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

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INVESTIGATIONS ON PLASMAS PRODUCED IN ELECTROMAGNETIC SHOCK TUBES *y GEORGE DOUGLAS CORMACK B.A.Sc, Un i v e r s i t y of B r i t i s h Columbia, 1955 M.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OP THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY . i n the Department of PHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1962 In presenting 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 o f 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 t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission 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 copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a U ^ e d without my w r i t t e n permission. Department of Physics The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date November 23, 1962 PUBLICATIONS Problems i n Plasma Physics. G.D. Cormack. UBC Engineer I, 17, 1960. Spectroscopic Studies of Helium and Argon Plasmas Produced by Electromagneti-c a l l y Driven Shock Waves. A.J. Barnard, G.D.Cormack and W.V. Simpkinson. Can. J . Physics 40, 531, 1962. Low Inductance Low Pressure Spark Gap Switch. G.D. Cormack and A.J. Barnard. Rev. S c i . I n s t r . 33, 606, 1962. A Low Inductance High Current Vacuum Switch. G.D. Cormack. B u l l . Am. Phys. Soc. ]_, Ser. I I , 156, 1962. k'l' f. )- -The U n i v e r s i t y of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of GEORGE DOUGLAS CORMACK B.A.Sc, The U n i v e r s i t y of B r i t i s h Columbia, 1955 M.Sc, The U n i v e r s i t y of B r i t i s h Columbia, 1960 FRIDAY, NOVEMBER 23, 1962, AT'3:30 P.M. IN ROOM 223, BUCHANAN BUILDING COMMITTEE IN CHARGE Chairman: F.H. Soward A.J. Barnard F.L. Curzon [. ; R.J. C h u r c h i l l P.R. Smy ' \- ' A.M. Crooker W.A.G. Voss ['4^ G.B. Walker .' . , External Examiner: J.H. de Leeuw, jfT' I n s t i t u t e of Aerophysics, • . U n i v e r s i t y of Toronto INVESTIGATIONS ON PLASMAS PRODUCED IN ELECTROMAGNETIC SHOCK.TUBES ABSTRACT The shape of the luminosity front, the homo-genity of the plasma and the shot-to-shot repro-d u c i b i l i t y of the structure of the plasma were found to be dependent upon the c h a r a c t e r i s t i c s of the d r i v i n g discharge, even at a time long a f t e r the d r i v i n g current had ceased to flow. In p a r t i -c ular, material from the walls of the d r i v e r assem-bl y was found to a f f e c t the properties of the plasma. The plasma was used to investigate the e l e c t r o -dynamical response of an inductive magnetohydro-dynamic power generator. Expressions for the out-put power were derived and compared with the experi-mental r e s u l t s . The electrodynamical response of a novel e l e c t -rodetype B^. magnetohydrodynamic power generator was c a l c u l a t e d . In an experiment performed with t h i s generator a magnetohydrodynamic i n t e r a c t i o n was observed i n d i c a t i n g that the plasma was trans-porting an azimuthal magnetic f i e l d . No output power was obtained. The probable cause for t h i s was that the applied magnetic f i e l d was i n s u f f i c i e n t to break down the sheath on the electrodes. A low pressure spark gap switch suitable for use as a main switch and as a "crowbar" switch on a capacitor bank was developed. The switch was operated over a voltage range of 0.5 to 25 kV, at energies up to 4 kJ and currents up to 500 kA. Under normal operating conditions the t r i g g e r i n g time was 40 nsec and the j i t t e r approximately 10 nsec. The inductance of the main switch was 4 n H and the inductance of the crowbar switch was about 1 nH. Other contributions are on a wide-voltage-range open-air spark gap switch, high voltage t r i g g e r c i r c u i t s and on the dynamics of the plasma i n an electromagnetic shock tube. The l a t t e r consists of an elementary treatment of the electromagnetic a c c e l e r a t i o n processes and a proposal of a model for the decelerating plasma. GRADUATE STUDIES F i e l d of Study: Plasma Physics Waves . ... J.C. Savage Spectroscopy A.M. Crooker P h y s i c a l E l e c t r o n i c s ........ R.E. Burgess Advanced Plasma Physics ...... F.L. Curzon Related Studies: Transients i n Linear Systems ... E.V. Bohn Analogue Computors E.V. Bohn ABSTRACT Electromagnetic shock tubes were used to generate 17 3 plasmas having a number density of the order of 10 per cm and an energy per p a r t i c l e of 1-3 ev. In the shock tubes employed,\the d r i v i n g current was passed v i a electrodes through a discharge at one end of the tube. The discharge gases that were driven down the shock tube plus the ambient gas that was picked up and heated constituted the plasma that was studied. Many workers have assumed that shock equations can describe the d i s c o n t i n u i t y at the front of the plasma. An i n v e s t i g a t i o n into'the e f f e c t s of changes i n the geometry of the dr i v e r mechanism has disclosed that the luminosity s t r u c t -ure that can be a t t r i b u t e d to the discharge gases stays very close to the luminosity f r o n t . The amount of ambient gas that i s entrained i n front of the discharge gases i s thus small. Therefore, some doubt exists about the a p p l i c a b i l i t y of the shock equations both i n the present shock tube and i n the electromagnetic shock tubes of other workers. The shape of the luminosity front of the plasma was found to be affected by the properties of the d r i v i n g discharge, even at a time long a f t e r the d r i v i n g current had ceased to flow. I n s t a b i l i t i e s of the discharge and contamin-ation by electrode material were found to d r a s t i c a l l y a f f e c t the homogeneity of the plasma.. The homogeneity and repro-d u c i b i l i t y of the plasma produced by a small-cathode dr i v e r were found to be f a i r l y good. However, there was a large - i i i -amount of contamination i n the plasma. The plasma was used to investigate the e l e c t r o -dynamic response of an inductive magnetohydrodynamic power generator. Expressions f o r the output power were derived and compared with the .experimental r e s u l t s . The electrodynamical response of a novel electrode-type B^ . magnetohydrodynamic power generator was calculated. In an experiment performed with t h i s generator a magneto-hydrodynamic interaction,was observed i n d i c a t i n g that the plasma was transporting an azimuthal magnetic f i e l d . No out-put power was obtained. The probable cause f o r t h i s was that the applied magnetic f i e l d was i n s u f f i c i e n t to break down the sheath on the electrodes. A low pressure spark gap switch .suitable f o r use as a main switch and as a "crowbar" switch on a capacitor bank was developed. The switch was operated over a voltage range of 0.5 to 25 kV, at energies up to 4 kJ and currents up to 500 kA. Under normal operating conditions the t r i g g e r i n g time was 40 nsec and the j i t t e r approximately 10 nsec. The inductance of the main switch was 4 nH and the inductance>of the crowbar switch was about 1 nH. Other contributions are presented on a wide-voltage-range open-air spark gap switch, high voltage t r i g g e r c i r c u i t s and on the dynamics of the plasma i n an electromagnetic shock tube. The l a t t e r consists of an elementary treatment of the electromagnetic a c c e l e r a t i o n processes and a proposal of a model f o r the decelerating plasma. - X ACKN0WLEDG1 The encouragement, guidance and i n t e r e s t that have been given by JJr. A.J. Barnard have been of invaluable help to me. The author i s also g r a t e f u l to many other members of the Plasma Physics group both f o r t h e i r suggestions and t h e i r assistance. The research upon which t h i s thesis i s based was greatly f a c i l i t a t e d by the tech n i c a l assistance that was pro-vided by the s t a f f of the Physics Workshop. Other valuable advice and assistance has been provided by J. Turner, i n el e c t r o n i c s , and by J . Lees, i n glass blowing. The f i n a n c i a l support f o r t h i s research project was provided by the Atomic Energy Control Board. The author i s gr a t e f u l f o r r e c e i v i n g a scholarship from the B r i t i s h Columbia Telephone Company (1960-1961), an award from the Association of Professional Engineers of the Province of Ontario (1960-1961), and a National Research Council Studentship (1961-1962). - i v -TABLE OP CONTENTS Page CHAPTER I INTRODUCTION 1 CHAPTER II APPARATUS ." 5 1 . Capacitor Bank 7 2. Switches 12 3. Shock Tube 19 4. A u x i l i a r y Equipment 20 i.Luminosity Detector 20 i i Kerr C e l l Camera 21 i i i C i r c u i t f o r F i r i n g Crowbar Switch.. 23 i v Magnetic Probes 25 CHAPTER III PROPERTIES OP THE PLASMA GENERATED IN AN ELECTROMAGNETIC SHOCK TUBE 27 1. D i s t o r t i o n of the Luminosity Structure by Driver Discharge Phenomena.. 27 2. E f f e c t of the Geometry of the Driver on the Luminosity Structure i n the Plasma. 37 3. Magnetic F i e l d s i n the Plasma 48 4. I n i t i a l Breakdown Phenomena 50 5. Dynamics of Electromagnetically A c c e l -erated Plasma 52 6. Dynamics of the Decelerating Plasma.... 68 CHAPTER IV MAGNETOHYDRODYNAMIC POWER GENERATION 77 1. Some Properties of an Electrode-Type B^. Magnetohydrodynamic Power Generator 77 2. E l e c t r i c a l C h a r a c t e r i s t i c s of an Electrodeless MHD Generator 97 - V -3. C h a r a c t e r i s t i c s of a Magnetohydro-dynamic Power Generator Employing Inductive Power Transfer 101 CHAPTER V CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK 115 APPENDIX A C h a r a c t e r i s t i c s of Various Spark Gap Trigger C i r c u i t s 119 APPENDIX B Properties of a Wide Voltage Range,' Open-Air Spark Gap Switch 126 APPENDIX C Low Inductance Low Pressure Spark Gap Switch 131 APPENDIX . D Properties of a Low Inductance Low Pres-sure Spark Gap Switch 137 APPENDIX E Theory f o r the Eruptive I n s t a b i l i t y 154 APPENDIX F Analysis.of the Experimental Data Ob-tained with the MHD Generator Employing Inductive Power Transfer 158 BIBLIOGRAPHY 161 - v i -LIST OF ILLUSTRATIONS Figure Page 1 Capacitor Discharge C i r c u i t 6 2 Capacitor Connections. Exploded View 7 3 Interconnections Between Each Set of Three Capacitors 8 4 C i r c u i t s f o r Control of Bank 12 5 Low Pressure Spark Gap Switches I n s t a l l e d Be-tween Capacitor Bank and Shock Tube 17 6 Layout of Shock Tube 19 7 Construction of Luminosity Detector 20 8 C i r c u i t of Luminosity Detector 21 9 Kerr C e l l Trigger C i r c u i t 23 10 Crowbar Switch Trigger C i r c u i t 24 11 Coplanar Driver f o r Electromagnetic Shock Tube. 28 12 Photographs of Plasma Generated by Various Drivers 29 13 T-Tube Drivers ' 30 14 The Protuberances on the Shock Front 31 15 A Possible Explanation f o r the Protuberances on the Shock Front 32 16 Proposed Mechanism f o r F i n a l Breakup of Dis-charge Column 35 17 Coaxial Electromagnetic Driver with Short Electrodes 38 18 Coaxial Electromagnetic Driver with Short Electrodes and a S t a t i c Magnetic F i e l d 39 19 Configurations of Axially-Symmetric Drivers That Were Tested 41 20 E f f e c t s of Driver Geometry and Gas Pressure on Luminosity of Plasma. . .. 43 - v i i -Figur e Page 21 S t r u c t u r e of Luminosity of Plasma 46 22 B_ Transported i n Plasma 49 23 Breakdown Time of the D r i v e r 51 24 Time When Maximum V e l o c i t y Occurs i f the D r i v -i n g Current i s Obtained from a Damped O s c i l l a -t o r y C i r c u i t 57 25 Time When Maximum V e l o c i t y Occurs i f the D r i v -i n g Current i s Obtained from a C r i t i c a l l y -Damped C i r c u i t 60 26 V e l o c i t y of Plasma During A c c e l e r a t i o n by Var i o u s Waveforms of D r i v i n g Current 63 27 T y p i c a l O s c i l l o g r a m s of Current i n D r i v e r of Shock Tube 67 28 x ( t ) Data f o r D e c e l e r a t i n g Plasma 70 29 G r a p h i c a l Determination of Parameters i n Propa-g a t i o n Equation f o r D e c e l e r a t i n g Plasma 71 30 Proposed Model f o r D e c e l e r a t i n g Plasma i n Shock Front 74v 31 The Conventional C a r t e s i a n MHD Generator 77 32 The D i s c and the C o a x i a l MHD Generator 78 33 The B^. MHD Generator 79 34 The E q u i v a l e n t C i r c u i t f o r the S i m p l i f i e d Car-t e s i a n MHD Generator 80 35 A Low Inductance B_ MHD Generator 81 36 The B MHD Generator E q u i v a l e n t C i r c u i t 84 37 A High Voltage B_ MHD Generator 87 38 E x t r a c t i o n of MHD H a l l Current 89 39 A method f o r Lessening I n s u l a t o r D e p o s i t i o n Problems 90 40 C o n s t r u c t i o n of B MHD Generator , 91 41 T y p i c a l S i g n a l Induced i n Probe at Base of B 0 MHD Generator 92 - v i i i -Figure Page 42 A Magnetohydrodynamic Interaction that Gould A l t e r the V e l o c i t y of the Plasma 94 43 Electrodeless B r MHD Generator 98 44 Equivalent C i r c u i t f o r the El e c t r o d e l e s s B MHD Generator 99 45 MHD Generator Employing Inductive Power Trans-f e r 102 46 The Conductivity and V e l o c i t i e s Being Considf-ered i n the Analysis 105 47 Power i n Load Resistance as a Function of Time 108 48 Inductive MHD Generator Experimental Apparatus 109 49 Equivalent C i r c u i t f o r Inductive MHD Generator Output C o i l . 110 50 V a r i a t i o n of Output Voltage with Load Resis-tance 111 51 Output Power as a Function of Load Resistance, Experimental 112 52 Trigger C i r c u i t s Employing the Discharge of a Cable 119 53 Derivative of Trigger Spark Current 121 54 Trigger C i r c u i t f o r P a r a l l e l Gaps.. 122 55 Voltage Quadrupler Trigger C i r c u i t 124 56 Voltage Doubler Trigger C i r c u i t s 125 57 Open-Air Three Electrode Spark Gap Switches... 126 58 Plasma Jet,Triggered Open-Air Spark Gap Switch 127 59 C i r c u i t f o r Testing Open-Air Spark Gap Switches 127 60 Triggering Time of Plasma Jet Triggered Switch 128 61 C i r c u i t f o r Simultaneous Observation of Trigger Current and Luminosity 138 62 Method of Measuring Triggering Time of Low Pressure Switch 139 - i x -Figure Page 63 Vacuum System f o r Switches on Capacitor Bank. 140 64 Triggering Time of the 4 kJ Switch as a Function of Pressure 141 65 Motion of Charged P a r t i c l e s i n Trigger Dis-charge ( 142 66 Subdivision of -the Main Switch into Regions f o r the Purpose of C a l c u l a t i n g the Inductance 151 67 Inductance of Crowbar Switch 151 68 Suggested Plasmoid Motion that Results i n Eruptive I n s t a b i l i t y of Discharge Column 154 69 Voltage Waveforms Calculated f o r the Conduct-i v i t y Function 1 60 TABLES Table 1. Results of Analyzing Deceleration Data.... 74 Table 2. Comparison of dc E l e c t r i c a l Formulae f o r the Cartesian and the B Q MHD Generators.. 87 Table 3. Predicted Shock Tube dc B^, MHD Generator C h a r a c t e r i s t i c s 88 Table 4. Predicted High Power dc B ^ MHD Generator C h a r a c t e r i s t i c s 88 - 1 -CHAPTER I  INTRODUCTION Electromagnetic shock tubes have "been adopted i n many labo r a t o r i e s f o r the generation of plasmas having a number 17 3 density of the order of 10 per cm and an energy per p a r t i c l e of 1 to 10 ev. Although a large amount of information has been published about such plasmas, there i s much research work that i s yet to be done. The r e s u l t s of two major i n v e s t i g a t i o n s on such plasmas are reported i n t h i s t h e s i s . These i n v e s t i g a t i o n s were on the properties of the plasma generated i n an e l e c t r o -magnetic shock tube and on magnetohydrodynamic power generation. Other contributions presented i n t h i s thesis are on a wide v o l t -age range open-air spark gap switch, on a low inductance low pressure spark gap switch and on the properties of various c i r -c u i t s s u i t a b l e f o r generating the high voltage pulse needed to t r i g g e r a spark gap switch. The plasma that i s generated i n an electromagnetic shock tube i s not homogeneous, often has poor shot-to-shot repro-d u c i b i l i t y , and u s ually has a non-planar f r o n t . Many workers have taken photographs that show the lack of homogeneity of the plasma and the non-planarity of the f r o n t . Representative of the pictures of the plasma generated i n various electromagnetic shock tubes are those by Kolb (1959)? Komelkov (1959)? a n ( i Chang (1961). Kolb (1959) has stated "further work on the mechanisms responsible f o r the formation of shock fronts i n high speed gas - 2 f l o w s i s n e e d e d " . He c o u l d n o t o b t a i n s h o t - t o - s h o t r e p r o d u c i -b i l i t y i n t h e s t r u c t u r e o f t h e p l a s m a g e n e r a t e d i n a p a r t i c u l a r c o n f i g u r a t i o n o f e l e c t r o m a g n e t i c s h o c k t u b e t h a t i s known as a T - t u b e . He e m p l o y e d a c o n s i d e r a b l e amount o f e q u i p m e n t t o o b t a i n a l l t h e d i a g n o s t i c d a t a w i t h one f i r i n g o f t h e s h o c k t u b e . S u c h e q u i p m e n t , h a s n o t b e e n a v a i l a b l e h e r e and i t h a s , t h e r e f o r e , b e e n n e c e s s a r y t o e s t a b l i s h why i r r e p r o d u c i b i l i t y does e x i s t and t o a t t e m p t t o l e s s e n t h e d e g r e e o f i r r e p r o d u c i b i l i t y . The e n e r g y o f t h e p l a s m a g e n e r a t e d i n a n e l e c t r o m a g -n e t i c s h o c k t u b e i s d e r i v e d f r o m a l o w i n d u c t a n c e c a p a c i t o r , b a n k . The l a r g e c u r r e n t o b t a i n e d f r o m t h e c a p a c i t o r bank i s p a s s e d v i a e l e c t r o d e s t h r o u g h a d i s c h a r g e a t one end o f t h e s h o c k t u b e . The d i s c h a r g e g a s e s t h a t a r e d r i v e n down t h e s h o c k t u b e p l u s t h e a m b i e n t gas t h a t i s p i c k e d up and h e a t e d c o n s t i t u t e t h e p l a s m a t h a t i s p r o d u c e d i n an e l e c t r o m a g n e t i c s h o c k t u b e . The e f f e c t o f t h e d r i v i n g d i s c h a r g e on t h e p r o p e r t i e s o f t h e p l a s m a g e n e r a t e d by a c o p l a n a r d r i v e r ( B a r n a r d , Cormack a n d S i m p k i n s o n 1 9 6 2 ) i s p r e s e n t e d i n some d e t a i l i n C h a p t e r I I I , S e c t i o n 1 . S i n c e t h e s t r u c t u r e o f t h e p l a s m a was observed~ t o be d e p e n d e n t u p o n t h e d r i v i n g d i s c h a r g e , t h e g e o m e t r y o f t h e d r i v e r a s s e m b l y was a l t e r e d a n d t h e r e s u l t i n g change i n t h e s t r u c t u r e o f t h e l u m i n o s i t y o f t h e p l a s m a s t u d i e d . T h i s i n v e s t i g a t i o n i n t o t h e e f f e c t s o f t h e g e o m e t r y o f t h e d r i v e r on t h e s t r u c t u r e o f t h e l u m i n o s i t y o f t h e p l a s m a i s d i s c u s s e d i n C h a p t e r I I I , S e c t i o n 2 . A t o r o i d a l m a g n e t i c f i e l d was d e t e c t e d i n t h e p l a s m a p r o d u c e d by a c o a x i a l d r i v e r and was a t t r i b u t e d t o a t r a p p i n g i n t h e p l a s m a o f t h e m a g n e t i c f i e l d o f t h e d r i v i n g d i s c h a r g e . The - 3 -detection of t h i s f i e l d i s discussed i n Chapter Section 3. An i n v e s t i g a t i o n into the suppression by a magnetic f i e l d of the e f f e c t s of a t r i g g e r spark i n the dri v e r i s presented i n Chapter I I I , Section 4. The equations of motion f o r the plasma are derived i n closed form i n Chapter I I I , Sections 5 and 6. In Section 5-, an analysis i s presented that i s based on s i m i l a r d i f f e r e n t i a l equations to those employed by Hart (1962) f o r the dynamics of a slug of plasma accelerated by electromagnetic forces. Hart (1962) solved the coupled d i f f e r e n t i a l equations with an analog computer and presented h i s r e s u l t s i n graphical form. Simpli-f y i n g assumptions that are p h y s i c a l l y r e a l i s t i c are made i n Section 5 i n order that solutions i n closed form can be obtained. The expressions thus obtained are v a l i d f o r both the e l e c t r o -magnetic a c c e l e r a t i o n of a slug of constant mass and of a slug gaining mass by a snow-plow action. Of p a r t i c u l a r i n t e r e s t i s an equation that predicts the maximum v e l o c i t y of the plasma. The f i t t i n g of an empirical r e l a t i o n to the experimental data for the deceleration of the plasma i s described i n Section 6. A model i s proposed that i s based on t h i s r e l a t i o n . The model can explain why various workers have obtained d i f f e r e n t values for the parameter 0 i n the often-quoted r e l a t i o n f o r the motion of the decelerating plasma i n an electromagnetic shock tube, n x o* t " where x i s the distance t r a v e l l e d by the slug i n time t . The function of an electromagnetic shock tube, the con-version of e l e c t r i c a l energy into k i n e t i c and thermal energy of - 4 -a p l a s m a i s t h e i n v e r s e o f t h e f u n c t i o n o f a m a g n e t o h y d r o d y n a m i c power g e n e r a t o r . C e r t a i n a s p e c t s o f m a g n e t o h y d r o d y n a m i c power g e n e r a t i o n , t h e d i r e c t c o n v e r s i o n o f t h e f l o w and h e a t e n e r g y o f a p l a s m a i n t o e l e c t r i c a l e n e r g y , a r e c o n s i d e r e d i n C h a p t e r I V . I n C h a p t e r I V , S e c t i o n 1, t h e e l e c t r o d y n a m i c a l b e h a v i o u r o f a n o v e l c o n f i g u r a t i o n o f m a g n e t o h y d r o d y n a m i c g e n e r a t o r i s s t u d i e d . I n t h i s g e n e r a t o r t h e p l a s m a i s i n c o n t a c t w i t h t h e e l e c t r o d e s t h a t a r e e m p l o y e d t o e x t r a c t t h e p o w e r . One o f t h e m a j o r p r o -b l e m s t h a t h a s b e e n e n c o u n t e r e d by o t h e r w o r k e r s i n t h e f i e l d o f MHD power e x t r a c t i o n i s c o n c e r n e d w i t h t h e c l e a n l i n e s s o f t h e e l e c t r o d e s w h i c h c o n t a c t t h e p l a s m a . T h e r e f o r e , i n S e c t i o n 2 t h e e l e c t r o d y n a m i c a l b e h a v i o u r o f a n i d e a l i z e d e l e c t r o d e l e s s MHD power g e n e r a t o r i s c o n s i d e r e d . I n S e c t i o n 3 t h e e l e c t r o -d y n a m i c a l b e h a v i o u r o f a ' p h y s i c a l l y r e a l i z a b l e c o n f i g u r a t i o n o f e l e c t r o d e l e s s MHD power g e n e r a t o r i s s t u d i e d . The r e s u l t s o f an e x p e r i m e n t a l d e t e r m i n a t i o n o f t h e e l e c t r o d y n a m i c p r o p e r t i e s o f t h i s g e n e r a t o r a r e a l s o p r e s e n t e d i n t h i s S e c t i o n . - 5 -CHAPTER I I APPARATUS The p r o p e r t i e s o f t h e p l a s m a g e n e r a t e d i n an e l e c t r o -m a g n e t i c s h o c k t u b e depend m a r k e d l y on t h e c h a r a c t e r i s t i c s o f t h e c a p a c i t o r d i s c h a r g e c i r c u i t . I t c a n be s h o w n , on t h e b a s i s o f e n e r g y c o n s i d e r a t i o n s , t h a t t h e t e m p e r a t u r e o f t h e p l a s m a i s h i g h e s t when t h e d r i v i n g c u r r e n t h a s b o t h a s h o r t r i s e - t i m e and a h i g h p e a k v a l u e . The u s u a l c o n f i g u r a t i o n o f c a p a c i t o r d i s c h a r g e c i r c u i t t h a t i s e m p l o y e d f o r t h e g e n e r a t i o n o f s u c h a p u l s e o f d r i v i n g c u r r e n t i s shown i n P i g 1. I n t h i s c i r c u i t n c a p a c i t o r s e a c h h a v i n g a c a p a c i t a n c e c , i n t e r n a l i n d u c t a n c e I and i n t e r n a l r e s i s t a n c e R a r e c o n n e c t e d i n p a r a l l e l w i t h t h e d r i v e r o f an e l e c t r o m a g n e t i c s h o c k t u b e by s m a i n s w i t c h e s e a c h h a v i n g a r e s i s t a n c e R o and an i n d u c t a n c e I • The i m p e d a n c e o f t h e d r i v e r s s o f a n e l e c t r o m a g n e t i c s h o c k t u b e i s a c c u r a t e l y r e p r e s e n t e d by a r e s i s t a n c e R^ i n s e r i e s w i t h a n i n d u c t a n c e . When a l l c i r -c u i t e l e m e n t s a r e c o n s i d e r e d t o be p a s s i v e a n d t h e c a p a c i t o r s a r e c o n s i d e r e d t o be i n i t i a l l y c h a r g e d t o a v o l t a g e V , t h e n t h e s i m u l t a n e o u s c l o s i n g o f t h e m a i n s w i t c h e s p r o d u c e s a n o s c i l l a -t o r y c u r r e n t t h r o u g h t h e d r i v e r o f t h e s h o c k t u b e V 0 - i t S i n ujt e where - 6 -I t i s e v i d e n t f r o m e q u a t i o n 1 t h a t a d r i v i n g c u r r e n t h a v i n g b o t h a s h o r t r i s e - t i m e and a h i g h peak v a l u e i s p r o d u c e d i n a d i s c h a r g e c i r c u i t t h a t h a s l o w i n d u c t a n c e and r e s i s t a n c e . The l o w i n d u c t a n c e c o n n e c t i o n s and p h y s i c a l l a y o u t o f t h e c a p a c i t o r bank t h a t h a s b e e n b u i l t a r e d e s c r i b e d i n S e c t i o n 1 o f t h i s C h a p t e r . The p r o p e r t i e s o f t h e l o w i n d u c t a n c e , l o w p r e s s u r e s p a r k gap s w i t c h t h a t h a s b e e n e m p l o y e d as a m a i n s w i t c h and as a c r o w b a r s w i t c h a r e d i s c u s s e d i n S e c t i o n 2 . The s h o c k t u b e i s t h e n d e s c r i b e d i n S e c t i o n 3 . I n S e c t i o n 4 t h e a u x i l i a r y e q u i p -ment r e q u i r e d f o r t h e o p e r a t i o n o f t h e s h o c k t u b e i s d i s c u s s e d . . . s s w i t c h e s P i g 1. C a p a c i t o r D i s c h a r g e C i r c u i t . 1. CAPACITOR BANK The low inductance capacitors that were i n s t a l l e d i n the capacitor bank are rated at 1.6y*F, 25 kV, 25 nH. ,The con-nections between and on each capacitor were made as i l l u s t r a t e d i n Pig 2. parts ABCD: 1/16 i n . Pig 2. Capacitor Connections. Exploded view. The connections shown i n Pig 2 permit the current to be taken from each capacitor v i a two paths that are on d i a m e t r i c a l l y opposite sides of the capacitor. This p a r t i c u l a r type of con-nection resulted i n a measured r i n g i n g frequency f o r one capac-i t o r of 900 kc or a c i r c u i t inductance of 19-5 nH, a c t u a l l y lower than the rated value, 25 nH, given by the manufacturer - 8 -f o r a c o m p l e t e l y s h o r t - c i r c u i t e d c a p a c i t o r . S i n c e t h e i n t e r n a l e l e c t r i c f i e l d i n t h e s e c a p a c i t o r s i s i n t h e r a d i a l d i r e c t i o n , minimum c i r c u i t i n d u c t a n c e w o u l d he o b t a i n e d i f t h e c o n n e c t o r s w e r e made so as t o e x t r a c t t h e c u r r e n t i n a r a d i a l d i r e c t i o n . S u c h c o n n e c t o r s w o u l d be . d i f f i c u l t t o d e s i g n and c o n s t r u c t . The c o n n e c t o r s shown i n P i g 2 r e s u l t e d i n a c u r r e n t f l o w t h a t i s a n a p p r o x i m a t i o n t o t h i s i d e a l a l l - r a d i a l f l o w . The c a p a c i t o r s were s e p a r a t e d and i n s u l a t e d f r o m e a c h o t h e r by t e n t h i c k n e s s e s o f . 0 0 1 i n . i n s u l a t i o n ( M y l a r ) . A r c - o v e r a c r o s s t h e s u r f a c e o f t h e M y l a r was a v o i d e d by m a i n t a i n i n g a minimum s u r f a c e p a t h l e n g t h o f 4 i n . b e t w e e n c o n d u c t o r s a t d i f f e r e n t p o t e n t i a l s . s P i g 3. I n t e r c o n n e c t i o n s B e t w e e n E a c h S e t o f T h r e e C a p -a c i t o r s . On t h e a c t u a l bank a. s e c o n d s e t o f 9 c a p a c i t o r s i s mounted i m m e d i a t e l y b e h i n d t h e 9 c a p a c i t o r s shown i n t h i s f i g u r e . The c o l l e c t o r p l a t e i s t h e common c o n n e c t i o n f o r t h e two s e t s o f 9 c a p a c i t o r s . - 9 -The i n t e r c o n n e c t i o n s between each set of three cap-a c i t o r s are. shown i n P i g 3. The e n t i r e bank capacitance of 28.8^<F or any of 24.0, 19.2, 14.4, 9.6 or 4.8^? was obtained by r e p l a c i n g or removing the i n t e r c o n n e c t i n g p l a t e s . A l l j o i n s between cu r r e n t c a r r y i n g conductors were s o l d e r e d , w i t h the exception of the i n t e r c o n n e c t i n g p l a t e s and the switches, i n order to l e s s e n c i r c u i t inductance. Some care has been e x e r c i s e d i n the choice of conductor t h i c k n e s s and the method of clamping the conductors. The l a r g e pulses of cu r r e n t t h a t f l o w d u r i n g the discharge of the bank cause the conductors to be r e p e l l e d from each other. Should the mass of the conductors be too s m a l l , then the motion w i l l generate a time dependent inductance i n the c i r c u i t t h a t w i l l a f f e c t the wave shape of the c u r r e n t . The f o l l o w i n g a n a l y s i s i n d i c a t e s the order of magnitude of the q u a n t i t i e s i n v o l v e d . The motion of one conductor r e l a t i v e to i t s r e s t p o s i t i o n w i l l be considered and i t w i l l be assumed t h a t the cu r r e n t flows on the f a c i n g s u r f a c e s of the conductors. The conductors are a meters wide and have a s e p a r a t i o n of b meters. The d i s p l a c e -ment of a conductor r e l a t i v e to i t s r e s t p o s i t i o n i s designated x ( t ) . When damping and n o n - l i n e a r f o r c e s are ne g l e c t e d , the equation of motion f o r the conductor i s M X + K x = I * 2 where M i s the mass of the conductor per u n i t l e n g t h , K i s the r e s t o r i n g f o r c e per u n i t l e n g t h exerted by e x t e r n a l clamps, and I i s the cur r e n t i n the conductor. I t i s assumed th a t b « a, that the motion of the conductors does not a p p r e c i a b l y a f f e c t I ( t ) , and t h a t I ( t ) h a s t h e f o r m I * I 0 e~^ 5 i n cut 3 The s o l u t i o n t o e q u a t i o n 2 when St « <5<< *0 and J K / M « I S I 4 . * _ ft) ? { i 2 -1 ; « a M [ S i n UJ X The r e s i s t a n c e p e r u n i t l e n g t h o f t h e c o n d u c t o r s t h a t i s due t o t h e m o t i o n d e s c r i b e d by e q u a t i o n 4 i s " l ' a dt 4a 4\A\ to J ^ A s p e c i f i c c a s e w i l l now be c o n s i d e r e d . I f I = 500 k A , a = 0 . 1 5 m, t h i c k n e s s o f a c o p p e r c o n d u c t o r = 1/16 i n . , M = 2 . 