@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Science, Faculty of"@en, "Physics and Astronomy, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Clements, Reginald Montgomery"@en ; dcterms:issued "2011-12-14T18:48:13Z"@en, "1964"@en ; vivo:relatedDegree "Master of Applied Science - MASc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """The conductance of a small electric probe has been determined for radial distances (2 - 15 cm) from a recovering spark gap as a function of time after discharge initiation. The times investigated were from 0.2 to 15 ms and the gas pressure was varied from 22 mmHg down to 0.1 mmHg. The voltage applied to the probes was a sawtooth pulse which rose to about 80 volts in 10 μs. It is shown theoretically that the probe conductance should be proportional to the three-halves power of the gas temperature. Prom a known value of the temperature, deduced from recovery measurements, and the known probe conductance the constant of proportionality was deduced. Hence it was possible to determine the temperature from the probe conductance. The probe conductance measurements show that at 200 mmHg pressure the spark channel is only 2 cm in radius and that there is no detectable ionization left 2 ms after the discharge. As the gas pressure decreases the spark channel increases in size and takes longer to deionize, until at 1 mmHg pressure the channel fills the whole spark chamber (spark channel radius is 15 cm) and requires almost 15 ms to deionize. At 1 mmHg gas pressure there is a radial temperature gradient, while at 0.1 mmHg pressure the gas everywhere in the channel recovers at the same rate. In this experiment it is theoretically predicted that volume recombination should be the dominant recovery method and this is experimentally verified."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/39690?expand=metadata"@en ; skos:note "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 = - 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 , 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. 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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 "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0085121"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Physics"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Radial temperature derived from probe conductance measurements in a recovering spark channel"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/39690"@en .