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Precursor ionization Whelan, Patrick James Thomas Aquinas 1964

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PRECURSOR IONIZATION by PATRICK JAMES ACJJINAS WHEIAN B.Sc. (Hons.), S t . Francis Xavier University, 19f>9 M.Sc, Dalhousie University, 196l A THESIS SUBMITTED IN PARTIAL FULFILMENT OF 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 September, 1961* I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f • B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 r e f e r e n c e and s t u d y , I f u r t h e r a g r e e t h a t p e r -m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t , c o p y i n g o r p u b l i -c a t i o n o f 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 n o t be a l l o w e d w i t h o u t my w r i t t e n permission® D e p a r t m e n t o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r 8, C a n a d a D a t e <~^ Hy 4 j I 94 ABSTRACT The preionization of a shock tube's gas before the shock passes through i t i s called the precursor effect. An experimental and theore-t i c a l study has been carried out on precursor ionization i n an electromagnetic shock tube. The precursor ionization was detected with different types of electric probes and also with photoraaltipliers. Extensive experiments indicated that the ionization was not due to diffusion of particles from the discharge i n the shock tube driver. The ionization i s primarily o caused by radiation from the discharge of wavelengths less than 2000 A. Radiation from the shock front makes a negligible contribution to the ionization. Langmuir double probe measurements indicated that the gas was about 0.1$ ionized and that the electrons i n the precursor were not i n thermal equilibrium with the gas atoms and ions. The time interval between detection of ionization at two stations was independent of the shock tube gas (air, argon, helium), and corresponded to a propagation speed greater than 1/20 the speed of l i g h t . The precursor had a main component lasting about $0 microseconds with ionization proportional to the square of the discharge current. There was also a weaker component which lasted for about £00 microseconds. The experimental results can be understood i n terms of a theoretical model based on black body radiation. Considering the driver to act as an - i i -i r ifinite slab radiator, whose temperature i s a function of the discharge parameters, an expression i s derived for the number of photons emitted i n some frequency interval. Assuming the electron density to be pro~ portional to radiation absorption from such a radiator, the electron density variation with distance from the driver can be adequately under-stood. When the shock tube is considered to behave as a transmission l i n e , whose resistance per unit length i s proportional to the electron density, one can explain the variation of the shock tube's gas potential both with distance from the driver and with time. - i i i -NOTATION Where possible the recommendations of the article t i t l e d SYMBOLS UNITS AND NOMENCLATURE IN PHYSICS appearing i n the June 1 ? 6 2 issue of Physics Today were followed. Liberal use was made of the symbols for various powers of 1 0 e.g. 5> mtorr = _j> 1 0 mm Hg of pressure; 6 Mm s""^ " - 6 x 1 0 ^ meters per second. Some other symbols were: N'(z,t) denoting the derivative of N with respect to z N (z,t) denoting the derivative of N with respect to t. - i v -TABLE OF CONTENTS Abstract i Notation i i i L i s t of Figures x L i s t of Tables x i i i Acknowledgements xiv Chapter I INTRODUCTION 1 II THEORETICAL CONSIDERATIONS 9 - 1 Diffusion Model 9 - 2 One Dimensional Radiation Absorption 12 - 3 Transmission Line with Time Dependent Resistance per Unit Length Ik - k Shock Tube as Transmission Line 16 - $ The Double Probe 19 A. The Current Density at a Probe 21 B. Temperature Determination 23 C. Determination of n ^ , n Q 26 III APPARATUS 28 - 1 The Driver 28 - 2 Capacitor Bank 31 - 3 Circuit Parameters 31 - k Power Supplies 31 - £ Gas Input 2>k - 6 Trigger Unit 37 -V-III - 7 Oscilloscope 37 - 8 Pick-up C o i l 37 - 9 Integrator U l -10 Shock Tube 4l -11 Pressure Measurement JU2 -12 Impurities 42 -13 Photomultiplier Units 42 -14 Capacitative Probes 46 -15 Ring Electrode Probe 46 -16 Pin Electrode Probe 46 -17 Two Wire Probes 48 -18 Probe Positioner 5l -19 Delay Unit 5l -20 Kerr C e l l Unit 59 17 EXPERIMENTAL RESULTS 59 - 1 Introduction 60 - 2 Photomultiplier vs Capacitative Ring Signals 6l - 3 Photomultiplier vs Pin Electrode Signals 62 - U Capacitative Ring vs Pin Electrode Signals 66 - 5 Capacitative Ring Around Shock Tube vs One Adjacent to I t 66 - 6 Two Wire vs Ring Electrode Probe 66 - 7 I vs Capacitative Ring Signals 71 - 8 I vs Gas Impedance 71 - 9 Shock Tube Potentials with Respect to Ground 76 -10 Bank Polarity Reversal 8l - v i -IV-11 I t s I and Gas Impedance 83 -12 L i F and Quartz Windows 86 -13 Wire Mesh Electrode 87 -1U Applied Fields 88 A. Electric F i e l d 88 B. Magnetic F i e l d 88 -l£ Variation of Probe Position Perpendicular to the Shock Tube Axis 91 - l 6 £0 cm Probe's Position vs 188 cm Probe's Response 91 -17 The 188 cm Probe's Response vs Its Per-pendicular Distance to the Shock Tube Axis 93 -18 £0 and 188 cm Probes Moved Simultaneously Perpendicular to the Shock Tube Axis 93 -19 Precursor vs Shock Photomultiplier Signals 95 -20 Variation of Capacitative Probe Signals with Probe Position 95 -21 Time Taken by Capacitative Ring to Attain o Potential Variation Proportional to I 100 -22 V t vs t t 100 -23 Time for Ring Electrodes to Attain Driver Potential 103 -2h Six Inch Diameter Driver vs Three Inch Diameter Driver 103 -25 Ring Measurements Using Applied Potentials 105 -26 Methods of Applying Voltage Across Two Wire Probes 106 - v i i -17-27 Two Wire Probe Precursor Investigation 106 -28 Comparison of A i r , Argon, and Helium 111* - 2 9 Double Probe Measurements llU V DISCUSSION OF RESULTS 121 - 1 Comparison of Precursor Detectors 121 A. Capacitative Ring Potential vs Photomultiplier Output 121 B. Pin Electrode vs Photomultiplier and Capacitative Ring Signals 122 C. Two Wire Probe 122 D. Comparison with Signals of Other Workers 122 - 2 Optical Aspects of the Precursor 123 A. Optical Signal vs E l e c t r i c a l Pick-up 123 B. Photomultiplier Observations 123 C. Precursor Produced by Radiation 12U D. Estimation of Driver Temperature 121* E. Comparison with Other Investigations 125 - 3 Optical Aspects of the Precursor 125 A". Precursor vs Pick-up rr<v..-r.o.? 125 B. Precursor vs I and I : - J - 126 C. Driver Potential vs Shock Tube Gas Potential 131 D. Applied Fields 133 E. Screen Electrode 133 F. Shock Tube Potentials with Respect to Ground 133 - v i i i V- 3 G. Bank Polarity Reversal 133 H. Transverse Variation 133 I. Longitudinal Variation 136 J . Driver Geometry Variation 137 K. Precursor Electron Temperature 139 L. Precursor Electron Density 139 M. Comparison of Gases IliO N. Comparison with Other Investigations ikl V I CONCLUSIONS ikh APPENDICES A. Black Body Radiation 11*6 B. Kerr C e l l Photographs of the Driver Discharge 150 C. Plot of f(t) vs t 153 D. Survey of Experimental Work on Precursors 151 a) Low speed precursors 151 1. Apparatus and operating conditions 151 2. Results 155 b) High speed precursor 158 1. Apparatus and operating conditions 158 2. Results 160 c) Applied fields l61i d) Bank polarity reversal l6ii e) Purity and boundary conditions I6I4. f) Energy transfer mechanisms 166 - i x -APPENDICES D. g) Measuring apparatus 1. Optical sensors 2. E l e c t r i c a l sensors E. Survey of Theoretical Work a) Diffusion b) Shock front radiation c) Radiation from the driver discharge F. Radiation Model-Point Source Radiator G. Transmission Line-Point Source Radiator BIBLIOGRAPHY - X -LIST OF FIGURES Figure I - l Summary of Precursor Investigations 4 - 2 Summary of Precursor Work Reported i n This Thesis 6 nr-i Block Diagram of Apparatus 29 - 2 Discharge Chamber 30 - 3 Power Supply - 8 kV - 0 . 3 A 32 - 4 Regulated Power Supply - 1 .5 kV 35 - 5 Trigger Unit 38 - 6 Pulse Forming Network and Distribution System 40 - 7 Integrator 41 - 8 Photomultlplier Unit Optics 43 - 9 Photomultiplier Circuits 44 - 1 0 Pin & Ring. Electrodes? Capacitative Probes 47 -11 Two Wire Probes 4 9 , 5 0 - 1 2 Probe Carriage Assembly 52 - 1 3 Ramp Generator 53 -14 Delay Channel 55 - 1 5 Delay Unit's Regulated Power Supply 57 - 1 6 Block Diagram of Kerr C e l l Unit 60 1 7 - 1 Capacitative Ring vs Photomultiplier Signals 6 3 , 64 - 2 Pin Electrode vs Photomultiplier Signals 65 - 3 Capacitative Ring vs Pin Electrode Signals 67 - h Two Wire Probe and Ring Electrode Circuits 68 - 5 Two Wire Probe vs Ring Electrode Signals 6 9 , 7 0 . - x i -IV- 6 I vs Capacitative Ring Signals 7 2 , 7 3 , 7 4 , 7 5 - 7 I vs Gas Impedance 7 7 , 7 8 - 8 Shock Tube Potentials 7 9 , 8 0 - 9 Bank Polarity Reversal 82 -10 I vs I and Gas Impedance _ 8 3 , 8 4 , 8 5 -11 Two Wire Probe Circuit 86 -12 -Effect of Wire Mesh Electrode 8 9 , 9 0 -13 Probe's Response Time vs Its Perpendicular Position 92 - 1 4 Probe's Response Time vs Perpendicular Position 92 - 1 5 188 cm Response vs 50 cm Probe's Position 94 - 1 6 188 cm Probe's Response vs Its Position 94 -17 Precursor vs Shock Photomultiplier Signals 9 6 , 9 7 - 1 8 Capacitative Probe Signals 98,99 -19 Determination of V*. and t^ 101 - 2 0 Plot of V t vs t t 102 - 2 1 A t (ring pairs) vs In p 106 -22 Double Probe Circuit 116 - 2 3 5 6 . 5 cm Double Probe V-I Curve at 5 us 116 - 2 4 5 6 . 5 cm Double Probe V-I Curve at 1 0 us 118 - 2 5 5 6 . 5 cm Double Probe V-I Curve at 30 us l l 8 - 2 6 2 0 8 . 5 cm Double Probe V-I. Curve at 5 us 119 - 2 7 2 0 8 . 5 cm Double Probe V-I Curve at 10 us 119 - 2 8 2 0 8 . 5 cm Double Probe V-I Curve at 30 us 119 V- 1 Rise to I Variation of trace e), Fig. IV - 6 128 - 2 Rise to I Variation of trace k), Fig. IV -6 128 - 3 Position from Driver vs const,^ % p" x f ( t ) 132 - a d i -V- k (V B A t ) vs In p 138 - £ ^Vg A t ) vs In p for A i r , Helium, and Argon 1^2 App-1 Kerr C e l l Photographs of Driver Discharge l£2 -2 Plot of f(t) vs t 153 - x l i l LIST OF TABLES Table I - l Experimental Conditions of Precursor Investigations 8 I I I - l Impurities of Experimental Gases 3 4 17-1 Times that 29 and 8 4 cm Probes Exhibit Potential 7ariation Proportional to Driver Potential 101 -2 Times that Ring Electrode Probes Attained Driver Potential 1 0 4 -3 A t Using 27 V across a Two Wire Probe 108,109 -k A t Using Sh 7 across a Two Wire Probe 110 -5 A t Using 109 7 across a Two Wire Probe 111 -6 At Using 136 7 across a Two Wire Probe 112 -7 A t Using. 