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An investigation of radial recovery of a high current spark channel Chan, Ping Wah 1963

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AN INVESTIGATION OF RADIAL RECOVERY OF A HIGH CURRENT SPARK CHANNEL by PING WAH CHAN B . S c , U n i v e r s i t y of Hong Kong, 1 9 6 2 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1 9 6 3 In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and study. I further agree that per-mission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publi-cation of this thesis for f i n a n c i a l gain shall not be allowed without my written permission. Department of S>' < s  The University of B r i t i s h Columbia, Vancouver 8, Canada. Date 3/ sh b~t<<~. ie^ i?t J ABSTRACT R e i g n i t i o n curves have been obtained f o r a high c u r r e n t (40ka) spark gap channel i n a i r at atmospheric pressure at v a r i o u s r a d i a l d i s t a n c e s down to de l a y times of 50 p.s. a f t e r i n i t i a t i o n o f spark. The r e i g n i t i o n curves i n the T t h e r m a l breakdown' regime are obtained by a constant v o l t a g e generator having a v a r i a b l e output r a n g i n g from 100 v o l t s t o 2.5 kv, w h i l e those i n the'spark breakdown' regime are obtained by the use of a r e s t r i k i n g v o l t a g e generator having a h i g h e r v o l t a g e output ranging from 1 kv to 15 kv. The experimental r e s u l t s show t h a t the gas at l a r g e r a d i a l d i s t a n c e s r e c o v e r s f a s t e r than t h a t at a s m a l l e r d i s t a n c e . A s p e c i a l f e a t u r e of the re c o v e r y curves i s the occurrence of a d i p which i s thought t o be the e f f e c t o f a thermal wave. Gas temperatures are d e r i v e d by u s i n g the equation of s t a t e , Paschen curves and the r e i g n i t i o n measurements. A temperature p r o f i l e o f the spark channel has been obtained which i n d i c a t e s t h a t the spark channel has a f a i r l y u n i form temperature up t o a r a d i a l d i s t a n c e of 2.5 cm. Beyond t h i s d i s t a n c e the temperature drops r a p i d l y to ambient temperature at a r a d i a l d i s t a n c e of 4 cm, D e i o n i z a t i o n and r e c o v e r y mechanisms are p r e d i c t e d t h e o r -e t i c a l l y and are v e r i f i e d d u r i n g the e a r l i e r recovery p e r i o d i n which 'thermal breakdown' occurs and d u r i n g the l a t e r r e c o v e r y p e r i o d when 'spark breakdown' i s observed. - v i i -AC KN OWLED GEMEN T I wish t o express my s i n c e r e thanks t o Dr. R.J. C h u r c h i l l f o r h i s s u p e r v i s i o n when I was working on t h i s p r o j e c t , and f o r h i s continued i n t e r e s t i n the work even a f t e r he l e f t the Department. I a l s o wish t o thank Dr. R.A. Nodwell f o r spending so many hours i n r e a d i n g over the manuscripts of the t h e s i s with me as w e l l as f o r h i s many f r u i t f u l s u g g e s t i o n s . The a s s i s t a n c e of Mr. John Turner i n the d e s i g n and c o n s t r u c t i o n of the e l e c t r o n i c u n i t s , the work of Mr. Alex i F r a s e r and members of the t e c h n i c a l s t a f f i n the c o n s t r u c t i o n of the apparatus, and the c o - o p e r a t i o n of my c o l l e a g u e Mr. M.S. Gautam are g r a t e f u l l y acknowledged. - i i i -TABLE OF CONTENTS A b s t r a c t i i L i s t o f I l l u s t r a t i o n s V Acknowledgement v i i INTRODUCTION 1 CHAPTER 1 - THEORY 3 1.1 Recovery Mechanisms of Spark Gap Channel 3 1.2 Spark and Thermal Breakdown Mechanisms 9 CHAPTER 2 - APPARATUS 15 2.1 General D e s c r i p t i o n of Apparatus 15 2.2 High Current Generator and Main T r i g g e r C i r c u i t 15 2.3 E e s t r i k i n g Voltage Generator 19 2.4 Step F u n c t i o n Generator 20 2.5 Dual Output T r i g g e r U n i t 22 2.6 E l e c t r o n i c Delay U n i t s 23 2.7 High V o l t a g e P o t e n t i a l D i v i d e r 26 2 .8 Current Shunt 29 2.9 Probes 32 CHAPTER 3 - EXPERIMENTAL TECHNIQUES 33 3.1 I n i t i a l Discharge Current Wave Form 33 3.2 R e s t r i k i n g V o l t a g e Wave Form 33 3.3 D e f i n i t i o n s and Measurements of R e i g n i t i o n Voltage 34 3.4 Measurements 36 - i v -CHAPTER 4 - EXPERIMENTAL RESULTS 33 4.1 C o o l i n g E f f e c t o f E l e c t r o d e s 33 4.2 E l e c t r o d e E r o s i o n E f f e c t 39 4.3 Time Lag C h a r a c t e r i s t i c s 39 4.4 Thermal R e i g n i t i o n Curves 41 4.5 Complete R a d i a l Recovery Curves 43 4.6 D e r i v e d Gas Temperature and Temperature P r o f i l e o f Channel 43 CHAPTER 5 - DISCUSSION 43 5.1 Recovery and Breakdown Mechanisms 43 5.2 Recovery Features 49 5.3 E f f e c t o f V a r y i n g Discharge Parameters 50 5.4 Time Lag E f f e c t 51 5.5 Thermal R e i g n i t i o n 53 5.6 D e r i v e d Gas Temperatures 54 CONCLUSIONS 57 REFERENCES 59 -V-LIST OF ILLUSTRATIONS FIGURE 1. Townsend Discharge Current and A p p l i e d V o l t a g e R e l a t i o n 9 2. Block Diagram of Apparatus 16 3 . Recovery Measuring Apparatus - O v e r a l l C i r c u i t 16 4 a . High Current Generator and Main T r i g g e r C i r c u i t 18 4 b . Discharge Current Wave Form 17 5a. R e s t r i k i n g V o l t a g e Generator 18 5b. R e s t r i k i n g V o l t a g e Wave Form 19 6 a . Step F u n c t i o n Generator 21 6b. Step F u n c t i o n Wave Form 22 7. Dual Output T r i g g e r U n i t 21 8a. Pulse Delay Unit 24 8b. Power Supply to Pulse Delay Unit 25 9 . Decade U n i t Delay 25 10a. High V o l t a g e P o t e n t i a l D i v i d e r 27 10b. Response of P o t e n t i a l D i v i d e r to a Step F u n c t i o n 29 11a. Current Shunt 27 l i b . C i r c u i t f o r T e s t i n g Frequency Response of Current Shunt 30 11c. Frequency Response of Current Shunt 30 l i d . R i s e Time of Current Wave Form 31 12. R e i g n i t i o n C h a r a c t e r i s t i c s with Probe Diameter as Parameter 40 - v i -13. Reignition Characteristics with Probing Gap Length as Parameter 40 li+a. Time Lag Cha r a c t e r i s t i c s 40 14b. Normalized Time Lag Characteristics 40 15a. Thermal Reignition Characteristics for Test Gap G]_ 42 15b. Thermal Reignition Characteristics f o r Test Gap G 2 42 l6a-e. Typical Voltage and Current Traces 44 17a. Complete Recovery Characteristics 45 17b. Normalized Recovery Characteristics 45 13a. Paschen Curve 47 13b. Normalized Paschen Curve 47 19. Temperature Decay of Channel 47 20. Temperature P r o f i l e of Channel 47 21. Time Lag to Spark Breakdown 52 INTRODUCTION Spark gaps have been employed f o r v a r i o u s purposes by s e v e r a l workers. B e l l a s c h i (1934) employed the spark gap f o r s w i t c h i n g a hig h energy c a p a c i t o r bank onto a t e s t specimen i n impulse t e s t i n g e f f e c t of h i g h v o l t a g e . S t e k o l n i k o v (1947) has used the spark d i s c h a r g e s as l i g h t n i n g s i m u l a t o r s . With the advent of thermonuclear r e s e a r c h i n recent y e a r s , the p o s s i b i l i t y of a p p l y i n g r e p e t i t i v e s w i t c h i n g o p e r a t i o n i n plasma p h y s i c s has s t i m u l a t e d much i n t e r e s t i n the r e c o v e r y p r o p e r t i e s of the spark gap a f t e r passage of a high c u r r e n t . P r o p e r t i e s of the hig h c u r r e n t spark gap channel have been s t u d i e d by Reynolds and Craggs (1952), A l l e n and Craggs (1954) and Braudo (1959). R e i g n i t i o n data are a v a i l a b l e f o r surge c u r r e n t up t o 23 ka (McCann and C l a r k , 1943) and up t o 235 ka by C h u r c h i l l (1961). Measurements of r e i g n i t i o n v o l t a g e c h a r a c t e r i s t i c s y i e l d u s e f u l i n f o r m a t i o n about the p h y s i c a l s t a t e of the gas d u r i n g the r e c o v e r y such as the temperature. The r e s i s t a n c e o f the gap may a l s o be determined i f the c u r r e n t i s measured. However, i n a l l the experiments performed i n high c u r r e n t spark gap recover y to date, measurements have been l i m i t e d to a time delay g r e a t e r than 75© jxs a f t e r the i n i t i a t i o n of the spark d u r i n g which p e r i o d 'spark breakdown' normally o c c u r s . (Spark Breakdown i s a term used t o d e s c r i b e an e l e c -t r i c a l breakdown i n which an a p p l i e d r e i g n i t i o n v o l t a g e c o l -—7 l a p s e s i n s t a n t a n e o u s l y (^-10"' sec) to z e r o ) . At s h o r t e r d e l a y -2-times a f t e r the spark i n i t i a t i o n , a d i s t o r t i o n of the probing v o l t a g e wave form due to p r e - i o n i z a t i o n of the gas and regu-l a t i o n of the generator complicates the i n t e r p r e t a t i o n . T h i s d i s t o r t i o n of the v o l t a g e wave form s i g n i f i e s c u r r e n t conduction p r i o r t o breakdown and thus the presence of a p p r e c i a b l e i o n i -z a t i o n i n the t e s t gap. Hence i t would be of i n t e r e s t to examine t h i s 'slow breakdown' or 'thermal breakdown' regime i n which the r e i g n i t i o n v o l t a g e drops s l o w l y to zero. The purpose of the present experiment i s , t o i n v e s t i g a t e the r e -covery of a high c u r r e n t spark gap at v a r i o u s r a d i a l d i s t a n c e s down to delay times as short as 50 ^ us. V a r i o u s d i a g n o s t i c techniques have been employed t o i n -v e s t i g a t e the p r o p e r t i e s of the spark gap, i n c l u d i n g the moving shock wave probe (Poole, Parker & C h u r c h i l l , 1 9 6 3) and the e l e c t r i c probe t e c h n i q u e s . In the present experiment, the l a t t e r technique i s employed. V -3-GHAPTER 1: THEORY In t h i s s e c t i o n , a q u a l i t a t i v e theory f o r the r e c o v e r y mechanisms o f the high c u r r e n t spark gap channel i s g i v e n . The processes of 'thermal breakdown' and 'spark breakdown' are d i s c u s s e d . Q u a n t i t a t i v e d i s c u s s i o n i s not attempted as the mechanisms i n v o l v e d are h i g h l y complicated and up to the present time, not w e l l understood. 