1 2 Kg/m, CO = J2 T T / 2 } x 10 ' 6 r a d / s e c , t h e n x ( t = 2 x 1 0 " 6 s e c ) = 4 . 9 x 1 0 ~ 5 cms, and R ( t = 2 x 1 0 " 6 s e c ) = 4 . 2 x 1 0 " 6 ohms/ m e t e r . S i n c e t h e n o n - t i m e - d e p e n d e n t r e s i s t a n c e o f a t y p i c a l c i r c u i t i s o f t h e o r d e r o f . 001 t o .01 ohms, i t i s a p p a r e n t t h a t t h e m o t i o n o f t h e c o n d u c t o r s h a s l i t t l e e f f e c t on t h e w a v e f o r m o f t h e c u r r e n t f o r t h e example j u s t c i t e d . One o t h e r i m p o r t a n t p o i n t t h a t does come o u t o f t h e above a n a l y s i s i s t h a t t h e c o n d u c t o r s s h o u l d be c l a m p e d r i g i d l y t o g e t h e r i n o r d e r t h a t t h e s e p a r a t i o n c a u s e d b y t h e p u l s e s o f c u r r e n t w i l l n o t be a p e r m a n e n t d e f l e c t i o n . I n t h e example p r e -s e n t e d i n t h e p r e c e d i n g p a r a g r a p h , t h e d e f l e c t i o n a t t h e end o f t h e f i r s t p u l s e was c a l c u l a t e d . T h i s d e f l e c t i o n i s n o t t h e maximum d e f l e c t i o n , w h i c h o c c u r s c o n s i d e r a b l y l a t e r i n t i m e and i s o f a m a g n i t u d e t h a t depends u p o n t h e c h a r a c t e r i s t i c s o f t h e c l a m p s on t h e c o n d u c t o r s . I f t h e c o n d u c t o r s do s u f f e r a p e r -- 11 -manent d e f l e c t i o n , then the inductance of the c i r c u i t i s i n -creased and the peak current c a p a b i l i t y of the c i r c u i t corres-pondingly decreased. The charging and discharging of the bank are con-t r o l l e d by e l e c t r i c a l r e l a y s . The bank control c i r c u i t s are shown i n F i g 4. The switches are designated: 1. A.C, on/off, 2. Bank, open c i r c u i t / s h o r t , 3. H.V. to Bank, connect/disconnect, 4. Trigger H.V. on/off, 5. H.V. to Trigger, connect/disconnect AND FIRE. The grounds and the high tension leads of the two high voltage power supplies are i s o l a t e d from the bank during a discharge. To further avoid the p o s s i b i l i t y of a ground loop occurring during a discharge, the following l o g i c c i r c u i t r y has been included i n the bank control u n i t . The numbers r e f e r to the switches just described: 2 operates i f 1 i s on, 3 operates i f both 1 and 2 are on, 4 operates i f 1 i s on, 5 operates i f 1 and 4 are on and 3 i s o f f . The normal f i r i n g sequence i s to operate the switches i n the order 12345. Spring returns on switches 3 and 5 provide automatic adherence to the l o g i c i f the f i r i n g sequence i s performed i n t h i s order. The high voltage t r i g g e r c i r c u i t s shown i n F i g 4 are described i n d e t a i l i n Appendix A. Several minor i n v e s t i g a -tions on the properties of s i m i l a r t r i g g e r c i r c u i t s are included i n t h i s Appendix. - 12 -S3" S4j^ 0 S5 charging relay- © f i r i n g j r e l a y S1 capacitor bank F i g 4. C i r c u i t s f o r Control of Bank. 2. SWITCHES An electromagnetic shock tube requires one or more switches between a capacitor bank and the dri v e r assembly i n the shock tube ( F i g 1). The capacitor bank t y p i c a l l y i s charged slowly from a high voltage dc supply to some p o t e n t i a l i n the range of 2 to 100 kV. On c l o s i n g the main switch, the bank d i s -charges and a large current (of order 0.5 MA) flows through the driv e r assembly f o r a time of the order of a few jUaec. The switches that pass t h i s current must close quickly, say i n a. time much l e s s than one yUsec, they must have n e g l i g i b l e impedance - 13 -d u r i n g c o n d u c t i o n and t h e y must n o t c l o s e b e f o r e b e i n g t r i g g e r e d . A l s o , t h e t r i g g e r i n g t i m e , t h e i n t e r v a l o f t i m e b e t w e e n t h e o n -s e t o f t h e t r i g g e r p u l s e a n d t h e s t a r t o f l a r g e s w i t c h c u r r e n t , must be s m a l l . A n a c c e p t a b l e v a l u e f o r t h e t r i g g e r i n g t i m e depends u p o n t h e e x a c t a p p l i c a t i o n o f t h e s w i t c h b u t c a n be as l o w as 5 n s e c . T r i g g e r e d o p e n - a i r s p a r k gaps c a n p o s s e s s a l l o f t h e s e p r o p e r t i e s when t h e y a r e c a r e f u l l y a d j u s t e d a n d t h e y h a v e t h e r e f o r e b e e n u s e d by many w o r k e r s . The e x p l o s i v e - l i k e n o i s e o f a n o p e n - a i r gap i s , h o w e v e r , o f t e n o b j e c t i o n a b l e . A l s o , t h e i n t e r - e l e c t r o d e s p a c i n g o f a n o p e n - a i r gap must be a d j u s t e d w h e n e v e r a v o l t a g e o u t s i d e o f t h e w o r k i n g v o l t a g e r a n g e i s t o be s w i t c h e d . The w o r k i n g v & l t a g e r a n g e r e p o r t e d by most w o r k e r s f o r a n o p e n - a i r gap i s f r o m a p p r o x i m a t e l y t o where i s t h e v o l t a g e a t w h i c h s p o n t a n e o u s b r e a k d o w n o r c o n d u c t i o n o f t h e gap o c c u r s . I t i s a p p a r e n t t h a t a c o n v e n t i o n ^ a l t r i g g e r e d o p e n - a i r s p a r k gap s w i t c h i s n o t a n i d e a l m a i n s w i t c h . A n i n v e s t i g a t i o n i n t o t h e p r o p e r t i e s o f a n o p e n - a i r s p a r k gap h a v i n g a w o r k i n g v o l t a g e r a n g e o f g r e a t e r t h a n t o i s r e p o r t e d i n A p p e n d i x B . The w o r k i n g v o l t a g e r a n g e o f t h i s gap i s e x t e n d e d by a n o v e l s y s t e m o f t r i g g e r i n g . I t i s shown i n t h i s A p p e n d i x t h a t t r i g g e r i n g c a n be e f f e c t e d a t e v e n z e r o v o l t a g e b e t w e e n t h e m a i n e l e c t r o d e s . The t r i g g e r i n g t i m e i s , h o w e v e r , u n d e s i r a b l y l o n g a t l o w v o l t a g e s and t h e gap does h a v e t h e d i s a d v a n t a g e o f e x c e s s i v e a c o u s t i c a l n o i s e . F o r t h e s e r e a s o n s t h i s o p e n - a i r gap was n o t e m p l o y e d as a s w i t c h on t h e c a p a c i t o r b a n k . - 14 -A u n i d i r e c t i o n a l pulse of current through the d r i v e r assembly of the shock tube i s often desired, rather than the more e a s i l y obtained damped o s c i l l a t o r y current pulse. For example, a damped o s c i l l a t o r y current pulse produces, i n quick succession, multiple regions of plasma that propagate down the shock tube (Kolb 1957). Experimental work i s f a c i l i t a t e d i f only one region of plasma i s produced. When s u f f i c i e n t re-sistance i s i n s e r t e d i n the c i r c u i t f o r c r i t i c a l damping, the peak current i s reduced excessively. A u n i d i r e c t i o n a l current pulse i n the load can be obtained -more e f f i c i e n t l y by short-c i r c u i t i n g the load with a low impedance switch at the end of the f i r s t h a l f cycle of current. The open-air spark gap cannot i n general be used as a load s h o r t - c i r c u i t i n g switch (a "crowbar" switch) on a capacitor bank because the working voltage range i s too small. For example, when the load i s the d r i v e r assem-bly of an electromagnetic shock tube and when the impedance of the d r i v e r i s l e s s than that of the remainder of the c i r c u i t , then the crowbar switch must not break down when the bank v o l t -age V Q appears across i t but must be capable of being triggered when a voltage of l e s s than V 0/2 i s applied. These two require-ments are not compatible with the known working voltage range fo r most open-air gaps of approximately to V^. An open-a i r spark gap i s thus, i n general, not s u i t a b l e as a crowbar switch on an electromagnetic shock tube. Ignitrons have been employed f o r crowbarring a load (Hughes 1961). An i g n i t r o n , however, w i l l not pass currents repeatedly of more than about 50 kA. An i g n i t r o n also has an inductance of about 100 nH, - 15 -considerably l a r g e r than the inductance of a t y p i c a l d r i v e r on an electromagnetic shock tube. An i g n i t r o n i s thus not suitable as the crowbar switch on an electromagnetic shock tube. A low pressure spark gap switch could be used as an e f f i c i e n t crowbar switch on an electromagnetic shock tube and as a main switch. Low pressure spark gap switches do not r e -quire mechanical adjustments i n order to operate over a wide range of voltage and various workers have constructed low pres-sure switches having inductances of from 5 to 30 nH. None of these switches has proven to be completely su i t a b l e f o r crow-barring an electromagnetic shock tube, p r i m a r i l y because the inductance was too high f o r the crowbarring a c t i o n to be e f f i -c i e n t . The inductance of the crowbar switch developed i n the present work was about 1 nH, considerably l e s s than that of the low pressure spark gap switches that have been developed by other workers. This switch has proven to be suitable as the main switch on the capacitor bank and as the crowbar switch on the electromagnetic shock tube. A considerable number of designs of low pressure spark gap switches (LPS) have been developed by other workers. Hagerman and Williams (1959) were the f i r s t to s u c c e s s f u l l y develop a LPS that operated at a pressure of a few microns Hg. Their switch and the s i m i l a r switch by Baker (1959) could d i s -charge currents of the order of MA. The t r i g g e r i n g time was about 1.5 /csec, the voltage range 30 to 75 kV, and the steady state inductance during conduction was about 30 nH. From the geometry of t h e i r switches i t can be i n f e r r e d that a large - 16 -expansion of the discharge must have taken place and that there-fore the impedance of the switch var i e d with time. This v a r i a -t i o n i n impedance would have caused a deformation of the wave-form of the current. In the switch of Mather and Williams (1959), such deformation must also have existed, but to a l e s s e r extent, since the expansion of the discharge was l i m i t e d by the smaller s i z e of the discharge chamber. The t r i g g e r i n g time of t h e i r switch was also about 10 nsec, the voltage range was 100 V to 20 kV and the steady state inductance during conduction was about 5 nH. Mather and Williams (1959) used t h e i r switch as a crowbar switch. Another LPS was developed by Brucker and Rogers (1960). The t r i g g e r i n g time of t h e i r switch was greater than 1 yt&aec, the voltage range was 4 to 30 kV and the steady state inductance during conduction was about 20 nH. Lobov and Tsukerman (1960) also developed a LPS. The t r i g g e r i n g time of t h e i r switch was of the order of .01 to 0.1 j u s e c , the voltage range was 5 to 10 kV and the steady state inductance during con-duction was not given but could be estimated to be about 10 nH. The LPS developed by S o k o l ' s k i i , Nastyukha and Lobikov (1960) had a t r i g g e r i n g time of the order of 10 y U s e c , a voltage range of 0.3 to 12 kV and an inductance that could be estimated to be of the order of 100 nH. Johannson and Smars (1961) have pre-sented considerable data on another LPS. The t r i g g e r i n g time was l e s s than 50 nsec, j i t t e r l e s s than 20 nsec, and the voltage range was a few hundred v o l t s to at l e a s t 50 kV. The steady state inductance during conduction was 20 to 25 nH. The s p e c i f i c requirements that were desired to be met - 17 -by the main and crowbar switch were: inductance l e s s than 5 nH, t r i g g e r i n g time small with small j i t t e r - so that shot-to-shot r e l i a b i l i t y might be obtained, a voltage range as wide as possible, a maximum working voltage of at l e a s t 25 kV, a b i l i t y to pass a current of the order of 1 MA f o r a few / i s e c , and a low noise l e v e l during f i r i n g . These requirements were not met by any of the switches developed by other workers, but were met by the low inductance low pressure spark gap switch used i n the present work. A d e s c r i p t i o n and a discussion of the operating char-a c t e r i s t i c s of the switch f i n a l l y adopted are presented i n Appendix C. The main switch i n s t a l l e d on the capacitor bank (Fig 5) i s i d e n t i c a l to that described i n Appendix C; the crow-bar switch i n s t a l l e d on the capacitor bank (Fig 5) d i f f e r s s l i g h t l y i n construction from the crowbar switch described i n Appendix D. rcrowbar switch F i g 5. low Pressure Spark Gap Switches I n s t a l l e d Between Capacitor Bank and Shock Tube, - 1 8 -The c r o w b a r s w i t c h shown i n P i g 5 was d e s i g n e d t o n o t b r e a k down when b a n k p o t e n t i a l a p p e a r e d a c r o s s i t . T h i s s w i t c h was c o n s t r u c t e d so t h a t i t c o u l d be f i r e d o p t i m u m l y d u r i n g t h e t i m e when t h e i n s t a n t a n e o u s a p p l i e d p o t e n t i a l was o f o p p o s i t e p o l -a r i t y t o t h e i n i t i a l a p p l i e d p o t e n t i a l . The o p t i m u m t i m e f o r f i r i n g t h i s c r o w b a r s w i t c h , when a n i n d u c t i v e l o a d was u s e d , was t h e r e f o r e i n t h e r a n g e o f t/4 t o 3 x / 4 where x was t h e p e r i o d o f t h e o s c i l l a t o r y d i s c h a r g e . The vacuum l i n e s f o r t h e s w i t c h e s shown i n P i g 5 w e r e n o t as s a f e , f o r r e a s o n s o f e l e c t r i c a l i s o l a t i o n , as w e r e t h e vacuum l i n e s f o r t h e s w i t c h e s d e s c r i b e d i n A p p e n d i x C . P r e l i m i n a r y e x p e r i m e n t s w i t h a n i n d u c t i v e l o a d were t h e r e f o r e p e r f o r m e d w i t h t h e s a f e r c r o w b a r s w i t c h d e s c r i b e d i n A p p e n d i x C . S u b s e q u e n t e x p e r i m e n t s , w i t h t h e d r i v e r o f t h e s h o c k t u b e as a l o a d , w e r e p e r f o r m e d w i t h t h e more d e p e n d a b l e c r o w b a r s w i t c h shown i n . P i g 5'-The s w i t c h e s t h a t a r e shown i n P i g 5 w e r e o p e r a t e d 2,000 t i m e s a t e n e r g y l e v e l s up t o 3 k J . O p e r a t i o n was f a i r l y s a t i s f a c t o r y w i t h e i t h e r a r g o n o r n i t r o g e n i n t h e s w i t c h e s . The a c o u s t i c a l n o i s e g e n e r a t e d by a d i s c h a r g e was i n s i g n i f i c a n t c o m p a r e d t o t h a t p r o d u c e d by a n o p e n - a i r s p a r k gap d i s c h a r g i n g t h e same e n e r g y . Some d i f f i c u l t y was e n c o u n t e r e d w i t h t h e L u c i t e . A c o n d u c t i n g d e p o s i t a c c u m u l a t e d u n t i l a p r e - f i r i n g b r e a k d o w n o f t h e m a i n s w i t c h o c c u r r e d . The s w i t c h t h e n h a d t o be d i s -a s s e m b l e d and t h e L u c i t e c l e a n e d w i t h a n a b r a s i v e compound once e v e r y 300 f i r i n g s . No components h a v e b e e n c h a n g e d i n t h e s w i t c h w i t h t h e e x c e p t i o n o f t h e e p o x y b o n d . A f t e r a b o u t 1,500 d i s c h a r g e s t h e h o l e i n t h e L u c i t e h a d become a b o u t 1/32 i n . - 19 -l a r g e r i n diameter than t h a t i n the dummy cathode. A c a r e f u l enlargement of the hole i n the dummy cathode and an adding of a s m a l l amount of epoxy r e s i n on the i n s i d e of the hole r e s t o r e d normal o p e r a t i o n . 3. SHOCK TUBE A p i c t o r i a l diagram of the l a y o u t of the shock tube and a s s o c i a t e d vacuum system i s g i v e n i n F i g 6. The l a r g e mechanical pump could q u i c k l y , evacuate the shock tube to a pres-sure of l e s s than 0.5 microns Hg. The j o i n s between the sec-t i o n s of the shock tube were sealed w i t h O-rings mounted i n such a manner tha t the shock tube could be r a p i d l y disassembled and cleaned. The working s e c t i J n of the shock tube was con-s t r u c t e d of quartz t u b i n g 31/32 i n . i n s i d e diameter, 1 9/64 i n . o u t s i d e diameter and 2 f t i n l e n g t h . to c a p a c i t o r bank F i g 6. l a y o u t of Shock Tube. - 20 -4. A U X I L I A R Y EQUIPMENT i . L u m i n o s i t y D e t e c t o r . The p l a s m a g e n e r a t e d i n a n em s h o c k t u b e e m i t s b o t h l i n e r a d i a t i o n and c o n t i n u u m r a d i a t i o n i n t h e v i s i b l e r e g i o n . A u n i t was c o n s t r u c t e d t o d e t e c t t h i s r a d i a t i o n w i t h p h o t o m u l t -i p l i e r s . T h i s u n i t h a s b e e n u s e d e x t e n s i v e l y t o m e a s u r e t h e v e l o c i t y o f t h e l u m i n o u s f r o n t and t o p r o v i d e a n e l e c t r i c a l p u l s e t h a t s i g n i f i e s t h e p a s s a g e o f t h e p l a s m a p a s t any p a r t i -c u l a r l o c a t i o n a l o n g t h e s h o c k t u b e . The e l e c t r i c a l p u l s e h a s b e e n u s e d t o t r i g g e r e q u i p m e n t . s u c h as o s c i l l o s c o p e s a n d a K e r r c e l l c a m e r a . The two p h o t o m u l t i p l i e r s v i e w e d t h e s h o c k t u b e t h r o u g h a p e r t u r e s t h a t l i m i t e d t h e f i e l d o f v i e w i n t h e p l a s m a t o two s l i t s h a v i n g a n a x i a l • s e p a r a t i o n o f 5 cms. E a c h s l i t h a d i t s g r e a t e r d i m e n s i o n p e r p e n d i c u l a r t o t h e a x i s o f t h e t u b e . The f i e l d o f v i e w i n t h e p l a s m a f o r e a c h p h o t o m u l t i p l i e r was 0.1 cm x 2.5 cm. The c o n s t r u c t i o n o f t h e u n i t i s shown i n P i g 7 and t h e e l e c t r i c a l c i r c u i t i n P i g 8. P i g . 7« C o n s t r u c t i o n o f L u m i n o s i t y D e t e c t o r . The u n i t shown i s e n c l o s e d by a box t h a t i s l i g h t - t i g h t w i t h t h e e x c e p t i o n o f t h e e n t r a n c e s l i t s . - 21 -When the output was loaded with 8 f t of unterminated RG-58/U cable, the cathode to ground capacitance was 230 pF. — 1 2 The r i s e time of the output s i g n a l was then (680)(230 x 10 ) = 0 . 1 6 / i s e c . The two photomultiplier c i r c u i t s were e l e c t r i c a l l y i s o l a t e d (separate'battery supplies and ground c i r c u i t s ) i n order that appreciable spurious e l e c t r i c a l signals generated by the discharge of the main capacitor bank would not be generated i n the photomultiplier c i r c u i t s . 100pP Pig 8. C i r c u i t of Luminosity Detector, i i . Kerr C e l l Camera. An Avco Type 060 Kerr c e l l with an exposure time of 0.1 ^sec and a modified Dumont Polaroid o s c i l l o s c o p e camera were employed to take photographs of the plasma. The pulse needed to t r i g g e r the spark g&p,switch i n the high voltage c i r c u i t of the - 22 -K e r r c e l l was g e n e r a t e d by t h e c i r c u i t shown i n P i g 9- T h i s c i r c u i t c a n be o p e r a t e d i n two modes w h i c h a r e d e s i g n a t e d s i n g l e p u l s e and b i n a r y . The b i n a r y mode o f o p e r a t i o n was u s e d when t h e t r i g g e r p u l s e was o b t a i n e d f r o m t h e l u m i n o s i t y d e t e c t o r . I t was f o u n d t h a t a s p u r i o u s s i g n a l g e n e r a t e d b y t h e d i s c h a r g e o f t h e m a i n b a n k t r i g g e r e d t h e b o o t - s t r a p p u l s e g e n e r a t o r V I . I n t h e b i n a r y mode o f o p e r a t i o n t h i s s p u r i o u s s i g n a l h a s b e e n u t i l i z e d as a p r i m i n g s i g n a l t o make t h e c i r c u i t r e c e p t i v e o n l y t o t h e s u b s e q u e n t l y a p p e a r i n g l u m i n o s i t y s i g n a l . I n t h e s i n g l e p u l s e mode o f o p e r a t i o n t h e f i r s t i n p u t p u l s e o f a m p l i t u d e g r e a t e r t h a n 2 v o l t s f i r e s t u b e V I . The w a v e f o r m o f t h e p u l s e a t t h e o u t p u t o f t h i s t u b e i s e s s e n t i a l l y i n d e p e n d e n t o f t h e w a v e f o r m o f t h e i n p u t p u l s e . The o u t p u t o f V I t h e n i s i n t e g r a t e d by t h e RC c i r c u i t . The f i r i n g t i m e o f t h y r a t r o n V3, o r t h e o v e r -a l l d e l a y o f t h e c i r c u i t , c a n t h u s be c o n t r o l l e d b y v a r y i n g R. S w i t c h S l a c o n t r o l s t h e d u r a t i o n o f t h e p u l s e g e n e r a t e d by V I , s w i t c h S i b adds R t o t h e c i r c u i t i n t h e s i n g l e p u l s e mode o f o p e r a t i o n , and s w i t c h S i c c o n t r o l s t h e p u l s e shape a p p e a r i n g a t Sg2 o f V3. I n t h e s i n g l e p u l s e mode o f o p e r a t i o n t h e . p o t e n t i a l o n Sg2 o f V3 i s b r o u g h t p o s i t i v e w i t h i n a b o u t 0.1 ^ i s e c a f t e r V I h a s f i r e d . I n t h e b i n a r y mode o f o p e r a t i o n , c a p a c i t o r C* a c t s as a n i n t e g r a t o r f o r t h e p u l s e a p p e a r i n g on Sg2 o f V3 t h a t i s g e n e r a t e d by t h e f i r i n g o f t h y r a t r o n V2 . The p o t e n t i a l o n Sg2 o f V3 i n t h e b i n a r y mode o f o p e r a t i o n does n o t become p o s i t i v e u n t i l a b o u t 7 yttsec •,&£ter. V I h a s f i r e d . S i n c e V3 w i l l n o t f i r e u n l e s s t h e p o t e n t i a l on b o t h G l and SG2 o f V3 i s p o s i t i v e , V3 w i l l n o t f i r e on t h e f i r s t f i r i n g o f V I , when t h e c i r c u i t i s i n - 23 -the b i n a r y mode of o p e r a t i o n . The second pulse coming i n t o VI w i l l , however, f i r e VI and V3 i f the second pulse a r r i v e s be-tween 7 and 300 / t s e c a f t e r the f i r s t pulse has f i r e d V I. P i g 9. Ke r r C e l l T r i g g e r C i r c u i t . i i i . C i r c u i t f o r F i r i n g Crowbar Swit.ch. The crowbar s w i t c h was t r i g g e r e d at a time measured w i t h r e s p e c t to the s t a r t of f l o w of the bank c u r r e n t . The stfert of f l o w of bank c u r r e n t was a more j i t t e r - f r e e r e f e r e n c e time than the s t a r t of f l o w of main s w i t c h t r i g g e r c u r r e n t because the breakdown times of the main s w i t c h and the d r i v e r d i d not then i n t r o d u c e a d d i t i o n a l delays (see F i g s 2-3 and 6.4-). I t was m a g n e t i c vro'be i n p u t H-O 4 O Ss o1 & 4 02 H-c+ O t r 4 H-Ot) 0*3 CD 4 O H-4 O e 8 1 IV) VTI o IV) s h o r t t o f i r e - 0 o o \6 . -n o .1 47-n. i — w - — 2 2 K i V S A -10K o o rv> • Q 0 1 A F T " ^ Q 4 7 0 K -AAA-, 4 7 K •MM rv> I I V\A-o o o w IV) AAA-fV) IV) o w |—V\A-o o (V) t IV) —AAA-i§5£., VJIO o - t 3 -found that the thyratron c i r c u i t of Pig 52a was not s a t i s -factory as a crowbar t r i g g e r c i r c u i t because the thyratron would f i r e on what seemed to be a ".signal appearing on the anode due to the high frequency, high p o t e n t i a l pulse gener-ated by the main switch t r i g g e r c i r c u i t . The crowbar switch t r i g g e r c i r c u i t f i n a l l y adopted and shown i n Pig 10 was e s s e n t i a l l y free of t h i s undesirable t r i g g e r i n g . i v . Magnetic Probes. • The bank current arid the current into the d r i v e r were observed with small c o i l s inserted through the ground sheets of"the coplanar conductors. Each c o i l consisted of 20 turns of AWG 45 wire wound as a single l a y e r 1 mm long on a form 1 mm i n diameter. Each c o i l was inserted into the closed end of a 2 i n . length of small bore quartz tubing. The leads were twisted, then connected to a BNC jack which was sealed to the quartz tubing with epoxy r e s i n . A length of terminated RG-58/U cable was then used to connect the c o i l to other equip-ment. The voltage s i g n a l appearing across the termination i s nAB, where n i s the number of turns of wire on the c o i l , A the area enclosed by a single turn and B the rate of change of magnetic induction through the c o i l . During use the c o i l was oriented to pick up the magnetic induction generated by the current that was to be measured. The voltage appearing across the termination was then proportional to the rate of change of t h i s current. The c o i l s i g n a l was often fed into an RC i n t e -grator i n order that the current could be observed on an • - 26 -o s c i l l o s c o p e . The r i n g i n g frequency of the c o i l was measured to "be 70 Mc when coupled without termination d i r e c t l y into a cathode follower having a low input capacitance. The high f r e -quency l i m i t a t i o n of the probes was thus comparable to that of the o s c i l l o s c o p e s employed (Tektronix 535 and 551). - 27 -CHAPTER I I I PROPERTIES OF THE PLASMA GENERATED  IN AN ELECTROMAGNETIC SHOCK TUBE 1. DISTORTION OF THE LUMINOSITY STRUCTURE BY DRIVER DISCHARGE PHENOMENA Some information presented by other workers indicates that the d r i v i n g discharge a f f e c t s the properties of the plasma. Burkhardt and Lovberg (1960) found that under c e r t a i n condi-tions of i n i t i a l gas d i s t r i b u t i o n and applied voltage the current d i s t r i b u t i o n i n a coaxial d r i v e r would lose i t s a z i -muthal symmetry and gather into a pinched discharge at one side of the tube. Fowler, Paxton and Hughes (1961) found that the mobil i t y of the ions i n the d r i v i n g discharge affected the v e l o c i t y of the plasma. The plasma generated i n an electromagnetic shock tube with coplanar d r i v e r , F i g 11, has been s p e c t r o s c o p i c a l l y anal-yzed by Barnard, Cormack and Simpkinson (1962) and Simpkinson (1961). The spectroscopic values f o r electron density and temperature were compared with the predictions of the theory for a plane shock wave. Subsequent to the completion of t h i s work a Kerr c e l l camera was constructed and used to check the pl a n a r i t y of the luminosity front of the plasma. The r e s u l t s of t h i s i n v e s t i g a t i o n into the p l a n a r i t y of the front are presented i n t h i s section. s c a l e 2 i n . = 1 i n . a) C r o s s - s e c t i o n a l V i e w b) P i c t o r i a l V i e w F i g 11. C o p l a n a r D r i v e r f o r E l e c t r o m a g n e t i c S h o c k T u b e . The K e r r c e l l p h o t o g r a p h s shown i n F i g 12 c l e a r l y i n d i c a t e t h a t t h e d i s c h a r g e i n t h e d r i v e r a f f e c t s b o t h t h e shape o f t h e l u m i n o s i t y f r o n t and t h e h o m o g e n e i t y o f t h e l u m -i n o s i t y o f t h e p l a s m a . S e v e r a l i m p o r t a n t p r o p e r t i e s o f t h e p l a s m a a r e r e -v e a l e d by t h e s e p h o t o g r a p h s . The good s h o t - t o - s h o t r e p r o d u c -i b i l i t y o f t h e p l a s m a s t r u c t u r e c a n be s e e n f r o m p h o t o g r a p h s m t o o i n F i g 12. T h i s f e a t u r e i s n o t s u r p r i s i n g as t h e h i s t o r i e s o f t h e l i n e i n t e n s i t i e s h a d p r e v i o u s l y b e e n o b s e r v e d t o h a v e good s h o t - t o - s h o t r e p r o d u c i b i l i t y ( B a r n a r d , Cormack a n d S i m p k i n s o n 1962). I n t h i s r e s p e c t t h e c o p l a n a r d r i v e r i s s u p e r i o r t o t h e T - t u b e d r i v e r s d e s c r i b e d b y K o l b(l957) and L i n k e (1961). These d r i v e r s , i l l u s t r a t e d i n F i g 13, h a d a g r e a t e r s u r f a c e a r e a o f e l e c t r o d e s e x p o s e d t o t h e d i s c h a r g e . - 29 -d) r) s) t) u) r w) y) 4 v) > 4 * ^ Pig 12. Photographs of Plasma Generated by Various Drivers. a) to p): Coplanar d r i v e r , 4/*F capacitor bank, 12.5 kV, period 4.5 /*sec, argon at 1 mm Hg. q) to t ) : Driver of Pig 17, 19.2/tP capacitor bank, 8 kV, per-iod 4.5/«sec, argon at 160 microns Hg. Pressure i n main switch'*'1.5 microns Hg. u) to z ) : Driver of P i g 18, conditions same as for pictures a) to t ) . P o l -lowing displacements measured i n cm from base of driver to luminosity front and times i n ^ s e c from onset of current flow. a)x<0.7. b)x = 1.4,t= 0.7, c)x=3.7,t=1.1, d)x=4.4,t=1.3, e)x=5.3,t=1.7, f)x=5.8, t=1.9, g)x=7.0,t=2.2, h)x=8/7, i)x=l6.1. In a) to i ) the upper electrode was p o s i t i v e ; i n j) to p) the lower electrode was p o s i t i v e . j)x=3.7, t=1.1, k)x= 4.4,t=1.3, l)x=5.3,t=1.7, m)to o)x=7.0, t=2.2,V p)x=16.1, q)x=10.5, r) to t)x=48, u) to z) x=53.5. I = current i n f i e l d c o i l , A . u) I = .2, v) I = .5, w) 1= 1, x) I = 2, y) I = 5, z) I = 17. Single p i c -tures are side views. Double pictures are top and side views. Driving currents not crowbarred. - 30 -The experimental work on the low pressure switch described i n Appendix C indicates that an o s c i l l a t o r y discharge of 100 kA peak value and frequency about 200 kc has a cr o s s - s e c t i o n a l p channel area of about 1 cm . The discharge i n the coplanar d r i v e r was thus forced to cover the electrodes (the area of p the electrodes was about 0.25 cm and the peak value of the current about 70 kA). I t i s suggested by the present author that the i r r e p r o d u c i b i l i t y observed by both l i n k e (1961) and Kolb (1959) can be a t t r i b u t e d to the large area of the e l e c t -rodes i n t h e i r T-tubes. I f the electrode si z e i s comparable to or l a r g e r than the si z e of the discharge channel, then the l o c a t i o n of contact of the discharge onto each electrode i s unpredictable.- The discharge w i l l move r a p i d l y over the sur-face of the cathode seeking always a l o c a t i o n o f f e r i n g more e f f i c i e n t electron emission (Seeker 1959). t a) Used by Kolb (1957) b) Used by Linke (1961) F i g 13. T-Tube Drivers. - 31 -One undesirable c h a r a c t e r i s t i c of the plasma revealed i n the photographs i n Pig 12 was the non-planarity of the lum-i n o s i t y f r o n t . Even at x = 16.1 cms, the departure from p l a n a r i t y was evident. The amount of departure from p l a n a r i t y i s s i m i l a r to that obtained by McLean et a l .