of output power would be reduced i f  the f l o w v e l o c i t y decreases Experimental  through  the  generator.  Results  The B^.  MHD  g e n e r a t o r shown i n F i g 40 was  installed  on a shock tube powered by the d r i v e r shown i n F i g 19c. l o a d on t h i s g e n e r a t o r was  a b r a s s d i s c , which c o n s t i t u t e d  e s s e n t i a l l y a s h o r t - c i r c u i t t e r m i n a t i o n f o r the This s h o r t - c i r c u i t output  current.  The  generator.  t e r m i n a t i o n should have r e s u l t e d i n a l a r g e  A typical  s i g n a l induced i n the B^.  magnetic  probe a t the base of the g e n e r a t o r i s p r e s e n t e d i n F i g 41. The  polarity  rotated electric  of t h i s s i g n a l was  i n v e r t e d when the probe  was  180°, thus c o n f i r m i n g t h a t a magnetic r a t h e r than s i g n a l was  being  observed.  •Lucite  , at  magnetic probe —s.  brass  •87 — cm  21  cm-  /  F i g 40. C o n s t r u c t i o n of B ^  zfc  MHD  Generator.  an  - 92 The  s i g n a l that  appeared a t t = 35/«sec was probably  caused by c o n t a c t o f the plasma w i t h the c e n t r a l r o d . suggested t h a t  this i n i t i a l  s i g n a l i s due to a d i s c h a r g e  occurs between the r o d and the charged plasma. the  Smy* has that  The base o f  g e n e r a t o r was connected to an e a r t h c o n n e c t i o n v i a the  oscilloscope.  The p o l a r i t y o f the i n t e g r a l o f the f i r s t  conforms w i t h t h a t  signal  expected f o r the c u r r e n t t h a t would be  generated by a p o s i t i v e l y charged plasma d i s c h a r g i n g to e a r t h via  the c e n t r a l r o d o f the MHD  generator.  .01V  11T  35/t sec  P i g 41. T y p i c a l B^. MHD The had  5 Asec  S i g n a l Induced i n Probe a t Base o f Generator.  s i g n a l that  appeared a t a time o f about 55.5 A sec  one v e r y i n t e r e s t i n g c h a r a c t e r i s t i c .  The time o f a r r i v a l  of t h i s s i g n a l c o u l d be a l t e r e d by changing the e x c i t i n g rent  o f the MHD  ection and  generator.  cur-  F o r example, d e s i g n a t i n g the d i r -  o f the e x c i t i n g c u r r e n t shown i n F i g 40 as p o s i t i v e ,  the time between the a r r i v a l  o f the s i g n a l s  shown i n F i g 41  * The author i s g r a t e f u l f o r r e c e i v i n g t h i s s u g g e s t i o n from P.R. Smy, P h y s i c s Dept., U n i v e r s i t y o f B r i t i s h Columbia.  - 93 as the t r a n s i t f  o  r  Exciting  0 A, t r a n s i t  =  time o f the plasma through the g e n e r a t o r , then 9  0  A  >  t  r  a  n  s  i  t  t  i  m  e  time = 20 = 5 /laec;  = 22.5/*sec; for I  e x c  for I  j_-tj_ g ~ n  1 2  e  x  c  l  t  i  5 A?  n  g  =  transit  time = 17-5 /4.sec. The i n t e n s i t y inside  i s 31 gauss.  c u r r e n t o f 200 A f l o w i n g down the c e n t r a l  The magnetic Reynold's number i n the plasma  was o f the o r d e r o f 5, so t h a t an a z i m u t h a l magnetic of  a t the  s u r f a c e o f the o u t e r e l e c t r o d e o f the MHD g e n e r a t o r ,  computed f o r an a x i a l rod,  o f the a z i m u t h a l magnetic f i e l d  intensity  the o r d e r o f 150 gauss c o u l d be i n the plasma by the time  t h a t the plasma was a p p r o a c h i n g the base o f the g e n e r a t o r . The magnetic p r e s s u r e a s s o c i a t e d w i t h a f i e l d 2 2 B /2/4.0 = 180 newtons/m .  The p r e s s u r e ,  of 150 gauss i s  , immediately behind  a s t r o n g shock moving w i t h v e l o c i t y X through a gas h a v i n g  -  2 5/3 i s 3/4j0 ^±) 0  gas i n f r o n t  w h e r e i s  of the shock.  the d e n s i t y o f the u n d i s t u r b e d 4  Thus i f a shock of v e l o c i t y  m/sec propagates i n t o argon a t an i n i t i a l microns Hg, then f> = 3.96 x 10"^ G/m  5  0  The magnetic p r e s s u r e i n f r o n t slow the plasma.  10  p r e s s u r e o f 160  and P =2980.0: newtons/m . 2  o f the shock i s s u f f i c i e n t to  A magnetic p r e s s u r e ahead o f the shock,  however, c o u l d not account f o r the observed dependence o f the transit  time on the p o l a r i t y  o f the e x c i t i n g c u r r e n t ,  n e t i c i n t e r a c t i o n o f the type shown i n P i g 42 c o u l d .  A magIn  Chapter I I I , S e c t i o n 3, the t r a n s p o r t o f a t r a p p e d magnetic f i e l d ' i n the plasma was n o t e d . Reynold-':s number, the c u r r e n t  At h i g h v a l u e s o f magnetic s u s t a i n i n g t h i s trapped f i e l d  c o u l d i n t e r a c t w i t h the a z i m u t h a l f i e l d  g e n e r a t e d by the  - 94 e x c i t i n g c u r r e n t o f the MHD g e n e r a t o r and produce a n e t f o r c e a g a i n s t the plasma.  Whether t h i s f o r c e would a c t to decrease  or i n c r e a s e the d e c e l e r a t i o n o f the plasma would depend upon the d i r e c t i o n o f flow o f the e x c i t i n g c u r r e n t .  •  o  / exciting  m  /  —  J  plasma  P i g 42. A Magnetohydrodynamic I n t e r a c t i o n t h a t Could A l t e r the V e l o c i t y o f the Plasma. An order o f magnitude estimate o f the v a l u e o f the t r a n s p o r t e d p o l o i d a l c u r r e n t d e n s i t y J i n the plasma can be o b t a i n e d by c o n s i d e r i n g the a l t e r a t i o n to the p r o p a g a t i o n e q u a t i o n t h a t would r e s u l t plasma.  i f a f o r c e o f magnitude  (^XB) V a c t s a g a i n s t the  The azimuthal magnetic i n t e n s i t y B t h a t d i f f u s e s  the f r o n t o f the plasma i s produced by the g e n e r a t o r current.  V i s the volume  volume f o r c e JXB.  The e q u a t i o n f o r c o n s e r v a t i o n o f momentum i s p  Q  exciting  o f the plasma b e i n g s u b j e c t e d to the  K'fr^-vfcls - * x  into  - ftI*  §  d  t  8 7  i s a u n i t v e c t o r i n the x d i r e c t i o n , and other v a r i a b l e s  have i d e n t i c a l meanings  to those employed i n e q u a t i o n 58.  Thus,  assuming t h a t J * J ( x , t ) , V * V ( x , t ) and B 4 B ( x , t ) , and dropping  - 95 v e c t o r n o t a t i o n , s i n c e a l l terms r e p r e s e n t v e c t o r s i n the x direction,  or  2  where t^ i s the time t h a t the plasma e n t e r s the MHD  generator  and x and t a r e the p o s i t i o n and time c o o r d i n a t e s o f the plasma i n the MHD g e n e r a t o r .  L e t t i n g t ^ denote the time o f a r r i v a l  at the downstream end o f the MHD d e v i c e when B = 0 and t _ 3  denote t h i s time when B + 0 l e a d s to  P f V V h  ± V  J  B  {*»-*.}*  .....go  For the p o l a r i t i e s o f J and B i n d i c a t e d i n F i g 42, J and B are p o s i t i v e ,  t ^ - t ^ p o s i t i v e and the d e c e l e r a t i o n o f the  plasma i s i n c r e a s e d by the magnetic A numerical  v a l u e f o r J w i l l now be c a l c u l a t e d .  Employing the v a l u e o f m /P  = .133 //sec/cm from Table  Q  a value f o r m 25-10  o  c a l c u l a t e d from the observed  pressure r i s e of *  The mean m o l e c u l a r weight o f the gases was  assumed to be 40. 1  1 and  microns Hg due to a f i r i n g gave a v a l u e f o r P o f 57 x  10 ^ kg m / s e c  t  interaction.  = 35/tsec,  t  2  A l s o , l e t t i n g B = .015 w/m , 2  = 55.5/isec  and t ^ = 56.0/tsec  r e s u l t s i n a v a l u e f o r J o f 8500 amp/cm . a l current density i s very high. c u r r e n t d e n s i t y determined 3 amp/cm .  5  i n e q u a t i o n 90  This value of p o l o i d -  The v a l u e f o r the p o l o i d a l  i n Chapter I I I , S e c t i o n 3 was only  P o s s i b l y some important  i n the above a n a l y s i s .  Y = 10~-'m-,  f a c t o r s have been  omitted  F o r example, a s t r o n g i n t e r a c t i o n may  - 96 have o c c u r r e d a t the x = 87 cm p o s i t i o n where the r o d c a r r y i n g the g e n e r a t o r e x c i t i n g c u r r e n t was p e r p e n d i c u l a r to the d i r e c t i o n o f f l o w o f the plasma.  The important p o i n t i s t h a t a  t r a n s p o r t e d p o l o i d a l c u r r e n t d e n s i t y c o u l d account observed  speeding and s l o w i n g e f f e c t s observed  f o r the  i n the MHD  generator. The  power g e n e r a t i n g c a p a b i l i t i e s o f the B^. MHD gen-  e r a t o r were n o t i n v e s t i g a t e d . experimentally d i f f i c u l t  The r e a s o n was t h a t i t was  to generate a s u f f i c i e n t l y  large  a z i m u t h a l magnetic  f i e l d w i t h the a v a i l a b l e dc power supply and  a s i n g l e conductor  central electrode.  tube was a l s o i n s u f f i c i e n t  The s i z e o f the shock  to permit the use o f a l a r g e  electrode c o n t a i n i n g m u l t i p l e conductors.  Sufficient  central  potential  was thus n o t generated between the e l e c t r o d e s to break down the sheath between the e l e c t r o d e s and the plasma, w i t h two probable  exceptions.  The s i g n a l a p p e a r i n g a t the time t ^ 55  JJL sec was o f the c o r r e c t p o l a r i t y to be the B s i g n a l  generated  by a v a l i d MHD c u r r e n t o f the type d i s c u s s e d i n the t h e o r y section.  T h i s s i g n a l was absent when no e x c i t i n g c u r r e n t was  a p p l i e d and was o f r e v e r s e d p o l a r i t y when the c o i l was r o t a t e d by 180°.  The sheath was p r o b a b l y broken  down by the r a d i a l  p o t e n t i a l generated by the i n t e n s e magnetic have e x i s t e d , due to magnetic plasma as the plasma neared The  second  cause  compression,  field  t h a t would  i n the f r o n t o f the  the c l o s e d end o f the MHD  generator.  f o r sheath breakdown i s d i s c u s s e d by Smy  (1962).  T h i s p a r t i c u l a r breakdown phenomenon i s i n evidence from the oscillations  t h a t occur d u r i n g the times 55< t < 50/^sec and  - 97 subsequent to the appearance o f the s i g n a l a t 55/*sec. 2. ELECTRICAL CHARACTERISTICS OP AN ELECTRODELESS B The and  deposits  r  MHD GENERATOR  problems o f sheath p o t e n t i a l s , e l e c t r o d e wear on e l e c t r o d e s  a r e avoided i n MHD  t h a t do n o t have e l e c t r o d e s  generators  i n c o n t a c t w i t h the plasma.  One  method o f e x t r a c t i n g e l e c t r i c a l power from a moving plasma without using  electrodes  to the magnetic f i e l d  i s to couple the l o a d i n d u c t i v e l y  generated by the c u r r e n t s  In t h i s S e c t i o n the e l e c t r o m a g n e t i c particular  i n the plasma.  behaviour o f a  c o n f i g u r a t i o n o f e l e c t r o d e l e s s magnetohydrodynamic  generator i s studied.  The c o n f i g u r a t i o n , shown i n P i g 43,  i s t h a t o f an a n n u l a r tube w i t h an a p p l i e d r a d i a l magnetic field.  The f i e l d  c o u l d be generated by a v a r i a b l e p i t c h  coil  i n s i d e the i n n e r tube or c o u l d be produced by an e n c l o s i n g yoke o f i r o n and an electromagnet as has been used by Barach (196.1) and by P a t r i c k (1959). the r a d i a l magnetic f i e l d  On a s m a l l  scale  experiment  c o u l d be produced by the method shown  i n P i g 19d. In order that w i l l  t h a t the a n a l y s i s w i l l  i n d i c a t e the order  result i n a solution  o f magnitude o f response time and  output power o f the g e n e r a t o r , c e r t a i n s i m p l i f y i n g assumptions are made.  I t i s assumed t h a t the magnetic Reynold's number i s  << 1, t h a t f i e l d little  edge e f f e c t s a r e n e g l i g i b l e , t h a t there i s  a l t e r a t i o n o f the plasma flow v e l o c i t y d u r i n g  of the plasma through the g e n e r a t o r , t h a t r  2 ~ 1 r  <  T  6~ 2' T  Also, a l l e l e c t r i c a l  - -] T  the passage  -]  < r<  a  n  ^ thait  q u a n t i t i e s a r e assumed  - 98 to Toe c o n s t a n t  over the w i d t h o f the annulus and a r e assumed  to be e v a l u a t e d  on the mean r a d i u s o f the annulus, A> » D i s -  placement c u r r e n t s and c o n v e c t i o n ~  x  "  -  currents are n e g l e c t e d .  axially-segmented  resistive cylinder  3 ^ V  t F i g 43. E l e c t r o d e l e s s B From Maxwell's  r  MHD  Generator.  equation  V x E = - B it  follows  •»•«»9 ^  that  « e a o o 92 where E ^ i s the azimuthal plasma, I  electric field  i s the a z i m u t h a l  i n t e n s i t y i n the  c u r r e n t i n the plasma, I»  t o t a l load current, L  p  i s the s e l f inductance  c o n t a i n i n g 1^, M i s the mutual inductance circuit  and the l o a d c i r c u i t .  <i  B =I 0  x i s the depth o f p e n e t r a t i o n the g e n e r a t o r .  between the plasma  = 2TT/V X X p  0  2TTA V0-X  o f the c i r c u i t  Ohm's Law, w i t h o u t H a l l  takes the f o l l o w i n g form when I  resistive  i s the  4L  P  p  t  <TX A  current  and B = B 0  JL I„ + MI^} p  .....94.  o f the f r o n t o f the plasma i n t o  A s i m i l a r treatment f o r the l o a d c i r c u i t , a  c y l i n d e r segmented i n the a x i a l d i r e c t i o n , r e s u l t s i n  where R^ / £ i s the azimuthal of the l o a d , and Jt  r e s i s t a n c e per u n i t a x i a l  i s the t o t a l l e n g t h o f the l o a d .  length  - 99 E q u a t i o n s 94 and 95 i n d i c a t e t h a t the e q u i v a l e n t c i r c u i t f o r the g e n e r a t o r i s t h a t shown i n P i g 44«  -AAA-  \/crx  2TT/t,irB Q  1  •p o E L * o  0  P i g 44. E q u i v a l e n t C i r c u i t B MHD Generator.  f o r the E l e c t r o d e l e s s  r  When f i e l d  and  edge e f f e c t s a r e  neglected,  e q u a t i o n s 94 and 95 can he reduced to  {|£)^AA4* where i  p  = I /x  and  p  + { * . ' + A T i V ] ^ ij = T^/t  .  +  = ° . . . .  The i n i t i a l  9  7  c o n d i t i o n s are  X (t - o) * A / e /TT A : > {i - (%f} P  P  X ( t = o) = where  e  p  = 217"/^ V  B  0  O  .... .98 .  The overdamped s o l u t i o n to  e q u a t i o n s 97 and 98 i s  e irt p  e  - e 99  -  100 -  where  _  i  R  100  i  ....  1  0  i  I t can be shown t h a t the p h y s i c a l l y r e a l i z a b l e response i s t h a t o f an over-damped s o l u t i o n s i n c e positive  sign. The  order  o f magnitude o f the output power w i l l  now be c a l c u l a t e d f o r the c o n d i t i o n s obtained  i s always o f  i n an em shock tube:  t h a t c o u l d be r e a d i l y  B« = 8 x 10  ohms, r / r . = 2,  v = 10 m/sec, t = 5 x 1 0 ~ sec, 0*= 10 " mhos/m, JL = .05 m, 4  6  4  —2 2 PJ = 100 gauss = 10 webers/m , and r . = 0.01 m. o I  '  to  6.28  '  v o l t s , i t = 1.687, « ^ = 4/3, and  43 w a t t s .  