1.1 RECOVERY MECHANISMS OF SPARK GAP CHANNEL In high c u r r e n t spark gap channels at atmospheric pr e s s u r e , the gas becomes h i g h l y i o n i z e d d u r i n g the c u r r e n t p u l s e because of the l a r g e amount of energy d e l i v e r e d t o i t from the di s c h a r g e of the condenser bank. Thermal e q u i l i b r i u m i s most probably e s t a b l i s h e d w i t h i n a s h o r t time a f t e r the disc h a r g e ( C r a i g & Craggs, 1953)» The degree of i o n i z a t i o n and gas temperature are r e l a t e d by Saha's equation, lOgio ^ige = -5040 ¥i + | l o g 1 0 T + 15.38 (1.1) where Nj_, N , and N a, are the p o s i t i v e i o n , e l e c t r o n , and n e u t r a l atom c o n c e n t r a t i o n s , Vj_ = i o n i z a t i o n p o t e n t i a l , T = dis c h a r g e temperature. During peak c u r r e n t , the temperature i s very h i g h (10^ to 10^ deg. K). The b o i l i n g p o i n t of the metal of the e l e c t r o d e i s soon reached and i t may be expected t h a t an a p p r e c i a b l e amount of metal vapour (evaporated from the e l e c t r o d e s ) w i l l be present i n the gap. T h i s metal vapour tends to lower the e l e c t r o n temperature and d e n s i t y due to the l a r g e Ramsauer c r o s s -s e c t i o n of the heavy atoms i n the vapour. During c u r r e n t f l o w and i n the e a r l y post-spark p e r i o d , the gas i n s i d e the gap i s i n a h i g h l y i o n i z e d s t a t e a t a high temperature, and r a d i a t i o n i s an important mechanism of energy-l o s s . C y c l o t r o n r a d i a t i o n i n a pulse c u r r e n t spark gap channel w i l l be n e g l i g i b l e as the c u r r e n t , and hence the magnetic f i e l d , l a s t s f o r a very short d u r a t i o n . From the formula given f o r r a d i a t i o n power per u n i t s o l i d angle by the n^*1 harmonic, where q = charge of e l e c t r o n ™b = B g i s the c y c l o t r o n frequency where B i s the m magnetic f i e l d and m the e l e c t r o n mass, v = v e l o c i t y of e l e c t r o n , c = v e l o c i t y of l i g h t , 6 = angle between d i r e c t i o n of r a d i a t i o n and B J n = B e s s e l f u n c t i o n of the n^*1 order e 0 = p e r m i t t i v i t y of f r e e space i t can be seen t h a t c y c l o t r o n r a d i a t i o n i s only important when the e l e c t r o n s are r e l a t i v i s t i c . For i f v/c i s s m a l l , J n (£J Sine) — ( B l ) n i s s m a l l as (nv )-~o. In the present case, e l e c t r o n s are f a r from being r e l a t i v i s t i c , and hence r a d i a t i o n due t o t h i s e f f e c t i s n e g l i b l e . Another p o s s i b l e u n ( 9 ) - 5 -source of r a d i a t i o n l o s s i s due to bremsstrahlung r a d i a t i o n when an e l e c t r o n i s a c c e l e r a t e d i n the f i e l d of an i o n . E l e c t r o n - e l e c t r o n bremstrahlung may be n e g lected unless the e l e c t r o n temperature i s very high, say g r e a t e r than 50 kev when r e l a t i v i s t i c e f f e c t s produce unequal a c c e l e r a t i o n s f o r the e l e c t r o n s . The power d e n s i t y w x r a d i a t e d by the e l e c t r o n , assuming a Maxwell-BoItzmann d i s t r i b u t i o n , i s g i v e n by (see f o r example Rose and C l a r k , 1961) w x =/T q i 2 q e 2 n i n e / 8kTe ( 1 > 3 a ) ^ 24x£ 0 3c3m eh J TL me = 4 . 3 x 10-37 z 2 n ^ g T e * watts / (1 .3b) whdre n^ i o n d e n s i t y n e = e l e c t r o n d e n s i t y e l e c t r o n temperature i n kev me = e l e c t r o n mass 3e = e l e c t r o n charge q i = charge of i o n h = Planck's constant k = Boltzmann's constant Z i o n i c charge number c = v e l o c i t y of l i g h t From the above e x p r e s s i o n we see t h a t the r a d i a t i o n i s p r o p o r t i o n a l t o product of e l e c t r o n and i o n d e n s i t y , Z 2 and T e^. Thus the l o s s i s g r e a t l y enhanced by the presence of i m p u r i t i e s of heavy i o n s . E x p e r i m e n t a l r e s u l t s show t h a t bremsstrahlung r a d i a t i o n l o s s becomes important at thermo-n u c l e a r temperatures (10$ deg. K). As the temperature of the present plasma i s low compared with thermonuclear temperature, probably l e s s than 50ev, bremsstrahlung r a d i a t i o n l o s s i s not an important l o s s mechanism. The main source of r a d i a t i o n l o s s i n the present case i s probably due t o ' o p t i c a l r a d i a t i o n ' . O p t i c a l R a d i a t i o n i s used here i n a very g e n e r a l sense f o r any k i n d of e l e c t r o m a g n e t i c r a d i a t i o n , no-matter what i t s wavelength, that i s due to energy t r a n s i t i o n s i n v o l v i n g outer e l e c t r o n s of any i n c o m p l e t e l y s t r i p p e d atomic s p e c i e s (Glasstone & Lovberg, i 9 6 0 ) . The plasma i n the channel i s i n a h i g h l y e x c i t e d s t a t e soon a f t e r spark i n i t i a t i o n , the e x c i t a t i o n energy w i l l subsequently be emitted as l i n e s p e c t r a , c a l l e d ' e x c i t a t i o n r a d i a t i o n ' . Since i n t h i s case the e x c i t e d e l e c t r o n i s a t t a c h e d to the atom at a l l times, the t r a n s i t i o n l e a d i n g t o t h i s emission i s r e f e r r e d t o as 'bound-bound'. Another r a d i a t i o n l o s s i s due to the capture of a f r e e e l e c t r o n by an i o n , with the emission of r a d i a t i o n i n the form of a continuum. T h i s recombination r a d i a t i o n , as i t i s c a l l e d , i s then due to 'free-bound' e l e c -t r o n i c t r a n s i t i o n s and emits continuous s p e c t r a . Both of these l o s s e s can be r e p r e s e n t e d by the f o l l o w i n g equation: A + + e = A + hv (1 .4) where hv r e p r e s e n t s the energy of the photon emitted. Sound r a d i a t i o n s a l s o c o n t r i b u t e a s u b s t a n t i a l l o s s . The i n i t i a l d i s c h a r g e of the c u r r e n t g i v e s r i s e to a shock wave, and a l o t of energy i s d i s s i p a t e d as sound. Recombination l o s s e s become important l o s s mechanisms a f t e r the peak cu r r e n t has passed and when the temperature o f the plasma becomes lowered. One form of recombination, namely, r a d i a t i v e recombination, has a l r e a d y been mentioned. R a d i a t i v e recombination processes may i n v o l v e the d i r e c t combination of an i o n and an e l e c t r o n (two-body recombination), or i n the presence of a t h i r d body (three-body r e c o m b i n a t i o n ) . When an e l e c t r o n approaches a p o s i t i v e i o n , i t may d e s c r i b e a path t h a t does not n e c e s s a r i l y c l o s e but may be a hy p e r b o l a . To form a n e u t r a l system the excess energy of the e l e c t r o n must be d i s s i -pated i n some way, and i f i t should f i n d a t h i r d body i n the immediate neighbourhood, i t may give up i t s energy to t h i s t h i r d body b e f o r e combining w i t h an i o n . Such a process i s c a l l e d three-body recombination. Although i t occurs some times, i t i s much l e s s probable than two-body recombination. Recom-b i n a t i o n l o s s e s are e s p e c i a l l y important i n hig h pressure spark gap channels as i n the present case. The process of heat d i f f u s i o n a l s o c o n t r i b u t e s t o the r e -covery mechanism of the channel. The equ a t i o n governing the process i s = q + D y 2 n _ ( 1 > 5 ) dt where 2^2 = r a t e of change of c o n c e n t r a t i o n o f ions (n) at u. t any p o i n t q = o r i g i n a l i o n d e n s i t y D = d i f f u s i o n c o e f f i c i e n t The above eq u a t i o n holds s t r i c t l y when there are no other i o n i z a t i o n agents. Whenever there i s a c o n c e n t r a t i o n g r a d i e n t of i o n s , t h e r e w i l l be a f l o w of ions from regions of high c o n c e n t r a t i o n t o regions of low c o n c e n t r a t i o n . Thus d i f f u s i o n produces a d e i o n i z i n g e f f e c t i n the former r e g i o n and an i o n i z i n g e f f e c t i n the l a t t e r . However the presence of con-f i n i n g w a l l s and e l e c t r o d e s u r f a c e s a i d s d i f f u s i o n processes t o d e i o n i z e the gas as a whole with the e f f e c t of s u r f a c e r e -combination. The r e s u l t of the s u r f a c e recombination i s to form a n e u t r a l gas l a y e r on the e l e c t r o d e s and on the w a l l s . Of course such a l a y e r can onl y form on the s u r f a c e of the e l e c t r o d e s when there i s l i t t l e or no th e r m i o n i c emission. Competing with the process of the d e i o n i z i n g mechanisms i s the process of 'thermal i o n i z a t i o n ' which i s a term a p p l i e d t o the i o n i z a t i o n a c t i o n of molecular c o l l i s i o n , r a d i a t i o n , and e l e c t r o n c o l l i s i o n s o c c u r r i n g i n a gas. T h i s f a c t o r of i o n i z a t i o n i s very important i n i n f l u e n c i n g r e c o v e r y e s p e c i a l l y i n h i g h pressure and hig h temperature d i s c h a r g e s . In such cases the v e l o c i t y of the e l e c t r o n s w i l l be h i g h , the mean f r e e path short and the c o l l i s i o n frequency h i g h and hence high i o n i z a t i o n e f f e c t i s produced. Other slower c o o l i n g processes begin to c o n t r o l the re c o v e r y f e a t u r e s at l a t e r d e lay times a f t e r the spark i n i t i a t i o n , namely, gas c o n v e c t i o n and thermal d i f f u s i o n . When thermal d i f f u s i o n process ceases, t h e r e w i l l be l e f t i n the gap a weakly i o n i z e d gas a t low d e n s i t y and at e l e v a t e d temperature at ambient p r e s s u r e . The d e n s i t y of the gas g r a d u a l l y i n c r e a s e s to i t s p r e - d i s c h a r g e v a l u e . 1 - 9 -On the above d i s c u s s i o n , r e c o v e r y i s complete when the energy o r i g i n a l l y s t o r e d i n the channel i s l o s t through r a d i -a t i o n , recombination, d i f f u s i o n , c o n v e c t i o n as d e s c r i b e d above. 1.2 BREAKDOWN DOWN MECHANISMS a) Spark breakdown The theory of spark breakdown mechanism at low pressure ( p d ^ 150 mm.Hg. cm.