1 , 4 k7 across a Two Wire Probe 113 - 8 A t Using 1,6 k7 across a Two Wire Probe 113 -9 A t Using Just Below Breakdown 7oltage across a Two Wire Probe llS -10 Double Probe Results 120 - x i v -ACKNOWLEDGEMENTS I wish to extend warm thanks to those persons who assisted me i n the performance of this project. To Dr. P. R. Smy, who proposed the nucleus of the work, and to Dr. R. A. Nodwell, whose appraisal of the manuscript was invaluable, I owe especial gratitude. The use of the Kerr C e l l , through the courtesy of Dr. A. J . Barnard, was greatly appreciated. I am indebted to Mr. J. Lees for inimitable glass blowing, Mr* P. Haas for his excellent assistance i n the design and building of the apparatus, and to Messrs. J . H. Turner, W. Ratzlaff, and G. A. Austin for their work on the electronics system. On an informal basis, I have also received much superior advice from the other members of the Plasma Physics group* For the financial assistance, without which this endeavour would have been impossible, I Owe thanks to the B. C. Hydro & Power Authority and the National Research Council who provided personal funds, as well as to the Atomic Energy Commission of Canada which grants monies to the Plasma Physics group. CHAPTER I INTRODUCTION High speed shock waves are commonly generated i n the laboratory b y discharging a condenser bank through a spark gap (shock tube driver) located at the end of a tube containing gas. The pressure pulse pro-duced by the discharge i s propagated down the tube as a high speed shock which ionizes the gas through which i t passes (see McLean 196l). Early experiments (Shreffler & Christian 1904, Voorhies & Scott 19S9) showed however that the gas i n the shock tube was ionized before the shock arrived. This ionization i s known commonly as precursor ionization (Gloerson i960). v. Since the precursor effect influences the properties of the shock wave propagated i n the shock tube, a detailed investigation of the phenomenon has been carried out by several workers (see appendix D). However due to the wide variety of experimental conditions and methods of investigation employed by previous workers i t i s d i f f i c u l t to establish the fundamental properties of precursor ionization. One of the reasons for the d i f f i c u l t y i s the wide variety of ionization detectors employed. Up to the present, the comparative performance of these detectors has not been studied. One of the major contributions of the work presented' i n this thesis has been to r e c t i f y this situation. The results of others indicate that ionization develops i n shock tube very rapidly ( ~» 10 seconds) and that the degree of ionization -2-produced i s relatively low (/^-> 0.1$)(see appendix D). Since the i o n i -zation travels very rapidly, i t might possibly be due to fast electrons emitted by the spark at the end of the shock tube (Weyman I960, 1962). It may also arise as a result of photo-electrons emitted from materials i n the shock tube when photo-ionizing radiation from the driver ( i . e . spark) f a l l s upon them (see appendix D ) . These effects form the chief topic of investigation reported i n the thesis. The main results of the experiments show that fast particles emitted by the source do not contribute significantly to the precursor effect. The use of light f i l t e r s demonstrates that at least 7% of the precursor ionization i s produced by electromagnetic radiation emitted by the driver at wavelengths between 160 and 200 nm. The precursor ionization density also depends on the square of the current passing through the shock tube driver. The ionized gas i n the shock tube constitutes a resistive impedance connected to the shock tube driver. By treating this gas as a conductor of a transmission line having variable resistance per unit length i t has proved possible to deduce the i n i t i a l changes of gas potential as a func-tion of time. This method of studying the precursor effect i s also one of the new results presented i n the thesis. For the transmission line i t i s assumed that the gas resistance i s proportional to the electron density, and that the resistance varies exponentially with length along the shock tube. The time dependence of the resistance corresponds with the variation of current i n the shock tube driver. If the precursor ionization results from the absorption of radiation emitted by the shock tube driver then one might expect the exponential dependence of the electron density, assumed i n the transmission line theory. - 3 -The correlation of the electron density with bank current i s also reasonable. A crude attempt has therefore been made to explain the results by a t t r i -buting the precursor ionization to absorption of radiation from the shock tube driver. The driver i s assumed to behave as a black body source whose tempera-ture varied with time i n the same way as the square of the driver current. This theory i s presented i n Chapter II where the number of photons being absorbed at any point i n the shock tube i s related to the experimental para-meters. More detailed calculations for this model appear i n the appendix A. Chapter II also contains a one dimensional diffusion theory for the motion of electrons produced i n the shock tube driver. The purpose of the theory i s to see whether the predicted dependence of electron density on position agrees with the experimental results. F i n a l l y the double probe theory of Johnson and Malter (19S>0) i s discussed, since double probes are used for the deter-mination of precursor electron density and temperature. In Chapter III sufficient details of the apparatus are given to enable i t s complete duplication. The lack of such detail i n the reports published by others has made i t very d i f f i c u l t to compare their results with those obtained by the author. The experimental conditions and procedures are des-cribed i n detail i n Chapter IV. An outline of the purpose of these experi-ments i s given as an introduction to the chapter. The results presented i n Chapter IV are discussed i n Chapter V. Chapter VI contains a summary of the main conclusions of the work reported i n the thesis, as well as suggestions for further work. Published data on precursors i s summarized i n Fig. I - l j a resume of the research reported here i s found i n F i g . 1 -2 . The experimental conditions of the work reported i n the literature and those i n the work reported here are li s t e d i n Table 1-1. A survey of both experimental and theoretical precursor work i s presented i n the appendices. -h-Gas •He 7 1 | CI. 1 Aft 11 L — 8 — . i e n i i t ^ 3 — 1 6 — 1 17 Ne W_16^4 Xe 1 1 n> 6 Kr H 2 H 8 D 2 **- V . a H N P 5 1 10% He 90^D 2 ' u SO* Ar 1 Butane Propane 1 A i r 1 14 Gas ] pressure .0 i n torr l b * Fig. 1-1. Summary of Precursor Investigations LEGEND FOR FIG. I - l 1 Schreffler-Christian (1954) 2 Hollyer (1957) 3 Jahn-Grosse (1958-59) 4 Voorhies-Scott (1959),. 5 Weyman (1960-61-63) 6 Gloersen (1959-60) 7 McLean et a l . (1961) 8 Fowler-Hood (1962) 9 Schoen et a l . (1962) 10 Groenig (1963) 11 Russel et a l . (1962) 12 Quinn-Boden (1963) !3 Mahaffrey et a l . (1963) 14 Charvet (1963) 1? Liepmann (1961) 16 Gerardo et a l . (1963) 17 Jones (1962) Indicates the pressure range used by 7, i . e . McLean Indicates work done at a single pressure by 7 Indicates work done at some unknown pressure by 7 1^ -7-^ 1 7 ® -6--7-LEGEND FOR FIG. 1-2 1 precursors observed using photomultipliers 2 precursors observed using capacitative rings 3 precursors observed using a pin electrode k precursors observed using ring electrodes types of two wire probes I II III IT V VI \ I \ denotes measurements over indicated region of pressure with type I two wire probe II denotes measurement made at single pressure with type II two wire probe TABLE 1-1 EXPERIMENTAL CONDITIONS OF PRECURSOR INVESTIGATIONS MECHANICAL SHOCK TUBES Gas and Worker Pressure Shock Tube Diameter Driver Shock Speed Type I precursor 8" and 5" x 5" 1-3/8" 1.5 cm Solid explosive 28.6 atms of He high pressure gas mach 8-12 Schreffler & Christian Jahn & Grosse Weyman He, Ar, C1,.SF 6, a i r , 50/50 A-N2 butane propane 1 atm N 2 10 torr Ar, 4-6 torr Types I and 11 '. precursor 2" 4-8 ktorr of He mach 9-11 Gloersen Xe, 1 & 1.3 torr ELECTROMAGNETIC SHOCK TUBE L(uH) C(kA) V(kV) T(us) Shock Tube Diameter • Types I and II precursor J(jiF) 15 12 Groenig Ar, 0.1 torr Type II precursor 30 14.5 150 0.65 448 0.60 0.051 140 200 186 18 21 20 10 17.5 42 2 ! 8.3 44 7.3 cm 0.8" 5 cm 6" 3 cm 1" Charvet Voorhies & Scott Gerardo Fowler & Hood Schoen, Sanga. Mahaffey . McLean et a l This thesis A i r 0.1-0.2 torr 90% D2-10£ He 0.15 torr Ar, He, 1-5 torr Ar; H2, 0.1-1 torr Ar, 0.1-1 torr He, 1 torr Ar, N 2, He, a i r 0.2 mtorr-100 torr 0-FINCH DISCHARGE 30 7.6 cm 15 10 x 10 cm Russel et a l . Quinn & Bodin Ar,D2,0.005-1 torr D2, 0.1-0.5 torr 2 178 INVERTED Z-PINCH 180J cm"1 i n 4 cm of 6.8 mil Cu wire Jones jAir,Ar, N, He 150-500 torr - 9 -CHA.PTER I I THEORETICAL CONSIDERATIONS I n t h i s c h a p t e r v a r i o u s e q u a t i o n s w i l l be d e r i v e d , w i t h t h e a s s u m p t i o n s l i s t e d a t f i r s t . Some o f t h e d e r i v e d e q u a t i o n s w i l l be r e f e r r e d t o i n one o r more o f t h e subsequent s e c t i o n s . O t h e r s w i l l be u s e d i n t h e d i s c u s s i o n o f t h e e x p e r i m e n t a l r e s u l t s , C h a p t e r V. I I - l D i f f u s i o n M o d e l The e l e c t r o n d e n s i t y as a f u n c t i o n o f p o s i t i o n and t i m e , n ( z , t ) , w i l l be i n v e s t i g a t e d , u s i n g t h e f o l l o w i n g a s s u m p t i o n s : 1) t h e p a r t i c l e c o n c e n t r a t i o n i s l o w enough t o c o n s i d e r t h e d i f f u s i o n c o e f f i c i e n t i n d e p e n d e n t o f p o s i t i o n and t i m e 2) t h e d i f f u s i o n p r o c e s s i s one d i m e n s i o n a l 3) i n i t i a l l y t h e d e n s i t y i s z e r o everywhere e x c e p t a t t h e s o u r c e 4) t h e i n i t i a l d e n s i t y i s p r o d u c e d b y a c o n d e n s e r d i s c h a r g e and i s p r o p o r t i o n a l t o t h e sq u a r e o f t h e i n i t i a l v o l t a g e a c r o s s t h e c o n d e n s e r 5) z 2 » UDt 6) t h e d i f f u s i o n c o e f f i c i e n t , D, i s r e l a t e d t o t h e ambient gas p r e s s u r e , p, and p a r t i c l e t e m p e r a t u r e , T, b y t h e r e l a t i o n pD = c o n s t . T. U s i n g a s s u m p t i o n 1) we may w r i t e t h e d i f f u s i o n e q u a t i o n (Margenau & -10-Murphy, 1956): n - a 2 d2n ( l - l ) 2 > 2 where a — D, the diffusion coefficient and O denotes the laplacian operator. Incorporating assumption 2) into equation 1) and putting n(z,t)= f(z) T(t) yields 2 ^ 2 l l Z ) m / L \ ~ « (1-2) a " a z f ^ ^ m = - a 2k 2 f(z) T(t) where k i s an arbitrary constant. From (2) we get the solutions for f(z) and T(t) as T(t) =• const exp (-a 2k 2t) (1-3) f(z) — c(k) exp (ikz) Thus the general solution for n(z,t) i s e o n(z,t) = c(k) exp(ikz - a 2k 2t) dk (1-4) At t = 0 we have r n(z,0) = c(k) exp(ikz) dk (1.