This value  p  I ( t = 5 x 10 2  sec) =  o f output power i s p r o b a b l y too low f o r  economical power g e n e r a t i o n . be more e f f i c i e n t .  When e =  P o s s i b l y a l a r g e r device  would  Por example, C o l g a t e and Aamodt (1957)  have proposed a somewhat s i m i l a r method o f power e x t r a c t i o n . T h e i r proposed d e v i c e and  150 f t l o n g  consisted  o f a tank 25 f t i n diameter  surrounded by a c o i l  t h a t c o u l d be used f o r  simultaneous d r i v i n g o f a l o a d and the g e n e r a t i o n currents  i n a plasma i n the tank.  of azimuthal  I t was proposed t h a t the  plasma c o u l d be d r i v e n back and f o r t h through the c o i l by 235 U  f i s s i o n r e a c t i o n s a t the ends o f the tank. The  preceding  c a l c u l a t i o n o f the order  o f magnitude  -  101 -  of the output power t h a t can he o b t a i n e d less B  r  from the e l e c t r o d e -  MHD g e n e r a t o r i n d i c a t e s t h a t i n d u c t i v e power e x t r a c t i o n  from a moving plasma i n a shock tube i s a very means o f power g e n e r a t i o n .  Inductive  o f f e r the advantage o f c l o s e d - c u r r e n t and  thus c i r c u m v e n t i o n  present  power e x t r a c t i o n does paths w i t h i n the f l u i d  problems, which i s a t  one o f the major problems encountered w i t h  type MHD g e n e r a t o r s . type  of electrode  inefficient  (Tenfold  1961,  I t i s p o s s i b l e t h a t the t r a v e l l i n g - w a v e Haus 1962)  t o r may prove t o be the most The preceding  electrode-  o f MHD i n d u c t i v e power generapractical.  somewhat r e s t r i c t i v e assumptions made i n the  a n a l y s i s to o b t a i n c i r c u i t  characteristics  that  c o u l d be expressed i n c l o s e d form are n o t s u f f i c i e n t l y to warrant e x p e r i m e n t a l v e r i f i c a t i o n .  A different  realistic  geometry  of i n d u c t i v e g e n e r a t o r t h a t i s amenable t o both a n a l y s i s and e x p e r i m e n t a l work w i l l be c o n s i d e r e d  i n the next  Section.  3. CHARACTERISTICS OP A MAGNETOHYDRODYNAMIC POWER GENERATOR EMPLOYING INDUCTIVE POWER TRANSFER Theory The  geometry o f the MHD g e n e r a t o r c o n s i d e r e d  i n this  S e c t i o n i s t h a t shown i n P i g 45. T h i s c o n f i g u r a t i o n has been employed by L i n , R e s l e r ment o f the e l e c t r i c a l a conventional  and K a n t r o w i t z (1955) f o r the measurec o n d u c t i v i t y o f the plasma generated i n  diaphragm-type shock tube, and has been con-  s i d e r e d by Woodson and Lewis (1961) as a p o s s i b l e MHD power generator.  Woodson and Lewis d e s c r i b e d  an i n v e s t i g a t i o n i n t o  -  102  -  the behaviour of t h i s g e n e r a t o r at h i g h v a l u e s Reynold's number.  The  primary i n t e r e s t was  magnetic f l u x t h a t c o u l d be  transported  by  i n the amount of the plasma.  means by which the f l u x c u t t i n g the l o a d c o i l verted  i n t o e l e c t r i c a l power was  r e s i s t o r chosen by L i n , R e s l e r value for  t h a t was  the  r e s u l t e d i n a very t h a t was  low  con-  The  load  K a n t r o w i t z (1955) had  critical  a  damping r e s i s t a n c e  of l o a d  power output, but  an  resistance  output  voltage  e s s e n t i a l l y independent of the l o a d r e s i s t a n c e . the  i n d u c t a n c e of the l o a d c o i l  and  output power P.  Pig  45.  It that there  MHD  In  e f f e c t of the l o a d r e s i s t a n c e Rj  and  Lj  on the  output v o l t a g e  Y  , i s determined.  Generator Employing I n d u c t i v e  Power  Transfer.  i s assumed t h a t the flow v e l o c i t y i s u n i f o r m ,  i s no  change i n the  radial  The  c o u l d be  considered.  Such a h i g h v a l u e  the a n a l y s i s to f o l l o w ,  no  and  a p p r o x i m a t e l y the  output c o i l .  not  of magnetic  electric  transverse field field  motion of gas  current  during  i n the plasma. E  the  and  t h a t there  interaction.  , i s neglected  and  is The also  - 103 it  -  assumed t h a t the magnetic f i e l d  s o l e l y t h a t due  to the f i e l d  were made by L i n , R e s l e r s i d e r e d to be  and  a c t i n g on the plasma i s  coils.  The  preceding  assumptions  K a n t r o w i t z (1955) and  a p p l i c a b l e to the present  are  analysis.  Thus  where x i s the a x i a l d i s p l a c e m e n t from the l o a d c o i l , r a d i u s , J ( x , r ) i s the 0"(x)  i s the  current  density  magnetic f i e l d  Applying  i s the flow  B ( x , r ) i s the r a d i a l r  t h a t i s d i r e c t l y due K i r c h h o f f ' s Law  r i s the  i n the plasma at  c o n d u c t i v i t y of the plasma,  o c i t y of the plasma and  con-  (x,r), vel-  component of  to the f i e l d  the  coil.  to the l o a d c i r c u i t r e s u l t s  in ^ where 1^  +  *  dt  i s the l o a d c u r r e n t , A i s the  of the l o a d passing  dF  coil  and  cross-sectional  area  ^ i , "the t o t a l induced magnetic f l u x s  through the l o a d 4>(s)  ....103  coil.  FR(T A.)dl  =  t  104 where I i s the  field  coil  c u r r e n t , -c i s the l e n g t h  of  the  plasma, s i s the p o s i t i o n of the f r o n t of the plasma r e l a t i v e to the l o a d c o i l , the  search  of r a d i u s  coil r and  T(x,r)  circuit  i s the magnetic f l u x p a s s i n g  due  through  to a u n i t c u r r e n t r i n g i n the  at p o s i t i o n x.  D e f i n i n g g(x)  as  plasma  - 104  -  results i n  <J>(s) =u 1  j o-(s-x) g M dx  2  . 106  s-4  The v e l o c i t y of the plasma ds U dt  f r o n t U i s g i v e n "by  E q u a t i o n s 103,  can be combined to y i e l d  106 and  107  ...107  108 When the c a l i b r a t i o n procedure of L i n , R e s l e r and K a n t r o w i t z (1955) i s used,  then the c o i l  c a l i b r a t i o n response  function  i s g i v e n by  .... 109 In  t h i s c a l i b r a t i o n procedure, a s l u g o f metal of c o n d u c t i v i t y  6~  , of l e n g t h about two  or  g r e a t e r , and o f the same diameter as the i n s i d e of the  c  times the diameter o f the shock  shock tube i s passed through the c o i l s a t v e l o c i t y the  field  the  coils,  Equations  coil  current i s I  XL  a  109  If  w h i l e the s l u g i s p a s s i n g through  then the v o l t a g e induced i n the l o a d c o i l 108 and  tube  is V (s). c  can be combined to y i e l d  - " t t J , L(o) V (s) -ff(i)V (s-i) Jfr" (s-x)V (x) d \ e  c  K  c  10 which i s e q u i v a l e n t to  (T(o) V (s) - 0-W V (s-i) / ( r ' M V(x)c/, aft s-i 111 e  -0*  c  +  c  - 105 The s o l u t i o n to e q u a t i o n 111  f o r a s t e p i n c r e a s e i n conduct-  i v i t y a t the shock f r o n t and a c o i l response f u n c t i o n V (s) c of  the form o f a Gaussian d i s t r i b u t i o n i s of p a r t i c u l a r  est.  The v a l i d i t y of such a s o l u t i o n c o u l d r e a d i l y be  e x p e r i m e n t a l l y s i n c e the plasma generated i n a shock  interchecked  tube  approximately possesses such a s t e p i n c r e a s e i n c o n d u c t i v i t y and the e x p e r i m e n t a l l y - o b s e r v e d c o i l response f u n c t i o n i s q u i t e c l o s e l y t h a t of a Gaussian d i s t r i b u t i o n f u n c t i o n . assumptions,  <r(s=o)=. cr  >  p  ff'(s-x) =  For these  .112  o  The c a l c u l a t i o n i s made o n l y f o r the shock f r o n t , not the t r a i l i n g p o r t i o n of the plasma, as i s shown i n F i g 46.  Fig The  46. The C o n d u c t i v i t y and V e l o c i t i e s B e i n g C o n s i d e r e d i n the A n a l y s i s . s o l u t i o n to e q u a t i o n 111, under these assumptions.  is  (t) =  - U Viz I  (Tp  V  t  e — OO  /e S  dt . . . 1  11 3  - 106 where the s u b s t i t u t i o n s = Ut + s^ has been employed. o r i g i n o f time  i s thus chosen as the time when the plasma f r o n t  i s h a l f way through The  the l o a d  coil.  i n t e g r a l i n e q u a t i o n 113 can be reduced  s t a n d a r d i n t e g r a l by changing The  The  to a  the v a r i a b l e o f i n t e g r a t i o n .  solution i s  Rib*  Rjt  2<r 2Cl Li c  c  erf  where  114  x  T h i s s o l u t i o n i s more u s e f u l i f the e r r o r f u n c t i o n i s expanded a c c o r d i n g t o one o f the f o l l o w i n g expansions erf  erf  x  I —  V/TT X  3\1  2\5  I -  .,..115  I-3-5  ,  4  ....116  voltage appearing  Equations  l'3 2*X  2X'  v*  the output  x <*° 2  l!3  The  A  2  2X  x  (see Lwight 1947)  ~  a c r o s s R^ i s g i v e n by ^J.  Ri  .... 117  114, 116 and 117 can be combined to o b t a i n  v o l t a g e when the c o n d i t i o n — ^ — — » T  |"t| i s s a t i s f i e d .  2 LpU*  When o n l y the f i r s t  two terms i n e q u a t i o n  116 a r e c o n s i d e r e d ,  then an e q u a t i o n i s o b t a i n e d t h a t i s i d e n t i c a l by L i n , R e s l e r and K a n t r o w i t z ments ,  to t h a t d e r i v e d  (1955) f o r c o n d u c t i v i t y measure-  - 107 -  .... 1 18 y  where  V* = U u o - l V / K o ; I 2  2  Expressions  P  t p  ....119  c  t h a t are of i n t e r e s t f o r e s t i m a t i n g the  order of magnitude o f  (t) are:  . . 120  • « • w  where y = R^I^/^L^U. y £ 1 and 121  Equation  I^ I  120 converges most r a p i d l y f o r  converges most r a p i d l y f o r y > 1.  The power i n the l o a d i s Xj fsj or 2.  .... 122 To o h t a i n the c o n d i t i o n s under which maximum energy d i s s i p a t i o n i n the l o a d would occur, i t would be n e c e s s a r y maximize  to  /^ °° +  ? (t)c\t A  .... 123 T h i s e q u a t i o n has not been s o l v e d .  An estimate o f  the peak value of P^ ( t ) can, however, be o b t a i n e d from equation  122 assuming t = 0.  The r e s u l t i n g e q u a t i o n can be s o l v e d  g r a p h i c a l l y f o r the v a l u e o f the l o a d r e s i s t a n c e  t h a t maxi-  mizes Pjj ( o ) .  L^U/b.  The v a l u e thus o b t a i n e d i s S j ^ 1.36  - 108 z  Then  .... 124 A graph  of  P [ t , R, = R i , U/b • 10 sec , K, =  j-^j^j J  —  |  i s g i v e n i n P i g 47.  0.3  0.2  0.1  0  Pig  -  1  0  t ,/c sec  of the v a l u e expected  mhos/m, I  c  ^ A  c  p  that i s representative  on a shock tube i s Pg(o) ^ 7.5 W.  assumed c o n d i t i o n s are U = 4  2  47. Power i n l o a d R e s i s t a n c e as a F u n c t i o n o f Time.  A n u m e r i c a l v a l u e f o r P^(o)  10  1  -  = 1 .8 x 1 0  10^ m/sec, b = 0.01 m, C = 5  amp m / s e c 2  2  v o l t , R^ b/2L_£ U  = 0.68, L  = 35 nH, I = TO amps,  ..0475 -A. .  An output power o f 7.5 W l a s t i n g f o r a time  £  order o f a microsecond The  electrodynamic  The  = .58 x 1 0 mhos/m, R 8  i =  o f the  i s i n s u f f i c i e n t t o slow the plasma.  a n a l y s i s p r e s e n t e d above i s thus  to d e s c r i b e the o p e r a t i o n , o f t h i s  sufficient  type o f MHD g e n e r a t o r .  A  - 109 magnetohydrodynamic a n a l y s i s i s n o t warranted output power c o u l d be o b t a i n e d .  unless a larger  M u l t i p l e output c o i l s and  l o a d s would be one method o f i n c r e a s i n g the output power. It  i s to be noted t h a t any i n d u c t i v e MHD g e n e r a t o r  i s i n h e r e n t l y an ac g e n e r a t o r and t h a t a dc output cannot be obtained. Experimental Results The v a l i d i t y experimentally. field of  coil  o f the above t h e o r y has been  The apparatus  used i s shown i n F i g 48. The  had an i n n e r diameter  o f 1.4 i n . , an o u t e r  4.6 i n . and a l e n g t h o f 1.0 i n .  of AWG 14 w i r e .  checked  diameter  T h i s c o i l had 296 t u r n s  The output c o i l had 6 t u r n s o f AWG 24 wire  wound as a s i n g l e l a y e r w i t h a mean diameter a l e n g t h o f 0.153 i n .  o f 1.228 i n . and  These c o i l s were c a l i b r a t e d by a method  s i m i l a r to t h a t used by L i n , R e s l e r and K a n t r o w i t z  (1955).  The r e s u l t s o f c a l i b r a t i o n were: x 10  4  amp m / 2  Fig  sec  2  volt,  b = .02 m, I v /V = 7.50 ' c c- cp = 0.581 x 1 0 mhos/m. 8  48. I n d u c t i v e MRT> Generator E x p e r i m e n t a l  Apparatus.  -110As was o r i e n t e d current  i s shown i n F i g 48c, the loadj, a one t u r n  coil?  so t h a t no magnetic f l u x generated by a z i m u t h a l  i n the plasma l i n k e d w i t h the l o a d .  The c u r r e n t  through the l o a d was thus generated only "by the r a t e o f change of magnetic f l u x l i n k i n g w i t h the output c o i l . of the output c o i l was 0 . 0 5 XL .  Since  The r e s i s t a n c e  the v a l u e  employed as a l o a d was always a p p r e c i a b l y  greater  the r e s i s t a n c e o f the output c o i l was c o n s i d e r e d ligible.  The c a l c u l a t e d v a l u e  than 0.05-ft? to "be neg-  o f i n d u c t a n c e of the 6 turn  output c o i l was 1.91/^H and the c a l c u l a t e d v a l u e ductance o f the l o a d 70 nH.  of resistance  o f the i n -  The output c o i l was thus assumed  to have o n l y an i n d u c t i v e impedance and the l o a d o n l y a r e sistive  impedance.  The e q u i v a l e n t  circuit,  d i s c u s s i o n , was t h a t shown i n F i g 4 9 .  the p r e c e d i n g  of C, as determined from the o s c i l l a t o r y unloaded c o i l , critical  on the b a s i s o f  33 Mc/s, was 12 pF.  The  value  f r e q u e n c y o f the  The l o a d r e s i s t a n c e f o r  damping was thus 800 -H. .  I  Fig  coil  49- E q u i v a l e n t C i r c u i t Output C o i l .  f o r Inductive  MHD  Generator  -1118  -21 -2  | -1  , 0  I +1  1 +2  y  1 +3  time, /x sec Pig  50. V a r i a t i o n of Output V o l t a g e w i t h Load R e s i s t a n c e . These curves were o b t a i n e d w i t h the d r i v e r shown i n P i g 19f» argon i n the shock tube a t a p r e s s u r e of 160 microns Hg, the 19.2 //P c a p a c i t o r bank d i s c h a r g i n g from 8 kV and the d r i v i n g c u r r e n t crowbarr e d a t the end of the f i r s t c u r r e n t p u l s e . The c e n t e r of the output c o i l was 39 cms from the base of the d r i v e r , t h e ' v e l o c i t y of the l u m i n o s i t y f r o n t was 2.0 cms/&sec,L^ was 1.98.