^ where p = pressure o f gas i n mm.Hg., and d = d i s t a n c e between e l e c t r o d e s i n cm.) has been developed by J . J . Thompson and J.S. Townsend (1906) i n t h e i r e a r l y s t u d i e s of v a r i a t i o n of current between p a r a l l e l plane e l e c t r o d e s i n a gas as a f u n c t i o n of an a p p l i e d e l e c t r i c f i e l d . The e x p e r i -mental r e s u l t s can be rep r e s e n t e d g e n e r a l l y by the f o l l o w i n g p l o t c OS ZJ FIGURE 1: TOWNSEND DISCHARGE CURRENT AND APPLIED VOLTAGE RELATION -10-The c u r r e n t f i r s t r i s e s t o a value i and remains more or l e s s o constant f o r a c o n s i d e r a b l e range of a p p l i e d v o l t a g e and then i n c r e a s e s a c c o r d i n g t o i = i P 6^ ( 1 6 ) v/here = Townsend's f i r s t i o n i z a t i o n c o e f f i c i e n t and r e p r e -sents the number of e l e c t r o n s produced by a s i n g l e e l e c t r o n as i t t r a v e r s e s a d i s t a n c e of 1 cm. i n the d i r e c t i o n of the f i e l d . T h i s r i s e o f c u r r e n t i s represented by the p o r t i o n be of the curve. I t i s to be noted t h a t e l e c t r o n i o n i z a t i o n i s r e s p o n s i b l e f o r t h i s Towns end ot-mechanism. To account f o r the steep^ r i s e c orresponding t o the part cd of the curve, other c o l l i s i o n p rocesses must be p o s t u l a t e d . These i n c l u d e i o n i z a t i o n by p o s i t i v e i o n s which produces secondary emission of e l e c t r o n s , and i s r e f e r r e d t o as ^-mechanism. The e x p r e s s i o n f o r the cu r r e n t can then be d e r i v e d as f o l l o w s : Let n = number of e l e c t r o n s r e a c h i n g the anode per sec. n Q = number of e l e c t r o n s r e l e a s e d from the cathode by e x t e r n a l means n + = number of e l e c t r o n s r e l e a s e d from cathode by p o s i t i v e i o n bombardment V = number of e l e c t r o n s r e l e a s e d from the cathode per p o s i t i v e i o n (Townsend's second c o e f f i c i e n t ) Then n = ( n 0 + n + ) e ~d , ( 1 . 7 ) n+ = V ( n-( n 0 + n +) ) (1.8) -11-E l i m i n a t i n g n + , n = n ° e ^ . (1.9) or i = i„ 0 1- y ( e * d - l ) (1.10a) * X ° 1- ye "-d (1.10b) e ^ >> 1 i n g e n e r a l . When Ve < 1, the d i s c h a r g e c u r r e n t i s not s e l f - m a i n t a i n -i n g and hence no breakdown occur s , d When / e ^ 1, the di s c h a r g e c u r r e n t becomes i n f i n i t e and p h y s i c a l l y t h i s means an e l e c t r i c a l breakdown. The number e ^  of i o n p a i r s produced i n the gap by the passage of one e l e c t r o n i s s u f f i c i e n t l y l a r g e t h a t the r e s u l t a n t p o s i t i v e i o n s , on bombarding the cathode, are able to r e l e a s e secondary e l e c t r o n s and so cause a r e p e t i t i o n of the process which i s s e l f - m a i n t a i n i n g and hence produce an avalanche e f f e c t . Now the above th e o r y agrees w i t h experimental r e s u l t s at low gas p r e s s u r e s . However, because of the absence of evidence to the c o n t r a r y i n e a r l y work, i t was assumed t h a t the same processes of i o n i z a t i o n growth take place at hi g h pressure breakdown. I t was only a f t e r the i n t r o d u c t i o n of methods of producing high v o l t a g e s from impulse generators and of o s c i l l o -graphic d i s p l a y techniques t h a t breakdown at high p r e s s u r e ( 150 mm.Hg.cm. < pd <1000 mm.Hg.cm.) was i n v e s t i g a t e d s y s t e -m a t i c a l l y . 12-Th e f i r s t experimental r e s u l t was obtained by Rogowski (1926), xHe a p p l i e d a s h a r p l y peaked impulse v o l t a g e to an a i r gap and d i s c o v e r e d that the v o l t a g e c o l l a p s e d i n times -6 -7 l e s s than 10 to 10 ' seconds. T h i s i s f a r too f a s t t o be e x p l a i n e d by the Townsend «- and Y c o e f f i c i e n t s i n t r o d u c e d so f a r to e x p l a i n the e l e c t r i c a l breakdown phenomena; f o r a c c o r d i n g to t h i s , breakdown would be at l e a s t 100 times slower. The e x p l a n a t i o n of t h i s d i s c r e p a n c y i s provided by another p h o t o - e l e c t r i c secondary e f f e c t ( <5 ) which has so f a r been n e g l e c t e d , f o r t h i s i s r e l a t i v e l y unimportant at low p r e s s u r e s . Two t h e o r i e s have been put forward - the Kanal Theory and the Streamer Theory. Both of the t h e o r i e s c o n s i d e r t h a t e l e c -t r o n s are generated by p h o t o - i o n i z a t i o n by photons produced i n the primary avalanche, but t h i s i o n i z a t i o n becomes r a p i d only when the o r i g i n a l f i e l d i s h i g h l y d i s t o r t e d by the p o s i t i v e i o n space charge at the head of the avalanche. The e l e c t r o n s are assumed to i n i t i a t e a d d i t i o n a l avalanches near the head of the main avalanche, producing e f f e c t i v e r a p i d propagation of the avalanche across the gap, which, i n e f f e c t , i s b r i d g e d . I t was maintained t h a t t r a n s i t times are approximately 10"^ second. Both of these t h e o r i e s are only g i v e n i n a q u a l i -t a t i v e form, and, although t h e r e i s some experimental evidence of streamers (the comparatively narrow luminous t r a c k s o c c u r r i n g at breakdown at high gas pressures) obtained by Rogowski and Loeb (1928), more experimental data are necessary before a q u a n t i t a t i v e theory can be e s t a b l i s h e d . The above -13-t h e o r i e s do not account f o r the process of the g e n e r a t i o n of the r e q u i s i t e photons, and the way i n which such photons produce e x t r a i o n i z a t i o n and c o n t r i b u t e to the i n c r e a s e of c u r r e n t i s not q u a n t i t a t i v e l y e x p l a i n e d , b) Thermal Breakdown Th i s form of e l e c t r i c a l breakdown i s even l e s s w e l l under-stood. I t was observed by Crawford & E d e l s ( i 9 6 0 ) i n t h e i r work i n low c u r r e n t a r c s and l a t e r by C h u r c h i l l (1961) i n h i s work i n high c u r r e n t spark gaps. Soon a f t e r the i n i t i a t i o n of the spark i . e . at. d e l a y times l e s s than 500 jus, the gas i n s i d e the gap has a f i n i t e (and v a r y i n g ) r e s i s t a n c e . A p p l i c a t i o n of a r e s t r i k i n g v o l t a g e can produce cu r r e n t and p o s s i b l y f o l l o w e d by r e i g n i t i o n of the channel. As soon as the d i s c h a r g e c u r r e n t ceases, the channel w i l l s t a r t t o decay by the v a r i o u s l o s s mechanisms such as r a d i a t i o n , recombination e t c . as d e s c r i b e d i n 1 .1. However the a p p l i c a t i o n of a r a p i d l y r i s i n g r e i g n i t i o n v o l t a g e may r e s u l t i n a power input g r e a t e r than the r a t e of l o s s . I f e i s the t o t a l energy d e n s i t y of the gas column, then .Ti - P " P L ••••••• ( 1 - U ) Where P = power input from the a p p l i e d v o l t a g e P L = power l o s s e s i n the channel The above equation governs the behaviour of the gass column of the gap. I f P - P L < 0 , t h e r e w i l l be no r e i g n i t i o n or - 1 4 -c u r r e n t conduction. When P - P L > 0 , i . e . the input power of the r e s t r i k i n g v o l t a g e i s g r e a t e r than the power l o s s , the space-charged zone of the gas column may be r e - e s t a b l i s h e d i n the gap. I t i s p o s s i b l e f o r the c u r r e n t to b u i l d up to s u f f i c i e n t v alue t o cause breakdown i n the gap. A steady s t a t e occurs i f P = P-^. Since the gap i s r e i g n i t e d through a continuous energy exchange process, the r e i g n i t i o n i s c a l l e d 'thermal'. T h i s form of breakdown occurs much more slo w l y than the cascade process which causes the 'spark-breakdown'. In between these two forms of breakdown, t h e r e i s a t r a n s i t i o n p e r i o d c a l l e d the 'glow-to-arc' t r a n s i t i o n . A l l these t h r e e modes of breakdown have been observed i n the work of Crawford and Edels ( I 9 6 0 ) , Various t h e o r e t i c a l attempts have been made to analyse the thermal r e i g n i t i o n ( C a s s i e , 1939 and Mayr, 1943), but more r e i g n i t i o n data are needed before a c l e a r understanding of t h i s breakdown can be o b t a i n e d . -15-CHAPTER 2: APPARATUS 2.1 General D e s c r i p t i o n of Apparatus F i g . 2 and f i g . 3 show the o v e r a l l apparatus i n a schematic manner. The o p e r a t i o n of the apparatus i s as f o l l o w s : the main c a p a c i t o r bank i s charged u s u a l l y to 19 to 20 kv from a v a r i a c - c o n t r o l l e d h i g h v o l t a g e supply, and the r e s t r i k i n g v o l t a g e generator i s charged i n a s i m i l a r manner. The hig h c u r r e n t d i s c h a r g e i s i n i t i a t e d from the c o n t r o l panel by a pulse from the main t r i g g e r u n i t . The c u r r e n t induces a vo l t a g e i n a pick-up c o i l p l a c e d near t o the spark gap a c c o r d i n g to Faraday's r e l a t i o n : <j)E.dl = ~ | | ! , (2.1) where $ i s the magnetic f l u x through the c o i l . T h i s induced vo]t age i s used t o t r i g g e r the d e l a y u n i t , which, a f t e r a pre-set d e l a y time, i n t u r n f i r e s the r e s t r i k i n g v o l t a g e gener-a t o r , thus a p p l y i n g the probing v o l t a g e a c r o s s the probi n g gap. The r e s u l t a n t c u r r e n t and v o l t a g e a c r o s s the probing gap are d i s p l a y e d on a double beam o s c i l l o s c o p e (type 551). The component p a r t s of the apparatus are d e s c r i b e d i n d e t a i l below. 2.2 High Current Generator & Main T r i g g e r C i r c u i t ( f i g . 4a) The h i g h c u r r e n t generator c o n s i s t s e s s e n t i a l l y o f two 20 kv, 5 u f , low inductance c a p a c i t o r s (NRG type 201) charged i n p a r a l l e l and then d i s c h a r g e d through the gap assembly. A -16-S A F E T Y INTERLOCK M A I N CONTROL P A N E L E _H T CHAR GING S E T KeSfRIKlUS VOLTAGE GENERATOR ELECTRONIC DELAY UNIT T 0 T R I G G E R C R 0 CAPACITOR BANK S P A R K CHAMBER a ELECTRODE SYSTEM MA I N TRIGGER U N I T C U R R E N T SHUNT a c R o POTENTIAL DIVIDER 8 CRO FIGURE 2 R E C 0 V E R Y M E A S U R N G A P P A R A T U S B L 0 C K D 1 A G R A M S T E P FUNCTION GENERATOR SPAR K C H A M B E R NON-LINEAR RESISTOR R-TO C R O I I S I PROBING I GAP "SHUNT = - ion 5 0 E L A Y U N I T I I _ l PICK-UP COIL 300 K 20KV SUPPLY - |5KV TRIGGER l O u f 20KV - T O C R O 20 K T R I G G E R U N I T TO CRO T Y P E 55 1 DOUBLE BEAM K- PLUG IN UNIT FIGURE 3 -17-u n i - d i r e c t i o n a l current pulse i s produced by c r i t i c a l l y damping the i n i t i a l discharge w i t h an a i r - c o o l e d n o n - l i n e a r r e s i s t o r ( 6 - i n diameter morganite r e s i s t o r , type 301). In the electrode assembly, G Q i s set to hold o f f the voltage V Q to which the condenser bank i s charged, w h i l s t G]_ and G£ are set to break down on a p p l i c a t i o n of V c. The t r i g g e r c i r c u i t i s shown i n the same diagram. The anode of the t r i g a t r o n i s charged to 15 kv by the p o t e n t i a l d i v i d e r provided by the r e s i s t o r s 20M and 60M. The t r i g a t r o n i s f i r e d by a pulse of -10 kv from the pulse transformer, and as a r e s u l t , the p o t e n t i a l of the t r i g a t r o n anode drops to zero and g i v i n g a -15 kv pulse t o the lower e l e c t r o d e of G Q. This breaks down the gap G 0 and i n i t i a t e s the discharge. The current wave form i s shown i n f i g . 