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Investigation of the characteristics of a pulsed mercury arc Campbell, Hugh Daniel 1965

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AN INVESTIGATION OP THE CHARACTERISTICS OP A PULSED MERCURY ARC  by HUGH DANIEL CAMPBELL B.Sc,  University of B r i t i s h Columbia, 1962  A THESIS SUBMITTED IN PARTIAL FULFILMENT OP THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA March, 1965  In the  requirements  British  mission  for  Columbia, I  available  for  for  an  reference  be  without  of my  Department  this  written  of  that  and  by  It  thesis  the  study,  the  of  for  Head  financial  permission*  19k  Columbia,  the  Library I  this  "^p-fcj Y o i ^ C ^  IQj  in partial  degree at  of  i s understood  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada Date  thesis  advanced  copying  granted  representatives.-  cation  this  agree  extensive  p u r p o s e s may his  presenting  thesis my  make i t  agree for  that  or  c o p y i n g or  shall  not  of  of • freely per-  scholarly  Department  that  gain  University  shall  further  fulfilment  be  by publi-  allowed  ABSTRACT  An test arc  investigation  dischargee  exhibited dicated probably The with was a  V a 1°^  the r e l a t i o n  Although  this  that a  Eg a r c h a s b e e n u n d e r t a k e n t o  of a pulsed  between the voltage the experimental  tendency,  V-I  and c u r r e n t  characteristic  further considerations  the agreement between  theory  o f an  strongly i n -  and experiment  was  coincidence.  Paschen breakdown  simultaneous possible  curve  measurements  t o measure  was d e t e r m i n e d ,  of the current  the average  and t o g e t h e r .  and v o l t a g e , i t  column f i e l d  strength  as  function of current. As  a result  o f an unexpected  namely an i n h e r e n t  motion  form  to obtain  could  combined the  be u s e d  thickness  average  field  ments d^ = J x l O agreement w i t h  feature  of the  of the electrodes,  ^cm, a n d the f i e l d  the voltage  wave-  an a p p r o x i m a t e measurement- o f t h e  o f t h e anode and c a t h o d e strength  apparatus,  i n these =  regions  2.4x10^  emission  falls  volt/cm  theory.  d^,, a n d a l s o The  measure-  appear  t o be i n  ACKNOWLEDGEMENT  I for of  sincere  thanks  t o E r . B. A h l b o r n  h i s encouragement and guidance  during  the f i n a l  to offer  am a l s o  and i n t h e w r i t i n g  grateful  the experiment  script  and o f f e r i n g  The  assistance  maintenance f6r  like  the experiment I  ing  would  of the thesis.  t o D r . P » R . Smy f o r h i s w o r k  a n d t o D r . A..J. B a r n a r d  i n initiat  f o r r e a d i n g t h e manu  helpful suggestions. o f Mr. J.Turner  of the electronic  glassblowing  completion  a n d M r . W„ R a t z l a f f f o r  equipment,  of the apparatus  and o f Mr. J . Lees  i sgratefully  acknowledged.  - i i i TABLE OP  CONTENTS  ABSTRACT  i i  L I S T OP ILLUSTRATIONS  v  ACKNOWLEDGEMENT  vi  INTRODUCTION  1  CHAPTER 1  3  - GENERAL FEATURES OF THE ELECTRIC ARC  1.1  Experimental  1.2  Theoretical  Observations  3  Considerations  6  CHAPTER 2 - APPARATUS AND EXPERIMENTAL DETAILS  10  2.1  Design  2.2  Electrical  2.5  Paschen Curve  15  2.4  Two T y p e s o f A r c T e r m i n a t i o n  17  Features  (i) (ii) (iii)  2.5  12  Measurements  Extinction  18  Shutting  21  Extinction  (iv)  10  of Apparatus  Independent Evidence  Relative  Velocity  25  versus Shutting  27  f o r the Motion  o f the E l e c t r o d e s  •'  27  3 - GENERAL MEASUREMENTS OBTAINED  32  3.1  E l e c t r o d e F a l l Regions  32  3.2  Column F i e l d  34  3.3  Voltage  CHAPTER  (i) (ii) (iii)  Strength  Current  Characteristic  36  Reduced C h a r a c t e r i s t i c  36  Direct  38  Summary  Characteristic of Both  Approaches  38  -ivCHAPTER 4 - SPOT CONDUCTION MODEL OP THE ARC 4.1  Development o f t h e Model (i) (ii) (iii)  4.2  41 41  Spot V o l t a g e  41  Plasma Voltage  42  Total Voltage  43  Discussion  44  CONCLUDING REMARKS  46  APPENDICES A - LCR S e r i e s C i r c u i t  47  B - Graphical Examination of E x t i n c t i o n  50  BIBLIOGRAPHY  52  ~v=  LIST OP ILLUSTRATIONS Figure  1  1  S h o c k Tube A r r a n g e m e n t  2  Voltage  3  Potential  4  Determination  5  Apparatus  6  Arrangement of E l e c t r i c a l  7  Discharge  Circuit  (schematic)  13  8  Schematic  Circuit  of R  14  9  Paschen Curve  16  10  Extinction  Mechanism  19  11  Extinction  Time Dependence  12  Arc Termination  13  Electromagnetic Force  14  S h u t t i n g Time Dependence  15  Extinction  16  Determination  17  Voltage  18  Column F i e l d  19  Reduced V-I C h a r a c t e r i s t i c  37  20  Voltage  39  21  Direct  22  LCR  23  C u r r e n t Waveform  Current  Variation  Between E l e c t r o d e s  Containing Mercury Electrodes  on V  11 13  Circuit  / 20  Q  22  by S h u t t i n g  23 on V  24  Q  26  or Shutting of Electrode V e l o c i t y  S t r e n g t h Dependence  Oscillogram  30 33  and C u r r e n t Waveforms  Current  4a 5  o f V^  on C u r r e n t  35  39  V-I C h a r a c t e r i s t i c  47  Series Circuit  48  f 24  4&  Characteristic  G r a p h i c a l I n t e g r a t i o n o f 1^  dt +  R  51  -1-  INTRODUCTION The to  work d e s c r i b e d  verify  the  in this  thesis started in.an  relation  voltage  V  and  r  a  V between, the  current  4  I  i n an  relation  R  had  t o be  valid  rents  passing  plasma.  1  the  S h o c k Tube Arrangement  In  data,  sary spot  on-the  liarity also  of  cal  shock  In  V-I  condensor  cathode  felt  a useful  tool  this  spots this  shown  Smy  (1963)  through a  order and  are  of  retain  been  The  pulse  current  current  found  small  tube arc.  physics,  was  short  time  supplied  limiting  I f so, as  arc  the  resistor  this  neces-  pecu-  expression  no  might  this  analytic known,  the  past  cen-  experiment  feature  by  heated  conducting  i s yet  pulsed  cur-  to i n t e r p r e t  extensively during  the  shock  a w e l l known  an  a  for  to derive  also  shock  relation,  which would  a  p r e v i o u s l y been  i t had  i n arc  studied  test  through  This  over a l l c h a r a c t e r i s t i c  have been to  that  discharge.  assume a  characteristic  f o r the  order  tube.  of  the  discharge  i s series  of  with  arc. It  to  arcs  designed  the  the  expression  tury.  a  to  As  i t was  w o u l d be  although  was  arcs  apply  equation  cathode.  to  arc  by  expression, Figure  attempt  was  found  that  interpret different  Andy as  an  examination  a  general  features of  knowledge of  the  Smy's t h e o r y  of  arcs  experimental would  was  required  results.  necessarily require  comparison with  1 was i n c l u d e d  ter of  accepted  arc  i n this  aspects thesis  of arcs,  to present  the following a brief  experimental  results  and t h e o r e t i c a l  Chapter 2 discusses  details  of the apparatus,  Ghap=  summary  concepts 6f  physics.  the an  theoretical  different  measuring  unexpected motion  and  a mechanism  techniques  employed.  of the electrodes  In  as well  particular,  i s examined  i s suggested which describes  as  i n detail,  the origin  of  this  motion. 3 goes  Chapter were  obtained  on t o d i s c u s s  i n this  characteristic,  project.  the E co  umn  field  strength),  the  average  field  and an order  strength  i s not very  most  significant  result  Chapter 4 contains  what  arc.  extent  precise',  of this  x  a detailed  the results  obtained  measurement o f  regions.  Although  this  a p p e a r t o be t h e  (1965)0  examination  The o b j e c t  which  (where E i s the col= co .  i twould  thesis  results  the over a l l ?-I  of magnitude  (1963).  b y Smy  include  i n the f a l l  measurement  to  These  •=! c h a r a c t e r i s t i c <  last  developed  t h e more g e n e r a l  of this b y Smy  of the theory  section  could  i s t o see  apply  t o kn  /  "3-  '  •  /  CHAPTER 1 - GENERAL FEATURES OF THE ELECTRIC ARC Electric century  carriers,  ficult  Difficulties  result  present  cepted 1.1  separate  processes  a r i s e when a n a l y z i n g  of  manner, i t i s d i f -  i n t o a unified  experimental  data,  arcs  As a  several different  have been p r o p o s e d .  some o f t h e e x p e r i m e n t a l l y also discuss  theory.  as the ex-  parameters i s o f t e n q u e s t i o n a b l e .  concerning  and w i l l  explained.  This  models  chapter  observed c h a r a c t e r i s t i c s  some o f t h e p r e s e n t l y w e l l a c -  theories.  EXPERIMENTAL OBSERVATIONS, The  all  these  o f these problems o f complexity,  of arcs,  a r e many  o r e n e r g y d i s s i p a t i o n by r a d i a t i o n and h e a t  of relevant  theories  the past  such as p r o d u c t i o n  c a n be u n d e r s t o o d i n an i s o l a t e d  t o combine  traction  there  o f an a r c w h i c h a r e y e t t o be s a t i s f a c t o r i l y  conductions  will  extensively during  many o f t h e i n d i v i d u a l p r o c e s s e s  charge  and  studied  and so i t might appear s u r p r i s i n g t h a t  features  While  a r c s have t e e n  most i m p o r t a n t  current-voltage  schematically linear  characteristic  ohmic r e s i s t o r .  