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Radial temperature derived from probe conductance measurements in a recovering spark channel Clements, Reginald Montgomery 1964

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RADIAL TEMPERATURE. DERIVED FROM PROBE CONDUCTANCE MEASUREMENTS IN A RECOVERING SPARK CHANNEL by REGINALD MONTGOMERY CLEMENTS B.A.Sc, Un i v e r s i t y of B r i t i s h Columbia, 1963 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of PHYSICS We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1964 • In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study* I f u r t h e r agree that per m i s s i o n f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t , c o p y i n g or p u b l i  c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l - n o t be allowed without my w r i t t e n p e r m i s s i o n . Department of P h y s i c s  The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada Date AugU3t 1 g. 1 96I4. . - i i - ABSTRACT The conductance of a s m a l l e l e c t r i c probe has boen d e t e r  mined f o r r a d i a l d i s t a n c e s (2 - 15> era) from a r e c o v e r i n g spark gap as a f u n c t i o n of time a f t e r d i s c harge i n i t i a t i o n . The times i n v e s t i g a t e d were from 0.2 to 1$ ms and the gas pressure was v a r i e d from 22 mmHg down to 0.1 rnraHg. The volta g e a p p l i e d to the probes was a sawtooth pulse which rose to about 80 v o l t s i n 10 J U S . I t i s shown t h e o r e t i c a l l y t h a t the probe conductance should be p r o p o r t i o n a l to the t h r e e - h a l v e s power of the gas temperature. Prom a known value of the temperature, deduced from r e c o v e r y measurements, and the known probe conductance the constant of p r o p o r t i o n a l i t y was deduced. Hence i t was p o s s i b l e to determine the temperature from the probe conductance. The probe conductance measurements show that at 200 rnraHg pressure the spark channel i s o n l y 2 era i n r a d i u s and th a t there i s no d e t e c t a b l e i o n i z a t i o n l e f t 2 ms a f t e r the d i s c h a r g e . As the gas pre s s u r e decreases the spark channel i n c r e a s e s i n s i z e and takes l o n g e r to d e i o n i z e , u n t i l at 1 rnraHg p r e s s u r e the channel f i l l s the whole spark chamber (spark channel r a d i u s i s 15 era) and r e q u i r e s almost 15> ras to d e i o n i z e . At 1 rnraHg gas pressure there i s a r a d i a l temperature g r a d i e n t , while at 0.1 mmHg pr e s s u r e the gas everywhere i n the channel recovers at the - i i i - same r a t e . In t h i s experiment i t i s t h e o r e t i c a l l y p r e d i c t e d that volume recombination should be the dominant recove r y method and t h i s i s e x p e r i m e n t a l l y v e r i f i e d . f - v i i i - ACKNOWLEDGEMENT I would l i k e to o f f e r ray s i n c e r e thanks to my s u p e r v i s o r , Dr. R.J. C h u r c h i l l , f o r the he l p which he gave me while I was s e t t i n g up and performing t h i s experiment, and a l s o f o r the hel p which he gave when I was a n a l y z i n g the r e s u l t s and w r i t i n g up the t h e s i s , even though he was no lon g e r a s s o c i a t e d w i t h t h i s U n i v e r s i t y . I a l s o g r a t e f u l l y acknowledge the work of Dr. R.A. Nodwell i n r e a d i n g the t h e s i s manuscript and o f f e r i n g h i s va l u a b l e s u g g e s t i o n s . I would a l s o l i k e to thank Mr. John Turner who b u i l t and maintained the e l e c t r o n i c equipment used i n t h i s experiment and o f f e r e d v a l u a b l e t e c h n i c a l a d v i c e . — i v - TABLE OF CONTENTS A b s t r a c t i i L i s t of I l l u s t r a t i o n s v i Acknowledgement v i i i INTRODUCTION 1 CHAPTER 1 - THEORY OF SPARK GAP RECOVERY AND THE THEORY OF PROBES 5 1.1 Recovery and D e i o n i z a t i o n 5 1.2 Probe and C o n d u c t i v i t y Theory 12 CHAPTER 2 - DEVELOPMENT OF APPARATUS 22 2.1 General D e s c r i p t i o n and O p e r a t i o n of Apparatus 22 2.2 Vacuum System 25> 2.3 High Current Generator and T r i g g e r i n g Mechanism 26 2.I4. T r i g g e r Pulse Generator 29 2.5 E l e c t r o n i c Delay U n i t 29 2.6 Probe Development and A s s o c i a t e d C i r c u i t r y 32 CHAPTER 3 - MEASUREMENTS AND DATA I4.O 3.1 Conductance Measurements I4.O 3.2 Data Obtained I4.2 3*3 Recovery Measurements Ifl CHAPTER k - ANALYSIS OF DATA U-9 I4..I D e r i v a t i o n of Temperatures from Recovery Curves I4.9 _v- J4..2 R a d i a l Temperatures D e r i v e d From Probe 50 Conductances CHAPTER 5 - DISCUSSION OF RESULTS 55 5.1 Features of R a d i a l Temperature Curves 55 5.2 General Recovery C h a r a c t e r i s t i c s 58 5.3 L i m i t s of Accuracy of the R e s u l t s 58 CONCLUSIONS 61 REFERENCES 63 - v i - LIST OF ILLUSTRATIONS FIGURE 1.1 P o t e n t i a l Diagram f o r Plasma Near a W a l l IJ4. 1.2 Double Probe C i r c u i t w i t h One Grounded Probe llj. 1.3 Probe P o t e n t i a l Diagrams w i t h Probe 2 Grounded 17 2.1 B l o c k Diagram of Apparatus 23 2.2 O v e r a l l C i r c u i t Diagram 23 2.3 O v e r a l l View of Apparatus 2I4. 2.I4, T r i g g e r i n g E l e c t r o d e s and Spark Gaps G Q and G]_ 2I4. 2.5 Spark Chamber and Probes Z\\. 2.6 Main E l e c t r o d e s J2 a n ^ J3 a n < l Probes 2i| 2.7 High Current Generator and T r i g g e r C i r c u i t s 27 2.8 E.H.T. Supply 27 2.9a Waveform f o r R i n g i n g Discharge 30 2.9b ~ Waveform 30 dt 2.9c I Waveform 30 2.10 T r i g g e r Pulse Generator 31 2.11 E l e c t r o n i c Delay U n i t 31 2.12 D e t a i l e d Probe C i r c u i t 33 2.13 Probe Dimensions 38 3*1 Current and Voltage i n Probe C i r c u i t I4J4. 3.2 Current and Voltage V a r i a t i o n Between Tests l\$ 3*3 Current and Voltage f o r High Gas Pressures l\£ - v i i - 3. k Large O s c i l l a t i o n s on the Current Waveform h$ Spark Breakdown Voltage i n A i r , 51 Spark Gap Recovery i n A i r f o r the Main Gap 51 it. 3 D e r i v e d Gas Temperatures f o r A i r i n the Main Gap 5i Probe Conductance G i n A i r at High Pressures 53 ( Probe Conductance G i n A i r at 10 mmHg Pressure 53 1^.6 Probe Conductance G i n A i r at 1 mmHg Pressure 53 I,. 7 Probe Conductance G i n A i r at 0.1 mmHg Pressure 53 D e r i v e d Temperatures f o r A i r at High Pressures 5k D e r i v e d Temperatures f o r A i r at 10 mmHg Pressure 5h 1^ .10 '. D e r i v e d Temperatures f o r A i r at 1 mmHg Pressure 5h 14-.11 D e r i v e d Temperatures f o r A i r at 0.1 mmHg Pressure 5h 5.1 D e r i v e d Temperature P r o f i l e of Spark Channel f o r A i r at 1 mmHg Pressure 57 INTRODUCTION The spark gap i s e x t e n s i v e l y employed as an e l e c t r i c a l s w i t c h i n various pulsed plasma generation d e v i c e s . I t i s al s o u s e f u l as a source of h i g h temperature plasma. F i s c h e r (1957) reports t h a t , using an e s p e c i a l l y developed low i n d u c t  ance c a p a c i t o r , he obtained temperatures of about 2f>0,000 °K i n a helium plasma at atmospheric pressure. The char a c t e r  i s t i c s , of the recovering plasma, formed from the passage of the spark, are of i n t e r e s t to engineers, not only i n the design of c i r c u i t breakers but a l s o i n the p o s s i b l e use of spark gaps as rec u r r e n t switches in•. some thermonuclear devices. From a more fundamental p o i n t of view, a knowledge of the p r o p e r t i e s , e s p e c i a l l y p a r t i c l e d e n s i t i e s and temperatures, would l e a d to a b e t t e r understanding of the basic processes r e s p o n s i b l e f o r the decay of the plasma. Due to the* usefulness of spark gaps as switches, the r e i g n i t i o n voltage c h a r a c t e r i s t i c s f o r surge currents as h i g h as 235 kA have been experimentally determined (23 kA. - McCann and Clark, 19]+3j 235 k4 - C h u r c h i l l , I960; 1+0 kA - Chan, 1963) . The l a t e r two i n v e s t i g a t o r s measured the r e i g n i t i o n voltage as a f u n c t i o n of the r a d i a l d i stance from the main spark gap as we'll as a f u n c t i o n of the time a f t e r spark i n i t i a t i o n . By assuming that the spark r e i g n i t e d i n accordance to Paschen's law, the gas temperature was d e r i v e d . This assumption, however, i s o nly t r u e d u r i n g the l a t e r p a r t of the recovery, s i n c e d u r i n g t h i s p e r i o d there i s l i t t l e or no i o n i z a t i o n present, i . e . r e i g n i t i o n v o l t a g e s are lowered mainly due to the decreased gas d e n s i t y . Poole, Parker, and C h u r c h i l l (1963) confirmed the temperatures d e r i v e d from reignition"measurements by u s i n g a plane shock wave to probe the r e c o v e r i n g gas. By measuring the v e l o c i t y of t h i s shock w i t h S c h l i e r e n techniques the r a d i a l temperature d i s t r i b u t i o n of; the spark channel was determined. This technique has a l s o been used, under d i f f e r e n t experimental c o n d i t i o n s , by A l l e n , E d e l s , and Whittaker (1961). Some time- r e s o l v e d s p e c t r o s c o p i c i n v e s t i g a t i o n s of r e c o v e r i n g spark channels have a l s o heen made. Vanyukov, et a l , (1959) made time r e s o l v e d measurements i n a system where the energy s t o r e d i n the c a p a c i t o r bank was q u i t e s m a l l ( l e s s than 2 j o u l e s ) and the gas p r e s s u r e was equal to or g r e a t e r than atmospheric p r e s s u r e . Craggs (1963) o b t a i n e d o s c i l l o g r a p h i c t r a c e s o f l i n e i n t e n s i t i e s f o r a number of s p e c t r a l l i n e s of argon and helium. The pr e s s u r e s i n v e s t i g a t e d were from 7&0 to $0 mm.Hg but the spark c u r r e n t was much lower than t h a t employed i n t h i s experiment. Both Craggs and Vanyukov found that the spark chanel was luminous only f o r a few micro-seconds a l t h o u g h the p e r i o d of l u m i n o s c i t y i n c r e a s e d when gas pressure decreased. Up to the present time i t does not appear that temperatures have been deduced on the b a s i s of e l e c t r i c probe measurements. In these measurements the probes are immersed i n the plasma and -3- a v o l t a g e a p p l i e d between the probes. T h i s voltage i s s m a l l enough so t h a t spark breakdown between the probes does not occur and the c u r r e n t flow between the probes i s dependent on the plasma c o n d u c t i v i t y . I n the prese n t i n v e s t i g a t i o n i t was o r i g i n a l l y planned to use the c l a s s i c a l double f l o a t i n g probe of Johnson and M a l t e r (1950) to determine the e l e c t r o n temper a t u r e . However, due to d i f f i c u l t i e s i n i s o l a t i n g the probes from ground w h i l e s t i l l e n s u r i n g t h a t the observed c u r r e n t was the a c t u a l c u r r e n t f l o w i n g i n the probe c i r c u i t , t h i s approach was abandoned and probe impedence measurements were made. Prom