4b , the magnitude at peak current i s about 40 ka. HIGH CURRENT GENERATOR PARAMETER Parameter Value No. of Capacitors 2 Capacitance of each Capacitor 5 M-f Working voltage 20 kv Maximum energy 2 KJ T o t a l c i r c u i t inductance .42 yuf Peak current 40 ka FIGURE 4b. DISCHARGE CURRENT WAVE FORM Time scale = 2 us/cm Amplitude of peak current = 40ka -18-2 0 M i 6 0 M 2 0 0 K - W v -IK •025 uf C V I 2 5 T R I G A T R O N f ^ 10 Hi 3 0 0 V -C H A R G I N G R E S I S T O R DAMPING R E S B T O R - I S K V - G , R E S T R I K I N G V O L T A G E G E N E R A T O R G 0 13mm -AM - V C 2 0 K V 3 0 0 K L I K 500pf 20K V IM 1—YA<— S H U N T = l O i l i SPARK C H A M B E R 2 0 K . ^ I O u f U K J B A N K ) 2 0 K V H I G H C U R R E N T G E N E R A T O R C I R C U I T I- 3 2 P U L S E T R A N S F O R M E R E A R T H F I G U R E 4 a M A 1 N T R G G E R C 1 R C U T C O N D E N S E R B A N K H I G H V O L T A G E P O T E N T I A L O I V I O E R 8 C R 0 E H T . P O W E R S U P P L Y : i -5K PROBING GAP i 2 0 O K •7cm r Vs" M A I N T R I G G E R C I R C U I T •05uf -I5KV D C TRIGGEJR G A P I5K 02 u f R, 'SHUNT % ion. r •05 u f 5 0 M I5KV D C I S P A R K C H A M B E R 25KV MULTIPLIER 500 M < A V O 1 5 0 a 500 p f T O O U T P U T O F D E L A Y U N I T 3 0 0 V 3 2 1 P U L S E T R A N S F O R M E R ^ 2 0 K E A R T H R E S T R I K I N G V 0 L T A G E G E N E R A T O R F I G U R E 5 a -19-2.3 R e s t r i k i n g V o l t a g e Generator ( f i g . 5a) A u n i t f u n c t i o n probing v o l t a g e i s produced by a s i n g l e stage impulse generator switched onto the pr o b i n g gap by means of a t r i g g e r gap, which i s charged t o the d e s i r e d p o t e n t i a l by a high t e n s i o n power supply. The output i s c o n t i n u o u s l y v a r i a b l e from 1 t o 15 kv. The 1.5 K r e s i s t o r provides i s o l a t i o n from the hig h current generator. T h i s r e s i s t o r t o g e t h e r with the s t r a y capacitance of the gap G2 (~ 50 pf ) c o n t r o l s the r i s e time ( RC < 0.5 yus ), while the 200K r e s i s t o r and the 0.05uf c a p a c i t o r c o n t r o l the f a l l time of the v o l t a g e wave form ( RC = 10^ yus). A t y p i c a l output generator wave form i s shown i n f i g . 5b. The f a l l i n 50 ^ us i s l e s s than 1% of f u l l v a l u e . FIGURE 5b. RESTRIKING VOLTAGE WAVE FORM Time s c a l e = 5us/cm Voltage s c a l e = 5kv/cm i ) No breakdown i i ) Spark breakdown -20-2.4 Step F u n c t i o n Generator ( f i g . 6a) The o r i g i n a l d e s ign of t h i s generator i s due to E t t i n g e r & E d e l s (1959). The output wave form of the present generator has the f o l l o w i n g s p e c i f i c a t i o n s : a) R i s e time ^ lyus b) Constant amplitude t o +_ 1% f o r 50 jms c) Amplitude independent of current output up to 10 amp. d) Output amplitude v a r i a b l e from 100 v.. t o 2.5 kv. e) Withstand 10 kv pulse at i t s cathode output. A c t u a l l y we want i t to withstand 20 kv as our present spark gap i s operated at t h i s v a l u e . However a t h y r a t r o n w i t h a 20 kv Peak Inverse V o l t a g e i s not r e a d i l y a v a i l a b l e . A p r o t e c t i v e gap i s connected across the cathode output of the generator as a s a f e t y d e v i c e . The working p r i n c i p l e of the c i r c u i t i s roughly as f o l l o w s : a pu l s e from the e l e c t r o n i c delay u n i t ( to be d e s c r i b e d l a t e r ) t r i g g e r s the 2D21 tube. When i t f i r e s , i t s cathode v o l t a g e r i s e s to p l a t e p o t e n t i a l (400 v)j, t h i s i n t u r n f i r e s the mercury t h y r a t r o n (FG41) and g i v e s an output v o l t a g e equal t o the v o l t a g e t o which the condenser bank (280uf) i s charged. A 200-ohm morganite r e s i s t o r (3 i n . i n diameter) i s pla c e d i n the cathode c i r c u i t t o a l l o w r a p i d conduction of the FG41. When the probing gap breaks down, the c u r r e n t w i l l flow a c r o s s the gap t o ground through the shunt Rg. Both the cu r r e n t and the v o l t a g e across the probi n g gap may be measured. F i g . 6b shows a t y p i c a l output wave form o f the generator, and i s f l a t over a d u r a t i o n of 200 us. -21-6 -I0OV A 400V t r i g - Q % * I I 0 V A C 50K c 0-2-5KV -vw—-=!= 2 80 uf 25 KV CONDENSER BANK FS 41 (MERCURY THYRATRON P. I V. = IOKV) POTENTIAL DIVIDER 8CR0 PROTECTIVE GAP , 20°" PROBING GAP BY 10 -OH- ;30uf SlSOK I50K BY 10  68 0-0. ^Wv-B- 10 OV —J-^ IKV—"J"— 6pV »-j30uf *- | -30llfV 1VOB2 FIGURE 6a C 0-25KV S T E P F 0 N C T 1 0 N GEN E R A T OR 8 P 0 W E R S U P P L 1 E S r 560K •Oluf IOK - W r f — 2D2I :IOOK 5 i o o a 005 uf Oluf L-Wv 1 IOK —VWT---30V EXTERNV OOluf 10  pf Oluf -VE h o 10 K 0 2D2I iooa lOOpf -VE 6-3 V A C BY I 00 680 A - 10V OB 2 FIGURE 7 DUAL OUTPUT TRIGGER UNIT -22-FIGURE 6b. STEP FUNCTION GENERATOR WAVE FORM i ) time base 10 yus/cm i i ) time base 5 /ts/cm i i i ) time base 20 yus/cm iv ) time base 1 yus/cm Amplitude of vo l t a g e = 500v 2 .5 Dual Output T r i g g e r U n i t ( f i g . 7) The c i r c u i t c o n s i s t s e s s e n t i a l l y o f two 2D21 s t a g e s . The pulse from the pick-up c o i l ( about + 60 v ) t r i g g e r s the f i r s t 2D21 tube. The cathode of t h i s tube r i s e s and f i r e s the second 2D21 tube. The output from the cathode i s a p o s i t i v e -pulse of about 200 v o l t s and the output from the anode i s a negative pulse of about 10 v o l t s used f o r t r i g g e r i n g the d e l a y -23-u n i t . The 50G K r e s i s t o r and the 0.005 / i f c a p a c i t o r of the input stage are chosen t o give a f a s t pulse whereas the 2M r e s i s t o r and the 0.001 uf c a p a c i t o r of the output stage c o n t r o l the r i s e time of the p u l s e . The 100 pf and 10 K i n the output stage form a. d i f f e r e n t i a t i n g network, chosen to give a negative pulse of 10 v o l t s which i s s u f f i c i e n t t o t r i g g e r the d e l a y u n i t . The other output of t h i s u n i t was used f o r another experiment. 2.6 E l e c t r o n i c d elay u n i t s a) Pulse Delay U n i t ( f i g . 8a. b) T h i s d e l a y u n i t produces a delay r a n g i n g from 1.5 /AS to 50 yus i n Range 1 and delay r a n g i n g from 50 /<s t o 700 i n Range 2. The input stage i s a b o o t - s t r a p t r i g g e r generator which produces a l a r g e , r a p i d l y r i s i n g p o s i t i v e square p u l s e t o t r i g g e r the f o l l o w i n g s t a g e s . The continuous d e l a y i s produced by a M i l l e r rundown and a v o l t a g e d i s c r i m i n a t o r . The r e g e n e r a t i v e t r i g g e r simply improves the l e a d i n g and f a l l i n g stages of the p u l s e . I t i s a g a i n i n v e r t e d by another u n i - v i b r a t o r b e f o r e being f e d i n t o the cathode f o l l o w e r stage at the output. The output delayed pulse has an amplitude o f 40 v o l t s and a pulse d u r a t i o n of 10yus. The a c t u a l apparatus has t h r e e channels to provide g r e a t e r v e r s a t i l i t y t o the apparatus. b) Decade Delay Unit ( f i g . 9 ) E s s e n t i a l l y t h i s i s a 5 decades of l o g a r i t h m i c a l l y spaced delays r a n g i n g from 100 JJLS to 10 sec. with 10 steps per decade. —w^Wrn iD I •vww—wv$/vw V V N ^ i — I —wvw--25-FIGURE 8b Power iu pp'y . M IJOK LlOK 68K : J 2 2 K : : I M ^ 2 2 0 K 33K PULSE TRANSFORMER FIGURE 9 V A R. I ABLE DELAY UNIT -26-Thus much lon g e r d e l a y can be reached with t h i s u n i t than with the one d e s c r i b e d p r e v i o u s l y . The u n i t c o n s i s t s of a mono-s t a b l e m u l t i v i b r a t o r g e n e r a t i n g delays chosen by the s w i t c h i n g of an RC time constant. The de l a y u n i t i s t r i g g e r e d by a pulse from the pick-up c o i l d u r i n g the i n i t i a l c u r r e n t d i s -charges and f i r e s a 10 kv pulse transformer from the balanced output at the anode. The output from i t s cathode i s used f o r t r i g g e r i n g the o s c i l l o s c o p e . By means of a t i m i n g marker generator, pulse generator and double-beam o s c i l l o s c o p e , the d e l a y times can be measured to + 2%, 2.7 High P o t e n t i a l D i v i d e r ( f i g . 10a) The design o f t h i s s p l i t c a p a c i t o r d i v i d e r f o r measuring high v o l t a g e s i s due to Burch (1932). I n the diagram CT_ and C2 ' are the c a p a c i t o r s which d i v i d e the input p o t e n t i a l , while the combination of R and C3 i s a compensating network. For any input v o l t a g e Vj_ at the end A B, a vo l t a g e V2 = C l y C l + G 2 1 appears at the other end CD. I f t h ^ r e i s no compensating network, a f t e r i n f i n i t e time the volt a g e V 2 w i l l drop t o C l ± where Cv i s the capacitance of the c a b l e . C X + C 2 + C K 1 T h i s w i l l cause an e r r o r C^/C 2 ( C 2 » CT_ ) i n the measurement of the v o l t a g e . For the r e d u c t i o n of t h i s e r r o r , the compen-s a t i n g network i s added.' Here a part of the low-voltage r L -27-200A.I I Oft COAXIAL CABLE CHARACTERISTIC IMPEDANCE W = 2 0 0 f t C A P A C I T A N C E PER FT = 6-4pf M E T A L B OX F O R E L E C T R O S T A T I C S H I E L D I N G T Y P E K P L U G IN UNIT H 1 G H V O L T A G E P 0 T E N T 1 A J . D 1 V 1 D E R R A T 1 0 1 0 0: 1 FIGURE 10 a D E T A I L S OF S H U N T = TOTAL LENGTH OF F E R R Y M E T A L : WIDTH = I cm T H I C K N E S S = • 02cm 60 cm SPECIFIC RESISTANCE R E S I S T A N C E = l O f l I N DUCTANCE = 6-7 uh CAPACITANCE = 25 pf OF FERRY METAL = 4 9 X 10 ohm-cm - 6 MICANITE INSULATOR C U R R E N T L E A D S POTENTIAL L E A D S ^ C O A X I A L S A D A P T O R FERRY M E T A L P E R S P E X SUPPORT NOT TO S C A L E FIGURE M a L 0 w 1 N O U C T A N C E C u R R E N T S H U N T - 2 8 -c a p a c i t y i s t r a n s f e r r e d t o the r e c e i v i n g end of t h e - c a b l e , being connected i n s e r i e s with a r e s i s t a n c e R at the output t e r m i n a l s . The droop of the v o l t a g e wave form due to the charge d r a i n e d from C 2 by the cable i s compensated by the simultaneous charge-up of C3. I f we make c l + 92 = c 3 + GK> the i n i t i a l value of the output wave form w i l l be the same a f t e r i n f i n i t e time because the compensation would be exact. The equations governing the d e s i g n of such a high poten-t i a l d i v i d e r are t h e r e f o r e : C 2 + C3 + C K = n C1 (2.2) where C K = C K + c C R 0 n = d i v i s i o n r a t i o of the d i v i d e r and C1 + C 2 = C3 + C K (2.3) For the present experiment, a 100:1 d i v i d e r would be s u i t a b l e , hence f o r n = 100, C]_ = 25 pf say, CR = (54 + 20) pf = 74 pf where the 54 p f i s due to the cable and the 20 pf i s the input c a p a c i -tance o f the type K input u n i t S o l v i n g the equations, we o b t a i n c 2 = 1240 pf C3 = 1190 pf By a c t u a l adjustment of the c a p a c i t o r s , optimum f l a t n e s s of -29-the output v o l t a g e i s obtained when C 2 = 1390 pf C3 = 1150 p f The response of the p o t e n t i a l d i v i d e r t o a step f u n c t i o n i s shown i n f i g . 