-5) c(k) i s related to n(z,0) by the fourier transform, thus -11-c(k) = f n(z«,0) expt-ikz 1) dz» (1-6) -aO Using equation (6) we may rewrite (h) as n(z,t) = - i . / / n(z',0) exp(ik(z-z') - a 2k 2t) dz» dk (1-7) Integrating over k leads to On using assumption 3 ) , equation ( 8 ) becomes 2 n(z,t) = - f ^ e x p / - - i i (1-9) (4rrDt)2 t ^Dt j Assumption h)s which i s equivalent to saying that the electron the. density in Asource i s proportional to the el e c t r i c a l energy dissipated i n i t , renders (9) as b V n 2 f „21 (1-10)  VB f z 2 n(z,t) - 1 e x P \ ° r r r (Dt) 2 I ^Dt where b i s a constant. Requiring that the density be a constant would be equivalent to having the experimental parameters satisfy the relation 2 V B (Dt) 2 exp(-z2/UDt) =. const ( l - l l ) -12-T h i s e q u a t i o n i s a p p l i c a b l e t o e x p e r i m e n t s i n v o l v i n g d e t e c t o r s t h a t r e s p o n d t o e l e c t r o n d e n s i t i e s e x c e e d i n g some minimum. U n d e r c o n d i t i o n s when a s s u m p t i o n 5) i s v a l i d e q u a t i o n ( l l ) may be s i m p l i f i e d t o v| e x p ( - z 2 / U D t ) - c o n s t . (1-12) s i n c e t h e e x p o n e n t i a l v a r i a t i o n w i l l t h e n d o m i n a t e . When Vg i s c o n s t a n t , and a s s u m p t i o n 6) i s u s e d , e q u a t i o n (12) may be w r i t t e n a s p z 2 — c o n s t t T e (1-13) f o r e l e c t r o n d i f f u s i o n , I I - 2 One D i m e n s i o n a l R a d i a t i o n A b s o r p t i o n C o n s i d e r r a d i a t i o n a b s o r p t i o n s u b j e c t t o t h e f o l l o w i n g a s s u m p t i o n s : . 1) The s o u r c e e f f e c t i v e l y behaves as an i n f i n i t e s l a b o f r a d i a t i n g gas so t h a t t h e i n t e n s i t y o f t h e s o u r c e a t a d i s t a n c e z f r o m i t s s u r f a c e i s t h e same as t h e v a l u e a t t h e s u r f a c e minus t h e a b s o r b e d i n t e n s i t y . 2) We may c o n s i d e r t h e s o u r c e t o be a b l a c k b o d y r a d i a t o r . 3) The La m b e r t - B e e r l a w o f r a d i a t i o n a b s o r p t i o n i s v a l i d ( W e i s s l e r 1956). U s i n g a s s u m p t i o n s .1) and 3) we may w r i t e f o r t h e number o f photons h a v i n g f r e q u e n c y ~V t o "V dl> t h a t N z ( V ) . - N 0(V) e " k * z (2-1) -13-where ky i s related to the absorbing gas temperature and pressure by and tf^i i s the absorption cross section 19 -3 no i s Loschmidt's constant (2.6872 x 10 cm ) p i s the gas pressure i n torr Tg i s the gas temperature i n °K For the number of photons at position z from the source, i n the frequency interval V ^ to iS 2» we write \(2/1 to2S2) = HQ^1t0 2/2) exp(-k^ 1z/ 2 z) (2-3) where Taking the derivative of (2-3) with respect to z yields N'CV-L t o ^ 2 ) - ^ k X ^ T" ^o^l t o 7 / 2 ) e x p ( ~ k ^ 1 ^ 2 z ) ( 2 " 5 ) I f the source acts as a black body radiator then (2*5) may be written as (see (A7) i n the appendices) - l l i -/ T g c (2-6) The average value of the absorption coefficient, y ^ ^ z / ' C & n be calculated from the known values of ky at individual frequencies. TJI-3 Transmission Line with Time Dependent Resistance per Unit Length In this section, the voltage across a transmission line at some position z from one end at some time t, V(z,t), i s derived subject to the following assumptions: 1) the resistance per unit length varies with both time and distance along the line such that we may write R(z,t)^* R(.t) exp(kz) 2 ) the voltage drop along the line i s determined mainly by the current along the line and the resistance per unit length, i . e . RI LI where L i s the inductance per unit length 3) the current across the line between the conductors due to the capacitance per unit length i s much greater than that due to the resistance between the conductors per unit length, i . e . CV ^  GV k) exp(kz) ~ 1 The equations (sometimes called the telegrapher's equations) for the change of voltage and current along a transmission l i n e are: V«( Z,t) = -R(z,t) I(z,t) - L i ( z , t ) (3-1) -15-I ' ( z , t ) s . -G V ( z , t ) - C V ( z , t ) (3-2) where t h e p r i m e d e n o t e s d i f f e r e n t i a t i o n w i t h r e s p e c t t o z and t h e d o t d i f f e r e n t i a t i o n w i t h r e s p e c t t o t i m e . I n c o r p o r a t i n g a s s u m p t i o n 2) i n t o e q u a t i o n (3-1) and a s s u m p t i o n 3) i n t o e q u a t i o n (3-2) g i v e s V ' ( z , t ) = - R ( z , t ) l ( z , t ) (3-3) I ' ( z , t ) = -C V ( z , t ) (3-4) where C i s c o n s t a n t w i t h r e s p e c t t o b o t h z and t . A g a i n d i f f e r e n t i a t i n g (3-3) w i t h r e s p e c t t o z and u s i n g a s s u m p t i o n 1) w i t h e q u a t i o n (3-4), we g e t V " ( z , t ) =• k V ' ( z , t ) -+- R ( z , t ) C V ( z , t ) (3-5) W r i t i n g V(z.,t) «= W ( z ) X ( t ) e n a b l e s t h e v a r i a b l e s t o be s e p a r a t e d and (3-5) t o be e x p r e s s e d as W " ( z ) - k W'(z) _ C R ( t ) X ( t ) » R2 / , 6 N W(z) e x p ( k z ) X ( t ) V B U b ) The s o l u t i o n f o r X ( t ) i s X ( t ) — c o n s t exp [ C R ( t ) d t ) C > 7 ) - 1 6 -The e q u a t i o n f o r W(z) i s W " ( z ) - k W f e ) - B 2 W ( z ) e x p ( k z ) ** 0 ( 3 - 8 ) w h i c h i s a n o n - l i n e a r d i f f e r e n t i a l e q u a t i o n . I f a s s u m p t i o n U) i s v a l i d we nay s e t k — 0 a p p r o x i m a t i n g ( 3 - 8 ) b y T h i s a p p r o x i m a t i o n i s o n l y v a l i d i f B ^ k. T h i s means a p p r o x i m a t -i n g t h e r e s i s t a n c e p e r u n i t l e n g t h ( a s s u m p t i o n 1 ) b y a r e s i s t a n c e p e r u n i t l e n g t h w h i c h i s t i m e dependent b u t i n d e p e n d e n t o f t h e p o s i t i o n a l o n g t h e l i n e , i . e . R ( z , t ) R ( t ) . I I - h Shock Tube as T r a n s m i s s i o n L i n e A shock t u b e ' s b e h a v i o u r as a t r a n s m i s s i o n l i n e i s i n v e s t i g a t e d u n d e r t h e f o l l o w i n g a s s u m p t i o n s : 1 ) The c o n d u c t i v i t y i s p r o p o r t i o n a l t o t h e f r e e e l e c t r o n d e n s i t y , n e . A n y i o n i c c o n t r i b u t i o n i s n e g l i g i b l e . 2) The e l e c t r o n m o b i l i t y t i m e s t h e gas p r e s s u r e i s a c o n s t a n t . 3 ) The c r o s s s e c t i o n a l a r e a o f t h e shock t u b e r e m a i n s a c o n s t a n t f o r a l l z, t h e d i s t a n c e f r o m t h e d r i v e r . h) The e l e c t r o n d e n s i t y a t a d i s t a n c e z f r o m t h e d r i v e r i s W " ( z ) - B 2 W(z) s* 0 ( 3 - 9 ) w h i c h h a s t h e s o l u t i o n W(z) = c o n s t e x p ( - B z ) ( 3 - 1 0 ) -17-.proportional to the radiation absorbed at that point i n the frequency range ^ to 2^ 2' 5) The driver acts as a black body radiator whose intensity diminishes with distance from the driver as a result of absorption. This i s equivalent to considering the driver to be an i n f i n i t e slab of radiating gas. 6) The line's resistance per unit length, R, maybe considered that of the shock tube gas. When assumption 1) i s valid, the conductivity may be expressed as <T=Qeuene (U-l) where Q e i s the electronic charge, u e i s the electron mobility, and nQ i s the electron number density. Equation (U-l) combined with assumptions 2) and. 3) enables us to write R(z,t) *»<. p/n (z,t) (4-2) Assumption 4) combines with (4-2) to yie l d R(z,t) =. R 0p / - N ^ ( ^ 1 to & 2) (4-3) where R0 i s a constant depending on the shock tube cross sectional area and the average number of electrons produced by the absorption of a photon i n the frequency range ^ x to - 1 8 -I n c o r p o r a t i i i g a s s u m p t i o n 5 ) , and e q u a t i o n (2-6) w i t h e q u a t i o n (4-3) g i v e s R ( z , t ) -R Q T g c e x p l k V ^ j z ) # 7 / ^ 2 8 T R V ' 2 /kT V , 2 /kT \ 2 (-) i + l i 3 i»l n«l 1 kT n hz/. e x p ( - n h y ± / k T ) - 1 (4-4) S e p a r a t i n g o u t t h e z and t dependence we may w r i t e R ( z , t ) - = - R ( z ) T ( t ) where R(z) J=. e x p ( k Z / ^ ^ Z ) (4-6) and R ( t ) R 0 c 3 T g kT e x p ( - n h Z / i / k T ) (li-7) The t i m e dependence a r i s e s f r o m t h e b l a c k body t e m p e r a t u r e ' s t i m e depend-ence T ( t ) ( s e e AS> i n t h e a p p e n d i c e s ) . A p p l y i n g a s s u m p t i o n 6) and com p a r i n g e q u a t i o n (U-5>) w i t h a s s u m p t i o n 1) o f s e c t i o n 3 i n d i c a t e s t h a t we s h o u l d i d e n t i f y t h e k o f a s s u m p t i o n 1 ) w i t h k 2 ^ y 2 o f e q u a t i o n (4-6) and t h a t R(t) w i t h (4-7). I f k ^ y ^ B -19-t h e a p p r o x i m a t e s o l u t i o n (3-10) may b e u s e d w i t h (3-7) t o g i v e a n e x p r e s s i o n f o r t h e v o l t a g e b e t w e e n t h e g a s a t some p o i n t a l o n g t h e s h o c k t u b e a n d g r o u n d as where R ( t ) i s g i v e n b y ( 4 - 7 ) . T h e D o u b l e P r o b e I n t h i s s e c t i o n e x p r e s s i o n s a r e d e r i v e d f o r t h e c u r r e n t d e n s i t y , J , t o a p r o b e , a n d f o r t h e e l e c t r o n t e m p e r a t u r e a n d number d e n s i t y o f a p l a s m a , a s m e a s u r e d b y a d o u b l e p r o b e . T h e e x p r e s s i o n s a r e s u b j e c t t o o n e o r more o f t h e f o l l o w i n g a s s u m p t i o n s : 1) The p l a s m a c o n s i s t s o f e l e c t r o n s a n d one o r more s p e c i e s o f i o n , e a c h o f w h i c h may b e r e g a r d e d as a p e r f e c t g a s . 2) T h e s y s t e m , composed o f t h e p l a s m a a n d s h e a t h s a r o u n d t h e p r o b e s , i s i n e q u i l i b r i u m . 