these measurements i t was p o s s i b l e to deduce the temperature. For a spark t a k i n g p l a c e i n a r e l a t i v e l y h i g h p r e s s u r e gas e q u i l i b r i u m between the e l e c t r o n s , i o n s , and the n e u t r a l gas p a r t i c l e s i s r a p i d l y e s t a b l i s h e d so t h a t the e l e c t r o n ( T e ) , i o n -(Tj_), and gas (Tg) temperatures a l l have the same value which i s r e f e r r e d to as the temperature (T) i . e . T e ~ T i ^ T g V T . This p o i n t i s c o n s i d e r e d i n some d e t a i l i n s e c t i o n 1.1, E l e c t r i c probes have c e r t a i n advantages over the above methods of temperature d e t e r m i n a t i o n . Compared to the s p e c t  r o s c o p i c and shock wave measurements the probes have a h i g h degree of s p a t i a l r e s o l u t i o n , and u n l i k e the r e i g n i t i o n measurements the temperature can s t i l l be determined when there i s a p p r e c i a b l e i o n i z a t i o n . As these probe measurements depend on the e l e c t r i c a l c o n d u c t i v i t y of the gas, low gas pr e s s u r e s (below 200 mmHg) were used i n order t h a t a reasonable c u r r e n t ( g r e a t e r than 1 jx&tap) flowed between the probes. U n f o r t u n a t e l y , i n a l l works p r e v i o u s l y r e f e r r e d t o , the gas pressures have been g r e a t e r than those used i n t h i s experiment so t h a t d i r e c t com pa r i s o n s are d i f f i c u l t to make. The next main s e c t i o n of t h i s t h e s i s d i s c u s s e s , t h e o r  e t i c a l l y , , the processes by which the spark cha r i i e l r e c o v e r s , the f o r m a t i o n o f i o n sheaths, and the temperature from probe con ductance measurements. F o l l o w i n g t h i s , the apparatus used i n the experiment and the methods by which the measurements were made are pr e s e n t e d . Samples of the data taken are reproduced and d i s c u s s e d . In Chapter \± the temperature i s determined from the probe conductance measurements. These r e s u l t s are d i s c u s s e d i n Chapter 5> and the l i m i t a t i o n s on them p o i n t e d out. I t i s concluded i n Chapter 6 t h a t probe measurements y i e l d a g r e a t d e a l of data and, even u s i n g the r e l a t i v e l y simple a n a l y s i s proposed here, i n f o r m a t i o n about temperatures of the r e c o v e r i n g plasma can be o b t a i n e d . CHAPTER Is THEORY OP SPARK GAP RECOVERY AND THE THEORY OF PROBES In t h i s s e c t i o n a b r i e f survey o f the mechanisms which e f f e c t the r e c o v e r y o f the spark gap i s g i v e n . As the math ematics y i e l d equations which cannot be s o l v e d without making approximations when there i s a combination of mechanisms i n  f l u e n c i n g the recovery, each mechanism w i l l be d e a l t w i t h s i n g l y , as i f i t were the) only mechanism r e s p o n s i b l e f o r the re c o v e r y . Probe theory and gas c o n d u c t i v i t y are d i s c u s s e d i n the second s e c t i o n and the r e l a t i o n s h i p s necessary to c a l  c u l a t e the temperature from the probe impedence are d e r i v e d . 1.1 RECOVERY AND DEIONIZATION Upon the passage of a h i g h c u r r e n t through a spark gap, the t e s t gas becomes h i g h l y i o n i z e d . The degree o f i o n i z a t i o n i s p r obably about 100 per cent, as Vayukov, et a l , (1959) have observed s p e c t r a of doubly i o n i z e d atoms i n a low energy spark. C r a i g and Craggs (1953) have estimated t h a t thermal e q u i l i b r i u m i s r a p i d l y e s t a b l i s h e d , but they c o n s i d e r e d o n l y cases of h i g h gas p r e s s u r e . I f times of i n t e r e s t are much g r e a t e r than the c h a r a c t e r i s t i c r e l a x a t i o n times f o r e l e c t r o n - e l e c t r o n ("C\), i o n - i o n ( t _ ) 9 and e l e c t r o n - i o n ( ~^o) -6- c o l l i s i o n s , then the plasma can be assumed to be i n thermal equilibrium© The i o n temperature w i l l be e s s e n t i a l l y e q u a l to the n e u t r a l gas temperature, as both the i o n and the atom have e s s e n t i a l l y the same mass. From D e l c r o i x (I960), and S p i t z e r (1956), one f i n d s that? x 3 .8 x I Q S T V 2 ( S E C < ) x n e In ^A. V ' 1Z * (lf\ ( s e c ) t o ^ M ^ i (sec.) J m where % M = i o n mass (kg) m = e l e c t r o n mass (kg) T = temperature (°K) XIQ= e l e c t r o n c o n c e n t r a t i o n ( e l e c t r o n s meter"^) Here: -^ D = Debye. s h i e l d i n g d i s t a n c e = / g o k T (meter) ' % n e b Q = impact parameter f o r 90° d e f l e c t i o n 2 ~ ^ (meter) 12 € Q k T •1, where: £ Q = p e r m i t i v i t y of vacuum ; ( f a r a d meter ) k = Boltzmann's: constant ( j o u l e s ° K ~ 1 ) q Q = e l e c t r o n charge (coulombs) Table I shows order of magnitude values of t ^ , ^2, and "£3 b O assuming 100 per cent i o n i z a t i o n and a temperature of 10 K. F o r the value of M, the mass of the n i t r o g e n i o n i s used and the values of l n ^ . are from S p ^ t z e r (1956, t a b l e 5 . 2 ) . TABLE I RELAXATION TIMES FOR ELECTRON-ELECTRON, ION-ION, AND ELECTRON-ION COLLISIONS Pressure n meter"" 3 T ln_/t- T l T 2 ^3 (mmHk'); (°K) approx. (sec.) (sec.) (sec.) 760 3 x 10 2 ^ 10* ' 5 ' i o " 1 1 • i o " 9 10 3 x 1 0 2 3 10* 7 -12 10 -9 10 -7 10 1 3 x 1 0 2 2 10* 8 I O - 1 1 -8 10 -6 10 0.1 3 x 1 0 2 1 10* 9 i o - 1 0 i o " 7 From t h i s t a b l e one sees that at atmospheric p r e s s u r e thermal e q u i l i b r i u m i s e s t a b l i s h e d very r a p i d l y but at lower p r e s s u r e s f o r c e r t a i n types of measurement, the assumption of thermal e q u i l i b r i u m may not be v a l i d . In t h i s experiment the channel was allowed to r e c o v e r f r e e l y f o r at l e a s t 200 us before any measurements were made, and by t h i s time, even f o r low p r e s s u r e s T ^ T ^ ^ T . The hot, h i g h l y i o n i z e d gas recovers to a n e u t r a l gas at room temperature by a number of p r o c e s s e s . During the a c t u a l d i s c h a r g e there i s a l a r g e c u r r e n t and hence an a s s o c i a t e d magnetic f i e l d . I t i s then p o s s i b l e t h a t c y c l o t r o n r a d i a t i o n f rom e l e c t r o n s could be an important energy l o s s mechanism. This mechanism i s p r o b a b l y not. very important as the c u r r e n t p u l s e , and hence the a s s o c i a t e d magnetic f i e l d i s of very s h o r t d u r a t i o n (about 10 us)» A l s o d e t a i l e d c o n s i d e r a t i o n of the power r a d i a t e d per u n i t s o l i d angle (see f o r example Rose and C l a r k , 1961, section'11*3) shows that the c y c l o t r o n r a d i a t i o n i s o n l y important f o r r e l a t i v i s t i c e l e c t r o n s . Another p o s s i b l e energy l o s s mechanism i s bremsstrahlung r a d i a t i o n produced by e l e c t r o n a c c e l e r a t i o n i n the f i e l d of an i o n . By assuming t h a t the e l e c t r o n s have a Maxwell- Boltzmann d i s t r i b u t i o n , the power d e n s i t y r a d i a t e d by a l l e l e c t r o n s (see f o r example Rose and C l a r k , s e c t i o n 11,2) i s p r o p o r t i o n a l to the product of the. e l e c t r o n and i o n d e n s i t i e s , T e s , and where Te i s the e l e c t r o n temperature and Z the i o n i c charge number. During the spark d i s c h a r g e a c o n s i d e r a b l e amount of e l e c t r o d e m a t e r i a l b o i l s o f f , which g i v e s r i s e to h i g h Z: i m p u r i t i e s . In p r a c t i c e , however, bremsstrahlung r a d  i a t i o n l o s s e s are not important, even i n the presence of h i g h Z', i m p u r i t i e s , f o r temperatures l e s s than thermonuclear temp e r a t u r e s . I n the p r e s e n t experiment maximum temperatures are w e l l below these v a l u e s . The p r e c e d i n g two energy l o s s mechanisms do not decrease the e l e c t r o n density,, i . e . l i t t l e , or no, d e i o n i z a t i o n takes p l a c e . In t h i s experiment d e i o n i z a t i o n occurs i n two ways. F i r s t , , the e l e c t r o n w i l l recombine w i t h p o s i t i v e i o n s . This - 9 - process, when i t occurs remote from the w a l l s , i s c a l l e d volume recombination or simply recombination. Secondly, the e l e c t r o n s w i l l d i f f u s e to the w a l l s , and because of the presence of a t h i r d body, w i l l d isappear by w a l l recombination. Recombination between p o s i t i v e ions and e l e c t r o n s may take p l a c e i n a v a r i e t y of ways. The two most important are d i r e c t r e combination of an i o n and an e l e c t r o n i n which the excess e l e c t r o n energy i s g i v e n o f f as r a d i a t i o n , and t h r e e - body recombination. I n three-body recombination the e l e c t r o n approaches an i o n which i s i n . t h e neighbourhood of a t h i r d body and the e l e c t r o n g i v e s up i t s excess energy to t h i s t h i r d body before combining w i t h the i o n . Th i s mechanism, alt h o u g h o c c u r r i n g , i s not Very probable, except near the w a l l s of the spark chamber. I f the plasma i s assumed to be approximately n e u t r a l (n«j. £?ne?sn) then the e f f e c t of recombination on p a r t i c l e c o n c e n t r a t i o n can be d e s c r i b e d by: 2 = -<n+n_ = -<n ... 1 dt + e where: t = time (sec.) n + = i o n c o n c e n t r a t i o n (i o n s meter"" 3) n Q = e l e c t r o n c o n c e n t r a t i o n ( e l e c t r o n s meter" 3) <• = recombination c o e f f i c i e n t ( m eter 3 sec.""^-) Prom e q u a t i o n 1 one sees t h a t the r e l a t i v e l o s s r a t e — ^ n dT - 1 0 - i s p r o p o r t i o n a l to the e l e c t r o n d e n s i t y . Hence volume recomb i n a t i o n would tend to make the d e n s i t y u n i f o r m s i n c e the r e  l a t i v e l o s s r a t e i s g r e a t e r i n r e g i o n s of h i g h e r c o n c e n t r a t i o n . Since the r a t e of e l e c t r o n l o s s by volume recombination i s 2 p r o p o r t i o n a l , t o n , volume recombination w i l l predominate over d i f f u s i o n l o s s e s when there i s a h i g h degree of i o n i z a t i o n p r e s e n t or a t h i g h p r e s s u r e s . In t h i s experiment where r e l  a t i v e l y h i g h p r e s s u r e s are used and the i n i t i a l degree of i o n i z a t i o n i s very h i g h , volume recombination i s the dominant d e i o n i z a t i o n mechanism, at l e a s t i n the e a r l y p a r t of the r e c o v e r y p e r i o d . The r a d i a t i o n emitted by the d i r e c t recomb i n a t i o n of an i o n and a f r e e e l e c t r o n accounts f o r the continuum r a d i a t i o n of the spark channel. I f the Debye s h i e l d i n g d i s t a n c e i s much s m a l l e r than the dimensions of the v e s s e l , then the charged p a r t i c l e s w i l l d i f f u s e by ambipolar d i f f u s i o n . F o r the d e n s i t i e s and temp e r a t u r e s i n t h i s experiment the f o r e g o i n g c r i t e r i o n h o l d s . Recombination takes p l a c e r e a d i l y at the w a l l s s i n c e the atoms or molecules of the w a l l m a t e r i a l s are a v a i l a b l e to a c t as a t h i r d body and take up the l i b e r a t e d energy. T h i s r e s u l t s i n a d e n s i t y g r a d i e n t away from the w a l l s . Because of the d i f f e r e n c e i n masses, the e l e c t r o n s d i f f u s e more r a p i d l y than the i o n s . T h i s leads to charge s e p a r a t i o n which r e s u l t s i n a space charge f i e l d . T h i s f i e l d r e t a r d s the d i f f u s i o n of the 11- e l e c t r o n s and i n c r e a s e s the d i f f u s i o n of the i o n s . Hence one would expect t h a t e l e c t r o n s and ions d i f f u c e a t the same r a t e * Assuming that t h i s i s t r u e , t h a t the plasma i s q u a s i n e u t r a l , that both e l e c t r o n s and ions have a Maxwell-Boltzmann d i s  t r i b u t i o n , t h a t the plasma i s i s o t h e r m a l and composed of one type of i o n . then the d i f f u s i o n i s d e s c r i b e d by: P = - D f t V n . . . . 