10b. I t i s seen t h a t l i t t l e droop ( < 1% ) occurs over a time of 200 us. FIGURE 10b. RESPONSE OF POTENTIAL DIVIDER TO A STEP FUNCTION Time base = 20 yus/cm Vo l t a g e = 1 KV 2 . 8 Current Shunt ( f i g . 11a) The d e s i g n o f the present low inductance c u r r e n t shunt f o r measuring surge c u r r e n t i s due to Park (1947). E s s e n t i a l l y i t 0 0nsists of a s t r i p of f e r r y metal (data concerning the metal are g i v e n on the same f i g u r e ) bent i n the form of a U-loop and having a t o t a l r e s i s t a n c e of 0.10 ohm. The frequency response of the shunt has been t e s t e d up to 1 Mc by u s i n g the f o l l o w i n g c i r c u i t : A-o. 5M 6-5 KV B+ -30-L=-8nnh C_= 5oo pf — (20 kv) T r V R-IK Rs= - i o n 3 KV FIGURE l i b , CIRCUIT FOR TESTING FREQUENCY RESPONSES OF CURRENT SHUNT. The response i s shown i n f i g . 11c, the upper t r a c e i s the response as measured by a T e k t r o n i x c u r r e n t probe ( P 6016 ) used i n c o n j u n c t i o n with a p a s s i v e t e r m i n a t o r at a s e n s i -t i v i t y of 2ma/cm, wh i l e the lower t r a c e i s obtained by the present shunt. FIGURE 11c. RESPONSE OF CURRENT SHUNT Time base i ) 5us/cm i i ) 2us/cm -31-Both measured the c u r r e n t t o be approximately 8 amp., ag r e e i n g with t h e o r e t i c a l values w i t h i n experimental e r r o r s . For i n such a c i r c u i t , the cu r r e n t I i s g i v e n by * (2.4) In the present c i r c u i t , ¥ = 9.5 kv, L = 0.8 mh C = 500 pf hence I = 7.$ amp. Al s o the r i s e time of the wave i s seen from the t r a c e s t o be about 1 y u s . T h i s a l s o agrees with the t h e o r e t i c a l value given by T = T • ±max. •'•rise | /Tc = 1 jus (2.5) Since the p e r i o d i s g i v e n by T = 2 n J~LC (2.6) T FIGURE l i d . RISE TIME OF CURRENT WAVE FORM - 3 2 -2.9 Probes Tungsten rods of diameters 3.2mnu, 1.6 mm., and 1 mm. are used as probes. Tungsten i s chosen because of i t s h i g h m e l t i n g p o i n t and s m a l l e r o s i o n and s p l u t t e r i n g e f f e c t . These rods are coated w i t h s e v e r a l t h i n l a y e r s of epoxy almost up to the end of the probes to reduce c o o l i n g e f f e c t of the gas due to the probes. The rods are s o l d e r e d onto brass b o l t s . The gap l e n g t h of the p r o b i n g gap as w e l l as the r a d i a l d i s t a n c e of the probing gap from the t e c t gap are e a s i l y a d j u s t a b l e . The c e n t r e s of the two gaps should be maintained i n a same h o r i z o n t a l l i n e . The probes are mounted h o r i z o n t a l l y i n the present experiment to f a c i l i t a t e experimental arrangement although i d e a l l y they should be mounted i n the v e r t i c a l d i r e c t i o n . - 3 3 -CHAPTER 3 EXPERIMENTAL TECHNIQUES In t h i s s e c t i o n we s h a l l b r i e f l y d i s c u s s the experimental methods employed i n t h i s i n v e s t i g a t i o n , i n c l u d i n g the choice of the i n i t i a l d i s c h a r g e c u r r e n t wave form, the r e s t r i k i n g v o l t a g e wave form, the d e f i n i t i o n of the r e i g n i t i o n v o l t a g e both i n the 'spark breakdown' regime and i n the 'thermal breakdown' regime, and the measurement of these breakdown v o l t a g e s . 3 . 1 I n i t i a l Discharge Current Wave Form I d e a l l y a r e c t a n g u l a r pulse of cu r r e n t having a c o n t r o l -l a b l e d u r a t i o n i s most s u i t a b l e f o r the purpose of i n i t i a t i n g the d i s c h a r g e . Such a cur r e n t i s r e a d i l y r e p r o d u c i b l e , b e s i d e s having the added advantage t h a t the d i s c h a r g e p r o p e r t i e s o f the gap such as the temperature and the r e i g n i t i o n v o l t a g e can be r e l a t e d t o a d e f i n i t e value of c u r r e n t . Although such a cu r r e n t d i s c h a r g e has been approximated i n low c u r r e n t d i s -charges (~ 700 amp), i t proves t o be q u i t e d i f f i c u l t i n h i g h c u r r e n t d i s c h a r g e s . Consequently a high c u r r e n t g e n e r a t o r ( d e s c r i b e d i n d e t a i l i n 2 .2) c r i t i c a l l y damped with n o n - l i n e a r r e s i s t o r was adopted f o r the i n i t i a l d i s c h a r g e c u r r e n t . 3.2 R e s t r i k i n g Voltage Wave Form Two forms of r e s t r i k i n g v o l t a g e have been employed i n reco v e r y work, the l i n e a r l y r i s i n g v o l t a g e and the u n i t f u n c t i o n -34-v o l t a g e . The use of the f i r s t type can in t r o d u c e e r r o r when the time l a g i s l a r g e , whereas the use of the u n i t v o l t a g e has the f o l l o w i n g advantages ( C h u r c h i l l , I 9 6 3 ) . 1) The r e i g n i t i o n v o l t a g e amplitude i s a c c u r a t e l y determined. 2) Time la g s t o breakdown may be examined. 3) The f a s t l e a d i n g edge of the pulse a l l o w s the f u l l r e i g -n i t i o n ^ c h a r a c t e r i s t i c s to be determined. Hence a u n i t f u n c t i o n v o l t a g e i s employed i n the present experiment. During the e a r l y post-spark p e r i o d , r e i g n i t i o n cannot be determined by the c o l l a p s e of the probing v o l t a g e alone owing t o the a p p r e c i a b l e i o n i z a t i o n of the gap, but r e q u i r e s the simultaneous measurements of the volt age and the c u r r e n t a c r o s s the gap. Such a simultaneous measurement a l s o g i v e s i n f o r m a t i o n about the r e s i s t a n c e of the gap. In the f i n a l r e c o v e r y p e r i o d , o b s e r v a t i o n of the r e s t r i k i n g v o l t a g e i s s u f f i c i e n t to determine the r e i g n i t i o n v o l t a g e as i n d i c a t e d by a sudden c o l l a p s e of the v o l t a g e wave form because pre-breakdown c u r r e n t i s n e g l i g i b l e . 3.3 D e f i n i t i o n s and Measurements of R e i g n i t i o n V o l t a g e To begin w i t h , we s h a l l s t a t e the c r i t e r i a with which we s h a l l use t o d e f i n e the r e i g n i t i o n v o l t a g e s i n both the thermal breakdown and spark breakdown regime: i ) The d e f i n i t i o n of the r e i g n i t i o n i n the spark breakdown regime w i l l be taken as T t h e lowest v o l t a g e o f a constant v o l t a g e generator which when connected i n s t a n t a n e o u s l y a c r o s s the probing gap w i l l cause a spark discharge to be formed i n a f i n i t e time' ( E d e l s & Crawford 1956). i i ) F o l l o w i n g E d e l s & E t t i n g e r (1962), i n t h e i r work i n thermal r e i g n i t i o n of low c u r r e n t a r c s , we d e f i n e the r e i g n i t i o n v o l t a g e i n the thermal r e i g n i t i o n regime t o be 'the minimum v o l t a g e of a constant v o l t a g e generator which when connected across i n s t a n -t a n e o u s l y a c r o s s the p r o b i n g gap, causes a surge c u r r e n t to flow. In order to measure the c u r r e n t , a s p e c i a l low inductance shunt has t o be used ( f i g . 11a). Three important requirements f o r a shunt f o r measuring sunge c u r r e n t s as p o i n t e d out by Park (1947) are 1) The e f f e c t i v e impedance considered as a 4-terminal network must be constant over as great a range i n frequency as p o s s i b l e . 2) I n d u c t i v e e f f e c t s of p a r t s of the c u r r e n t c i r c u i t , o ther than the shunt, upon the p o t e n t i a l leads of the shunt, should be minimum. 3) I t must be p o s s i b l e to connect the sheath of the cable from the shunt to the o s c i l l o s c o p e , t o ground at or near shunt without i n t r o d u c i n g induced v o l t a g e i n the shunt p o t e n t i a l c i r c u i t . The present shunt t o g e t h e r with the a c t u a l c o n n e c t i o n s a t i s f y the above requirements. I t may be p o i n t e d out t h a t although the c o a x i a l t u b u l a r shunt i s a b e t t e r d e s i g n ( i n g e n e r a l g i v i n g a lower i n d u c t a n c e ) , i t . i s more d i f f i c u l t to c o n s t r u c t . - 3 6 -The probing v o l t a g e r e q u i r e s two measurements to be made: amplitude and wave shape. The h i g h v o l t a g e must be d i v i d e d i n order i t may be observed i n an o s c i l l o s c o p e . The choice of p o t e n t i a l d i v i d e r types i n v o l v e s a compromise of the r i s e time of the r e s t r i k i n g v o l t a g e and the d i s t o r t i o n l e s s r e p r o -d u c t i o n of the wave form. A r e s i s t o r p o t e n t i a l d i v i d e r cannot be employed because the s t r a y c a p a c i t y w i l l combine with the output impedance of the d i v i d e r to g i v e an i n t e -g r a t i n g e f f e c t . A s p l i t c a p a c i t o r d i v i d e r w i t h a low input capacitance and v a r i a b l e d i v i s i o n r a t i o i s s a t i s f a c t o r y f o r the present purpose. Such a d i v i d e r i s d e s c r i b e d i n d e t a i l i n 2 . 6 , i t d i v i d e s a step f u n c t i o n without d i s t o r t i o n ( f i g . 1 0 c ) . 