(1960) but i s con-siderably l e s s than the worst reported by Kolb (1959). The photographs i n Pig 12 i n d i c a t e that the p o l a r i t y applied to the electrodes a f f e c t s the shape of the luminosity f r o n t . The leading portion of the luminosity front i s always adjacent to the anode. I t i s suggested by the author that the eruptive i n s t a b i l i t y , observed i n a pinch discharge by Kvartzhava, Kervalidze and Gvaladze (1959), i s responsible f o r the protuberances on the luminosity f r o n t . The i n t e r n a l lum-i n o s i t y structure that i s f a i n t l y v i s i b l e i n the photographs i n Pig 12 i s drawn more c l e a r l y i n Pig 14. a) t = 0.7>*sec b) t = 1 . ly^sec c) t = 1.3/»sec Pig 14. The Protuberances on the Shock Front. - 32 -The double-pronged front shown i n Figs 12b to p i s a c h a r a c t e r i s t i c of not only the plasma produced by a coplanar driver but also of the plasma produced by a T-tube dr i v e r (Kolb 1957). The double-pronged front evident i n F i g H a could be caused by the JXB forces acting on the discharge channel. The magnetic f i e l d i n t e n s i t y i n the corners of the discharge i s greater than at the center of the shock tube as can be shown by a c a l c u l a t i o n employing Biot and Savart's law. The fa c t that the protuberance nearest the anode, as shown i n F i g Ha, i s the more prominent i s probably caused by the ions i n the discharge imparting some of t h e i r momentum to the d i s -charge as a whole. This momentum e f f e c t has been observed by Fowler, Paxton and Hughes (1961) i n an electromagnetic shock tube of quite d i f f e r e n t design from that being considered here. Very close examination of photographs c, d and e i n Pig 12 discloses the c r a t e r - l i k e shape shown near the top of F i g H e A mechanism that could be responsible f o r the protuberances shown i n F i g 14 i s drawn i n more d e t a i l i n F i g 15. Fi g 15. A Possible Explanation f o r the Protuberances on the Shock Front. - 33 -I t i s s u g g e s t e d b y t h e a u t h o r t h a t t h e J X B f o r c e a c t i n g o n t h e i n s i d e c o r n e r o f t h e d i s c h a r g e a c c e l e r a t e s a r e g i o n o f t h e p l a s m a away f r o m t h e c o r n e r i n t o t h e d i s c h a r g e . As t h i s c y l i n d r i c a l l y - s h a p e d r e g i o n moves away f r o m t h e i n s i d e c o r n e r o f t h e d i s c h a r g e t h e m a g n e t i c f i e l d i n s i d e t h e r e g i o n s t a r t s t o d i f f u s e o u t w a r d s . W h i l e i t i s d i f f u s i n g , a l o o p c u r r e n t I i s s e t up a r o u n d t h e r e g i o n by t h e d i f f e r e n c e b e t w e e n t h e i n t e n s i t y o f t h e m a g n e t i c f i e l d i n s i d e t h e r e g i o n and t h a t i m m e d i a t e l y o u t s i d e b u t s t i l l i n t h e d i s c h a r g e . The r e g i o n i s t h u s c h a r a c t e r i z e d by a l a r g e k i n e t i c e n e r g y d i r e c t e d away f r o m t h e i n s i d e c o r n e r a n d by b o t h a t r a p p e d m a g n e t i c f i e l d and a l o o p c u r r e n t I . The s t r u c t u r e o f t h e r e g i o n i s t h a t o f a p l a s m o i d , a p l a s m a - m a g n e t i c e n t i t y . t h a t h a s b e e n s t u d i e d by B o s t i c k ( 1 9 5 6 ) . The c u r r e n t I i n t e r a c t s w i t h t h e m a g n e t i c i n t e n s i t y B g e n e r a t e d b y t h e c u r r e n t i n t h e d i s c h a r g e t o p r o -duce a d e c e l e r a t i n g f o r c e a g a i n s t t h e p l a s m o i d . The p l a s m o i d c a n p a s s c o m p l e t e l y a c r o s s t h e d i s c h a r g e i f i t s i n i t i a l k i n e t i c e n e r g y i s s u f f i c i e n t t o overcome t h e e f f e c t s o f t h e I X B d e -c e l e r a t i n g f o r c e . Once t h e p l a s m o i d h a s p a s s e d o u t o f t h e a r c , t h e r e p u l s i v e f o r c e b e t w e e n t h e c u r r e n t I a n d t h e d i s c h a r g e c u r r e n t w o u l d r e s u l t i n a d e p r e s s i o n i n t h e r e g i o n where t h e p l a s m o i d was e j e c t e d . T h i s d e p r e s s i o n i s e v i d e n t i n P i g s 12c t o e as a c r a t e r - l i k e shape i n t h e m a i n d i s c h a r g e c o l u m n b e h i n d t h e e j e c t e d p l a s m o i d . The p r e s e n c e o f t h i s c r a t e r - l i k e shape i n t h e d i s c h a r g e c o l u m n i n d i c a t e s t h a t a n e r u p t i v e i n s t a b i l i t y m e c h a n i s m i s p r o b a b l y o p e r a t i v e r a t h e r t h a n a n e j e c t i o n m e c h -a n i s m b a s e d o n t h e i o n momentum e f f e c t n o t e d b y F o w l e r , P a x t o n - 34 -and Hughes (1961). Further substantiation of the existence of an eruptive i n s t a b i l i t y mechanism i s provided by the f a c t that a protuberance appears at each corner of the discharge. An order of magnitude c a l c u l a t i o n of the dynamics of a .plasmoid moving according to the preceding suggested eruptive i n s t a b i l -i t y theory i s presented i n Appendix E. The c a l c u l a t i o n shows that the eruptive i n s t a b i l i t y could account f o r the protuber-ances . A second breakup of the discharge column i s i n evidence i n photographs e and f " i n F i g 12. At a time of about 1.7>t*sec a f t e r the discharge current has started to flow, luminous gas appears to be ejected from the center of the d i s -charge back towards the d r i v e r . The period of the discharge was 4.5_^sec, so that t h i s breakup occurred at about the time that the plasma attained a maximum v e l o c i t y (see Section 5 of t h i s Chapter). F i g 16 pictures the sequence that could lead to the observed luminosity patterns. In the t r a n s i t i o n shown i n F i g 16 a to b, a region of high luminosity and p a r t i c l e energy occurs at the center of the discharge, due .to l a t e r a l compression. This region has a high conductivity and r e t a i n s a trapped magnetic f i e l d f o r a s u f f i c i e n t time f o r the motion pictured i n F i g 16c and d to occur. In F i g 16c the t o t a l d i s -charge current i s decreasing and i n F i g 16d the loop currents generated by the magnetic f i e l d trapped i n the plasma become comparable i n magnitude to the t o t a l discharge current. In F i g I6e the loop currents combine and are ejected back toward the d r i v e r . Bostick (1956) has established that a plasmoid - 35 -F i g 16. Proposed Mechanism f o r F i n a l Breakup of D i s -charge Column. The p e r i o d of the discharge was 45 jmaec. i s elongated when i t passes through a magnetic f i e l d o r i e n t e d p e r p e n d i c u l a r to the plane c o n t a i n i n g the cu r r e n t i n the p l a s -moid. The same phenomenon i s apparent i n F i g I6e i n which a t h i n wedge of plasma i s shown "being e j e c t e d backwards from the discharge. The c o a l e s c i n g of the plasmoid w i t h the discharge formed by the second pulse of cu r r e n t i s due to the f o r c e of a t t r a c t i o n between the c u r r e n t i n the plasmoid and the d i s -charge c u r r e n t ( F i g 1 6 f ) . I t i s of i n t e r e s t t h a t the i n t e r n a l s t r u c t u r e of the plasma generated by t h i s second pulse of current i s q u i t e s i m i l a r to tha t generated by the f i r s t as i s i n d i c a t e d i n F i g 12i and p. The l u m i n o s i t y p a t t e r n t h a t can be d i r e c t l y a t t r i b u t e d to the d r i v i n g discharge stays very c l o s e to the f r o n t of the - 36 -p l a s m a e v e n a f t e r t h e p l a s m a h a s t r a v e l l e d a c o n s i d e r a b l e d i s -t a n c e down t h e s h o c k t u b e ( F i g s 12i a n d p ) . The r e g i o n o f u n c o n t a m i n a t e d , s h o c k - h e a t e d gas i s t h u s q u i t e t h i n . H o o k e r (1961) h a s shown t h a t i n a d i a p h r a g m d r i v e n s h o c k t u b e a n a p -p r e c i a b l e amount o f s h o c k - h e a t e d gas f l o w s t h r o u g h t h e boundary-l a y e r b e t w e e n t h e d r i v e r gas and t h e w a l l o f t h e s h o c k t u b e . T h i s same t h e o r y s h o u l d a p p l y t o e l e c t r o m a g n e t i c s h o c k t u b e s . The shape o f t h e l u m i n o s i t y f r o n t d u r i n g t h e e a r l y s t a g e s o f t h e d i s c h a r g e c o u l d n o t p l a u s i b l y be c a u s e d b y s c a t -t e r e d l i g h t . I t i s s u g g e s t e d by t h e a u t h o r t h a t t h e l u m i n o s i t y p a t t e r n shown i n F i g 12a a n d b i s a n i n d i r e c t r e s u l t o f c o n -d u c t i o n t h r o u g h a l a r g e v o l u m e o f t h e gas i n t h e s h o c k t u b e d u r i n g t h e i n i t i a l s t a g e s o f b r e a k d o w n . As s o o n as v o l t a g e i s a p p l i e d t o t h e d r i v e r a n e l e c t r i c f i e l d i s c r e a t e d b e t w e e n t h e e l e c t r o d e s o f t h e d r i v e r . The c o n d u c t i v i t y o f t h e gas s u b j e c t -ed t o t h i s e l e c t r i c f i e l d w i l l r i s e . The r e g i o n o f r i s i n g c o n d u c t i v i t y w i l l e x t e n d down t h e s h o c k t u b e f o r a d i s t a n c e o f s e v e r a l c m s . As t h e c u r r e n t d e n s i t y i n t h i s r e g i o n r i s e s , a p i n c h i n g o f t h e c u r r e n t c a r r i e r s w i l l r e s u l t . The p i n c h s h a p e , w o u l d be t h a t o f a " V o n i t s s i d e " and t h e " Y o n i t s s i d e " shape c o u l d be -due t o a n i n s t a b i l i t y o f t h e p i n c h e d c o l u m n f o r c i n g p a r t i c l e s down t h e c e n t e r o f t h e t u b e . The f a c t t h a t t h e l u m i n o s i t y p a t t e r n does n o t p r o p a g a t e down t h e t u b e s u p p o r t s u t i h i s t h e o r y . The p e r s i s t e n c e o f t h e p a t t e r n f o r some 1 >tsec i s o f i n t e r e s t . E i t h e r t h e r e i s a s t e a d y f l o w o f p a r t i c l e s t o w a r d t h e l u m i n o s i t y p a t t e r n d u r i n g t h i s t i m e o r t h e r a d i a t i n g p a r t i c l e s do n o t l e a v e t h e p i n c h e d r e g i o n d u r i n g t h i s t i m e . - 37 -I t h a s b e e n shown i n t h i s S e c t i o n t h a t t h e d r i v i n g d i s c h a r g e h a s a p r o n o u n c e d e f f e c t on t h e p r o p e r t i e s o f t h e p l a s m a g e n e r a t e d ' i n a n e l e c t r o m a g n e t i c s h o c k t u b e . I n p a r t i -c u l a r , i n s t a b i l i t i e s o f t h e d r i v i n g d i s c h a r g e a f f e c t t h e h o m o g e n e i t y o f t h e p l a s m a , e v e n a t a c o n s i d e r a b l e t i m e a f t e r t h e d r i v i n g c u r r e n t h a s c e a s e d t o f l o w . I t h a s a l s o b e e n shown t h a t u n d e r t h e e x p e r i m e n t a l c o n d i t i o n s s t u d i e d , t h e d r i v e r g a s s t a y s v e r y c l o s e t o t h e f r o n t o f t h e p l a s m a . 2. EFFECT OF THE GEOMETRY OF THE DRIVER ON THE LUMINOSITY STRUCTURE I N THE PLASMA I n t r o d u c t i o n The c o n c l u s i o n s r e a c h e d i n t h e p r e c e d i n g S e c t i o n , t h a t t h e h o m o g e n e i t y and r e p r o d u c i b i l i t y o f t h e p l a s m a g e n -e r a t e d i n a n e l e c t r o m a g n e t i c s h o c k t u b e depend m a r k e d l y on t h e p r o p e r t i e s o f t h e d r i v i n g d i s c h a r g e , i n d i c a t e t h a t t h e s t r u c -t u r e o f t h e l u m i n o s i t y i n t h e p l a s m a c a n be a l t e r e d b y c h a n g -i n g t h e g e o m e t r y o f t h e d r i v e r . The o b j e c t o f t h e w o r k d e -s c r i b e d i n t h i s S e c t i o n was t o a s c e r t a i n t h e p o s s i b i l i t y o f g e n e r a t i n g a r e p r o d u c i b l e p l a s m a t h a t was b o t h f a i r l y f r e e o f c o n t a m i n a t i o n and t h a t was p r o d u c e d b e h i n d a p l a n e f r o n t . S u c h a p l a s m a w o u l d be r e a d i l y amenable t o a n a l y s i s . A l s o , t i m e - r e s o l v e d s p e c t r o s c o p i c s t u d i e s on s u c h a p l a s m a w o u l d be f a c i l i t a t e d . A c o u r s e o f r e s e a r c h was t h e r e f o r e a d o p t e d t h a t w o u l d l e a d e i t h e r t o t h e g e n e r a t i o n o f a, p l a s m a w i t h r e p r o -d u c i b l e . p r o p e r t i e s ; " o r t h a t w o u l d c l a r i f y why i r r e p r o d u c i b i l i t y m i g h t be a c h a r a c t e r i s t i c p r o p e r t y o f t h e p l a s m a g e n e r a t e d i n - 38 -an electromagnetic shock tube. In t h i s section Kerr c e l l photographs of the plasma generated "by several configurations of d r i v e r are presented and discussed. Experimental Results The f i r s t configuration of d r i v e r that was tested i s pictured i n Pig 17. Like the other drivers described i n t h i s Section, t h i s d r i v e r has c y l i n d r i c a l symmetry. a) P i c t o r i a l View b) Gross-Sectional View, P u l l s i z e . Pig 17- Coaxial Electromagnetic Driver with Short Electrodes Kerr c e l l photographs of the plasma produced by the driver shown i n Pig 17 are presented i n Pig 12q to t. This driver obviously did not r e s u l t i n good shot-to-shot reproduc-i b i l i t y of the structure of the luminosity i n the plasma. The i r r e p r o d u c i b i l i t y evident from these photographs i s con-siderably worse than that indicated by the photographs i n Pig 12a to p. That i s , the i r r e p r o d u c i b i l i t y was dependent upon - 39 -the geometry of the d r i v e r . Al-fven, Lindberg and M i t l i d (1959) observed that the luminosity front of the plasma generated by a coaxial e l e c t r o -magnetic d r i v e r could be made more plane by applying a r a d i a l magnetic f i e l d at the e x i t of the d r i v e r . The d r i v i n g current was s t i l l flowing through the plasma while the plasma passed through the r a d i a l magnetic f i e l d . The current rose with 3 / 6 s e c to about 100 kA, the magnetic f i e l d i n t e n s i t y was 0.03 -0.09 Wb/m2 (300 - 900 G) and the corresponding s t a t i c f l u x 0.3 - 0.95 mWb. A s i m i l a r configuration of d r i v e r shown i n Pig 18 was tested. A small t r i g g e r spark promoted breakdown i n i t i a l l y at the base of the d r i v e r . This method of t r i g g e r i n g the d r i v e r was employed i n a l l of the drivers that are subsequently described i n t h i s Section. Pig 18. Coaxial Electromagnetic Driver with Short Electrodes and a S t a t i c Magnetic P i e l d . The magnetic f i e l d i n -t e n s i t i e s shown were measured when a 5A c o i l current was flowing i n the f i e l d c o i l . - 40 -T y p i c a l photographs of the plasma generated by the d r i v e r shown i n P i g 18 are presented i n P i g 12u to z. I t was found t h a t the s t r u c t u r e of the l u m i n o s i t y i n the plasma was not r e p r o d u c i b l e , r e g a r d l e s s of the magnitude of the magnetic f i e l d ( c o i l c u r r e n t £ 20A). At low values of c o i l current? 1^  the l u m i n o s i t y f r o n t tended to be composed of one or more l a r g e protuberances. At h i g h v a l u e s , 5 to 20 amperes, the f r o n t tended to be composed of many s m a l l e r protuberances. At an i n t e r m e d i a t e value of f i e l d , which w i l l be c a l l e d the s t a -b i l i z i n g v a l u e , the shock f r o n t o f t e n tended to be plane. The value of the s t a b i l i z i n g f i e l d depended on the pressure i n the low pressure main s w i t c h on the c a p a c i t o r bank. As mentioned i n Appendix C, a decrease i n gas pressure decreased the i n i t i a l r a t e of r i s e of bank c u r r e n t . An i n c r e a s e i n the i n i t i a l r a t e of r i s e of bank curren t thus decreased the magnitude of the s t a b i l i z i n g f i e l d r e q u i r e d . This e f f e c t was as i f the amount of a p p l i e d f i e l d trapped i n the plasma was i n c r e a s e d by an i n c r e a s e i n the i n i t i a l r a t e of r i s e of c u r r e n t . A l a r g e r i n i t i a l r a t e of r i s e of c u r r e n t , which would r e s u l t i n a higher i n i t i a l v e l o c i t y of the l u m i n o s i t y f r o n t and cause more exten-s i o n of the l i n e s of f o r c e trapped i n the advancing dis c h a r g e , p o s s i b l y r e s u l t s i n a "breaking" (the term employed by Lindberg and Jacobsen 1960) of more l i n e s of f o r c e than a s m a l l e r i n i t i a l r a t e of r i s e of c u r r e n t would. The amount of the a p p l i e d f i e l d trapped i n the plasma thus should have been increased by an i n c r e a s e i n the i n i t i a l r a t e of r i s e of c u r r e n t , a r e s u l t t h a t i s confirmed by the experimental data. a) D r i v e r w i t h , d o w n s t r e a m B b) D r i v e r w i t h s h o r t anode e) D r i v e r w i t h f ) D r i v e r w i t h s m a l l g) D r i v e r w i t h d i s c anode a r e a c a t h o d e p i n c a t h o d e F i g 19. C o n f i g u r a t i o n s o f A x i a l l y - S y m m e t r i c D r i v e r s T h a t Were T e s t e d . - 42 -In an attempt to obtain a plasma having reproducible properties, the configurations of dr i v e r shown i n Pig 19 were tested. Most of the tests were conducted with a 19.2/iP bank charged to 8 kV and with argon at a pressure of 160 microns Hg i n the shock tube. The length of the center pin i n the dri v e r s shown i n Pig 19a to d was greater than the distance over which a c c e l e r a t i o n of the plasma occurred. Wo s i g n i f i c a n t improve-ment i n r e p r o d u c i b i l i t y was obtained with the configurations shown i n Pig 19a and b over that shown i n Pig 18. Some i n -crease i n v e l o c i t y and luminosity was obtained with a d r i v e r , Pig 19c, having a large area anode. The extent of the increase i n luminosity and the e f f e c t of the applied magnetic f i e l d on the luminosity of the plasma i s indicated by the photographs i n Pig 20 a and b. Again a value of applied magnetic f i e l d that tended to s t a b i l i z e the plasma could be noted. A time integrated spectrum of the v i s i b l e r a d i a t i o n from the plasma generated by the dr i v e r of Pig 19c was taken. The spectrum was taken at a distance of 50 cms from the Teflon at the base of the d r i v e r , and the i n i t i a l pressure of argon i n the shock tube was 160 microns Hg. The 19.2/<P capacitor bank was discharged from 8 kV and the dr i v e r was crowbarred. The waveform of the d r i v i n g current was therefore e s s e n t i a l l y the f i r s t pulse of a sine wave. No s t a t i c magnetic f i e l d was applied to the dr i v e r and the v e l o c i t y of the luminosity front where the spectrum was taken was 2.3 cm^wsec. The spectrum contained l i n e s of AH, Gal, CI, weak Cul and a- narrow Horline. It was of some i n t e r e s t that no S i l i n e s were observed and that a) ID) C ) d) e) P i g 20. E f f e c t s of D r i v e r Geometry and Gas Pressure on Luminosity of Plasma. a ) D r i v e r of P i g 19b. 19.2 M R c a p a c i t o r bank, 8kV, uncrowbarred, 160 mic-rons Hg argon i n shock tube, 20 microns Hg argon i n switches. F i d u c i a l marks at 45 and 50 cms. b) D r i v e r of F i g 19c. Co n d i t i o n s same as f o r case a ) . Lens opening unchanged f o r cases a) and b ) . c) to e) D r i v e r of F i g 19d. F i d u c i a l marks at 30 and 35 cm. 19.2/fF c a p a c i t o r bank, 8 kV, crowbar-red, 20 microns Hg argon i n switches. Shock tube pressures i n microns Hg of argon: c) 160, d) 600, e) 1000. F i e l d c o i l c u r r e n t s i n A, readin g down: a) and b): 0, .033, .1, .3, 1, 3, 10, 15. c): 0, 1, 3, 3.4, 4, 5, 7.5, 10. d) and e): 0, 2, 4, 6, 9, 12, 15, 0. Two views c o n s t i t u t e one photograph. The upper p i c t u r e i s a top view of the plasma, the lower i s a si d e view. - 44 -the o v e r a l l number of i m p u r i t y l i n e s was very low. The e f f e c t of the i n i t i a l pressure i n the shock tube on the s t r u c t u r e of the l u m i n o s i t y of the plasma i s shown i n F i g 20c to e. The d r i v e r employed i s shown i n F i g 19d. The s t a b i l i z i n g e f f e c t on the plasma of a h i g h i n i t i a l pressure i n the shock tube i s evide n t . This d r i v e r , i n c i d e n t a l l y , produced a plasma having a g r e a t e r v e l o c i t y than the plasma produced by any other d r i v e r t e s t e d . I t was found t h a t the magnitude of the a p p l i e d mag-n e t i c f i e l d a f f e c t e d the pressure r i s e i n the system due to 3 f i r i n g . For example, the pressure i n the 1200 cm shock tube vacuum system rose from 160 microns Hg to 185 microns Hg f o r a crowbarred 8 kV discharge i n t o argon when no magnetic f i e l d was a p p l i e d to the d r i v e r . With a 10 A c u r r e n t i n the magnetic f i e l d c o i l , the pressure rose only to 175 microns Hg. The d r i v e r i n F i g 19e was developed w i t h the ob j e c t of d e c r e a s i n g the area of the e l e c t r o d e s . I t was b e l i e v e d t h a t i r r e p r o d u c i b i l i t y of the l u m i n o s i t y s t r u c t u r e of the plasma might be due to movement of the arc over the surfa c e of the e l e c t r o d e s . Photographs r e v e a l e d t h a t the l u m i n o s i t y s t r u c t u r e , i n p a r t i c u l a r the p l a n a r i t y of the f r o n t , was more r e p r o d u c i b l e f o r t h i s d r i v e r than f o r any of those p r e v i o u s l y t e s t e d . A t i m e - i n t e g r a t e d spectrogram of the l u m i n o s i t y from t h i s plasma contained a l a r g e number of G r I I l i n e s . The i n n e r s u r f a c e of the s t a i n l e s s s t e e l anode was in s p e c t e d and found to have assum-ed a c l e a n roughened appearance. I t was concluded t h a t the l a r g e amount of e l e c t r o d e m a t e r i a l i n the plasma was probably - 45 -due to the small i n t e r - e l e c t r o d e spacing. The electrons i n the discharge were probably able to pass from cathode to anode with low c o l l i s i o n a l energy losses, then impart t h e i r energy to the anode, which was heated and l o s t ions and atoms to the plasma. The dr i v e r shown i n F i g 19f produced a plasma having a f a i r l y reproducible luminosity structure, as pictured i n F i g 21a to h. A l l f i r i n g s with t h i s d r i v e r were crowbarred at the f i r s t zero of the current. The prominent l i n e s appearing i n a time integrated spectrum taken at x = 50 cms, x = 2.0 cm/ /isec, were of A l l . Weak l i n e s of Cul, Znl, and the H»rlines were also noted. No S i l l l i n e s appeared. The h i s t o r y of the i n t e n s i t y of c e r t a i n l i n e s was observed with a photomultiplier that was f i t t e d to a monochromator. The shot-to-shot repro-d u c i b i l i t y of the peak i n t e n s i t y of each s p e c t r a l l i n e observed was only f a i r . The r e p r o d u c i b i l i t y was, however, better than obtained with the other d r i v e r s , with the exception of the co-planar d r i v e r . Another i n d i c a t i o n of the r e p r o d u c i b i l i t y of the plasma produced by the small-cathode d r i v e r i s revealed by the oscillograms of the signals observed with the luminosity detector (Fig 21i to p0 . Several crowbarred f i r i n g s at an energy of 3 kJ were attemped with t h i s d r i v e r . The hole i n the Teflon was i n s u f f i c i e n t l y large to pass the higher current and the Teflon was considerably decomposed by these f i r i n g s . One undesirable feature of t h i s d r i v e r was that i t produced a lower v e l o c i t y than the d r i v e r i n F i g 19d. - 46 -P i g 21. S t r u c t u r e of Luminosity of Plasma. 19.2,aF c a p a c i t o r "bank, 8 kV. crowbarred. a) to o) D r i v e r of P i g 19f. p) to w) D r i v e r of P i g 19g. Shock tube pressure: a) to f ) , and i ) to v) 160 microns Hg of argon, g) 600 microns Hg of argon, h) and w) 1000 microns Hg of argon. F i d u c i a l mark at 40 cm. Photographs i ) and o) are s i g n a l s from p h o t o m u l t i p l i e r ( l u m i n o s i t y d e t e c t o r ) at 40 cm. S c a l e s : 5V/div and .4 ><* s e c / d i v . - 47 -A c o n f i g u r a t i o n o f d r i v e r t h a t was a c o m p r o m i s e b e -t w e e n t h o s e shown i n P i g 19d a n d f i s shown i n P i g 19g . The l u m i n o s i t y s t r u c t u r e o f t h e p l a s m a p r o d u c e d b y t h i s d r i v e r i s p i c t u r e d i n P i g 21 cp t o isr. The v e l o c i t y o f t h e l u m i n o s i t y f r o n t was q u i t e h i g h , n e a r l y t h e same as t h a t p r o d u c e d by t h e d r i v e r i n P i g 1 9 d , b u t t h e l u m i n o s i t y s t r u c t u r e was q u i t e i r r e p r o d u c -i b l e . The c o p p e r c a t h o d e o f t h i s d r i v e r was f o u n d t o be p l a t e d w i t h a t h i n l a y e r o f what a p p e a r e d t o be b r a s s by t h e c r o w b a r -r e d f i r i n g s . The b r a s s must h a v e b e e n b o i l e d o r s p u t t e r e d o f f t h e anode b y e l e c t r o n b o m b a r d m e n t . The i o n bombardment o f t h e c a t h o d e r e s u l t e d i n d e p o s i t i o n r a t h e r t h a n l o s s o f c a t h o d e m a t e r i a l . D i s c u s s i o n The d r i v e r shown i n P i g 19d p r o d u c e d t h e p l a s m a h a v -i n g t h e l e a s t c o n t a m i n a t i o n a n d t h e h i g h e s t v e l o c i t y . The shqfcfc-t o - s h o t r e p r o d u c i b i l i t y o f t h e s t r u c t u r e o f t h e l u m i n o s i t y a n d o f t h e p l a n a r i t y o f t h e f r o n t was i n s u f f i c i e n t t o a l l o w d e p e n -d a b l e t i m e - r e s o l v e d s p e c t r o s c o p i c m e a s u r e m e n t s t o be made. The p l a s m a c o u l d n o t be s a t i s f a c t o r i l y s t a b i l i z e d by a p p l y i n g a r a d i a l m a g n e t i c f i e l d t o t h e d r i v e r . The d r i v e r shown i n P i g 1 9 f g e n e r a t e d t h e most repro-r d u c i b l e p l a s m a a n d t h e b e s t p l a n a r i t y o f f r o n t . A p p a r e n t l y t h e l a r g e a r e a anode r e s u l t e d i n a l o w c u r r e n t d e n s i t y a t the, anode a n d t h i s l e s s e n e d c o n t a m i n a t i o n o f t h e p l a s m a b y anode e l e c t r o d e m a t e r i a l s . A l s o , t h e s m a l l a r e a c a t h o d e r e d u c e d t h e s h o t - t o - s h o t v a r i a t i o n i n t h e l o c a t i o n o f t h e c a t h o d e end o f t h e d r i v i n g d i s c h a r g e . The s m a l l a r e a c a t h o d e was t h e m a j o r - 48 -cause of the good shot-to-shot r e p r o d u c i b i l i t y . 