//H. the f i e l d c o i l c u r r e n t was 10 A andff" was 10 mhos/m (see Appendix P ) . The l o a d r e s i s t o r s down to 10-ft- were commercial 1/2 watt u n i t s ; r e s i s t o r s of lower v a l u e were c o n s t r u c t e d w i t h 3/4 i n . l e n g t h s of d i f f e r e n t s i z e s o f nichrome wire s o l d e r e d a c r o s s 1/2 W r e sistors .  -112The  curves shown i n F i g 50 o b t a i n e d f o r R^ = 3.25-A-  and R^ = 0.50 .AThe  were d i s p l a c e d s p u r i o u s l y l a t e  i n time.  s i g n a l s observed w i t h the l u m i n o s i t y d e t e c t o r a t x = 38  cms were not o f the u s u a l f l a t - t o p shots.  waveshape f o r these two  The d e v i a t i o n from the u s u a l l y - o b s e r v e d f l a t - t o p  shape and the d i s p l a c e m e n t  i n time o f the c o i l  thus b o t h due to s h o t - t o - s h o t i r r e p r o d u c i b i l i t y  Power, watts  A 4  8  1 1  j  ij  /' ^ = 1.35^7  // / si  a !i / 'i /  !/ /  //  // /  /  /  /  s i g n a l s were o f the plasma.  / »\  1  1  wave-  VRj =3.2 51). \  \  ^  If  \\  \\ R j = .5 Oft > /  0 -1  0  +1 time,  Fig  +2  +3  /xsec  51. Output Power as a F u n c t i o n o f Load R e s i s t a n c e , Experimental.  - 113 The  power d i s s i p a t i o n curves shown i n P i g 51 were  o b t a i n e d from of  the data shown i n P i g 50.  load r e s i s t a n c e that optimized  The t h e o r e t i c a l  (t=0) was 1.36  2.1 SL , and the maximum v a l u e o f P^ (t=0) was from 124,  8.6 W.  value  U/b = equation  Prom P i g 51 the e x p e r i m e n t a l l y - d e t e r m i n e d  maximum  v a l u e o f P^ (t=0) was 7.0 W, o b t a i n e d when R_g = 2.2 - 1 S L . The  p r e d i c t e d and the observed v a l u e s o f P^ (t=0, R^ = R_^)  and  of  were thus i n agreement.  by the assumption was  Some e r r o r was i n t r o d u c e d  t h a t the observed waveform o f the v o l t a g e  t h a t o f a normal d i s t r i b u t i o n curve.  An a n a l y s i s t h a t i s  more a p p l i c a b l e f o r the observed waveforms i s p r e s e n t e d i n Appendix P. ically  c l o s e agreement between the t h e o r e t -  p r e d i c t e d response  response are  The f a i r l y  o f the g e n e r a t o r and the observed  i n d i c a t e s t h a t the assumptions made i n the a n a l y s i s  justified.  Discussion An  output power o f the order o f 10 watts  i s very  low i n comparison w i t h t h a t which can be o b t a i n e d from rode-type MHD g e n e r a t o r s . Por example, an e l e c t r i c a l of up t o 0.32 MW was e x t r a c t e d i n the experiments Smy (1961).  The MHD g e n e r a t o r  employing  t r a n s f e r does have one q u i t e important rode-type  MHD g e n e r a t o r s  disadvantage  power  o f P a i n and  i n d u c t i v e power  advantage over  elect-  that' p o s s i b l y c o u l d c o u n t e r a c t the  o f the low output power.  One o f the o b j e c t s i n  MHD g e n e r a t o r r e s e a r c h has been to develop operate dependably f o r a c o n s i d e r a b l e time. e x t r a c t e d from  elect-  a unit that w i l l When the power i s  the plasma w i t h e l e c t r o d e s , and the u n i t i s  - 114 operated f o r times of g r e a t e r e l e c t r o d e s must he c o o l e d  than a few microseconds, the  to p r e v e n t h o i l i n g and v a p o r i z a t i o n  of the e l e c t r o d e m a t e r i a l .  The c o o l e d  electrodes  then serve  as a r e a s f o r d e p o s i t i o n o f the plasma seed m a t e r i a l , cesium or potassium.  The e l e c t r o d e s  often  soon hecome f o u l e d w i t h  the seed m a t e r i a l and the u n i t has to he disassembled and cleaned.  The MHD  g e n e r a t o r employing  i s f r e e from t h i s e l e c t r o d e  i n d u c t i v e power t r a n s f e r  c o o l i n g and c l e a n i n g  problem.  CHAPTER  V  CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK  The research  two major problems encountered i n contemporary-  i n plasma p h y s i c s ,  c o n t a m i n a t i o n and i n s t a b i l i t i e s ,  have been found to e x i s t i n an e l e c t r o m a g n e t i c An  experimental  program conducted w i t h  a c l e a n and r e p r o d u c i b l e tube has met w i t h  shock tube.  the o b j e c t o f p r o d u c i n g  plasma i n an e l e c t r o m a g n e t i c  only p a r t i a l  success.  shock  The s m a l l - c a t h o d e  d r i v e r which was developed produced a plasma h a v i n g plane l u m i n o s i t y f r o n t than t h a t c h a r a c t e r i s t i c  a more  o f the plasma  produced e i t h e r by the w i d e l y - u s e d T-tube d r i v e r or by a c o a x i a l driver.  The amount o f c o n t a m i n a t i o n i n the plasma was compar-  a b l e to t h a t i n the plasma produced by a T-tube. I t was e s t a b l i s h e d t h a t the d r i v i n g d i s c h a r g e i n fluenced  the shape o f the shock f r o n t and the homogeneity o f  the plasma. discharge, with  The p e r s i s t e n c e  o f the e f f e c t s o f the d r i v i n g  and i n p a r t i c u l a r o f the i n s t a b i l i t i e s  the d r i v i n g d i s c h a r g e ,  associated  on the p r o p e r t i e s o f the plasma  were n o t i c e a b l e a t a time l o n g a f t e r the d r i v i n g c u r r e n t had ceased to f l o w .  The s t r u c t u r e o f the l u m i n o s i t y  t h a t c o u l d be d i r e c t l y a t t r i b u t e d to the d r i v i n g stayed  c l o s e to the l u m i n o s i t y f r o n t .  little  shock-heated gas p r e c e d i n g  considerable  o f the plasma discharge  There was, t h e r e f o r e ,  the d r i v e r gases even a t a  d i s t a n c e from the d r i v e r .  -116The  plasma produced by a c o a x i a l d r i v e r was  to  be  t r a n s p o r t i n g a magnetic f i e l d  to  the d r i v i n g d i s c h a r g e .  The  found  t h a t c o u l d be a t t r i b u t e d  r e s u l t s of a magnetic  inter-  a c t i o n experiment i n d i c a t e d t h a t the magnitude of t h i s muthal magnetic f i e l d d e n s i t y was  and  appreciable.  i t s supporting p o l o i d a l current I t would be  of i n t e r e s t to  gate f u r t h e r the p r o p e r t i e s of a plasma s u p p o r t i n g t r a n s p o r t e d magnetic The and  such a  dynamics of the plasma d u r i n g both a c c e l e r a t i o n  gases i n the plasma.  the d r i v i n g d i s c h a r g e .  The  strongly influenced  Such d i s c h a r g e  c o n s i s t of m a t e r i a l evaporated from any with  d r i v i n g current while maintaining  gases would  surfaces i n contact  amount of t h i s  c o u l d most e a s i l y be l e s s e n e d by d e c r e a s i n g  contamination  the d u r a t i o n of  the amplitude  obtained  by r e p l a c i n g the p r e s e n t  i t o r bank w i t h an u l t r a - f a s t , h i g h - v o l t a g e The  amount of c o n t a m i n a t i o n  by an e l e c t r o m a g n e t i c  high  energy capac-  c a p a c i t o r bank.  i n the plasma produced  employed.  e l e c t r o d e l e s s d r i v e r s to determine whether or not  in  efficiency  c o u l d be  with  the  expected  o f f s e t by the advantage of h i g h p u r i t y  the plasma generated by  used such a d r i v e r and has i e n c y by u s i n g a f a s t  elect-  It i s , therefore,  suggested t h a t some experiments should be performed  low  current  shock tube c o u l d be reduced i f an  r o d e l e s s shock tube d r i v e r was  the  constant.  Such a change i n the c h a r a c t e r i s t i c s of the d r i v i n g c o u l d be  investi-  field.  d e c e l e r a t i o n were i n t e r p r e t e d as b e i n g  by d i s c h a r g e  azi-  such a d r i v e r .  Rockman (1961) has  overcome the problem of low  c a p a c i t o r bank.  effic-  — 117 — The  i n v e s t i g a t i o n s r e p o r t e d i n Chapter  t h a t a problem of c o n s i d e r a b l y more fundamental than c o n t a m i n a t i o n  should be  with electromagnetic  studied.  III indicate importance  N e a r l y a l l workers  shock tubes have assumed t h a t a plane  shock wave i s produced i n an e l e c t r o m a g n e t i c  shock  tube.  C e r t a i n l y under c o n d i t i o n s of low p r e s s u r e and h i g h v e l o c i t y , the r e s u l t s p r e s e n t e d  i n Chapter  I I I indicate that i t i s  q u e s t i o n a b l e whether a shock wave i s produced.  The  discharge  gases appear to a c t as a h i g h l y permeable p i s t o n , pushing little  of the encountered  needed b e f o r e d e f i n i t e  gas  ahead of them.  F u r t h e r work i s  c o n c l u s i o n s can be drawn about  the  c o n d i t i o n s f o r the e x i s t e n c e of t r u e shock f r o n t s i n low sure e l e c t r o m a g n e t i c The  shock  pres-  tubes.  development of the small-cathode  d r i v e r was  made  p o s s i b l e by the development of a crowbar s w i t c h t h a t could short-circuit  the low  impedance d r i v e r e f f i c i e n t l y .  bar s w i t c h and main s w i t c h operated project  reliably.  crow-  A research  c o u l d , however, be u s e f u l l y s t a r t e d on one  extending  The  or more o f :  the maximum v o l t a g e c a p a b i l i t y of the s w i t c h to  g r e a t e r than 25 kV,  extending  the power h a n d l i n g  capability  to over 4 kJ or i n v e s t i g a t i n g the problems of a b l a t i o n and c o a t i n g of the i n s u l a t i o n s e p a r a t i n g the e l e c t r o d e s . The  plasma t h a t was  s t u d i e d i n Chapter  I I I was  used  to i n v e s t i g a t e the p r o p e r t i e s of c e r t a i n magnetohydrodynamic generators.  Three g e n e r a t o r s h a v i n g a z i m u t h a l  proposed i n Chapter and  the o t h e r two  IV.  One  utilized  was  symmetry were  an e l e c t r o d e - t y p e of  i n d u c t i v e power t r a n s f e r .  generator The  -118e l e c t r o d y n a m i c a l behaviour  o f each g e n e r a t o r was c a l c u l a t e d on  the b a s i s of a simple model and experiments w i t h two o f the g e n e r a t o r s . e l e c t r o d e - t y p e B^. MHD  The f i r s t  generator, f a i l e d  were  performed  to be t e s t e d , an to operate as expected  p r o b a b l y because o f the e x i s t e n c e of a sheath on the e l e c t r o d e s . The  last  to he t e s t e d , an e l e c t r o d e l e s s c o n f i g u r a t i o n of gen-  e r a t o r , operated i n c o n f o r m i t y w i t h the t h e o r e t i c a l The  predictions.  output power o f the two e l e c t r o d e l e s s c o n f i g u r a t i o n s con-  s i d e r e d was extremely  low - f a r too low f o r the g e n e r a t o r s  to be c o n s i d e r e d as p r a c t i c a l power g e n e r a t o r s .  The e l e c t r o d e -  "type g e n e r a t o r t h a t was c o n s i d e r e d c o u l d , however, p o s s i b l y be developed  i n t o a p r a c t i c a l power g e n e r a t o r .  APPENDIX  A  CHARACTERISTICS OF VARIOUS SPARK GAP  TRIGGER CIRCUITS  C e r t a i n p r o p e r t i e s o f the v o l t a g e d o u h l e r spark gap trigger c i r c u i t  o r i g i n a l l y used by Theophanis  been i n v e s t i g a t e d . ized.  Three major  They have been:  (1960) have  o b j e c t i v e s have been r e a l -  (a) To determine the v a l i d i t y  of  Theophanis' statement t h a t e i t h e r n e g a t i v e or p o s i t i v e i t y p u l s e s c o u l d be o b t a i n e d from the c i r c u i t 52a, by a l t e r i n g the ground  gering p a r a l l e l  shown i n F i g  c o n n e c t i o n w i t h s w i t c h S1.  (b) .To determine the l o s s o f p u l s e power due of the t h y r a t r o n .  polar-  to the impedance  (c) To determine the f e a s i b i l i t y  spark gaps w i t h the t r i g g e r c i r c u i t s  of t r i g shown  i n F i g 52b.  (a)  (b)  F i g 52. T r i g g e r C i r c u i t s Employing Cable.  (c) the D i s c h a r g e o f a  -120The p o l a r i t y b e h a v i o u r o f the c i r c u i t  o f P i g 52a  has been i n v e s t i g a t e d by d e t e r m i n i n g the minimum t h y r a t r o n anode v o l t a g e r e q u i r e d f o r breakdown o f the t r i g g e r  spark  gap f o r v a r i o u s gap s p a c i n g s and f o r s w i t c h S1 i n p o s i t i o n s A and B. for  I t was found t h a t the t h y r a t r o n v o l t a g e r e q u i r e d  breakdown o f a gap was about 1.7 times g r e a t e r when S1  was i n p o s i t i o n A r a t h e r than B.  Thus the c i r c u i t  o f P i g 52a  generates p u l s e s o f p o l a r i t y depending upon the p o s i t i o n o f S1; however the n e g a t i v e p u l s e s have a v o l t a g e t h a t i s about 1.7 times l a r g e r than p o s i t i v e p u l s e s . The c i r c u i t s  o f P i g 52a and 52c were used t o i n v e s t i -  gate the l o s s o f p u l s e v o l t a g e a t the t r i g g e r gap due to the impedance o f the t h y r a t r o n .  The spark g e n e r a t e d by the c i r -  c u i t o f P i g 52c when R = 0 was o f c o n s i d e r a b l y g r e a t e r power than t h a t generated by the t h y r a t r o n c i r c u i t as determined  shown i n P i g 52a,  by v i s u a l o b s e r v a t i o n o f the spark.  ohm, the spark c u r r e n t was decreased by about 10$.  When R = 1 The time  d e r i v a t i v e o f the spark c u r r e n t was observed w i t h a one t u r n f l u x p i c k u p l o o p connected  t o an o s c i l l o s c o p e .  ohms, the t r i g g e r spark was o f n e g l i g i b l y was  concluded t h a t the t h y r a t r o n c i r c u i t  s m a l l energy.  Further tests  p u l s e o f the t r i g g e r  spark c u r r e n t was i n c r e a s e d and the amplitude presence  It  possessed a h i g h e r  impedance than d i d the o p e n - a i r gap c i r c u i t . d i s c l o s e d t h a t the d u r a t i o n o f the f i r s t  When R = 50  decreased by the  o f an ~ 1 0 0 nH i n d u c t a n c e i n s e r t e d i n p l a c e o f the  r e s i s t a n c e R shown i n F i g 52c.  F i g 53 shows the time  deriva-  t i v e o f the t r i g g e r spark c u r r e n t f o r the t r i g g e r c i r c u i t  shown  - 121 i n P i g 52c but w i t h R = 0 and low i n d u c t a n c e gap  i n the o p e n - a i r  circuit.  T  1  J  'S  P i g 53. D e r i v a t i v e o f T r i g g e r Spark C u r r e n t Generated by C i r c u i t o f P i g 52c. R = 0 ohms; 0.1//sec/ div. The c i r c u i t  i n P i g 52b d i d n o t operate  The t e s t c i r c u i t was c o n s t r u c t e d  satisfactorily.  