very  r a p i d l y t o some  again  2  falls  A typical  196l).  (Goldman,  i s quite  different  minimum  below V  voltage  values  the a r c w i l l  a r c i s the over c a s e i s shown  The r e s u l t a n t  from  F o r lower c u r r e n t s ,  f o r increasing higher  voltage  o f the e l e c t r i c  characteristic.  i n Figure  dard  feature  that  of a  non-  stan-  the a r c v o l t a g e  V^, and t h e n  of current. extinguish  slowly  falls rises  I f the a p p l i e d - as a w e l l  known  m e x a m p l e , one c a n e x t i n g u i s h apart. the  an a r c by d r a w i n g the e l e c t r o d e s  I t c a n a l s o be s e e n t h a t  same g e n e r a l  behavior,  arcs  the longer  of d i f f e r e n t arcs  lengths  requiring a  have  higher  -4-= applied  voltage  The a  potential  typical  ferent that  f o ra particular variation  a r ci sgiven  values  there  (with net voltage  between t h e anode and cathode o f 3 f o r two d i f -  schematically i nFigure  of current  are three  current.  196l)»  (Eeker,  main  regions  This  o f an a r c j  d r o p V )i t h e l o n g  figure indicates the cathode  region  c e n t r a l column r e g i o n  (V  C and  t h e anode r e g i o n The  trode  (V ).  classified  material.  according  o r carbon electrodes  very  different  mercury  this  The the  o r copper  cathode  cathode vapour ments have  (high b o i l i n g those  (lowboiling  solely, with  henceforth  same o r d e r  to theboiling  p r o p e r t i e s from  thesis deals  presented  theelectrode  will  fall  voltage  point metals),  point metal  shown t h a t V  tung-  have  arcs  such  electrodes).  As  a r ca l l d e t a i l s  to this  class of arcs.  (V ) o f a n a r c i s g e n e r a l l y o f  o f magnitude as t h e i o n i z a t i o n (typically  of the elec-  o f c o l d cathode  only  are fre-  formed w i t h  a c o l d cathode  apply  regions  point  Thermal a r c s , such as those  sten  as  CO  problems a s s o c i a t e d w i t h  quently  ),  around  potential  10 v o l t s ? .Brown,'196l) .  i srelatively  independent  o f t h e .. Experi-  of the eur-  c rent  flow  cepted  (Gerthsen  that V  acts  and Schulz, over  1955)»  a distance  and i t i s g e n e r a l l y a c -  comparable w i t h  t h e mean  c free  path  of the surrounding  ment o f t h i s determine  First, tions proach  h a s b e e n made.  values  gas, although Two t e c h n i q u e s  f o rthe f a l l ^  approximate  requires that  values  have been used t o  v o l t a g e s , V , Y , and V„ = V + V . C £1 X C 3,  extrapolating the linear gives  no s u c c e s s f u l measure-  region for V  the potential  c  of Figure and V . a  variation  3 i n both  direc-  However t h i s a p across  t h e column  I  10  10°  Figure  2  7  —i  I (amp)  10  1  io  3  1  Voltage-Current C h a r a c t e r i s t i c (schematic) o f an A r c f o r two e l e c t r o d e separations w i t h d,> d . 0  Figure  3  P o t e n t i a l V a r i a t i o n between (schematic)  Electrodes  V cathode f a l l voltage? V anode f a l l voltage5 V , column v o l t a g e drops c a t h o d e fa5S d i s t a n c e § d anode falf distance; d t o t a l e l e c t r o d e separation,. &t  t  9  &  o 9  9  be  determined  experimental  (see task  and t h i s  A second  a n d more d i r e c t the  Vblfaqe so  with  time  >•  slowly  ,  that  together  •' •  .  c a n be measured touching  1955)*  4  approach i st o b r i n g  .  before  difficult  ( H i n r i c h s and  two e l e c t r o d e s  ,,  Figure  i sa  i n v o l v i n g probe measurements  1959)*  Wienecke,  figure 3 again),  (Gerthsen  electrode  just and Schulz  By taking several  different  .  trials materials,  n i possible t o extract values for V and V from t h e measureS  Determination of V  a  c  f  ments o f Y^, second  technique  was u s e d  of magnitude  value  d„  (see  = d  + d  t h e anode  thode  fall  voltage  fall  (V  current  luminous  A  i s much s m a l l e r  have  i sconcentrated  known a s t h e c a t h o d e  cordingly.  improved  ously, .then t h e current calculated. tained  Probably  b y Froome  duration The  the value  I f the current  arcs  he f o u n d  most v i s i b l e  and spot  density  obtained area  Using  that part  order  b y b o t h methan  the c a -  1954), and  into  spot. that  a  small,  Many  attempts  as measuring  h a s gone down a c -  a r e measured  j i n t h e cathode  t h e most r e l i a b l e  (l950).  an  f o r our purposes.  b e e n made t o m e a s u r e A , a n d i t a p p e a r s  techniques  of this  distances,  = v /l0$ Bauer and Schulz,  a t the cathode area  t o obtain  I t h a s been found  voltage  g e n e r a l l y be n e g l e c t e d  highly have  3=l)»  Section  that  The  experiment  f o r t h e sum o f t h e f a l l  thods  will  i nthis  A variation  spot  simultanec a n be  measurements were ob-  k e r r c e l l photography 6 2 j =•• 10 amp/cm .  on s h o r t  o f t h e a r ci s t h e a r c column,  which  serves The  as  a  current  important  fully The  properties  examined  by  B  by  their  hence  These  3s  be  E  between  region  can  include  the  rate  determined  E  column  by  Q  many o r d e r s  length, E  probe the  the  electrical  and  of  the  success-  techniques,,  related to  radial  over  column f i e l d  the  length  tem-  thermal strength  energy d i s s i p a t i o n .  =  CO d~~  of  As  the  column,  co d  1  0  CO d^<£d  been v e r y  cathode  by  _ co  as  have  anode and  be  i s constant  c q  the  a n a l y s i s and  strongly affect  c o n t r o l on  can  this  interest  which  C 0 shown i n F i g u r e and  of  profile.  conductivities,  of  path  spectroscopic  main f e a t u r e s  perature  conducting  of magnitude.  Although  i s h i g h l y dependent upon  the  independent magnitude  of  of  G0 the  current.  dence have The  Most experiments which have measured  involved  the  use  experiment described  technique  of  probes  in this  to determine E  i n the  lower  thesis describes  ( i ) i n the  high  current  this  depen-  current an  ranges  approximate  range.  0-0 1.2  THEORETICAL COBSIDERATIONS The  theoretical  same m a n n e r a s servations. the  fall  again,  the  :  to  (in particular  the  problems  the  the  behavior  be  of  classified  the  fall  region  ob-  column  region).  have been e n c o u n t e r e d  electrode  the  experimental  e i t h e r the  cathode  in  rather  or And  in  than  region.  basic  determine  can  theories describe  most f o r m i d a b l e  column  The  of arcs  u s e d when c o n s i d e r i n g  M o d e l s and  regions  explaining in the  was  aspects  problem to  the  be  solved  i n the  mechanism r e s p o n s i b l e  electrode  region  f o r e x t r a c t i o n of  i s  elec-  =7trona  o u to f t h e cathode.  emission of very metals for  by Richardson high  boiling  points.  thermal  have  been  sion  due t o m e t a s t a b l e  p u tf o r t h ,  binations of  h a s been  i t i simpossible  appreciable  The o r i g i n a l  shown t o be a p p l i c a b l e t o m e t a l s  However,  temperatures  emission  t o occur.  atoms  ( v o n Engel<  mechanisms 1951)•  proposals,  satisfactory  important The the at and  features high  cathode  of this  positive  fall  the surface  However  where,  o  accumulation,  Employing Poisson's fall  The discussed.  which  intense  produces  electric  field fall  {(i - Y) [ 18 4- 5) '  a t cathode  -  / a  surface  Yj  free  ...(i)  (volt/cm)  voltage  „ electron current density of — , , , — ., . total current density  density i nthef a l l  region  (amp/cm )  ,f  verification j and Y have  (1951)  field  equation  t o be one mean  ., v = ratio  Wasserab together  t o have been t h e  current  as both  emission  now b e b r i e f l y  i na very  com-  f o r a summary  j = total  experimental  difficult  o rvarious  thefollowing expression,  S  = cathode  o r emis-  thef i e l d  appears  o f t h e cathode  7 5 7 , 1 0 Vc  =  E^ = e l e c t r i c Y.  charge  voltage, results  Mackeown d e r i v e d  1957)»  high  theories  l a r g e number o f w o r k e r s .  o f the cathode.  E-l  Several  (see Ecker  model w i l l  space  assuming the length  path,  The  toa fairly  9  point  sufficiently  such as p h o t o - e l e c t r i c e m i s s i o n ,  m o d e l b y L o n g m u i r a n d Mackeown (1929) most  f o r lowboiling  t o reach  o f two d i f f e r e n t  thedifferent  proposition of thermionic  used  of this  equation  h a sbeen  very  t o be m e a s u r e d .  theFowler  w i t h Mackeown's e q u a t i o n  Nordheim equation  t o show t h a t  (1928)  Y was u n i q u e l y  determined  as a f u n c t i o n of j .  a c u r r e n t d e n s i t y o f the o r d e r produce  appreciable  F o r a Hg cathode o f 1 0 ' amp/cm  emission  field  result  available  of electrons.  6  data  amp/cm  or r e j e c t point  can only  workers,  and hence  show a l o w e r  the field  emission  model f o rt h e case  limit  2  , the  of  and t h e d i f f e r e n t  approaches  vations.  