3. MAGNETIC FIELDS IN THE PLASMA Marshall (1960) detected an azimuthal magnetic f i e l d i n the plasma ejected by a coaxial d r i v e r . His measurements were made on a plasma moving into a vacuum. Sim i l a r measure-ments were made i n the present work on the plasma produced i n an electromagnetic shock tube powered by the d r i v e r shown i n F i g 19c. Measurements were made with a magnetic probe, pre-v i o u s l y described, oriented to pick up the azimuthal component of magnetic f i e l d at a distance of 1 mm i n from the insi d e waH of the shock tube. The observed waveshape i s shown i n F i g 22 along with an explanation f o r the existence of t h i s f i e l d . The t o r o i d a l magnetic f i e l d i n t h i s explanation i s a t t r i b u t e d to a trapping of the d r i v i n g f i e l d . A quantitative i n t e r p r e -t a t i o n of the probe signals would be i n error because i t was believed that the probe disturbed the plasma. The r e s u l t s of a c a l c u l a t i o n based on the observed probe s i g n a l , and on the adoption of a simple model, was that B T y,„ v«4 G, I. n, o n - 20 A, max xo xa_L J - 3 A/cm . The shape of the si g n a l had shot-to-shot repro-d u c i b i l i t y but the amplitude did vary somewhat. The si g n a l was inverted when the c o i l was rotated 180°, i n d i c a t i n g that the si g n a l was generated by a rate of change of f l u x linkage rather than by e l e c t r o s t a t i c e f f e c t s . The shot-to-shot repro-d u c i b i l i t y i n the shape of the si g n a l disappeared when the c o i l was placed 5 mm i n from the w a l l . The v a r i a t i o n of the s i g n a l along the length of the shock tube was not investigated. - 49 -,03V a) t= b) t= 4>tsec c) t= 35 /(sec, x= 87 cm Fi g 22. B^ . Transported i n Plasma. The d r i v i n g current J ceased to flow when t*2.3/<sec. I n i t i a l pres-sure 160 microns Hg, luminosity front v e l o c i t y at x = 87 cm was 2.0 cm/a sec. Further v e r i f i c a t i o n that a current dipole was pro-pagating down the tube was obtained during experiments conducted with the MHD generator. These experiments are described i n d e t a i l i n Chapter IV, Section 1. The relevant r e s u l t from these experiments that offered further confirmation of the existence of a current dipole was that the v e l o c i t y of the plasma could be alt e r e d by applying a s t a t i c azimuthal magnetic f i e l d i n front of the plasma. The normal deceleration of the plasma was either decreased or increased by an applied f i e l d that r e s p e c t i v e l y aided or opposed the trapped magnetic f i e l d . - 50 -4. INITIAL BREAKDOWN PHENOMENA The magnitude of the magnetic f i e l d (see F i g 18 and Figs 19a to d) applied to the coaxial d r i v e r was found to a f f e c t the breakdown time of the d r i v e r . This dependency i s given i n F i g 23 f o r the d r i v e r shown i n F i g 19d. The break i n the curve occurs at a value of current through the dc f i e l d c o i l that produced a magnetic f i e l d at the i n j e c t i o n point of the t r i g g e r i n g plasma that s a t i s f i e d the r e l a t i o n E/B = C. The e l e c t r i c f i e l d at the t r i g g e r i n j e c t i o n point was p r i m a r i l y i n the r a d i a l d i r e c t i o n and the applied magnetic f i e l d i n the a x i a l d i r e c t i o n . The probable explanation f o r the dependence of magnetic f i e l d on the breakdown time i s that charged p a r t i -cles o r i g i n a t i n g i n the t r i g g e r spark move i n an azimuthal d i r e c t i o n i n the crossed E and B f i e l d s and are returned to the cathode. They thus cannot leave the cathode. There are two major i n t e r e s t i n g points about t h i s phenomenon. The f i r s t i s that the i n j e c t i o n of charged p a r t i c l e s , very probably electrons by the t r i g g e r spark, i s the primary i n i t i a t i n g mechanism that leads to breakdown. The second point i s that eit h e r free electrons come from the t r i g g e r spark or that the plasma i n the t r i g g e r spark can be stopped by crossed E and B f i e l d s . The curve i n F i g 23 indicates that breakdown was i n i t i a t e d at the base of the d r i v e r by the t r i g g e r spark, when B<E/C. The phenomenon noted by Hart (1959), that breakdown occurred i n i t i a l l y at the open end of the d r i v e r , was thus not observed i n the present experiments. There are two possible - 51 -2 4 6 F i e l d c o i l current i n A. 8 10 F i g 23. Breakdown Time of the Driver shown i n F i g 19d. Argon i n shock tube at pressure of 160 microns Hg, 19.2^3? bank discharging from 8 kV. Break-down time of untriggered d r i v e r was 2.2./asec. explanations f o r t h i s discrepancy. A negative center electrode was employed i n the present work; Hart used a p o s i t i v e center electrode. Also a t r i g g e r spark was employed i n the present shock tube. When B> E/C, the preceding curve indicates that the t r i g g e r spark has no e f f e c t on the breakdown time. Possibly i n t h i s region of operation, breakdown does occur i n i t i a l l y at the open end of the d r i v e r , as,noted by Hart (1959). A t r i g g e r was i n s t a l l e d i n each of the drivers de-scribed i n Section 2 of t h i s Chapter with the exception of that shown i n F i g 17. The c i r c u i t f o r the t r i g g e r pulse generator i s given i n F i g 4. The t r i g g e r discharge r a i s e d the pressure i n the 1200 cm shock tube by 0.02 microns Hg. The amount of the contamination i n the plasma that could be d i r e c t l y a t t r i b u t -ed to the discharge of the t r i g g e r pulse was thus small. - 52 -5. DYNAMICS OP ELECTROMAGNETICALIY ACCELERATED PLASMA Introduction In t h i s Section expressions are derived f o r the motion of a plasma accelerated by electromagnetic forces. Numerous authors, f o r example Dattner (1959), Hart (1962), and Mostov, Neuringer and Rigney (1961), have considered t h i s problem. The published r e s u l t s are often given as a series s o l u t i o n to two coupled d i f f e r e n t i a l equations or, i n the case of Hart, as curves obtained with the aid of an analog computer. Neither form of presentation provides a c l e a r picture of the e f f e c t s on the dynamics of the plasma of a change i n the d i -mensions of the d r i v e r , the kind or pressure of gas employed, or the e f f e c t of a gross change i n the waveform of the d r i v i n g current. A closed form f o r x ( t ) , the displacement of the plasma as a function of time, could be used to predict the e f f e c t s of such changes. In the analysis that follows, closed forms f o r x ( t ) , x(t) and x(t) are derived. The analysis i s v a l i d f o r both the a c c e l e r a t i o n of a slug of plasma and the a c c e l e r a t i o n of a plasma gaining mass by a snowplow action. The closed forms f o r x ( t ) , x(t) and x(t) are obtained by assum-ing 'that l ( t ) , the d r i v i n g current as a function of time, i s known. Theory K i r c h h o f f s law f o r the current I from a capacitor C, i n i t i a l l y charged to voltage V Q, discharging into a s e r i e s inductance LQ,. s e r i e s resistance R Q and a d r i v i n g assembly of resistance R(I,t) and inductance per u n i t length of i s - 53 -^ ( ( L 0 . L , x ) l ] + | R . + R , ( i ^ ] l + ^ j l ( f ) « i e = V 0 6 o where x(t) i s the displacement of the plasma from the base of the d r i v i n g assembly. I t i s assumed that the d r i v i n g assembly has a constant inductance per u n i t distance t r a v e l l e d by the plasma. The coaxial d r i v e r shown i n Pig 19d possesses such an inductance as do also to a close approximation the other drivers shown i n Pigs 19 and those shown i n Pigs 11, 13, 17 and 18. When i t i s assumed that energy expended i n i o n i z i n g and heating the plasma can be included as a Joule heat term, the energy equation f o r the system i s where Y i s the voltage across the capacitor, mQ i s the i n i t i a l slug mass and m^  i s the mass increase of the plasma per uni t a x i a l length of the -electrode assembly. I t i s assumed that the advancing plasma entraps the gas i t encounters; thus the snow-plow model i s considered to be applicable. The Kerr c e l l photographs shown i n Pig 12 indicate that there i s v i r t u a l l y no shock-heated plasma i n front of the discharge during the a c c e l e r a t i o n period. The standard shock equations are therefore not applicable. A permeable snowplow act i o n can be included i n the model by s u i t a b l y choosing m^ . S i m i l a r l y the e f f e c t of contamination of the plasma by electrode material can be included by s u i t a b l y choosing mQ and m^ . I t i s further assumed that the plasma i s t h i n i n the d i r e c t i o n of motion, that current - 54 -flow i n the plasma i s perpendicular to both the d r i v i n g mag-ne t i c f i e l d and the d i r e c t i o n of plasma motion, and that no external magnetic f i e l d s are applied. Taking the time d e r i v a t i v e of equation 7, , noting that CV = - I , d i v i d i n g by I, subtracting equation 6, then i n -tegrating y i e l d s the momentum conservation equation f o r the plasma [m. + m,x( i ) ]x ( t ) - g(t) 8 . where § ( t ) = | L, [i{t)f 9 The analysis thus f a r i s s i m i l a r to that of Hart (1962) and of Dattner (1959). The method of s o l u t i o n of eq-uation 8 departs from that of other workers from t h i s point; onwards. I t i s of i n t e r e s t to solve equation 8 f i r s t without sp e c i f y i n g the form of the function g ( t ) . The s o l u t i o n when x(t=0) = 0 i s : „/ .x / m , 2 + 2 m , g ( t ) - mQ x(t) = 10 * ( t ) « 9 / m e 2 + 2m,g(t) 11 or ' ~ [m. J + 2 m , g ( t ) ] V a - 55 -2 .... .15 Defining t * as the time when maximum v e l o c i t y occurs X (t'j = 0 14 therefore [m.» + 2 W , g ( f ) ] § ( f ) = m . f j f t f j j or § ( t * ) = ^ . [ x f t * ) ] * .....16 Prom equations 10 and 11, x/^.*\ _ i/nOo 2* 2 n o , q ( t * ) - mnQ 1 ? 1 ' y M , « • 2 m , g ( f ) 18 Equation 18 i s equivalent to * { t > i g l , m , - o 2 0 The maximum v e l o c i t y i s a figur e of merit f o r an electromagnetically accelerated plasma. Therefore, equations 19 and 20 are of value f o r p r e d i c t i n g the maximum v e l o c i t y that can be obtained i n any p a r t i c u l a r constant cross-section e l e c t -romagnetic shock tube. I t i s of i n t e r e s t to compare the v e l o c i t i e s obtained by other authors with those predicted by equations 19 and 20. For example, the computer solutions given i n Hart's Pig 4 are e s s e n t i a l l y i d e n t i c a l to the values pre-dicted by equation 19. I t i s also of i n t e r e s t to compare equation 19 with the equation obtained by assuming that a shock model i s applicable rather than a snowplow model. Por example, the r e l a t i o n x = 1.1 A^L I can be obtained from the v rn, - 56 -analysis of Chang (1961). Several s p e c i f i c forms f o r g(t) w i l l now "be consid-ered,. Although only one current waveform, a sinusoid, i s of immediate importance, i t i s of i n t e r e s t to determine also the e f f e c t of other waveforms of d r i v i n g current on the dynamics of the ac c e l e r a t i n g plasma. In many plasma a c c e l e r a t i o n experiments L Q » L^d and R Q » R ( l , t ) , where d i s the distance that the plasma t r a v e l s during the f i r s t current pulse. Under these assumptions, equation 6 can be l i n e a r i z e d and the o s c i l l a t o r y s o l u t i o n i s then i ( t ) = i 0 e~ 4 t S i n to't 21 where & = R o / 2 L 0 , 6 J = / l 7 c - ? , * 0 = V . / c J L . The values of g ( t ) , g(t) and g(t) f o r s u b s t i t u t i o n into equations 10 to 12 are then •• /1 \ I | i-2 - 2 i " t . 2 i cj(t) = j L, I 0 e w t ; r CO I [ e - l 4 t ] i [ » s r ] 23 -ait'- r 24 The maximum v e l o c i t y and p o s i t i o n where the maximum v e l o c i t y occurs can be found from equations 17 and 18 a f t e r t * has been determined. A graphical s o l u t i o n of equation 15 f o r - 57 -t* i s given i n Pig 24 when the current waveform i s that of equation 21. The equation that i s solved g r a p h i c a l l y i s Pig 24. Time When Maximum V e l o c i t y Occurs i f the Dri v i n g Current i s Obtained from a Damped O s c i l l a t o r y C i r c u i t . Lot*(<* = o, * = o) = io8-9°. - 58 -I t i s to be noted that wt* does not vary greatly with changes i n <* when «*<!, In the graph of Pig 24 i t i s assumed that only the f i r s t current pulse i s operative i n acc e l e r a t i n g the plasma. This assumption has been v e r i f i e d experimentally by s h o r t - c i r c u i t i n g the coaxial d r i v e r of a shock tube at the end of the f i r s t current pulse and studying the x(t) c h a r a c t e r i s t i c s of the shock fr o n t . They were e s s e n t i a l l y i d e n t i c a l to the x(t) c h a r a c t e r i s t i c s obtained when the discharge was not crowbarred, thus confirming, at l e a s t under the conditions studied,' that only the f i r s t current pulse was operative i n generating the f i r s t shock. Quite simple expressions are obtained f o r x(t) and ±(t) when damping i s assumed to be n e g l i g i b l e during the f i r s t current pulse. Thus, assuming l i t ) - I „ s i n 6ot .... .26 r e s u l t s i n cj(t) = —• L, I0 2 s i n 2 601 2 ? q M - ^ L . I ^ V - s i n ' w t ] . . . . . 2 9 .2 , m - + L,I. 2 m, r , , , 2 * 2 - s i n 2 c o t ] _ m < x ( t ) = L|Ip \fj)j:. - s i n c u t c o s a ) " t ] 4 lo  1 J 31 And t * i s defined by the equation - 59 -t a n •&• -32 wheree-and JT are the var i a b l e s that were previously defined. In t h i s case, however, to i s defined by the r e l a t i o n t0 2L oC=1 . The s o l u t i o n to equation 32 i s presented as the <* = 0 curve i n Pig 24. Another current waveform that i s of i n t e r e s t as a possible shock-generating waveform i s that generated i n a c r i t -,2 i c a l l y damped c i r c u i t . Then o = 1/1 C and l i t ) « & t e - S t -2<£t 33 34 - 2 4 f 35 9 ( t ) " ALU' 2 4 I 2 4 1 36 The time when maximum v e l o c i t y occurs, t * , can be determined from the equation that i s obtained by s e t t i n g x(t) equal to zero: y f a e - ? = e " 2 f { . + 2 f - f - f J - f 4 A } + e - f { - 2 - 2 f + 2 f . f ] + i 37 where € =2dt and V = ° , V , . The s o l u t i o n to equation 37 i s given i n graphical form i n Pig 25. When f = 0, maximum vel-o c i t y .. occurs when <St* = 1.29 or l ( t * ) = 0.355 V . - 60 -fo 1 4 F i g 25. Time When Maximum V e l o c i t y Occurs i f the Dri v i n g Current i s Obtained from a C r i t i c a l l y -Damped C i r c u i t . Equation 8, the momentum conservation equation f o r the plasma, i s v a l i d not only f o r a d r i v i n g current generated by the discharge of a capacitor (see equations 6 and 7), but i s also v a l i d f o r d r i v i n g currents of unusual waveshape gener-ated by other c i r c u i t s . For example, Hart (1962) has suggested that a ramp waveshape of current may produce a high v e l o c i t y shock wave. Applying the above methods to a ramp waveform I(t)= r e s u l t s i n g( t ) = L , I 0 2 t 2 / 2 t 2 g ( t ) - L . l I t ' A t * 9 ( t ) « iXt'A^x' x( t ) * / m g a + m , L , I 0 2 t y i 2 r ,38 , 59 ,40 41 42 - 61 -» ( t ) _ [ L , I 0 2 t a / 2 t 4 ] [ m 0 a + m , L t I 0 a t y 3 6 T 2 ] |W + m . L . I o H V l Z T * ] * 4 •••••44 x(t) possesses no maximum value since x ( 0 £ t £ T ) 4 0. As i t i s probable that a sawtooth current waveform would r e s u l t i n the generation of one shock front for each current pulse, i t w i l l be assumed that the maximum v e l o c i t y occurs at the end of the f i r s t current pulse. Then x ( t - f - t ) = L | I ° X / b  / V + m 1 L 1 I . , r V l 2 45 One l a s t d r i v i n g current waveform w i l l be considered; I ( t ) ={ * 46 Then 1 ° > t < 0 x (t) = +rn,L,I 0 at a/2 - ™< rr), L , I 0 a t / 2 rr), /m. 8 + m ( L , I e a t a / 2 I t i s of i n t e r e s t to note that when mQ = 0, the v e l o c i t y of the plasma i s a constant x ( t , «.-o) = x(t*/3£m« ,«vo,w.>o)-^ I . .47 48 49 - 62 -A step waveform of current thus r e s u l t s i n a plasma v e l o c i t y of 1/0.946 (see F i g 24) that of a plasma accelerated by a sine waveform of current, when mQ = 0. The equations of motion f o r a plasma slug moving into a vacuum w i l l now be considered. The equations of motion are obtained from equation 8 by putting m^  = 0. x ( t ) = g ( t ) / n o 0 50 i ( t ) = .....51 5 c ( t ) . c j ( t ) / m 4 .52 The maximum v e l o c i t y of such a slug i s attained at the time when g(t) = 0, or l ( t ) =0. For the o s c i l l a t o r y cur-rent waveform the maximum slug v e l o c i t y i s attained when out* = TT , when we once more assume that only the f i r s t current pulse i s operative i n a c c e l e r a t i n g the plasma. For the c r i t i c a l l y -damped c i r c u i t , maximum slug v e l o c i t y i s approached as t-*"°°. Artsimovich et a l (1958) derived an equation f o r a slug being accelerated by an o s c i l l a t o r y undamped current wave-form. Their a n a l y t i c s o l u t i o n , which i s v a l i d f o r small time, i s i d e n t i c a l to that which can be r e a d i l y obtained from equation 50. They also solved, with the a i d of an analog computer, two equations s i m i l a r to equations 6 and 8. Their computer s o l -utions i n d i c a t e that the assumption made just p r i o r to equation 21, namely that L 1d<^L , can be stated more r i g o r o u s l y when m. =0, as * *-i x » « L e -1 m 0 t o a 0 F i g 26. V e l o c i t y of Plasma During Acceleration "by Various Waveforms of D r i v i n g Current. - 64 -A comparison of the e f f e c t s of the shape of the current waveform on ±(t) i s presented i n Pig 26. In the preceding analysis i t has "been assumed that the e f f e c t s of discharge contaminants (material eroded "by the discharge from the electrodes and i n s u l a t i o n i n the driver) can he included i n the analysis by s u i t a b l y choosing mQ and m^ . Starr and Naff (1960) found that the t o t a l mass i n a plasma that consisted of only discharge gases was proportional to the time i n t e g r a l of the square of the current. They indicated that the instantaneous mass i n the plasma was proportional to the time i n t e g r a l of the square of the current up to the time of measurement. Thus under t h i s assumption the momentum equa-t i o n f o r the ac c e l e r a t i n g plasma can be expressed as > x 2 J 53 where K = m f j _ n a ] _ / J I dt, mf^nai = "the f i n a l mass of the plasma at the end of the ac c e l e r a t i o n period, X - the time at which a c c e l e r a t i o n ceases. The s o l u t i o n to equation 53 when the d r i v i n g current i s the f i r s t h a l f cycle of a sine wave (equation 26) i s a L, I * TT X = Experimental Results The motion of the plasma during a c c e l e r a t i o n i n the coaxial d r i v e r s shown i n Pigs 19c to g could not be observed d i r e c t l y because the metal outer cyli n d e r prevented d i r e c t - 65 -detection of the plasma with the luminosity detector. An experimental value for the peak v e l o c i t y could, however, be calculated by extrapolating the x(t) c h a r a c t e r i s t i c observed for the decelerating plasma back to a p o s i t i o n of x = 10 cms (the approximate p o s i t i o n of maximum v e l o c i t y ) and then calcu-l a t i n g the v e l o c i t y at t h i s l o c a t i o n . When t h i s procedure was applied to the data presented as curve b i n Pig 28, the value ' Experimental = 3.5 cm/usec was obtained. The current waveform was the f i r s t h a l f - c y c l e of a sine wave i n which I = 200,000 A and£o= 1.34 x 10 rad/sec. An estimate of the amount of electrode material and other contaminants i n the plasma was obtained from the pressure r i s e i n the system caused by a f i r -ing. The pressure increased i n the 1200 cm shock tube from 160 - 5 to 195 - 5 microns Hg for a f i r i n g that was crowbarred at the f i r s t zero of the current. This pressure r i s e was that due to non-condensable vapors released by the f i r i n g , since a l i q u i d a i r trap removed the condensable vapors. The mass corresponding to t h i s pressure r i s e and an assumed mean mol-ecular weight of 40 was 104 /tg. When complete trapping of the gas encountered by the advancing current sheet was assumed to occur and when the mass contributed by the discharge, 104/*g, was considered to be deposited i n the plasma at a rate propor-t i o n a l to the distance that the discharge had t r a v e l l e d , then mQ = 0 and m1 = (0.213 + 1.04) x 10" 8 kg/cm. Prom Pig 24, the maximum v e l o c i t y occurred when u)t* = 108.9°. Prom equation 19 noting that L 1 = 1.4 x 10" 7 H/m, i t follows that x(t*)^ l i c Q r„ = 4.7 cm/ttsec. The discrepancy between the experimental and - 66 -t h e o r e t i c a l values of x ( t * ) could be resolved by considering a higher rate of contamination of the plasma by discharge materials. When the l i q u i d a i r trap was not on the shock tube, the pressure r i s e was higher than that obtained with the trap on. Also, a t h i n layer of material was appearing on the walls of the shock tube near the d r i v e r . The amount of electrode material i n the plasma at the time that maximum v e l o c i t y was achieved was thus larger than 104Ag. The v e l o c i t y of the plasma at x = 10 cms for the case presented as curve c i n P i g 28 i s 6.9 cm/asec. The pres-sure increased i n the 1200 cm shock tube from 0.1 microns Hg to 30 - 5 microns Hg. The mass of gases causing t h i s r i s e i n pressure, assuming a mean molecular weight f o r the gases of 40, was 89/*g. The maximum v e l o c i t y as predicted from equation 54 under the conditions of ^ = 1.4 i 10 H/m, I = .2 MA, 6 —R 1.34 x 10 rad/sec and m„. , = 8.9 x 10 kg was x,, „ ' f i n a l ° theory = 3.7 cm/// sec. I t i s apparent that the large amount of electrode material i n the plasma renders comparison of the experimental r e s u l t s With the t h e o r e t i c a l predictions quite d i f f i c u l t . The oscillograms shown i n Pig 27 of f e r i n d i r e c t confirmation of the large amount of contamination i n the plasma. The distance over which acce l e r a t i o n should have occurred, according to the above theory, f o r a f i r i n g i n which PQ= 160 microns Hg, no electrode 0 -7 contamination present,co = 1.34 x 10 rad/sec, = 1.4 x 1 H/m, L Q = 2-9 nH, I = 200 kA, no damping, was 10 cms., The value of L,|d was therefore 14 nH. Thus for t h i s case the c r i t e r i o n - 6 7 -zoo loo a) Pig 27. Typical Oscillograms of Current i n Driver of Shock Tube, a) I n i t i a l pressure = 1000 microns Hg. h) I n i t i a l pressure = 160 microns Hg. c) I n i t i a l pres-sure = 0.1 microns Hg. The 19.2//P hank was d i s -charged from a p o t e n t i a l of 8 kV, the d r i v e r was the small cathode driver shown i n Pig 19f, the gas i n the shock tube was argon, the switches contained nitrogen at a pressure of 20 microns Hg and the driver was crowharred at a time that resulted i n the u n i d i r e c t i o n a l current pulse that i s shown. for the a p p l i c a b i l i t y of the above theory, I ^ d « L Q , should not have been s a t i s f i e d . The current waveform should, therefore, have been appreciably d i s t o r t e d by the e f f e c t s of the time-vary-ing inductance of the c i r c u i t . The oscillograms i n Pig 27 show that there was no difference i n the current waveform when the pressure i n the shock tube was varied from 0.1 to 1000 microns Hg. A large amount of contamination i n the plasma would account f o r the observed independence of the pressure i n the shock tube on l ( t ) . - 68 -Discussion • I t has been assumed throughout the present Section that the d r i v i n g forces on the plasma are p r i m a r i l y e l e c t r o -magnetic forces rather than forces caused by the expansion of a Joule-heated gas. Mechanisms such as f r i c t i o n a l energy losses, r a d i a t i v e energy losses and thermal conduction losses have also been neglected. The approximate agreement between the t h e o r e t i c a l and experimental v e l o c i t i e s (see also Hart 1962) i n d i c a t e s that the neglect of these a d d i t i o n a l energy tran s f e r mechanisms i s j u s t i f i e d , at l e a s t .under the experi-mental conditions studied. A more complete analysis i s not j u s t i f i e d because the e f f e c t s of the large amount of contamin-ation i n the plasma are i n s u f f i c i e n t l y known. A major conclusion i s that the plasma generated by the small cathode drivEr shown i n Pig 19f contains considerable electrode material. The t h e o r e t i c a l analysis' indicates that the amount of t h i s material could be lessened by decreasing the .period of the d r i v i n g current. 6. DYNAMICS OP THE DECELERATING PLASMA Introduction Various workers have observed that the deceleration of the plasma a f t e r the d r i v i n g current has ceased flowing can be represented by fi x oc t p .... .55 D i f f e r e n t workers have assigned values to the parameter {3 which are independent of x or t. One of the objects of the - 69 -present Section i s to show that such an assignment i s v a l i d only over a l i m i t e d range of x or to Kash et a l (1958) obtained a value 0.667 at an i n i t i a l pressure of under 100 microns Hg and |3= 0.4-17 at an i n i t i a l pressure of 10 mm Hg. Bershader (1960) states that the former figu r e i s i n agreement with b l a s t wave theory and Harris (1960) derives the value f? = 0.667 on the basis of hydrodynamic theory. Bershader (1960) c i t e s data of other workers who have obtained (3-1 at pressures i n a i r of under 100 microns Hg i n a x i a l discharge tubes of diameter 3 to 6 i n . Cormack (1960) obtained @= 0.48 f o r a T-tube driven shock passing through argon i n i t i a l l y at 500 microns Hg pressure, P - 0.79 f o r a coplanar driven shock i n helium at 300 microns Hg pressure and jS = 0.61 f o r a coplanar driven shock i n argon at 1000 microns Hg pressure. I t i s apparent that the dependence of ^ on various parameters should be c l a r i f i e d . Experimental data i s presented i n t h i s Section that shows that the value of the parameter (3 decreses as the plasma tra v e l s down the tube. The experimental value of (S i s shown to depend on the i n i t i a l pressure i n the tube and the time of observation. An empirical r e l a t i o n i s f i t t e d to the data.and i s discussed i n terms of a proposed model. According to t h i s model, (9 depends upon the i n i t i a l pressure i n the tube, the d r i v i n g mass, the time of observation, energy losses from the plasma and the i n i t i a l momentum of the plasma. Experimental Data The data presented i n Pigs 28 and 29 were obtained with the luminosity detector that has been described i n Chapter - 70 -II , Section 4, i . The time of the a r r i v a l of the f i r s t de-tectable luminosity front (but not that due to precursor radiation) measured r e l a t i v e to the onset of d r i v e r current, i s designated t. The a r r i v a l time was measured as a function of the distance x down the shock tube from the base of the d r i v e r . The experimental curves shown i n Pig 28 have values of (3 from .44 to .86. In p a r t i c u l a r , curve b) shows that the value of {3 decreases from .81 to .53 over the range of x = 30 cm to x = 80 cm. The increase at constant time t i n the value of 3 due to a decrease i n the i n i t i a l pressure i n the tube i s also evident. x cm 80 70 60 50 40 30 20 5 b) a) > e) _ t, /jl sec Pig 28. x(t) Data f o r Decelerating Plasma, a)Small cathode dr i v e r , Pig 1°,f, i n i t i a l pressure 1 mm Hg, b)Small cathode d r i v e r , Pig 19f, i n i t i a l pressure .16 Hg, c)Small cathode driver^ Pig 19f> i n i t i a l pressure .1 micron Hg, d)Coaxial d r i v e r with non-smooth anode, Pig 19c, i n i t i a l pressure .16 mm-Hg, e) Driver with disc--anode,, Pig 19e, i n i t i a l pressure .16 mm Hg.-All d r i v i n g currents were crowbarred -at the end of the f i r s t current pulse. - 71 -The s t r a i g h t l i n e s that are f i t t e d to the data i n F i g 29 s a t i s f y the equation t/x = Rx/2P + S/P 56 where P, R and S are parameters that w i l l he discussed i n the following section. The values of P, R and S do not depend on x or t. t/x 1 .2 ^sec/cm 1 .0 ,8 0 a) / - ^ ^ ^ ^ ^ ^ i ^^ ^^ ^ ^ - * * e ) *~ c) "** 0 20 40 x, cm 60 80 F i g 29. Graphical Determination of Parameters i n Propaga-t i o n Equation f o r Decelerating Plasma.a) to e) designations are explained i n F i g 28. - 72 -Theory-Equation 56 i s equivalent to the d i f f e r e n t i a l equa-t i o n (S + Rx)x = P .... .57 In a simple i n t e r p r e t a t i o n , P can he considered to be the momen-tum of the plasma when x = 0 and S the mass of the plasma when x = 0. This mass, which w i l l be designated m , i s not the true mass at x = 0 but rather i s the mass that the plasma would have possessed at x = 0 i f i t had been decelerating over the range 0 £ x $ 30 cms according to the same equations that applied over the range 30 cmsS xS 80 cms. Again, i n a simple i n t e r -pretation, R would be the mass i n f l u x to the plasma per unit of distance t r a v e l l e d . Curve c i n Pig 29 should be a s t r a i g h t l i n e with e s s e n t i a l l y zero slope according to t h i s i n t e r p r e -t a t i o n . Since the slope i s appreciable, the above i n t e r p r e -t a t i o n f o r R i s not s t r i c t l y v a l i d . A more r e a l i s t i c i n t e r -p r e t a t i o n f o r R i s that i t i s the mass i n f l u x to the plasma per u n i t of distance t r a v e l l e d plus the drag on the plasma per unit of d(xx)/dt. Denoting the l a t t e r qunatity as m^  and the former as m^  leads to: {n0o + [nr>, +nn d]x]x = P 58 The parameter m^  i s r e l a t e d to energy losses from the plasma. The quantity m^  i s assumed to be the mass of the gas i n i t i a l l y f i l l i n g the, tube per u n i t length of the shock tube. A complete snowplow ac t i o n i s thus assumed to take place. , The s o l u t i o n to the preceding equation i s Jm* + 2p*>t mcj]Pt - rY)o X — — — — — — _ M _ mj + m,! 59 - 73 -or i n a form that i s usefu l f o r data reduction t / x = {nn, +m ( 1]x/2P + w 0 / P .....60 Equation 59 can he approximated by x ^y2Pt/m,i-mj| 1 2P(m,+ m d } t > > ™ 2 .„.„ 61 o o o o e O 2 The proposed model thus predicts that the value of |S i n equa-t i o n 55 can be between 0.5 and 1 depending upon the time of observation, the mass per u n i t length of the gas i n i t i a l l y i n the shock tube, the d r i v i n g mass at x = 0, the momentum of the plasma at x = 0 and the energy loss parameter m^ . The proposed model f o r the decelerating plasma i s pictured i n Pig 30. The energy loss parameter m^  i s i n t e r p r e t -ed i n t h i s f i g u r e as being due to loss of p a r t i c l e s v i a the boundary la y e r and loss of i n t e r n a l energy of the plasma by both heat conduction to the walls and r a d i a t i o n losses from the plasma. A mechanism that i s not shown i n Pig 30, but that might be operative, i s d i f f u s i o n of the shock-heated gas through the d r i v i n g gas. The r e s u l t s that have been discussed i n Chapter I I I , Section 1 in d i c a t e that the structure of the luminosity of the plasma that can be d i r e c t l y a t t r i b u t e d to the d r i v i n g discharge stays extremely close to the shock f r o n t . A large flow of the shock-heated gas past the d r i v i n g gas must thus occur. This flow could occur both through the boundary layer between the d r i v i n g gases and the walls of the shock tube, and through the body of the d r i v i n g gas. The flow through the boundary layer has been considered by Hooker (1961). - 74 -v e l o c i t y ?0 3|gS£_..g&SeS _ ~. mp y^g-rw i t h 'n^63^3City ! i . > near-equilibrium shock- j ^J-sj ©< v e l o c i t y < x r a d i a t i o n h ted gas non-equilibrium shock-heated gas Pig 30. Proposed Model f o r Decelerating Plasma i n Shock Pront-Pixed Coordinates. Analysis of Experimental Data The values of the variables given i n Table 1 were obtained by f i t t i n g equations of the form of equation 60 to the data i n Pig 29. Case m. + m, d P 2 /csec/cm V/ P /tsec/cm m o / m 1 + m d cm Driver I n i t i a l Pressure microns Hg a) - - - small area cathode,Pig crowbarred 19f, 1000 b) .0056 .230 41 .1 small area cathode,Pig crowbarred t9t, 160 c) .0018 .127 70.6 small area cathode,Pig crowbarred 19f, 0.1 a) .0058 .133 22.9 coa x i a l , P i g crowbarred 19c, 160 e) .0050 .223 44.6 d i s c , P i g 19e crowbarred > 160 Table 1. Results of Analyzing Deceleration Data. - 75 -The experimental data f o r case a) (see F i g 29) could hot he f i t t e d to a function of the form of equation 60. The increasing slope of curve a) i n F i g 29 with increasing x indicates that m^  + m^  increased with x. A possible explana-t i o n f o r t h i s anomalous behaviour was suggested by the shape of the s i g n a l observed with the luminosity detector. At x = 80 cm, a pronounced spike of luminosity preceded the main si g n a l by ~4 mm. Also, the main sign a l rose to a peak value at a considerable distance, ~5 cms, l a t e r . This spike of luminosity was probably due to r a d i a t i o n from impurities at the boundary between the wall of the shock tube and the shock fr o n t . The important point i s that the region of n o n - e q u i l i -brium shock-heated gas (Fig 50) was ^ 4 mm in, length.and the near-equilibrium shock-heated gas was very probably several cms i n length. A spike of luminosity preceding the main s i g n a l was never observed at eith e r lower pressures or at higher v e l o c i t i e s . Also m^ + m^  was independent of x f o r cases b) to e). I t i s thus indicated that case a) d i f f e r e d fundamentally from the others. The probable cause f o r the difference was that i n case a) a true shock front formed i n f r o n t of the dri v e r gases and that the energy of the shock-heated gas was the dominant energy i n the plasma rather than the energy of the d r i v e r gases. The model shown i n F i g 50 would thus not 'be applicable f o r case a) since i t was assumed i n t h i s model that the energy of the d r i v e r gases predominated. The impurity s p e c t r a l l i n e s observed i n the r a d i a t i o n emitted by the plasma confirm that d r i v e r gases are present. - 76 -This evidence supports the v a l i d i t y of the model drawn i n F i g 30, i n which only a small region of shock-heated plasma i s shown. Further evidence f o r the "slug" structure of plasma drawn i n F i g 30 i s provided by the oscillograms i n F i g 21 i to' a. Rockman (1961) found that the v e l o c i t y of the lumin-o s i t y f r o n t was predicted f a i r l y accurately by b l a s t theory ( P = 0.667) i f a f i c t i t i o u s o r i g i n f o r x was chosen. Rockman employed an electrodeless d r i v e r to produce hi s plasma and was thus not concerned with a large amount of discharge gases, as has been the case with the experiments here. In the present Chapter several i n v e s t i g a t i o n s into the properties of the plasma produced i n an em shock tube have been described. These in v e s t i g a t i o n s have indicated that the plasma that has been produced i s not s u i t a b l e for d e t a i l e d spectroscopic studies. The plasma i s , however, good enough to be used f o r t e s t i n g magnetohydrodynamic power generators. - 77 -CHAPTER IV MAGNETOHYDRODYNAMIC POWER GENERATION 1. SOME PROPERTIES OF AN ELECTRODE-TYPE B^. MAGNETOHYDRODYNAMIC POWER GENERATOR Introduction The majority of workers who have investigated the properties of MHD power generators have considered the Car-te s i a n geometry of generator shown i n F i g 31. In t h i s con-f i g u r a t i o n the current i s c o l l e c t e d v i a p a r a l l e l plates which are i n e l e c t r i c a l contact with the plasma. h F i g 31. The Conventional Cartesian MHD Generator. Less commonly considered geometries are the disc and coaxial types shown i n F i g 32. In the coaxial type ?power i s generated by the H a l l current. Power i s generated i n the disc generator by the conduction current, Rosa (1961) discusses the geometries shown i n Figs 31 and 32 and concludes that the F i g 32. The Disc and the Coaxial MHD Generators. Cartesian form has the bettnr c h a r a c t e r i s t i c s , f o r the follow-ing reasons. The f i r s t reason i s that the Cartesian form w i l l operate at any value of cOT(&>= electron cyclotron resonant frequency,X- average free time of an electron i n the gas), since , i t can he connected to give a power output from either the H a l l current or the conduction current, or from hoth cur-rents. Secondly, v a r i a t i o n s i n conductivity ((f ) and 60 X, which occur as the gas expands and cools, can he r e a d i l y accounted f o r since there exists a r e l a t i v e l y high degree of decoupling between the upstream and downstream parts of the flow when the Cartesian form i s operated as a conduction-current generator. Such features as v a r i a b l e cross-section and segmented "electrodes can be used i n t h i s type ,of generator to control v a r i a t i o n s i n 0", V (flow v e l o c i t y ) and cOZ, These two advantages,discussed by Rosa (1961) i n favour of the Cartesian geometry over the disc or coaxial type are also inherent i n the B^. MHD generator shown i n Pig 33. This - 79 -p a r t i c u l a r configuration has not previously "been considered by other workers. Pig 33. The B^. MHD Generator. The object of t h i s section i s to determine the e l e c t r i c a l c h a r a c t e r i s t i c s of the B^. MHD gensrator and, to compare i t s properties with those of the more conventional Cartesian form. The E l e c t r i c a l Equations of the Cartesian MHD Generator As the major i n t e r e s t i s i n the order of magnitude of the va r i a b l e s appearing i n the e l e c t r i c a l equations, the following s i m p l i f i e d analysis should s u f f i c e . I t i s assumed that l i t t l e of the flow energy i s extracted and thus that the v e l o c i t y of the plasma i s constant through the generator. Then,.Ohm's Law f o r the conduction current flowing through the conventional MHD generator shown i n Pig 31 i s J , o r [ E + U x B ] _ . . 