2 where: T = p a r t i c l e f l u x (number meter s e c . ) D A = ambipolar d i f f u c i o n c o e f f i c i e n t = 2 u +kT (meter 3 s e c . " 1 ) ... 3 <*e and: u + = p o s i t i v e i o n m o b i l i t y = v e l o c i t y / u n i t f i e l d ( v o l t s s e c . - 1 ) . S u b s t i t u t i n g e q u a t i o n 2 i n t o the c o n t i n u i t y e q u a t i o n y i e l d s a d e s c r i p t i o n of the time and s p a t i a l v a r i a t i o n of d e n s i t y s 4 T = D V 2 n u S> t a ... 4 Prom II i t i s seen t h a t a l a r g e value of D w i l l make ^ w a d i f f u s i o n the predominant r e c o v e r y mechanism. The c o n d i t i o n s f o r t h i s , as the m o b i l i t y i n c r e a s e s as the p r e s s u r e decreases, are low p r e s s u r e ; and high_ temperature. In t h i s experiment the e a r l y p a r t of the r e c o v e r y i s c o n t r o l l e d p r i m a r i l y by recombination, e s p e c i a l l y a t h i g h p r e s s u r e s , but a t lower pre s s u r e s d i f f u s i o n s h o u l d become more -12- important. When both these e f f e c t s are t a k i n g p l a c e s i m u l t a n  e o u s l y i t i s , however, very d i f f i c u l t to say which, i f e i t h e r , i s predominant. Competing a g a i n s t the processes of d e i o n i z a t i o n i s the process of thermal i o n i z a t i o n . This term a p p l i e s to i o n i z a  t i o n produced by m o l e c u l a r or e l e c t r o n c o l l i s i o n s and by r a  d i a t i o n . E s p e c i a l l y at h i g h p r e s s u r e s , where the mean f r e e p a t h i s very s h o r t , t h i s may be an important f a c t o r i n the de t e r m i n a t i o n of the o v e r - a l l recovery, and i t i s the prime source of i o n i z a t i o n d u r i n g the r e c o v e r y p e r i o d . The l a t t e r p a r t of the recovery, where i o n i z a t i o n i s low, i s c o n t r o l l e d p r i m a r i l y by gas c o n v e c t i o n and thermal conduc t i o n . Here the hot gas t r a n s f e r s i t s energy to the c o o l w a l l s and c o o l e l e c t r o d e s . The e l e c t r o d e t i p s may be h o t t e r than the gas i s , i n which case the process w i l l be r e v e r s e d i n t h i s r e g i o n of space. The gas i s f u l l y recovered when i t r e t u r n s to i t s un i o n i z e d s t a t e at ambient temperature. 1.2 PROBE AND CONDUCTIVITY THEORY As was shown i n S e c t i o n 1.1, f o r the c o n d i t i o n s of t h i s experiment, the plasma i s i n thermal e q u i l i b r i u m . Even under these circumstances the e l e c t r o n v e l o c i t y w i l l be much g r e a t e r -13- than the i o n v e l o c i t y , due to the s m a l l e r mass of the e l e c t r o n , and many more e l e c t r o n s , per u n i t time, w i l l s t r i k e the w a l l s of the chamber than i o n s . These e l e c t r o n s b u i l d up a n e g a t i v e s u r f a c e charge on the w a l l s . This s u r f a c e charge r e p e l s those e l e c t r o n s near the w a l l s and r e s u l t s i n a s m a l l r e g i o n next to the w a l l where there i s an excess of p o s i t i v e ions -- the p o s i  t i v e i o n space-charge sheath. The t h i c k n e s s of t h i s sheath i s approximately the Debye s h i e l d i n g d i s t a n c e . This p o i n t of view y i e l d s a p h y s i c a l i n t e r p r e t a t i o n of the Debye d i s t a n c e , as that d i s t a n c e over which charge n e u t r a l i t y i s not n e c e s s a r i l y main t a i n e d . The p r e c e d i n g arguments are not then i n c o n t r a d i c t i o n to the assumption of plasma n e u t r a l i t y , over l a r g e d i s t a n c e s from the e l e c t r o d e s compared w i t h the Debye d i s t a n c e , which was made i n the d i s c u s s i o n on ambipolar d i f f u s i o n . The r e s u l t of the p o s i t i v e i o n sheath i s that the plasma p o t e n t i a l w i l l be s l i g h t l y above the f l o a t i n g w a l l p o t e n t i a l . I t i s assumed t h a t the sheath p o t e n t i a l , or i n g e n e r a l any e x t e r n a l p o t e n t i a l a p p l i e d to the plasma, has l i t t l e or no e f f e c t on the i o n motion. This assumption i s due to the f a c t t h a t the e l e c t r o n m o b i l i t y i s much g r e a t e r than the i o n m o b i l i t y On the b a s i s of the f o r e g o i n g arguments, the expected p o t e n t i a l s near to a w a l l of the spark chamber are shown i n F i g u r e 1.1. -11+. Plasma P o t e n t i a l N e u t r a l Plasma Wall P o t e n t i a l P o s i t i v e Space-Charge W a l l Sheath FIGURE 1.1 POTENTIAL DIAGRAM FOR PLASMA NEAR A WALL Two probes, of equal area and w i t h no v o l t a g e between them^ when i n s e r t e d i n the plasma, w i l l be a l s o surrounded by a p o s i  t i v e i o n sheath i n the same way t h a t the w a l l s a r e . F i g u r e 1.2 shows a schematic diagram of the double probe c i r c u i t where one probe i s grounded. E a r t h V a r i a b l e V o l t a g e FIGURE 1.2 DOUBLE PROBE CIRCUIT WITH ONE GROUNDED PROBE -15- No c u r r e n t w i l l f low between the probes s i n c e the random e l e c  t r o n and i o n c u r r e n t s to each are the same, assuming that there i s no temperature g r a d i e n t between the probes, which i s l i k e l y to be t r u e i n a decaying plasma. I f a vol t a g e V i s a p p l i e d between the probes such that probe 1 becomes p o s i t i v e , the e l e c t r o n s are a t t r a c t e d to probe 1. This leaves a d e f i c i e n c y of e l e c t r o n s i n the r e g i o n between the probes, hence th© plasma p o t e n t i a l r i s e s . In o t h e r words, the plasma assumes a poten t i a l approximately the same as the most p o s i t i v e e l e c t r o d e w i t h which i t makes c o n t a c t . T h i s means t h a t the grounded probe (probe 2) i s at a n e g a t i v e p o t e n t i a l w i t h r e s p e c t to the plasma. By K i r c h h o f f ' s laws, the c u r r e n t r e g i s t e r e d by the ammeter w i l l be c o n t r o l l e d by the number of p o s i t i v e ions s t r i k i n g probe 2f or the number of e l e c t r o n s s t r i k i n g probe 1 and f l o w i n g i n the e x t e r n a l c i r c u i t to probe 2, whichever i s s m a l l e r . As the v o l  tage between probes 1 and 2 i s i n c r e a s e d , e v e n t u a l l y v o l t a g e V s i s reached when enough e l e c t r o n s s t r i k e probe 1 to e q u a l i z e the number of ions s t r i k i n g 2. T h i s i s not n e c e s s a r i l y the p o s i  t i v e i o n d r i f t c u r r e n t because probe 2 i s connected to ground, i . e . the probe c i r c u i t i s not f l o a t i n g . Because the plasma i s i n c o n t a c t w i t h the chamber w a l l s and a l s o the main spark gap e l e c t r o d e s , which during the a f t e r g l o w are at ground p o t e n t i a l , the p o t e n t i a l d i s t r i b u t i o n i n the plasma i s d i s t o r t e d from the case where the probe c i r c u i t f l o a t s . F u r t h e r i n c r e a s e i n the v o l t a g e between the probes, beyond V s, s h o u l d cause l i t t l e -16- i n c r e a s e i n tha c u r r e n t f l o w i n g i n the e x t e r n a l c i r c u i t , and probe 2 i s s a t u r a t e d , i . e . i t c o l l e c t s a l l the p o s i t i v e i o n c u r r e n t . This s a t u r a t i o n p o i n t shows as the "knee" i n the cur r e n t waveform. Around probe 2 there i s even a g r e a t e r d e f i c i e n c y of e l e c  trons now t h a t V £ 0 than there was when V = 0. This i s due to the a c c e l e r a t i n g f i e l d ( f o r e l e c t r o n s ) which i s now presen t between the probes. Hence, when V i s g r e a t e r than zero most of the v o l t a g e impressed between the probes appears as a v o l t a g e drop across the p o s i t i v e i o n sheath. The e x i s t e n c e of t h i s p o s i t i v e i o n sheath around probe 2 was v e r i f i e d e x p e r i m e n t a l l y by c o v e r i n g a p o r t i o n of the exposed area of both probes 1 and 2 w i t h an i n s u l a t i n g s l e e v e . The r e s u l t s were as f o l l o w s : a. w i t h no s l e e v e on e i t h e r probe 1 or probe 2 the peak c u r r e n t I ^ flowed i n the probe c i r c u i t b. w i t h the i n s u l a t i n g sleeve c o v e r i n g a g i v e n f r a c t i o n o f the area of probe 1, the peak c u r r e n t was I , p i c. w i t h the i n s u l a t i n g s l e e v e c o v e r i n g a g i v e n f r a c t i o n of the area of probe j 2 , theIpeak Current.waso l ^ . r ; ; ' : ; reduced by t h i s f r a c t i o n . d. with, the i n s u l a t i n g s l e e v e c o v e r i n g "a g i v e n f r a c t i o n of the area of both probes 1 and 2, the peak c u r r e n t was 1 ^ reduced by the f r a c t i o n of the area of probe 2 which was covered. -17- A l l these steps were c a r r i e d out under the same experimental c o n d i t i o n s , and the shape of the c u r r e n t waveform remained constant, independent of the exposed probe areas. Only the magnitude of the c u r r e n t waveform changed. One can t h e r e f o r e conclude t h a t i t i s the a r e a of probe 2 which c o n t r o l s the magnitude of the c u r r e n t i n the probe c i r c u i t . In o t h e r words, by reducing the exposed area of probe 2, the s i z e of the p o s i  t i v e i o n sheath and the number of p o s i t i v e ions c o l l e c t e d are reduced p r o p o r t i o n a t e l y . Around probe 1 the p o s i t i v e i o n sheath, which was pres e n t when the v o l t a g e between the probes was zero, i s no l o n g e r p r e s e n t because of the i n f l u x of e l e c t r o n s to t h i s probe. F i g u r e 1.3 shows the p o t e n t i a l diagrams f o r the probes. Probe 2 \ Plasma t e n t i a l * L _ - - Plasma Sheath V = 0 -Plasma P o t e n t i a l •Probe 1 round P o t e n t i a l Probe 