so t h a t the t r a n s i t  time o f  a s i g n a l from p o i n t A to p o i n t B (see P i g 52b) was 2 - 3 Synchronized  nsec.  breakdown o f the two main gaps was thus p o s s i b l e  o n l y i f t r i g g e r i n g was e f f e c t e d w i t h i n t h i s time. spark c u r r e n t e v i d e n t  The s m a l l  i n P i g 53 d u r i n g t = 0 to t « 3 nsec  suggested t h a t d i f f i c u l t y would be encountered w i t h the parallel  gap c i r c u i t .  obtained  Satisfactory parallel firing  f o r capacitor charging voltages  when the s e l f - t r i g g e r i n g v o l t a g e  c o u l d o n l y be  o f 8.25 to 9.5 kY,  (breakdown v o l t a g e  o f the  main gaps) was 9«5 kV. Considerably tained with  the c i r c u i t  b e t t e r p a r a l l e l gap o p e r a t i o n was obo f P i g 54.  Por a t r i g g e r c i r c u i t i n  which L = 40 nH, C = 1.6/iP, t r i g g e r c a p a c i t o r c h a r g i n g  voltage  = +10 kV, R = 8 ohms, number o f c a b l e s , main gaps and main capa c i t o r s = 2, main gaps s e t f o r 13 kV breakdown,  the two main  - 122 gaps would t r i g g e r s i m u l t a n e o u s l y of from + 7.5 t o + 13 kV.  f o r main c a p a c i t o r v o l t a g e s  They would not t r i g g e r  l y f o r a main c a p a c i t o r v o l t a g e o f 6.25 kV.  simultaneous-  The t r a n s i t time  of a s i g n a l between p o i n t s .A and B was a g a i n 2 - 3 nsec, so t h a t the r i s e time of the t r i g g e r v o l t a g e a t the t r i g g e r of the main gaps must have been l e s s than  2 - 3  pins  nsec.  hi manual switch  —'WV— c  —  *-  I  - «  V 1  :  - O I  •0 A^  c —V\A  _ ~10 R  C  —VSA-  nH  B  -0 i h  F i g 54. T r i g g e r C i r c u i t f o r P a r a l l e l Gaps. The o p e r a t i o n o f the c i r c u i t d e s c r i b e d by H i n t z and Beerwald (1959). t h a t these workers reached analysis,  Since i t i s b e l i e v e d  an erroneous c o n c l u s i o n i n t h e i r  t h i s c i r c u i t w i l l now be a n a l y z e d .  ance and the dynamic i n d u c t a n c e switch are neglected, cuit  shown i n F i g 54 has been  When the r e s i s t s  o f the d i s c h a r g e  i n the manual  the v o l t a g e a c r o s s R i n the t r i g g e r  cir-  shown i n F i g 54 i s  where R  125  RZo/n  = —=:  =—;— , Z  Q  - the c h a r a c t e r i s t i c impedance o f  p R + Zo/n the t r i g g e r c a b l e s and n = the number o f t r i g g e r c a b l e s .  large value  A  o f V can be o b t a i n e d w i t h i n a time o f the order o f  - 123 a few nsec  -  a f t e r the t r i g g e r gap has  v a l u e much g r e a t e r than 1.  2  c l o s e d i f RpC/4L has  a  Then,  V(P c/4L»i, t«R,c) = V |i - e x p [ - R t / L J J  ^  a  r  The  e  voltage appearing  capacitance effect  P  on a t r i g g e r p i n V.  between the t r i g g e r p i n and  depends on ground.  the  When the  of m u l t i p l e c a b l e r e f l e c t i o n s i s n e g l e c t e d , the  appearing  on a t r i g g e r p i n  voltage  is  2Vc > + T - g r [ ^ e x p { - t A ^ ~ e x p { - t R / i | J  or  f  127  V , (R, C/4L»l, t« R,C , l/C ?. = R p / L ) = a  t  t  2V { I - [l + M ] e x p { - t R , / L \ " .  128  e  In o r d e r t h a t V^.  w i l l r i s e w i t h i n a few nsec  p a r a b l e to V  must be  r  ,  small.  The  to a v a l u e com-  optimum v a l u e i s  and not C.Z R = L as s t a t e d by H i n t z and Beerwald x o p A further simplification be made.  of equations  127  and  128  = 0  (1959). can o f t e n  If R «  Z /n, then R = R or a l t e r n a t i v e l y i f R » o p ' = Z /n. A p r a c t i c a l case w i l l now be c o n s i d e r e d . d  Z /n, Q  then R^  Q  For G = 1.6//F, I = 40 nH,  t = 5 nsec, R  = 8 ohms, C, = 0, P  then V  t r  ( t = 5 nsec) = 1.264  nsec) = 0.528 V circuit  .  Vc.  If C Z t  Q  Other f a c t o r s should be  i s employed.  x  - I/R  then  be of .-'sufficient l e n g t h t h a t the sparks a t the t r i g g e r  the t r i g g e r p u l s e should be  t r  c o n s i d e r e d when t h i s  For example, the t r i g g e r c a b l e s  are not a f f e c t e d by c a b l e r e f l e c t i o n s .  V (t=5  should pins  A l s o , the p o l a r i t y  chosen to i n c r e a s e the  electric  of  field  between the The  ger  circuit  as  shown i n P i g  the  time of the  at the  I t was  voltage quadrupler The  t r i g g e r p i n of the  p o l a r i t i e s f o r minimum  to the  however, t h a t  the  shown i n P i g  54.  q u a d r u p l e r c i r c u i t was  was  closing  w i d e s t range of main gap  voltage  cathode of  t h i s c i r c u i t might prove to be  circuit  in  volt-  It  a negative t r i g g e r pulse feeding into-the that  trig-  object  main gap.  t r i g g e r p u l s e f e e d i n g i n t o the  believed  alternative  electrode.  to o b t a i n as h i g h a t r i g g e r  s w i t c h over the  and  facing  55 were i n v e s t i g a t e d .  most d e s i r a b l e  were a p o s i t i v e main gap  the  c h a r a c t e r i s t i c s of the  possible  found t h a t  -  t r i g g e r p i n and  d e v e l o p i n g t h i s c i r c u i t was age  124  a  the  anode. suitable  T e s t s showed,  not  suitable  for  trig-  g e r i n g p a r a l l e l gaps. +2.5  W 1M  ii  3  Manual Switch  t Pig Por  the as  55.  V o l t a g e Quadrupler T r i g g e r  non-parallel  c i r c u i t s shown i n P i g 1  the  circuit  t u r e d dc  Even f u r t h e r former on  the  o p e r a t i o n of spark gap 56 were found to be  shown i n P i g  i s o l a t i o n of the i s o l a t i o n was output as  Circuit.  55.  satisfactory  Both c i r c u i t s i n P i g  trigger circuit p r o v i d e d by  shown m  as  switches,  Pig  from the  56  main  employing a p u l s e  56b.  A  transformer  feacircuit, transwas  - 125 made t h a t reproduced  40 nsec,  w i n d i n g c a p a c i t y of ~ 40 was  pF.  -  30 kV p u l s e s and had A low  an  interwinding capacity  d e s i r a b l e i n order t h a t o n l y a s m a l l ground l o o p  would f l o w a c r o s s the p u l s e t r a n s f o r m e r . shown i n P i g 56a was  inter-  The  trigger  current circuit  employed to t r i g g e r the main s w i t c h  the d r i v e r of the shock tube (see P i g 4 ) .  '-flLZZfcHI  HI  (a) Pig  56.  1  U 0>)  Voltage Doubler T r i g g e r C i r c u i t s .  P  and  - 126 -  APPENDIX  B  PROPERTIES OP A WIDE VOITAGE RANGE, OPEN-AIR SPARK GAP  SWITCH  The t h r e e - e l e c t r o d e spark gap s w i t c h e s shown i n P i g 57 have working v o l t a g e ranges of about is  to V^, where  the v o l t a g e a t which breakdown o f the gap o c c u r s .  c h a r a c t e r i s t i c s of a s w i t c h w i t h the c o n v e n t i o n a l  The  geometry,  P i g 57a, have been d e s c r i b e d by Lupton (1961) and by H i n t z and Beerwald  (1959).  The c h a r a c t e r i s t i c s o f the t r i g a t r o n  s w i t c h have been i n v e s t i g a t e d by Craggs, -.Haine. and Meek (1946), Shkuropat  (1961) and Broadbent  a) C o n v e n t i o n a l  (1960).  b)  Trigatron  P i g 57. Open-Air Three E l e c t r o d e Spark Gap Switches. I t has been found t h a t the working v o l t a g e range of a t h r e e e l e c t r o d e spark gap s w i t c h c o u l d be g r e a t l y by u s i n g the plasma  increased  j e t t r i g g e r system shown i n P i g 58.  The  major d i f f e r e n c e s between the o p e r a t i o n o f t h i s system and those shown i n P i g 57 was  t h a t an a x i a l t r i g g e r c u r r e n t  f o r c e d to f l o w and t h a t r a d i a l  was  expansion o f the channel o f the  - 127 -  t r i g g e r spark was suppressed.  The plasma i n the t r i g g e r d i s -  charge was thus e s s e n t i a l l y f i r e d i n t o the gap "between the  main  electrodes.  trigger pin  insulation  F i g .58. Plasma J e t Triggered Open-Air Spark Gap Switch. The c i r c u i t shown i n P i g 59 was employed f o r d e t e r mining the t r i g g e r i n g time c h a r a c t e r i s t i c s of the plasma j e t triggered switch.  The s w i t c h was connected to discharge a  1 .6 /I'F c a p a c i t o r i n a c i r c u i t having an inductance of about 40 nH. H-O.  -AAA-  ±4 kV=V,  manual switch  — > - •<—  8n_ AAA-  100  0-  kA  1M.flAAA  1.  1 .6/fP  1.6  trigger capacitor  main  capacitor F i g 59. C i r c u i t f o r T e s t i n g Open-Air Spark Gap Switches. The p o l a r i t y and t r i g g e r i n g time data p l o t t e d i n F i g 60 i n d i c a t e that the plasma j e t t r i g g e r e d switch operates at c a p a c i t o r voltages of l e s s than 1-^/2, but w i t h some increase i n t r i g g e r i n g time a t these lower v o l t a g e s . anomalous p o i n t s on the Y _ . , capacitor  The seemingly  = 0 a x i s i n d i c a t e that the  * 128 switch w i l l  c l o s e even when no v o l t a g e  e x i s t s between the main  electrodes.  main c a p a c i t o r  voltage  P i g 60. T r i g g e r i n g Time o f Plasma J e t T r i g g e r e d The  a c t u a l t r i g g e r i n g mechanism has n o t been  oughly i n v e s t i g a t e d .  I t i s believed,  He e s t a b l i s h e d  a t l e a s t f o r low v a l u e s o f the a p p l i e d v o l t a g e , three-electrode  emitted by the t r i g g e r spark.  thor-  however, t h a t the t h e o r y  proposed by Saxe (1961) i s a p p l i c a b l e .  a conventional  Switch.  that,  breakdown o f  gap i s caused by the shock wave I n the plasma j e t t r i g g e r e d gap.  a f a c t o r c o n t r i b u t i n g to breakdown i s the e j e c t i o n o f l u m i n ous  gas and What appeared to be p a r t i c l e s from the t r i g g e r  spark i n t o the main gap.  Highly  l u m i n o u s • s p a r k s were observed  to t r a v e l about 1/2 i n . a x i a l l y from the t r i g g e r h o l e when the  o t h e r main e l e c t r o d e  these sparks a c r o s s the  was removed.  D u r i n g the passage o f  the gap, c o l l i s i o n s between the sparks and  gas atoms p r o b a b l y r e s u l t e d i n the f o r m a t i o n o f a back-  ground i o n i z a t i o n i n the gap which a i d e d  i n bringing  about  - 129 breakdown.  The luminous gas e j e c t e d by the t r i g g e r  i n t o the main gap was v i s i b l e  spark  f o r a .distance o f about 1/16  i n . when the t r i g g e r energy was d e r i v e d from the c i r c u i t shown i n P i g 59.  I t i s probable  that t h i s short l i v e d  j e t g e n e r a t e d a non-luminous shock wave o f the type by  plasma  discussed,  Saxe. The  p o i n t s on the V .. = 0 a x i s o f P i g 60 o f f e r * capacitor D  some c o n f i r m a t i o n t h a t the t h e o r y  o f Powler, Paxton and Hughes  (1961) i s a p p l i c a b l e to the plasma j e t t r i g g e r .  A c c o r d i n g to  t h e i r i n t e r p r e t a t i o n , the motion o f the p o s i t i v e i o n s i n the t r i g g e r discharge  markedly a f f e c t s the motion o f the plasma  i n the d i s c h a r g e .  The p o i n t s on the V .. capacitor  0  occur  =0  c  o n l y when the t r i g g e r p u l s e i s p o s i t i v e w i t h  axis respect  to the r e f e r e n c e  e l e c t r o d e , the e l e c t r o d e c o n t a i n i n g the t r i g -  ger components.  The d i r e c t i o n of motion o f the p o s i t i v e i o n s ,  when the t r i g g e r p u l s e i s p o s i t i v e , i s outwards through the small hole.  These i o n s i n p a s s i n g a c r o s s  the main gap c o u l d  account f o r the c l o s i n g o f the s w i t c h a t c a p a c i t o r v o l t a g e s l e s s than V^/2.  Other mechanisms t h a t c o u l d c o n t r i b u t e to  the breakdown process  a r e d i s c u s s e d i n Appendices C and D.  A l t h o u g h the plasma j e t t r i g g e r e d s w i t c h can be used a d v a n t a g e o u s l y i n p l a c e o f a c o n v e n t i o n a l  three  electrode  spark gap s w i t c h f o r c e r t a i n a p p l i c a t i o n s , t h e r e a r e two factors that l i m i t  its applicability.  The f i r s t  plasma j e t t r i g g e r e d s w i t c h p o s s e s s e s no d i s t i n c t over c o n v e n t i o n a l  switches  electrodes i s large.  i s t h a t the advantage  when the s p a c i n g between the main  The second c o n s i d e r a t i o n p e r t a i n s to  - 130 e l e c t r o d e wear.  -  I f the t r i g g e r spark or the main d i s c h a r g e  are of too h i g h energy then the s m a l l h o l e where the  trigger  d i s c h a r g e occurs w i l l he r e s p e c t i v e l y e i t h e r e n l a r g e d or closed*, r e s u l t i n g i n a decreased The  switch  o p e n - a i r s w i t c h t h a t has been d e s c r i b e d was  used i n the d i s c h a r g e c i r c u i t tube.  The  life.  f o r the e l e c t r o m a g n e t i c  plasma j e t t r i g g e r i n g system was,  i n the low p r e s s u r e f o l l o w i n g Appendix.  spark gap  not  shock  however, employed  s w i t c h t h a t i s d e s c r i b e d i n the  - 131 -  APPENDIX  C  LOW INDUCTANCE LOW PRESSURE SPARK GAP SWITCH  ( R e p r i n t from Rev. S c i . I n s t s . 33,'606-610, 1962)  Reprinted from  T H E REVIEW  OK S C I E N T I F I C I N S T R U M E N T S , , V o l . ' 3 3 , N o . P r i n t e d i n U . S. A .  6,  606-610,  June,  1962  L o w Inductance L o w Pressure Spark G a p Switch* G . D . CORMACK A N D A. J . B A R N A R D  Physics Department, University of British Columbia, Vancouver, British Columbia,  Canada  (Received January 1 7 , 1 9 6 2 ; and in final form, M a r c h 12, 1 9 6 2 ) A low pressure spark gap switch suitable for use as a main switch and as a "crowbar" switch on a capacitor bank is described. The switch has been operated over a voltage range of 0.5 to 2 5 k V , at energies up to 4 k j and currents up to 5 0 0 k A . Under normal operating conditions the triggering time is 4 0 nsec and the jitter approximately 1 0 nsec. The inductance of the main switch is 4 m ^ H and the inductance of the crowbar switch is about 1 m ^ H . INTRODUCTION  T  i n the current waveform during the first fraction of a microsecond when the i n i t i a l air pressure i n their switch is of the order of a few microns. T h e y have attributed these high frequency components to inductive effects caused b y pinching of the discharge channel. T h e d y n a m i c inductive effects observed^ at low pressure i n the present switch appear to be less than those reported b y M a t h e r and W i l l i a m s , although a direct comparison is not possible since argon rather than air has been used i n the present i n vestigation. A low pressure switch also exhibits a "closing t i m e " of the order of 0.1 jusec. T h i s closing time, first observed by Hagerman and W i l l i a m s ' and later investigated b y Johansson and Smars, manifests itself as a slow i n i t i a l rate of rise of the current. H a g e r m a n and W i l l i a m s have suggested that the closing time can be attributed to the time required to fill the switch with plasma. B o t h the d y namic inductive effects and the closing time are decreased b y an increase i n pressure so that i n normal operation of the present switch (at a pressure i n excess of about 15 fi) there is little distortion of the current waveform.  