6 3 When edge e f f e c t s and sheath p o t e n t i a l s are neglected, the e l e c t r i c f i e l d between the electrodes i s - 80 -| = ~T 1° and the current through the plasma i s I a uzti or .... 64 .... 65 From equations 63 to 65: I = a-hi, (vB - v/s} V = sirB - sl/fl-h-t, .. 66 The equivalent c i r c u i t i s therefore that of F i g 34. WV o s v 8 6 F i g 34. The Equivalent C i r c u i t f o r the S i m p l i f i e d Cartesian MHD Generator. The preceding o v e r - s i m p l i f i e d analysis could be made more r e a l i s t i c . Such complicating f a c t o r s as a decrease i n the v e l o c i t y of the plasma or a variable c r o s s - s e c t i o n a l area (to obtain a constant plasma v e l o c i t y ) could be included (Harris 1960). S i m i l a r l y , the e f f e c t of a tensor conductivity could be included (Hurwitz, K i l b and Sutton 1-961). Smy (1961) has considered the generation of a l t e r n a t i n g current by such - 81 -a generator, and Pain and Smy (1960) have considered the e f f e c t of modification of the applied magnetic f i e l d "by the f i e l d due to the induced current i n the plasma. The E l e c t r i c a l C h a r a c t e r i s t i c s of the B^. MHD Generator The model that i s considered i s shown i n Pig 35. The inductance of the load c i r c u i t i s considered to be low i n order that the high frequency response of the generator can be determined. A t h i n disc of plasma of thickness A moving with constant v e l o c i t y v i s considered to pass through the MHD generator. Plasma i n s t a b i l i t i e s are neglected. The load i s considered to be a r e s i s t i v e disc at the base of the gen-erator. X = v t • velocity V z z \ K Re s i'S t iVe ^ *» ' (Re) Pig 35. A Low Inductance B~ MHD Generator. Charge de n s i t i e s and displacement currents w i l l be neglected. The e l e c t r i c f i e l d i n t e n s i t y and current i n the plasma w i l l be assumed to have only r a d i a l components. I t i s implied by t h i s assumption that H a l l currents and edge e f f e c t s on the f i e l d s are neglected. The existence of non-radial com-- 82 -ponents of both the e l e c t r i c f i e l d i n t e n s i t y and the current i n the plasma w i l l depend upon the boundary conditions that e x i s t at the i n t e r f a c e between the plasma and the electrodes. An analysis that includes the e f f e c t s of the a x i a l components of e l e c t r i c f i e l d i n t e n s i t y and current i n the plasma would be too involved to be of immediate i n t e r e s t . The r a d i a l e l e c t r i c f i e l d i n the plasma E p ( r , f , t ) can be expressed as E p ( r , f , t ) = E ( j f , t ) / r . S i m i l a r r e l a t i o n s are v a l i d f o r the r a d i a l current density J p ( r , f , t ) i n the plasma and the azimuthal magnetic induction f i e l d Bp(r,^,t) generated by plasma currents. I t i s assumed that (rv/c0A« I . The applied magnetic f i e l d B ( r , t ) i s thus independent of f. The value of , the plasma conductivity, i s independent of the magnetic induction f i e l d s since H a l l currents have been neglected. S p a t i a l coordinates are defined i n Pig 35. Equation 63 67 and Ampere's Law, 57 " A> Jf 68 Vt. I f ~ 3 f 9 ? 69 Prom Faraday's Law i t follows that I.R A + V e + E p o ( ? t ) U a A , = ~itfB^^ + d a region PQRS ^ where V i s the sum of the sheath p o t e n t i a l s and I. i s the e ^ 1 current into the load ( i = induced). The i n t e g r a l in,equation 70 can be evaluated by considering the regions PQTU and UTRS - 83 -(Pig 35) separately. Then PQRS ? •••••71 D i f f e r e n t i a t i n g equation 70 with respect to j$ and equation 71 with respect to t then f y i e l d s O 9 • • • 7 2 and s u b s t i t u t i n g t h i s into equation 69 gives _!_ 3 a B p . u , t ) = v 3 B P , ( g , t ) + 3 B P o ( t t ) , a a . t t ) *s*o dez 9e c2t 3 t ' • • • • © f .2 Noting that I (t) = 2TT / Jpe(f,t)«lf , B p o ( ^ t ) = J"P<> ( 2 , t ) c l £ and B (t) =/Z e T a ( t ) / 2 I T , then equations 67, 70 and 71 can be combined to give ^ /4 VA.T.K-V!, _ I„A,A, f i. (t) r B , ., /• / ?8„fet) + v e * i ^ { L ( r r » 74 The steady-state s o l u t i o n to equation 73 f o r the model shown i n Pig 35 i s (since B p Q ( f = 0) = 0 and B T ) Q( f = A) 2-rr po B P . (?)=A„I,{e""-'-, Equation 74 now has the steady-state s o l u t i o n TT * * 2TT which,-isince GVjU0A « I , s i m p l i f i e s to 75 e - 1 76 TT x1^ 2TTC"A .77 84 -\v\A.,/a.x 2TT <rA - W — Potential Drop = ° ,hf*. 5LTT . i " J ' 5^ I , Ibstihelcol yUXBJ-*- Inductance = M b* ' o p j - v - j p - ' M u t u a l o n o f h ^ A - i A j . a) Time-Dependent C i r c u i t prmr^ lKe|ucta«te I h A t / A , 1TTCTA - A V — -tit) _ fVe^" {reg ion bouMelecl a i d X«i , a Hoi K £\i A t TT b) Steady-State C i r c u i t , Plasma Disc Traversing Generator Pig 36. The B^ , MHD Generator Equivalent C i r c u i t The steady-state s o l u t i o n to equation 73 f o r a stea d i l y - f l o w i n g plasma passing through the generator i s • 78 • 79 and equation 74 then has the steady-state s o l u t i o n An estimate of the response time of the generator shown i n Pig 35 can be obtained by assuming that equation 75 i s v a l i d even when = I^-(t). Then equation 74 y i e l d s when I (t) = I and crvu0A «l 7T E A V ' L * 2TTiT/\ 5 2TT I 3 J i • • « o30 - 85 -which has the s o l u t i o n TT ve f *•* + 2TT0-A 3 v a o » • 3 1 Thus the current into a s h o r t - c i r c u i t termination when J » A/3 and when V i s neglected i s e D X i ( R l B V e » o , t) = 20-LTAoA 82 The steady-state current that could he obtained from a generator containing a ste a d i l y - f l o w i n g plasma i s found from equation 79 to be T . a i r P. + which f o r the assumptions YQ = R^  = 0, reduces to the follow-ing expression C I ^  ••.••84 The assumption about magnetic Reynold's number, that 0"U-/4oA « 1, appears to be the major reason why the output current i s predicted to be small f o r the generator tested on the shock tube (equations 76,77 and 82). The reason why t h i s assumption, was introduced was to take advantage of the simple r e l a t i o n B Q ( r , t ) = /i0Ia(t)/2TTr. When crvjJ.0A <{; 1, f i e l d a a compression ahead of the plasma and f l u x transport by the plasma would a l t e r t h i s simple r e l a t i o n . A s i t u a t i o n can be envisaged when B ( r , t ) V t f l (t)/2 tt r . For example, i n the case of the plasma disc (with cns/^A > 1) approaching the base of the genera-tor, equation 76 predicts a value of 1^ that i s too small. S i m i l a r l y , equations 79, 81 and 84 under c e r t a i n conditions - 86 -predict values of I^(t) that are too small i f R^ > 1. The steady state value of 1^ (equation 83) can thus he very large when R^ > 1 . The p o t e n t i a l l y large output current that can he obtained from the B^. MHD generator when R^ > 1 i s due to the f l u x a m p l i f i c a t i o n c h a r a c t e r i s t i c of the generator. The magni-tude of the induced current i s increased by i t s own magnetic f i e l d u n t i l the equilibrium condition expressed by equation 83 i s reached. The process of a m p l i f i c a t i o n i s s i m i l a r to that which has been considered by Kolm and Mawardi (1961) i n the Hydromagnet. This device d i f f e r s from the B^. MHD generator i n that i t has a B^ f i e l d and a r a d i a l flow v e l o c i t y . According to Rosa (1961), Y &8 v o l t s . However, according to Smy (1961), ion bombardment at high current den-s i t i e s heats the cathode to a s u f f i c i e n t l y high temperature to r e s u l t i n a n e g l i g i b l e electrode p o t e n t i a l drop. In the B^ . MHD generator, the electrode p o t e n t i a l drop may impose a serious l i m i t a t i o n since the voltage generated i s qu^te low. For a t y p i c a l case of v = 10^ m/sec, \r\Kj\= 1 , 1 = 10 A, then ,02 v o l t s 2TT Obviously, the B^. MHD generator w i l l not function unless V g < .02 V. Experimental work could v e r i f y wnether such a low value f o r V e i s obtainable. Again, one way of surmounting t h i s d i f f i c u l t y , i f a current supply capable of generating a very large I i s not a v a i l a b l e , could be to pass the e x c i t i n g cl current I down multiple wires imbedded i n a tubular central cl conductor as shown i n Pig 37. Then f o r n wires, the generator - 87 -voltage V i s given by Pig 37. A High Voltage B^. MHD Generator. Comparison of E l e c t r i c a l C h a r a c t e r i s t i c s of the Two Generators When transient e f f e c t s and electrode contact po-t e n t i a l e f f e c t s are neglected, the e l e c t r i c a l formulae shown i n Table 2 are applicable f o r the case of a s t e a d i l y flowing plasma. V g R g P m a x (occurs when H g=B^) v o l t s ohms A n c (Y )2 = 0.25 ±_j*L_ w a t t s g Cartesian S v B s/arlnl, 0.25sarhl,{v&} 2ir « r { e " ^ . } L J Table 2. Comparison of dc E l e c t r i c a l Formulae f o r the Cartesian and the BA MHD Generators. For a shock tube application' i n which cfxrji0£ = 2, - 88 -h = .02 m, 1=.1 m, B = 1 weber/m2, n l = 104", C = lO^mhos/m,, S = 0.02 m, IT= lO^m/sec, \nAi/\= 1, then the dc character-i s t i c s shown i n Table 3 are v a l i d . R P g g max Cartesian 200 v o l t s 10" 5 ohms 10 Mw 20 v o l t s .31 x 10~5ohm:s 0.32 Mw Table 3. Predicted Shock Tube dc B MHD Generator C h a r a c t e r i s t i c s . For a dC'-high power a p p l i c a t i o n i n which C T V / i ^ t - 2, <T= 10 2 mhos/m, S = 0.2 m, h = 0.2 m, i , = 5 m, B = 1 W/m2,, n l & = 10 6, V= ^Q^> m/sec, \V%A^/A.X= 1, then the e l e c t r i c a l c h a r a c t e r i s t i c s are as shown i n Table 4. V R P g g max Cartesian 200 v o l t s 2 x 10~ 5 ohms 5 Mw 200 v o l t s .31 x 10~ 4 ohms 320 Mw Table 4. Predicted High Power dc B^ . MHD Generator C h a r a c t e r i s t i c s . The object of presenting the above comparisons i s to show that the B^. generator does have s i m i l a r e l e c t r i c a l c h a r a c t e r i s t i c s to the Cartesian generator. The differences are worthy of note. For example, the lower resistance of the B^. generator presents some d i f f i c u l t y in the matching of the - 89 -generator to a load. This d i f f i c u l t y could he surmounted Toy employing a s u i t a b l y designed rotary converter which acts e s s e n t i a l l y as an impedance matching device. The low r e s i s t -ance of the B e generator may also cause d i f f i c u l t i e s with the transient response i n , f o r example, an ac B.Q. MHD generator, A l t e r n a t i n g power could be obtained from a plasma flowing s t e a d i l y through a B^. generator by e x c i t i n g the generator with a s i n u s o i d a l l y varying I ( t ) . a Discussion H a l l current has been neglected. A c t u a l l y , i t should be possible to extract and use t h i s current by employing segmented electrodes as shown i n F i g 38. The p r i n c i p l e would be s i m i l a r to that which has been proposed by Rosa (1961) to extract the H a l l current from a Cartesian generator. H W h u 7 / 7 "sIe««J«t», t S3 3 -^Cemol. (b) F i g 38. E x t r a c t i o n of MHD H a l l Current. a) Cartesian MHD Generator with Segmented Electrodes. b) B^ MHD Generator with Segmented Electrodes, - 90 -Ohm's Law i n the form used "by Rosa (1961) i s : 86 The l a s t term i n t h i s equation represents the H a l l current flowing i n the plasma. Its importance i s about the same i n both the B.Q. and Cartesian generators since both Can be con-nected to extract the H a l l current (which becomes large when CJX > 1). F i g 38b shows the B^. generator connection that could be used to extract the H a l l current. M u l t i p l e segments could also be used but would require multiple loads, or a f a i r l y complicated design of rotary convertor. comparison to the Cartesian generator i s the r e l a t i v e freedom from eventual shorting between the electrodes due to the deposition of a conducting l a y e r on the i n s u l a t i o n between the electrodes. One geometry that would e x p l o i t t h i s advantage i s shown i n F i g 39. One major advantage that the B^. generator has i n B MHD generator ou t l e t 8*. r cooled region (to lessen cooled region i n l e t deposition) to load < i F i g 39. A Method fo r Lessening Insulator Deposition Problems. The analysis that has been presented has been f o r a plasma having a constant flow v e l o c i t y through the B^. generator. The amount of the power extracted that i s shown i n Tables 3 and 4 could be large enough to appreciably a l t e r t h i s flow v e l o c i t y . These values of output power would be reduced i f the flow v e l o c i t y decreases through the generator. Experimental Results The B^. MHD generator shown i n F i g 40 was i n s t a l l e d on a shock tube powered by the d r i v e r shown i n F i g 19c. The load on t h i s generator was a brass disc, which constituted e s s e n t i a l l y a s h o r t - c i r c u i t termination f o r the generator. This s h o r t - c i r c u i t termination should have resu l t e d i n a large output current. A t y p i c a l s i g n a l induced i n the B^. magnetic probe at the base of the generator i s presented i n F i g 41. The p o l a r i t y of t h i s s i g n a l was inverted when the probe was rotated 180°, thus confirming that a magnetic rather than an e l e c t r i c s i g n a l was being observed. •Lucite , at brass magnetic probe —s. •87 — cm 21 cm-/ zfc F i g 40. Construction of B^ MHD Generator. - 92 -The signal that appeared at t = 35/«sec was probably caused by contact of the plasma with the ce n t r a l rod. Smy* has suggested that t h i s i n i t i a l s i g n a l i s due to a discharge that occurs between the rod and the charged plasma. The base of the generator was connected to an earth connection v i a the osc i l l o s c o p e . The p o l a r i t y of the i n t e g r a l of the f i r s t s i g n a l conforms with that expected f o r the current that would be generated by a p o s i t i v e l y charged plasma discharging to earth v i a the ce n t r a l rod of the MHD generator. 1 1 -T 35/t sec . 0 1 V 5 Asec Pig 41. Typical Signal Induced i n Probe at Base of B^ . MHD Generator. The signal that appeared at a time of about 55.5 A sec had one very i n t e r e s t i n g c h a r a c t e r i s t i c . The time of a r r i v a l of t h i s s i g n a l could be a l t e r e d by changing the e x c i t i n g cur-rent of the MHD generator. For example, designating the d i r -ection of the e x c i t i n g current shown i n F i g 40 as p o s i t i v e , and the time between the a r r i v a l of the signals shown i n F i g 41 * The author i s g r a t e f u l f o r r e c e i v i n g t h i s suggestion from P.R. Smy, Physics Dept., Un i v e r s i t y of B r i t i s h Columbia. - 93 -as the t r a n s i t time of the plasma through the generator, then f o r E x c i t i n g = 9 0 A> t r a n s i t t i m e = 22.5/*sec; f o r I e x c l t i n g = 0 A, t r a n s i t time = 20 = 5 /laec; f o r I e x c j _ - t j _ n g ~ - 1 2 5 A? t r a n s i t time = 17-5 /4.sec. The i n t e n s i t y of the azimuthal magnetic f i e l d at the inside surface of the outer electrode of the MHD generator, computed f o r an a x i a l current of 200 A flowing down the central rod, i s 31 gauss. The magnetic Reynold's number i n the plasma was of the order of 5, so that an azimuthal magnetic i n t e n s i t y of the order of 150 gauss could be i n the plasma by the time that the plasma was approaching the base of the generator. The magnetic pressure associated with a f i e l d of 150 gauss i s 2 2 B /2/4.0 = 180 newtons/m . The pressure, , immediately behind a strong shock moving with v e l o c i t y X through a gas having -2 5/3 i s 3/4j00^±) w h e r e i s the density of the undisturbed 4 gas i n front of the shock. Thus i f a shock of v e l o c i t y 10 m/sec propagates into argon at an i n i t i a l pressure of 160 microns Hg, then f>0 = 3.96 x 10"^ G/m5 and P =2980.0: newtons/m2. The magnetic pressure i n front of the shock i s s u f f i c i e n t to slow the plasma. A magnetic pressure ahead of the shock, however, could not account f o r the observed dependence of the t r a n s i t time on the p o l a r i t y of the e x c i t i n g current, A mag-neti c i n t e r a c t i o n of the type shown i n Pig 42 could. In Chapter I I I , Section 3, the transport of a trapped magnetic f i e l d ' i n the plasma was noted. At high values of magnetic Reynold-':s number, the current sustaining t h i s trapped f i e l d could i n t e r a c t with the azimuthal f i e l d generated by the - 94 -e x c i t i n g current of the MHD generator and produce a net force against the plasma. Whether t h i s force would act to decrease or increase the deceleration of the plasma would depend upon the d i r e c t i o n of flow of the e x c i t i n g current. • o / m / — J plasma ex c i t i n g Pig 42. A Magnetohydrodynamic Interaction that Could A l t e r the V e l o c i t y of the Plasma. An order of magnitude estimate of the value of the transported po l o i d a l current density J i n the plasma can be obtained by considering the a l t e r a t i o n to the propagation equation that would r e s u l t i f a force of magnitude (^XB) V acts against the plasma. The azimuthal magnetic i n t e n s i t y B that d i f f u s e s into the front of the plasma i s produced by the generator e x c i t i n g current. V i s the volume of the plasma being subjected to the volume force JXB. The equation f o r conservation of momentum i s K'fr^-vfcls - p * - f t I * § d t 8 7 x Q i s a unit vector i n the x d i r e c t i o n , and other variables have i d e n t i c a l meanings to those employed i n equation 58. Thus, assuming that J * J ( x , t ) , V * V(x,t) and B 4 B(x,t), and dropping - 95 -vector notation, since a l l terms represent vectors i n the x d i r e c t i o n , or 2 where t^ i s the time that the plasma enters the MHD generator and x and t are the p o s i t i o n and time coordinates of the plasma i n the MHD generator. L e t t i n g t ^ denote the time of a r r i v a l at the downstream end of the MHD device when B = 0 and t_ 3 denote t h i s time when B + 0 leads to P f V V h ± V J B { * » - * . } * .....go For the p o l a r i t i e s of J and B indicated i n F i g 42, J and B are p o s i t i v e , t ^ - t ^ p o s i t i v e and the deceleration of the plasma i s increased by the magnetic i n t e r a c t i o n . A numerical value f o r J w i l l now be calculated. Employing the value of mQ/P = .133 //sec/cm from Table 1 and a value f o r m calculated from the observed pressure r i s e of o * 2 5 - 1 0 microns Hg due to a f i r i n g gave a value f o r P of 57 x 10 ^ kg m/sec The mean molecular weight of the gases was assumed to be 40. Also, l e t t i n g B = .015 w/m2, Y = 10~-'m-5, t 1 = 35/tsec, t 2 = 55.5/isec and t ^ = 56.0/tsec i n equation 90 r e s u l t s i n a value f o r J of 8500 amp/cm . This value of po l o i d -a l current density i s very high. The value f o r the p o l o i d a l current density determined i n Chapter I I I , Section 3 was only 3 amp/cm . Possibly some important factors have been omitted i n the above anal y s i s . For example, a strong i n t e r a c t i o n may - 96 -have occurred at the x = 87 cm p o s i t i o n where the rod carrying the generator e x c i t i n g current was perpendicular to the d i r -ection of flow of the plasma. The important point i s that a transported p o l o i d a l current density could account f o r the observed speeding and slowing e f f e c t s observed i n the MHD generator. The power generating c a p a b i l i t i e s of the B^. MHD gen-erator were not investigated. The reason was that i t was experimentally d i f f i c u l t to generate a s u f f i c i e n t l y large azimuthal magnetic f i e l d with the av a i l a b l e dc power supply and a single conductor central electrode. The size of the shock tube was also i n s u f f i c i e n t to permit the use of a large central electrode containing multiple conductors. S u f f i c i e n t p o t e n t i a l was thus not generated between the electrodes to break down the sheath between the electrodes and the plasma, with two probable exceptions. The sign a l appearing at the time t ^ 55 JJL sec was of the correct p o l a r i t y to be the B sign a l generated by a v a l i d MHD current of the type discussed i n the theory section. This sig n a l was absent when no e x c i t i n g current was applied and was of reversed p o l a r i t y when the c o i l was rotated by 180°. The sheath was probably broken down by the r a d i a l p o t e n t i a l generated by the intense magnetic f i e l d that would have existed, due to magnetic compression, i n the front of the plasma as the plasma neared the closed end of the MHD generator. The second cause f o r sheath breakdown i s discussed by Smy (1962). This p a r t i c u l a r breakdown phenomenon i s i n evidence from the o s c i l l a t i o n s that occur during the times 55< t< 50/^sec and - 97 -subsequent to the appearance of the sign a l at 55/*sec. 2. ELECTRICAL CHARACTERISTICS OP AN ELECTRODELESS B r MHD GENERATOR The problems of sheath p o t e n t i a l s , electrode wear and deposits on electrodes are avoided i n MHD generators that do not have electrodes i n contact with the plasma. One method of extracting e l e c t r i c a l power from a moving plasma without using electrodes i s to couple the load i n d u c t i v e l y to the magnetic f i e l d generated by the currents i n the plasma. In t h i s Section the electromagnetic behaviour of a p a r t i c u l a r configuration of electrodeless magnetohydrodynamic generator i s studied. The configuration, shown i n Pig 43, i s that of an annular tube with an applied r a d i a l magnetic f i e l d . The f i e l d could be generated by a va r i a b l e p i t c h c o i l i nside the inner tube or could be produced by an enclosing yoke of i r o n and an electromagnet as has been used by Barach (196.1) and by Patri c k (1959). On a small scale experiment the r a d i a l magnetic f i e l d could be produced by the method shown i n Pig 19d. In order that the analysis w i l l r e s u l t i n a s o l u t i o n that w i l l i n d i cate the order of magnitude of response time and output power of the generator, c e r t a i n s i m p l i f y i n g assumptions are made. I t i s assumed that the magnetic Reynold's number i s << 1, that f i e l d edge e f f e c t s are n e g l i g i b l e , that there i s l i t t l e a l t e r a t i o n of the plasma flow v e l o c i t y during the passage of the plasma through the generator, that - T - ] < < r-] a n ^ thait r2 ~ r 1 < T6~T2' Also, a l l e l e c t r i c a l quantities are assumed - 98 -to Toe constant over the width of the annulus and are assumed to be evaluated on the mean radius of the annulus, A> » Dis-placement currents and convection currents are neglected. x ~ " - axially-segmented r e s i s t i v e cylinder 3 ^ V t F i g 43. Electrodeless B r MHD Generator. From Maxwell's equation V x E = - B i t follows that •»•«»9 ^  « e a o o 9 2 where E^ i s the azimuthal e l e c t r i c f i e l d i n t e n s i t y i n the plasma, I i s the azimuthal current i n the plasma, I» i s the P 4L t o t a l load current, L p i s the s e l f inductance of the c i r c u i t containing 1^, M i s the mutual inductance between the plasma c i r c u i t and the load c i r c u i t . Ohm's Law, without H a l l current takes the following form when I = 2TT/V X X and B = B 0 p 0 2TTA < iV0-X B0 = I p t <TX A JL pI„ + MI^} .....94. x i s the depth of penetration of the front of the plasma into the generator. A s i m i l a r treatment f o r the load c i r c u i t , a r e s i s t i v e cylinder segmented i n the a x i a l d i r e c t i o n , r e s u l t s i n where R^ /£ i s the azimuthal resistance per unit a x i a l length of the load, and Jt i s the t o t a l length of the load. - 99 -Equations 94 and 95 indicate that the equivalent c i r c u i t f o r the generator i s that shown i n Pig 44« -AAA-2 T T / t , i r B 0 Q \/crx •p o o E L * 1 Pig 44. Equivalent C i r c u i t f o r the Electrodeless B r MHD Generator. When f i e l d edge e f f e c t s are neglected, and equations 94 and 95 can he reduced to { | £ ) ^ A A 4 * + { * . ' + A T i V ] ^ + = ° . . . . 9 7 where i p = I p/x and ij = T^/t . The i n i t i a l conditions are XP (t - o) * A/ eP/TT A : > {i - (%f} X ( t = o) = O .... .98 where e p = 217"/^ V B 0 . The overdamped s o l u t i o n to equations 97 and 98 i s e p i r t e - e 99 - 100 -where _ 100 i R i . . . . 1 0 i I t can be shown that the p h y s i c a l l y r e a l i z a b l e response i s that of an over-damped s o l u t i o n since i s always of po s i t i v e sign. The order of magnitude of the output power w i l l now be calcula t e d f o r the conditions that could be r e a d i l y obtained i n an em shock tube: B« = 8 x 10 ohms, r / r . = 2, v = 104m/sec, t = 5 x 10~ 6 sec, 0*= 104" mhos/m, JL = .05 m, — 2 2 PJ = 100 gauss = 10 webers/m , and r. = 0.01 m. When e = o to ' ' I p 6.28 v o l t s , i t = 1.687, « ^ = 4/3, and I 2(t=5 x 10 sec) = 43 watts. This value of output power i s probably too low for economical power generation. Possibly a la r g e r device would be more e f f i c i e n t . Por example, Colgate and Aamodt (1957) have proposed a somewhat s i m i l a r method of power extraction. Their proposed device consisted of a tank 25 f t i n diameter and 150 f t long surrounded by a c o i l that could be used f o r simultaneous d r i v i n g of a load and the generation of azimuthal currents i n a plasma i n the tank. I t was proposed that the plasma could be driven back and f o r t h through the c o i l by 235 U f i s s i o n reactions at the ends of the tank. The preceding c a l c u l a t i o n of the order of magnitude - 101 -of the output power that can he obtained from the electrode-l e s s B r MHD generator indicates that inductive power extraction from a moving plasma i n a shock tube i s a very i n e f f i c i e n t means of power generation. Inductive power extraction does o f f e r the advantage of closed-current paths within the f l u i d and thus circumvention of electrode problems, which i s at present one of the major problems encountered with electrode-type MHD generators. I t i s possible that the travelling-wave type (Tenfold 1961, Haus 1962) of MHD inductive power genera-tor may prove to be the most p r a c t i c a l . The somewhat r e s t r i c t i v e assumptions made i n the preceding analysis to obtain c i r c u i t c h a r a c t e r i s t i c s that could be expressed i n closed form are not s u f f i c i e n t l y r e a l i s t i c to warrant experimental v e r i f i c a t i o n . A d i f f e r e n t geometry of inductive generator that i s amenable to both analysis and experimental work w i l l be considered i n the next Section. 