2 Probe 1 Ground P o t e n t i a l •Sheath V > 0 FIGURE 1*3 PROBE POTENTIAL DIAGRAMS WITH PROBE 2 GROUNDED -.18- The p r e c e d i n g two diagrams l o o k very much l i k e the poten t i a l diagrams f o r the f l o a t i n g double probes d e s c r i b e d by Johnson and M a l t e r (1950). The main f e a t u r e s of the p o t e n t i a l diagrams f o r both the f l o a t i n g double probes and the double probes, where one probe i s grounded, are the same. Fo r the exact mathematical a n a l y s i s of Johnson and M a l t e r (1950) to be a p p l i c a b l e , however, the probes must be f l o a t i n g . From the preceding a n a l y s i s of plasma sheaths i t i s e v i  dent t h a t the f i e l d between the probes i s not g i v e n by |. where: V = v o l t a g e a p p l i e d between the probes ( v o l t s ) a = d i s t a n c e between the probes (meters) or even c l o s e l y approximated by i t . Assume t h a t the whole v o l t a g e V a p p l i e d between the probes appears across the sheath at probe 2, which i s a good assumption i f V i s g r e a t e r than kT ^ t and approximate the v o l t a g e g r a d i e n t by a l i n e a r f u n c t i o n . The f i e l d E across the sheath i s then (see F i g u r e 1.3) E = — ( v o l t s meter"" 1) d where: V = v o l t a g e between the probes ( v o l t s ) d = sheath t h i c k n e s s (meters). Assuming t h a t the probes are c y l i n d r i c a l , the a r e a of the : sheath A (which i s the area c o l l e c t i n g ions) i s : A = 2 7 7 - ( r + d ) X ( m e t e r s 2 ) s where: r = probe r a d i u s (meters) 2 = probe l e n g t h (meters). -19- The c u r r e n t I f l o w i n g through the ammeter i s : I = J i A s (amps) where the p o s i t i v e i o n c u r r e n t d e n s i t y a t s a t u r a t i o n i s g i v e n by: T - *s (amp meter"^) J i 2T(V + d ) i and: I = ammeter c u r r e n t at s a t u r a t i o n (amps), s The p o s i t i v e i o n c o n d u c t i v i t y a-^ i s g i v e n by: cr = J l (mho meter" 1) • .1 T T I d . = 3 it 2 7T(r + d ) ^ V ° r : ^ = G 2 7T(r + iy where the probe conductance G i s g i v e n by: G = J j . (mho) V s - - and: V g = v o l t a g e between the probes at c u r r e n t s a t u r a t i o n . The c o n d u c t i v i t y , as i t i s u s u a l l y d e f i n e d , i s c a l c u l a t e d by t a k i n g i n t o account e l e c t r o n motion o n l y . The r a t i o of the c o n d u c t i v i t y due to e l e c t r o n s , to the c o n d u c t i v i t y due to ions i s p r o p o r t i o n a l to the r a t i o of the e l e c t r o n v e l o c i t y to the i o n v e l o c i t y . Where the e l e c t r o n s and ions are a t the same temperature, these v e l o c i t i e s are i n v e r s e l y p r o p o r t i o n a l to the square r o o t of the p a r t i c l e mass. Hence, assuming t h a t the ions are o n l y s i n g l y charged, which i s reasonable, as the temperature -20- i s at most a few e l e c t r o n v o l t s , then the c o n d u c t i v i t y cr i s l/2 -1 cr - cr. fMl (mho meter" ) l | s J  • • 5 • • o = G 2^pT^i[mj where: M = i o n mass (kg) m = e l e c t r o n mass ( k g ) . In h i s book, S p i t z e r (1956).gives the f o l l o w i n g formula f o r the c o n d u c t i v i t y cr of a h i g h l y i o n i z e d gas : 0 = 1 . 5 3 x 1 0 L — (mho meter" 1) ... 6 where: T = temperature (°K) _/t_ = r a t i o of the Debye s h i e l d i n g d i s t a n c e to the impact parameter f o r 90° c o l l i s i o n s . I f one assumes that t h i s formula holds f o r a weakly i o n i z e d plasma, as i s the case here, at l e a s t i n the l a t t e r p a r t of the recov e r y p e r i o d , then the two values f o r c" i n equations 5 and 6 can be equated. The values of l n _ A change very s l o w l y w i t h changes i n temperature and e l e c t r o n d e n s i t y (see t a b l e 5*1, S p t i z e r ) . The sheath thickness ;.d s h o u l d a l s o be r e l a t i v e l y constant w i t h changes i n T as the v o l t a g e V , which i s the probe v o l t a g e at c u r r e n t s a t u r a t i o n , . i s always much g r e a t e r kT than •qp" i n t h i s experiment. T h e r e f o r e , V g r a t h e r than T w i l l determine the sheath t h i c k n e s s . Because InJL and d can be c o n s i d e r e d constant, the p r e c e d i n g a n a l y s i s shows t h a t the -21- probe conductance G i s p r o p o r t i o n a l t o the c o n d u c t i v i t y <r~t which i n t u r n i s p r o p o r t i o n a l to the t h r e e - h a l v e s power of the temperature. Hence: Now, i f i t i s p o s s i b l e to c a l c u l a t e K or to e x p e r i m e n t a l l y determine i t , then the temperature can be deduced from the measured probe conductance. The accuracy of t h i s c a l c u l a t e d temperature, (which w i l l be c o n s i d e r e d i n d e t a i l i n Chapter 5>, D i s c u s s i o n of R e s u l t s ) , w i l l depend p r i m a r i l y on whether K i s r e a l l y constant throughout the range of experimental c o n d i t i o n s i n v e s t i g a t e d . The a n a l y s i s i n d i c a t e s t h a t i t i s immaterial, i n t h i s experiment, whether the f i e l d i n the sheath v a r i e s l i n e a r l y or not, so long as the form of the f i e l d does not change i n time or throughout the experiment. The f i e l d was assumed to vary l i n e a r l y as t h i s assumption l e d to a simple a n a l y s i s of the f i e l d and the p o s s i b i l i t y t h a t an estimate of the constant K might be obtained from experimental values of the sheath t h i c k  ness d and the parameterJL. (mho) 7 where the constant K i s : (mho -22- CHAPTER 2: DEVELOPMENT OP APPARATUS 2.1 GENERAL DESCRIPTION AND OPERATION OP APPARATUS F i g u r e s 2.1 and 2,2 are b l o c k diagrams of the apparatus. With r e f e r e n c e to these diagrams, the o p e r a t i o n of the appara tus i s as f o l l o w s . The nominal 9 ^iF h i g h v o l t a g e c a p a c i t o r bank i s charged to 20 kV from the v a r i a c c o n t r o l l e d E.H.T. s e t . The d i s c h a r g e i s i n i t i a t e d by a p u l s e from the c o n t r o l p a n e l . The magnetic f i e l d a s s o c i a t e d w i t h the r a p i d l y r i s i n g c u r r e n t i n the 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 , induces a v o l t a g e i n a s m a l l pick-up c o i l ( v i s i b l e i n F i g u r e 2.5) which i s propor t i o n a l t o the r a t e of change of c u r r e n t i n the main discharge c i r c u i t . T h i s v o l t a g e t r i g g e r s a delay u n i t which, a f t e r some s e t delay, t r i g g e r s the sawtooth generator which gener ates a s i n g l e waveform. The sawtooth wave passes through a cathode f o l l o w e r (CF) and from thence to the probes. The c u r r e n t and v o l t a g e f l o w i n g i n the probe c i r c u i t are d i s p l a y e d on a T e k t r o n i x type 5>5l double beam o s c i l l o s c o p e which i s a l s o t r i g g e r e d from the output of the d e l a y u n i t . The c o n s t r u c t i o n of the apparatus i s shown i n F i g u r e s 2.3 to 2.6. T h i s system i s s i m i l a r i n p r i n c i p l e to t h a t d e s c r i b e d by C h u r c h i l l , Parker and Craggs (1961) and Chan (1963). The main spark chamber i s a 6 i n c h i n s i d e diameter cross made -23- E o H . T . Sawtooth Generator Main C o n t r o l Panel C »F o E l e c t r o n i c Delay- C a p a c i t o r Bank 9 )xF Spark Chamber and Probes Main T r i g g e r U n i t Probe Current Shunt & CRO _J Probe Voltage and CRO FIGURE 2.1 BLOCK DIAGRAM OF APPARATUS +V C-20 kV Supply 9 pF Non L i n e a r R e s i s t o r R^ > 500 MA -11+ kV T r i g g e r ^50 y. amp 25 k/i , To CRO Upper Beam Type 55l Double Beam D- Plug i n U n i t s E a r t h To CRO T r i g g e r FIGURE 2.2 OVERALL CIRCUIT DIAGRAM of pyrex g l a s s and can be evacuated. The main e l e c t r o d e s are 6.I4. mm. diameter tungsten s l u g s , the ends machined f l a t , and mounted i n brass h o l d e r s . The d i s t a n c e between the e l e c t r o d e s can be v a r i e d by screwing the e l e c t r o d e t i p i n t o the s u p p o r t i n g s h a f t (see F i g u r e 2.6). The t r i g g e r e l e c t r o d e s (see F i g u r e 2.I4.) are 16 mm diameter tungsten s l u g s and the whole t r i g g e r gap mechanism i s mounted i n s i d e a t i g h t f i t t i n g perspex box i n order to reduce n o i s e . 2.2 VACUUM SYSTEM In o r d e r to f a c i l i t a t e experiments at pre s s u r e s l e s s than atmospheric, i t -.is, p o s s i b l e to evacuate the spark chamber. The vacuum i s c r e a t e d by a P h i l l i p s Duo 5 two stage r o t a r y vacuum pump w i t h a putipihg speed o f 1.5 l i t e r s per second. Using c o n v e n t i o n a l "0" r i n g vacuum s e a l s at the j o i n t s , the system has a base pressure of about 10 1^. Hg. There i s a needle v a l v e f i t t e d to the system so that a c o n t r o l l e d l e a k can be maintained. Gas p r e s s u r e s are measured on the f o l l o w i n g i n s t r uments. For p r e s s u r e s down to about 10 mmHgj a mercury U-tube i s used. Below t h i s p r e s s u r e two vacu s t a t s are employed, one from 0 to 10 mmHg and the oth e r from 0 to 1 mmHg . A l s o , below 2 mmHg.;; the pre s s u r e can be c o n t i n u o u s l y monitored by a P i r a n i , vacuum gauge type GP-110 which has two ranges, one from 6 to -26- 2000 uHg and the o t h e r from 0 to £0 uHg and i s c a l i b r a t e d from the v a c u s t a t s . 