3.4 Measurements Since the d i a g n o s t i c technique employed i n t h i s e x p e r i -ment p e r t u r b s the r e c o v e r i n g channel, o n l y one t e s t i s taken f o r each d i s c h a r g e , and the f u l l r ecovery curve i s obtained i n a s t a t i s t i c a l manner. Previous work ( C h u r c h i l l , Parker & Craggs, 1961) shows t h a t the r e p r o d u c i b i l i t y of r e i g n i t i o n measurements i s g r e a t l y i n f l u e n c e d by e l e c t r o d e and gas c o n d i t i o n s and r e p e t i t i o n r a t e of the d i s c h a r g e . About 20 t e s t s are necessary t o determine one r e i g n i t i o n c o n d i t i o n to w i t h i n +_ 15%9 Delay times as w e l l as the o s c i l l o -scope s e n s i t i v i t y must be checked before and a f t e r each run. Constant check must be kept on the gap l e n g t h of the probes and i t s r e l a t i v e p o s i t i o n t o the t e s t gap. I t i s important - 3 7 -t o c l e a n the e l e c t r o d e s a f t e r each run. The u s u a l high v o l t a g e p r e c a u t i o n s must be observed. The s a f e t y d e v i c e s i n c l u d e e a r t h i n g rods and a s a f e t y gap connected a c r o s s the output of the mercury t h y r a t r o n . Measurement of thermal r e i g n i t i o n of the main t e s t gap cannot be made as the t e s t gap i s at present o p e r a t i n g at 20 kv while the only a v a i l a b l e t h y r a t r o n (used i n the constant v o l t a g e generator) has a peak i n v e r s e v o l t a g e (P.I.V.) of 10 kv so t h a t i t becomes d i f f i c u l t t o connect the v a l v e d i r e c t l y t o the t e s t gap. I t i s not i m p o s s i b l e but proved t o be time consuming. Thus i t was decided t o measure recover y at r a d i a l d i s t a n c e s from the t e s t gap. In t h i s way the P.I.V. l i m i t a t i o n i s o f no consequence u n l e s s spurious breakdown o c c u r s . Probes are p l a c e d at l e a s t at 2 cm, from the centre of the t e s t gap t o avoid spurious breakdown. CHAPTER 4: EXPERIMENTAL RESULTS The r e i g n i t i o n v o l t a g e i s measured a c c u r a t e to +_ 50 v. by the s t e p - f u n c t i o n generator ( f i g . 6a) and t o +_ 125 v. by the r e s t r i k i n g v o l t a g e generator ( f i g . 5 a ) . The c r i t e r i a adopted were gi v e n i n 3 . 3 . During thermal r e i g n i t i o n regime, sharp t r a n s i t i o n from very s m a l l c u r r e n t t o v ery l a r g e c u r r e n t i s u s u a l l y observed. In a l l the f o l l o w -i n g i n v e s t i g a t i o n s , tungsten rods are used as probes, and experiments are performed i n a i r a t atmospheric pressure unless otherwise s t a t e d . 4 . 1 C o o l i n g E f f e c t of E l e c t r o d e s a) E l e c t r o d e Diameter ( f i g . 12) Tungsten rods of diameters 1mm, 1.6mm, 3.2mm are used f o r the p r o b i n g gap. The r e c o v e r y curves obtained show f a i r l y l a r g e c o o l i n g e f f e c t f o r the 3.2mm diameter gap which r e c o v e r s about twice as f a s t as the 1.6mm diameter gap and t h r e e times as f a s t as the 1mm diameter gap. I t would seem t h a t e i t h e r the 1.6mm or 1mm diameter rod should be used f o r probes i n order to minimize the c o o l i n g e f f e c t of the e l e c t r o d e s on the gas. However the choice of probe s i z e i s l i m i t e d by both the e l e c t r o d e e r o s i o n e f f e c t and the time l a g e f f e c t to be d i s c u s s e d l a t e r i n s e c t i o n s 4 . 2 and 4 . 3 . -39-b) Gap len g t h ( f i g . 13) The gas rec o v e r s completely i n about 20 ms when the probin g gap s e p a r a t i o n i s at 2 mm. Both the 5 mm and 10 mm gap r e c o v e r at approximately the same r a t e ; they r e c o v e r almost completely i n 50 ms. The reason f o r t h i s i s due t o the g r e a t e r c o o l i n g e f f e c t of the gas by the e l e c t r o d e s when the gap l e n g t h i s s m a l l . The c o o l i n g e f f e c t seems t o be s m a l l i f the gap s e p a r a t i o n i s equal t o or g r e a t e r than 5 mm. Owing to the l i m i t i n g v o l t a g e of one of the ge n e r a t o r s , the step f u n c t i o n generator (2.5 KV), we f i x the probing gap length at 5 mm i n a l l the f o l l o w i n g i n v e s t i g a t i o n s . 4.2 E l e c t r o d e E r o s i o n E f f e p t , Owing to the l a r g e amount of energy d e l i v e r e d t o the probes by the step f u n c t i o n generator and over a long p e r i o d of time, i t i s observed the 1.6 mm d i a . probes develop sharp p o i n t s a f t e r the generator has been f i r e d a few times when the a p p l i e d v o l t a g e i s above 800 v o l t s , while e r o s i o n i s t o l e r a b l e below 500 v o l t s . For the 3.2 mm probes, i t i s found t h a t e r o s i o n i s t o l e r a b l e and t h e r e f o r e they are used. 4.3 Time Lag C h a r a c t e r i s t i c s The t i m e - l a g between the a p p l i c a t i o n of an impulse v o l t a g e and the consequent breakdown of a gap i s measured u s i n g probes of d i f f e r e n t diameters. I t i s seen from f i g * 14a t h a t the sm a l l e r e l e c t r o d e s have a ve r y l o n g t i m e - l a g which would cause a l a r g e e r r o r i n the measurement of r e i g n i t i o n v o l t a g e i f they 15 3 -2 _ FIGURE 12 S P A R K GAP R E C O V E R Y IN AIR P R E S S U R E = 760mm HS-P E A K C U R R E N T * 4 0 K A T E S T G A P : 16mm TUNGSTEN ELECTRODES, 7mm SAP SEPARATION P R O B I N G GAP : TUNGSTEN ELECTRODES MOUNTED HORIZONTALLY, 5mm SEPARATION DISTANCE OF PROBING GAP TO TEST GAP = 2 c m SPARKING VOLTAGE — PARAMETER : PROBE DIAMETER ~T~ T I M E A F T E R SPARK I N I T I A T I O N - M t k L l M C -TIME LAG CHARACTER'S f ICS FOR AIR PRESSURE = 760 mm HG T U N G S T E N E L E C T R O O E S AT 5 mm SEPARATION MINIMUM IMPULSE SPARKING POTENTIAL P A R A M E T E R ; E L E C T R O N O i A M E T E R TIME LAG - M1 CR O S E C S7" FIGURE 13 SPARK GAP RECOVERY IN AIR PRESSURE : 760 mm HG PEAK CURRENT : 4 0 KA TEST G A P : 6-4 mm TUNGSTEN ELECTRODES AT 5mm SEPARATION PROBING GAP; 3-2 mm TUNGSTEN ELECTRODES MOUNTED HORIZONTALLY DISTANCE Of PROBING GAP FROM T E S T * 2 cm SPARKING VOLTAGE PARAMETER • PROBING GAP LENGTH TIME AFTER SPARKING INITIATION - MILLISEC- o TIME LAG CHARACTERISTICS FOR AIR PRESSURE 76 0 mm HG -TUNGSTEN E L E C T R O D E S AT 5mm SEPARATION PARAMETER : E L E C ' R O D E DIAMETER FIGURE 14 b M I C R O S E C . -41-were used as probes. The 3.2 mm diameter probe has a short t i m e - l a g . In f i g . 14b, the t i m e - l a g to breakdown of the d i s -charge i s p l o t t e d a g a i n s t the % ov e r v o l t a g e o f the minimum impulse s p a r k i n g p o t e n t i a l . T h i s graph i s u s e f u l i n making c o r r e c t i o n of o v e r - v o l t a g e . For example, i f we f i x 40 JJ<S t o be the t i m e - l a g of the d i s c h a r g e , a breakdown a t 20 jxs would be Wfo o v e r v o l t e d . The c o r r e c t i o n i s not necessary i n t h i s work because the e r r o r caused by the 3.2 nun probe i s s m a l l and may be n e g l e c t e d . 4«4 Thermal R e i g n i t i o n Curves ( f i g . 15a and 15b) As a r e s u l t of the above i n v e s t i g a t i o n s , 3.2 mm diameter probe a t 5 mm gap s e p a r a t i o n i s used throughout the prese n t experiment. Owing t o the l i m i t a t i o n of the peak i n v e r s e v o l t a g e o f the mercury t h y r a t r o n (FG 41), which i s 10 KV, the re c o v e r y i n the main t e s t gap cannot be i n v e s t i g a t e d . Recovery curves are obtained s t a r t i n g from a d i s t a n c e o f 2 cm from the t e s t gap; nearer d i s t a n c e s are not attempted t o a v o i d s p u r i o u s breakdown between the t e s t gap and the pr o b i n g gap. Recovery curves are ob t a i n e d both f o r the upper gap G i and f o r the lower gap G2 ( f i g . 3) at de l a y time r a n g i n g from 50 jxs t o 500yus when thermal breakdown i s l i k e l y t o occur ( E t t i n g e r and E d e l s , I962). The r e s u l t s f o r GT_ show a g r a d u a l r i s e of r e i g -n i t i o n v o l t a g e as the delay i n c r e a s e s . At 4 cm d i s t a n c e from the c e n t r e of the t e s t gap, no breakdown i s obtained up to 2 .5 KV — the maximum v o l t a g e o f the constant v o l t a g e step f u n c t i o n generator ( f i g . 6a). In the lower gap no breakdown - 4 2 -260C 2400 -2 2 a -2000-! 1800 -5 I 2 0 0 -> _ I coo _ 5 800 — ( 9 u j a. 6 0 0 — 20C — O FIGURE RADIAL RECOVERY OF SPARK GAP CHANNEL IN AIR IN THE 'SLOW-BREAKDOWN ' REGIME P R E S S U R E : 760 mm HG PEAK C U R R E N T : 4 0 K A TEST GAP : 16mm DIA. TUNGSTEN ELECTRODES AT 7 mm SEPARATION PROBING GAP •• 3 2 mm DIA. TUNGSTEN ELECTRODES AT 5mm SEPARATION PARAMETER • DISTANCE OF PROBING GAP TO T E S T GAP 3 cm 2cm l I I J L 10 100 TIME AFTER SPARK I Nl Tl A TI ON - MICROSEC 1000 2600 — 240C — 2 2 T X -2 0 0 0 --1800 — j ) |1600 -} | 4 0 C -[ >I2 0 0 -. IOOC -FIGURE 15 b RADIAL RECOVERY OF SPARK GAP CHANNEL IN AIR IN THE 'SLOW-BREAKDOWN' REGIME P R E S S U R E •  760 mm HG PEAK CURRENT : 40 KA T E S T GAP -6 4mm DIA. TUNGSTEN ELECTRODES AT 5mm SEPARATION PROBING GAP : 3 2 mm DIA. TUNGSTEN ELECTRODES AT 5mm SEPARATION PARAMETER: DISTANCE OF PROBING GAP TO T E S T GAP 2-5cm 2cm J I I I I I I I I l i l l 10 100 TIME AFTER SPARK INI Tl A TI ON - MICROSEC-1000 i s observed at 3 cm d i s t a n c e from the t e s t gap up t o 2.5 Kv. In a d d i t i o n a d i p i s observed at about 200yus delay i n the curve obtained at 2.5 cm r a d i a l d i s t a n c e . I t seems t h a t the channel diameter i n G2 i s s m a l l e r than i n G^. The e f f e c t of the d i p i s d i s c u s s e d i n more d e t a i l i n the next chapter. The r e c o v e r y curves at 2cm r a d i a l d i s t a n c e f o r both gaps are very much the same. Some t y p i c a l p i c t u r e s of the c u r r e n t and v o l t a g e waveforms are shown i n f i g . 16 a-e. 4 . 5 Complete R a d i a l Recovery Curves ( F i g . 17a and 1 7 b ) . . The preceding data have been extended by the use. of a r e s t r i k i n g v o l t a g e generator ( f i g . 5a) which has a v a r i a b l e output v o l t a g e from 1 KV to 15 KV. The r e c o v e r y a t l a t e r time d e l a y as w e l l as a t . f a r t h e r r a d i a l d i s t a n c e s have been i n v e s t i -gated. The r e s u l t s are c o n s i s t e n t with those obtained p r e v i o u s l y ( C h u r c h i l l , 1961). Curves at r a d i a l d i s t a n c e s of 2.5 cm, 3 cm, 3.5 cm, 4 cm a l l show a drop i n the r e i g n i t i o n v o l t a g e between 200 yus to 900yus a f t e r i n i t i a l spark. These d i p s s h i f t to l a t e r d e lay time as the d i s t a n c e of the probe from the t e s t gap i s i n c r e a s e d . Owing to d i f f e r e n t e l e c t r o d e c o n d i t i o n s , the r e c o v e r y curves obtained i n f i g . 17a have d i f f e r e n t s p a r k i n g p o t e n t i a l — the breakdown v o l t a g e at s t a t i c c o n d i t i o n . A normalized r e i g n i t i o n curve i s shown i n f i g . 17b. 4 . 