R I G G E R E D open air spark gaps are widely used as the switching elements i n high voltage circuits. L o w pressure spark gap switches offer distinct advantages i n many of these circuits. F o r example, low pressure switches do not require mechanical adjustments i n order to operate  over a wide range of voltage. There are two types of low pressure s w i t c h : the graded v a c u u m spark gap developed b y H a g e r m a n and W i l l i a m s , B a k e r , and M a t h e r and W i l l i a m s , and the two-electrode switch developed b y Johansson and Smars. T h e present switch, of a two-electrode design, has similar operating characteristics to the switch of Johansson and Smars, but has a m u c h lower inductance. T h e inductance 4 m/iH is comparable to that of graded vacuum spark g a p s . Such a low value of inductance suggests suitability of the switch as a " c r o w b a r " (a short circuiting switch). M a t h e r and W i l l i a m s have used their switch as a crowbar and have stated that its inductance is ~ 5 m ^ H . I n the crowbar version of the present switch, the inductance of the shorting link is about 1 m/uH. A n open air spark gap has a m i n i m u m triggering time w h e n ' the gap spacing is set close to the breakdown value, the electrode containing the trigger p i n (the reference electrode) is the cathode of the m a i n gap, and the trigger pulse is negative with respect to the reference electrode. F o r a low pressure switch, it is a g r e e d that the reference electrode should be the cathode, but no mention has been made of the polarity of the trigger pulse. I t has been found that the triggering time of the present switch is a-minimum when the trigger pulse is positive w i t h respect to the reference electrode.  3  1  2  3  4  4  4  1  1-3  3  6  CONSTRUCTION  6  Construction of the switch is shown i n F i g . 1. T h e switch is axially symmetric with the exception of the sheet conductor leads which connect onto parallel-plate conductors between the capacitor bank and the load. T h e discharge occurs between the parallel-plate steel electrodes designated anode and cathode. T h e switch is held together with an external L u c i t e clamp which is not shown in' the figures.  2-4  o  L o w pressure spark gap switches, i n contrast to open air spark gaps, often distort the current waveform. M a t h e r and W i l l i a m s have observed high frequency components  LUCITE BONDED WITH EPOXY RESIN TO DUMMY CATHODE  3  * This work was supported by the Atomic Energy Control Board and the National Research Council of Canada. D . C . Hagerman and A . H . Williams, R e v . Sci. Instr. 3 0 , 1 8 2  r •  BRASS •  STEEL  TRIGGER PIN[£f^ DISCHARGE CHAMBER  1  7  (1959).  W . R . Baker, R e v . Sci. Instr. 3 0 , 7 0 0 ( 1 9 5 9 ) . J . W . Mather and A . H . Williams, Rev. Sci. Instr. 3 1 , 2 9 7 ( 1 9 6 0 ) . R. B . Johansson and E . A . Smars, Proceedings of the Fifth International Conference on Ionization Phenomena i n Gases, 1 9 6 1 (to be published by North-Holland Publishing Company, Amsterdam). W . H . L u p t o n , Proceedings of the Fifth International Conference on Ionization Phenomena i n Gases, 1 9 6 1 (to be published by N o r t h Holland Publishing Company, Amsterdam). P . I . Shkuropat, Soviet P h y s . — T e c h . Phys. 5, 8 9 5 ( 1 9 6 1 ) . 2 3  4  6  FROM CAPACITOR BANK.  TO LOAD  F I G . 1. A cross-sectional view of the 4 - k J switch.  6  606  607  SPA.RK  G A P  There are several essential features in the construction. The Lucite insulation must be bonded with epoxy resin to a dummy cathode—a thin disk of aluminum. The epoxy bond greatly reduces the size of any interstices, or gaps, that exist at the low pressure edge of the junction between the dummy cathode and the Lucite. Experimental work has shown that pre-ignition is primarily caused by breakdown in these unavoidable gaps. This junction phenomenon has been investigated by Kofoid at lower pressures than have been used in the present work. Every firing of the switch raises the pressure in the discharge" chamber to about an atmosphere and forces considerable gas into these gaps. Pre-ignition occurs if voltage is applied across the switch before these gaps' are sufficiently evacuated. The presence of the epoxy bond makes the switch unable to withstand large reverse dc voltages (which occur when the  S W I T C H  vent holes and the size of the hole in the Lucite. The trigger components, the tungsten wire, and polyethylene sleeve are essentially free of wear because the main discharge does not enter the small trigger hole and the trigger discharge is of insufficient energy to evaporate much material from the components.  OPERATING CHARACTERISTICS  7  electrode that is bonded to the insulation is made positive with respect to the electrode containing the vent holes). Furthermore, the triggering time is drastically increased when a reverse voltage is switched, as has also been observed by Johansson and Smars. The dummy cathode is in electrical contact with the main cathode but is not rigidly attached to it. Therefore pressure against the main cathode, caused mainly by J X B forces in the facing surfaces of the electrodes and less so by the forces discussed by Wehner, does not break the very important epoxy bond. For example, the J X B force for a 500-kA firing gives rise to a pressure of the order of 140 atm against the active area of the cathode. Earlier models of the switch, constructed without the aluminum disk but with the Lucite bonded directly to the cathode, worked well until required to discharge more than 2.5 kj. The bond then failed and the switch would no longer hold off appreciable voltage. This switch was simpler to construct and had slightly better pre-ignition characteristics than the switch shown in Fig. 1. There is an optimum size for the hole in the Lucite. If it is too large, several low energy firings result in the deposition of carbon on the Lucite over small areas opposite each vent hole. For example, carbon was deposited by 20 firings of the 19.2-^F capacitor bank charged to 500 V. This carbon was removed by a higher energy firing that occurred at 11 k V while the bank voltage .was being slowly raised. If the hole in the Lucite is too small,.the active area of the cathode is worn differentially; a trench appears on the cathode just inside the junction of the cathode and the Lucite. The vent holes connecting the discharge chamber to the dump chamber allow some of the discharge gases to pass over the surface of the Lucite during and after a firing, thus preventing the deposition of a conducting layer. The amount of scavenging of the Lucite by the discharge gases depends upon the size and number of 4  8  ' M . J. Kofoid, Trans. Am. Instr. Elec. Engrs., Part III, 79, 991 and 999 (1960-1961). G. K. Wehner, J. Appl. Phys. 31, 1392 (1960). 8  The switch has been in use with 19.2-/nF and 9.6-fiF capacitor banks. The total circuit inductance has been varied from 13 to 30 m^H and the voltage on the bank from 0.5 to 25 kV. This range in voltage over which the switch operates without adjustments is much greater than that of atmospheric-pressure spark gaps. Damped oscillatory currents having peak values of 10 to 500 k A and frequencies from 200 to 400 kc have been switched. The triggering time depends primarily upon the kind of gas in the discharge chamber, the pressure of this gas, the bank voltage, and the trigger characteristics. The triggering time r is defined as the time lag between the start of the flow of the trigger current and the start of the flow of appreciable switch current. Appreciable switch current is interpreted, for experimental convenience, as about 1/50 of the peak value of the switch current. Figure 2 shows the triggering time vs pressure (p) behavior for the switch of Fig. 1 when filled with argon. Preliminary experiments with both air and helium in the discharge chamber have indicated that the r (p) relation for these gases differs from that for argon. As the difference has not been fully investigated, only the results for argon will be discussed. Jitter in'r is not shown in Fig. 2. The jitter is about 10 nsec when the trigger is positive and 18 <p <60 /i. These curves are valid in a voltage range of 2 to 25 k V and each point is an average of five measurements. The r(p) curves for a bank voltage of 500 V are below the given curves if p<10ju and are coincident with them if p>10/i. A t 25 kV, the argonfilled switch breaks down when the pressure is in excess of about 50 /x. At 5 kV, it breaks down at a pressure of about 150 MThe curves shown in Fig. 2 were obtained with a trigger circuit (see Fig. 3) comprising a 75-ft length of RG-58/u  ,Q< _ '  tn z FIG. 2. The triggering time T as a function of initial argon gas pressure.  to 5 SicP-  \\  -f- positive trigger o negative trigger  \\ \Q ^N} \ \  —  ^-Pv DI 0.1  | I PRESSURE  I |_ 10 100 (MICRONS)  G .  DELAY AND 5C22 THYRATRON CIRCUIT  D .  C O R M A C K  C 500 nnp R  r  J  I  meg  A N D  A . J .  B A R N A R D  608  Once the trigger current has ceased, thermionically emitted electrons from the trigger pin do not enter the discharge chamber because a small amount of the thermionic current feeding into the relatively high impedance of the external  B  trigger circuit rapidly causes the formation of a retarding  PICKUP LOOP^L O A D < =  3ff  electric field around the trigger pin. Thermionic emission from the trigger pin is then severely space-charge-limited.  CROWBAR SWITCH-  The T (p) data therefore substantiate the ionization by collisions theory of Mather and Williams.  15  kV  MAIN  O—  3  Motion of the discharge column due to pinching can re-  SWITCH  sult in a high frequency modulation of the current during  '°f\>  the first fraction of a microsecond. The amplitude of the  if"  modulation increases with decreasing current. In fact, when the initial value of dl/dl  FIG. 3. Triggering circuit.  is sufficiently large, the oscilla-  tions are absent, thus indicating that the column does not cable initially charged to 15 kV and connected to the trigger pin with a voltage doubler determination that provided dc isolation. The first pulse of trigger current through the trigger pin [see Fig. 4(a)] has a duration of 40 nsec. The relay shown in Fig. 3 provides electrical isolation of the main switch trigger circuit from the 115-V ac supplyduring the discharge of the bank. The relay could be replaced by a thyratron should synchronization of the firing of the bank with an electrical signal be required. It can be seen from Fig. 2 that r is less when the polarity of the trigger pulse is positive rather than negative. The curves roughly obey the relation first observed by Mather and Williams, 3  r«l/p.  (1)  To account for this relation, they have assumed that collisions between electrons and gas atoms produce a linear increase of ionization with time and that appreciable switch current starts to flow when a certain stage of ionization is reached in the discharge chamber. The presence of the plateau in the positive trigger curve in Fig. 2 for 18 <p <60 n is further evidence that this collision mechanism, rather than photoionization, is probably the dominant ionization mechanism. It is proposed that the plateau can be explained as follows. The collision-dominated trigger discharge results in ion bombardment and heating of a small region where the trigger discharge strikes the cathode, when the trigger pulse is positive. The trigger pin is not appreciably heated by a positive pulse because the electrons striking the pin have lost most of their energy in the plasma region of the trigger discharge. When the positive trigger current has ceased, thermionically emitted electrons from the heated region of the cathode will be accelerated across the discharge chamber. The sudden increase in electron density in the discharge chamber will enhance the production of ion pairs and decrease r from what it would be if thermionic emission were not important. For example, it is not important when the trigger is negative because then the trigger pin is heated by the trigger discharge.  contract. Such behavior can be expected for large currents,  L  (a) i  )  c  1 usee  (b) 0  1 Msec  (c) c>  1 usee  (d)Hi I, 0  (e)L c)  1 Msec  .lllf  "f 1 2 usee  FIG. 4. Typical oscillograms of: (a) the time derivative of the trigger current at the trigger pin of the main switch; (b) the time derivative of the load current dl/dl for an initial pressure of 1.8 n and a bank voltage of 2 kV; (c) dl/dl for an initial pressure of 47 fi and a bank voltage'of 2 kV; (d) dl/dl for an initial pressure of 4.6 and a bank voltage of 15 kV; and (e) dl/dl through an ^ 8 - m j i H load for an initial pressure of 21 /x in both switches and a bank voltage of IS kV. The vertical scales are uncalibrated. The ~30-Mc oscillations appearing on traces (b) to (e) are due to pickup of spurious signals. M  S P A R K  609  GAP  since material from the electrodes and the Lucite will contribute greatly to'the particle density in the discharge. If the particle density increases sufficiently fast, then the first contraction of the discharge is opposed by the rapidly rising internal pressure. The duration of modulation increases with decreasing gas pressure. Low gas pressure also results in a greater number of oscillations, a characteristic that has been noted by Mather and Williams, although in the present work the maximum number observed has been two. The observed time to the first pinch approximately obeys the dependence on density and initial value of dl/dt predicted by Rosenbluth and Garwin. When p is 1.8 fi, with bank voltage 2 kV and total circuit inductance 29 m/iH, a first pinch occurs at about 200 nsec [see Fig. 4(b)] and a second pinch can just be detected at about 500 nsec. Since dl/dt remains positive during this time, the oscillations do not make the current waveform depart appreciably from a damped sifiusoid. The departure is considerably less at higher pressures and bank voltages as is shown by the subsequent oscillograms in Fig. 4.  