The f i r s t  investigations  (1925)••  Considering  diffusing the  accept  of low b o i l i n g  s t r u c t u r e o f the a r c column has been examined  other,  gases,  general  as w e l l  appear  b y many  t o be i n r e a s o n a b l e  as with experimental were c a r r i e d  out by  obserSchottky  the e l e c t r o n s , i o n s , and n e u t r a l s as  he o b t a i n e d  macroscopic  much more e x t e n s i v e  a mobility  behavior theory  fairly  equation well.  inter-  which  described  Maecker  developed  by c o n s i d e r i n g the energy  balance  the column, electrical  energy  input = energy  lost  by and  Neglecting the radiation E ( i ) i ft h e e l e c t r i c a l co ' v  discharge  equation  radiation.  F o r t h e case t.  of a  cylindrically  w i t h a monatomic g a s ,Maecker found E  this  conduction  term t h i s e q u a t i o n c a n be s o l v e d f o r a n d t h e r m a l c o n d u c t i v i t i e s a r e known  f u n c t i o n s of temperature.  symmetric  and  amp/cm  i ti s n o t p o s s i b l e t o completely  agreement w i t h each  •as  7  metals. The  in  the t h e -  •2  10  a  While .  r e q u i r e s a c u r r e n t d e n s i t y o f 10  experimental  that  was r e q u i r e d t o  i,  oretical  he f o u n d  was f o u n d 1959)•  co  rt  o I *  4  ,  t o agree  surements  (Maecker,  radiation  losses are negligible  that ...(2) '  with  Unfortunately, limits  the experimental  mea-  the condition that  the application  of this  -9equation (see Section 3 * 2 ) . As shown above, some features of the arc are f a i r l y well understood, but i t i s interesting to note that very l i t t l e  suc-  cessful work has been reported on the determination of an anal y t i c a l expression describing the V-I characteristic of the arc. As recently as 1961 empirical curve f i t t i n g was s t i l l being used (Goldman, 196l).  In view of this f a c t , a l l models which  can be used to explain any portion of the c a r a c t e r i s t i c are of interest to the general theory of arcs. In his work on shock-tubes Smy developed an expression for the V-I characteristic of two electrodes immersed i n a shockheated plasma.  Experimental results indicated that i n the high  current range, production of electrons i n the electrode region was probably accomplished by a conducting spot i d e n t i c a l to the ,  cathode spot of an arc.  f  Using Mackeown's f i e l d emission equation  he found V  a  I° ,  . . . ( 3 )  4  which i s similar to the result obtained by Maecker. I t was f e l t that the s i m i l a r i t i e s , both i n assumptions used and results obtained, between this model and accepted ideas on arcs were s u f f i c i e n t to warrant experimental in the high current range.  examination  The apparatus and experimental tech-  niques used i n this experiment w i l l now be discussed i n the f o l lowing chapter.  -10CHAPTER 2 - APPARATUS AND EXPERIMENTAL DETAILS 2.1  DESIGN FEATURES OF APPARATUS The  apparatus designed 5.  shown i n F i g u r e (2.5  pool ode wire  (.1  glass  to allow  piece  The c a t h o d e  raising  i s that  t o a second p o o l  a fairly  easily.  pool.  over s o l i d  to flow  down t h e t u b e .  cleaned  took p l a c e .  by l o w e r i n g  surface  This  before  could that  also  easily  the lower  i n the tygoh tubing.  A l l of  t o t h e t u b i n g when P  t o i t s normal p o s i t i o n .  that during  encountered while  the course  a t i o n was c o n t i n u a l l y c h a n g i n g . will  on  portion of  a c l e a n anode  v e s s e l P t o such a l e v e l  serious disadvantage  was t h e f a c t  reproducible  a new s u r f a c e  The l o w e r e l e c t r o d e  Contamination then adhered  was r a i s e d a g a i n  difficulty  ensured  enclosed  metal e l e c -  surfaces with  A f t e r each discharge  This  s e n s i t i v e method  of the cathode  o f u s i n g Hg e l e c t r o d e s  P by  i n t o the s e -  u p p e r e l e c t r o d e was f o r m e d by a l l o w i n g a s m a l l  A  tungsten  the e x t e r n a l  r o d was f i t t e d  to provide  the l e v e l  e l e c t r o d e was c o m p l e t e l y the  A lucite  one c a n e s t a b l i s h c l e a n  each discharge be  of  be i n s e r t e d t o a n y d e s i r e d d e p t h .  or lowering  geometry v e r y  Hg  p o o l was c o n n e c t e d  t h e n be u s e d  One a d v a n t a g e  the  Two p i e c e s  o f t h e Hg e l e c t r o d e s w i t h  o f tygon t u b i n g .  motion could  trodes  cm i n n e r d i a m e t e r ) .  contact  cond p o o l and c o u l d  for  and a l o n g tube f o r s u s p e n d i n g t h e a n -  cm d i a m e t e r and 5 cm l o n g ) were i n s e r t e d t h r o u g h t h e  circuit. a  (.3  the Hg e l e c t r o d e s i s  I t c o n s i s t s of a v e s s e l f o r the cathode  cm d i a m e t e r ) ,  hemisphere  f o r holding  be d i s c u s s e d  using  of a discharge  Complications  i n Sections  2.4  the l i q u i d t h e gap  dealing with  and 2 . 5 »  separthis  -11-  Stob  Dock—s.  Tungsten Rod  (T  -Gas Inlet  Adjustable Plunder Assembly— —  H  3  Vessel P "Tycjon Tubing  Figure 11 Apparatus Containing Mercury Electfodes  \  -122.2  E L E C T R I C A L MEASUREMENTS A general  in  6.  Figure  arrangement The v a l u e s  ponents a r e those the  course  tinously a  large  tic  simple by  of the experiment.  charging  current  RC d e c a y  t o hold  A regulated  i n t h e time  interval  fora l l practical technique  to within  inherent  The  of a  was v e r i f i e d  i n A p p e n d i x A, a n d was  L^ o f t h e c i r c u i t c o u l d  T .  waveform  be  deter-  and measuring t h e time  A s s u m i n g L ^ t o be s m a l l  enough  to satisfy  condition  then T  i srelated  t o L. b y  "V shown i n A p p e n d i x A.  Figure be  schema7»  i nFigure  This  with  3$.  o f maximum  ffl  A  2-70 j u s e c w a s t h a t  purposes.  described  inductance  current  com-  throughout  switch.  c i r c u i t i sgiven  the current  as  circuit  power s u p p l y , c o n -  R^ a n d a m e c h a n i c a l  mined by observing  the  f o r the various  100-1500 v o l t s , w a s u s e d i n s e r i e s  of the discharge  waveform  The  from  resistor  the measuring  found  quoted  w h i c h were most f r e q u e n t l y u s e d  variable  diagram  of the e l e c t r i c a l c i r c u i t i s given  6, a n d a t y p i c a l  approximately The  across  current  the series  R  T T  Using value  the values  o f R and C given i n  o f 2 ^ s e c f o r T , L ^ was f o u n d t o ffl  .75 /ih» was d e t e r m i n e d resistor  R.  by measuring Simultaneously,  the voltage  drop  the voltage  V  A 1 3  AD  between  p o i n t s A and B (see F i g u r e  8 ) was m e a s u r e d .  I n order  -13-  Figure  6  Arrangement  of E l e c t r i c a l  Circuit  Y , v a r i a b l e power s u p p l y ? R^(200 k i l ) , charging resistor5 S, m e c h a n i c a l s w i t c h ? C ( 3 0 jaf), c o n d e n s o r b a n k ? • R.( . 96.fi) , c u r r e n t measuring resistor? A, l e a d t o anode? B lead to cathode. 0  9  Figure  7  Schematic  of Discharge  Circuit  R 9,arc resistance? R contact resistance? L^(o75 / ! h ) 9 i n h e r e n t i n d u c t a n c e o f c i r c u i t ? R, a s s h o w n i n F i g u r e 6. c9  -14to  determine  drop across this arc  part  the the  of  arc  voltage  tungsten  the  i t was  rods  circuit  and  necessary the  Hg,  t o know t h e  as  i s comparable w i t h  the the  voltage  resistance  of  r e s i s t a n c e of  the  itself. The  circuit  used  to measure R  i s shown s c h e m a t i c a l l y  in  •c Figure  8.  This  sistances} the  the  value  of  resistance i s in fact  r e s i s t a n c e of  the  tungsten  a  rods,  sum the  of  three  re-  resistance  of  contact  C : R  Figure  8  Schematic  Circuit  of  R  c  R ( . 9 6 l T ) , S e r i e s R e s i s t o r ? C(30 /if), C a p a c i t o r } S, M e c h a n i c a l S w i t c h } A , T u n g s t e n r o d t o anode5 B, T u n g s t e n r o d t o c a t h o d e } G, H g b u b b l e i n c o n t a c t w i t h Hg p o o l } R , C o n t a c t resistance. between  the  stationary until  tungsten Hg  complete  corresponding scope.  By  several  shots,  cal  between  voltage  b e a m 551  Hg,  the  contact  R  c  Tektronix  the  r e s i s t a n c e of  the  pool  were d i s p l a y e d slope  was  found  the  arc  a d d i t i o n to  and  contacts.  with  measuring the  resistance of In  and  the  was  of  t o be  cold  The  bubble  was  lowered  was  made.  The  current  on  the  the  a  536  Tektronix  resulting  .012X1..  In  and  oscillo-  oscillograms  comparison,  a  for typi-  .05X1.  o s c i l l o s c o p e mentioned  o s c i l l o s c o p e was  used  above,  to measure  a  the  dualvoltage-  -15time  and  2.3  PASCHEN An  the current-time  variable, The  CURVE  important  separation  d .  initiated  standard  cular  The  conditions The  tical  independent  to  use a s m a l l e r  (lOXZ).  of this  This  However,  c u r c u i t used i n Figure  combination  not essential.  accurate this  ensured The  to  to +  most  .005  several mine  t o measure Within  common m e t h o d and  As breakdown shots  As  must  the c o r r e c t  be  should  Q  be  a r e many  curve  given  factors  f o r the  parti-  that this  A  i t was  and  more  a larger  sparking  V  Q  convenient resistor would r e -  c a l i b r a t e d eyepiece  t h e gap  separation  the range  e r r o r of +  which  used  was used  5$«  the Paschen  at a particular This  was  of measurements  the corresponding  voltage.  