6 D e r i v e d Gas Temperature and Temperature P r o f i l e of Channel In order to determine the temperatures of the t e s t gap both as a f u n c t i o n of delay time and r a d i a l d i s t a n c e , a Paschen curve -44-Figure l6. Current (upper trace) and voltage (lower trace) during Thermal Breakdown. Time base 10 jxz/cm. No breakdown. Delay time = 2 0 0 j i s V=700 V 1=0 amps. Current conduction. Delay time = 60jis V=100 V 1=25 amps. Thermal breakdown. Delay time 6 0/is V=200 V 1=300 amps. Thermal breakdown. Delay time = 500/us V=l KV 1=4 KA Thermal breakdown. Delay time = 500/is V=1.25 KV 1=4.2. KA -45-13 12 10 > r 9 UJ S8 § 7 z o UJ cc RADIAL RECOVERY OF SPARK GAP CHANNEL IN AIR FOR THE WHOLE RECOVERY REGIME PEAK CURRENT • 4 0 KA , PRESSURE = 760mm HG T E S T GAP -6-4 mm DIA. TUNGSTEN ELECTRODES AT 5 mm SEPARATION PROBING GAP : 3 2mm DIA. TUNGSTEN ELECTRODES AT 5 mm SEPARATION SPARKING POTENTIAL : PARAMETER. DISTANCE OF PROBING GAP FROM TEST GAP 25cm 2cm FIGURE 17 a J I 1—I I I I I I I I L J_L 01 TIME AFTER SPARK INITIATION 10 ILLISEC-50 < K . Z UJ I -o ICO a. RADIAL RECOVERY OF SPARK GAP CHANNEL IN AIR FOR THE WHOLE RECOVERY REGIME P E A K CURRENT : 40 KA , PRESSURE = 760 mm HG TEST GAP : 6 4 m m DIA. TUNGSTEN ELECTRODES AT 5mm SEPARATION PROBING GAP - 3-2mm DIA-TUNGSTEN ELECTRODES AT 5 mm SEPARATION SPARKING POTENTIAL : PARAMETER"- DISTANCE OF PROBING GAP FROM T E S T GAP AFTER SPARK IN IT IATION—Ml LLISEC. -46-i s o btained by v a r y i n g the pressure of the spark chamber and n o t i n g the s p a r k i n g p o t e n t i a l s ( f i g . 18a). In f i g . 18b the normalized s p a r k i n g p o t e n t i a l i s p l o t t e d a g a i n s t the p r e s s u r e . The r e s u l t s d e r i v e d are summarized i n f i g . 19 and f i g . 20 i n which the temperature i s p l o t t e d as a f u n c t i o n of d e l a y time and r a d i a l d i s t a n c e r e s p e c t i v e l y . F i g . 19 shows t h a t the temperature drops r a p i d l y i n the e a r l y part of the recove r y curve ( 1 ms - 3 ms ) and then drops g r a d u a l l y t o ambient temperature. The decay i s approximately e x p o n e n t i a l . The temperature shows t h a t up t o a d i s t a n c e of 2.5 cm from the centre of the t e s t gap, the temperature i s n e a r l y uniform, beyond 2.5 cm i t decreases very q u i c k l y t o ambient temperature. The c e n t r e of the channel has been probed by u s i n g the t e s t gap (6.4mm. d i a . ) as probe, and r e s u l t s i n d i c a t e t h a t at e a r l y d e l a y times (1ms - 2 ms), the temperature at zero r a d i a l d i s t a n c e i s 200 to 300 deg. h i g h e r than t h a t a t 2 cm. r a d i a l d i s t a n c e . At l a t e r d e l a y times, the d i f f e r e n c e becomes s m a l l e r . DETRIVED GAS TEMPERATURES J5 SPARK BREAKDOWN VOLTAGE— KV 1—i—I—r—T—i—r TEMPERATURE SPARK BREAKDOWN VOLTAGE AS A PERCENTAGE OF SPARKING POTENTIAL AT 760mmHG PRESSURE _ -48-CHAPTER 5: DISCUSSION 5.1 Recovery'and Breakdown Mechanisms I t was d i s c u s s e d i n the t h e o r e t i c a l chapter, s e c t i o n 1.1 t h a t o p t i c a l r a d i a t i o n loss i s the mlTJbr l o s s mechanism d u r i n g r e c o v e r y of the channel. No measurements were made to examine these l o s s e s , but c a l c u l a t i o n s ( K i t d l l o v , I960) i n d i c a t e t h a t i n many cases the. g r e a t e r part of the energy i n the plasma i s l o s t by r a d i a t i o n , the e f f e c t becomes more important when i m p u r i t i e s are p r e s e n t , as i n the present case. T h i s i s c o n s i s t e n t with the r e s u l t s obtained f o r the temperature of the channel ( f i g . 19 and 20) to be about 2000°K i n the e a r l y d e lay times. For i n such low temperatures, low compared with thermonuclear temperature, bremstrahlung r a d i a t i o n l o s s i s n e g l i g i b l e compared wi t h o p t i c a l r a d i a t i o n l o s s . The break-down mechanisms as p r e d i c t e d t h e o r e t i c a l l y i n s e c t i o n 2.2 are a l s o observed. In the spark breakdown case ( f i g . 5b i i ) , the r e s t r i k i n g v o l t a g e c o l l a p s e s i n l e s s than 10~7 second, and as mentioned i n the same s e c t i o n , t h i s cannot be accounted f o r by the Townsend OL and y mechanisms. In the case of thermal breakdown, the r e s t r i k i n g v o l t a g e at breakdown as i n d i c a t e d by a sudden r i s e of c u r r e n t , i s u s u a l l y very i r r e g u l a r . That thermal breakdown should occur i n the e a r l i e r d e l a y s and spark breakdown a t l a t e r d e l a y times a g a i n agree with the theory of re c o v e r y mechanisms. -49-5 . 2 Recovery Features The r e c o v e r y of h i g h current spark gap i n t h i s i n v e s t i -g a t i o n shows the gen e r a l c h a r a c t e r i s t i c s observed by p r e v i o u s workers (e.g. C h u r c h i l l , I 9 6 I ), t h a t i s , a r a p i d r i s e of the r e i g n i t i o n i n the e a r l y delay (~ 1ms ) and a more g r a d u a l r i s e as the f i n a l stage i s reached. A s p e c i a l f e a t u r e about these r e c o v e r y curves i s the occurrence of a d i p ( f i g . 1 7 a ) . A s i m i l a r d i p has been observed by B u t t e r (I963) i n h i s work on r a d i a l r e c o v e r y of spark gap channel i n hydrogen. I t seems p o s s i b l e t h a t the d i p may he caused by the e f f e c t of a thermal wave which o r i g i n a t e s from the centre of the channel, s i n c e these d i p s occur at l a t e r delay times at l a r g e r r a d i a l d i s t a n c e s . The cause of such a wave propagation i s under-standable on the b a s i s t h a t the i n i t i a l d i s c h a r g e g i v e s a temperature pulse at the centre of the channel. The e q u a t i o n governing the temperature d i s t r i b u t i o n i s g i v e n by the o r d i n a r y heat conduction equation: XT2 T = £ X I c t \ V I ^ ^ t • • • • • • • • • • • • • • \ y # X / where T = T ( r , t ) • k = s p e c i f i c heat c o n d u c t i v i t y c = s p e c i f i c heat f ~ f (£> t ) = d e n s i t y I f we assume T( r , t ) = v ( r ) g ( t ) , then i t would be p o s s i b l e t o do a l e a s t square approximation to f i n d a f u n c t i o n T ( r , t ) t o f i t the experimental curves i n f i g . 19 and 2 0 . The assumption of such a thermal wave can be checked by e v a l u a t i n g the values of the two s i d e s of equation ( 5 o l ) . Such a c a l c u l a t i o n has not been c a r r i e d out because i t i s found t h a t both the amount and accuracy of a v a i l a b l e data are not s u f f i c i e n t f o r t h i s a n a l y s i s . F u r t h e r and more accurate experimental s t u d i e s are needed to co n f i r m t h i s e f f e c t . That t h i s e f f e c t has not been observed i n re c o v e r y i n the main gap i n previous work i s con-s i s t e n t w i t h the i d e a proposed here. 5.3 E f f e c t s of V a r y i n g Discharge Parameters Although the e f f e c t on v a r y i n g d i s c h a r g e parameters have not been i n v e s t i g a t e d s y s t e m a t i c a l l y i n the present work, C h u r c h i l l ( I 9 6 I ) had made d e t a i l s t u d i e s on the e f f e c t s of gap le n g t h , c u r r e n t amplitude and e l e c t r o d e s i z e and m a t e r i a l i n h i s work i n recovery i n a i r , and i t was observed t h a t the e l e c t r o d e s i z e has a powerful i n f l u e n c e upon the recover y p r o c e s s . In the present case, i t i s c l e a r from f i g . 12 t h a t the e l e c t r o d e s i z e has a dominant c o n t r o l l i n g e f f e c t . I d e a l l y the s m a l l e s t probe s i z e should be used otherwise, one would be measuring the c h a r a c t e r i s t i c s of the probes i n s t e a d of the t e s t gap. I t must be admitted t h a t i n the present work, c o o l i n g e f f e c t i s not s m a l l (see f i g . 1 2 ) . Another parameter which has been i n v e s t i g a t e d i s the gap l e n g t h . Again i t should be as l o n g as p o s s i b l e t o avoid c o o l i n g of the i n t e r - e l e c t r o d e gas. However, the f i n i t e s i z e of the spark channel and the maximum amplitude of the v o l t a g e generator both l i m i t the leng t h o f the gap. -51-5.4 Time Lag E f f e c t The time which elapses between the a p p l i c a t i o n of a vo l t a g e and the occurrence of breakdown i s known as the t o t a l time l a g , or simply time l a g . I t c o n s i s t s o f two p a r t s : the s t a t i s t i c a l time l a g and the for m a t i v e time l a g . To understand these concepts, we r e c a l l t h a t e l e c t r i c a l breakdown cannot occur u n l e s s an i n i t i a t o r y e l e c t r o n i s present i n the gap. I f a d.c. p o t e n t i a l (or any s l o w l y v a r y i n g f i e l d ) i s a p p l i e d across a gap, there i s no problem of f i n d i n g an e l e c t r o n from n a t u r a l sources, e.g. cosmic r a y s , detachment from gaseous i o n s . Under impulse f i e l d s t h i s i s not the case, and i t may be d i f f i c u l t to f i n d an i n i t i a t o r y e l e c t r o n w i t h i n the very short time i n t e r v a l i n which the v o l t a g e i s a p p l i e d . The time t s which elapses between the a p p l i c a t i o n o f a v o l t a g e V g r e a t e r than V s (the d.c. s p a r k i n g p o t e n t i a l ) and the appearance o f an i n i t i a t o r y e l e c t r o n i s c a l l e d the s t a t i s -t i c a l time l a g , the appearance of such an e l e c t r o n b e i n g u s u a l l y s t a t i s t i c a l l y d i s t r i b u t e d . F u r t h e r , the mechanism a l s o depends on the a p p l i e d f i e l d E. A f t e r the p r o v i s i o n of the e l e c t r o n , i t s t i l l takes some -time t f f o r a d i s c h a r g e t o be formed. The time tf. i s known as the for m a t i v e time l a g and the t o t a l time l a g t = t s + tf. The s i t u a t i o n f o r breakdown on a step v o l t a g e pulse i s i l l u s t r a t e d i n the f o l l o w i n g diagram: -52-B r C o 11 a p s e of * a p p l i e d v o l t a g e TIME FIGURE 21: TIME LAG TO SPARK BREAKDOWN In p r a c t i c e t g » t f , so t h a t t - t s , but to measure t ^ , the gap w i l l have t o be i r r a d i a t e d a r t i f i c i a l l y , e.g. by a r a d i o a c t i v e source t o minimize t g , and t - t ^ . T h e o r e t i c a l c a l c u l a t i o n on the s t a t i s t i c a l time l a g has been g i v e n by von Laue (1925). Let P be the number o f primary e l e c t r o n s formed per sec. i n the gap by i r r a d i a t i o n , and W be the p r o b a b i l i t y t h a t such an e l e c t r o n w i l l i n i t i a t e an avalanche, and i f f ( t ) i s the p r o b a b i l i t y t h a t a discharge w i l l occur d u r i n g the i n t e r v a l a f t e r a time t measured from the i n s t a n t of the a p p l i c a t i o n of v o l t a g e , then c f ( t ) d t = WP exp(- WPdt) (5.2) J0 -53-With a constant v o l t a g e , W i s constant, and hence f o r a constant P, •yr f ( t ) d t = WPexp(-WPt) (5.3) The number n of time l a g s which have a time l a g g r e a t e r than t i s then n = N e ~ W P t • ' d L) Hence the mean s t a t i s t i c a l time l a g i s g i v e n by t q = 1 (K C.) I t can be seen t h a t f o r a l a r g e r diameter gap, P i s l a r g e r and hence the time l a g ( t s ) decreases f o r a g i v e n a p p l i e d v o l t a g e as the diameter i n c r e a s e s . The experimental r e s u l t s i n f i g . 