2.3 HIGH CURRENT GENERATOR AND TRIGGERING MECHANISM The h i g h c u r r e n t generator i s composed of two JuF, low inductance c a p a c i t o r s (NRG type 201) connected i n p a r a l l e l and charged through an E.H.T. power supply to V„. These c a p a c i t o r s are d i s c h a r g e d through the spark gaps. The dis c h a r g e c i r c u i t i s c r i t i c a l l y damped w i t h a n o n - l i n e a r r e s i s t o r (6 i n c h diame t e r morganite r e s i s t o r type 801) i n o r d e r t o produce a, u n i  d i r e c t i o n a l c u r r e n t p u l s e . The n o n - l i n e a r r e s i s t o r i s used as i t produces a h i g h e r peak c u r r e n t than does a l i n e a r r e s i s t o r . In the f o u r e l e c t r o d e gap assembly the gap G Q i s s e t so that i t w i l l not break down on a p p l i c a t i o n of V*c but w i l l break down when the neg a t i v e t r i g g e r p u l s e i s a p p l i e d . G^ and a l s o the main gap are s e t to break down upon a p p l i c a t i o n of V c. The h i g h c u r r e n t g e n e r a t o r i s t r i g g e r e d by a negative p u l s e a p p l i e d to e l e c t r o d e The pul s e i s generated i n the f o l l o w i n g manner (see F i g u r e 2.7)• The anode of the t r i g a t r o n i s charged to +llj. kV through the p o t e n t i a l d i v i d e r composed of the 50 MA and 120 MA r e s i s t o r s which are connected across the main bank. A 10 kV p u l s e from the pul s e transformer causes the t r i g a t r o n to break down and drop i t s anode p o t e n t i a l to zero. T h i s process a p p l i e s a n e g a t i v e p u l s e of lio- kV to -27- Charging Resistor 300 kA- Main Bank 9 uP 20 kV ~ G, 12 mm i kA -05 /JF Non Linear Resistor ftamp ^25 k A > .20 MA L-Spark Chamber X 10 kA> CV125 J 500 pF 1 MA> To Trigger Pulse Gen. Earth FIGURE 2.7 HIGH CURRENT GENERATOR AND TRIGGER CIRCUITS 32:1 Pulse Transformer Transformers FIGURE 2.,8 E.H.T SUPPLY -28- e l e c t r o d e ^ a n c * S aP & 0 breaks down i n i t i a t i n g the d i s c h a r g e . The c i r c u i t diagram f o r the E.H.T. power supply i s shown i n F i g u r e 2.8. T h i s supply i s simply a f u l l wave r e c t i f i e r , each arm of which is. composed of t w e n t y - f i v e BY 100 diodes connected i n s e r i e s and shown s c h e m a t i c a l l y by a s i n g l e d i o de. The maximum c u r r e n t which can be drawn from t h i s supply i s 200 mA. Because there i s o f t e n some d e l a y i n the t r i g g e r c i r c u i t , a l l the e l e c t r o n i c apparatus i s t r i g g e r e d from the output of a s m a l l pick-up c o i l . As s t a t e d p r e v i o u s l y , the v o l t a g e produced by t h i s c o i l i s p r o p o r t i o n a l to Hence the output of t h i s c o i l can be used to determine the parameters of the c i r c u i t . With the r e s i s t o r R^ s h o r t e d out the p e r i o d of the r i n g i n g d i s c harge determines the o v e r a l l c i r c u i t inductance L. F o r low values of s t r a y c i r c u i t r e s i s t a n c e T 2 — (henry) kV2G where: T = p e r i o d of r i n g i n g d i s c h a r g e (sec.) C = c a p a c i t a n c e of system = 9 ^uF. j T By e l e c t r i c a l l y i n t e g r a t i n g the p u l s e , a pulse propor t i o n a l to the d i s c h a r g e c u r r e n t i s o b t a i n e d . Because the area under the c u r r e n t vs. time curve i s equal to the o r i g i n a l charge s t o r e d i n the c a p a c i t o r bank, CV , the constant of c -29- d l p r o p o r t i o n a l i t y can be deduced. Current and j r ; waveforms are shown i n F i g u r e s 2.9a, b, and c. Table I I l i s t s the parameters of the h i g h c u r r e n t g e n e r a t o r . TABLE I I CIRCUIT PARAMETERS Parameter • Value Number of c a p a c i t o r s 2 Capacitance of each c a p a c i t o r 1+.5 uF Working v o l t a g e 20 kV Maximum energy 1.8 k J T o t a l c i r c u i t inductance 0.86 uH Peak c u r r e n t 25 kA 2.1+ TRIGGER PULSE GENERATOR (FIGURE 2.10) The u n i t u s u a l l y operates w i t h a m i c r o - s w i t c h connected to the manual i n p u t . T h i s switch, when.depressed, connects the g r i d of the 2D21 tube through 100 kA to ground. T h i s f i r e s the tube y i e l d i n g a p o s i t i v e p u l s e at the cathode and a balanced output across 1 M^ at the anode. The p u l s e from the anode goes to the p u l s e transformer i n the main bank t r i g g e r c i r c u i t and thence i n i t i a t e s the d i s c h a r g e . 2.5 ELECTRONIC DELAY UNIT (FIGURE 2.11) T h i s i s e s s e n t i a l l y a monostable m u l t i v i b r a t o r which ' 3 0 - FIGURE 2.9o WAVEFORM FOR d t RINGING DISCHARGE Time 10 ps/div FIGURE 2.9b -§ f WAVEFORM dt _. _ . . . Time 2 us/div FIGURE 2 . 9 c I WAVEFORM Time 2 us/div Peak current = 25 kA -31- PIGURE 2.10 TRIGGER PULSE GENERATOR INPUT PL/LSE T8A MSFORMER FIGURE 2.11 ELECTRONIC DELAY UNIT - 3 2 - generates delays c o n t r o l l e d by the R-C time constant of the c i r c u i t . With t h i s u n i t , delays are a v a i l a b l e f o r a range of 5 decades w i t h t e n steps per decade. The delay times range from 100 JJ.S to 10 sec. The main bank c u r r e n t r i s e generates a p u l s e i n the p i c k  up c o i l . T h i s p u l s e i s then used to t r i g g e r the d e l a y u n i t . The output of the d e l a y u n i t t r i g g e r s the r e c o r d i n g o s c i l l o  scope and the sawtooth pulse g e n e r a t o r . The delay u n i t i s c a l i b r a t e d by means of an o s c i l l o s c o p e to an accuracy of approximately 2$. 2.6 PROBE DEVELOPMENT AND ASSOCIATED CIRCUITRY The probe c i r c u i t r y i s shown i n b l o c k form i n F i g u r e s 2.5 and 2.6 and i s shown i n the form which was f i n a l l y adopted f o r t h i s experiment i n F i g u r e 2.12. A T e k t r o n i x 5>l5 o s c i l l o s c o p e serves as the sawtooth pulse g e n e r a t o r . The 5>l5 o s c i l l o s c o p e was chosen f o r the g e n e r a t o r p r i m a r i l y because i t was r e a d i l y a v a i l a b l e , i t c o u l d supply a sawtooth p u l s e w i t h a r i s e time from 2 us to a number of seconds and a peak amplitude of 150 v o l t s , and i t c o u l d be t r i g g e r e d e a s i l y . The v o l t a g e between the probes, and the c u r r e n t f l o w i n g i n the p r o b e . c i r c u i t were d i s p l a y e d on the upper and lower beams r e s p e c t i v e l y of a type 55l double beam o s c i l l o s c o p e w i t h typeD TO SAWTOOTH O U T T E K T R O N I X 515 S C O P E U P P E R B E A M T Y P E D P R E AMP C O N N E C T E D T O CIRCUIT W I T H T Y P E P 6 0 0 0 IOX A T T E N U A T I N G P R O B E C A S E OF T E K T R O N I X T Y P E 551 S C O P E F I G U R E 2.12 D E T A I L E D P R O B E C I R C U I T L O W E R - B E A M T Y P E D P R E A M P - 3 1 * - p r e a m p l i f i e r s and were reco r d e d on p o l a r o i d f i l m . The v o l t a g e between probe 1 and ground (see F i g u r e 2.12) was measured w i t h a ten times a t t e n u a t i n g probe ( T e k t r o n i x type P 6000} which has a frequency response of dc to 30 Mc). The s m a l l c o r r e c t i o n necessary to account f o r the p o t e n t i a l drop across the 1 k ^ c u r r e n t shunt i s n e g l i g i b l e , hence, the upper beam d i s p l a y e d d i r e c t l y the v o l t a g e between the probes. The c u r r e n t was measured as a p o t e n t i a l drop across a 1 k ^ one p e r c e n t carbon d e p o s i t r e s i s t o r . The type D p r e a m p l i f i e r was used because of i t s h i g h s e n s i t i v i t y . The s e n s i t i v i t y of t h i s p r e a m p l i f i e r i s 1 mV/div to £0 v o l t s / d i y c a l i b r a t e d , and the frequency response i s dc to 300 kc at 1 mV/div s e n s i t i v i t y , i n c r e a s i n g to dc to 2 Mc a t 5>0 mV/div and lower s e n s i t i v i t i e s . T h i s narrow pass band might appear to s e v e r e l y l i m i t i t s u s e f u l n e s s . E x p e r i m e n t a l l y , however, i t was found that the p r e a m p l i f i e r d i d not i n t r o d u c e any n o t i c e a b l e d i s t o r t i o n i n a sawtooth pu l s e of 10 p.s r i s e t i m e . Throughout most of the experiment a p u l s e w i t h a r i s e t i m e of 10 ^us was used and hence t h i s p r e a m p l i f i e r was a c c e p t a b l e . The manner i n which the probes were s h i e l d e d and the de t a i l s of the probe c i r c u i t e v o l v e d as s o l u t i o n s to numerous problems were o b t a i n e d . Measurements of very s m a l l c u r r e n t s , which are f l o w i n g a t the same time as very l a r g e c u r r e n t s , or even a s h o r t time a f t e r the l a r g e c u r r e n t p u l s e has ceased, are -35- d i f f i c u l t to make. In t h i s experiment the main c u r r e n t p u l s e was about 10^" amps while the c u r r e n t s i n the probe c i r c u i t were from 10"^  to 10°^  amps, a d i f f e r e n c e of 8 to 10 orders of mag n i t u d e . When the main bank di s c h a r g e d , the changing magnetic f i e l d a s s o c i a t e d w i t h the c u r r e n t p u l s e induced l a r g e (500 to 1,000 v o l t s ) v o l t a g e s i n the probes and as a r e s u l t l a r g e c u r  rents flowed i n each probe. The o s c i l l o s c o p e p r e a m p l i f i e r s , which were s e t at h i g h g a i n , became s a t u r a t e d . I t then r e q u i r e d a f i n i t e time f o r these p r e a m p l i f i e r s to d e s a t u r a t e so that waveforms were a g a i n a c c u r a t e l y d i s p l a y e d on the o s c i l l o s c o p e . The l e n g t h of time r e q u i r e d f o r these p r e a m p l i f i e r s to d e s a t u r  ate depended upon the magnitude of the pulse induced by the main di s c h a r g e and the g a i n s e t t i n g s of the p r e a m p l i f i e r s . In p r a c t i c e t h i s means t h a t measurements can not be made f o r times l e s s than 0.2 ms a f t e r the d i s c h a r g e . I f . one were i n t e r e s t e d i n i n v e s t i g a t i n g t h i s r e g i o n of time delays, some k i n d of g a t i n g c i r c u i t would have to be used whereby the probes c o u l d be d i s  connected from the measuring c i r c u i t w h i l e the main di s c h a r g e was t a k i n g p l a c e . T h i s pick-up p u l s e would a l s o cause the sawtooth gene r a t o r (5l5 o s c i l l o s c o p e ) to t r i g g e r prematurely. In the experiment t h i s problem was' cured r e l a t i v e l y e a s i l y by i n s e r t i n g a cathode f o l l o w e r stage between the t r i g g e r g e n e r a t o r and the probes. This cathode f o l l o w e r i s o l a t e d the generator from the probes. 3 6 - The v o l t a g e across the probes was p u l s e d and hence the c u r r e n t f l o w i n g i n the probe c i r c u i t was a l s o p u l s e d . Because of the p u l s e d nature of the v o l t a g e , s t r a y c a p a c i t a n c e s i n the c i r c u i t had to be c a r e f u l l y balanced or e l i m i n a t e d . The capa c i t a n c e between each probe and ground had to be the same and d i r e c t c a p a c i t a n c e between the probes was, as f a r as was pos s i b l e , e l i m i n a t e d . I f t h i s was n o t d o n e , the vo l t a g e across the 1 k A c u r r e n t shunt, when the probes had i n f i n i t e impedance between them, was the d i f f e r e n t i a l of the voltage a p p l i e d be tween the probes. C l o s e l y r e l a t e d to the problem of s i g n a l d i f f e r e n t i a t i o n was the problem of n o i s e p i c k up. By m a i n t a i n i n g c o a x i a l sym metry, as f a r as p o s s i b l e , and by s h i e l d i n g a l l p a r t s of the c i r c u i t , a c l e a n c u r r e n t waveform c o u l d be o b t a i n e d . The probes were s h i e l d e d c o a x i a l l y to w i t h i n i n c h of t h e i r t i p s . I n o r d e r to m a i n t a i n c o a x i a l symmetry i n the probe c i r c u i t a c o a x i a l vacuum connector was used to pass through the w a l l s of the spark chamber (see F i g u r e 2.5 ;). The cathode f o l l o w e r a l s o s e r v e d to reduce the o v e r a l l n o i s e of the c i r c u i t by changing the h i g h output impedance of the sawtooth gen e r a t o r to a low impedance of about 1 0 0 ohms. A f t e r a l l these p r e c a u t i o n s were taken, the o s c i l l o s c o p e i n d i c a t e d zero c u r r e n t f l o w i n g i n the probe c i r c u i t upon a p p l i  c a t i o n of the v o l t a g e sawtooth when there was i n f i n i t e impedance between the probe t i p s . When a r e s i s t o r of 2 M./t was connected