iden-  s e t of measurements, a l -  phenomena i s s t a t i s t i c a l taken  was  the surfaces  of measuring  observe  measurement  the breakdown v o l t a g e  current  a maximum i n s t r u m e n t  f i xthe distance  voltage.  6.  throughout  mm.  which resulted  a p p l i e d between the  and d  i n this  ensured  though  a cathetometer  conditions.  this  (.002yuf),  capacitor  clean  with  initial  experiment.  of the discharge  was  independent  was q  electrode  n o t an  as t h e r e  t o measure  main r e l a t i v e l y this  i s the  mechanism,  p o t e n t i a l V^  necessary  shown  is  by  r e l a t i o n s h i p between V  electrical  to that  was  Q  determined  Paschen curves.  i t was  d  by a s p a r k i n g  electrostatic  electrodes.  of a r c discharges  experiment  b u t i n s t e a d , was  a r c was  involved,  parameter  In this  Q  when a h i g h  by  relationship.  curve  i s  breakdown i n nature,  distance  approach  to  turned  deterout  -16-  S p a r k b r e a k d o w n i n A r g o n gas ( w i t h Hg vapour) at atmospheric pressure with " h e m i s p h e r e - p l a n e " Hg e l e c t r o d e s .  -17to  be q u i t e  ment.  F o r as the c h a r g i n g  decreased faces. one  difficulty  particular  voltage  these  down,, d i s t a n c e .  a fair  device 2.4  TWO  q  were u s e d .  could  that  a t times  surements were  were  the  two c a s e s  p l e m e n t a r y manner. of  the a r c ,while  of  the a r c . The  energy the  a r c from  found  more  convenient  the corresponding t o determine  break-  the Paschen  could  be c o n t r o l l e d  of the l e v e l  control  different  values  and v o l t a g e  o f R and traces i n -  two p o s s i b l e mechanisms by w h i c h  later  termination that  i t was f e l t lead  the times that  the second  understanding  c a n be v i e w e d  i s essentially  as a r e s u l t  falls  t h e mea-  an i n v e s t i g a t i o n o f t h e  i s essentially  the c a p a c i t o r bank. the condensor  at which  of  particular arc.  of arc termination The f i r s t  the arc  by e i t h e r method  to a better over-all  o p e n - c i r c u i t occurs  from  than  separation.  of the current  phenomena o c c u r r i n g i n t h i s The  sur-  P.  Although  much  two m e c h a n i s m s w o u l d  separation  t o o b t a i n more  b y means  of the experiment  taken,  experi-  TERMINATION  Examination there  t h e gap  The g a p s e p a r a t i o n  vessel  be t e r m i n a t e d .  occurred  9»  i n this  o f t h e two l i q u i d  i t was  observe  of sensitivity  T Y P E S OF ARC the course  dicated  attration  a p p r o a c h was u s e d  inserted into  In V  degree  increased,  f o r a c e r t a i n gap  and then  This  used  made i t i m p o s s i b l e  plotted i n Figure  with  voltage  special conditions  f i xthe v o l t a g e ,  curve  the apparatus  due t o e l e c t r o s t a t i c  This  For to  impractical with  com-  an o p e n - c i r c u i t i n g a  short-circuiting  o f t h e RC d e c a y o f  When t h e v o l t a g e below V  i n a  . nil yi  applied to  (see Figure 2 ) , ° ' '  -18the  arc extinguishes  to t h i s  T h u s we  refe  phenomenon as t h e " E x t i n c t i o n " c a s e .  The s h o r t trodes sible  and t h e c o l u m n p l a s m a d e c a y s .  circuit  come i n t o f o r this  i s the net r e s u l t  contact with  effect  will  when t h e two l i q u i d e l e  each o t h e r .  The mechanism  respon-  be r e f e r r e d t o as t h e " S h u t t i n g "  mechanism, (i)  Extinction Oscillograms  ting At  the e x t i n c t i o n case  o f the v o l t a g e  across  .jumps f r o m V . mm r  tage  shows  suddenly  appears  7 ® w  as a f u n c t i o n o f t i m e .  voltage  where I R i s t h e v o l e  the e x t i n c t i o n .  jump e f f e c t  to Fifure  + I E, e  10.  a b r u p t l y , and  T h i s means t h a t t h e e l e c t r o d e  before  this  Referring  on t h e c o n d e n s o r  t o t h e v a l u e V, . mia  across R just  clearly  tage  present  the e l e c t r o d e s .  indica-  o f t h e a r c a r e shown i n F i g u r e  the e x t i n c t i o n time t , the c u r r e n t ceases  all  u  o f t h e c u r r e n t and v o l t a g e w a v e f o r m  The v o l t a g e  ( f o r the case can determine  of R =  waveform  liT.).  the c a p a c i t o r  A p p l i c a t i o n of K i r c h h o f f ' s  vol-  Law  leads to § -  where,  Q •» c h a r g e I  = —  left  I(R  +  R}  =  a  0,  on c a p a c i t o r a s a f u n c t i o n o f t i m e  = current through  circuit  R = ohmic r e s i s t a n c e o f t h e a r c . a The v o l t a g e  drop across  differential citor  voltage  equation  L. a n d R has been n e g l e c t e d . X c  has t h e s t a n d a r d  solution  This  f o r the capa-  -19-  "fc t i m e (.2 msec/cm) v o l t a g e (5 v o l t / c m ) c u r r e n t (2 amp/cm) voltage current  Figure  10  t i m e (2 voltage current  zero zero  msec/cm) (10 v o l t / c ) ( 1 0 amp/cm) m  at top of oscillograms a t bottom of oscillograms  Extinction  Mechanism  B o t h o s c i l l o g r a m s t a k e n w i t h B. = 5 - f L and V - 600 v o l t s . Lower diagrams a r e schematic waveforms w h i c h a r e n o t drawn t o s c a l e . 0  -20-  1ZOO  800 te  (/traec) 400  \£ Ms) • 800  400 Figure  11  Extinction  Time  Dependence  upon  V  E x p e r i m e n t a l V a l u e s (») , w i t h R = 5H» V a l u e s d e t e r m i n e d b y means o f E q u a t i o n 5 () w i t h Y ^ ( t ) = 12 v o l t s a s t h e a v e r a g e v a l u e . x  g  where  V  natural  Q  i s the i n i t i a l logs  of t h i s  C  of  tance cuit is  dt' (R + R  varies a t time  used  simple  over  as does  a  =  )  l n  c  constant  t ) i n this  from  period.  the i n t e r v a l  zero  TTTT c  v  e'  e  •••(4)  J  throughout however,  to i n f i n i t y  of i n t e g r a t i o n  V  *e  o  v  RC  we  Taking  obtain  the  interval  the arc  resis-  (an open  I f the approximation  i — expression f o r the e x t i n c t i o n  E C l n  we  V 7 1 ) •••  t h e c a p a c i t o r C,  approximately  =  t V  series, r e s i s t o r R remains integration  on t h e c a p a c i t o r b a n k .  e x p r e s s i o n a t time  (  The  voltage  cir-  R^R  can determine  a  •' time,  (mv  o  - inv (t |. c  e  ...(5)  This  expression  to  calculate t  in  the lower  e  was u s e d ,  together  as a f u n c t i o n of V  curve  of Figure  11.  with  , and the r e s u l t s o' The v a r i a t i o n  shown s c h e m a t i c a l l y , b u t a s V ( t ) * c e' J  introduced upper  curve It  low  of Figure  c a n be s e e n  R  was  mine R for  check  and h i g h  our simple  35$»  This  on e q u a t i o n  q  (t ) i s c & the error  n o t be t o o l a r g e . points  The  observed.  model p r e d i c t s values  too  due t o t h e  fact  the discharge.  To p e r f o r m  a  4»  i t was n e c e s s a r y  This  calculation  g  a r e shown  error i s mainly  to within  an a r c v o l t a g e  V , q  a t a time  to deter-  was  completed 4  was  10$.  a high  observe typical On  should parated  t  t o as the s h u t t i n g t i m e ) .  (referred  there  was  of a  that  o f t h e two e l e c t r o d e s  increase  sensitivity  this  waveform f o r the case  i t was n o t e d  the result  corresponding  Using  a  will  V (t )  Shutting  d r o p was  to  that  verified  Observing  a  i n a l l cases  of  (one i s shown i n A p p e n d i x B ) , and e q u a t i o n  experimentally  zero  o  i n V  shows t h e e x p e r i m e n t a l  as a f u n c t i o n o f time.  two p o i n t s  (ii)  11  value  changing throughout  more c a r e f u l  R  an average  by a p p r o x i m a t e l y  that  V  x  by u s i n g  an average value  a sudden drop t o  touching  should  be  current  i t was  found  simultaneous  current  increase.  I f this  each  i n the current probe,  small  other,  observable. possible  Figure  12  shows  o s c i l l o g r a m o f the s h u t t i n g mechanism.  first  view,  move t o g e t h e r indefinately  i t i s not understandable during  the discharge,  when t h e a p p a r a t u s  why  the electrodes  as they  remain se-  i s not i n use.  An  e x a m i n a t i o n o f a l l f o r c e s a c t i n g on t h e b u b b l e s u r f a c e must be u n d e r t a k e n i n o r d e r t o u n d e r s t a n d this motion. These i n c l u d e ?  Figure  12  Arc  Termination  by Shutting  Dual-beam o s c i l l o g r a m s w i t h upper t r a c e d i s p l a y i n g v o l t a g e (5 v o l t / c m w i t h z e r o at top o fboth o s c i l l o g r a m s ) , and lower t r a c e d i s p l a y i n g c u r r e n t (50 amp/cm a n d 1 0 amp/cm i n u p p e r a n d l o w e r o s c i l l o g r a m s respectively)• B o t h o s c i l l o g r a m s were t a k e n w i t h h o r i z o n t a l sweep o f 2 0 yusec/cm f o r the case of V = 200 v o l t , and R = I I I ,  surface  t e n s i o n , g r a v i t y , and  of magnitude force  could  down t o t h e neglected of  the  calculation not  be t h e  lower  one.  because  this  upper electrode.  electromagnetic  q u i c k l y shows t h a t  main force A n d the force  would  the  drawing the  surface tend  I t i s probable  forces.  