3. CHARACTERISTICS OP A MAGNETOHYDRODYNAMIC POWER GENERATOR EMPLOYING INDUCTIVE POWER TRANSFER Theory The geometry of the MHD generator considered i n t h i s Section i s that shown i n Pig 45. This configuration has been employed by L i n , Resler and Kantrowitz (1955) fo r the measure-ment of the e l e c t r i c a l conductivity of the plasma generated i n a conventional diaphragm-type shock tube, and has been con-sidered by Woodson and Lewis (1961) as a possible MHD power generator. Woodson and Lewis described an i n v e s t i g a t i o n into - 102 -the behaviour of t h i s generator at high values of magnetic Reynold's number. The primary i n t e r e s t was i n the amount of magnetic f l u x that could be transported by the plasma. The means by which the f l u x c u t t i n g the load c o i l could be con-verted into e l e c t r i c a l power was not considered. The load r e s i s t o r chosen by L i n , Resler and Kantrowitz (1955) had a value that was approximately the c r i t i c a l damping resistance for the output c o i l . Such a high value of load resistance resulted i n a very low power output, but an output voltage that was e s s e n t i a l l y independent of the load resistance. In the analysis to follow, the e f f e c t of the load resistance Rj and inductance of the load c o i l Lj on the output voltage Y and output power P. , i s determined. Pig 45. MHD Generator Employing Inductive Power Transfer. It i s assumed that the flow v e l o c i t y i s uniform, that there i s no transverse motion of gas and that there i s no change i n the f i e l d current during the i n t e r a c t i o n . The r a d i a l e l e c t r i c f i e l d i n the plasma. E , i s neglected and also - 103 -i t assumed that the magnetic f i e l d a cting on the plasma i s s o l e l y that due to the f i e l d c o i l s . The preceding assumptions were made by L i n , Resler and Kantrowitz (1955) and are con-sidered to be applicable to the present a n a l y s i s . Thus where x i s the a x i a l displacement from the load c o i l , r i s the radius, J (x,r) i s the current density i n the plasma at ( x , r ) , 0"(x) i s the conductivity of the plasma, i s the flow v e l -o c i t y of the plasma and B r(x,r) i s the r a d i a l component of the magnetic f i e l d that i s d i r e c t l y due to the f i e l d c o i l . Applying Kirchhoff's Law to the load c i r c u i t r e s u l t s i n ^ dF + * d t ....103 where 1^ i s the load current, A i s the c r o s s - s e c t i o n a l area of the load c o i l and ^ i , s "the t o t a l induced magnetic f l u x passing through the load c o i l . 4>(s) = FR(TtA.)dl 104 where I i s the f i e l d c o i l current, -c i s the length of the plasma, s i s the p o s i t i o n of the front of the plasma r e l a t i v e to the load c o i l , T ( x , r ) i s the magnetic f l u x passing through the search c o i l c i r c u i t due to a u n i t current r i n g i n the plasma of radius r and at p o s i t i o n x. Defining g(x) as - 104 -r e s u l t s i n <J>(s) =u21 j o-(s-x) g M dx s-4 The v e l o c i t y of the plasma front U i s given "by U . 106 ds dt ...107 Equations 103, 106 and 107 can be combined to y i e l d When the c a l i b r a t i o n procedure of L i n , Resler and Kantrowitz (1955) i s used, then the c o i l c a l i b r a t i o n response function i s given by 108 .... 109 In t h i s c a l i b r a t i o n procedure, a slug of metal of conductivity 6~c , of length about two times the diameter of the shock tube or greater, and of the same diameter as the insi d e of the shock tube i s passed through the c o i l s at v e l o c i t y XL I f the f i e l d c o i l current i s I while the slug i s passing through the c o i l s , then the voltage induced i n the load c o i l i s V c ( s ) . Equations 108 and 109 can be combined to y i e l d a - " t t J , L(o) Ve (s) - ff(i) Vc (s-i) Jfr" (s-x)Vc (x) dK \ 10 which i s equivalent to (T(o) Ve (s) - 0-W Vc (s-i) +/(r'M Vc(x)c/, s - i aft 111 -0* - 105 -The s o l u t i o n to equation 111 f o r a step increase i n conduct-i v i t y at the shock front and a c o i l response function V (s) c of the form of a Gaussian d i s t r i b u t i o n i s of p a r t i c u l a r i n t e r -est. The v a l i d i t y of such a s o l u t i o n could r e a d i l y be checked experimentally since the plasma generated i n a shock tube approximately possesses such a step increase i n conductivity and the experimentally-observed c o i l response function i s quite c l o s e l y that of a Gaussian d i s t r i b u t i o n function. For these The c a l c u l a t i o n i s made only f o r the shock front, not the t r a i l i n g portion of the plasma, as i s shown i n F i g 46. assumptions, <r(s=o)=. crp ff'(s-x) = o > .112 F i g 46. The Conductivity and V e l o c i t i e s Being Considered i n the Analysis. The s o l u t i o n to equation 111, under these assumptions. i s (t) = - U Viz I (Tp Vt e /e — OO S dt . . . 1 11 3 - 106 -where the s u b s t i t u t i o n s = Ut + s^ has been employed. The o r i g i n of time i s thus chosen as the time when the plasma front i s h a l f way through the load c o i l . The i n t e g r a l i n equation 113 can be reduced to a standard i n t e g r a l by changing the var i a b l e of i n t e g r a t i o n . The s o l u t i o n i s 2 < r c 2 C l c L i Rib* Rjt where erf x 114 This s o l u t i o n i s more usefu l i f the error function i s expanded according to one of the following expansions (see Lwight 1947) erf x 2X 2 A l!3 2\5 3\1 x2 <*° .,..115 erf x I — V/TT X I - 2X' l'3 2*X 4 I - 3 - 5 , ....116 The voltage appearing across R^  i s given by v* ~ ^J. R i .... 117 Equations 114, 116 and 117 can be combined to obtain the output voltage when the c o n d i t i o n — ^ — — T » |"t| i s s a t i s f i e d . 2 L p U * When only the f i r s t two terms i n equation 116 are considered, then an equation i s obtained that i s i d e n t i c a l to that derived by L i n , Resler and Kantrowitz (1955) f o r conductivity measure-ments , - 107 -.... 1 18 where y V* = Uu 2o- PlV t p/K 2o; I c ....119 Expressions that are of i n t e r e s t f o r estimating the order of magnitude of (t) are: . . 120 • « • w I ^  I where y = R^I^/^L^U. Equation 120 converges most r a p i d l y f o r y £ 1 and 121 converges most r a p i d l y f o r y > 1. The power i n the load i s Xj fsj or 2. .... 122 To ohtain the conditions under which maximum energy d i s s i p a t i o n i n the load would occur, i t would be necessary to maximize /^ +°° ?A(t)c\t .... 123 This equation has not been solved. An estimate of the peak value of P^ (t) can, however, be obtained from equa-t i o n 122 assuming t = 0. The r e s u l t i n g equation can be solved g r a p h i c a l l y f o r the value of the load resistance that maxi-mizes Pjj (o). The value thus obtained i s S j ^ 1.36 L^U/b. - 108 -Then z .... 124 A graph of P | [ t , R, = Ri , U/b • 10 sec , K, = — j - ^ j ^ j J i s given i n Pig 47. 0.3 0.2 0.1 0 - 1 0 1 2 t ,/c sec Pig 47. Power i n load Resistance as a Function of Time. A numerical value f o r P^(o) that i s representative of the value expected on a shock tube i s Pg(o) ^ 7.5 W. The assumed conditions are U = - 10^ m/sec, b = 0.01 m, C = 10 4 mhos/m, I c ^ A c p = 1 .8 x 10 5 amp m 2/sec 2 v o l t , R^ b/2L_£ U = 0.68, L£ = 35 nH, I = TO amps, = .58 x 10 8 mhos/m, Ri = ..0475 -A. . An output power of 7.5 W l a s t i n g f o r a time of the order of a microsecond i s i n s u f f i c i e n t to slow the plasma. The electrodynamic analysis presented above i s thus s u f f i c i e n t to describe the operation,of t h i s type of MHD generator. A - 109 -magnetohydrodynamic analysis i s not warranted unless a la r g e r output power could be obtained. Multiple output c o i l s and loads would be one method of increasing the output power. I t i s to be noted that any inductive MHD generator i s inherently an ac generator and that a dc output cannot be obtained. Experimental Results The v a l i d i t y of the above theory has been checked experimentally. The apparatus used i s shown i n F i g 48. The f i e l d c o i l had an inner diameter of 1.4 i n . , an outer diameter of 4.6 i n . and a length of 1.0 i n . This c o i l had 296 turns of AWG 14 wire. The output c o i l had 6 turns of AWG 24 wire wound as a single layer with a mean diameter of 1.228 i n . and a length of 0.153 i n . These c o i l s were c a l i b r a t e d by a method s i m i l a r to that used by L i n , Resler and Kantrowitz (1955). The r e s u l t s of c a l i b r a t i o n were: b = .02 m, I v /V = 7.50 ' c c- cp x 10 4 amp m2/ s e c 2 v o l t , = 0.581 x 10 8 mhos/m. Fi g 48. Inductive MRT> Generator Experimental Apparatus. - 1 1 0 -As i s shown i n F i g 48c, the loadj, a one turn c o i l ? was oriented so that no magnetic f l u x generated by azimuthal current i n the plasma l i n k e d with the load. The current through the load was thus generated only "by the rate of change of magnetic f l u x l i n k i n g with the output c o i l . The resistance of the output c o i l was 0 . 0 5 XL . Since the value of resistance employed as a load was always appreciably greater than 0.05-ft? the resistance of the output c o i l was considered to "be neg-l i g i b l e . The calculated value of inductance of the 6 turn output c o i l was 1.91/^H and the calculated value of the i n -ductance of the load 70 nH. The output c o i l was thus assumed to have only an inductive impedance and the load only a r e -s i s t i v e impedance. The equivalent c i r c u i t , on the basis of the preceding discussion, was that shown i n F i g 4 9 . The value of C, as determined from the o s c i l l a t o r y frequency of the unloaded c o i l , 33 Mc/s, was 12 pF. The load resistance f o r c r i t i c a l damping was thus 800 -H. . I c o i l F i g 49- Equivalent C i r c u i t f o r Inductive MHD Generator Output C o i l . - 1 1 1 -8 -21 | , I 1 y 1 -2 -1 0 +1 +2 + 3 time, /x sec Pig 50. V a r i a t i o n of Output Voltage with Load Resistance. These curves were obtained with the dr i v e r shown i n Pig 19f» argon i n the shock tube at a pressure of 160 microns Hg, the 19.2 //P capacitor bank d i s -charging from 8 kV and the d r i v i n g current crowbar-red at the end of the f i r s t current pulse. The center of the output c o i l was 39 cms from the base of the d r i v e r , t h e ' v e l o c i t y of the luminosity front was 2.0 cms/&sec,L^ was 1.98.//H. the f i e l d c o i l current was 10 A andff" was 10 mhos/m (see Appendix P). The load r e s i s t o r s down to 10-ft- were commercial 1/2 watt units; r e s i s t o r s of lower value were constructed with 3/4 i n . lengths of d i f f e r e n t sizes of nichrome wire soldered across 1/2 W re-s i s t o r s . - 1 1 2 -The curves shown i n F i g 50 obtained f o r R^ = 3.25-A-and R^ = 0.50 .A- were displaced spuriously l a t e i n time. The signals observed with the luminosity detector at x = 38 cms were not of the usual f l a t - t o p waveshape f o r these two shots. The deviation from the usually-observed f l a t - t o p wave-shape and the displacement i n time of the c o i l signals were thus both due to shot-to-shot i r r e p r o d u c i b i l i t y of the plasma. Power, watts 8 0 4 / » \ 1 1 1 1 j ij A VRj =3.2 51). \ /' ^ = 1.35^7 // / si If \ ^ \\ a !i / 'i / !/ / > // / / \ \ R j = .5 Oft // / / / -1 0 +1 time, /xsec +2 + 3 F i g 51. Output Power as a Function of Load Resistance, Experimental. - 113 -The power d i s s i p a t i o n curves shown i n Pig 51 were obtained from the data shown i n Pig 50. The t h e o r e t i c a l value of load resistance that optimized (t=0) was 1.36 U/b = 2.1 SL , and the maximum value of P^ (t=0) was from equation 124, 8.6 W. Prom Pig 51 the experimentally-determined maximum value of P^ (t=0) was 7.0 W, obtained when R_g = 2.2 - 1 S L . The predicted and the observed values of P^ (t=0, R^ = R_^ ) and of were thus i n agreement. Some error was introduced by the assumption that the observed waveform of the voltage was that of a normal d i s t r i b u t i o n curve. An analysis that i s more applicable f o r the observed waveforms i s presented i n Appendix P. The f a i r l y close agreement between the theoret-i c a l l y predicted response of the generator and the observed response in d i c a t e s that the assumptions made i n the analysis are j u s t i f i e d . Discussion An output power of the order of 10 watts i s very low i n comparison with that which can be obtained from e l e c t -rode-type MHD generators. Por example, an e l e c t r i c a l power of up to 0.32 MW was extracted i n the experiments of Pain and Smy (1961). The MHD generator employing inductive power transfer does have one quite important advantage over e l e c t -rode-type MHD generators that' possibly could counteract the disadvantage of the low output power. One of the objects i n MHD generator research has been to develop a unit that w i l l operate dependably f o r a considerable time. When the power i s extracted from the plasma with electrodes, and the un i t i s - 114 -operated f o r times of greater than a few microseconds, the electrodes must he cooled to prevent h o i l i n g and vaporization of the electrode material. The cooled electrodes then serve as areas f o r deposition of the plasma seed material, often cesium or potassium. The electrodes soon hecome fouled with the seed material and the unit has to he disassembled and cleaned. The MHD generator employing inductive power transfer i s free from t h i s electrode cooling and cleaning problem. CHAPTER V CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK The two major problems encountered i n contemporary-research i n plasma physics, contamination and i n s t a b i l i t i e s , have been found to ex i s t i n an electromagnetic shock tube. An experimental program conducted with the object of producing a clean and reproducible plasma i n an electromagnetic shock tube has met with only p a r t i a l success. The small-cathode d r i v e r which was developed produced a plasma having a more plane luminosity front than that c h a r a c t e r i s t i c of the plasma produced e i t h e r by the widely-used T-tube d r i v e r or by a coaxial d r i v e r . The amount of contamination i n the plasma was compar-able to that i n the plasma produced by a T-tube. I t was established that the d r i v i n g discharge i n -fluenced the shape of the shock front and the homogeneity of the plasma. The persistence of the e f f e c t s of the d r i v i n g discharge, and i n p a r t i c u l a r of the i n s t a b i l i t i e s associated with the d r i v i n g discharge, on the properties of the plasma were noticeable at a time long a f t e r the d r i v i n g current had ceased to flow. The structure of the luminosity of the plasma that could be d i r e c t l y a t t r i b u t e d to the d r i v i n g discharge stayed close to the luminosity f r o n t . There was, therefore, l i t t l e shock-heated gas preceding the d r i v e r gases even at a considerable distance from the d r i v e r . - 1 1 6 -The plasma produced by a coaxial d r i v e r was found to be transporting a magnetic f i e l d that could be attributed to the d r i v i n g discharge. The r e s u l t s of a magnetic i n t e r -a ction experiment indicated that the magnitude of t h i s a z i -muthal magnetic f i e l d and i t s supporting p o l o i d a l current density was appreciable. I t would be of i n t e r e s t to i n v e s t i -gate further the properties of a plasma supporting such a transported magnetic f i e l d . The dynamics of the plasma during both acceleration and deceleration were interpreted as being strongly influenced by discharge gases i n the plasma. Such discharge gases would consist of material evaporated from any surfaces i n contact with the d r i v i n g discharge. The amount of t h i s contamination could most e a s i l y be lessened by decreasing the duration of the d r i v i n g current while maintaining the amplitude constant. Such a change i n the c h a r a c t e r i s t i c s of the d r i v i n g current could be obtained by r e p l a c i n g the present high energy capac-i t o r bank with an u l t r a - f a s t , high-voltage capacitor bank. The amount of contamination i n the plasma produced by an electromagnetic shock tube could be reduced i f an e l e c t -rodeless shock tube d r i v e r was employed. I t i s , therefore, suggested that some experiments should be performed with electrodeless d r i v e r s to determine whether or not the expected low e f f i c i e n c y could be o f f s e t by the advantage of high p u r i t y i n the plasma generated by such a d r i v e r . Rockman (1961) has used such a d r i v e r and has overcome the problem of low e f f i c -iency by using a f a s t capacitor bank. — 117 — The i n v e s t i g a t i o n s reported i n Chapter III indicate that a problem of considerably more fundamental importance than contamination should be studied. Nearly a l l workers with electromagnetic shock tubes have assumed that a plane shock wave i s produced i n an electromagnetic shock tube. C e r t a i n l y under conditions of low pressure and high v e l o c i t y , the r e s u l t s presented i n Chapter III i n d i c a t e that i t i s questionable whether a shock wave i s produced. The discharge gases appear to act as a highly permeable piston, pushing l i t t l e of the encountered gas ahead of them. Further work i s needed before d e f i n i t e conclusions can be drawn about the conditions f o r the existence of true shock fronts i n low pres-sure electromagnetic shock tubes. The development of the small-cathode d r i v e r was made possible by the development of a crowbar switch that could s h o r t - c i r c u i t the low impedance d r i v e r e f f i c i e n t l y . The crow-bar switch and main switch operated r e l i a b l y . A research project could, however, be u s e f u l l y started on one or more of: extending the maximum voltage c a p a b i l i t y of the switch to greater than 25 kV, extending the power handling c a p a b i l i t y to over 4 kJ or i n v e s t i g a t i n g the problems of a b l a t i o n and coating of the i n s u l a t i o n separating the electrodes. The plasma that was studied i n Chapter III was used to i n v e s t i g a t e the properties of c e r t a i n magnetohydrodynamic generators. Three generators having azimuthal symmetry were proposed i n Chapter IV. One was an electrode-type of generator and the other two u t i l i z e d inductive power tr a n s f e r . The - 1 1 8 -electrodynamical behaviour of each generator was calculated on the basis of a simple model and experiments were performed with two of the generators. The f i r s t to be tested, an electrode-type B^. MHD generator, f a i l e d to operate as expected probably because of the existence of a sheath on the electrodes. The l a s t to he tested, an electrodeless configuration of gen-erator, operated i n conformity with the t h e o r e t i c a l p r e d i c t i o n s . The output power of the two electrodeless configurations con-sidered was extremely low - f a r too low f o r the generators to be considered as p r a c t i c a l power generators. The electrode-"type generator that was considered could, however, possibly be developed into a p r a c t i c a l power generator. APPENDIX A CHARACTERISTICS OF VARIOUS SPARK GAP TRIGGER CIRCUITS Certain properties of the voltage douhler spark gap t r i g g e r c i r c u i t o r i g i n a l l y used by Theophanis (1960) have been investigated. Three major objectives have been r e a l -i zed. They have been: (a) To determine the v a l i d i t y of Theophanis' statement that ei t h e r negative or p o s i t i v e polar-i t y pulses could be obtained from the c i r c u i t shown i n F i g 52a, by a l t e r i n g the ground connection with switch S1. (b) .To determine the l o s s of pulse power due to the impedance of the thyratron. (c) To determine the f e a s i b i l i t y of t r i g -gering p a r a l l e l spark gaps with the t r i g g e r c i r c u i t s shown i n F i g 52b. (a) (b) (c) F i g 52. Trigger C i r c u i t s Employing the Discharge of a Cable. - 1 2 0 -The p o l a r i t y behaviour of the c i r c u i t of Pig 52a has been investigated by determining the minimum thyratron anode voltage required f o r breakdown of the t r i g g e r spark gap f o r various gap spacings and fo r switch S1 i n positions A and B. I t was found that the thyratron voltage required for breakdown of a gap was about 1.7 times greater when S1 was i n p o s i t i o n A rather than B. Thus the c i r c u i t of Pig 52a generates pulses of p o l a r i t y depending upon the p o s i t i o n of S1; however the negative pulses have a voltage that i s about 1.7 times l a r g e r than p o s i t i v e pulses. The c i r c u i t s of Pig 52a and 52c were used to i n v e s t i -gate the lo s s of pulse voltage at the t r i g g e r gap due to the impedance of the thyratron. The spark generated by the c i r -c u i t of Pig 52c when R = 0 was of considerably greater power than that generated by the thyratron c i r c u i t shown i n Pig 52a, as determined by v i s u a l observation of the spark. When R = 1 ohm, the spark current was decreased by about 10$. The time d e r i v a t i v e of the spark current was observed with a one turn f l u x pickup loop connected to an o s c i l l o s c o p e . When R = 50 ohms, the t r i g g e r spark was of n e g l i g i b l y small energy. I t was concluded that the thyratron c i r c u i t possessed a higher impedance than did the open-air gap c i r c u i t . Further tests disclosed that the duration of the f i r s t pulse of the t r i g g e r spark current was increased and the amplitude decreased by the presence of an ~100 nH inductance inserted i n place of the resistance R shown i n F i g 52c. F i g 53 shows the time deriva-t i v e of the t r i g g e r spark current f o r the t r i g g e r c i r c u i t shown - 121 -i n Pig 52c but with R = 0 and low inductance i n the open-air gap c i r c u i t . 1 T 'S J Pig 53. Derivative of Trigger Spark Current Generated by C i r c u i t of Pig 52c. R = 0 ohms; 0.1//sec/ div. The c i r c u i t i n Pig 52b did not operate s a t i s f a c t o r i l y . The te s t c i r c u i t was constructed so that the t r a n s i t time of a s i g n a l from point A to point B (see Pig 52b) was 2 - 3 nsec. Synchronized breakdown of the two main gaps was thus possible only i f t r i g g e r i n g was eff e c t e d within t h i s time. The small spark current evident i n Pig 53 during t = 0 to t « 3 nsec suggested that d i f f i c u l t y would be encountered with the par-a l l e l gap c i r c u i t . S a t i s f a c t o r y p a r a l l e l f i r i n g could only be obtained f o r capacitor charging voltages of 8.25 to 9.5 kY, when the s e l f - t r i g g e r i n g voltage (breakdown voltage of the main gaps) was 9«5 kV. Considerably better p a r a l l e l gap operation was ob-tained with the c i r c u i t of Pig 54. Por a t r i g g e r c i r c u i t i n which L = 40 nH, C = 1.6/iP, t r i g g e r capacitor charging voltage = +10 kV, R = 8 ohms, number of cables, main gaps and main cap-a c i t o r s = 2, main gaps set f o r 13 kV breakdown, the two main - 122 -gaps would t r i g g e r simultaneously f o r main capacitor voltages of from + 7.5 to + 13 kV. They would not t r i g g e r simultaneous-l y f o r a main capacitor voltage of 6.25 kV. The t r a n s i t time of a s i g n a l between points .A and B was again 2 - 3 nsec, so that the r i s e time of the t r i g g e r voltage at the t r i g g e r pins of the main gaps must have been l e s s than 2 - 3 nsec. manual switch —'WV— I *- - « 1 - O : c — I R V c — V \ A •0 ^ hi A _ ~10 nH C —VSA- -0 i h B F i g 54. Trigger C i r c u i t f o r P a r a l l e l Gaps. The operation of the c i r c u i t shown i n F i g 54 has been described by Hintz and Beerwald (1959). Since i t i s believed that these workers reached an erroneous conclusion i n t h e i r analysis, t h i s c i r c u i t w i l l now be analyzed. When the r e s i s t s ance and the dynamic inductance of the discharge i n the manual switch are neglected, the voltage across R i n the t r i g g e r c i r -c u i t shown i n F i g 54 i s RZo /n where R = —=: =—;— p R + Zo/n 125 , ZQ - the c h a r a c t e r i s t i c impedance of the t r i g g e r cables and n = the number of t r i g g e r cables. A large value of V can be obtained within a time of the order of - 123 -2 a few nsec a f t e r the t r i g g e r gap has closed i f RpC/4L has a value much greater than 1. Then, V(P r ac/4L»i, t«R,c) = V e|i - exp[-R Pt / L J J ^ The voltage appearing on a t r i g g e r p in V. depends on the capacitance between the t r i g g e r pin and ground. When the e f f e c t of multiple cable r e f l e c t i o n s i s neglected, the voltage appearing on a t r i g g e r pin i s or 2Vc > + T J - g r [ ^ e x p { - t A ^ ~ e x p { - t R f / i | Vt, (R,aC/4L»l, t« R,C , l/C t?. = Rp/L) = 2Ve{ I - [l + M ] e x p{-tR,/L\". 127 128 In order that V^.r w i l l r i s e within a few nsec to a value com-parable to V , must be small. The optimum value i s = 0 and not C.Z R = L as stated by Hintz and Beerwald (1959). x o p A further s i m p l i f i c a t i o n of equations 127 and 128 can often be made. I f R « Z /n, then R = R or a l t e r n a t i v e l y i f R » o p d ' Z Q/n, then R^ = Z Q/n. A p r a c t i c a l case w i l l now be considered. For G = 1.6//F, I = 40 nH, t = 5 nsec, R = 8 ohms, C, = 0, P x then V t r ( t = 5 nsec) = 1.264 Vc. I f C t Z Q - I/R then V t r(t=5 nsec) = 0.528 V . Other fact o r s should be considered when t h i s c i r c u i t i s employed. For example, the t r i g g e r cables should be of .-'sufficient length that the sparks at the t r i g g e r pins are not af f e c t e d by cable r e f l e c t i o n s . Also, the p o l a r i t y of the t r i g g e r pulse should be chosen to increase the e l e c t r i c - 124 -f i e l d between the t r i g g e r pin and the f a c i n g electrode. The c h a r a c t e r i s t i c s of the voltage quadrupler t r i g -ger c i r c u i t shown i n Pig 55 were investigated. The object i n developing t h i s c i r c u i t was to obtain as high a t r i g g e r v o l t -age as possible at the t r i g g e r pin of the main gap. I t was found that the most desirable p o l a r i t i e s f o r minimum c l o s i n g time of the switch over the widest range of main gap voltage were a p o s i t i v e t r i g g e r pulse feeding into the cathode of the main gap and a negative t r i g g e r pulse feeding into-the anode. It was believed that t h i s c i r c u i t might prove to be a s u i t a b l e a l t e r n a t i v e to the c i r c u i t shown i n Pig 54. Tests showed, however, that the quadrupler c i r c u i t was not suitable f o r t r i g -gering p a r a l l e l gaps. +2.5 W 1M Manual Switch 3 ii t Pig 55. Voltage Quadrupler Trigger C i r c u i t . Por n o n - p a r a l l e l operation of spark gap switches, the c i r c u i t s shown1 i n Pig 56 were found to be as s a t i s f a c t o r y as the c i r c u i t shown i n Pig 55. Both c i r c u i t s i n Pig 56 fea-tured dc i s o l a t i o n of the t r i g g e r c i r c u i t from the main c i r c u i t , Even further i s o l a t i o n was provided by employing a pulse trans-former on the output as shown m Pig 56b. A transformer was - 125 -made that reproduced 40 nsec, 30 kV pulses and had an i n t e r -winding capacity of ~ 40 pF. A low interwinding capacity was desirable i n order that only a small ground loop current would flow across the pulse transformer. The t r i g g e r c i r c u i t shown i n Pig 56a was employed to t r i g g e r the main switch and the d r i v e r of the shock tube (see Pig 4). ' - f l L Z Z f c H I HI 1 U P (a) Pig 56. 0>) Voltage Doubler Trigger C i r c u i t s . - 126 -APPENDIX B PROPERTIES OP A WIDE VOITAGE RANGE, OPEN-AIR SPARK GAP SWITCH The three-electrode spark gap switches shown i n Pig 57 have working voltage ranges of about to V^, where i s the voltage at which breakdown of the gap occurs. The c h a r a c t e r i s t i c s of a switch with the conventional geometry, Pig 57a, have been described by Lupton (1961) and by Hintz and Beerwald (1959). The c h a r a c t e r i s t i c s of the t r i g a t r o n switch have been investigated by Craggs, -.Haine. and Meek (1946), Shkuropat (1961) and Broadbent (1960). a) Conventional b) Trigatron Pig 57. Open-Air Three Electrode Spark Gap Switches. It has been found that the working voltage range of a three electrode spark gap switch could be g r e a t l y increased by using the plasma j e t t r i g g e r system shown i n Pig 58. The major differences between the operation of t h i s system and those shown i n Pig 57 was that an a x i a l t r i g g e r current was forced to flow and that r a d i a l expansion of the channel of the - 127 -t r i g g e r spark was suppressed. The plasma i n the t r i g g e r d i s -charge was thus e s s e n t i a l l y f i r e d into the gap "between the m a i n electrodes. t r i g g e r p in i n s u l a t i o n F i g .58. Plasma Jet Triggered Open-Air Spark Gap Switch. The c i r c u i t shown i n Pig 59 was employed f o r deter-mining the t r i g g e r i n g time c h a r a c t e r i s t i c s of the plasma j e t triggered switch. The switch was connected to discharge a 1 .6 /I'F capacitor i n a c i r c u i t having an inductance of about 40 nH. H-O. -AAA-±4 kV=V, 1.6 t r i g g e r capacitor manual switch — > - •<— 8n_ AAA-100 k A 0- 1M.fl-A A A 1. 