3) T h e t e m p e r a t u r e o f a n y t y p e o f p a r t i c l e i s t h e same w h e t h e r t h e p a r t i c l e i s i n t h e s h e a t h o r i n t h e p l a s m a o u t s i d e t h e s h e a t h r e g i o n . D i f f e r e n t t y p e s o f p a r t i c l e s may h a v e d i f f e r e n t t e m p e r a t u r e s . h) T h e c h a r a c t e r i s t i c l e n g t h o f the p l a s m a i s g r e a t e r t h a n t h e s h e a t h t h i c k n e s s w h i c h i n t u r n i s g r e a t e r t h a n t h e D e b y e l e n g t h . I f t h i s c o n d i t i o n i s n o t s a t i s f i e d t h e c o n c e p t o f a s h e a t h c a n n o t be u s e d . 5>) T h e mean f r e e p a t h i s g r e a t e r t h a n t h e s h e a t h t h i c k n e s s . t V ( z , t ) sss c o n s t e x p ( - B z + B_ d t / R ( t ) ) (4-8) =20-6) A probe's sheath does not intersect any other sheath. 7) The ion current to either probe of a double probe system i s not appreciably affected by the v a r i a t i o n i n potential d i f -ference between the probe and the plasma. 8) Kirchhoff's law holds; therefore the sum of the electron currents to the probes i s the same as the sum of the ion currents. 9) The only important char a c t e r i s t i c of a probe i s i t s surface area. 10) Each type of p a r t i c l e has a Maxwell-Boltzmann d i s t r i b u t i o n . 11) The temperature of the ions i s very close to the gas temperature. 12) The plasma consists only of si n g l y charged: ions, electrons, and neutrals. 13) The ion current to a probe i s space charge l i m i t e d . Consider a probe which i s maintained at some po t e n t i a l , negative with respect to the plasma p o t e n t i a l . The potential energy of any species of p a r t i c l e w i l l drop to that of the mean k i n e t i c energy of the equivalent p a r t i c l e i n the plasma at some distance from the probe. Thus a sheath or region of disturbed plasma i s assumed to form around the probe. I f the probe were simply immersed i n the plasma, the sheath thickness would be of the order of the Debye length (Thompson 1962, Delcroix I960). When the probe i s maintained at some potential such that the potential energy of a p a r t i c l e i n the probe's sheath can be greater than the mean ki n e t i c energy of the p a r t i c l e , the Debye theory i s not v a l i d . The resulting deficiency i n knowledge about the sheath i s -21-one o f t h e o b s t a c l e s y e t t o be overcome b e f o r e probe measurements a r e f u l l y u n d e r s t o o d (Boyd 1950,5l). A. The C u r r e n t D e n s i t y a t t h e P r o b e L e t u s c o n s i d e r t h e thermodynamic sy s t e m composed o f t h e s h e a t h r e g i o n sf. and t h e r e s t o f t h e plasma r . U s i n g a s s u m p t i o n l ) we may w r i t e , f o r a s p e c i e s o f p a r t i c l e ' [ n s -{? nj. (5-1) where &ns i s a s m a l l change i n t h e number o f p a r t i c l e s i n t h e s h e a t h and ^ * n r i s a s m a l l change i n the number o f t h e same s p e c i e s o f p a r t i c l e i n t h e r e g i o n o u t s i d e t h e s h e a t h . E q u a t i o n (5-1) and a s s u m p t i o n 2) combine t o g i v e I S = 'b nsS^ <5"ns+ b n-S.. fn = ( $> n_S a - 3 n rS_) I n q - 0 (5-2) where S i s t h e e n t r o p y (see K i t t e l 1958)• S i n c e Sns i s a r b i t r a r y , t h e e x p r e s s i o n between t h e b r a c k e t s must be z e r o . U s i n g t h i s and t h e d e f i n i t i o n o f t h e c h e m i c a l p o t e n t i a l , t h e c o n d i t i o n f o r e q u i l i b r i u m i s ^sAs * where /i i s t h e c h e m i c a l p o t e n t i a l Thus when a s s u m p t i o n 3) h o l d s , and T is t h e p a r t i c l e t e m p e r a t u r e , t h e c h e m i c a l p o t e n t i a l o f any t y p e -22-o f p a r t i c l e must be t h e same i n t h e s h e a t h as i n t h e r e g i o n o u t s i d e t h e s h e a t h . I n t h e absence o f any. f i e l d , t h e c h e m i c a l p o t e n t i a l o f a p e r f e c t gas i s p0 = kT l n p f f ( T ) (5-W I n t h e p r e s e n c e o f an e l e c t r i c f i e l d t h e c h e m i c a l p o t e n t i a l becomes jx =- u Q - r QV (5-5) where Q i s t h e cha r g e o f the p a r t i c l e V i s t h e p o t e n t i a l a t t h e p o i n t where p. i s c o n s i d e r e d . A s s u m p t i o n 3 ) and e q u a t i o n s (5-3) *° (5-5) combine t o y i e l d kT I n p + QV = c o n s t . o r • ' (5-6) p •=• c o n s t . exp(-QV/kT) T h i s means t h a t t h e p r e s s u r e must v a r y t o m a i n t a i n t h e e q u i l i b r i u m i f T s a t i s f i e s a s s u m p t i o n 3 ) . The p r e s s u r e on, and t h e c u r r e n t d e n s i t y t h r o u g h , an a r b i t r a r y s u r f a c e element i n t h e p l a s m a a r e b o t h p r o p o r t i o n a l t o t h e number d e n s i t y and t h e average s p e e d p e r p e n d i c u l a r t o t h e s u r f a c e . We t h e r e f o r e assume -23-t h a t t h e c u r r e n t d e n s i t y v a r i e s i n t h e same manner as t h e p r e s s u r e . Because o f a s s u m p t i o n 5) p a r t i c l e s e n t e r i n g t h e s h e a t h p e r p e n d i c u l a r t o t h e probe s u r f a c e w i l l be c o l l e c t e d b y i t . We t h e r e f o r e w r i t e J =- J 0 exp(-QV') (5-7) where J Q i s t h e random c u r r e n t d e n s i t y t h a t e n t e r s t h e s h e a t h p e r p e n d i c u l a r t o t h e probe s u r f a c e Q I s t h e c h a r g e o f t h e p a r t i c l e s V i s t h e p o t e n t i a l o f t h e p r o b e minus t h e p o t e n t i a l o f t h e p l a s m a . B. Temperature D e t e r m i n a t i o n We now c o n s i d e r a system c o n s i s t i n g o f a plasma i n w h i c h two pr o b e s a r e immersed. U n d e r c o n d i t i o n s o f a s s u m p t i o n s 6) ^and 7) ( s e e J o h n s o n & M a l t e r 1950 f o r f u r t h e r d e t a i l s ) < £ l T = £ l e - - I e l - V I e 2 ( 5 - 8 ) I n t erms o f t h e e l e c t r o n c u r r e n t t o t h e p r o b e s t h i s becomes ( u s i n g (5-7)) A X J o l e x p ( - e V T/1C Tq) -r A G J o 2 e x p ( - e V 2 / k T e ) (5-9) where V - ^ and V 2 . a r e t h e p o t e n t i a l o f t h e pl a s m a w i t h r e s p e c t t o p r o b e s 1 and 2 r e s p e c t i v e l y A ] _ and A 2 a r e t h e a r e a s o f t h e p r o b e s -24= k i s B o l t z m a n n ' s c o n s t a n t J 0 ^ and J Q 2 a r e t h e random c u r r e n t d e n s i t i e s t o t h e p r o b e s , The p r o be p o t e n t i a l s a r e r e l a t e d t o one a n o t h e r b y t h e e x p r e s s i o n V l V 2 + V d - V c (5-10) where i s t h e p o t e n t i a l o f p r o b e 2 w i t h r e s p e c t t o p r o b e 1 V i s t h e p l a s m a p o t e n t i a l o u t s i d e t h e s h e a t h o f probe 2 w i t h r e s p e c t t o t h e e q u i v a l e n t p o t e n t i a l f o r p r o b e 1. W r i t i n g 4 =. e/k T e , (5-11) and u s i n g t h e r e l a t i o n b etween t h e probe p o t e n t i a l s we o b t a i n f o r t h e sum o f probe c u r r e n t s - £ l e ~ A X J O ] _ e x p ( - ^ ( V 2 4 - V d - V c ) ) T A 2 J q 2 e x p ( - ^ V 2 ) (5-12) T h i s e x p r e s s i o n , c o u p l e d w i t h t h e e x p r e s s i o n f o r I g 2 i n (5-9), g i v e s . I e 2 = £ I + / ( <T e x p ( - / V d) t 1) (5-13) where CT- ( A i J 0 i / A 2 J o 2 ) e x p ( - ^ V c ) (5-14) -25-Taking the derivative with respect to V d yields — I-t-CTV exp(-/ Vd) . ^ v - j - - — (5-15) ° V d L e 2 ( c ~ e x p ( ^ Vd)+D2 Evaluating (5-1.5) at V d « 0 we arrive at ( a V d I e 2 ) v d = 0 = J + 6 - - v l ) 2 (5-16) I f probe 2 i s less negative with respect to the plasma than probe 1, more electrons w i l l flow to the former. There w i l l be a flow of elec-trons from probe 2 to probe 1, I d , through the external c i r c u i t , such that I e 2 ^ l e l t 2 I d (5-17) Equation (5-17) and assumption 6) give a i / d - « a V d i e 2 ) ( 2) i ^ i d ) ) " 1 ( * v d i e 2 ) = 1 (5-18) Combining equations (5-11), (5-15) and (5-18) we may write an expression for T e as The expression for T can be expressed more conveniently by using -26-t h e s u b s t i t u t i o n s <T - - i ) v « 0 , (5-20) Ae2 ' G^{-Jj*\ = — (5-21) £ I ^ I M " 0 i + c p R o - (^ i d vd)v d =o ~^22> We may now r e w r i t e (5-19) i n the f o r m T e - (G - G 2 ) R Q £ I t ( i n eV) = 11,600 (G - G 2) R 0 f I + ( i n °K) (5-23) C. D e t e r m i n a t i o n o f n^., n e A n e s t i m a t e o f t h e i o n and e l e c t r o n number d e n s i t i e s i s made i n t h e f o l l o w i n g way. U s i n g t h e a s s u m p t i o n s 5)> 6), 10), 12), and 13) we may w r i t e a n e x p r e s s i o n f o r t h e p o s i t i v e i o n c u r r e n t J = < ( l + ) / A s = n^e ( v ) M . B M s ^ " 2 ^ where n + i s t h e i o n d e n s i t y -19 e i s t h e e l e c t r o n i c c h a r g e 1.6 x 10 coulombs ( v ) ^ g i s t h e average speed o f t h e i o n s o v e r a M a x w e l l - B o l t z m a n n d i s t r i b u t i o n . -27-A s i s the area of the ionic sheath surface which i s i n common with the rest of the plasma. From equation (5-2U)> upon rearranging and using the expression for the average velocity, one finds that i <i+)Ux 10 \ / T ° K \ * L R T Using assumption 11 ), equation (5-25) yields n + = 6.31* x 10lh — ^ cm"3 (5-26) A s I f assumption 12) i s valid, then the number density of the electrons i s the same as that of the ions. - 2 8 -CHAPTER I I I APPARATUS F i g u r e I I I - l i s a b l o c k d i a g r a m o f t h e a p p a r a t u s u s e d i n t h i s t h e s i s . Those p i e c e s o f a p p a r a t u s c o n n e c t e d b y a s o l i d l i n e were a l w a y s u s e d t o g e t h e r and t h o s e b y a b r o k e n l i n e were sometimes u s e d t o g e t h e r . I n t h i s c h a p t e r a g e n e r a l d e s c r i p t i o n o f t h e a p p a r a t u s i s g i v e n and t h e s p e c i f i c a p p l i c a t i o n s a r e d i s c u s s e d i n c h a p t e r I V . I I I - l The D r i v e r The d r i v e r c o n s i s t e d o f t h e d i s c h a r g e chamber p o r t r a y e d i n F i g . I l l - 2 . The m a t e r i a l s u s e d were b r a s s and p e r s p e x , w h i c h a r e e a s y t o work, and g l a s s , w h i c h i s a good r e s i s t o r o f e r o s i o n b y t h e d i s c h a r g e and f u r t h e r m o r e e n a b l e s one t o p h o t o g r a p h t h e d i s c h a r g e . R a p i d a b l a t i o n o f t h e p e r s p e x was p r e v e n t e d b y c o v e r i n g t h e s u r f a c e e xposed t o t h e d i s -c h a r g e w i t h g l a s s . A n a n n u l a r p i e c e o f g l a s s 1/16" t h i c k , when cemented on w i t h e p o x y r e s i n , was s a t i s f a c t o r y f o r t h i s p u r p o s e . The a u x i l i a r y anode p e r m i t t e d t h e d r i v e r ' s breakdown v o l t a g e t o be l o w e r e d s i n c e i t s h o r t e n e d t h e c a t h o d e t o anode d i s t a n c e . Gas was a d m i t t e d t o t h e a p p a r a t u s t h r o u g h a h o l e i n t h e s e c t i o n o f b r a s s t u b i n g c o n n e c t i n g t h e end p l a t e o f t h e d r i v e r t o t h e g l a s s s e c t i o n o f t h e shock t u b e . -29-P r e s s u r e Measurement Shock Tube Pump V I I I — I n t e g r a t o r -1 , D e l a y U n i t — -K e r r C e l l U n i t i I 1 i , »• < ~T 1 1 * 1 1 1 1 i ( f i Camera O s c i l l o s c o p e P r o b e s F i g . I I I - l . B l o c k D i a g r a m o f A p p a r a t u s -30-cathode glass shock tube gas xn brass glass cylinder auxiliary anode normal ' anode F K S ^ l lucite I88%5g glass trigger input to bank Fig. III-2. Discharge Chamber -31-TII-2 The C a p a c i t o r Bank A bank was c o n s t r u c t e d b y c o n n e c t i n g two C o r n e l l - D o u b l i e r NRG 212 c a p a c i t o r s i n p a r a l l e l . Copper l e a d s 9" and l U n w i d e were b o l t e d t o t h e c e n t e r t e r m i n a l s and t h e c a s e c o n n e c t i o n s r e s p e c t i v e l y . I n s u l a t i o n between t h e l e a d s c o n s i s t e d o f s e v e r a l l a y e r s o f p o l y e t h y l e n e . 