gravitational  upper  tension  An order  electrode  force  can be  t o impede the  motion  that  force  the  main  is  due  to  carrying  the parts  This row  jxB  electromagnetic of  the  would  As  upper electrode  the to  Electromagnetic Force  the  time  t  g  , and  As  hence, would  both 2  B are  and  the  of  bridge  Hg  of  a  disturbed  current, i t  This  that  out  result  between anode  nar-  portion  i s  i s forced as  the  incompres-  bottom  conceivable  force.  effectively directly  the  passage  cathode  pinching  Hg  as  appear  column  liquid  i s almost  of  Cathode,-  establish a  Hg  and  would  then  the  sible,  due  13  a l l current  have most e f f e c t upon  upper electrode.'  Anode  Figure  a c t i n g on  circuit.  pinch-like force  cylindrical  force  towards  of  this  motion  and  a  would  cathode, at  short-circuit  the  arc.  p r o p o r t i o n a l t o >the c u r r e n t  I,  2 the is  electromagnetic given  This for  approximately  expression the  force  case  of  i s proportional  to I  •  The  current  by  follows  from  R^R  Thus,  .  the  previous  i t can  s e c t i o n on e x t i n c t i o n  beseen  that  the  electro-  a  ...... 2 magnetic  force  character Using  due  i s proportional to  the  Newton's  qualitatively  to  exponential Law  an  i n d i c a t e s the  ( V / R ) , and O  factor e  expression  an  impulsive  ^t/RC^  can  be  t  may  dependence  has  determined have upon  which the  s different  circuit  parameters.  Consider  em where  F  e f f l  i s the  electromagnetic  force,  and  \ i s the  factor  of  -24-  80  i  60 40  10  400  200  Figure  14  S h u t t i n g Time Dependence upon Experimental points a n d C = 3 0 ja.f.  proportionality.  QOO  600  Integrating this aV  «*)  2  C  with  twice  -2t/RC  - i l - l  1  0  R = l / 2 SL.  expression  /  ^  we  obtain  . . a (6)  -  and,  •••(?)  2R  with  a = \/m.  hence  Generally,  ^> t ^ 2RC, s  Now  x ( t g ) I s the distance  the  time  t  s  e  —21 / RC '• ^ 1 , and 8  i t follows, 2 «v a V 2Cp  given  so t h a t  gives,  travelled  t , and hence i s j u s t s  by the Paschen  ,  curve.  RC  by the upper electrode i n  the i n i t i a l  gap  separation  d  o  ,  S u b s t i t u t i n g , and r e a r r a n g i n g f o r  t  BC 2  s  o  A s n e i t h e r A. n o r m c a n h e assumed viewed  t o be  constant,  strictly  determined,  the above  i n a qualitative  more r e a s o n a b l e  the f i n a l The  and  one  expression  dependence case  obtained  Faschen  curve  by  upon R  sense.  a  Ed  i s taken  with,an  x-y  a relatively  o'  and  /7  for t  In this  14•  verified The  l a r g e amount  when t h e s c a t t e r  point arose  when e x a m i n i n g  oscilloscope) of a discharge  linear  After  decrease  s h u t t i n g had  of voltage with  of R  measured  could  be  i n t e r p r e t e d as t h e r e s i s t a n c e o f t h e Hg  posed  by  the s h u t t i n g mechanism.  Having  we  the slope 3x10  i n s e c t i o n 2-2.  versus  proposed  possibilities,  by  SI - a p p r o x i m a t e l y  cylinder of height -5 2 5x10 cm .  Extinction  i n the  curve  than  and  was  the  added r e s i s t a n c e column  procorres-  c r o s s - s e c t i o n a l area  0  Shutting  models  should  of this  I f so, i t would then d  there  current i n  —2 XL l a r g e r  This  trace  terminated  occurred  value  —2  of  t h e I-V  4x10  (iii)  i ti s  experimentally  t o be  the order  respect  time.  found  of  be  into consideration.  resistance indicated  t o a Hg  must  g  • • • (8)  The  pond  been  2  i;ime.  c  have  o  was  expected  the s h u t t i n g mechanism.  was  expression  f o r the s h u t t i n g  i s t o be  interesting  (obtained  s  i s shown i n F i g u r e  scatter  An  and as both  t o use t  as  2Rda  +  now  f o r t h e two a r c t e r m i n a t i o n examine  the c o n d i t i o n s under  which  extinction shutting then of  o r s h u t t i n g i s t o be  precedes  extinction  extinction  extinction  cannot  expected.  (as i s the case  possibly occur.  preceding  shutting (t < t  Upon  s t i l l  be  observed  examination  with  that i f  whenever t < t  However,  f o r the  ),  case  ), the usual  shutting  a s t h e jjxB. f o r c e s a r e s t i l l  present.  Q should  I t i s clear  a long, time  3  scale this  was  found  t o be  true. Consider  the schematic  diagram i l l u s t r a t i n g the dependence of t and t upon V . I t c a n be s e o seen that f o r v o l t a g e s l e s s than 9  01'  t < t , and so e s'  should  Figure  15  Extinction Shutting  or  prevail.  and  t  T h i s was  higher  t h a n QQ_9  then  shutting  should  prevail.  This  t e n d e n c y was  Q  curves,  probably  a result  and a l s o due  Similarly, for  voltages  however fined.  extinction  V  experimentally was  very  o f the low slope  to the high  scatter  found  poorly der of the t  of the Paschen i  curve. While mining was  the value  which  role  i n this  favoured  ferred  extinction.  s  and t , t h i s e'  directly  o  was  shown  o f t h e two mechanisms  values  t  of V  soon n o t i c e d that  tant  3  the choice  determination.  shutting, while According  f e a t u r e was  p r o p o r t i o n a l t o R.  t o be a f a c t o r  would  of R  terminate  played  I t was  found  failure  impor-  that low R  to the expressions  The  the a r c ,i t  a much more  higher R values  not expected  i n deter-  as both  generally  pre-  derived f o r times  are  to explain this  exper-  -27imental  result  i s an u n e x p l a i n e d  short-coming  of the  proposed  models. (iv) Independent To the in  perform  Evidence  an experiment  Motion  which  would  g i v e some s u p p o r t  p r o p o s a l o f the s h u t t i n g mechanism a m o d i f i c a t i o n the design of the apparatus.  replaced  by a s o l i d  was  i n series  used  charged arc  to V  trode was  = 1000  that  results  shutting,  the  a r c a t a time  for  these  &a  was  This  a n o d e was  to  around  the a c t i o n  have  would  of was  .6-Ainitially  ensured  that  whenever  as a s o l i d  elec-  of the jxB forces, i t be  observed.  were v e r y  encouraging.  occurred a t a time  Instead, extinction  200 y u s e c  (1930)  and Galloway  - a reasonable  carefully  taken  mention;that  t o become c o v e r e d cleaned f o r each  found  less  than  terminated value  of t  solid electrodes  w i t h a t h i n Hg  film,  important discharge.  t o be n e c e s s a r y ,  for after  p l a c e , the t e r m i n a t i n g mechanism  several  suddenly  shutting.  R E L A T I V E V E L O C I T Y OP As p r e v i o u s l y  electrode  A resistor  However,  experiment  not observed.  p r e c a u t i o n was  changed  Hg.  made  parameters.  Jones  shots had  under  would  ^.n H g d i s c h a r g e s t e n d the  liquid  was  to  Hg e l e c t r o d e was  These c o n d i t i o n s  only extinction  which  yusec,  upper  occur by s h u t t i n g mechanism  of this  100  electrode.  volts.  not d i s t o r t  expected  The  w i t h the c a p a c i t o r bank which  e l e c t r o d e was  would  The The  o  brass  t e r m i n a t i o n would  the upper  2.5  f o r the  THE  mentioned  ELECTRODES i n the Paschen  s e p a r a t i o n i s an i m p o r t a n t  curve  parameter  section,  o f an a r c  the  which  -28should  be d e t e r m i n e d .  determining  The i n i t i a l  the Paschen  moved t o w a r d s  the lower  is  this  clear  reason  that  between  extracted The  was f o u n d varied  resulting  (see  from  o f R = 1/1,  time  c a n be  the s h u t t i n g  values  curve,  time  voltage of  break-  and t h e  60-140  was a p p r o x i m a t e l y  the s h u t t i n g mechanism p r o p o s a l the i n c r e a s i n g breakdown  6 a n d 7»  A t time  v ^ c o u l d be e s t i m a t e d  voltage  S  and r e a r r a n g i n g i t then  appears  velocity  d-o/^a  involves  drastic  , and by d i -  0  0  - EC/2  " t  should  •  --'  (  9  )  as v^ i s l a r g e r  than  the average  be s t r e s s e d t h a t  this  calculation  approximations^.  i n the c a l c u l a t i o n  v,, w a s f o u n d  f  s  X  of equa-  follows that  reasonable,  51  b y means  t , x ( t ) = v„, x ( t ) = d  d  in  be  6).  T  used  could  as t h e breakdown  on t h e P a s c h e n  increases with  velocity  result  discharge  The c o r r e s p o n d i n g  S  This  For this  of the relative  r e l i a b l e data  the t o t a l  i n the v e l o c i t y  The.final  viding  some e s t i m a t e  150-100 y u s e c  c o u l d be f o u n d  variation  equation  tions  case  300-800 v o l t s .  velocity  of a discharge, i t  the breakdown d i s t a n c e by the s h u t t i n g  I n agreement w i t h  average  electrode  obtained.  over  the standard  down d i s t a n c e  cm/sec.  velocity  t o vary  from  t o make  the waveforms  by d i v i d i n g  Using  one i n t h e c o u r s e  the surfaces before  average  obtained time.  from  but as the upper  d i s t a n c e was c o n s t a n t l y c h a n g i n g .  