between the probe t i p s , the cu r r e n t waveform e x a c t l y f o l l o w e d the vo l t a g e and the c u r r e n t was the expected 75 ^iarnp f o r an a p p l i e d v o l t a g e of 150 v o l t s . The 1 kA c u r r e n t shunt was e x p e r i m e n t a l l y chosen from values between 100 ohms and 100 k A t o produce the c l e a n e s t c u r r e n t waveform when v a r i  ous r e s i s t a n c e s were connected between the probe t i p s . The f i n a l d e s i g n of the probes used i n t h i s experiment i s shown i n F i g u r e 2.13. The o r i g i n a l s e t of probes were made of two p i e c e s of p l a t i n u m wire, 0.5 mm i n diameter, 1 cm long and o r i e n t e d p a r a l l e l to each o t h e r w i t h a s e p a r a t i o n of 5 mm. These probes were used f o r the p r e l i m i n a r y i n v e s t i g a t i o n s , but had two disadvantages, namely, the p l a t i n u m wire l a c k e d r i g i  d i t y and, as the probe wires were p a r a l l e l , the c a p a c i t a n c e between the two probes was h i g h . In the f i n a l d e s i g n tungsten wire was chosen f o r the probe m a t e r i a l because of i t s s t r e n g t h , h i g h m e l t i n g p o i n t , and i t s r e s i s t a n c e to e r o s i o n and s p u t t e r  i n g . At the c o n c l u s i o n of the experiment the probes were viewed under a microscope and appeared to have s u f f e r e d l i t t l e damage from s p u t t e r i n g or e r o s i o n . The main spark gap e l e c  trodes were a l s o tungsten and i n t h i s way the tungsten probes e l i m i n a t e d the problem of probe contamination from metal vapour b o i l e d o f f the main e l e c t r o d e s d u r i n g the d i s c h a r g e . The s m a l l wire s i z e (0.5 mm i n diameter) minimized the c o o l i n g e f f e c t of the probes on the plasma. The probes were o r i e n t e d as • P Y R E X G L A S S TUBING W A L L T-HICK NESS ~ 5mm T 5 mm BRAID SHIELD OF MINIATURE COAX C A B L E P U L L E D DOWN G L A S S NSULATOR TO i DOTTED LINE TUNGSTEN WIRE 5 mm NOT TO SCALE F I G U R E 2.13 P R O B E D I M E N S I O N S - 3 9 - i n a h o r i z o n t a l plane and were c o - l i n e a r w i t h a d i s t a n c e of 5 mm between the t i p s . T h i s o r i e n t a t i o n reduced the probe to probe ca p a c i t a n c e c o n s i d e r a b l y over t h a t of the o r i g i n a l p l a  tinum probes. The probes were mounted on bracke t s at the end of a l u c i t e r o d so that t h e i r r a d i a l p o s i t i o n c o u l d be v a r i e d w i t h r e s p e c t to the t e s t gap. -14-0- GHAPTER 3: MEASUREMENTS AND DATA I n t h i s s e c t i o n the measurement methods are d i s c u s s e d , t y p i c a l o s c i l l o s c o p e t r a c e s of c u r r e n t v o l t a g e vs. time are reproduced and d i s c u s s e d , and some comments are made on the re c o v e r y measurements which were used to supplement the probe conductance measurements. 3.1 CONDUCTANCE MEASUREMENTS As was s t a t e d i n Chapter 2, the conductance of the probes was deduced by a p p l y i n g a sawtooth shaped vo l t a g e p u l s e across the probes and measuring s i m u l t a n e o u s l y the vo l t a g e and the cu r r e n t i n the probe c i r c u i t . Even though measurements of t h i s type do not d i s t u r b the r e c o v e r i n g gas very much, there i s s t i l l some d i s t u r b a n c e , and so only one sawtooth p u l s e was a p p l i e d at a s e t d e l a y time a f t e r the main discharge took p l a c e . The complete conductance curve was obt a i n e d i n a s t a t i s t i c a l manner. Each p o i n t i s an average of three t e s t s . I d e a l l y many more t e s t s (say 20) should be used to form an average, but the purpose of t h i s experiment was p r i m a r i l y to deduce the u s e f u l n e s s of the probes and to determine e x p e r i  mental o p e r a t i n g c o n d i t i o n s . The r i s e t i m e of the sawtooth used i n these conductance measurements i s 10 ^ us. The r i s e time was chosen as i t . i s s h o r t compared to a p p r e c i a b l e changes i n the temperature, but long compared to the l e n g t h of time f o r an i o n to t r a v e l through the sheath surrounding probe 2. In or d e r to determine t h a t t h i s r i s e t i m e was not a f a c t o r i n determining the conductance, runs were taken w i t h sawtooth r i s e t i m e s of 2 and 100 / i s . The con ductance determined from these runs was compared.to t h a t d e t e r  mined f o r 10 ^ us r i s e t i m e , and., w i t h i n experimental e r r o r , there was no d i f f e r e n c e , hence 10 us was used. The sawtooth p u l s e a t t a i n e d a peak v o l t a g e of about 80 v o l t s . The r a d i a l d i s t a n c e between the probes and the main t e s t gap was v a r i e d from 2 to l£ cm f o r gas pressures above 1 mmHg, and from 5 to 15 cm f o r gas p r e s s u r e s of 0.1 mmHg. The minimum d i s t a n c e was chosen so as to reduce the p o s s i b i l i t y of an arc forming between the main e l e c t r o d e s and the probes and subse q u e n t l y damaging the probe c i r c u i t and the a s s o c i a t e d e l e c t r o n i c c i r c u i t r y . The parameters which a f f e c t the main d i s c h a r g e were c a r e  f u l l y c o n t r o l l e d . P r i o r t o, and f o l l o w i n g each run, the cu r - r e n t and waveforms of the main d i s c h a r g e were taken and compared to pr e v i o u s r e c o r d s . The d i s t a n c e between the main e l e c t r o d e s was a l s o checked d u r i n g each run, as was the distance between the probes. A r e p e t i t i o n r a t e of about one t e s t per minute was chosen so t h a t the n o n - l i n e a r r e s i s t o r would not overheat and so t h a t the a i r i n the spark chamber would have -1+2- . time to c o o l between t e s t s . A f t e r every l£ to 20 t e s t s the a i r i n the chamber was changed. For a l l gas pres s u r e s except 1 mmHg and 0.1 mmHg the gas pressure was s t a t i c , but f o r these two the pressure was main t a i n e d by b a l a n c i n g the pumping speed a g a i n s t the c o n t r o l l e d l e a k r a t e . 3.2 DATA OBTAINED Measurements were made at d i f f e r e n t gas press u r e s and d i f f e r e n t r a d i a l d i s t a n c e s from the a x i s of the t e s t gap. The pres s u r e s chosen were 760, 200, £0, i o , 1, and 0.1 mmHg; the r a d i a l d i s t a n c e s were l£, 10, f?, and 2 cm, except i n the case of p r e s s u r e s of 0.1 mmHg where no measurements were made f o r a r a d i a l d i s t a n c e of 2 cm. Table III g i v e s a summary of the data taken. There are c e r t a i n v a l u e s of pressure and r a d i a l d i s  tances which are not l i s t e d i n t h i s t a b l e . F o r these values there was no d e t e c t a b l e c u r r e n t f l o w i n the probe c i r c u i t f o r the range of del a y time which c o u l d be i n v e s t i g a t e d . -1*3- TABLE I I I RANGE OP EXPERIMENTAL CONDITIONS FOR WHICH PROBE CONDUCTANCE COULD BE MEASURED Gas Pressure R a d i a l D i a t . Range of No. of Delay of Probes Delay Times Times Used (mmHg) (cm) (ms) 200 2 0.25 - 2.2 5 . 50 2 0.39 - 3.0 7 10 2 0.25 - 6.6 7 5 0.25 - 2.2 7 1 2 0.25 - 5.0 7 5 0.25 - 16 10 10 0.25 - 11 9 15 0.314- - 16 10 0.1 5 o.3h - 5 7 10 0.31+ - 11 8 15 0.31+ - 11 8 One photograph, of the t h r e e taken f o r a complete run of data at a gas p r e s s u r e of 1 mmHg and w i t h the probes at a r a d i a l d i s t a n c e of 10 cm from the main gap, i s shown i n F i g u r e 3.1. The v o l t a g e a p p l i e d between the probes i s r e c o r d e d on the upper t r a c e and the c u r r e n t on the lower t r a c e . This s e r i e s of photographs show a number of e f f e c t s common to many or a l l the r e c o r d s . The expected c u r r e n t s a t u r a t i o n i s shown i n a l l the photographs although f o r very s m a l l and very long delays the s a t u r a t i o n e f f e c t i s not as pronounced. I t i s a l s o n o t i c e d t h a t the c u r r e n t waveform i s not the same shape duri n g the time when the v o l t a g e i s d e c r e a s i n g as i t i s while the v o l t a g e i s i n c r e a s i n g . T h i s i s presumably due to the f a c t t h a t For a l l photographs: Voltage upper benm, rarrent lower Voltage s c a l e = 50 v o l t s / d i v . Time base = 2 u s / d i v . I n c r e a s i n g from r i g h t to l e f t Gas pressure = 1 mm.Hg Probes 10 cm. from mnin gap Delay =11 ms Gurrent= 2 ^iamp/div Delpy =2.9 ms C u r r e n t= 2 0 jianm/div Delay = 0 . $ 6 ms 0 u r r e n t = 5 0 ^.amp/div Delay =1.6 ms rhirrent=10 ^lamo/div Delay = 5 . 0 ms Current= 1 0 jiamp/div Delay Current = 0 . 9 ? =50 p ms amp/di "* T Delay =0.3*1. ms Delay = 0 . 2 5 ms Current= 1 0 0 ^iamp/div Current= 2 0 0 ^iamp/div FIGURE 3 . 1 CURRENT AND VOL TAG?. I N PROBE C I r i C J I T - 1 * 5 - For a l l photographs: Voltage upper beam, c u r r e n t lower Voltage s c a l e = £ 0 v o l t s / d l v . Time base = 2 u s / d i v . i n c r e a s i n g from r i g h t to l e f t a. b . c. Gas p r e s s u r e = 1 mm.Hg Probes 1 5 cm. from main gap Delay = 5 . 0 ms Current a. = 5 >*arap/div. b.,c. = 2 uamp/div. FIGURE 3.2 CURRENT AND VARIATION BETWEEN TESTS Gas p r e s s u r e = 2 0 0 mm.Hg Probes 2 cm from gap Delay = 0 . 7 1 + ms Current = 5 0 uamp/div FIGURE 3.3 CURRENT AND VOLTAGE FOR HIGH GAS PRESSURES Gas p r e s s u r e = 0 . 1 mm.Hg Probes 1 0 cm from gap Delay = 5 . 0 ms Current = 1 0 uamp/div FIGURE 3.1+ LARGE OSCILLATIONS ON THE CURRENT WAVEFORM -14.6- the sheath surrounding the grounded probe acts as a s m a l l capa c i t o r and s t o r e s e l e c t r i c a l energy. This e f f e c t was not i n v e s  t i g a t e d i n t h i s experiment but under s i m i l a r experimental con d i t i o n s , Smy (1963) used t h i s e f f e c t to estimate the sheath t h i c k n e s s . Superimposed on some of the c u r r e n t waveforms are o s c i l l a t i o n s . These o s c i l l a t i o n s o n l y appear on the records taken at 1 and 0,1 mmHg gas pressure and f o r r e l a t i v e l y l o n g delay times. The amplitude of these o s c i l l a t i o n s i s much l a r g e r at the lower p r e s s u r e (see F i g u r e 3• I4.). These o s c i l l a  t i o n s , which are a r e l a t i v e l y common phenomena i n probe s t u d i e s , occur because the plasma i s d i s t u r b e d by the probes. Loeb (1955) d i s c u s s e s t h i s type of o s c i l l a t i o n and shows t h a t i t occurs at the p o s i t i v e i o n frequency a> }^ > ~ / n i q i 2 - i - JZT^ where: q^ = p o s i t i v e i o n charge (coulombs) n^ = p o s i t i v e i o n d e n s i t y (ions meter" 3) M = i o n mass (kg) £ Q = p e r m i t t i v i t y of vacuum ( f a r a d meter" 1) F o r t h i s experiment where o s c i l l a t i o n s occur an average value of the c u r r e n t i s taken i n computing the probe conductance. In S e c t i o n 3»1 i t was p o i n t e d out t h a t the c u r r e n t f l o w i n g i n the probe c i r c u i t v a r i e s from d i s c h a r g e to dis c h a r g e , even though the main d i s c h a r g e and the probe parameters remain c o n s t a n t . F i g u r e 3.2 shows three photographs w i t h the same e x t e r n a l parameters, i n which the c u r r e n t i s q u i t e d i f f e r e n t from t e s t to t e s t . One e x p l a n a t i o n o f t h i s wide v a r i a t i o n i s that the main discharge i t s e l f i s sometimes symmetric and some times not w i t h the d i r e c t i o n of the asymmetry completely r a n  dom. Hence, at a g i v e n p o i n t i n space, the measured conduc tance w i l l be d i f f e r e n t from d i s c h a r g e to d i s c h a r g e . The asymmetry of the d i s c h a r g e channel i s w e l l e s t a b l i s h e d and has been r e c o r d e d by A l l e n and Craggs (195*4-) w i t h a r o t a t i n g m i r r o r camera. 