6" wide c o p p e r l e a d s c a r r i e d c u r r e n t t o a s t a n d a r d s p a r k - g a p s w i t c h and t h e n c e t o t h e d r i v e r . A l l l e a d s were c o n s t r u c t e d f r o m c o p p e r s t o c k l / l 6 " t h i c k . s I I I - 3 C i r c u i t P a r a m e t e r s The c i r c u i t p a r a m e t e r s o f t h e a s s e m b l e d bank d i s c h a r g e c i r c u i t were: Bank C a p a c i t a n c e ( n o m i n a l ) Uk8 pF D i s c h a r g e C i r c u i t I n d u c t a n c e 5 l nH Maximum Bank O p e r a t i n g P o t e n t i a l 5 kV Maximum Bank E n e r g y 5.6 k J Maximum C u r r e n t U6i* kA D i s c h a r g e P e r i o d f r o m f i r s t q u a r t e r c y c l e 30.1+ us f r o m f i r s t h a l f c y c l e hh us The c i r c u i t i n d u c t a n c e was c a l c u l a t e d f r o m the measured f i r s t q u a r t e r c y c l e o f o s c i l l a t i o n t o be 51 nH. Over t h e f i r s t two c y c l e s , t h e t i m e p e r h a l f c y c l e o f o s c i l l a t i o n r e m a i n e d a p p r o x i m a t e l y c o n s t a n t . T h i s t i m e y i e l d s an i n d u c t a n c e o f 109 nH. I I I - l j . Power S u p p l i e s A power s u p p l y c a p a b l e o f s u p p l y i n g 8 kV a t 0.3 A was used t o c h a r g e t h e c a p a c i t o r bank. A s i s shown i n F i g . 111=3 t h e s u p p l y i s -32-> . to > ix r m n r o or a: - d r -ee: <~0 z: CCl < X J *0 5T _J O 3 F i g . III-3. Power Supply - 8 kV - 0.3 A -33-LEGEND FOR F I G . III-3 T x 7.5 A v a r i a c - Ohmite VT8A T 2 Hammond T 8 3 T^ F i l a m e n t 2.5 V- 5A V-_ A m p h r i t e 115NO30 V 2 866 M]_ 0 t o 1 n* M 2 0 t o lO'Q pk Rg c a l i b r a t i n g s hunt f o r M]_ (0 - 1A) R i 470 k f l R 2 U70 k 0_ R3 2 k H R^ 10 M f L Ni NE51 N 2 NE51 N3 NE51 R]_ 15 A h e a v y d u t y r e l a y F1 10 A F 2 15 A C x 0.5 / i F - 600 V S x DPST 5 2 DPST 5 3 R e v e r s i n g s w i t c h t o change p o l a r i t y o f s u p p l y ' s o u t p u t -34-divided into two units. The unit containing a l l high tension components was mounted inside a wire cage Just above the bank. Low voltage leads • i • . • ' i , ' ' , .' connect this unit with the control unit thus ensuring a maximum of safety for the operator. Figure III - 4 i s the scheme of a regulated supply that supplies 0.4 to 1,5 kV at 20 mA either positive or negative with respect to ground. Other special power supplies for the trigger unit, the delay unit, and the Kerr c e l l are discussed with the respective units, III-5 Gas Input The gases used i n a l l experiments, except for the atmospheric a i r , were obtained from Canadian Liquid A i r . The high pressure cylinders were connected to an Edwards type LB2A needle valve by copper tubing i n which the gas pressure was maintained at approximately 10 p s i . Before being admitted to the shock tube the gas from the needle valve passed through a trap that was immersed i n a pool of l i q u i d a i r . Throughout the duration of an experiment gas was continuously admitted and pumped from the system. The information supplied by Canadian Liquid A i r on the gases i s summarized i n Table I I I - l . TABLE III-l* IMPURITIES OF EXPERIMENTAL GASES Gas Purity (%) Nominal Impurities (%) i Ar 99.995 N 2 (0.0033); o2 (o.ooo5); Hp (0.0002); H 2 0 ( 0.0001) N 2 99.5 0 2 (0.487) ; H 2 0 (0.0128) He 99.995 H 2 (0.0020); Ne (0.0015) 0 2 & N 2 (0.0002); HgO ( 0.0001) -36. LEGEND FOR F I G . I I I - 4 R. 10 % 100 SL 10% 1W R 2 2.2 M SL. 10% 1W R 3 100 SL \ 1 M i X R^ 100 k _ f L R 6 22 k _0_ R y 4.7 M X L R8 100 k SL. . $00 k Si. 4.7 M n. 10 k SL 1 M SL i M r i _ 180 k 47.5 k H s t e p s (10 s t e p s ) 1% 1W 50 k n p o t e n t i o m e t e r 1# 470 k£l s t e p s (10 s t e p s ) 1% 1W R L 8 470 k j l 1# 1W C1 16 uF 6007 C 2 1 juF 2 kV R 11 R 12 R-R. 13 14 R i 5 R i 6 R-17 °3 c4 c 5 C6 V, V 4 v 5 v 6 D l Do T l T 2 F N 5 M 0.1 pF 6007 0.001 ;aF 600V 0.02 pF 2k7 1 uF 2kV 6DQ6 12AT7 5651 5651 5651 12AT7 BT100 ( P h i l i p s ) BY100 BY100 Hammond 262 E 6 Hammond 21560 3A NE 51 D o u b l e p o l e s i n g l e t h r o w t o g g l e s w i t c h 0 - 1.5 kV v o l t m e t e r Notes A l l r e s i s t a n c e s a r e 10$, \ w a t t u n l e s s o t h e r w i s e s p e c i f i e d -37-I I I - 6 T r i g g e r U n i t The s p a r k gap s w i t c h e s were a c t i v a t e d b y r e d u c i n g t h e r e s i s t a n c e o f t h e gas between t h e e l e c t r o d e s w i t h a h i g h v o l t a g e p u l s e . The p u l s e was g e n e r a t e d b y d i s c h a r g i n g a l e n g t h o f c h a r g e d c o a x i a l c a b l e w i t h a t h y r a t r o n (5C22) ( T h e o p h a n i s i960). Diagrams o f t h e equipment u s e d a r e shown i n F i g . II1-5 and 6. Power was f e d t o t h e t r i g g e r u n i t b y a r e g u l a t e d s u p p l y (A model 28) and t h e 115V a.c. m a i n s . The u n i t was s e t i n t o o p e r a t i o n b y e i t h e r s h o r t i n g i n p u t 2 t o ground o r a p p l y i n g a n e g a t i v e p u l s e t o i n p u t 1. I I I - 7 O s c i l l o s c o p e • A T e k t r o n i x model 551 d o u b l e beam o s c i l l o s c o p e s e r v e d t o o b s e r v e e l e c t r i c a l s i g n a l s . The c a l i b r a t i o n o f a l l o s c i l l o s c o p e p l u g - i n u n i t s was c h e c k e d b e f o r e t a k i n g measurements. T h i s c a l i b r a t i o n was c a r r i e d out u s i n g t h e o s c i l l o s c o p e ' s s q u a r e wave g e n e r a t o r , whose c a l i b r a t i o n was a l s o c h e c k e d . A l l T e k t r o n i x p r o b e s were compensated t o match t h e p l u g - i n u n i t s w i t h w h i c h t h e y were u s e d . S y n c h r o n i z a t i o n o f t h e beams and v e r t i c a l a m p l i f i e r r i s e t i m e s were •wef-e c h e c k e d u s i n g a T e k t r o n i x model 107 s q u a r e wave g e n e r a t o r . The b e a m s A i n phase t o w i t h i n a b out 1 ns and t h e r i s e t i m e s were t h e m a n u f a c t u r e r ' s s p e c i f i e d 13 n s . A DuMont o s c i l l o s c o p e camera was used t o p h o t o g r a p h t r a c e s on t h e o s c i l l o s c o p e s c r e e n . I I I - 8 P i c k u p C o i l To o b s e r v e t h e d i s c h a r g e c i r c u i t ' s I waveform, a s m a l l c o i l (Cormack (1963), and H a r t (1962)) was p l a c e d between t h e l e a d s f r o m t h e b) 16 kV Supply B + < S 2 c) -100 V and Filament Supply Fig.. Trigger Unit -39-LEGEND R l 100 k i t 68 k XL R3 330 k n. % 1 k XL 1 MIL R 6 47 kiL. R 7 5o Mn R 8 100 kXL R 9 100 k l L R 1 0 1.5 k XL R l l 1 k XL R 12 6.8 k i L R13 1 MIL R l U 100 XL R 10 kXL 15 R 16 10 k XL a 17 680 XI C 0.01 pF 600 V C 0.047 ; i F 0.6 kV C ho pF O.k kV C 200 pF C 680 pF 0.6 kV F I G . I I I - 5 c 470 pF 0.6 kV c 0.047 ^UF 0.6 kV c o.o47 uF 0.6 kV c 0.1 jsF 0.6 kV c 5oo pF 20 kV v l 2D21 V 2 5C22 V 3 12AU7 \ 6DQ6 v 5 IB 3 v 6 6AX4 v 7 032 D BY100 ( P h i l i p s ) 11 A d m i r a l 79DU1-1 T 2 A d m i r a l 4-20 mH h o r i z o n t a l c o i l ( f e r r i t e s l u g ) Hammond 167B Hammond 1128X Hammond 1129X N NE51 S]_ DPST t o g g l e S ? . SP3T t o g g l e -liO-Junction Box Isolated from Trigger Unit ZL.C JC J C _ r T _ Line Terminating Network 12' RG8/U Coaxial Cable Termination Resistors Spark Gap Cathodes trigger pins R' = k7n R = V k x U70 k_fL- resistors coaxially grouped about C C = 500 pF 20 kV to 5C22 i F i g . I l l - 6 . Pulse Forming Network and Distribution System - U l -bank to the driver. The c o i l consisted of 30 ,1.2 mm diameter turns of AWGU3 copper wire. A length of RG 58/U cable fed the signal to the oscilloscope input, which was shunted with a 5 0 f L resistor. III-9 Integrator Integration of I to give I was accomplished using the circuit of Fig. III-7. The integrated signal could be observed on the double beam oscilloscope screen simultaneously with I. RG8/U R 2 RG 8/U R1 = U7 -H-R 2 =- 10 k -O-C =. 25 nF FIG. T i l - 7 . Integrator 111-10 Shock Tube,, The shock tube was made from standard 1" Corning Double Tough Pyrex pipe and f i t t i n g s . Apiezon type M vacuum grease was used on a l l stop cocks and joins. Small leaks were readily eliminated with acrylic spray. The system was evacuated by connecting a Cenco Hyvac l U pump through a series l i q u i d a i r trap and stop cock to the shock tube's downstream end. -1*2-I I I - l l P r e s s u r e Measurement P r e s s u r e s were measured b y a U tube f i l l e d w i t h m e r c u r y f o r p r e s s u r e s g r e a t e r t h a n 10 m t o r r , Edwards t y p e 1G and 2G v a c u s t a t gauges f o r p r e s s u r e s between 1 m t o r r and 10 t o r r , and a C o n s o l i d a t e d E l e c t r o n i c s P h i l l i p s gauge f o r p r e s s u r e s l e s s t h a n 1 m t o r r . The P h i l l i p s gauge was c a l i b r a t e d a g a i n s t t h e v a c u s t a t a t 1 m t o r r . I I I - 1 2 I m p u r i t i e s I m p u r i t i e s a r i s e f r o m l e a k s i n t h e s y s t e m as w e l l as those a s s o c i a t e d w i t h the w o r k i n g gas ( s e e Gas I n p u t ) . S i n c e t h e s y s t e m was a c o n t i n u o u s f l o w one, t h e amount o f i m p u r i t i e s may be assumed t o be t i m e i n d e p e n d e n t . T h e ' u s u a l b a s e p r e s s u r e was about 1 m t o r r . A ssuming c o n s t a n t i m p u r i t y i n f l u x , a b a s e p r e s s u r e o f 1 m t o r r w o u l d g i v e r i s e t o l e a k i m p u r i t i e s o f "about 1 mole % at a w o r k i n g p r e s s u r e o f 100 m t o r r . I l l - 1 3 P h o t o m u l t i p l i e r U n i t s • O p t i c a l r a d i a t i o n f r o m a s m a l l c r o s s s e c t i o n o f t h e shock tube was d e t e c t e d b y p l a c i n g two c o l l i m a t i n g s l i t s i n f r o n t o f a p h o t o m u l t i p l i e r . F i g . I I I - 8 d e p i c t s t h e arrangement o f t h e s l i t s and t h e . RCA 931 p h o t o -m u l t i p l i e r t u b e . E a c h u n i t was b u i l t i n t o a Hammond l ) | ) | l i - l l i c h a s s i s ( 2 " x 5" x 9 " ) , w h i c h p r o v i d e d b o t h o p t i c a l and e l e c t r i c a l s h i e l d i n g . W i t h s l i t w i d t h s o f 2 mm, a c r o s s s e c t i o n o f t h e shock t u b e , 2. cm o r l e s s t h i c k , c o u l d be v i e w e d b y U mm o f t h e c a t h o d e when t h e u n i t was p l a c e d a g a i n s t t h e shock t u b e . Two t y p e s o f c i r c u i t were u s e d w i t h t h e p h o t o m u l t i p l i e r t u b e s and t h e i r schema a r e shown i n F i g . I I I - 9 . S e n s i t i v i t i e s o f s e v e r a l p h o t o m u l t i p l i e r s were compared b y u s i n g -hk-> 0-Hr > 8 I >4i r-O or f 4 3. X > o o 5= \£> L 3 fl 0 rf a: I . 