i t was n e c e s s a r y  velocity  curve,  by-  d i s t a n c e was m e a s u r e d  With  the i d e n t i c a l conditions  of the average v e l o c i t y ,  t o be a p p r o x i m a t e l y  65-160  the  cm/sec.  variation  -29An  independent  obtained series the  when a l a r g e  with  tg = 2  The  yusec)  after  decrease  then could  was  was p l a c e d i n  increased  s l o w l y , and  be m e a s u r e d a t two  times  the a r c plasma had been e s t a b l i s h e d .  i n voltage AV  attributed, t o a decrease caused by the motion  of the electrodes  L (32 yuH)  inductance  f o r t h e same c u r r e n t  observed  brief  on t h e m o t i o n  t h e a r c . The c u r r e n t  voltage  (t^,  check  = V(t^)  i n the a r c column  of the electrodes  - V(t^) length.  could This  be was  a s shown i n t h e f o l l o w i n g  discussion. The  total  voltage  drop across V = V  in  accordance with  of  this  equation  + V  c  f i g u r e 3»  the electrodes  co  + V  Taking  i s given  by  a  the f i r s t  time  derivative  gives i i ."Mc dt dt  dVcj> dt  +  +  dla dt  which approximates to dV dt because the  the f a l l  current  tion  voltages  (Gerthsen  and S c h u l z ,  a column).  that  1955)»  co  =  over  t o changes i n both and the e l e c t r o d e  the a r c i s s u f f i c i e n t l y  The c o l u m n f i e l d E  constant  0  are insensitive  (we i n h e r e n t l y a s s u m e  to e s t a b l i s h  dVf. " dt  separa-  long  strength  dx  is  approximately  t h e c o l u m n '(see  is  h i g h l y dependent upon t h e c u r r e n t .  f i g u r e 3),  Assuming that E  but i s  -30-  m  WI AM  fc^^U ^ ^ ^ U  <Ug  • H I IHife  SBil  II!•:Si  Figure  16  Determination  of Electrode  Velocity  O s c i l l o g r a m s were t a k e n s i m u l t a n e o u s l y on two d i f f e r e n t o s c i l l o s c o p e s f o r t h e c a s e o f E = 211$ C • 30 y u f , V - 600 v o l t . Q  Upper t r a c e : c u r r e n t above  bottom  (50 amp/cm w i t h line)  versus  zero  time  2 cm  (20yusec/cm)  L o w e r t r a c e s c i x r r e n t (20 amp/cm w i t h z e r o o n b o t t o m l i n e ) v e r s u s v o l t a g e (2.5 v o l t / c m w i t h z e r o 1 cm f r o m l e f t h a n d b o r d e r ) .  unaffected current  by a s l i g h t  we h a v e  motion  the following Yno dt d  or,  of the e l e c t r o d e s , then  dV dx  O Q  dx dt  • E v co  f o ra  fixed  -31Using V  Q  »  600  Prom  the  volt,  the  Then,  strength  f o r these  over  the  interval  case  was  at I  thus  giving  ing  the  v  reasonable  R  obtained  »  2-ft, C  At  =  175  =  62  =  -  amp  where  cm/sec.  figure  18,  c o u l d be At  =  This  30 yuf,  = 16  and  were  obtained.  f o r several values  corresponding  c u r r e n t s from  no  exact  column  the  figure  of  =  A  1.1  a  field  average  determined.  3 3 ^ 8 6 0 , AV  determination  i s of  i n mind i t would  first  should  ph,  t a k i n g the  velocity  for  measurements the  be  agreement between  relative  figure  32  =  velocity typical volt,  i s reasonable  consider-  experimental conditions.  Although  the  can  At  current.  L  o s c i l l o g r a m s shown i n f i g u r e  AV t r a c e s r-r  these  fixed  parameters,  2-15  vary  a  yusec  less  the the  appear  particular of  than  three order  V-I  from  the  c o u l d be  approaches of  reasonable  100  then  made,  t o assume  the  the  indicated  cm/sec.  characteristic  a discharge, 10$  of v  are  With  that this  that i f taken  in  electrode separation  measured breakdown d i s t a n c e .  6  -32CHAPTER 3.1  3 - G E N E R A L MEASUREMENTS  ELECTRODE F A L L An  value  order  REGIONS  of magnitude value  of f i e l d  tained  from Equation  may b e d e t e r m i n e d  for  the voltage  the  fall  t o drop  r e g i o n may  then  B y u s i n g t h e 545  velocity J  9,  o f R = IfL a n d V  measured loscope should  a s shown  b e 3$ h i g h e r  time is  and  correspond  given  = 400  this  volts, 17.  than  time  field  T.  a value  T  taken  strength i n  triggering  F o r the standard  o f T = 40 n s e c  As the r i s e  i s approximately  time  10 n s e c ,  of the  this  value  was oscilof T  the actual value.  9 with  t  t o the case  was c a l c u l a t e d  t o b e 72  = 140 jisec,  g  °f'  v 0  = 400  cm/sec.  d  Q  = 9x10  volts),  The t o t a l  'cm,  (values  the s h u t t i n g fall  distance  by  was f o u n d  similar  and  Equation  The a v e r a g e  - o s c i l l o s c o p e on t h e d e l a y e d  i n Figure  and pre-amp.  Using which  Q  o f the time  fall  calculated.  mode i t w a s p o s s i b l e t o m e a s u r e case  of  thickness of the  by measurement  also  the time  of the electrodes at t s  the t o t a l  to zero.  (the average  r e g i o n s ) , c o u l d be o b -  the v o l t a g e waveform near  s h u t t i n g t . As the r e l a t i v e ° s  regions  f o r d^. a n d E^  strength i n the f a l l  by o b s e r v i n g  may b e f o u n d  OBTAINED  t o be  manner  was f o u n d  2.9x10  ^cm.  T h e n E^. i s d e t e r m i n e d  i n a  by t h e e q u a t i o n  t o be 2 . 4 x l 0 ^ v o l t / c m , u s i n g V  was t h e a v e r a g e  value  accurate  t o +.5  F  volt).  = 7»5  volt  (this  -33-  Figure  17  Voltage  and  Current  Waveforms  G r a p h i c a l enlargements of three oscillograms taken with R = 111, C = 30 / i f , a n d V = 400 volts.  -34As than  indicated  Eg w h i c h  physics. drop  1  i n Chapter  i s o f importance  According  i s about  t e n times  that  Then by s u b s t i t u t i n g value  ^  Vc  oV +  JO.  for E  o  io i  io J E  ofarc  the cathode  and so  (note  a n d r e a r r a n g i n g we  <t  rather  Vc oL -t-dc  9  dc  c  theory  o f t h e anode d r o p ,  the expression  again)  of E  (1955)*  and Schulz  W +  =  *  average  to the general  t o Gerthsen  p  the  i ti s the value  this  i s only  obtain  1  dTJS-  +  6  T h u s , we for  E  see that although 7  , values  upon  the r a t i o  3.2  COLUMN The  o f 10  volt/cm  column  field  are possible  depending  STRENGTH  simultaneous  with  and h i g h e r  d /d .  FIELD  gether  2.2x10 v o l t / c m i s t h e m i n i m u m v a l u e  measurement  the Paschen strength E  curve c  Q  o f c u r r e n t and v o l t a g e t o -  could  over  be u s e d  the total  t o determine  column  the  l e n g t h ' t o be  calculated. E  co  may b e d e t e r m i n e d  only during the i n i t i a l  (2 y u s e c = t = 15 y u s e c ) , w h e n t h e c h a n g e  discharge separation  i s s m a l l compared w i t h d .  F L  where V i s t h e t o t a l tion  Then,  Q  h a d t o b e made  voltage  -  ^  stages  of the  of electrode  s i n c e d^,<^d  Q  V-W do  c o  across  the electrodes.  to V f o rthe voltage  drop  A correc-  across R  as  c measured The lations.  i n Section average  2.2.  value  of  = 7-5  The u s e o f a c o n s t a n t  volts  value  was u s e d  should  i n a l l calcu-  be a good  approxi-  -35-  V  2000  So  1*  1  1000 800  an  600  0  / /  400  i  200 WO amps 200  Figure  mation high  18  according  currents  sumed c o n s t a n t Figure  100 600 1000  Column F i e l d S t r e n g t h upon Current  t o Bauer and Schulz  (say greater  than  Dependence  (l955)»  who f o u n d  1 0 0 amp) t h e f a l l  that f o r  voltages a s -  voltages.  18 shows  the result  of plotting E  as a f u n c t i o n co  of  current  (on log-log paper).  which i n d i c a t e s a  The s l o p e  relation  .£>6  o f the curve  i s  .66,  -36Thia (see  result  Chapter  quence  i s very  l ) .  First,  losses,  will  n o t be a c c o u n t e d  3.3  VOLTAGE-CURRENT The  arc.  initial  ments w i t h were u s e d  objective of this  the results to obtain  reduced  derived  Reduced As  consebe men-  radiation mechanism i n  o f the dynamic  thesis  b y Smy  aspects  by Maecker.  was t o ' o b t a i n t h e o v e r -  from  these  the f i r s t ,  oscillograms  Both approaches  a  results  current  mechanism  range  plot,  i n Chapter  according  2,  t h e a r c was i n i t i a t e d  t o the Paschen  curve.  I f only  by a  spark-  the  2 - 1 5 yusec o f t h e t r a c e w e r e t o b e u s e d , t h e n t h e c u r r e n t  small ent  (see Figure  tained in  f o ra particular  initial  V  that  0  only  —  Characteristic  discussed  obtained  plot-  single  to similar  over a larger  methods  the second,  t o give  lead  Two  a direct  the oscillograms?  extending  measure-  ( s e e C h a p t e r 4)•  the characteristic?  characteristic  than d i d the d i r e c t  ing  should  f o ran a r c and t o compare  characteristic.  reduced  a  CHARACTERISTIC  combining of several different  (i)  which  neglects  the effect  by Maecker  f o ri n t h e d.c. model developed  o f measurements o b t a i n e d  the  obtained  i s probably  theory  completely  Second,  V-I characteristic  ting  that  w h i c h may b e t h e m a j o r e n e r g y d i s s i p a t i o n  particular  a  of Maecker's  h i sderivation  this  all  from  The a p p a r e n t d i s c r e p a n c y  o f two f e a t u r e s  tioned.  different  17) •»  breakdown d i s t a n c e  To i n c r e a s e  maximum c u r r e n t  could  would  the current  differ-  could  be o b -  However, a  i n d , and t h i s  we w e r e e x a m i n i n g a d i f f e r e n t  range  relatively  range, a  be u s e d , a n d t h i s  by changing the breakdown v o l t a g e .  