3.3 RECOVERY MEASUREMENTS Due to the e x t e n s i v e r e c o v e r y work which has been done on s i m i l a r apparatus, ( C h u r c h i l l , Parker, & Craggs/ 1961; C h u r c h i l l & Poole, 1963; C h u r c h i l l 1961, 1963; Craggs, 1963; Chan, 1963) and as. t h i s technique i s w e l l developed, i t was c o n s i d e r e d advantageous to determine the r e c o v e r y c h a r a c t e r i s  t i c s of the main spark gap. T h i s f a c i l i t a t e s comparison be tween t h i s apparatus and that used by the workers r e f e r r e d to above. The r e c o v e r y c h a r a c t e r i s t i c s were d e r i v e d by the method used by C h u r c h i l l (1961) i n which a u n i t f u n c t i o n v o l t a g e i s a p p l i e d t o the main gap e l e c t r o d e s at a g i v e n d e l a y time a f t e r the main d i s c h a r g e has taken p l a c e . A f a s t o s c i l l o s c o p e , - U n  connected to, a p o t e n t i a l d i v i d e r which i s across the main gap, enables one to determine i f the gap r e i g n i t e s . The v o l t a g e of the u n i t f u n c t i o n i s v a r i e d u n t i l the minimum value which causes r e i g n i t i o n i s found. This i s c a l l e d the r e i g n i t i o n v o l t a g e . The experimental apparatus and the d e t a i l e d experimental method are the same as th a t used by Chan (1963) and are d i s c u s s e d i n gr e a t d e t a i l i n h i s t h e s i s . -1+9- CHAPTER k: ANALYSIS OF DATA In t h i s s e c t i o n the temperature w i l l be d e r i v e d from the probe conductance curves. The probe conductance f o r a gas p r e s  sure of 200 mmHg and delay time of 2 ms was measured experimen t a l l y . The gas temperature can be found from the r e i g n i t i o n curves f o r these c o n d i t i o n s , hence, the constant K (see equa t i o n 7) which r e l a t e s the conductance G to the three h a l v e s power of the temperature can be found. When K i s found o r de termined, the values of the probe conductance can be converted i n t o temperatures. I4..I DERIVATION OF TEMPERATURES FROM RECOVERY CURVES During the l a t t e r p a r t of the r e c o v e r y the r e i g n i t i o n v o l t a g e ( V R ) obeys Paschen's law ( C h u r c h i l l , 1961; Chan, 1963) i . e . the r e i g n i t i o n v o l t a g e i s lowered due to decreased gas d e n s i t y . The manner i n which the r e i g n i t i o n v o l t a g e v a r i e s w i t h gas d e n s i t y may be determined by measuring the impulse breakdown v o l t a g e as a f u n c t i o n of gas pr e s s u r e f o r the t e s t gas at ambient temperature. Assuming t h a t the t e s t gas i s a p e r f e c t gas and t h a t i t obeys a p e r f e c t gas law durin g r e i g n i  t i o n , and assuming t h a t f o r a g i v e n r e i g n i t i o n v o l t a g e 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 , then: T P R 8 T. R « • • P where: T R = r e c o v e r i n g gas temperature (°K) T ambient gas temperature (assumed 300°K) = ambient gas pressure (mmHg) P p r e s s u r e , corresponding to the value V^, which i s found from the p l o t of the impulse breakdown v o l  tage vs. ambient gas p r e s s u r e (mmHg). F i g u r e I4..I shows the p l o t of the impulse breakdown v o l t a g e vs. ambient gas p r e s s u r e f o r 6,l\. mm diameter tungsten e l e c t r o d e s , 0.5 cm apart, from which P i s found. F i g u r e Ij..2 shows r e i g n i  t i o n curves f o r the 6.I4. mm diameter main e l e c t r o d e s and F i g u r e I4..3 shows the gas temperatures d e r i v e d from equation 8. These curves agree, i n g e n e r a l form, w i t h those d e r i v e d by C h u r c h i l l (1961) and Chan (1963) under d i f f e r e n t e xperimental c o n d i t i o n s . 1+.2 RADIAL TEMPERATURES DERIVED FROM PROBE CONDUCTANCES Measurements made by Chan (1963) show t h a t the spark channel has a u n i f o r m temperature up to a r a d i a l d i s t a n c e of 2.5 cm at atmospheric p r e s s u r e . Although the apparatus used by Chan (1963) was not i d e n t i c a l to t h a t used i n t h i s experiment they were very s i m i l a r and i t i s reasonable to assume, i n t h i s experiment, that at a p r e s s u r e of 200 mmHg the channel i s FGURE 4.1 SWRK BREAKDOWN VOLTAGE IN AIR 6.4 mnv TUNGSTEN GAP AT 5 mm. SEPARATION SPARKING POTENTIAL AT 760 mm.Hg PRESSURE: > 6 S o £ 2 400 PRESSURE (mmHg) -sAo- 1000 K800 FIGURE 4. 2 SWRK GAP RECOVERY IN AIR FOR THE MAIN GAP MAIN GAP: 6.4 mm. TUNGSTEN ELECTRODES AT 5 mm SEPARATION SPARKING VOLTAGE: PARAMETER: GAS P R E S S U R E 760 mm Hg 200 mm. Hg —1 I I I II _l I i i i i DELAY AFTER SPARK INITIATION (ms) DELAY AFTER SPARK INITIATION (ms) -52- uniform out to a r a d i a l d i s t a n c e of at l e a s t 2 cm. This i s e s p e c i a l l y true as the r e s u l t s i n t h i s experiment show that the spark channel r a d i u s i n c r e a s e s w i t h d e c r e a s i n g p r e s s u r e . With t h i s assumption, then, the temperature deduced from r e i g n i t i o n measurements i s the same as the temperature where the probes are l o c a t e d . Hence, f o r a pressure of 200 mmHg the observed conductance at a del a y time of 2 ms and the measured tempera ture from r e i g n i t i o n measurements are both known. The constant K of equ a t i o n 7 i s , t h e r e f o r e , c a l c u l a t e d as: K = 1+.31J, x 1 0 ~ 1 3 mho ( ° K ) - 3 / 2 or e q u a t i o n 7 i s now: G = I4..3I; x 1 0 " 1 3 T 3 / / 2 ... 9 F i g u r e s to Ij.. 7 show the probe conductance, which i s the r a t i o o f the c u r r e n t at s a t u r a t i o n to the corresponding v o l t a g e , p l o t t e d a g a i n s t the delay time a f t e r spark i n i t i a t i o n . F i g u r e s I4..8 to I4..II show the temperatures which are d e r i v e d from e q u a t i o n 9 and from the probe conductance curves. These r e s u l t s w i l l be d i s c u s s e d i n d e t a i l i n Chapter 5. - 5 3 - F I G U R E 4.4 P R O B E C O N D U C T A N C E G IN AIR AT HIGH P R E S S U R E S MAIN G A P : 6 . 4 m m T U N G S T E N E L E C T R O D E S AT 5 m m S E P A R A T I O N P E A K C U R R E N T = 25 K A P R O B E S ^ 0 .5mm DIA. T U N G S T E N A T 5 m m S E P A R A T I O N , M O U N T E D H O R I Z O N T A L L Y I 1 1 I I I I 0 2 4 6 8 10 12 14 D E L A Y A F T E R SPARK INITIATION (ms) F I G U R E 4.5 P R O B E C O N D U C T A N C E G IN AIR AT 1 0 m m H g P R E S S U R E MAIN G A P : 6 . 4 m m T U N G S T E N E L E C T R O D E S AT 5 m m S E P A R A T I O N P E A K C U R R E N T = 2 5 K A P R O B E S : 0 . 5 m m DIA. T U N G S T E N AT 5mm S E P A R A T I O N , M O U N T E D H O R I Z O N T A L L Y ,-5 . P A R A M E T E R : R A D I A L D I S T A N C E OF P R O B E S TO MAIN G A P D E L A Y A F T E R S P A R K INITIATION (ms) F I G U R E 4 . 6 P R O B E C O N D U C T A N C E G IN A IR A T Imm Hg P R E S S U R E MAIN G A P : 6.4 mm T U N G S T E N E L E C T R O D E S AT 5 m m S E P A R A T I O N P E A K C U R R E N T = 2 5 K A P R O B E S : 0 5 mm DIA. T U N G S T E N A T 5mm S E P A R A T I O N , M O U N T E D H O R I Z O N T A L L Y P A R A M E T E R : R A D I A L DIST. O F P R O B E S TO MAIN G A P I0" : F I G U R E 4 . 7 P R O B E C O N D U C T A N C E G IN AIR AT 0.1 mm Hg P R E S S U R E MAIN GAP- . 6 . 4 m m T U N G S T E N E L E C T R O D E S AT 5 m m S E P A R A T I O N P E A K C U R R E N T = 2 5 K A P R O B E S : 0 5 mm D I A . T U N G S T E N A T 5 m m S E P A R A T I O N , M O U N T E D H O R I Z O N T A L L Y P A R A M E T E R : R A D I A L D I S T A N C E OF P R O B E S TO MAIN G A P 5 cm • 10 cm x 15 cm Q 4 6 8 10 D E L A Y A F T E R S P A R K INITIATION (ms) 4 6 8 10 D E L A Y A F T E R S P A R K INITIATION (ms) FI6URE 4.8 . DERIVED TEMPERATURES FOR AIR AT HIGH PRESSURES - N. PROBES 2cm FROM MAIN GAP \ MAIN GAP: 6.4mm TUNGSTEN ELECTRODES AT 5mm \ SEPARATION V PROBES0-5mm DIA. TUNGSTEN AT 5 mm SEPARATION - \ PARAMETER'• GAS PRESSURE 1 1 1 1 1 1 1 \ ?L—200 mm Hg • - \^ Y^ *—50mm Hg X 1 II  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Mil LO 10 DELAY AFTER SPARK INITIATION (m •) 1.0 10 DELAY AFTER SPARK INITIATION (m s) FIGURE 4.10 DERIVED TEMPERATURES FOR AIR AT Imm Hg PRESSURE MAIN GAP: 6.4mm TUNGSTEN ELECTRODES AT 5mm SEPARATION PROBES: 0-5 mm DIA.TUNGSTEN AT 5mm SEPARATION PARAMETER*. RADIAL OISTANCE OF PROBES TO MAIN GAP. IX) 10 DELAY AFTER SPARK INITIATION (ms) FIGURE 4.11 DERIVED TEMPERATURES FOR AIR AT O.lmm PRESSURE MAIN GAP'. 6-4 mm TUNGSTEN ELECTRODES AT 5mm SEPARATION PROBES: 0.5mm DIA. TUNGSTEN AT 5mm SEPARATION PARAMETER: RADIAL DISTANCE OF PROBES TO MAIN GAP I I I I I I I I J I I I I I I I I 1.0 10 DELAY AFTER SPARK INITIATION (ms) I I I I I I -55- CHAPTER 5: DISCUSSION OF RESULTS I n t h i s s e c t i o n some g e n e r a l f e a t u r e s of the r a d i a l tem pera t u r e curves are d i s c u s s e d and g e n e r a l comments about these measurements and re c o v e r y measurements are made. The d e r i v e d temperatures f o r very s h o r t d e l a y times are h i g h e r than one would expect, hence, a d i s c u s s i o n of the e r r o r s i n v o l v e d i n the measurements and i n the assumption t h a t the probe conductance i s p r o p o r t i o n a l to the th r e e - h a l v e s power of the temperature. 