5 X cr > a) <r > F i g . 1 1 1 - 9 . Photomultiplier Circuits -hS-LEGEND FOR FIG. II 1 - 9 R 100 k_fL h 3S0 SL R2 10 k XL R3 1 k i L . \ l.S M I L R 5 330 k J i -R6 560 k -T--c 0.5 UF 200V c l 2 nF 600V V 931 RCA A l l r e s i s t o r s §• watt - 10% the tubes, i n turn, i n a single photomultiplier unit. The light source used was a General Radio Stroboscope (neon bulb) and the operating voltage of the tube was 8I4.O V. The largest output voltage,0 a | measured with an oscilloscope, was about 20 times the minimum. This indicates great variation of sensititivy can be found even among new photo-multiplier tubes. Two units having equal response were obtained by adjusting the s l i t widths. I I I - l l l Capacitative Probes Capacitative probes consisted simply of Belden 20 A.WG wire. Both the single loop, using insulated wire, and the completed ring, using bare wire, were constructed. Both types are il l u s t r a t e d i n F i g . Ill - 1 0 . II1-15 Ring Electrode Probe Brass rings, having the same internal diameter as the shock tube inserted i n the pipe section junctions,- formed ring electrodes i n contact with the shock tube gas. A vacuum tight seal was ensured by the use of teflon washers between pyrex and brass surfaces. This probe i s depicted i n Fig. 111-10. HI-16 Pin Electrode Probe One millimeter diameter tungsten wire was inserted into the walls of a six inch section of piping, at diametrically oposite points (see Fig. 111-10), with several millimeters of wire exposed to the shock tube gas. However, the pins protruded less than two millimeters beyond the normal position of the wall's inner surface. -47-teflon Fig. 111-10. Pin and Ring Electrodes; Capacitative Probes Ill-17 Two Wire Probes Several two wire probes were used and these are i l l u s t r a t e d i n Fig. i n - 1 1 . Probe I - This probe was made from a perspex cylinder 6.4 cm long and 2.5 cm i n diameter (see Fig. I I I - l l ) . A slot, 1 cm wide and 3.8 cm long, was cut i n the cylinder 4.5 mm from the front edge. A 1.5 cm hole through the front edge extended to the slot. Forty mil tungsten wires, par a l l e l to the s l i t width axis and through the perspex cylinder axis, were centered 0.9 and 1.9 cm from the cylinder's front edge. Leads embedded i n the perspex connected the tungsten wires to external c i r c u i t s . Thus only. 1 cm of each tungsten wire was i n contact with the shock tube gas. Probe II - A modification of probe I by blocking some of the openings with Apiezon Q compound. Probe III - As probe II but with the outside of the cylinder painted with black acrylic spray. Probe IV - This probe differed from III i n that more of the openings were blocked and the effective distance between the wires was reduced to 1 mm. Probe V - Identical to IV except that the opening at the front edge was enlarged. Probe VI - This probe i^as constructed using a perspex cylinder 3 cm long and 1.3 cm i n diameter. Along the cylinder axis holes, diametrically opposite and having centers separated by 0.5 cm, were d r i l l e d to take 40 mil tungsten wires. These wires were affixed so that 0.5 cm protruded from the front edge of the perspex cylinder. -U9-3.8 cm h.f? mm leads to termination unit brass cylinder perspex cylinder UO mil tungsten wires front elevation view Probe I F i g . III-11. Two Wire Probes Q compounc. Probes II - III 3/k f i l l e d with compound 'completely f i l l e d with compoum Probe IV Probe V set screw^ leads to external c i r c u i t perspex "^tungsten Probe VI Fig. ni-11. Two Wire Probes -51-At the rear of the cylinder, adjacent holes were d r i l l e d next to those for the tungsten so that leads could be f i r m l y clamped against the tungsten by.set screws. These leads passed through the brass tube probe holder to external c i r c u i t s . 111-18 Probe Positioner By mounting the brass tube probe holder on a carriage, the probe's po s i t i o n with respect to the shock tube axis could be continuously adjusted to within 0.1 mm ( F i g . I l l - 1 2 ) . 111-19 Delay Unit The delay unit consisted of a ramp generator, three delay channels, and a power supply.. The application of a negative pulse to C 2 of the ramp generator, F i g . 111-13, causes a ramp pulse to be generated across C 1 2, "the output.. I n most cases the input was the charge of an 0.5 uF condenser, charged to 300 V. The ramp's r i s e time depended on whether C-j_2 or C]_^ was employed. Three delay channels were connected to the ramp generator's output. Connection was made to R]_, F i g . III-L4, of each delay channel. Each channel produced a 1(0 V positive output pulse, of 10 ^is duration. V a r i a t i o n of R^ adjusted the delay to the desired amount. The regulated power supply,.Fig.. 111-15, delivered plus 300 V at 300 mA,. minus 300 V at. 100 mA, and 6.3 V at 10 A. 1 turn , 1 mm Scale i n tenths of a revolution Position indicator " 0 " rings Probe Terminal unit Leads waxed i n to maintain vacuum seal Brass pipe Knurled nut « p\—1 <£— Double " 0 " ring seal — T o f i t standard «? piping flange Shock tube Gross piece of pyrex piping Fig. II1-12- Probe Carriage Assembly -53-F i g . I l l - 1 3 . Ramp Generator -54-LEGEND FOR FIG. HI - 1 3 R l 1 0 0 kJL- R 2 2 1 0 0 k Xu c 7 1 0 0 pF R2 1 0 0 k J L R 2 3 470 k X L C8 33 P F R 3 1 0 kfL R 24 680 k X L C9 33 pF R 4 1 0 kXL R 25 4.7 k XL C 1 0 1 0 nF R 5 1 0 k J L R 2 6 h.7 k X u ° 1 1 0 . 5 uF R6 1 . 2 k A. R 2 7 2 2 0 k j u ° 1 2 47 PF R7 2 7 0 X L RoQ 680 k XL C 1 3 2 nF R 8 3 3 0 k ft. R 2 9 2 8 0 k X L C 1 4 2 0 0 pF Ro 1 0 0 k X L R 3 0 15 k X L V l \ 6J6 R 1 0 3 . 3 k f L R 3 1 47 k X L V \ 6J6 R l l 3.3 k_Tl- R 3 2 15 k X L V 3 i 6J6 R 1 2 1 0 0 X L R - , o 33 1 MXL V 4 1 6J6 R 1 3 1 0 0 X L . R 34 68 k X L . v 5 | 1 2 A T 7 R l 4 1 M - T L R 35 15 k I L v 6 i 6AL5 R l 5 3.3 k J L R 36 1 0 0 k -fr 7 7 \ 6AL5 ^ 6 3.3 k X L c l 0 . 1 pF v 8 | 1 2 A T 7 R17 5 k a ° 2 1 0 pF V9 6 A M 6 R18 . 1 0 k XL c 3 0 . 1 ^F V 1 0 6AM6 R19 1 0 0 k Xu c 4 400 pF D F 4 R 2 0 470 k XL c 5 1 0 0 pF S S P D T R 2 1 680 k XL c 6 1 0 0 pF F i g . ni-14. D e l a y C h a n n e l - 5 6 -L E G E N D F O R F I G . H I - U J , h 47 Si R 2 10 k XL R 3 hl k i L . % 50 k J l R 5 50 k XL R 6 330 k XI R 7 h70 k -TL R 8 27 k n -R 0 220 k X L R i o 100 k 11 R l l 10 k X L R 12 3 . 3 k XL. R 1 3 220 k XL R l 4 100 k -H— R 1 5 10 k -fL he 1 M XL 100 XL 17 R 1 8 3 .3 k XL R 1 9 3 . 3 k -XL potentiometer R 2 0 5 k XL R 2 1 6 . 6 k XL R „ 1 0 0 X L 2 2 R 2 3 3 3 0 kXL R o i 24 1 0 0 k XL R 2 5 1 k XL R 2 6 1 . 5 kXL R27 6 8 0 k XL ° 1 10 pF c 2 47 PF G 3 33 PF % 10 nF c 5 10 pF c6 0.1 uF v l 6 U 8 V 2 6 U 8 V 3 6J6 v 4 6CL6 - 5 7 --58= LEGEND FOR F I G . III-15 h 470 k J l 1 W C5 0.1 jaF 600 V 15 k X L 5 W c6 0.1 /aF 600 V R3 470 k i t 1 WW V l 6AS 7 R4 15 k-TL 5 w V 2 6AS7 R5 15 k X V 5 w V3 12AT7 R6 15 k XL 5 w V 4 12AT7 R7 .. 15 kXL 5 w D l BY100 ( P h i l i p s ) R8 15 k XL 5 w D 2 BY100 Ro 470 k SL 1 w D3 BY100 R 1 0 15 k XL 5 w D4 BY100 R l l 470 k XL 5 w T l Hammond 272 HX R 1 2 1 M SI i w Hammond 10-300 X R 1 3 1 M i l | w . T3 Hammond 273 X R l 4 68 k i L 1 w T4 Hammond 10-100 X Ri5 68 k X L 1 w % NE 51 R16 47 kXT. | w N 2 NE 51 R 1 7 47 k XL i w S DPST t o g g l e C l 16 jaF 600 V XX F i l a m e n t s o f ramp g e n e r a t o r and d e l a y c 2 16 uF 600 V c h a n n e l s 16 pF 600 V yy. F i l a m e n t s o f power s u p p l y t u b e s % 16 ^ F 600 V -59-111-20 K e r r C e l l U n i t The K e r r C e l l S y s t e m i n F i g . I I I-16, A v c o t y p e KCS-020-2, c o n s i s t e d o f a K e r r c e l l a n d a p u l s e g e n e r a t o r . P u l s e s w e r e g e n e r a t e d b y s h o r t i n g o n e e n d o f a c o a x i a l c a b l e w i t h a s p a r k gap i n f r e o n gas a t a p r e s s u r e o f 8 p o u n d s p e r s q u a r e i n c h . T h i s p u l s e o p e n e d t h e K e r r c e l l f o r 100 n s . T r i g g e r i n g o f t h e s p a r k gap was e f f e c t e d w i t h a t r i g g e r u n i t . The. , p u l s e f r o m t h e l i n e t e r m i n a t i n g n e t w o r k , F i g . I U - 6 , was f e d t o t h e K e r r C e l l S y s t e m . T h e l i g h t p a s s e d t h r o u g h t h e K e r r c e l l a n d t h e n t h r o u g h a b a f f l e w i t h a c i r c u l a r h o l e , a n d was t h e n f o c u s s e d on t h e f i l m o f a m o d i f i e d DuMont o s c i l l o s c o p e c a m e r a . T h e b a f f l e r e d u c e d s t r a y l i g h t f r o m t h e s i d e s o f t h e c e l l . B o t h p o l a r o i d hi a n d r o l l f i l m c o u l d b e u s e d i n t h e c a m e r a . T h e c a m e r a s h u t t e r was o p e n e d j u s t b e f o r e o p e r a t i n g t h e K e r r c e l l a n d c l o s e d a g a i n a f t e r t h e K e r r c e l l s h u t t e r c l o s e d . A n A v c o t y p e PS-060-1 p o w e r s u p p l y was e m p l o y e d t o c h a r g e t h e p u l s e g e n e r a t o r ' s c o a x i a l c a b l e . I Camera j B a f f l e K e r r 1 . C e l l S y s t e m S h o c k i 1 Tube T r i g g e r U n i t F i g n i - l 6 . B l o c k D i a g r a m o f K e r r C e l l U n i t -60-CHAPTER IV EXPERIMENTAL RESULTS IV-1 Introduction This chapter w i l l be devoted to a detailed description of the experiments which have been performed. The interpretation of the results w i l l be discussed i n Chapter V, but occasionally these interpretations may be anticipated i n this chapter i n order to c l a r i f y the reason for performing a particular experiment. Several