i s accompanied by a change  be  0  characteristic  would  first  then  change mean  determined by  -37-  V  25  (volf)  d,= .0(4 cm.  20  15  do = 0 1 0 c m  10  .200  150  Figure this  30O  19  some i n t e r m e d i a t e  say  d^»  the  characteristic  an approximate  a modified  chosen value acteristic The  Seduced V-I  500  foOO  700  Characteristics  new s e p a r a t i o n ( s e e F i g u r e 2 ) . Choosing  into  4-00  reduced  obtained  Consider  technique  V  2  -  t o the d^  correspond o  n  2  - v 2 - Av 2 ,  to the  t h e dg  char-  characteristic.  a s (V/g,!^) » w h e r e ,  I .  to convert  separation, say dg,  some p o i n t - ( V g j l g )  point i s designated  2  was u s e d  which would  i s t o be r e d u c e d  I'  of electrode separation,  f o ra different  characteristic  o f d^.  which  reducing  value  800  -36-  AV  It  follows  2  technique  essential the  potential  an  { 2  =  variation «= 7«5  that  across  volts  was  19?  there the  of the  Direct The  V-I  obtained  (see Figure  o n l y measurements  20)  cates than for  very  that the  slope  4  4  same  linear  over  15  i t was  of the curve  measurements i n Figure  ^isec were  found  a longer  that  period a period  15 yusec o b t a i n e d i n s e c t i o n 2.5» cases  cases  indicated  4  5  from the  21.  Initially,  taken. the  However,  characteristic  of time. of The  This  50yusec  indi-  rather  average  p l o t t e d gave t h e e x p e r i m e n t a l V a I '  slope  result  .  Summary o f B o t h A p p r o a c h e s The  aver-  .  a r e shown  the a r c i s s t a b l e over  the three  (iii)  The  i n a l l calculations again.  by d i r e c t l y  i n the f i r s t  upon f u r t h e r e x a m i n a t i o n remained  gradient i n  Characteristic  results  traces  i s a linear  the  form  V a I ' (ii)  i n s e c t i o n 3»2,  c a l c u l a t e d f o r t h e two  and the average  impedance r e l a t i o n  .  column r e g i o n .  used  were  + 7.5  2  to that used  characteristics  i n Figure  -•7*5Jdi/d  V  i s identical  o f V^  Reduced shown  2  assumption being  age v a l u e  7.5).  T  that  V  This  --t?( 2 -  results  of both  approaches  c a n be d e s c r i b e d  by the  -39-  20  Pigure  Voltage-Current  Oscillogram  V o l t a g e (2.5 volt/cm) versus amp/cm) w i t h o r i g i n i n l o w e r c o r n e r , f o r the parameters B C = 30yuf, V = 500 volt.  current (40 r i g h t hand » l i l ,  0  I 10  J  l  I  1  I50  200  300  400  Figure  21  D i r e c t V-I  (amp)  Characteristics  1  1  1—  5O0  bOO  7OO  -40equation V where  the  constant  This V  <x I "  should  cidental ination theory.  be  result  Smy.  the  In  a general  s i m i l a r i t y ) the of  k T  4  5  ,  i s dependent upon the  experimental  d e v e l o p e d by  4  result  k  =  i s very order  feature  to  similar see  to the  separation. relation  whether or not  arcs  (and  not  f o l l o w i n g chapter  will  present  d e r i v a t i o n and  of  electrode  assumptions  just  this an i n -  an  i n v o l v e d i n Smy's  exam-  -41CHAPTBR 4 - SPOT CONDUCTION MODEL OP THE ARC 4.1  DEVELOPMENT OP THE MODEL The current-voltage relationship derived by Smy ( 1 9 6 3 ) .  was o r i g i n a l l y developed to determine the impedance between two electrodes immersed i n a shock heated plasma.  The essen-  t i a l features of this theory are very similar to generally accepted ideas i n arc physics;  The t o t a l arc voltage was con-  sidered to be made up of two components; the voltage across the cathode spot V , (which i s equal to the cathode f a l l voltage Vc), and the ohmic Voltage drop across the intervening plasma V^. It was found that both V  g  and V; were dependent upon the spot area,  and that there existed a possible optimum area for which the tot a l arc voltage w a s a minimum. This optimization resulted i n the f i n a l expression V ,  a I'  4  min which was shown t o g i v e order of magnitude agreement with the experiments conducted by Smy and Driver (Smy, 19^3f Driver, 1964). (i)  Spot Voltage The main experimental observation by Smy which lead to his  theory was the occurrence of a particular voltage regime i n which the current-voltagecharacteristic was independent of -the electrode area. -  This was shown to be so by placing elec-  trodes of various sizes across the shock tube for both increasing  and decreasing currents.  spot a n a l o g o u s t o t h a t w h i c h  The proposal of a small conducting arises i n arcs was found to be  very successful i n explaining the unusual features of the observed c h a r a c t e r i s t i c .  As the objective of this chapter i s to  -42-  examine how well Smy's theory applies to an arc, the details and p l a u s i b i l i t y arguments for the conducting spot i n the shock tube have been omitted (for details see Smy,  I963).  This was  done because the phenomena of spot conduction i n an arc has been well accepted (see Proome, 1950)*  Using Mackeown's f i e l d emis-  sion equation (see Chapter l ) and assuming t y p i c a l values for E  and v, "the spot voltage i s related to the spot area A  •C  1  X  "= Kf-  A5  by s  ,  ...di)  with k^ constant, (ii)  Plasma voltage The expression for the resistance of the intervening plasma  was derived i n accordance with standard electromagnetic theory (Smythe, 1950).  Assume that an i n f i n i t e , isotropic medium of  constant r e s i s t i v i t y f separates two conductors A, and B.  If  the separation distance I , i s large compared to a typical length of the conductors, then i t can be shown that the resistance of the intervening plasma i s given by  where C , C- are the capacities of the two isolated A  A, B respectively.  conductors  Taking conductors A and B to refer to the  negative and positive electrodes respectively, then C^ would be the effective capacity of the cathode spot. spot was formed on B, then C^ = Cg.  I f an i d e n t i c a l  However, the occurrence  of such an anode spot was thought to be unlikely ( i n analogy with an arc again), and so C_ * was neglected in comparison  -43-1  with  .  The c a p a c i t y o f a t h i n  disc  of radius  r i s given  by C,  d  according  t o standard  Assuming a c i r c u l a r  tables  cathode  =  8e r o  ( H a n d b o o k o f Chem. a n d P h y s . , spot  forms  on t h e n e g a t i v e  1964).  electrode,  then  " as  only  one f a c e  plasma.  and  o f the "cathode  i s then V  Total The  sum  of V  total  comparison  is  with the  P  given by - IH .  P  a r cvoltage  c a n now b e d e t e r m i n e d  by t a k i n g t h e  and V , p'  s  t h e case  The  i s i n contact  Voltage  V  For  disc"  Now t h e p l a s m a r e s i s t a n c e i s g i v e n b y  t h e plasma voltage  (iii)  /V TV  ^  >  =  - p A t -+ k 1 A ;  2 S  4- £ / T A - *  t o t h e second  that  loss  -  v  2  o f Smy's s h o c k t u b e  power  assumed  -  term  the last  k i 3  .  .„(  t e r m was n e g l i b l e i n  so that  i n the a r ci sgiven  given  -  sufficient  time  by the product  the spot  area  IV. I t  will  adopt  1 3 )  -44that  value  particular  which w i l l I.  This  differentiation ing  the  final  of  minimize  this  optimum a r e a the  voltage  given  corresponding  determined  respect  L «J  to  the  by  for  a  partial  area,  '  4k  k,'  2  E x a m i n i n g Smy's s h o c k optimum a r e a  for this  two  this  1  giv-  ...(15) particular  area  - ki .  4  is  ...(16)  3  approximation,  remains unchanged,  i s a l s o worth  achieved,  r  Hi  tube  Vk,m.-n  the  be  minimizing V  by  lrl  It  with  voltage  v,„ =  the  can  by  result,  ~ Then the  loss  and  i t i s found  that  so  =|Vk;Vr . 4  ...(17)  n o t i n g t h a t when optimum c o n d i t i o n s h a v e  approximation  voltages  are  i n the  gives  the  interesting  been  result  that  ratio  V s _ V 4.2  spot voltage _ plasma voltage  1 4  .  ...(18)  DISCUSSION .43  In and  this  spot was  Sec.  3«3  result  would  conduction shown t h a t  i t was  appear  model. the  experimental It  t 2>  A  0  t o be  found  i n good  that V  i s only  model which  fortuitous, cannot  = k l  ,  agreement w i t h  However, upon d e t a i l e d  agreement  a s s u m p t i o n s made i n t h i s our  experimentally  be  Smy's  examination as  i t  there  satisfied  are by  arc.  i s easily does not  shown t h a t hold  the  f o r our  shock  tube  particular  approximation, conditions.  Consider  -45a  typical  case  f o ra p a r t i c u l a r  separation  c a n be d e t e r m i n e d  timum a r e a  i s given by Equation  it  was f o u n d  proach  t h a t -t ^10  t o determine  2  cm,  c u r r e n t maximum; t h e e l e c t r o d e  by the Paschen 15•  and  a measure  curve,  and t h e op-  F o r a c u r r e n t o f 500  A  ^ 10  / z 0  o f the spot  ^cm.  area  Another  value  f o r I = 500  give  values  of  certainly  for  this An  A  amp, A  ^  which  evident  10  important  difference  between  to another  conduction  reason  model  passage  the  gas, whereas  and  i s constantly being  which  i s invalid  that  of constant  not apply  resistivity  be q u i t e  gives  the use o f the spot  the ionization i n  the gas i s already  resistivity  o f an i n f i n i t e  may a p p l y  to a regular arc.  of the current flow  net result  tube  the assumption  the  then  plasma  r e p l a c e d by the plasma f l o w .  