5.1 FEATURES OF RADIAL TEMPERATURE CURVES The curves shown i n F i g u r e s I4..8 to I4..II w i l l be d i s c u s s e d i n three c a t e g o r i e s and, f o r convenience, w i l l be r e f e r r e d to as: h i g h p r e s s u r e , where the gas pressure i s 10 mmHg or g r e a t e r ; medium p r e s s u r e or 1 mmHg gas p r e s s u r e ; and low p r e s  sure o r 0.1 mmHg gas p r e s s u r e . The curves i n each category are of e s s e n t i a l l y the same form. The curves i n the h i g h p r e s s u r e category a l l show that the gas rec o v e r s q u i c k l y and th a t there i s l i t t l e i o n i z a t i o n p r e s e n t a f t e r 5 ms. C h u r c h i l l (1963) r e p o r t s t h a t , u s i n g r e i g n i t i o n techniques, he found no g r e a t v a r i a t i o n i n the r e c o v e r y of the spark channel i n the pr e s s u r e range i n v e s t i g a  t e d (200 - 76O mmHg). The temperatures deduced i n t h i s e x p e r i  ment from probe conductance measurements c o n f i r m t h i s i n a -56- p r e s s u r e range between 10 and 200 mmHg. For a gas p r e s s u r e of 1 mmHg the r e c o v e r y was much slower. The spark channel had expanded to f i l l the whole spark chamber and t h i s a l lowed one to to measure the r a d i a l temperature pro f i l e shown i n F i g u r e 5«1« This graph shows that f o r long d e l a y times the temperature i s lower c l o s e to the e l e c t r o d e s than i t i s at l a r g e r r a d i a l d i s t a n c e s . T h i s e f f e c t i s probably due to the c o o l i n g e f f e c t of the main e l e c t r o d e s . The e x i s t e n c e of de t e c t a b l e i o n i z a t i o n at a r a d i a l d i s t a n c e of 15 cm im p l i e s t h a t v i r t u a l l y the whole spark chamber i s f i l l e d w i t h plasma. T h i s plasma i s i n c o n t a c t w i t h the l a r g e c o l d brass rods sup p o r t i n g the main e l e c t r o d e s and i s c o o l e d by them. At lower p r e s s u r e s , where the r e c o v e r y i s slower, one would then expect t h a t the thermal 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 and t h e i r supports would be n o t i c e a b l e , as i s the case. I n the low pre s s u r e r e g i o n the temperature curves show th a t w i t h i n the expected e r r o r (see S e c t i o n 5*3) the gas throughout the spark chamber i s at the same temperature. The mean f r e e p a t h of the p a r t i c l e s , i n t h i s r e g i o n , i s of the same order of magnitude as the chamber dimensions and because of the long mean f r e e p a t h the gas everywhere i n the chamber i s at the same temperature and d e i o n i z a t i o n and re c o v e r y take p l a c e at the same r a t e . - 5 7 - F I G U R E 5.1 D I S T A N C E OF P R O B E . TO T E S T G A P ( c m ) 5 . 2 GENERAL RECOVERY CHARACTERISTICS Assume t h a t the r e g i o n where some probe conductance i s d e t e c t a b l e i s an i n d i c a t i o n of the r a d i a l extent of the spark channel. Prom Table I I I (page I4.3) one sees t h a t the spark chan n e l r a d i u s i n c r e a s e s w i t h d e c r e a s i n g gas pressure u n t i l at 1 mmHg i t extends to the r a d i a l extent of the spark chamber. The temperatures which are d e r i v e d from the probe conductance measurements show t h a t the spark gap takes l o n g e r to r e c o v e r at low p r e s s u r e s than i t does at h i g h . T h i s o b s e r v a t i o n supports the f a c t t h a t the main d e i o n i z a t i o n mechanism i s volume recom b i n a t i o n (see Craggs, 1963) although f o r complete v e r i f i c a t i o n the values of the e l e c t r o n , i o n , and n e u t r a l c o n c e n t r a t i o n s s h o u l d be known. 5.3 LIMITS OP ACCURACY OP THE RESULTS There are a number of e f f e c t s which l i m i t the accuracy of the experimental r e s u l t s . As was p o i n t e d out i n Chapter 3, the v a r i a t i o n i n the measured probe conductance from t e s t to t e s t was l a r g e and, as i s to be expected, there i s a l a r g e s c a t t e r i n the p l o t t e d experimental p o i n t s (see F i g u r e s I4..J4. to L}_.T) • The r e i g n i t i o n v o l t a g e c a l c u l a t e d f o r the d e l a y time of 2 ms was very c l o s e to the minimum vo l t a g e o b t a i n a b l e from the 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 . -59- The value o f the d e r i v e d temperature i s much h i g h e r f o r sh o r t d e l a y times than one would expect, based on temperature measurements and esti m a t e s made by oth e r workers (Craggs,1963; Poole, Parker, and C h u r c h i l l , 1963). The reason f o r the d i s  crepancy i s probably t h a t the assumed constant K i n equation 7 does vary due to two f a c t o r s which compose t h i s constant, I n l  and the sheath t h i c k n e s s d. Both these f a c t o r s vary w i t h changes i n temperature and p a r t i c l e d e n s i t y . R e f e r r i n g to the t a b u l a t e d values of ln_A. i n S p i t z e r (1956), one sees t h a t f o r expected changes i n d e n s i t y and temperature l n , A may change by a f a c t o r of two or t h r e e . The sheath t h i c k n e s s i s a l s o a f u n c t i o n of the gas temperature. Although i t i s d i f f i c u l t to estimate sheath t h i c k n e s s v a r i a t i o n s , they should be s m a l l , as c u r r e n t s a t u r a t i o n always occurs f o r approximately the same k T a p p l i e s v o l t a g e and t h i s v o l t a g e i s much i n excess of qg—• The arguments advanced i n t h i s s e c t i o n imply t h a t the d e r i v e d temperature curves o b t a i n e d i n t h i s experiment w i l l a c c u r a t e l y d e s c r i b e the s t a t e o f the gas near the values of conductance, or temperature, f o r which K was c a l c u l a t e d , w i t h the accuracy o f the d e r i v e d temperature d e c r e a s i n g as the values of the temperature change from the c a l i b r a t i o n v a l u e . Hence low values of temperature (about 10 3 °K) are r e l a t i v e l y a c c u rate but the h i g h values which occur a t short (0.2 - 0.5 ms) d e l a y times are probably i n e r r o r by a f a c t o r of two or t h r e e . -60- However, as was shown e a r l i e r i n the Chapter, a gr e a t d e a l of i n f o r m a t i o n can s t i l l be d e r i v e d from these temperature curves. -61- CONCLUSION From the r e s u l t s of t h i s experiment i t can be concluded t h a t : a. The conductance of two e l e c t r i c probes p l a c e d i n a r e c o v e r i n g spark channel, which i s c r e a t e d by a 25 kA u n i d i r e c t i o n a l c u r r e n t p u l s e , can be measured u s i n g apparatus i n which the minimum measureable value of the probe conductance i s 8 about 10~ mho. The f o l l o w i n g c o n d i t i o n s must app l y : the gas p r e s s u r e l e s s than or e q u al to 200 mmHg, the d e l a y time g r e a t e r than 0.2 ms, and the r a d i a l d i s t a n c e of the probes to the main gap at l e a s t 2 cm. b. From these conductance measurements the tempera ture can be d e r i v e d by assuming that the probe conductance i s p r o p o r t i o n a l to the t h r e e - h a l v e s power of the temperature. However, f o r delay times l e s s than ms the gas temperature i s h i g h e r than one would expect from estimates and measure ments by other workers ( f o r example Craggs, 1963; Poole, Parker, and C h u r c h i l l , 1963) u s i n g s i m i l a r apparatus. T h i s d i s c r e p a n c y i s probably because the assumed constant of p r o p o r t i o n a l i t y between the probe conductor and the temperature, i n -62- a c t u a l i t y changes s l o w l y w i t h changes i n p a r t i c l e d e n s i t y and temperature, c. The s i z e of the spark channel and a l s o the time r e q u i r e d f o r the channel to d e i o n i z e i n c r e a s e s w i t h d e c r e a s i n g gas p r e s s u r e . This i m p l i e s t h a t the dominant method of channel r e c o v e r y i s volume recombination. The r e l a t i v e success of t h i s experiment i n d i c a t e s t hat f u r t h e r probe s t u d i e s should be undertaken, i n which the probe conductance i s measured to a h i g h e r degree of accuracy and the probe c i r c u i t gated (see S e c t i o n 2,6) so t h a t d e l a y times l e s s than 0.2 ms can be i n v e s t i g a t e d . I t i s recommended t h a t the c l a s s i c a l f l o a t i n g double probe of Johnson and M a l t e r (195>0) be used to determine e l e c t r o n temperature and e l e c t r o n d e n s i  t i e s f o r gas p r e s s u r e s below 1 mmHg. I f i t i s p o s s i b l e to determine,, i n a d e t a i l e d q u a n t i t a t i v e manner, the e f f e c t t h a t grounding one probe has on the p o s i t i v e i o n d r i f t c u r r e n t , then the i o n d e n s i t y can a l s o be determined, u s i n g the d r i f t c u r r e n t equation, from the data i n t h i s e x p e r i  ment. - 6 3 - REFERENCES A l l e n , J.E. and Craggs, J.D., 1951+. B r i t . J . A p p l . Phys., 5, A l l a n , J.W.S., E d e l s , H., and Whittaker, D., 1961. Proc. Phys. S o c , 78, 911-8. B u t t e r , D.A.M., 1963. M. Sc. Th e s i s , U n i v e r s i t y of B r i t i s h Columbia. Chan, P,W., 1963. M. Sc. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia. C h u r c h i l l , R.J., 1961. Proceedings F i f t h I n t e r n a t i o n a l Confer ence on I o n i z a t i o n Phenomena i n Gases, Munich 1961, (North H o l l a n d , Amsterdam, page 1075). C h u r c h i l l , R. J . , 1961. Plasma Physics ( J . Nuclear Energy, p t . C) 3, 291. C h u r c h i l l , R.J., 1963. Can. J . Phys., I4JL, 612. 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 r . and Contr., 11, 17. 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. Cobine, J.D,,. 1958. Gaseous Conductors. (Dover, New Y o r k ) . Craggs, J.D., 1963. Proceedings 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, (page I4.23). C r a i g , R.D. and Craggs, J.D., 1953. P r o c . Phys. Soc. B., 66, 500. D e l c r o i x , J.L., I960, I n t r o d u c t i o n t o the Theory of I o n i z e d Gases. ( I n t e r s c i e n c e , New York) pages II2-HI4.. F i s c h e r , H., 1957. J . Opt. Soc. Amer., hjj 981. F i s c h e r , H.,. 1958. Proceedings of Conference on Extremely High Temperatures, New York. -614.- Johnson, E.O. and Malter, L., 1950. Phys. Rev., 80, 58. Loeb, L.B., 1955. Basic Processes of Gaseous E l e c t r o n i c s . (University of C a l i f o r n i a Press, Berkley). Mc Cann, G.D. and Clark, J.J., 1914-3. Trans. Amer. Inst. Elec. Engrs., 62, I4.5. Poole, D.E., Parker, A.B. and C h u r c h i l l , R.J.,. 1963. J. Ele c t r o , and Contr., 15, 131. Rose, J.D. and Clark, M., 1961. Plasmas and Controlled Fusion. (M .I.T. Press, Cambridge, Mass.). Smy, P.R.r 1963. Can. J . Phy., IjJL, 131+6. Spitzer, L., 1956. Physics of F u l l y Ionized Gases. (Inter- science, New York). Stotz, K.C., 1963. NASA Technical Note D-2226. (Investigation of Plasma Afterglows with Application i n Nitrogen). Vanyukov, M.P.,-Mak, A.A. and Muratov, V.R., 1959. Optics and Spectroscopy, 6, 8. Vanyukov, M.P., Mak, A.A. and Muratov, V.R., I960. Optics and Spectroscopy, £, 233. Vanyukov, M.P., Muratov, V.R., and Mukhitdinova, I.A., 1961. Optics and Spectroscopy, 10. 291*.. LE3 BT 1964 AT C 5 Clements, R e g i n a l d M o n t g o m e r y , 1940- R a d i e a l t e m p e r a t u r e d e r i v e d f r o m p r o b e c o n d u c t a n c e measurements i n a r e c o v e r i n g s p a r k c h a n n e l . [ V a n c o u v e r ] The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1964. 64 1. i l l u s . , d i a g r s . , t a b l e s . 28 cm. T h e s i s(M.A.S c . I n P h y s i c s ) - The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1964. " R e f e r e n c e s " : leaves : 63-64. 1. E l e c t r i c C~~\ c o n d u c t i v i t y . 2. I o n i z a t i o n o f \ J G a s e s . I . T i t l e . nb 

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