S W I T C H  3  9  Inspection of the electrodes after many firings at a fixed bank voltage shows the existence of a central clean region that has an area that depends upon the bank voltage. For example, firings at a bank voltage of 5 kV produce a clean area of about 1 cm . Since the observed current waveform is essentially a damped sine wave after the first fraction of a microsecond, it can be inferred that gross movements of the discharge channel are not present, and therefore that the clean area represents the cross-sectional area of the discharge. This area corresponds to a current density in the discharge of at least 30 000 A/cm . 2  2  Even when the initial gas density is high enough to result in no observable high frequency oscillations in the first quarter cycle of the dl/dl waveform, dl/dl still exhibits a slow rise to the first maximum. This slow rise can be discussed in terms of a closing time /„, defined as the time interval between appreciable departure of dl/dt from zero and the peak value of dl/dt. The observed values of t have been in the range of 50 to 200 nsec, the lower value being obtained for a high initial gas density. Little variation of t with bank voltage has been noted, although this dependency has not been investigated as thoroughly as it has by Johansson and Smars, who have found that a peaking of exists somewhere between 1 and 30 kV. The observed variation of l with gas density suggests that the switch possesses a dynamic resistance. It is proposed that t can be attributed to the time required for the establishment of a small cathode fall region and an essentially neutral plasma column. The ion density in the plasma will be higher than the initial gas density, most of the additional particles being sputtered from the cathode by impinging c  c  4  c  c  M . N . Rosenbluth and R. Garwin, 'Los Alamos Scientific Laboratory Report LA-1850 (1954). 9  FIG. 5. Pictorial view of the crowbar switch and the main switch. The insulating clamps are not shown.  ions. Thus an increase in initial gas density causes a decrease in t . c  The lifetime of the switch is as yet unknown. However, 400 firings under various conditions (0.5 to 25 kV, 10 to 500 kA) have been made; most of the firings have been in the 1- to 2-kJ range with about 30 being at 4 kj. The active surfaces of the electrodes are roughened but are not visibly worn. The surface of the Lucite appears to have been melted and slightly discolored but is still nonconducting. The 4-kJ discharges softened the surface of the Lucite but did not result in serious ablation. Should the lifetime of the switch be limited by eventual ablation of the Lucite, then it is planned that this insulation be replaced by a sheet of cementable Teflon. Preliminary experiments have indicated that ablation of Teflon is considerably less than that of Lucite. A thin coating of carbon has accumulated in the dump chamber but this coating has not affected the operation. Pre-ignition of the switch has occurred in about 2 % of the firings when the voltage has been greater than 15 kV. When the switch is adequately pumped out between firings it has been found that pre-ignition is greatly suppressed, indicating that the electrodes and the cathodeinsulator junction should be well outgassed before each firing. A second switch, of design shown in Fig. 5, is in use to short out the load near the end of the first halfcycle of current. This crowbar switch and the main switch are mounted close together and are connected to the same vacuum system. The trigger circuit for firing the crowbar switch is shown in Fig. 3 and a typical waveform of the derivative of the short-circuited current in a load in Fig. 4(e). The crowbar switch is a three-terminal circuit element and has a "through inductance" of about 4 m/iH and a shorting inductance of about 1 m^H. The former value could be reduced by increasing the width of the sheet conductor leads or by employing thinner Lucite. The latter indicates that the short-circuited load current is essentially unidirectional, even for values of load inductance as low as 10 rmxH. The load can be short-circuited at essentially any  G.  D  C 0RM ACK  A N D A .  time during the discharge because the crowbar switch can  J.  B A R N A R D  6L0  than the voltage initially on the condenser bank because  be fired at very low voltages. Even though the crowbar  the impedance of the load is less than that of the remainder  switch is subjected to a reverse voltage during the first  of the circuit.  quarter cycle of the current (the electrode that is sealed to the Lucite is made positive with respect to the electrode containing the vent holes), pre-ignition has not occurred, probably because the reverse voltage then occurring is of small magnitude and duration. The magnitude of this reverse voltage appearing across the crowbar switch is less  ACKNOWLEDGMENTS The authors wish to express their thanks to Dr. R. A. Nodwell and Dr. R. J. Churchill, and also to Dr. 0. A. Anderson of the Lawrence Radiation Laboratory, Berkeley, and Dr. M. J. Kofoid of the Boeing Airplane Company, for their helpful suggestions.  - 137  -  APPENDIX  D  PROPERTIES OF A LOW LOW  INDUCTANCE  PRESSURE SPARK GAP  SWITCH  I n the p r e s e n t Appendix f u r t h e r i n f o r m a t i o n i s p r e sented on the switches d e s c r i b e d i n Appendix C. is  The  emphasis  on a d e s c r i p t i o n of the e x p e r i m e n t a l methods employed to  t e s t the switches and c a l processes The convenience,  on a f u r t h e r e l a b o r a t i o n of the p h y s i -  t h a t are b e l i e v e d to occur i n the t r i g g e r i n g time X  and  measured, f o r e x p e r i m e n t a l  as the time i n t e r v a l between the onset of l u m i n -  o s i t y from a s m a l l o p e n - a i r gap gap,  was  switches.  the s t a r t  i n s e r i e s w i t h the  trigger  of the f l o w of a p p r e c i a b l e s w i t c h c u r r e n t .  A s p e c i a l t e s t w i t h a T e k t r o n i x 551  oscilloscope, a high  speed  p h o t o m u l t i p l i e r c i r c u i t and a s i n g l e t u r n 1 i n . diameter t e r m i n a t e d f l u x pickup c o i l the s e r i e s o p e n - a i r gap f i v e nsec  showed t h a t the l u m i n o s i t y from *  s t a r t e d w i t h i n a time l e s s than about  a f t e r the t r i g g e r c u r r e n t had  S i n c e the r i s e t i m e of the e l e c t r o n i c surements was  about H  nsec,  s t a r t e d to f l o w .  c i r c u i t s f o r a l l mea-  t h e r e was  no need to o b t a i n a  more a c c u r a t e measurement of the d e l a y between the onset c u r r e n t and l u m i n o s i t y .  I t was  necessary  to employ the  of lumin-  o s i t y s i g n a l as a r e f e r e n c e f o r a l l measurements of  trigger-  i n g time because the o s c i l l o s c o p e , a T e k t r o n i x 551,  would not  t r i g g e r dependably on the s i g n a l generated located  c l o s e to the t r i g g e r p i n .  i n a pickup  The v o l t a g e induced  coil across  - 138 such a p i c k u p c o i l obscured  due to the t r i g g e r c u r r e n t was  by e l e c t r i c a l n o i s e .  completely  This e l e c t r i c a l noise disap-  peared when the t r i g g e r c i r c u i t was d i s c o n n e c t e d from the switch. was,  The d e l a y between the onset o f c u r r e n t and l u m i n o s i t y  t h e r e f o r e , measured w i t h t r i g g e r c i r c u i t n o t connected to  the s w i t c h as i s shown i n P i g 61. T e k t r o n i x 551 Dual Beam Oscilloscope  trigger spark  photomultiplier P i g 61. C i r c u i t f o r Simultaneous O b s e r v a t i o n o f T r i g g e r C u r r e n t and L u m i n o s i t y . Some care was e x e r c i s e d to ensure  t h a t the o p e n - a i r gap i n  s e r i e s w i t h the t r i g g e r p i n had l i t t l e i n g time  o f the s w i t c h .  Por example, the t r i g g e r i n g time o f  the s w i t c h measured r e l a t i v e  to the time  t r i g g e r c a b l e was c o m p a t i b l e . w i t h relative gap  to the onset o f l u m i n o s i t y from  was made both w i t h and w i t h o u t ger c i r c u i t  o f s h o r t i n g the  the t r i g g e r i n g time measured  i n s e r i e s w i t h the t r i g g e r gap.  cable.  e f f e c t on the t r i g g e r -  the s m a l l o p e n - a i r  The former  measurement  the o p e n - a i r gap i n the t r i g -  and t a k i n g due account  o f the t r a n s i t time  The l u m i n o s i t y s i g n a l was o f a s i n g l e p o l a r i t y ,  f o r about a microsecond, and had a f a s t i n i t i a l  had an amplitude  rate of r i s e .  o f the lasted  o f about two v o l t s  I t was, t h e r e f o r e , a  more dependable s i g n a l f o r t r i g g e r i n g the sweep c i r c u i t s o f the o s c i l l o s c o p e than e i t h e r the s m a l l a m p l i t u d e , s m a l l  duration  - 139 f l u x p i c k u p s i g n a l t h a t c o u l d he o b t a i n e d a t the s h o r t i n g end of the t r i g g e r c a b l e or the n o i s e - r i d d e n f l u x  pickup  s i g n a l t h a t c o u l d he o b t a i n e d a t the t r i g g e r p i n end of the trigger cable.  The t r i g g e r i n g time was, therefore., measured  w i t h the c i r c u i t  shown i n F i g 62.  F i g 62. Method of Measuring T r i g g e r i n g Time of Low P r e s s u r e Switch. The vacuum system f o r the switches i s shown i n F i g 63.  I t was found  t h a t the switches  operated  o r i l y when a c o n s t a n t p r e s s u r e was m a i n t a i n e d  quite s a t i s f a c t i n the system  w i t h the n e e d l e - v a l v e , and when the bank -voltage was l e s s about 10 kV.  than  O p e r a t i o n a t h i g h e r v o l t a g e s n e c e s s i t a t e d pump-  i n g the switches  out to a p r e s s u r e of about a micron  after a  f i r i n g and then a d m i t t i n g f r e s h gas to the vacuum system u n t i l the d e s i r e d p r e s s u r e was a t t a i n e d . g e r i n g time were made employing  A l l measurements of t r i g -  the l a t t e r  system to ensure  that the gas. i n the switches was of f a i r l y h i g h p u r i t y . a l l measurements of X were performed  w i t h the switches  Also., isolated  - 140 from both the gas i n l e t  and the vacuum pump.  measured w i t h the P i r a n i sure.  The P i r a n i  guage was thus a s t e a d y - s t a t e pres-  r e a d i n g s were c o n v e r t e d t o t r u e p r e s s u r e  r e a d i n g s i n microns  Hg w i t h the a i d o f c a l i b r a t i o n  s u p p l i e d w i t h the P i r a n i  i'TT  litre  dump  supply  needle valve Pirani  tank  guage  <8>  To mechanical pump and diffusion pump  to main switch to crowbar/ switch h Pig The  ft  trap 63. Vacuum System f o r Switches measured t r i g g e r i n g  on C a p a c i t o r Bank,  time f o r the 4 k J main s w i t c h  as a f u n c t i o n o f the p r e s s u r e i n i t i a l l y i n P i g 64.  curves  guage. from argon  20  The p r e s s u r e  i n the s w i t c h i s g i v e n  Data f o r both h e l i u m and argon  and two t r i g g e r i  pulses of d i f f e r e n t effect  energy  on X o f the p u r i t y  by the c i r c l e d p o i n t s . fillings  and waveform a r e p r e s e n t e d .  o f the gas i n the s w i t c h i s i n d i c a t e d  A l l o t h e r data was o b t a i n e d w i t h  o f gas i n the s w i t c h and a time  ings o f 5 t o 30 minutes.  The  i n t e r v a l between  fresh fir-  -  141 -  10'  o ra •rl  a •H  1000  -p si  •H fH 0 tiO tiO •H  triqejer  circuit  fH  -P  *o II 100 Hiql» energy t r i g g e r  CiVeu'it  Low energy trigger circuit  10  0.1  1  10  100  P r e s s u r e i n microns Pig  1000  Hg  64. T r i g g e r i n g Time o f the 4 k J S w i t c h as a F u n c t i o n of P r e s s u r e . The p o i n t marked (§) was o b t a i n e d a f t e r the system had "been pumped a t a p r e s s u r e of about 0.2 microns Hg f o r two hours then f i l l e d w i t h h e l i u m to a p r e s s u r e o f 240 microns Hg. The p o i n t marked @ was o b t a i n e d w i t h a gas i n the s w i t c h c o n s i s t i n g o f h e l i u m and the i m p u r i t i e s r e l e a s e d by the p r e c e d i n g f i r i n g . A t r i g g e r pulse of p o s i t i v e p o l a r i t y r e s u l t e d i n a  lower v a l u e o f X than d i d a n e g a t i v e p u l s e . is  The mechanism t h a t  probably r e s p o n s i b l e f o r t h i s t r i g g e r p o l a r i t y  w i l l now be d i s c u s s e d .  behaviour  A t r i g g e r p u l s e of p o s i t i v e  r e s u l t s i n motion of more p o s i t i v e l y  charged  polarity  i o n s and l a r g e r  - 142  -  p a r t i c l e s i n t o the d i s c h a r g e chamber o f the main gap does a n e g a t i v e t r i g g e r p u l s e . was  The  than  e m i s s i o n of such p a r t i c l e s  observed when the t r i g g e r i s operated a t atmospheric p r e s -  sure as mentioned  i n Appendix B.  The  c o n j e c t u r e d motion of the  charged p a r t i c l e s i n the t r i g g e r d i s c h a r g e i s shown i n F i g 65 f o r both p o s i t i v e and n e g a t i v e p o l a r i t i e s of t r i g g e r p u l s e . cathode  a) t = 5 nsec  of main gap  b) t = 30 nsec  c) t = 45 nsec  p o s i t i v e p o l a r i t y of t r i g g e r p u l s e  a) 't = 5 nsec  b) t = 30 nsec c) t = 45 nsec negative p o l a r i t y of t r i g g e r pulse  F i g 65. Motion of Charged P a r t i c l e s i n T r i g g e r D i s c h a r g e . The low energy t r i g g e r p u l s e g e n e r a t o r shown i n F i g 64 i s b e i n g c o n s i d e r e d . The d u r a t i o n of the c u r r e n t p u l s e i s about 40 nsec as i s shown i n F i g 53. Data t h a t i s p r e s e n t e d on page 47 i n d i c a t e s jected  to h i g h energy e l e c t r o n  The p o s i t i v e  t h a t r e g i o n s sub-  bombardment l o s e  particles.  i o n c u r r e n t i s thus composed o f i o n i z e d  i o n s from the p o s i t i v e  gas atoms,  e l e c t r o d e and i o n s from the s u r f a c e of  - 143 the l u c i t e . cates the  The data p r e s e n t e d  i n Chapter I I I , S e c t i o n A i n d i -  t h a t breakdown i s p r i m a r i l y due to e l e c t r o n s i n j e c t e d by  t r i g g e r spark.  