dependent  also  t»  i n a shock heated  invalidates  i n the shock  radially  the  of magnitude i t  the e l e c t r i c a r c and t h e  of current i n the arc maintains  c a n be s e e n  expected  t h e two approaches  to describe the e l e c t r i c arc characteristic.  The  axis  ,  situation.  rise  will  While  that the approximation  o f two e l e c t r o d e s immersed  plasma  cm.  d i f f e r by an order  case  it  2  f o r t h e c u r r e n t d e n s i t y , s a y j = 10 amp/cm V? -2  then  is  ap-  i s t o assume an  6 accepted  amp,  t o the shock  (see Maecker,  that the f i n a l  different.  this  tube b u t i n a  h a s a minimum v a l u e  1959).  t h a t t h e e x p r e s s i o n f o r R^ w o u l d being  Prom  isotropic  The c u r r e n t r e s u l t s  which  ionized  along  I t would  be m o d i f i e d  expression f o r  w  be —  ould  -46CONCLUDING It ables  field  the overall strength  that  tive  these  nature.  factor was  was p o s s i b l e  t o measure  o f an a r c with  curve,  ed  REMARKS  voltage-current  of the important  namely  the Paschen  characteristic,  dependence upon c u r r e n t .  However,  motion  well  established,  and even  could  r e s u l t s obtained  t o agree  fairly  f o rthe overall  well with  I t was shown t h a t  fortuitous  however,  a s many o f t h e a s s u m p t i o n s  derivation  are not satisfied  The  observed  approximate anode  regions.  The  motion  determination  fall  regions  Although  appropriate  to  obtain  o f the combined  re-design  an accurate  field  emission  acceptance  encouraging feature  be  approxi-  of this  ( o r reject) the f i e l d  only f o r the  i n these  i s consistent  the accuracy theory  i tmight  of the  be  i s that  may b e s u f f i c i e n t  to  by  possible  of the shutting v e l o c i t y .  theory.  with  beyond any doubt.  measurement, however,  emission  an  of the cathode  strength  strength  theory,  spot  made p o s s i b l e  thickness  i n the apparatus,  obtained  required  were  i n this arc.  field  of this  measurement  the r e s u l t s thereby  accept  only  a g r e e m e n t was  o f t h e Hg e l e c t r o d e s  the measured  does n o t a l l o w  this  by c o n d i t i o n s  and t h e average  predictions of field  an  so,  the motion  t h e p r e d i c t i o n s o f Smy's  theory.  result  was t h e m a i n  V-I characteristic  conduction  the  quantita-  measured.  The  and  than  though  i t s velocity  breakdown  i t must be s t r e s s -  of the electrodes  feature,  vari-  and t h e column  m e a s u r e m e n t s a r e more o f a q u a l i t a t i v e  contributing to this  mately  found  Hg e l e c t r o d e s ,  The o b s e r v e d  reasonably  several  I f  completely  -47-  APPBHDIX A The V  0  ICR SERIES  case  of a capacitor C i n i t i a l l y  discharging current  tance  L describes  very  well.  rent  limiting  taken  CIRCUIT  i through  the behavior  The r e s i s t a n c e resistor  as c o n s t a n t s  charged  t o some  a r e s i s t o r R and s e r i e s  of our basic  measuring  induc-  circuit  o f t h e a r c i s much l e s s t h a n  so that  voltage  the cur-  t h e 3 p a r a m e t e r s R, C, L may b e  f o r the a n a l y s i s .  L  R  Figure  22  LCR S e r i e s  Circuit  B y a p p l i c a t i o n o f K i r c h h o f f s Laws we 8  tial  equation  f o r the current  flow  obtain  the differen-  i n the c i r c u i t ,  iii  i R di dt*"*" Lett  which  i s subject There  the  has  are three  relative  condition  t o the i n i t i a l  R  current  magnitude />4L/C  c o n d i t i o n i(0) •  responses  of the c i r c u i t  i s satisfied  then  the form  (  )  " F ^  e  r  0.  possible depending parameters. the current  upon  When t h e response  -48(i)  Current All  q u a n t i t a t i v e , measurements were  components tion  Waveform  satisfied  the i n e q u a l i t y  R ^4k/C.  f o r the c u r r e n t and u s i n g the l i n e a r  1  I  we  t a k e n when t h e c i r c u i t  —  4.L  '  1 —  —  Taking  the equa-  approximation  2L-  obtain,  For  times  g r e a t e r than  2L/R  this  equation reduces  further  to  Hi) which  i s the equation  current matic  o f the waveform i s given  Resistance  23  the  decay  i t was  a n d 17»  Typical  and a  sche-  (schematic)  of the Arc  possible  condition R  circuit.  below.  C u r r e n t Waveform  By p e r f o r m i n g a v e r y trace  RG  w a v e f o r m s a r e s h o w n i n F i g u r e s 12  Figure  (ii)  of a simple  a r c  simple  measurement upon t h e c u r r e n t  to determine  < ^ R was  valid.  the p e r i o d of time An a p p r o x i m a t i o n  i n which  of this  time  -49was u s e f u l i n t h e d i s c u s s i o n s o f t h e s h u t t i n g a n d mechanisms For measure  of Chapter  any time the slope  2.  t">2I»/R d r a w t h e t a n g e n t which  i s given _  ra m  The  slope  of the simple  H e n c e , we  s e e t h a t At = RC  from  value  It  was  found  Ai _ _ i ( t ) ~ At  At  =  f o r an e x a c t  a rough measure  f o r a l l cases  and  by  1_ \L ^-VRC RC R ^  dt —  give  to the curve  RC d e c a y w a v e f o r m i s g i v e n  cU_  this  extinction  that R  _ —  ) ~RC  RC d e c a y ,  by  . ,v U  ;  '  and d e v i a t i o n s  of the arc resistance . 4CR  f o r a l l t = 2RC  by  this  arc technique. (iii)  Inherent It  tance  was f o u n d  Inductance  t h a t a measure  of the inherent  L ^ , c o u l d b e made b y o b s e r v i n g  current of  Circuit  flow  on t h e o s c i l l o g r a m .  the current  (either  s h o w n i n ( i i ) we  Taking  ation  of  the f i r s t  maximum derivative  approximation  L.'  ffl  c a n be s o l v e d e i t h e r technique  m  induc-  obtain  m e a s u r i n g .T , a n d s u b s t i t u t i n g  tion  T  one) and u s i n g the l i n e a r  R By  the time  circuit  values  f o rR  a n d C„  by g r a p h i c a l t e c h n i q u e s  f o r the value  of  .  this  equa-  o r by an  iter-  -50-  APPENDIX B  GRAPHICAL EXAMINATION  Referring  2»4  to section  we  OP  EXTINCTION  had d e r i v e d the  n  dt  equation  Vo  .  s  o which  simplifies  to  if  the approximation  As  shown i n F i g u r e  sults  and E q u a t i o n  suggested  11,  careful  i n which  R  Then by p l o t t i n g  the  integrating,  integral With  the  curve  l.h.s. voltage of  waveform V  Equation  of  Figure  line  to within 11.  of Figure  possible to  p o s s i b l e to determine  R = 517.9  V  Q  the value  = 300  volts,  of  the area  Then the  3«46 a s C = 30 y u f .  From the ,  found  t o 12  volt,  and so the r . h . s .  =3.22.  the agreement between both  i s much more  encloses  under  24.  s e c / i f l a s shown i n F i g u r e  satisfactory  I t i s also interesting 24  determine  4»  ( t ) was  ifo  oscil-  and g r a p h i -  9  has the value  time,  should  used.  i t i s not possible to obtain a value  extinction  equation  4  4  c u r r e n t - t i m e and v o l t a g e - t i m e  4 has the value ln(300/l2)  Although pected  l„04xl0~  disagreement  of Equation  the f u n c t i o n l/{R + R \ ^ a)  i t was  the parameters  of Equation  0 = t = t • .  This  was n o t  c o n d i t i o n s i t was  i n Equation  was  examination  the approximation  of p a r t i c u l a r  cally  interval  30-40  approximately  t a k i n g simultaneous  ( t ) .  i n the time  the d i s c r e p a n c y between e x p e r i m e n t a l r e -  lograms a  holds  5 was  t h a t a- m o r e  be u n d e r t a k e n By  R^R  t o note  the effective  f o r the exsides of the  than  the  results  that the dotted  area which  i s used i n  in two  Equation areas  between  5»  i s of  the  two  and the  i t can  be  seen  same o r d e r  curves  t h a t the  of magnitude  of F i g u r e  H o  difference as  the  in  the  discrepancy  BIBLIOGRAPHY A h l b o r n , B., Journal B a u e r , A.  B a r n a r d , A . J . , and of Physics.  and  Schulz,  Campbell,  (1965)  H.D.  Canadian  P (1954)» Z,.P. 1_3_2, 197.  B r o w n , S.C. ( l 9 6 l ) " B a s i c D a t a o f P l a s m a P h y s i c s " , M . I . T . Cambridge, Mass. Driver,  (1964)  H.S.T.  Ph.D.  Ecker,  G.  (l96l)  Engel,  A.  v.  Engel,  A.  v. and Robson,  Thesis, University  E'rgebn. d. e x a c t . N a t u r w .  (1955)  (1957)  A.E.  F o w l e r , R.H. A119,  and Hordheim,  (1950)  Gerthsen,  and  P.  Proc.  Schulz,  of Chemistry  Hinrichs,  E.  Jones,  and  (1929)  (1959)  (London)  Soc.  Smy,  (1963)  Physics  (London)  S m y t h e , W.R. H i l l , N.  (1950)  Wasserab,  ( 1 9 5 1 )  B_6_3_, 377.  Phenomena  (1964=65).  (1959) Proc.  Phys. Rev.  Z.P.  15_6, 592.  Phys. Soc.  _5_0, 207.  611.  JL5_J, 1.  Z.P.  Proc.  (London)  I n t . C o n f . on I o n i z a t i o n  (1938)  Z.P.  W. (1925)  T.  5th  and  Galloway,  Schottky, P.R.  Roy.  Press.  (1955) Z.P. I4O, 510.  a n d W i e n e c k e , R.  M a c k e o w n , S.S. M a e c k e r , H.  Phys. Soc.  (1928) P r o c .  Phys. Soc. P  G o l d m a n , K. ( I 9 6 I ) P r o c . i n Gases.  L.  Clarendon  173.  F r o o m e , K.D.  Handbook  L.W.  Proc.  Columb  XXXIII.  " I o n i z e d Gases", Oxford,  A243, 217.  of B r i t i s h  Press,  Jil  163.  s  Phys, Soc. 82,  "Static  and Dynamic  Y. Z.P.  446.  1^0,  311.  Electricity",  McGraw  

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