1 .6/fP m a i n capacitor F i g 59. C i r c u i t f o r Testing Open-Air Spark Gap Switches. The p o l a r i t y and t r i g g e r i n g time data plo t t e d i n Fig 60 i n d i c a t e that the plasma j e t triggered switch operates at capacitor voltages of l e s s than 1-^/2, but with some increase i n t r i g g e r i n g time at these lower voltages. The seemingly anomalous points on the Y_ . , = 0 axis indicate that the capacitor * 128 -switch w i l l close even when no voltage e x i s t s between the main electrodes. main capacitor voltage Pig 60. Triggering Time of Plasma Jet Triggered Switch. The actual t r i g g e r i n g mechanism has not been thor-oughly investigated. I t i s believed, however, that the theory proposed by Saxe (1961) i s app l i c a b l e . He established that, at l e a s t f o r low values of the applied voltage, breakdown of a conventional three-electrode gap i s caused by the shock wave emitted by the t r i g g e r spark. In the plasma j e t triggered gap. a f a c t o r contributing to breakdown i s the e j e c t i o n of lumin-ous gas and What appeared to be p a r t i c l e s from the t r i g g e r spark into the main gap. Highly luminous•sparks were observed to t r a v e l about 1/2 i n . a x i a l l y from the t r i g g e r hole when the other main electrode was removed. During the passage of these sparks across the gap, c o l l i s i o n s between the sparks and the gas atoms probably r e s u l t e d i n the formation of a back-ground i o n i z a t i o n i n the gap which aided i n bringing about - 129 -breakdown. The luminous gas ejected by the t r i g g e r spark into the main gap was v i s i b l e f o r a .distance of about 1/16 i n . when the t r i g g e r energy was derived from the c i r c u i t shown i n Pig 59. I t i s probable that t h i s short l i v e d plasma je t generated a non-luminous shock wave of the type discussed, by Saxe. The points on the V .. = 0 axis of Pig 60 o f f e r * capacitor D some confirmation that the theory of Powler, Paxton and Hughes (1961) i s applicable to the plasma j e t t r i g g e r . According to t h e i r i n t e r p r e t a t i o n , the motion of the p o s i t i v e ions i n the tr i g g e r discharge markedly a f f e c t s the motion of the plasma i n the discharge. The points on the V .. =0 axis 0 c capacitor occur only when the t r i g g e r pulse i s p o s i t i v e with respect to the reference electrode, the electrode containing the t r i g -ger components. The d i r e c t i o n of motion of the p o s i t i v e ions, when the t r i g g e r pulse i s p o s i t i v e , i s outwards through the small hole. These ions i n passing across the main gap could account f o r the cl o s i n g of the switch at capacitor voltages l e s s than V^/2. Other mechanisms that could contribute to the breakdown process are discussed i n Appendices C and D. Although the plasma j e t triggered switch can be used advantageously i n place of a conventional three electrode spark gap switch f o r c e r t a i n a p p l i c a t i o n s , there are two factors that l i m i t i t s a p p l i c a b i l i t y . The f i r s t i s that the plasma j e t triggered switch possesses no d i s t i n c t advantage over conventional switches when the spacing between the main electrodes i s large. The second consideration pertains to - 130 -electrode wear. I f the t r i g g e r spark or the main discharge are of too high energy then the small hole where the t r i g g e r discharge occurs w i l l he r e s p e c t i v e l y e i t h e r enlarged or closed*, r e s u l t i n g i n a decreased switch l i f e . The open-air switch that has been described was not used i n the discharge c i r c u i t f o r the electromagnetic shock tube. The plasma jet t r i g g e r i n g system was, however, employed i n the low pressure spark gap switch that i s described i n the following Appendix. - 131 -APPENDIX C LOW INDUCTANCE LOW PRESSURE SPARK GAP SWITCH (Reprint from Rev. S c i . Insts. 33,'606-610, 1962) Reprinted from T H E R E V I E W OK S C I E N T I F I C I N S T R U M E N T S , , V o l . ' 33 , N o . 6, 6 0 6 - 6 1 0 , June, 1 9 6 2 P r i n t e d i n U . S. A . Low Inductance Low Pressure Spark Gap Switch* G . D . C O R M A C K A N D A . J . B A R N A R D Physics Department, University of British Columbia, Vancouver, British Columbia, Canada (Received January 17, 1 9 6 2 ; and in final form, March 12, 1962) A low pressure spark gap switch suitable for use as a main switch and as a "crowbar" switch on a capacitor bank is described. The switch has been operated over a voltage range of 0 .5 to 2 5 kV , at energies up to 4 k j and currents up to 5 0 0 kA. Under normal operating conditions the triggering time is 4 0 nsec and the jitter approximately 1 0 nsec. The inductance of the main switch is 4 m ^ H and the inductance of the crowbar switch is about 1 m ^ H . I N T R O D U C T I O N TR I G G E R E D open air spark gaps are widely used as the switching elements in high voltage circuits. L o w pressure spark gap switches offer distinct advantages in many of these circuits. For example, low pressure switches do not require mechanical adjustments in order to operate over a wide range of voltage. There are two types of low pressure switch: the graded vacuum spark gap developed by Hagerman and Wi l l i ams , 1 Baker , 2 and Mather and Wil l iams, 3 and the two-electrode switch developed by Johansson and Smars. 4 The present switch, of a two-electrode design, has similar operating characteristics to the switch of Johansson and Smars, 4 but has a much lower inductance. The inductance 4 m/iH is comparable to that of graded vacuum spark gaps . 1 - 3 Such a low value of inductance suggests suitabili ty of the switch as a "crowbar" (a short circuiting switch). Mather and Wi l l i ams 3 have used their switch as a crowbar and have stated that its inductance is ~5 m ^ H . I n the crowbar ver-sion of the present switch, the inductance of the shorting l ink is about 1 m/uH. A n open air spark gap has a min imum triggering time when 6 ' 6 the gap spacing is set close to the breakdown value, the electrode containing the trigger p in (the reference electrode) is the cathode of the main gap, and the trigger pulse is negative with respect to the ref-erence electrode. For a low pressure switch, it is agreed 2 - 4 that the reference electrode should be the cathode, but no mention has been made of the polarity of the trigger pulse. I t has been found that the triggering time of the present switch is a-minimum when the trigger pulse is positive wi th respect to the reference electrode. L o w pressure spark gap switches, i n contrast to open air spark gaps, often distort the current waveform. Mather and Wi l l i ams 3 have observed high frequency components * This work was supported by the Atomic Energy Control Board and the National Research Council of Canada. 1 D . C . Hagerman and A . H . Williams, Rev. Sci. Instr. 3 0 , 182 ( 1 9 5 9 ) . 2 W . R. Baker, Rev. Sci. Instr. 3 0 , 7 0 0 ( 1 9 5 9 ) . 3 J . W . Mather and A . H . Williams, Rev. Sci. Instr. 3 1 , 2 9 7 ( 1 9 6 0 ) . 4 R. B . Johansson and E . A . Smars, Proceedings of the Fif th Inter-national Conference on Ionization Phenomena in Gases, 1961 (to be published by North-Holland Publishing Company, Amsterdam). 6 W . H . Lupton, Proceedings of the Fif th International Conference on Ionization Phenomena in Gases, 1961 (to be published by North-Holland Publishing Company, Amsterdam). 6 P. I . Shkuropat, Soviet Phys.—Tech. Phys. 5, 8 9 5 ( 1 9 6 1 ) . in the current waveform during the first fraction of a microsecond when the ini t ia l air pressure i n their switch is of the order of a few microns. They have attributed these high frequency components to inductive effects caused by pinching of the discharge channel. The dynamic inductive effects observed^ at low pressure i n the present switch appear to be less than those reported by Mather and Wil l iams, 3 although a direct comparison is not possible since argon rather than air has been used i n the present in-vestigation. A low pressure switch also exhibits a "closing t ime" of the order of 0.1 jusec. This closing time, first ob-served by Hagerman and Wil l iams ' and later investigated by Johansson and Smars, 4 manifests itself as a slow ini t ia l rate of rise of the current. Hagerman and Wi l l i ams 1 have suggested that the closing time can be attributed to the time required to fill the switch with plasma. B o t h the dy-namic inductive effects and the closing time are decreased by an increase i n pressure so that in normal operation of the present switch (at a pressure in excess of about 15 fi) there is little distortion of the current waveform. C O N S T R U C T I O N Construction of the switch is shown i n F i g . 1. The switch is axially symmetric with the exception of the sheet con-ductor leads which connect onto parallel-plate conductors between the capacitor bank and the load. The discharge occurs between the parallel-plate steel electrodes designated anode and cathode. The switch is held together with an external Luci te clamp which is not shown in' the figures. o r LUCITE BONDED WITH EPOXY RESIN TO DUMMY CATHODE • BRASS • STEEL TRIGGER PIN-7 [ £ f ^ DISCHARGE CHAMBER FROM CAPACITOR BANK. TO LOAD F I G . 1. A cross-sectional view of the 4 - k J switch. 606 607 S P A . R K G A P S W I T C H There are several essential features in the construction. The Lucite insulation must be bonded with epoxy resin to a dummy cathode—a thin disk of aluminum. The epoxy bond greatly reduces the size of any interstices, or gaps, that exist at the low pressure edge of the junction between the dummy cathode and the Lucite. Experimental work has shown that pre-ignition is primarily caused by break-down in these unavoidable gaps. This junction phenomenon has been investigated by Kofoid 7 at lower pressures than have been used in the present work. Every firing of the switch raises the pressure in the discharge" chamber to about an atmosphere and forces considerable gas into these gaps. Pre-ignition occurs if voltage is applied across the switch before these gaps' are sufficiently evacuated. The presence of the epoxy bond makes the switch unable to withstand large reverse dc voltages (which occur when the electrode that is bonded to the insulation is made positive with respect to the electrode containing the vent holes). Furthermore, the triggering time is drastically increased when a reverse voltage is switched, as has also been ob-served by Johansson and Smars.4 The dummy cathode is in electrical contact with the main cathode but is not ri-gidly attached to it. Therefore pressure against the main cathode, caused mainly by JXB forces in the facing sur-faces of the electrodes and less so by the forces discussed by Wehner,8 does not break the very important epoxy bond. For example, the JXB force for a 500-kA firing gives rise to a pressure of the order of 140 atm against the active area of the cathode. Earlier models of the switch, con-structed without the aluminum disk but with the Lucite bonded directly to the cathode, worked well until required to discharge more than 2.5 kj. The bond then failed and the switch would no longer hold off appreciable voltage. This switch was simpler to construct and had slightly better pre-ignition characteristics than the switch shown in Fig. 1. There is an optimum size for the hole in the Lucite. If it is too large, several low energy firings result in the deposition of carbon on the Lucite over small areas opposite each vent hole. For example, carbon was deposited by 20 firings of the 19.2-^F capacitor bank charged to 500 V. This carbon was removed by a higher energy firing that occurred at 11 kV while the bank voltage .was being slowly raised. If the hole in the Lucite is too small,.the active area of the cathode is worn differentially; a trench appears on the cathode just inside the junction of the cath-ode and the Lucite. The vent holes connecting the dis-charge chamber to the dump chamber allow some of the discharge gases to pass over the surface of the Lucite during and after a firing, thus preventing the deposition of a con-ducting layer. The amount of scavenging of the Lucite by the discharge gases depends upon the size and number of vent holes and the size of the hole in the Lucite. The trigger components, the tungsten wire, and polyethylene sleeve are essentially free of wear because the main discharge does not enter the small trigger hole and the trigger discharge is of insufficient energy to evaporate much material from the components. OPERATING CHARACTERISTICS The switch has been in use with 19.2-/nF and 9.6-fiF capacitor banks. The total circuit inductance has been varied from 13 to 30 m^H and the voltage on the bank from 0.5 to 25 kV. This range in voltage over which the switch operates without adjustments is much greater than that of atmospheric-pressure spark gaps. Damped oscillatory cur-rents having peak values of 10 to 500 kA and frequencies from 200 to 400 kc have been switched. The triggering time depends primarily upon the kind of gas in the discharge chamber, the pressure of this gas, the bank voltage, and the trigger characteristics. The triggering time r is defined as the time lag between the start of the flow of the trigger current and the start of the flow of appreciable switch current. Appreciable switch current is interpreted, for experimental convenience, as about 1/50 of the peak value of the switch current. Figure 2 shows the triggering time vs pressure (p) behavior for the switch of Fig. 1 when filled with argon. Preliminary experiments with both air and helium in the discharge chamber have indi-cated that the r (p) relation for these gases differs from that for argon. As the difference has not been fully investigated, only the results for argon will be discussed. Jitter in'r is not shown in Fig. 2. The jitter is about 10 nsec when the trigger is positive and 18 <p <60 /i. These curves are valid in a voltage range of 2 to 25 kV and each point is an average of five measurements. The r(p) curves for a bank voltage of 500 V are below the given curves if p<10ju and are coincident with them if p>10/i. At 25 kV, the argon-filled switch breaks down when the pressure is in excess of about 50 /x. At 5 kV, it breaks down at a pressure of about 150 M-The curves shown in Fig. 2 were obtained with a trigger circuit (see Fig. 3) comprising a 75-ft length of RG-58/u ,Q< _ -f- positive trigger ' o negative trigger tn \ z \ FIG. 2. The triggering t- \ \ time T as a function of o \ Q initial argon gas pressure. 5 N^} SicP- \ \ — ^-Pv ' M . J. Kofoid, Trans. Am. Instr. Elec. Engrs., Part III, 79, 991 and 999 (1960-1961). 8 G. K. Wehner, J. Appl. Phys. 31, 1392 (1960). D I | I |_ 0.1 I 10 100 PRESSURE (MICRONS) G . D . C O R M A C K A N D A . J . B A R N A R D 608 D E L A Y A N D r 5 C 2 2 T H Y R A T R O N J CIRCUIT B P ICKUP L O O P ^ -15 kV O — L O A D < = CROWBAR S W I T C H -C 500 nnp R I m e g 3ff '°f\> MAIN S W I T C H i f" FIG. 3. Triggering circuit. cable initially charged to 15 kV and connected to the trig-ger pin with a voltage doubler determination that pro-vided dc isolation. The first pulse of trigger current through the trigger pin [see Fig. 4(a)] has a duration of 40 nsec. The relay shown in Fig. 3 provides electrical isolation of the main switch trigger circuit from the 115-V ac supply-during the discharge of the bank. The relay could be re-placed by a thyratron should synchronization of the firing of the bank with an electrical signal be required. It can be seen from Fig. 2 that r is less when the polarity of the trigger pulse is positive rather than negative. The curves roughly obey the relation first observed by Mather and Williams,3 r«l/p. (1) To account for this relation, they have assumed that col-lisions between electrons and gas atoms produce a linear increase of ionization with time and that appreciable switch current starts to flow when a certain stage of ionization is reached in the discharge chamber. The presence of the plateau in the positive trigger curve in Fig. 2 for 18 <p <60 n is further evidence that this collision mechanism, rather than photoionization, is probably the dominant ionization mechanism. It is proposed that the plateau can be ex-plained as follows. The collision-dominated trigger dis-charge results in ion bombardment and heating of a small region where the trigger discharge strikes the cathode, when the trigger pulse is positive. The trigger pin is not appreciably heated by a positive pulse because the elec-trons striking the pin have lost most of their energy in the plasma region of the trigger discharge. When the positive trigger current has ceased, thermionically emitted elec-trons from the heated region of the cathode will be acceler-ated across the discharge chamber. The sudden increase in electron density in the discharge chamber will enhance the production of ion pairs and decrease r from what it would be if thermionic emission were not important. For example, it is not important when the trigger is negative because then the trigger pin is heated by the trigger discharge. Once the trigger current has ceased, thermionically emitted electrons from the trigger pin do not enter the discharge chamber because a small amount of the thermionic current feeding into the relatively high impedance of the external trigger circuit rapidly causes the formation of a retarding electric field around the trigger pin. Thermionic emission from the trigger pin is then severely space-charge-limited. The T (p) data therefore substantiate the ionization by collisions theory of Mather and Williams.3 Motion of the discharge column due to pinching can re-sult in a high frequency modulation of the current during the first fraction of a microsecond. The amplitude of the modulation increases with decreasing current. In fact, when the initial value of dl/dl is sufficiently large, the oscilla-tions are absent, thus indicating that the column does not contract. Such behavior can be expected for large currents, (a) L i c ) 1 usee (b) 0 1 Msec (c) c > 1 usee (d) Hi I, 0 1 Msec (e) L . l l l f "f 1 c ) 2 usee FIG. 4. Typical oscillograms of: (a) the time derivative of the trigger current at the trigger pin of the main switch; (b) the time derivative of the load current dl/dl for an initial pressure of 1.8 n and a bank voltage of 2 kV; (c) dl/dl for an initial pressure of 47 fi and a bank voltage'of 2 kV; (d) dl/dl for an initial pressure of 4.6 M and a bank voltage of 15 kV; and (e) dl/dl through an ^ 8 - m j i H load for an initial pressure of 21 /x in both switches and a bank voltage of IS kV. The vertical scales are uncalibrated. The ~30-Mc oscillations appearing on traces (b) to (e) are due to pickup of spurious signals. 609 S P A R K G A P S W I T C H since material from the electrodes and the Lucite will con-tribute greatly to'the particle density in the discharge. If the particle density increases sufficiently fast, then the first contraction of the discharge is opposed by the rapidly rising internal pressure. The duration of modulation in-creases with decreasing gas pressure. Low gas pressure also results in a greater number of oscillations, a characteristic that has been noted by Mather and Williams,3 although in the present work the maximum number observed has been two. The observed time to the first pinch approximately obeys the dependence on density and initial value of dl/dt predicted by Rosenbluth and Garwin.9 When p is 1.8 fi, with bank voltage 2 kV and total circuit induc-tance 29 m/iH, a first pinch occurs at about 200 nsec [see Fig. 4(b)] and a second pinch can just be detected at about 500 nsec. Since dl/dt remains positive during this time, the oscillations do not make the current waveform depart appreciably from a damped sifiusoid. The departure is considerably less at higher pressures and bank voltages as is shown by the subsequent oscillograms in Fig. 4. Inspection of the electrodes after many firings at a fixed bank voltage shows the existence of a central clean region that has an area that depends upon the bank voltage. For example, firings at a bank voltage of 5 kV produce a clean area of about 1 cm2. Since the observed current waveform is essentially a damped sine wave after the first fraction of a microsecond, it can be inferred that gross movements of the discharge channel are not present, and therefore that the clean area represents the cross-sectional area of the discharge. This area corresponds to a current density in the discharge of at least 30 000 A/cm2. Even when the initial gas density is high enough to re-sult in no observable high frequency oscillations in the first quarter cycle of the dl/dl waveform, dl/dl still ex-hibits a slow rise to the first maximum. This slow rise can be discussed in terms of a closing time /„, defined as the time interval between appreciable departure of dl/dt from zero and the peak value of dl/dt. The observed values of tc have been in the range of 50 to 200 nsec, the lower value being obtained for a high initial gas density. Little variation of tc with bank voltage has been noted, although this de-pendency has not been investigated as thoroughly as it has by Johansson and Smars,4 who have found that a peaking of exists somewhere between 1 and 30 kV. The observed variation of lc with gas density suggests that the switch possesses a dynamic resistance. It is proposed that tc can be attributed to the time required for the establishment of a small cathode fall region and an essentially neutral plasma column. The ion density in the plasma will be higher than the initial gas density, most of the additional particles being sputtered from the cathode by impinging 9 M . N. Rosenbluth and R. Garwin, 'Los Alamos Scientific Labora-tory Report LA-1850 (1954). FIG. 5. Pictorial view of the crowbar switch and the main switch. The insulating clamps are not shown. ions. Thus an increase in initial gas density causes a de-crease in tc. The lifetime of the switch is as yet unknown. However, 400 firings under various conditions (0.5 to 25 kV, 10 to 500 kA) have been made; most of the firings have been in the 1- to 2-kJ range with about 30 being at 4 kj. The active surfaces of the electrodes are roughened but are not visibly worn. The surface of the Lucite appears to have been melted and slightly discolored but is still nonconducting. The 4-kJ discharges softened the surface of the Lucite but did not result in serious ablation. Should the lifetime of the switch be limited by eventual ablation of the Lucite, then it is planned that this insulation be replaced by a sheet of cementable Teflon. Preliminary experiments have indi-cated that ablation of Teflon is considerably less than that of Lucite. A thin coating of carbon has accumulated in the dump chamber but this coating has not affected the operation. Pre-ignition of the switch has occurred in about 2 % of the firings when the voltage has been greater than 15 kV. When the switch is adequately pumped out be-tween firings it has been found that pre-ignition is greatly suppressed, indicating that the electrodes and the cathode-insulator junction should be well outgassed before each firing. A second switch, of design shown in Fig. 5, is in use to short out the load near the end of the first halfcycle of current. This crowbar switch and the main switch are mounted close together and are connected to the same vacuum system. The trigger circuit for firing the crowbar switch is shown in Fig. 3 and a typical waveform of the derivative of the short-circuited current in a load in Fig. 4(e). The crowbar switch is a three-terminal circuit element and has a "through inductance" of about 4 m/iH and a shorting inductance of about 1 m^H. The former value could be reduced by increasing the width of the sheet con-ductor leads or by employing thinner Lucite. The latter indicates that the short-circuited load current is essentially unidirectional, even for values of load inductance as low as 10 rmxH. The load can be short-circuited at essentially any G . D C 0 R M A C K A N D A . J . B A R N A R D 6L0 time during the discharge because the crowbar switch can be fired at very low voltages. Even though the crowbar switch is subjected to a reverse voltage during the first quarter cycle of the current (the electrode that is sealed to the Lucite is made positive with respect to the electrode containing the vent holes), pre-ignition has not occurred, probably because the reverse voltage then occurring is of small magnitude and duration. The magnitude of this re-verse voltage appearing across the crowbar switch is less than the voltage initially on the condenser bank because the impedance of the load is less than that of the remainder of the circuit. ACKNOWLEDGMENTS The authors wish to express their thanks to Dr. R. A. Nodwell and Dr. R. J. Churchill, and also to Dr. 0. A. Anderson of the Lawrence Radiation Laboratory, Berkeley, and Dr. M. J. Kofoid of the Boeing Airplane Company, for their helpful suggestions. - 137 -APPENDIX D PROPERTIES OF A LOW INDUCTANCE  LOW PRESSURE SPARK GAP SWITCH In the present Appendix further information i s pre-sented on the switches described i n Appendix C. The emphasis i s on a d e s c r i p t i o n of the experimental methods employed to test the switches and on a further elaboration of the physi-c a l processes that are believed to occur i n the switches. The t r i g g e r i n g time X was measured, f o r experimental convenience, as the time i n t e r v a l between the onset of lumin-o s i t y from a small open-air gap i n series with the t r i g g e r gap, and the s t a r t of the flow of appreciable switch current. A s p e c i a l t e s t with a Tektronix 551 o s c i l l o s c o p e , a high speed photomultiplier c i r c u i t and a sing l e turn 1 i n . diameter terminated f l u x pickup c o i l showed that the luminosity from * the ser i e s open-air gap started within a time l e s s than about f i v e nsec a f t e r the t r i g g e r current had started to flow. Since the risetime of the e l e c t r o n i c c i r c u i t s f o r a l l mea-surements was about H nsec, there was no need to obtain a more accurate measurement of the delay between the onset of current and luminosity. I t was necessary to employ the lumin-o s i t y s i g n a l as a reference f o r a l l measurements of t r i g g e r -ing time because the o s c i l l o s c o p e , a Tektronix 551, would not t r i g g e r dependably on the s i g n a l generated i n a pickup c o i l located close to the t r i g g e r pin. The voltage induced across - 138 -such a pickup c o i l due to the t r i g g e r current was completely obscured by e l e c t r i c a l noise. This e l e c t r i c a l noise disap-peared when the t r i g g e r c i r c u i t was disconnected from the switch. The delay between the onset of current and luminosity was, therefore, measured with t r i g g e r c i r c u i t not connected to the switch as i s shown i n Pig 61. Tektronix 551 Dual Beam Oscilloscope t r i g g e r spark photomultiplier Pig 61. C i r c u i t f o r Simultaneous Observation of Trigger Current and Luminosity. Some care was exercised to ensure that the open-air gap i n series with the t r i g g e r p i n had l i t t l e e f f e c t on the t r i g g e r -ing time of the switch. Por example, the t r i g g e r i n g time of the switch measured r e l a t i v e to the time of shorting the tr i g g e r cable was compatible.with the t r i g g e r i n g time measured r e l a t i v e to the onset of luminosity from the small open-air gap i n serie s with the t r i g g e r gap. The former measurement was made both with and without the open-air gap i n the t r i g -ger c i r c u i t and taking due account of the t r a n s i t time of the cable. The luminosity s i g n a l was of a single p o l a r i t y , l a s t e d f o r about a microsecond, had an amplitude of about two v o l t s and had a f a s t i n i t i a l rate of r i s e . I t was, therefore, a more dependable s i g n a l f o r t r i g g e r i n g the sweep c i r c u i t s of the o s c i l l o s c o p e than eit h e r the small amplitude,small duration - 139 -f l u x pickup signal that could he obtained at the shorting end of the t r i g g e r cable or the noise-ridden f l u x pickup signal that could he obtained at the t r i g g e r pin end of the tr i g g e r cable. The t r i g g e r i n g time was, therefore., measured with the c i r c u i t shown i n F i g 62. F i g 62. Method of Measuring Triggering Time of Low Pressure Switch. The vacuum system f o r the switches i s shown i n F i g 63. I t was found that the switches operated quite s a t i s f a c t -o r i l y when a constant pressure was maintained i n the system with the needle-valve, and when the bank -voltage was l e s s than about 10 kV. Operation at higher voltages necessitated pump-ing the switches out to a pressure of about a micron a f t e r a f i r i n g and then admitting f r e s h gas to the vacuum system u n t i l the desired pressure was attained. A l l measurements of t r i g -gering time were made employing the l a t t e r system to ensure that the gas. i n the switches was of f a i r l y high p u r i t y . Also., a l l measurements of X were performed with the switches i s o l a t e d - 140 -from both the gas i n l e t and the vacuum pump. The pressure measured with the P i r a n i guage was thus a steady-state pres-sure. The P i r a n i readings were converted to true pressure readings i n microns Hg with the aid of c a l i b r a t i o n curves supplied with the P i r a n i guage. to main switch 20 l i t r e dump tank to crowbar/ switch h from argon supply i'TT needle valve <8> P i r a n i guage ft To mechanical pump and d i f f u s i o n pump trap Pig 63. Vacuum System f o r Switches on Capacitor Bank, The measured t r i g g e r i n g time f o r the 4 kJ main switch as a function of the pressure i n i t i a l l y i n the switch i s given i n Pig 64. Data f o r both helium and argon and two t r i g g e r i pulses of d i f f e r e n t energy and waveform are presented. The ef f e c t on X of the pu r i t y of the gas i n the switch i s indicated by the c i r c l e d points. A l l other data was obtained with fr e s h f i l l i n g s of gas i n the switch and a time i n t e r v a l between f i r -ings of 5 to 30 minutes. - 141 -o ra • r l a •H -p si •H fH 0 tiO tiO •H fH -P II 10' 1000 t r i q e j e r c i r c u i t *o 100 10 Hiql» energy tr igger C i V e u ' i t Low energy trigger circuit 0.1 1 10 100 1000 Pressure i n microns Hg Pig 64. Triggering Time of the 4 kJ Switch as a Function of Pressure. The point marked (§) was obtained a f t e r the system had "been pumped at a pressure of about 0.2 microns Hg f o r two hours then f i l l e d with helium to a pressure of 240 microns Hg. The point marked @ was obtained with a gas i n the switch c o n s i s t i n g of helium and the impuri-t i e s released by the preceding f i r i n g . A t r i g g e r pulse of p o s i t i v e p o l a r i t y r e s u l t e d i n a lower value of X than did a negative pulse. The mechanism that i s probably responsible f o r t h i s t r i g g e r p o l a r i t y behaviour w i l l now be discussed. A t r i g g e r pulse of p o s i t i v e p o l a r i t y r e s u l t s i n motion of more p o s i t i v e l y charged ions and l a r g e r - 142 -p a r t i c l e s into the discharge chamber of the main gap