different types of detectors have been used by other workers for detecting the precursor effect. There i s very l i t t l e information available about the relative merits of these detectors so the i n i t i a l project undertaken i n this research has been a systematic comparison of detectors performance. These experiments are described i n section IV-2 to IV-6. While investigating the performance of the detectors i t became apparent that the precursor parameters are markedly dependent upon the bank current. The investigation of this dependence i s described i n the next five sections. In section TV-7 and IV-8 i t i s shown that the poten-t i a l of the shock tube gas depends on the rate of change of bank current. The relationship between bank current and several precursor parameters i s discussed i n section IV-11. The I dependence indicates that the pre-cursor potential may be strongly dependent on the driver potential - 6 1 -r e l a t i v e t o ground ( L I ) and t h i s a s p e c t i s i n v e s t i g a t e d i n s e c t i o n s I V - 9 and XV - 1 0 . I n t h e work r e p o r t e d i n t h e n e x t t h r e e s e c t i o n s ( 1 2 - l U ) , an a t t e m p t has b e e n made t o d e t e r m i n e w h e t h e r t h e p r e c u r s o r i o n i z a t i o n i s due t o r a d i a t i o n f r o m t h e d r i v e r o r t o some f o r m o f p a r t i c l e t r a n s f e r . I n s e c t i o n IV - 1 2 t h e r e s u l t s o f p l a c i n g r a d i a t i o n f i l t e r s ( L i F and q u a r t z ) between t h e d r i v e r and t h e d e t e c t o r i s r e p o r t e d . S e c t i o n s IV - 1 3 and I V - l l ; d i s c u s s a t t e m p t s t o d e v i a t e t h e f l o w o f c h a r g e d p a r t i c l e s b y means o f a p p l i e d e l e c t r i c and m a g n e t i c f i e l d s . The p r e c u r s o r i o n i z a t i o n i s a p p a r e n t l y due t o r a d i a t i o n and not t o p a r t i c l e t r a n s f e r . S e c t i o n s IV-l£ t o I V - 1 8 r e p o r t on a s e r i e s o f i n v e s t i g a t i o n s i n t o t h e p r e s e n c e o f i o n i z a t i o n i n a s i d e t u b e p e r p e n d i c u l a r t o t h e main shock t u b e . T h i s s e r i e s o f e x p e r i m e n t s i n d i c a t e s t h a t t h i s s i d e i o n i -z a t i o n i s p r o b a b l y due t o r a d i a t i o n f r o m t h e p h o t o - e x c i t e d gas i n t h e main t u b e . The d i r e c t dependence o f t h e gas p o t e n t i a l on t h e d r i v e r p o t e n t i a l m e n t i o n e d e a r l i e r , s u g g e s t s t h a t t h e shock t u b e may be c o n s i d e r e d as one arm o f a t r a n s m i s s i o n l i n e . T h i s model i s f u r t h e r i n v e s t i g a t e d i n s e c t i o n I V - 1 9 t o I V - 2 2 , i n w h i c h v a r i a t i o n o f gas p o t e n t i a l and i o n i z a t i o n i s d e t e r m i n e d as a f u n c t i o n o f t i m e and d i s t a n c e a l o n g t h e t u b e . The t h e o r e t i c a l s t u d i e s o f t h e r a d i a t i o n model o f t h e p r e c u r s o r p r e d i c t t h e r e l a t i o n s h i p between t h e l o n g i t u d i n a l d i s t a n c e between two p r o b e s and t h e d i f f e r e n c e i n t h e t i m e s a t w h i c h each p r o b e r e s p o n d s t o t h e i o n i z a t i o n ( s e e e q u a t i o n V - l l ; , p. 1 3 6 ) . E x p e r i m e n t a l i n v e s t i g a t i o n s - 6 l a -o f t h i s r e l a t i o n s h i p a r e r e p o r t e d i n s e c t i o n s IV-26 t o IV-28. Measurements made o f t h e e l e c t r o n d e n s i t y and t e m p e r a t u r e i n t h e p r e c u r s o r a r e r e p o r t e d i n s e c t i o n I V - 2 Q . The p o s i t i o n o f t h e p r o b e s a l o n g t h e shock t u b e was measured f r o m t h e d r i v e r ' s b a c k p l a t e when t h e a u x i l i a r y anode was n o t i n u s e , and f r o m t h e a u x i l i a r y anode when i t was i n u s e . IV-2 P h o t o m u l t i p l i e r v s C a p a c i t a t i v e R i n g S i g n a l s The p r e c u r s o r e f f e c t was s i m u l t a n e o u s l y o b s e r v e d a t a p o i n t a l o n g t h e shock t u b e b y a t y p e I p h o t o m u l t i p l i e r u n i t and a b a r e w i r e c a p a c i -t a t i v e r i n g . The c a p a c i t a t i v e r i n g p o t e n t i a l was o b s e r v e d on t h e o s c i l l o s c o p e ' s u p p e r beam. The r i n g was c o n n e c t e d t o a T e k t r o n i x P 6 0 0 0 p r o b e ' s c e n t e r c o n d u c t o r , w h i c h was i n t u r n c o n n e c t e d t o a t y p e L p l u g - i n u n i t . A s i m i l a r p l u g - i n u n i t i n t h e l o w e r beam c i r c u i t was c o n -n e c t e d v i a RG 58/u c a b l e t o t h e p h o t o m u l t i p l i e r o u t p u t . The a p p a r a t u s was s e t i n t o o p e r a t i o n b y t r i g g e r i n g t h e d e l a y u n i t . A f t e r some a r b i t r a r y d e l a y a p u l s e f r o m one o f t h e u n i t ' s c h a n n e l s t r i g g e r e d t h e o s c i l l o s c o p e sweep. A f t e r some a r b i t r a r y d e l a y one o f t h e o t h e r c h a n n e l ' s p u l s e s s e t a t r i g g e r u n i t i n t o o p e r a t i o n . T h i s t r i g g e r u n i t ' s o u t p u t was s i m u l t a n e o u s l y f e d t o t h e c a t h o d e s o f t h e main bank s w i t c h and t h e d r i v e r . N o r m a l l y t h e o s c i l l o s c o p e ' s sweep was t r i g g e r e d b e f o r e t h e t r i g g e r u n i t , t h u s e n a b l i n g e a s y e x a m i n a t i o n o f t h e f i r s t few - 6 2 -microseconds of the bank's discharge. Argon was used as the shock tube's working gas. The bank was i n i t i a l l y charged to 2 kV. In F i g . IV-1 are examples of signals due to the precursor, traces a) and b), and signals due to the shock a r r i v a l at the observation point, traces c) and d). Traces a) and b) show that during the f a s t precursor the gas p o t e n t i a l o s c i l l a t e s while the photomultiplier signal remains negative. Neither trace returned to the base l i n e within the sweep time. Traces c) and d) taken over a longer sweep time i l l u s t r a t e the return to the base l i n e . At the lower pressure of 280 mtorr, the potential of the gas had returned to ground before the a r r i v a l of the shock and upon i t s a r r i v a l became p o s i t i v e , traces e) and f ) . In contrast to t h i s , at 3 t o r r , the potential of the gas attained that of ground and remained there at the shock front's a r r i v a l , traces g) and h). A difference i n signal shape i s to be noted, as w e l l as the v a r i a t i o n of the observation point. IY - 3 Photomultiplier vs P i n Electrode Signals The same experimental arrangement that was used to compare the photomultiplier and capacitative ring signals was used i n t h i s experiment with a p i n electrode substituted f o r the capacitative r i n g . In F i g . IV - 2 are shown examples of pin electrode signals due to the precursor effect i n argon (trace a ) ) , and due to the effect of the shock front's arrival (trace c ) ) . The corresponding photomultiplier signals aire shown i n traces b) and d) respectively. An i n i t i a l bank voltage of 2 W was employed. The response to the precursor starts at the same time for each pressure 1 torr - sweep 10 us era" a) capacitative ring at 50.3 cm - ve r t i c a l scale 20 V cm" b) photomultiplier at 50.2 cm - vertical scale 0.5 V cm~^ " pressure 1 torr - sweep 100 jxs cm c) capacitative ring at 8U.0 cm - vertical scale 1 V cm""'" d) photomultiplier at 8i|.0 cm » vertical scale 0.1 V cm Fig. IV-1 . Capacitative Ring vs Photomultiplier Signals p r e s s u r e 280 m t o r r - sweep 100 u s cm e) c a p a c i t a t i v e r i n g a t 84.0 cm - v e r t i c a l s c a l e 0.5 V cm" f ) p h o t o m u l t i p l i e r a t 84.0 cm - v e r t i c a l s c a l e 0.05 V cm" 1 p r e s s u r e 3.0 t o r r - sweep 10 ^ i s cm" 1 g) c a p a c i t a t i v e r i n g 35.9 cm - v e r t i c a l s c a l e 20 V cm" 1 h) p h o t o m u l t i p l i e r a t 35.9 cm - v e r t i c a l s c a l e 2 V cm" 1 F i g . 1 7 - 1 . C a p a c i t a t i v e R i n g v s P h o t o m u l t i p l i e r S i g n a l s -65-p r e s s u r e 280 m t o r r - sweep 10 / i s cm" 1 a) p i n e l e c t r o d e a t 73.1 cm - v e r t i c a l s c a l e 50 V cm"' b) p h o t o m u l t i p l i e r a t 73.1 cm - v e r t i c a l s c a l e 1 V cm' c) d) p r e s s u r e 1 t o r r - sweep 100 jus cm a) p i n e l e c t r o d e a t 73.1 cm - v e r t i c a l s c a l e 2 V cm""1" b) p h o t o m u l t i p l i e r a t 73.1 cm - v e r t i c a l s c a l e 0.05 V cm" F i g . I V - 2. P i n E l e c t r o d e v s P h o t o m u l t i p l i e r S i g n a l s - 6 6 -d e t e c t o r and t h e d u r a t i o n o f t h e r e s p o n s e p u l s e i s i n d e p e n d e n t o f t h e d e t e c t o r . 17-4 C a p a c i t a t i v e R i n g v s F i n E l e c t r o d e S i g n a l s W i t h t h e same e x p e r i m e n t a l s e t - u p e x c e p t t h a t t y p e K p l u g - i n u n i t s were u s e d f o r t y p e L, t h e p i n e l e c t r o d e s i g n a l was compared t o t h a t f r o m a c a p a c i t a t i v e r i n g . The t r a c e s o b s e r v e d a r e shown i n F i g . XV-3. We s e e t h a t t h e shape o f t h e s i g n a l s i s t h e same b u t t h a t t h e a m p l i t u d e o f t h e p i n e l e c t r o d e s i g n a l i s about 20 t i m e s t h a t o f t h e c a p a c i t a t i v e r i n g . 17-5 R i n g A r o u n d Tube v s One A d j a c e n t t o I t A c a p a c i t a t i v e r i n g s i g n a l was compared t o t h e s i g n a l f r o m a n i d e n t i c a l r i n g a d j a c e n t t o t h e t u b e a t t h e same p o s i t i o n , 57.8 cm. The s i g n a l s were i d e n t i c a l e x c e p t t h a t t h e one f r o m t h e r i n g wrapped aroun d t h e t u b e was about f i v e t i m e s l a r g e r i n a m p l i t u d e t h a n t h e o t h e r . 17 -6 Two W i r e v s R i n g E l e c t r o d e P r o b e B y c e n t e r i n g t h e i n t e r s e c t i n g axes o f a g l a s s t e e j u n c t i o n a t a p o s i t i o n o f 111.2 cm, a t y p e I two w i r e p r o b e was i n s e r t e d i n t o t h e shock t u b e . A t t h e p o i n t s where t h e t e e s e c t i o n was b o l t e d t o t h e r e s t o f t h e shock t u b e , 104.2 and 118.2 cm, r i n g e l e c t r o d e s were i n s e r t e d . F i g . 