The q u e s t i o n now a r i s e s , i s the cathode o f  the main gap a b e t t e r e m i t t e r  o f e l e c t r o n s when the t r i g g e r  p u l s e -is p o s i t i v e or n e g a t i v e ? indicate  t h a t the cathode i s a b e t t e r e m i t t e r  when the t r i g g e r p u l s e the  The T ( p ) curves i n F i g 64  i s positive.  £ ( p ) curve f o r the argon f i l l e d  In f a c t , switch  of electrons the p l a t e a u i n  t r i g g e r e d by the  p o s i t i v e p o l a r i t y low energy t r i g g e r c i r c u i t  i s probably  to the c o p i o u s e l e c t r o n e m i s s i o n  upon c e s s a t i o n o f  the t r i g g e r p u l s e . passing has  t h a t occurs  due  The cathode o f the main gap i s no longer-  e l e c t r o n s to the t r i g g e r p i n when the t r i g g e r c u r r e n t  ceased f l o w i n g .  There i s s t i l l  appreciable  i o n bombardment  of the cathode o f the main.gap by the i o n s formed i n the t r i g ger  discharge,  directed ficient for  because these i o n s s t i l l  toward the cathode.  The i n e r t i a o f the i o n s i s s u f -  some time a f t e r the t r i g g e r c u r r e n t has ceased.  current  i s due to both t h e r m i o n i c  although i t i s d i f f i c u l t the s u r f a c e  The cathode  emit a l a r g e e l e c t r o n c u r r e n t  to the space charge o f the incoming i o n s .  that t h i s  at  velocities  to p e r m i t t h e i r motion toward the cathode to continue  of the main.gap can thus s t i l l due  have l a r g e  to c o n j e c t u r e  I t i s probable  and f i e l d  emission.,  what the temperature  o f the cathode o f the main gap might be.  e l e c t r o n emission  The  o c c u r r i n g d u r i n g 0< t < 40 nsec c o o l s the  cathode o f the main gap whereas i o n bombardment h e a t s i t . A negative  t r i g g e r p u l s e r e s u l t s i n no i o n bombardment o f the  cathode of the main gap, but some h e a t i n g  due to e l e c t r o n  - 144 bombardment.  The temperature  o f the cathode  o f the main gap at  the c e s s a t i o n o f the n e g a t i v e t r i g g e r p u l s e i s a g a i n unknown, as the cathode  i s heated  by the incoming  c o o l e d by the i o n s e m i t t e d . cathode  The important  p o i n t i s t h a t the  o f the main gap i s n o t s u b j e c t e d to i o n bombardment  immediately it  e l e c t r o n s , but i s  a t the end o f the n e g a t i v e t r i g g e r p u l s e , whereas  i s i f the t r i g g e r p u l s e i s p o s i t i v e .  When the t r i g g e r p u l s e  i s n e g a t i v e , the t r i g g e r p i n i s s u b j e c t e d to i o n bombardment a f t e r the t r i g g e r c u r r e n t has ceased cannot left The  flowing.  The t r i g g e r p i n  emit many e l e c t r o n s a t t h i s time due to the space  on the t r i g g e r p i n by the few e l e c t r o n s t h a t a r e e m i t t e d . slight  e m i s s i o n t h a t does occur charges  up the c a p a c i t a n c e  t h a t e x i s t s between the t r i g g e r p i n and the cathode main gap and''produces an e l e c t r i c ents t h a t reduces the cathode  field  o f the  between these  compon-  E m i s s i o n o f e l e c t r o n s from  o f the main gap upon c e s s a t i o n o f a p o s i t i v e  l i m i t e d because the l a r g e e l e c t r i c  the low e n e r g y , . s h o r t caused  The p l a t e a u i n the X (p)  curve  duration p o s i t i v e t r i g g e r pulse  by e m i s s i o n o f e l e c t r o n s from  the cathode  main gap a t the c e s s a t i o n o f the t r i g g e r c u r r e n t .  the cathode  a t i o n of f i e l d  caused  by incoming  thus  o f the I t i s not  d e f i n i t e whether the e m i s s i o n i s due to the h i g h e l e c t r i c at  trig-  a l r e a d y e x i s t i n g a c r o s s the main gap i s e s s e n t i a l l y  u n a f f e c t e d by t h i s e m i s s i o n .  is  field  f u r t h e r emission.  ger p u l s e i s not space-charge  for  charge  field  i o n s or i s due to a combin-  and t h e r m i o n i c e m i s s i o n .  The e x i s t e n c e o f t r a n s -  i e n t s i n the t h e r m i o n i c e m i s s i o n o f an a r c a f t e r a l a r g e change in  c u r r e n t has been e s t a b l i s h e d by G. L i s t  and G. Pardemann  - 145 (1959)?  however  -  under c o n d i t i o n s q u i t e d i f f e r e n t from  those  e x i s t i n g f o r the t r i g g e r d i s c h a r g e s t u d i e d h e r e . The first  T(p)  curves f o r argon r o u g h l y obey the r e l a t i o n  observed by Mather and W i l l i a m s  T  *  To account f o r t h i s r e l a t i o n ,  (1960):  I/p  129  they assumed t h a t  between e l e c t r o n s and gas atoms produced  collisions  a l i n e a r i n c r e a s e of ,  i o n d e n s i t y w i t h time and t h a t a p p r e c i a b l e s w i t c h c u r r e n t started  to f l o w when a c e r t a i n i o n d e n s i t y was  d i s c h a r g e chamber. valid  reached i n the  I t i s i n t e r e s t i n g t h a t such a r e l a t i o n i s  over a t l e a s t two  decades of p r e s s u r e f o r the low  energy  trigger circuit  and one decade of p r e s s u r e f o r the h i g h  energy  trigger circuit  even though  the waveform of the t r i g g e r c u r r e n t  generated by these ' c i r c u i t s d i f f e r s g r e a t l y .  I t i s possible  t h a t a mechanism proposed by Raether  i s operative.  t h a t p h o t o i o n i z a t i o n i n the v i c i n i t y  of the c l o u d of p o s i t i v e  i o n s i n an avalanche  He  found  c o n t r i b u t e d to the breakdown p r o c e s s .  P h o t o i o n i z a t i o n of the gas i n the d i s c h a r g e chamber by  photons  r e l e a s e d from the t r i g g e r spark would e x i s t i n the p r e s e n t s w i t c h and w i t h time.  c o u l d r e s u l t i n a l i n e a r i n c r e a s e of i o n d e n s i t y I t i s a l s o p o s s i b l e , of course, t h a t  e m i s s i o n from the cathode  electron  of the main s w i t c h (see P i g 65c),  then i o n i z a t i o n of the gas atoms by e l e c t r o n - a t o m might  collisions,  be "the major mechanism l e a d i n g to breakdown.  mechanism i s of major importance, justified  then e q u a t i o n 129  I f this c o u l d be  o n l y i f a c o n s t a n t r a t e of e m i s s i o n of e l e c t r o n s  into  the d i s c h a r g e chamber of the main s w i t c h i s i n i t i a t e d by the  start  146-  of the t r i g g e r c u r r e n t and i f the r a t e of e m i s s i o n i s  e s s e n t i a l l y independent of the subsequent waveform of the trigger  current.  The p o l a r i t y behaviour d i s c u s s e d i n the  p r e c e d i n g paragraph causes a s m a l l d e p a r t u r e of the c a r v e s from l i n e a r i t y and i s q u i t e d e f i n i t e l y due  to the copious  number of e l e c t r o n s e m i t t e d from the cathode of the main gap at the c e s s a t i o n of a t r i g g e r p u l s e of p o s i t i v e p o l a r i t y . p l a t e a u i n the  T(p)  curve f o r a low energy p o s i t i v e  The  trigger  thus i n d i c a t e s t h a t e i t h e r c o l l i s i o n s between e l e c t r o n s and atoms i s the major mechanism of i o n i z a t i o n or t h a t breakdown i s brought about by the t r i g g e r spark at the cathode of the main d i s c h a r g e . , I f the l a t t e r p r o c e s s i s o f major it  importance,  cannot be concluded whether p h o t o i o n i z a t i o n of the gas i n  the d i s c h a r g e chamber or i o n i z a t i o n o f t h i s gas by emitted by the t r i g g e r d i s c h a r g e i s the dominant t h a t l e a d s to the  *C(p)  The v a l i d i t y  electrons  mechanism  r e l a t i o n given i n equation  129.  of a few of the statements i n the p r e -  c e d i n g d i s c u s s i o n depend upon the o r d e r o f magnitude o f c e r t a i n quantities.  For example, one q u e s t i o n t h a t i s r e l e v a n t i s ,  what i o n motion e x i s t s i n a spark d i s c h a r g e o f 40 nsec duration?  An o r d e r of magnitude c a l c u l a t i o n w i l l be made.  and Wooding  (1959)  b e l i e v e d t h a t the i n i t i a l  l a s t i n g f o r a time o f about d i s c h a r g e i n argon was  due  100  Porter  peak of r a d i a t i o n  nsec from a low p r e s s u r e spark  to B r e m s s t r a h l u n g .  On the b a s i s  of t h i s statement i t i s not unreasonable to conclude t h a t a v o l t a g e t h a t i s an a p p r e c i a b l e f r a c t i o n o f the s u p p l y v o l t a g e e x i s t s a c r o s s the t r i g g e r d i s c h a r g e and t h a t the d i s c h a r g e i s  - 147 not c o l l i s i o n dominated.  The  -  l a t t e r assumption i s not  j u s t i f i e d because the t r i g g e r d i s c h a r g e w i l l evaporate  fully  t r a c k over  some of the s u r f a c e of the p o l y e t h y l e n e .  and  It will  be assumed t h a t the t r i g g e r d i s c h a r g e i s r e s i s t i v e and has v o l t a g e waveform t h a t i s the f i r s t  p u l s e of a s i n e wave.  normal d i s t r i b u t i o n waveform would be a c l o s e r  field  justified.  experienced  dimensional  I t i s assumed t h a t the  involved  electric  by the p a r t i c l e s i n the d i s c h a r g e i s one  and homogeneous.  charge q. moving i n the  For a p a r t i c l e  of mass m  ....130  d v where d i s the d i s t a n c e over which the e l e c t r i c Q  i s the peak v a l u e  e i n  Q\4 T  X = —i—  :  -rr _Sd  s i n TT Y  x = -^p  r —  |  V = 30 kV,  discharge  +1  - COS IT-L  ....133  = 0) = 0, x ( t = 0) = 0.  d = 6.1  acts  ....131  m d T T * L "C  where i t i s assumed t h a t ±(t = X = 40 nsec,  field  of v o l t a g e a c r o s s the t r i g g e r I  X  and  field  E=-j-sinTr-^-  and Y  A  approximation  to the t r u e waveform but the mathematical complexity would not be  a  mm,  and  If t  the motion of an  argon i o n i s c o n s i d e r e d , then ±(t  = 40'nsec) = 30.4  and x ( t = 40 nsec) = 6.1  actual inter-electrode dis-  tance  mm.  The  of the t r i g g e r d i s c h a r g e i s a t l e a s t  3 mm.  cm///sec  The  motion  of i o n s i n the t r i g g e r d i s c h a r g e i s thus a p p r e c i a b l e and i o n motion c o n j e c t u r e d i n F i g 65  realistic.  the  - 148 The be e s t i m a t e d  number o f e l e c t r o n s emitted by the t r i g g e r can from the energy i n the t r i g g e r spark.  c u r r e n t i n the spark was o f the order o f 600 A.  The maximum  The t o t a l num-  ber o f e l e c t r o n s , N , e m i t t e d by t h i s p u l s e o f 40 nsec  duration  must, t h e r e f o r e , have been o f the order o f .4-0  q  /  1  nsec d  t  J © ... 13 4 o where q i s the charge on an e l e c t r o n and i i s the t r i g g e r current. When i i s assumed t o have the shape o f a s i n g l e  13 o n e - h a l f c y c l e o f a s i n e wave, N = 8 x 10 g  electrons.  This  number o f e l e c t r o n s i s the t o t a l number p a s s i n g through the t r i g g e r spark and i s n o t the number e m i t t e d i n t o the d i s c h a r g e chamber. The  energy i n the t r i g g e r spark i s  I  Volt  4 0 n s e C  Pt. -  f *  ... .135 where Y i s the p o t e n t i a l a p p e a r i n g limit i  a c r o s s the spark.  An upper  f o r the v a l u e o f P^. can be e s t i m a t e d by assuming t h a t g  and V have peak v a l u e s o f 600 A and 32,000 V r e s p e c t i v e l y  and  t h a t the waveshape o f both i and V i s t h a t o f a s i n g l e  half-cycle  o f a s i n e wave.  Then, P, u  The  = 0.-3 J» S  number o f e l e c t r o n s t h a t can be emitted  by the  t r i g g e r p i n a t the c e s s a t i o n o f a n e g a t i v e t r i g g e r p u l s e space charge l i m i t s f u r t h e r e m i s s i o n i s o f i n t e r e s t .  before  Prom the  geometry o f the main s w i t c h i t can be i n f e r r e d t h a t the capac i t y between the t r i g g e r p i n and the cathode o f .the main s w i t c h i s about 1.5 p f .  I f i t i s assumed t h a t none o f the e l e c t r i c  - 149 field  due  -  to the v o l t a g e a c r o s s the main gap  i s present at  the t r i g g e r p i n , then the number of e l e c t r o n s t h a t can  be  emitted by the t r i g g e r p i n b e f o r e a p o t e n t i a l of say +1 appears gap  on the p i n w i t h r e s p e c t to the cathode  i s c/q or 0.9  x 10'  electrons.  The  of the main  one v o l t  p o t e n t i a l then s e t up would be s u f f i c i e n t  volt  of r e t a r d i n g  to prevent  further  e m i s s i o n of e l e c t r o n s from the t r i g g e r p i n . An upper l i m i t  f o r the number of e l e c t r o n s t h a t can  be e m i t t e d by the cathode a positive  a t the c e s s a t i o n of  t r i g g e r p u l s e can be e s t i m a t e d from  the t r i g g e r spark. ted  of the main gap  the energy  I f i t i s assumed t h a t every e l e c t r o n  c o o l s the a r e a of e m i s s i o n by 2 ev, then an energy  in emit-  of  0.3J  17 could r e s u l t charge  i n the e m i s s i o n of 9 x 10  on the cathode  of the main gap  e l e c t r o n s would not a f f e c t of  electrons. due  to e m i s s i o n of  the e m i s s i o n r a t e a t the c e s s a t i o n  a p o s i t i v e t r i g g e r p u l s e because the a c c e l e r a t i n g  a c r o s s the main gap charge  t h a t might be The  127.  The  Space  field  i s f a r l a r g e r than any p o s s i b l e space generated.  Z (p) curve f o r h e l i u m does not obey e q u a t i o n  suggested  r e a s o n i s t h a t the p r o c e s s e s l e a d i n g to  breakdown d i f f e r from those f o r argon. The  inductance  of the low p r e s s u r e s w i t c h has  s t e a d y - s t a t e and a t i m e - v a r y i n g component.  The  time-varying  component i s d i s c u s s e d i n the p r e c e d i n g Appendix. state inductance  The  of the main low p r e s s u r e s w i t c h was  e x p e r i m e n t a l l y by o b s e r v i n g the p e r i o d of  both a  steadydetermined  a 500  V triggered  d i s c h a r g e of the bank i n t o an o p e n - a i r spark gap  inserted i n  -150p l a c e o f the d r i v e r o f the shock tube. s p a c i n g o f the o p e n - a i r  The i n t e r - e l e c t r o d e  gap was s e t so t h a t breakdown  when 500 V was a p p l i e d .  The main low p r e s s u r e  removed from the c i r c u i t  and a l e n g t h o f c o p l a n a r  led  i n i t s place.  and  the p e r i o d o f the f r e e - r u n n i n g d i s c h a r g e  change i n c i r c u i t low  pressure  s w i t c h was then  inductance  was the i n d u c t a n c e  s w i t c h and had a v a l u e  planar in.  