than does a negative t r i g g e r pulse. The emission of such p a r t i c l e s was observed when the t r i g g e r i s operated at atmospheric pres-sure as mentioned i n Appendix B. The conjectured motion of the charged p a r t i c l e s i n the t r i g g e r discharge i s shown i n F i g 65 for both p o s i t i v e and negative p o l a r i t i e s of t r i g g e r pulse. cathode of main gap a) t = 5 nsec b) t = 30 nsec c) t = 45 nsec p o s i t i v e p o l a r i t y of t r i g g e r pulse a) 't = 5 nsec b) t = 30 nsec c) t = 45 nsec negative p o l a r i t y of t r i g g e r pulse F i g 65. Motion of Charged P a r t i c l e s i n Trigger Discharge. The low energy t r i g g e r pulse generator shown i n F i g 64 i s being considered. The duration of the current pulse i s about 40 nsec as i s shown i n Fi g 53. Data that i s presented on page 47 indicates that regions sub-jected to high energy electron bombardment lose p a r t i c l e s . The p o s i t i v e ion current i s thus composed of ionized gas atoms, ions from the p o s i t i v e electrode and ions from the surface of - 143 -the l u c i t e . The data presented i n Chapter I I I , Section A i n d i -cates that breakdown i s p r i m a r i l y due to electrons i n j e c t e d by the t r i g g e r spark. The question now a r i s e s , i s the cathode of the main gap a better emitter of electrons when the t r i g g e r pulse -is p o s i t i v e or negative? The T(p) curves i n F i g 64 indicate that the cathode i s a better emitter of electrons when the t r i g g e r pulse i s p o s i t i v e . In f a c t , the plateau i n the £(p) curve f o r the argon f i l l e d switch triggered by the po s i t i v e p o l a r i t y low energy t r i g g e r c i r c u i t i s probably due to the copious electron emission that occurs upon cessation of the t r i g g e r pulse. The cathode of the main gap i s no longer-passing electrons to the t r i g g e r pin when the t r i g g e r current has ceased flowing. There i s s t i l l appreciable ion bombardment of the cathode of the main.gap by the ions formed i n the t r i g -ger discharge, because these ions s t i l l have large v e l o c i t i e s directed toward the cathode. The i n e r t i a of the ions i s suf-f i c i e n t to permit t h e i r motion toward the cathode to continue for some time a f t e r the t r i g g e r current has ceased. The cathode of the main.gap can thus s t i l l emit a large electron current due to the space charge of the incoming ions. I t i s probable that t h i s current i s due to both thermionic and f i e l d emission., although i t i s d i f f i c u l t to conjecture what the temperature at the surface of the cathode of the main gap might be. The electron emission occurring during 0< t< 40 nsec cools the cathode of the main gap whereas ion bombardment heats i t . A negative t r i g g e r pulse r e s u l t s i n no ion bombardment of the cathode of the main gap, but some heating due to electron - 144 -bombardment. The temperature of the cathode of the main gap at the cessation of the negative t r i g g e r pulse i s again unknown, as the cathode i s heated by the incoming electrons, but i s cooled by the ions emitted. The important point i s that the cathode of the main gap i s not subjected to ion bombardment immediately at the end of the negative t r i g g e r pulse, whereas i t i s i f the t r i g g e r pulse i s p o s i t i v e . When the t r i g g e r pulse i s negative, the t r i g g e r pin i s subjected to ion bombardment af t e r the t r i g g e r current has ceased flowing. The t r i g g e r pin cannot emit many electrons at t h i s time due to the space charge l e f t on the t r i g g e r pin by the few electrons that are emitted. The s l i g h t emission that does occur charges up the capacitance that e x i s t s between the t r i g g e r pin and the cathode of the main gap and''produces an e l e c t r i c f i e l d between these compon-ents that reduces further emission. Emission of electrons from the cathode of the main gap upon cessation of a p o s i t i v e t r i g -ger pulse i s not space-charge l i m i t e d because the large e l e c t r i c f i e l d already e x i s t i n g across the main gap i s e s s e n t i a l l y unaffected by t h i s emission. The plateau i n the X (p) curve for the low energy,.short duration p o s i t i v e t r i g g e r pulse thus i s caused by emission of electrons from the cathode of the main gap at the cessation of the t r i g g e r current. I t i s not d e f i n i t e whether the emission i s due to the high e l e c t r i c f i e l d at the cathode caused by incoming ions or i s due to a combin-ation of f i e l d and thermionic emission. The existence of t r a n s -ients i n the thermionic emission of an arc a f t e r a large change i n current has been established by G. L i s t and G. Pardemann - 145 -(1959)? however under conditions quite d i f f e r e n t from those e x i s t i n g f o r the t r i g g e r discharge studied here. The T(p) curves f o r argon roughly obey the r e l a t i o n f i r s t observed by Mather and Williams (1960): T * I / p 129 To account f o r t h i s r e l a t i o n , they assumed that c o l l i s i o n s between electrons and gas atoms produced a l i n e a r increase of , ion density with time and that appreciable switch current started to flow when a c e r t a i n ion density was reached i n the discharge chamber. I t i s i n t e r e s t i n g that such a r e l a t i o n i s v a l i d over at l e a s t two decades of pressure f o r the low energy t r i g g e r c i r c u i t and one decade of pressure f o r the high energy t r i g g e r c i r c u i t even though the waveform of the t r i g g e r current generated by these ' c i r c u i t s d i f f e r s g r e a t l y . I t i s possible that a mechanism proposed by Raether i s operative. He found that photoionization i n the v i c i n i t y of the cloud of p o s i t i v e ions i n an avalanche contributed to the breakdown process. Photoionization of the gas i n the discharge chamber by photons released from the t r i g g e r spark would e x i s t i n the present switch and could r e s u l t i n a l i n e a r increase of ion density with time. I t i s also possible, of course, that electron emission from the cathode of the main switch (see Pig 65c), then i o n i z a t i o n of the gas atoms by electron-atom c o l l i s i o n s , might be "the major mechanism leading to breakdown. I f this mechanism i s of major importance, then equation 129 could be j u s t i f i e d only i f a constant rate of emission of electrons into the discharge chamber of the main switch i s i n i t i a t e d by the - 146-s t a r t of the t r i g g e r current and i f the rate of emission i s e s s e n t i a l l y independent of the subsequent waveform of the t r i g g e r current. The p o l a r i t y behaviour discussed i n the preceding paragraph causes a small departure of the carves from l i n e a r i t y and i s quite d e f i n i t e l y due to the copious number of electrons emitted from the cathode of the main gap at the cessation of a t r i g g e r pulse of p o s i t i v e p o l a r i t y . The plateau i n the T(p) curve f o r a low energy p o s i t i v e t r i g g e r thus in d i c a t e s that either c o l l i s i o n s between electrons and atoms i s the major mechanism of i o n i z a t i o n or that breakdown i s brought about by the t r i g g e r spark at the cathode of the main discharge., I f the l a t t e r process i s of major importance, i t cannot be concluded whether photoionization of the gas i n the discharge chamber or i o n i z a t i o n of t h i s gas by electrons emitted by the t r i g g e r discharge i s the dominant mechanism that leads to the *C(p) r e l a t i o n given i n equation 129. The v a l i d i t y of a few of the statements i n the pre-ceding discussion depend upon the order of magnitude of c e r t a i n q u a n t i t i e s . For example, one question that i s relevant i s , what ion motion exists i n a spark discharge of 40 nsec dura-tion? An order of magnitude c a l c u l a t i o n w i l l be made. Porter and Wooding (1959) believed that the i n i t i a l peak of r a d i a t i o n l a s t i n g f o r a time of about 100 nsec from a low pressure spark discharge i n argon was due to Bremsstrahlung. On the basis of t h i s statement i t i s not unreasonable to conclude that a voltage that i s an appreciable f r a c t i o n of the supply voltage exists across the t r i g g e r discharge and that the discharge i s - 147 -not c o l l i s i o n dominated. The l a t t e r assumption i s not f u l l y j u s t i f i e d because the t r i g g e r discharge w i l l track over and evaporate some of the surface of the polyethylene. I t w i l l be assumed that the t r i g g e r discharge i s r e s i s t i v e and has a voltage waveform that i s the f i r s t pulse of a sine wave. A normal d i s t r i b u t i o n waveform would be a closer approximation to the true waveform but the mathematical complexity involved would not be j u s t i f i e d . I t i s assumed that the e l e c t r i c f i e l d experienced by the p a r t i c l e s i n the discharge i s one dimensional and homogeneous. For a p a r t i c l e of mass m and charge q. moving i n the f i e l d E = - j - s i n T r - ^ - ....130 d v where d i s the distance over which the e l e c t r i c f i e l d acts and YQ i s the peak value of voltage across the t r i g g e r discharge I e i n -rr _Sd x = -^p s i n TT Y ....131 Q\4 T r +1 X = —i— : — | - COS IT-L X mdTT* L "C ....133 where i t i s assumed that ±(t = 0) = 0, x ( t = 0) = 0. I f t = X = 40 nsec, V = 30 kV, d = 6.1 mm, and the motion of an argon ion i s considered, then ±(t = 40'nsec) = 30.4 cm///sec and x ( t = 40 nsec) = 6.1 mm. The actual i n t e r - e l e c t r o d e d i s -tance of the t r i g g e r discharge i s at l e a s t 3 mm. The motion of ions i n the t r i g g e r discharge i s thus appreciable and the ion motion conjectured i n F i g 65 r e a l i s t i c . - 148 -The number of electrons emitted by the t r i g g e r can be estimated from the energy i n the t r i g g e r spark. The maximum current i n the spark was of the order of 600 A. The t o t a l num-ber of electrons, N , emitted by t h i s pulse of 40 nsec duration must, therefore, have been of the order of .4-0 nsec q / 1 d t J © ... 13 4 o where q i s the charge on an electron and i i s the t r i g g e r current. When i i s assumed to have the shape of a single 1 3 one-half cycle of a sine wave, Ng= 8 x 10 electrons. This number of electrons i s the t o t a l number passing through the tr i g g e r spark and i s not the number emitted into the discharge chamber. The energy i n the t r i g g e r spark i s 4 0 n s e C Pt. - f * I V o l t ... .135 where Y i s the p o t e n t i a l appearing across the spark. An upper l i m i t f o r the value of P^ .g can be estimated by assuming that i and V have peak values of 600 A and 32,000 V re s p e c t i v e l y and that the waveshape of both i and V i s that of a single h a l f - c y c l e of a sine wave. Then, P, = 0.-3 J» u S The number of electrons that can be emitted by the tr i g g e r p in at the cessation of a negative t r i g g e r pulse before space charge l i m i t s further emission i s of i n t e r e s t . Prom the geometry of the main switch i t can be i n f e r r e d that the capa-c i t y between the t r i g g e r pin and the cathode of .the main switch i s about 1.5 pf. I f i t i s assumed that none of the e l e c t r i c - 149 -f i e l d due to the voltage across the main gap i s present at the t r i g g e r pin, then the number of electrons that can be emitted by the t r i g g e r p in before a p o t e n t i a l of say +1 volt appears on the pin with respect to the cathode of the main gap i s c/q or 0.9 x 10' electrons. The one v o l t of retarding p o t e n t i a l then set up would be s u f f i c i e n t to prevent further emission of electrons from the t r i g g e r pin. An upper l i m i t f o r the number of electrons that can be emitted by the cathode of the main gap at the cessation of a p o s i t i v e t r i g g e r pulse can be estimated from the energy i n the t r i g g e r spark. I f i t i s assumed that every electron emit-ted cools the area of emission by 2 ev, then an energy of 0.3J 1 7 could r e s u l t i n the emission of 9 x 10 electrons. Space charge on the cathode of the main gap due to emission of electrons would not a f f e c t the emission rate at the cessation of a p o s i t i v e t r i g g e r pulse because the a c c e l e r a t i n g f i e l d across the main gap i s f a r l a r g e r than any possible space charge that might be generated. The Z (p) curve f o r helium does not obey equation 127. The suggested reason i s that the processes leading to breakdown d i f f e r from those f o r argon. The inductance of the low pressure switch has both a steady-state and a time-varying component. The time-varying component i s discussed i n the preceding Appendix. The steady-state inductance of the main low pressure switch was determined experimentally by observing the period of a 500 V triggered discharge of the bank into an open-air spark gap inserted i n - 1 5 0 -place of the driver of the shock tube. The inte r - e l e c t r o d e spacing of the open-air gap was set so that breakdown occurred when 500 V was applied. The main low pressure switch was then removed from the c i r c u i t and a length of coplanar lead i n s t a l -l e d i n i t s place. The bank p o t e n t i a l was then r a i s e d to 500 V and the period of the free-running discharge observed. The change i n c i r c u i t inductance was the inductance of the main low pressure switch and had a value of 4.0 nH. The steady-state inductance of the main switch can also be computed from the geometry of the switch. The t o t a l inductance of the switch i s the sum of that due to the three regions indicated i n F i g 66. The inductance of region a i s estimated f o r current flowing on the inner surfaces of co-planar conductors 4 i n . long (&), 6 i n . wide (w) and of 1/16 i n . separation ( t ) . Thus I a= JU0~ -t - 1.3 nH. The inductance of region b i s approximately that due to current flowing on the inner surfaces of coplanar conductors .10 i n . apart, 3 i n . long and 6 i n . wide. Thus L^= 1.6 nH. The inductance of region c i s approximately that due to the inductance between two cylinders of length 5/16 i n . , and inner and outer r a d i i of 1/4 i n . and 1 i n . Thus L c= 1.1 nH. The t o t a l inductance of the main switch, c a l c u l a t e d from switch dimensions, i s 4.0 nH, the same value as observed experimentally. Pig 66. Subdivision of the Main Switch into Regions fo r the Purpose of C a l c u l a t i n g the Inductance. The inductance of the crowbar switch can be i n f e r r e d from the r e s u l t s of the c a l c u l a t i o n s i n the preceding para-graph. The crowbar switch i s thus a three-terminal device that has the inductances shown i n Pig 67. o R^T^ - ° o r^Tpv—f—HTfi^ o I.I n H a) Before f i r i n g b) A f t e r f i r i n g Pig 67. Inductance of Crowbar Switch. The resistance of the low pressure switch has both a steady-state and a time-varying component. The steady-state value of the resistance of the main switch could be computed from the damping of the discharge current, provided that the resistance of the remainder of the c i r c u i t was known. The time-- 152 -varying component of the resistance of the switch affected the r i s e time of dl/dt (see also Andreev and Vanyukov 1962), Both energy and time are involved i n the processes of: i o n -i z a t i o n of the gas i n the discharge chamber, evaporation of p a r t i c l e s from the electrodes and motion of ions i n the d i s -charge. The ion density required to e s t a b l i s h n e u t r a l i t y i n the plasma column i s l a r g e r than the gas density i n i t i a l l y i n the switch. The electrodes must, therefore, contribute p a r t i c l e s to the discharge. Some time i s required before the electron and ion bombardment of the electrodes can r e s u l t i n the c o n t r i b u t i o n of s u f f i c i e n t p a r t i c l e s and before these p a r t i c l e s can move an appreciable distance i n the arc. The experimental evidence that does suggest that the p o s i t i o n i n g time of the ions i s the major explanation f o r the existence of t i s that the minimum value of t that has been observed, c c -^50 nsec, i s compatible with the ion t r a n s i t time across the gap.. I f an ion i s accelerated across a p a r a l l e l - p l a t e gap with spacing d, then the t r a n s i t time i s l^rf d where m i s the mass of the ion, q the charge on the ion and V the poten-t i a l across the plates. Thus i f an argon ion i s considered to be accelerated by a p o t e n t i a l of 20 kY across a 5/16 i n . gap, then the t r a n s i t time i s 53 nsec. A f t e r the completion of the 400 t e s t f i r i n g s mention-ed i n the preceding Appendix, the d r i v e r of a shock tube was connected into the c i r c u i t i n place of the inductive load. I t was found that the crowbar switch broke down as soon as bank p o t e n t i a l appeared across i t . This breakdown was not - 153 -unexpected - see the l a s t paragraph of the text In the preced-ing Appendix - because the p o t e n t i a l appearing across the crowbar switch was of the opposite p o l a r i t y f o r which the switch was designed. No crowbar breakdown problems had, how-ever, been encountered u n t i l the switches were connected to the shock tube. Inversion of the crowbar switch and a change i n the l o c a t i o n of the t r i g g e r components solved t h i s break-down problem. This redesigned crowbar switch i s that shown i n F i g 5• A second set of two switches s i m i l a r to those shown i n F i g 5 has been i n s t a l l e d by Whelan* on another e l e c t r o -magnetic shock tube. The capacitor bank employed has a cap-a c i t y of 450 / I F and a maximum voltage r a t i n g of 5 kV. The switches have operated s a t i s f a c t o r i l y at energies up to 4 kff-'! even though the period of the discharge i s 32//sec. The l u c i t e has needed cleaning twice during the l a s t 500 shots. In conclusion i t can be stated that the low pressure switch that has been developed i s an excellent crowbar switch on an electromagnetic shock tube. As a main switch, the low pressure switch o f f e r s some advantages over the more widely used open-air spark ggp switch but has two disadvantages. They are that p r e i g n i t i o n does occur occasionally and that the l u c i t e i n s u l a t i o n has to be cleaned every few hundred f i r i n g s . *The author i s g r a t e f u l f o r r e c e i v i n g t h i s information from P.J. Whelan, Physics Dept., U n i v e r s i t y of B r i t i s h Columbia. - 154 -APPENDIX E  THEORY POP THE ERUPTIVE INSTABILITY ' The equations of motion f o r the eruptive i n s t a b i l i t y suggested i n Chapter I I I , Section 1 are derived, on the basis of a s i m p l i f i e d model, i n t h i s Appendix. The motion of a c y l i n d r i c a l plasmoid across a discharge column i s considered (Pig 68)'. Pig 68. Suggested Plasmoid Motion that Results i n Eruptive I n s t a b i l i t y of Discharge Column. The photographs shown i n Pig 12c and j indicate that the radius of the c y l i n d r i c a l plasmoid i s of the order of 3 mm. These photographs also indicate that the plasmoid has a v e l o c i t y , r e l a t i v e to the discharge column,, of about 3 cm/«sec. The magnetic Reynold's number f o r t h i s v e l o c i t y , t h i s r a d i a l dimension and an assumed value of conductivity of 10^ mho/m i s 1.2. The plasmoid thus transports appreciable magnetic f l u x . w i t h i n i t s e l f as i t moves across the discharge •column, In order to s i m p l i f y the following calculation;, it. - 155 -w i l l be assumed that the leakage of magnetic flux from the plasmoid i s n e g l i g i b l e . erated away from the insi d e corner of the discharge w i l l not be considered. The reason f o r t h i s omission i s that i t would be d i f f i c u l t to determine a r e a l i s t i c value f o r the magnitude of the magnetic induction f i e l d inside the cusp at t h i s i n s i d e corner. This magnetic induction f i e l d would i n t e r a c t with the current density i n the discharge to compress and then acceler-ate, i n a diagonal d i r e c t i o n (see Pig 68), the portion of the discharge column that i s near the point of the cusp. Rose and Clarke (1961) have considered an a c c e l e r a t i o n mechanism that i s s i m i l a r to that which i s proposed i n the present work. The motion of the plasmoid during i t s subsequent motion insid e the discharge column w i l l now be considered. The v e l o c i t y of the plasmoid, once a c c e l e r a t i o n has ceased, measured with respect to a coordinate system moving with the discharge column i s designated ± I t i s assumed that the plasmoid ° max att a i n s t h i s v e l o c i t y before i t has passed an appreciable distance into the discharge column. The plasmoid i s slowed down by electromagnetic forces as i t moves subsequently i n the diagonal direction. I f forces due to gas pressure are neglected and i f the plasmoid i s assumed to be neutral and of mass density J> , then the forces acting on the plasmoid are where r i s the radius of the plasmoid, L i s the length, x i s The motion of the plasmoid while i t i s being a c c e l -.136 volume of plqsmofd - 156 -the diagonal coordinate of the center of the plasmoid,, J i s the azimuthal current density on the surface of the plasmoid and B, i s the magnetic induction f i e l d due to the discharge d current. When B^ varies l i n e a r l y with x (B^ = - Ax defines the constant A) inside the discharge column, and when I i s the azimuthal current on the surface of the plasmoid, i t f o l -lows from equation 136 that L/>'i + A I = o ....137 When I * L ( x ) , /> (x) , x(t=0) = -W/2 and I - LA(x + W/2)//^o the s o l u t i o n to equation 137 i s X = Xa S i n o j t - W/2 . . . .138 where ^^ o^ * « o • "1 3 9 The dimension W i s the diagonal width of the discharge column. The c r i t e r i o n f o r the escape of the plasmoid out of the discharge column i s then X ~ " > • • • • U 0 I t i s of i n t e r e s t that the analysis has indicated that the plasmoid i s confined insi d e what appears to he a p o t e n t i a l w e l l . The plasmoid does not escape i f i t has an i n s u f f i c i e n t k i n e t i c energy. I'f i t does once escape from the discharge column then the electromagnetic force acting upon i t i s no longer a r e s t o r i n g force. The above analysis does -not p r e d i c t the subsequent motion of the plasmoido Actually, the electromagnetic force i s i n such a d i r e c t i o n as to then cause the plasmoid to move further from the discharge column. - 157 -The discharge shown i n Pig 12a) t o p) would have values of A * 3 Wb/m3, W * 0.006 m and J> « 0.1 kg/m 5„ The c r i t e r i o n f o r escape of the plasmoid i s thus from equation 140, ± ^ o > 1.7 cm//tsec. Such a value of i n i t i a l plasmoid v e l o c i t y i s not unreasonable. I t can be concluded that the eruptive i n s t a b i l i t y mechanism could account for the observed protuberances at the front of the plasma. In the preceding analysis i t has been assumed that the plasmoid loses no magnetic f l u x as i t moves across the discharge column. I f the d i f f u s i o n of magnetic f l u x i s ap-preciable, the c r i t e r i o n expressed by equation 140 can be relaxed. A lower value of x „ than predicted, by t h i s equation max e would then allow the plasmoid to escape from the discharge column. - 158 -APPENDIX F ANALYSIS OF THE EXPERIMENTAL DATA OBTAINED WITH THE MHD GENERATOR EMPLOYING 'TDTDUCrTIYE POWER TRANSFER The curves shown i n F i g 50 suggest that the con-d u c t i v i t y of the plasma being studied i s not described by equation 112. The overshoot of the observed signals i n d i -cates that the conductivity of the plasma i s quite c l o s e l y described by „ 1 $ >0 o-(f) = cr* e 0"(f) = 0 , £ < o ....141 This conductivity function has been previously considered by Cormack (1960). I t has since been found that the numerical i n t e g r a t i o n believed to be necessary by Cormack was not r e -quired but that the voltage could be expressed i n closed form as: V ( t ) = U U « 3 > * V C P ... y(t) where fit)' e 20 r j n 2 _ Ut .142 143 This equation i s , of course, only v a l i d i f —i—»» 111 . The expression f o r (t) f o r any value of R^  i s found from equa-t i o n 111 to be Nxl dt 44 - 159 -Equation 144 cannot be solved by a n a l y t i c a l methods., A solu-tion by numerical methods would not contribute gr e a t l y to the aim of Chapter IV. Section 3 - which was to present the e l e c t r o -dynamic properties of the generator. The form of the function Y'(t) i n equation 143 f o r various values of {3 i s shown i n Pig 69. The observed waveform? the Ej = 200A curve i n Pig 50, i s quite c l o s e l y of the same shape as the |3 = 4b curve i n Pig 69» The maximum conductivity of the plasma i s given by where TP, i s the maximum value of V ("t) and V i s the peak value of voltage observed. Thus fo r U - u 1 - 2 x 10^m/sec;, mhos/m, V p = 7.5 V, I = 10 A, X= 0.82, then 0* = 1 .0 x 10 4 mhos/m. The value f o r the conductivity of the plasma (f on page 111, i s thus given as 10^ mhos/m. 8 - 160 -.8 .6 .4 .2 0 -.2 -.4 e = b - \ \ g=2b \ > —V— \ * \ - 2 - 1 0 1 2 u t A 3 4 Pig 69. Voltage Waveforms Calculated f o r the Conductivity Function, 0 - * e * p - [ ? / p ] - 161 -BIBLIOGRAPHY Alfven, H., Lindberg. L., M i t l i d P., (1960) J. Nucl. Energy, Part C: Plasma Physics, 1_, 116. Andreev S.I., Vanyukov M.P. (1962) Sov. Phys. - Tech. Phys. 6, 700. Artsimovich L.A., Luk'ianov S.I.U., Podgornyi I.M., Chuvatin S.A. (1958), JETP 6, 1. Baker W.R. (1959), Rev. S c i . In s t r . , 30, 700. Barach J.P. (1961), Phys. F l u i d s 4, 1474. Barnard A.J., Cormack G.D., Simpkinson W.V. (1962), Can. J n l . Phys., 40, 531. Bershader D. (1960), Rev. of Modern Physics, 32, 780. Bostick W.H. (1956), Phys. Rev. 104, 292. Broadbent T.E. (1960), I.E.E., Proc. C, 107, 213. Brucker G.J., Rogers K.C.(1960), Nuclear I n s t r . and Methods, 8, 236. Burkhardt L.C., Lovberg R.H. (1960), B u l l . American Phys. S o c , 5, 350. Chang C.T. (1961), Phys. F l u i d s 4, 1085. Colgate S.A., Aamodt R.L. (1957), Nucleonics 15, 50. Cormack G.D. (1960), M.Sc. Thesis, Univ. of B r i t i s h Columbia. Craggs J.D., Haine M.E. and Meek, J.M. (1946), J . Inst. E l e c . Engrs. Part III A, 93, 963. Dattner A. (1959), Proc. Fourth Conf. Ion. Phen. i n Gases, 1151. Dwight 'H.B.(1957), Tables of Integrals and Other Mathematical Data, The MacMillan Co. 129. Fowler R.G^, Paxton G.W.,Hughes H.G. (1961), Phys. F l u i d s , 4 S 234. Hagerman D.C., Williams A.H. (1959), Rev. S c i . In s t r . 30, 182. Harris E.G. (1956), Naval Research Laboratory Report NRL-4858 (unpublished). - 162 -Harris L.P. (1960), General E l e c t r i c Research Laboratory Re-port 60^RL-2515G. Hart P.J. (1959), Lockheed Technical Memorandum LMSD-288000. Hart P.J. (1962), Phys. F l u i d s 5, 38. Haus H.A. (1962), J . Appl. Phys., 33, 2161. Hintz E., Beerwald H., (1959), Proc. Fourth Conf. on Ion. Phen. i n Gases, 468. Hooker W.J. (1961), Phys. F l u i d s 4, 1451. Hughes H.G. (1961), Rev. S c i . In s t r . 32. Hurwitz H., K i l b R.W. and Sutton G.W. (1961), J . Appl. Phys. 32, 205. Johansson R.B., Smars E.A. (1961), Proc. F i f t h Conf. Ion. Phen. . i n Gases. Kash S.W., Gauger J . , Starr W., and V a l i V. (1958), The Plasma i n a Magnetic F i e l d , R.K.M. Landshoff, E d i t o r (Stanford U n i v e r s i t y Press), 99. Kofoid M.J. (1960-61), Trans. Am. Inst. E l e c . Engrs.. Part I I I , 79, 991 and 999. Kolb A.C. (1957), Phy. Rev. 107, 345. Kolb A.C. (1959), Proc. Fourth Conf. Ion. Phen. i n Gases, 1021. Kolm H.H. ,Mawardi O.K. (1961), J . Appl. Phys. 32, 1296. Komelkov V.S. et a l (1959), Proc. Fourth Conf. Ion. Phen. i n (- Gases, 1141 . Kvartzhava I.P., Kervalidze K.N., Gvaladze J.S. (1959), Proc. Fourth Conf. Ion. Phen. i n Gases, 876. L i n . S . C , Resler E.L. , Kantrowitz A. ( 1955), J . Appl. Phys. 26, 95. Lindberg L., Jacobsen C. (1961), The Astrophysical Journal, 155, 1043. Linke R., (1961), Univ. of Maryland, Physics Dept., Report, "Construction of an Electromagnetic Shock Tube". L i s t G., Pardemann G. (1959), Proc. Fourth Conf. Ion. Phen. i n Gases, 285. Lobov S.I., Tsukerman V.A. (1960), P r i b . Tekh. Eksp. 1, 89. - 163 -Lupton W.H. (1961), Proc. F i f t h Conf. Ion. Phen i n Gases. Marshall J . (1960), Plasma Acceleration, S.W. Kash, E d i t o r (Stanford U n i v e r s i t y Press), 70. Mather J.W., Williams A.H. (1960), Rev. S c i . In s t r . , 31, 297. McLean E.A., Faneuff C.E., Kolb A.C, Griem H.R. (1960), Phys. F l u i d s , 3, 843. Mostov P.M., Neuringer J.L. and Rigney D.S. (1961), Phys. F l u i d s 4, 1097. Pain H.J., Smy P.R. (1960) Proc. Phys. Soc. LXXVI, 849-P a i n € , J . , Smy P.R. (1961), J . F l u i d Mech. JO, 51. P a t r i c k R.M. (1959), Phys. F l u i d s 2, 599. Penfold A.S. (1961), L i t t o n Systems, Inc. Technical Memorandum 61 . Porter G., Wooding E.R. (19^9), Proc. Fourth Conf. Ion. Phen. i n Gases, 515. Raether H. (1959) Proc. Fourth Conf. Ion. Phen. i n Gases, 124. Rockman CM. (1961), Ph.D. Thesis, Princeton U n i v e r s i t y . Rosa R.J. (1961), Phys. F l u i d s 4, 182. Rose D.J., Clark M.J. (1961), Plasmas and Controlled Fusion, J. Wiley and Sons, Inc., 538. Rosenbluth M.N., Garwin R (1954), Los Alamos S c i e n t i f i c Labor-atory, Report LA-1850i Saxe R.F. (1961), Proc. F i f t h Conf. Ion. Phen i n Gases. Seeker P.E. (1959), Proc. Fourth Conf. Ion. Phen. i n Gases. 350. Shkuropat P.I. (1961), Sov. Phys. Tech. Phys. 5, 895. Simpkinson W.V. (1961), M.A.Sc. Thesis, Univ. of B r i t i s h Columbia. Smy P.R. (1961), J. Appl. Phys. 32, 1946. Smy P.R. (1962), Submitted to J . Appl. Phys. S o k o l ' s k i i V.V., Nas tyukha;. A. I., Lobikov E.A. (1960), P r i b . Tekh. Eksp. 2, 132. - 164 -Starr W.L., Naff J.T. (1960), Plasma Acceleration, S.W. Kash, E d i t o r (Stanford U n i v e r s i t y Press) 52. Theophanis G.A. (1960), Rev. S c i . Insts. 31, 427. Woodson H.H., Lewis A.T. (1961), Engineering Aspects of Mag-netohydrodynamics, ed. C. Mannal and N.W. Mather, Columbia U n i v e r s i t y Press, 277. 

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