14 a,b agree with t h i s . In a d d i t i o n , they show t h a t the time l a g decreases as the a p p l i e d v o l t a g e ( >V ) i n c r e a s e s . T h i s f a c t a l s o agrees with e x i s t i n g t h e o r i e s of i o n i z a t i o n growth. Because of the s t a t i s t i c a l nature of the time l a g s , each p o i n t of the time l a g curve i s obtained by at l e a s t 50 p o i n t s to g e t a f a i r degree of accuracy. 5.5 Thermal R e i g n i t i o n The q u a l i t a t i v e theory g i v e n i n s e c t i o n 1.2b requires, a p p r e c i a b l e conduction before breakdown occurs i n the thermal r e i g n i t i o n regime. Such cu r r e n t conduction i s not normally observed i n the present work. Sharp t r a n s i t i o n s from s m a l l c u r r e n t s to very l a r g e c u r r e n t u s u a l l y g i v e s good i n d i c a t i o n of breakdown t o occur. Once the gap breaks down, the r a t i o between the a p p l i e d p o t e n t i a l and peak c u r r e n t remains a p p r o x i -mately constant even f o r i n c r e a s e d a p p l i e d p o t e n t i a l . The - 5 4 -p o i n t obtained at 6 0 jms delay ( f i g . 1 5 b ) r e q u i r e s some d i s -c u s s i o n . The r e i g n i t i o n v o l t a g e at t h i s p o i n t i s 2 0 0 v o l t s which i s l e s s than the minimum s p a r k i n g volt age f o r a i r ( 3 0 0 v . ) . The d e t e r m i n a t i o n of t h i s p o i n t i s not very d e f i n i t e and i s based on the f o l l o w i n g experimental r e s u l t s o b t ained at t h a t p o i n t : A p p l i e d V o l t a g e V ( v o l t s ) R a t i o o f V t o peak di s c h a r g e Current A c c o r d i n g to our c r i t e r i o n , 200v i s chosen as the r e i g n i t i o n v o l t a g e because we see t h a t the r a t i o V / l i s not decreased at h i g h e r a p p l i e d v o l t a g e . A c t u a l l y t h e r e i s no c o n t r a -d i c t i o n between t h i s r e s u l t and the minimum spark breakdoiirn v o l t a g e because the former occurs i n a h i g h l y i o n i z e d gap. T h i s r e s u l t of course depends on the c r i t e r i o n we use. I t must be remarked t h a t the r e i g n i t i o n v o l t a g e i s not s h a r p l y d e f i n e d at t h i s p o i n t . No c u r r e n t i s observed at a p p l i e d v o l t a g e < 100 v o l t s . 5 . 6 D e r i v e d Gas Temperatures The gas temperatures of the channel at v a r i o u s d e l a y times and at v a r i o u s r a d i a l d i s t a n c e s are d e r i v e d by assuming the v a l i d i t y of Paschen's Law at l a t e r p e r i o d of re c o v e r y V/I ohms 1 0 0 . 4 0 . 2 6 o 3 0 „ 2 6 -o 3 3 0 2 3 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 -55-( d e l a y times ^ 1 msec.) T h i s assumption i s j u s t i f i e d on the b a s i s t h a t d u r i n g the f i n a l r e c o v e r y p e r i o d the r e i g n i t i o n c h a r a c t e r i s t i c s d e p i c t s the manner i n which the gas d e n s i t y changes with time, as confirmed by the occurrence of spark breakdown f o r d e l a y times g r e a t e r than 1 ms. A c c o r d i n g t o Paschen's law, the s p a r k i n g v o l t a g e i s g i v e n by "VjJ^  K ( P e l ) • o o « O 0 o e o o * » o o o o » o ( 5 o 6 ) Where t = time d = gap l e n g t h P = gas pressure K, N = constants V R = r e i g n i t i o n breakdown v o l t a g e Now the equation o f s t a t e f o r a gas i s P = n / k T (5.7) Where j> = gas d e n s i t y n = number of molecules per u n i t volume k = Boltzmann's constant T = ambient temperature We can w r i t e down a s i m i l a r equation of s t a t e f o r the gas under r e i g n i t i o n c o n d i t i o n P R = fn N K T R ' • • (5.*) where P^ = 760 mm Hg. i n the present experiment. The gas d e n s i t y corresponding to each r e i g n i t i o n v o l t a g e may be de-termined by measuring the impulse breakdown v o l t a g e as a f u n c t i o n of pressure f o r the t e s t gas a t ambient temperature. For a g i v e n r e i g n i t i o n v o l t a g e V^, the corresponding gas d e n s i t y i s equal to the. s t a t i c gas d e n s i t y which g i v e s a -56-breakdown v o l t a g e V R . I f we put f = f R , we get TR = T P R (5,9) T — ' where P. i s the s t a t i c gas pressure corresponding t o the p a r t i c u l a r V R we are c o n s i d e r i n g , and i s obtained from the Paschen curve ( f i g . 18 a,b). In t h i s way the temperatures of the gas are c a l c u l a t e d as a f u n c t i o n of space and time and d i s p l a y e d g r a p h i c a l l y i n f i g . 19 and 20. At times l e s s than 1 ms or so, the d e r i v e d gas temperatures r i s e r a p i d l y , thus i n d i c a t i n g t h a t mechanisms other than the decreased gas d e n s i t y , are r e s p o n s i b l e f o r the lowering of the r e i g n i t i o n v o l t a g e . Thermal i o n i z a t i o n and t h e r m i o n i c emission are some of the p o s s i b i l i t i e s . I t i s f o r t h i s reason t h a t Paschen 1s law cannot be used t o d e r i v e the gas temperatures at e a r l i e r d e l a y . Saha's equation may be used i n s t e a d t o d e r i v e the gas temperatures f o r t h i s e a r l y d e l a y i f one knows the i o n , e l e c t r o n and n e u t r a l c o n c e n t r a t i o n s . A s i m i l a r work has been done by C h u r c h i l l & Poole (I963) on r a d i a l r e c o v e r y of spark gap channel i n a i r . T h e i r experimental c o n d i t i o n s are d i f f e r e n t from the present work. However t h e r e i s s u f f i c i e n t agreement between the two i n most of the r e s u l t s . -57-CONGLUSION The technique employed i n the present work by making simultaneous measurements of the current and voltage across the probing gap has proved to be f a i r l y successful i n extending the r e i g n i t i o n data down to the early delay times a f t e r the i n i t i a l current discharges $ 500 us. The general recovery and breakdown features agree with previous work i n high current spark gap recovery and are con-sistent with the theories of recovery mechanisms and breakdown, at least q u a l i t a t i v e l y . The time lag c h a r a c t e r i s t i c s have been studied f o r various electrode sizes and the experimental re s u l t s are found to agree with the present time lag theories. The dip observed i n the r e i g n i t i o n curves i s thought to be due to the e f f e c t of a thermal wave propagated from the centre of the test gap. However no quantitative analysis can be made i n the present experiment and further work, p a r t i c u l a r l y i n gases of widely varying atomic numbers, e.g. H2 and A, i s necessary to confirm t h i s . The temperature decay as well as the temperature p r o f i l e of the channel obtained appear to be a reasonable representation of the physical state of the gas inside the gap. C h u r c h i l l and Poole (I963) have r e p o r t e d the e x i s t e n c e of a l a r g e r a d i a l d i s t a n c e over which the r e c o v e r i n g gas temperature i s uniform f o r d e l a y times ) 1 ms, T h i s i s not observed i n the present experiment, but of course t h e r e i s no c o n t r a d i c t i o n as the present channel appears to be v e r y much s m a l l e r than t h e i r s . F u r t h e r experimental work should i n c l u d e a study of thermal r e i g n i t i o n i n the main t e s t gap by a p p l y i n g the r e s t r i k i n g v o l t a g e d i r e c t l y t o the t e s t gap and a d e t a i l e d i n v e s t i g a t i o n of the r e g i o n from 0 to 2 cm. not t r e a t e d i n the present work. -59-REFERENCES A l l e n , J.E. and Craggs, J.D., 1954. B r i t . J . Appl. Phys. I , 446. B a l l a s c h i , P.L., 1934. E l e c t . Engng., 51, 86. Braudo, C.J., 1959. Ph.D. T h e s i s , U n i v e r s i t y of L i v e r p o o l . Burch, F.P., 1932. P h i l . Mag. 13, 760. B u t t e r , D., I 9 6 3 . M.Sc. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbl: C a s s i e , A.M., 1939. C.I.G.R.E., Paper No. 102. C h u r c h i l l , R.J., Parker, A.B. and Craggs, J.D., 1961. J . of E l e c t , and Cont., 11, No. 1, 17. C h u r c h i l l , R.J., 1961, Plasma P h y s i c s ( J . Nuclear Energy, pt, 3, 291. C h u r c h i l l , R.J., 19^3. Can. J . Phy., 41, 612. C h u r c h i l l , R.J. and Poole, D.E., 1963. Paper Presented at the S i x t h I n t e r n a t i o n a l Conference on I o n i z a t i o n Phenomena i n Gases, Orsay, France, J u l y 8-13. C r a i g , R.D. and Craggs, J.D., 1953. Proc. Phys. Soc. B, 66, 51 Crawford, F.W» and E d e l s H., i960. Proc. I n s t n . E l e c t . E n g r s Q 107A, 202. • E d e l s , H. and Crawford, F.W., 1956. C.I.G.R.E. Paper No. 102. E d e l s , H. and E t t i n g e r , Y. 1962. Proc. I.E.E., 109A , 89. E t t i n g e r , Y. and E d e l s , H. 1959. J . of S c i . I n s t . , 36, 362. G l a s s t o n e , S. and Lovberg, R.H. C o n t r o l l e d Thermonuclear R e a c t i o n s . Van Nostrand, N.Y. i960. K i r i l l o v , V.D. i960. J.E.T.P. 10, 812 (Zhur. E k s p t t . i Teoret F i g . 1959, 37, 1142). von Laue, M. 1925. Ann. Phys. Lpz., 76, 2 6 l . Loeb, L.B. 1923. J . Franklin Inst., 20j5, 305. Mayr, 0. 1943. Archiv. fur Elektuotechnik, 22, 588. McCann, G.D. and Clark, J . J . 1943. Trans. Amer. Inst. E l e c t , Engrs., 62, 45. Park, J.H. 1947. J . of Research, Nat. Bur. Standards, 2£> 191. Poole, D.E., Parker, A.B. and C h u r c h i l l , R.J. 1963. J . El e c t , and Cont. 1£, No. 2, 131. Reynolds, P.R., and Craggs, J.D., 1952. P h i l . Mag., 258. Rogowski, W. 1926. Arch. Elektrotech, 16, 496. Rogowski, W. 1928. Arch. Elektrotech, 20, 99. Rose, D.J. and Clark, M.C. Plasma and Controlled Fusion. M.I.T. and Wiley, 1961. Stekolnikov, I., 1947. Elektrichestvo, 2» 67. Thompson, J . J . Conduction of E l e c t r i c i t y through Gases. 2nd edit i o n , Cambridge: University Press, 1906. 

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