The  o f the main  o f 4.0 nH.  inductance  o f the main s w i t c h can The t o t a l  o f the s w i t c h i s the sum o f t h a t due to the three  i n d i c a t e d i n F i g 66.  estimated  instal-  observed.  a l s o be computed from the geometry o f the s w i t c h .  regions  lead  The bank p o t e n t i a l was then r a i s e d to 500 V  The s t e a d y - s t a t e  inductance  occurred  The i n d u c t a n c e  of region a i s  f o r c u r r e n t f l o w i n g on the i n n e r s u r f a c e s o f co-  conductors 4 i n . l o n g  separation  (t).  (&), 6 i n . wide (w) and o f 1/16  Thus I = JU ~ -t 0  a  of r e g i o n b i s a p p r o x i m a t e l y  conductors  Thus L^= 1.6 nH.  region c i s approximately  1.3 nH.  The  .10 i n . a p a r t ,  The i n d u c t a n c e  t h a t due to the i n d u c t a n c e  two c y l i n d e r s o f l e n g t h 5/16 i n . , and i n n e r and outer of 1/4 i n . and 1 i n . Thus L = 1.1 nH. c  of the main s w i t c h ,  inductance  t h a t due to c u r r e n t f l o w i n g on  the i n n e r s u r f a c e s o f c o p l a n a r l o n g and 6 i n . wide.  -  The t o t a l  of  between radii  inductance  c a l c u l a t e d from s w i t c h dimensions, i s  4.0 nH, the same v a l u e  as observed  experimentally.  3 in.  Pig  66. S u b d i v i s i o n o f the Main S w i t c h i n t o Regions f o r the Purpose o f C a l c u l a t i n g the Inductance. The  inductance  o f the crowbar s w i t c h can be i n f e r r e d  from the r e s u l t s o f the c a l c u l a t i o n s i n the p r e c e d i n g graph.  The crowbar s w i t c h i s thus a t h r e e - t e r m i n a l d e v i c e  t h a t has the i n d u c t a n c e s  o  para-  ^RT^-  shown i n P i g 67.  °  r^Tpv—f—HTfi^  o  I.I  a) B e f o r e  firing  Pig The  67. Inductance  b) A f t e r o f Crowbar  o  nH  firing  Switch.  r e s i s t a n c e o f the low p r e s s u r e  a s t e a d y - s t a t e and a t i m e - v a r y i n g component.  s w i t c h has both The s t e a d y - s t a t e  v a l u e o f the r e s i s t a n c e o f the main s w i t c h c o u l d be computed from the damping o f the d i s c h a r g e c u r r e n t , p r o v i d e d t h a t the r e s i s t a n c e o f the remainder o f the c i r c u i t  was known.  The time-  - 152 varying  -  component of the r e s i s t a n c e of the  the r i s e  switch a f f e c t e d  time of d l / d t (see a l s o Andreev and  Both energy and  Vanyukov 1962),  time are i n v o l v e d i n the p r o c e s s e s  i z a t i o n of the gas  i n the  p a r t i c l e s from the  e l e c t r o d e s and motion of i o n s i n the  charge.  The  discharge  of:  chamber, e v a p o r a t i o n  switch.  The  e l e c t r o n and  i o n bombardment of the  can move an a p p r e c i a b l e  experimental  electrodes  distance  ^50  i s t h a t the minimum v a l u e nsec, i s compatible w i t h  gap.. with  of t  spacing  across  the  d, then the  transit  A f t e r the ed i n the p r e c e d i n g connected i n t o the  f o r the  the in  these The  existence  been observed, time a c r o s s  a parallel-plate  t r a n s i t time i s l^rf  i o n , q the  the p l a t e s .  then the  I t was  before  i n the a r c .  ion transit  d  charge on the i o n and  Thus i f an argon i o n i s  to be a c c e l e r a t e d by a p o t e n t i a l of 20 kY gap,  contribute  can r e s u l t  t h a t has  c  I f an i o n i s a c c e l e r a t e d a c r o s s  the mass of the tial  initially  evidence t h a t does suggest t h a t the p o s i t i o n i n g  time of the i o n s i s the major e x p l a n a t i o n c  dis-  Some time i s r e q u i r e d b e f o r e  c o n t r i b u t i o n of s u f f i c i e n t p a r t i c l e s and  particles  of t  density  e l e c t r o d e s must, t h e r e f o r e ,  p a r t i c l e s to the d i s c h a r g e .  the  of  i o n d e n s i t y r e q u i r e d to e s t a b l i s h n e u t r a l i t y i n  the plasma column i s l a r g e r than the gas i n the  ion-  across  the  gap  where m i s V the  poten-  considered a  5/16  in.  time i s 53 n s e c .  c o m p l e t i o n of the 400  t e s t f i r i n g s mention-  Appendix, the d r i v e r of a shock tube circuit  found t h a t the  -  i n place  crowbar s w i t c h  bank p o t e n t i a l appeared a c r o s s  it.  was  of the i n d u c t i v e l o a d . broke down as soon as T h i s breakdown was  not  - 153  -  unexpected - see the l a s t paragraph  of the t e x t In the  i n g Appendix - because the p o t e n t i a l a p p e a r i n g crowbar s w i t c h was s w i t c h was  the  of the o p p o s i t e p o l a r i t y f o r which the  designed.  No  ever, been encountered the shock tube.  across  crowbar breakdown problems had,  until  how-  the switches were connected  to  I n v e r s i o n of the crowbar s w i t c h and a change  i n the l o c a t i o n of the t r i g g e r components s o l v e d t h i s down problem.  preced-  This redesigned  break-  crowbar s w i t c h i s t h a t shown  i n F i g 5• A second s e t of two  switches  s i m i l a r to those  i n F i g 5 has been i n s t a l l e d by Whelan* on another magnetic shock tube. a c i t y of 450 / I F and  The  electro-  c a p a c i t o r bank employed has  a cap-  a maximum v o l t a g e r a t i n g of 5 kV.  switches have operated  s a t i s f a c t o r i l y a t e n e r g i e s up  The  to 4  kff-' even though the p e r i o d of the d i s c h a r g e i s 32//sec.  The  !  l u c i t e has needed c l e a n i n g twice d u r i n g the l a s t  500  I n c o n c l u s i o n i t can be s t a t e d t h a t the low s w i t c h t h a t has  been developed  on an e l e c t r o m a g n e t i c pressure  shock tube.  spark ggp  s w i t c h but has  i n s u l a t i o n has  to be  pressure  As a main s w i t c h , the  two  low  the more w i d e l y disadvantages.  They are t h a t p r e i g n i t i o n does occur o c c a s i o n a l l y and the l u c i t e  shots.  i s an e x c e l l e n t crowbar s w i t c h  s w i t c h o f f e r s some advantages over  used o p e n - a i r  shown  c l e a n e d every few  that  hundred  firings.  *The author i s g r a t e f u l f o r r e c e i v i n g t h i s i n f o r m a t i o n from P.J. Whelan, P h y s i c s Dept., U n i v e r s i t y of B r i t i s h Columbia.  - 154 -  APPENDIX THEORY POP  The  E  THE ERUPTIVE INSTABILITY '  equations of motion f o r the e r u p t i v e  instability  suggested i n Chapter I I I , S e c t i o n 1 are d e r i v e d , on the b a s i s of a s i m p l i f i e d model,  i n t h i s Appendix.  The motion of a  c y l i n d r i c a l p l a s m o i d a c r o s s a d i s c h a r g e column i s c o n s i d e r e d ( P i g 68)'.  P i g 68. Suggested P l a s m o i d Motion t h a t R e s u l t s i n E r u p t i v e I n s t a b i l i t y o f D i s c h a r g e Column. The photographs shown i n P i g 12c and  j indicate  that the r a d i u s of the c y l i n d r i c a l p l a s m o i d i s of the o r d e r of 3 mm.  These photographs a l s o i n d i c a t e t h a t the p l a s m o i d  has a v e l o c i t y , r e l a t i v e to the d i s c h a r g e column,,  of about  3 cm/«sec.  The magnetic Reynold's number f o r t h i s  this radial  dimension and an assumed v a l u e of c o n d u c t i v i t y  of 10^ mho/m i s 1.2.  The p l a s m o i d thus t r a n s p o r t s  magnetic f l u x . w i t h i n i t s e l f as i t moves a c r o s s •column,  I n o r d e r to s i m p l i f y  velocity,  appreciable  the d i s c h a r g e  the f o l l o w i n g c a l c u l a t i o n ; , it.  - 155 will  be assumed t h a t the leakage  plasmoid  of magnetic  f l u x from  the  is negligible. The  motion of the plasmoid w h i l e  i t i s being  accel-  e r a t e d away from the i n s i d e c o r n e r of the d i s c h a r g e w i l l be c o n s i d e r e d . be d i f f i c u l t of  The  r e a s o n f o r t h i s o m i s s i o n i s t h a t i t would  to determine a r e a l i s t i c  v a l u e f o r the magnitude  the magnetic i n d u c t i o n f i e l d i n s i d e the cusp a t t h i s  corner.  inside  T h i s magnetic i n d u c t i o n f i e l d would i n t e r a c t w i t h  c u r r e n t d e n s i t y i n the d i s c h a r g e to compress and ate,  not  i n a diagonal d i r e c t i o n  (see P i g 6 8 ) ,  then a c c e l e r -  the p o r t i o n of the  d i s c h a r g e column t h a t i s near the p o i n t of the cusp. and C l a r k e  the  Rose  (1961) have c o n s i d e r e d an a c c e l e r a t i o n mechanism  t h a t i s s i m i l a r to t h a t which i s proposed i n the p r e s e n t work. The motion of the plasmoid  d u r i n g i t s subsequent motion  the d i s c h a r g e  column w i l l  now  be c o n s i d e r e d .  the plasmoid,  once a c c e l e r a t i o n has  ceased,  The  d i s t a n c e i n t o the d i s c h a r g e down by  column.  passed The  plasmoid  an a p p r e c i a b l e  plasmoid  i s slowed  e l e c t r o m a g n e t i c f o r c e s as i t moves subsequently  the d i a g o n a l direction. n e g l e c t e d and  I f f o r c e s due  i f the plasmoid  of  discharge  I t i s assumed t h a t the  a t t a i n s t h i s v e l o c i t y b e f o r e i t has  velocity  measured w i t h  r e s p e c t to a c o o r d i n a t e system moving w i t h the column i s d e s i g n a t e d ± ° max  inside  to gas p r e s s u r e  in are  i s assumed to be n e u t r a l and  mass d e n s i t y J> , then the f o r c e s a c t i n g on the plasmoid  volume of plqsmofd where r i s the r a d i u s of the plasmoid,  of  are  .136 L i s the l e n g t h , x i s  - 156  -  the d i a g o n a l c o o r d i n a t e of the c e n t e r of the plasmoid,, the a z i m u t h a l  c u r r e n t d e n s i t y on the s u r f a c e of the  and B, i s the magnetic i n d u c t i o n f i e l d d current.  due  to the  the a z i m u t h a l  plasmoid  defines  when I i s  c u r r e n t on the s u r f a c e of the plasmoid,  lows from e q u a t i o n  136  + AI  = o  ....137  /> (x) , x(t=0) = -W/2  the s o l u t i o n to e q u a t i o n X  =  i t fol-  that  L/>'i When I * L ( x ) ,  is  discharge  When B^ v a r i e s l i n e a r l y w i t h x (B^ = - Ax  the c o n s t a n t A) i n s i d e the d i s c h a r g e column, and  J  a  I - LA(x + W/2)//^o  137 i s Sinojt  X  and  - W/2  ...  .138  ^^^o  *«o•  "1 3 9  where  The  dimension The  of  W i s the d i a g o n a l w i d t h  of the d i s c h a r g e  c r i t e r i o n f o r the escape of the plasmoid  out  the d i s c h a r g e column i s then X  It  ~ "  i s of i n t e r e s t  t h a t the plasmoid potential well.  ••••  >  t h a t the a n a l y s i s has  The  does not escape i f i t has  energy.  I'f i t does once escape from  i s no l o n g e r a r e s t o r i n g f o r c e .  The  cause the plasmoid  an the  f o r c e a c t i n g upon  above a n a l y s i s does -  not p r e d i c t the subsequent motion of the plasmoido the e l e c t r o m a g n e t i c  a  plasmoid  d i s c h a r g e column then the e l e c t r o m a g n e t i c  U 0  indicated  i s c o n f i n e d i n s i d e what appears to he  insufficient kinetic  it  column.  Actually,  f o r c e i s i n such a d i r e c t i o n as to to move f u r t h e r from the d i s c h a r g e  then column.  The  157 -  d i s c h a r g e shown i n P i g 1 2 a ) t o p) would have  v a l u e s o f A * 3 Wb/m , W * 0.006 m and J> « 0.1 kg/m „ 3  c r i t e r i o n f o r escape 140,  5  o f the plasmoid i s thus from e q u a t i o n  ± ^ > 1.7 cm//tsec. o  The  Such a v a l u e o f i n i t i a l  v e l o c i t y i s not u n r e a s o n a b l e .  plasmoid  I t can be concluded t h a t the  e r u p t i v e i n s t a b i l i t y mechanism c o u l d account  f o r the observed  p r o t u b e r a n c e s a t the f r o n t o f the plasma. In the p r e c e d i n g a n a l y s i s i t has been assumed the plasmoid l o s e s no magnetic d i s c h a r g e column. preciable, relaxed.  that  f l u x as i t moves a c r o s s the  I f the d i f f u s i o n o f magnetic  f l u x i s ap-  the c r i t e r i o n expressed by e q u a t i o n 140 can be A lower value o f x „ than predicted, by t h i s max  equation  e  would then a l l o w the plasmoid to escape column.  from the d i s c h a r g e  -  158 -  APPENDIX  F  ANALYSIS OF THE EXPERIMENTAL DATA OBTAINED WITH THE MHD GENERATOR EMPLOYING 'TDTDUCrTIYE POWER TRANSFER  The  curves shown i n F i g 50 suggest t h a t the con-  d u c t i v i t y o f the plasma b e i n g e q u a t i o n 112. cates  i s n o t d e s c r i b e d by  The overshoot o f the observed s i g n a l s  t h a t the c o n d u c t i v i t y o f the plasma i s q u i t e  o-(f) = cr*  closely  $ >0  e  0"(f) = 0  , £< o  ....141  c o n d u c t i v i t y f u n c t i o n has been p r e v i o u s l y  Cormack  indi-  „ 1  d e s c r i b e d by  This  studied  (1960).  c o n s i d e r e d by  I t has s i n c e been found t h a t the n u m e r i c a l  i n t e g r a t i o n b e l i e v e d t o be n e c e s s a r y by Cormack was n o t r e q u i r e d but t h a t the v o l t a g e  c o u l d be expressed i n c l o s e d form  as: V  (t)  =  U U « 3 > * V C P  ...  y(t)  .142 where  fit)' This  r j n _ Ut 2  e  20  e q u a t i o n i s , o f course, o n l y v a l i d i f  expression  for  ( t ) f o r any v a l u e  —i—»» 111 .  143 The  o f R^ i s found from equa-  t i o n 111 t o be  Nxl  dt 44  - 159 Equation  144  cannot  -  be s o l v e d by a n a l y t i c a l methods.,  A  solu-  t i o n by n u m e r i c a l methods would not c o n t r i b u t e g r e a t l y to the aim of Chapter  IV. S e c t i o n 3 - which was  dynamic p r o p e r t i e s of the The  form  shape as the  electro-  generator.  of the f u n c t i o n Y'(t) i n equation  v a r i o u s v a l u e s of {3 i s shown i n P i g 69. the E j = 200A  to p r e s e n t the  curve i n P i g 50,  The  143 f o r  observed  waveform?  i s q u i t e c l o s e l y of the same  |3 = 4b curve i n P i g 69»  The maximum c o n d u c t i v i t y  of the plasma i s g i v e n by  where TP, i s the maximum value of V ("t) and V v a l u e of v o l t a g e observed.  Thus f o r U - u  1  i s the peak - 2 x 10^m/sec , ;  8 0.82,  then 0* = 1 .0 x  p  mhos/m.  The v a l u e f o r the c o n d u c t i v i t y of the plasma (f  page 111,  = 7.5  V, I = 10 A, X=  mhos/m, V  i s thus g i v e n as 10^ mhos/m.  10  4  on  - 160 -  .8  .6  .4  .2  0 e=b-\ g=2b  -.2  -.4  - 2 - 1  0  \  \ >  —V—  1  \  *\  2  u  t  A  3  P i g 69. 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