17-4 d e p i c t s t h e a r r a n g e m e n t . I n t h i s f i g u r e i s a l s o shown t h e c i r c u i t • u s e d t o o b s e r v e t h e probe p o t e n t i a l s . E a c h r i n g e l e c t r o d e was c o n n e c t e d t o a P6000's c e n t r a l e l e c t r o d e . These P6000 p r o b e s were t h e n c o n n e c t e d t o t h e i n p u t s o f a t y p e G d i f f e r e n t i a l a m p l i f i e r i n t h e o s c i l l o s c o p e ' s u p p e r beam c i r c u i t . -67-p r e s s u r e 1 t o r r a r g o n - bank 2.0 kV - sweep 20 us cm a) p i n e l e c t r o d e a t 7 3ol cm - v e r t i c a l s c a l e 100 V cm""^ b) c a p a c i t a t i v e r i n g a t 73«6 cm - v e r t i c a l s c a l e 10 V cm" F i g . IV -3» C a p a c i t a t i v e R i n g v s P i n E l e c t r o d e S i g n a l s A s i m i l a r arrangement was u s e d t o m o n i t o r t h e p o t e n t i a l o f t h e two w i r e p r o be o n t h e o s c i l l o s c o p e ' s l o w e r beam« Assuming t h a t t h e impedance between t h e p r o b e ' s w i r e s i s . i n f i n i t e , t h e probe v o l t a g e i s about 27 V. The t i m e t o a t t a i n t h i s p o t e n t i a l d i f f e r e n c e , L 6 ms, was much l o n g e r t h a n t h e e x p e r i m e n t a l t i m e , 20 us. Thus b a t t e r y c u r r e n t has a n e g l i g i b l e e f f e c t upon t h e probe p o t e n t i a l d u r i n g t h e o b s e r v a t i o n t i m e . When t h e probe impedance d r o p s b e l o w 200 ItSX t h e probe p o t e n t i a l w i l l d r o p b elow 27 V a t a r a t e dependent o n t h e r a t e o f change o f t h e -68-RG 58/U cable Equivalent Circuit for P6000 Probes and G type plug-in unit i n oscilloscope Two Wire Probe Shock tube Ring electrode 10 M i l 15 pF 10 M i l 15 PF Oscilloscope measuring c i r c u i t Fig. IV - U . Two Wire Probe and Ring Electrode Circuits - 6 9 -impedance. The new probe p o t e n t i a l w i l l depend on the probe's impedance as compared to 20 M-fL . Thus a change i n probe voltage i n d i c a t e s a change i n gas impedance. Upon s h o r t i n g the t r i g g e r u n i t ' s i n p u t 2 t o ground, an output pulse was a p p l i e d to the d r i v e r ' s cathode. This i n i t i a t e d the bank discharge. Before t r i g g e r i n g , the bank was charged to a p o t e n t i a l of 0.1| kV and the shock tube f i l l e d w i t h argon t o a pressure of 180 mtorr. F i g . I V - 5 shows p a i r s o f t r a c e s with the two wire probe center, l . l l cm from the capsule's f r o n t edge, at 5 . 6 , 7.6, and 9»9 cm perpendi-c u l a r t o the shock tube a x i s . We note t h a t as the probe moves away from the a x i s i t takes l o n g e r to detect i o n i z a t i o n . I t i s a l s o to be noted t h a t the p o t e n t i a l d i f f e r e n c e between the r i n g probes was not r e p r o d u c i b l e f o r the f i r s t 5 /i s and d i d not r e t u r n t o zero during the experimental time. b) I sweep 1 jus cm a) two wire probe 5 . 0 cm from shock tube a x i s - v e r t i c a l s c a l e 10 V cm" 1 b) r i n g electrodes - v e r t i c a l s c a l e 0.5 V cm" 1 17-5. Two Wire Probe vs Ring E l e c t r o d e S i g n a l s -70-c) d) sweep 2 ^ i s cm"-^  a) two w i r e probe 7.6 cm from shock tube a x i s -v e r t i c a l s c a l e 10 V cm"l b) r i n g e l e c t r o d e s - v e r t i c a l s c a l e 0 . 5 V cm""1" e) f ) / • • i f --1 sweep 2 u s cm e) two w i r e probe a t °.0 cm fr o m shock t u b e a x i s -v e r t i c a l s c a l e 10 V c m ~ l f ) r i n g e l e c t r o d e s - v e r t i c a l s c a l e 0.5 V cm"^" 17-5. Two W i r e Probe v s R i n g E l e c t r o d e S i g n a l s -71-IV-7 I vs Capacitative Ring Signals The bank current's time derivative, I, was compared to the capaci-tative ring probe's signal. The observed signals depended on the values of the gas pressure, i n i t i a l bank voltage, and position along the shock tube. The working gas was argon and the experiments were performed using the shock tube as described i n Chapter IV-2. Pick-up c o i l signals were transferred to the oscilloscope's lower beam by a length of RG/5>8U cable. The plug-in unit used, K or L, was matched to the cable by shunting i t s input with a 50 JX. resistor. Using a P6000 probe's central conductor and the same type of plug-in unit, the capacitative ring signal was displayed on the upper beam. For times greater than 10 JIS, the observed signals were independent of the experimental parameters (Fig. IV-6 traces a) and b)), except for an i n i t i a l bank voltage of 1 kV (traces c) and d)). The effect of gas pressure variation i s illu s t r a t e d by traces e) to f) and that of position variation by traces g), h) and m), n). Traces o) and p) show that while I goes to 0 after about £0 us the ring signals may last for some l£0^us. IV-8 I vs Gas Impedance The shock tube was operated and the I waveform observed i n the same manner as that described i n the preceding comparison. A measure of the gas impedance was obtained by connecting the two diametrically opposite pin electrodes, at 73.1 cm, i n series with a 39 kJl_ resistor and a 90 V battery. Neglecting battery resistance, the voltage across the 39 k i l _ resistor determines the gas impedance between the pin electrodes. This resistor voltage was monitored by connecting each of i t s ends to central -72-a) b) p r e s s u r e 1 t o r r - bank 3 kV - sweep 5 cm - 1 a) c a p a c i t a t i v e r i n g a t 85.5 cm - v e r t i c a l s c a l e 50 V cm -1 b) I - v e r t i c a l s c a l e 2 V cm' - 1 IPiPiliiliSil c ) d) p r e s s u r e 1 t o r r - bank 1 kV - sweep 5 ^ s cm a) c a p a c i t a t i v e r i n g a t 85.5 cm - v e r t i c a l s c a l e 50 V cm - 1 b) I - v e r t i c a l s c a l e 2 V cm - 1 F i g . IV-6, I v s C a p a c i t a t i v e R i n g S i g n a l s -73-e) f) pressure 0.3 t o r r - bank 2 kV - sweep 0.5/is cm"1 e) capacitative ring 85.5 cm - v e r t i c a l scale 20 V cm - 1 \ • -1 f ) I - v e r t i c a l scale 2 V cm g) h) 1 - l pressure 1 t o r r - bank 2 kV - sweep 0.5 /is cm g) capacitative r i n g at 85.5 cm - v e r t i c a l scale 20 V cm"1 h) I - v e r t i c a l scale 2 V cm"1 F j g . 1,7-6. . I vs Capacitative Ring Signals -74--1 p r e s s u r e 3 t o r r - bank 2 kV - sweep 1 p.s cm i ) c a p a c i t a t i v e r i n g a t 8^.5 cm - v e r t i c a l s c a l e 20 7 cm" 1 j ) I - v e r t i c a l s c a l e 2 7 cm"'-'-o F i g . 1 7 " 6 . I v s C a p a c i t a t i v e R i n g S i g n a l s -75-pressure 1 t o r r - bank 2 kV - sweep 0.5 us cm~l m) capacitative ring at 29.8 cm - v e r t i c a l scale 50 V cm • -i n) I - v e r t i c a l scale 2 V cra~ x -1 o) P ) pressure 1 t o r r - bank 2 kV - sweep 50 ;u.s cm~^ -o) capacitative ring at 50.3 cm - v e r t i c a l scale 1 V cm"'*" p) I - v e r t i c a l scale 0.1 V cm -1 F i g . IV-6. I vs Capacitative Ring Signals -76-P6000 probe c o n d u c t o r s a t t a c h i n g t h e l a t t e r t o t h e i n p u t s o f a t y p e G p l u g - i n u n i t i n t h e o s c i l l o s c o p e ' s u p p e r beam c i r c u i t . The P6000 o u t e r c o n d u c t o r s s e r v e d a s s h i e l d s f o r s t r a y p i c k - u p . A l l o b s e r v a t i o n s were p e r f o r m e d u s i n g a r g o n as t h e w o r k i n g gas and 2 kV as t h e i n i t i a l bank v o l t a g e . T r a c e s a) t o d) i n F i g , IV - 7 i l l u s t r a t e t h e o b s e r v e d s i g n a l s f o r t h e f i r s t £0 ^ i s a s w e l l as t h e f i r s t 10 u s . O n l y t h e f i r s t 10yus showed an y s i g n i f i c a n t change w i t h a v a r i a t i o n i n p r e s s u r e , t h i s b e i n g d e p i c t e d b y t r a c e s c ) t o h ) . We n o t e t h a t t h e r i s e t i m e o f t h e gas c o n d u c t i v i t y i n c r e a s e d as t h e gas p r e s s u r e was i n c r e a s e d . IV-9 Shock Tube P o t e n t i a l s w i t h Respect, t o Ground The t i m e v a r i a t i o n o f t h e d r i v e r ' s p o t e n t i a l w i t h r e s p e c t t o t h e e a r t h i n g p o i n t and t o a r i n g e l e c t r o d e a t a p o s i t i o n o f 1*8.7 cm was o b s e r v e d . The d r i v e r ' s p o t e n t i a l , c o n s i d e r e d t o be t h a t o f i t s - f r o n t p l a t e w i t h r e s p e c t t o g r o u n d , was t h e same as t h e p o t e n t i a l d i f f e r e n c e a c r o s s t h e r e t u r n l e a d , f r o m t h e d r i v e r t o t h e o u t e r c a s e o f t h e bank. The shock t u b e was o p e r a t e d as i n s e c t i o n IV-2 f o r a l l e x p e r i m e n t s , w h i c h were c a r r i e d out i n a r g o n . A l l p o t e n t i a l d i f f e r e n c e s were measured i n t h e same way as was t h e v o l t a g e i n t h e p r e c e d i n g e x p e r i m e n t . T r a c e s a) t o d ) , F i g . I V - 8 , show t h e e f f e c t o f v a r y i n g t h e i n i t i a l bank v o l t a g e w h i l e m a i n t a i n i n g a c o n s t a n t gas p r e s s u r e . D u r a t i o n , a m p l i t u d e , a nd shape o f t h e o b s e r v e d p o t e n t i a l d i f f e r e n c e p u l s e s were a f f e c t e d . We see t h a t a l t h o u g h t h e d r i v e r s t a y s n e g a t i v e w i t h r e s p e c t t o e a r t h f o r 10 ;as, t h e gas a l o n g t h e t u b e a t t a i n s t h e d r i v e r p o t e n t i a l a f t e r a few u s , i . e . l e s s t h a n 20 V. p r e s s u r e 1 t o r r - sweep 5 ps cm a) v o l t a g e a c r o s s 39 k i t - v e r t i c a l s c a l e 50 V cm' . . -1 b) I - v e r t i c a l s c a l e 2 V cm h i m m m m m • i i PI • m 1II M l p r e s s u r e 1 t o r r - sweep 0.5 / i s cm c) v o l t a g e a c r o s s 39 k J L r e s i s t o r - v e r t i c a l s c a l e 50 V cm d) I - v e r t i c a l s c a l e 2 V c n T x F i g . I V - 7 . I y s G a s Impedance ^ -78-e) f) p r e s s u r e 0.3 t o r r - sweep 0.5 ,us cm" 1 e) v o l t a g e a c r o s s 39 kSL - v e r t i c a l s c a l e 50 V cm" 1 • -I f ) I - v e r t i c a l s c a l e 2 V cm g) H ) p r e s s u r e 3.0 t o r r - sweep 0.5 / i s cm" 1 g) v o l t a g e a c r o s s 39 k It - v e r t i c a l s c a l e 50 V cm" 1 h) I - v e r t i c a l s c a l e 2 7 cm -1 F i g . 17-7. I v s Gas Impedance - 7 9 -a) b) — ' • • -1 p r e s s u r e 1 t o r r - bank 3.0 kV - sweep 1 / i s cm a) V ( d r i v e r ) - V ( g r o u n d ) - v e r t i c a l s c a l e 200 V cm" 1 b) V ( e l e c t r o d e ) - V ( d r i v e r ) - v e r t i c a l s c a l e 200 V cm -1 c) d) -1 p r e s s u r e 1 t o r r - bank 2 kV - sweep 1 / i s cm c) V ( d r i v e r ) - V ( g r o u n d ) - v e r t i c a l s c a l e 200 7 cm"-1-d) V ( e l e c t r o d e ) - V ( d r i v e r ) v e r t i c a l s c a l e 200 V cm -1 F i g . 17-8. Shock Tube P o t e n t i a l s -80-e) f) pressure 9 . 0 torr - bank 2 kV - sweep 1 pa cm"1 e) V(driver) - V(ground) - vertical scale 2 0 0 V cm"1 f) V(electrode) - V(driver) - vertical scale 2 0 0 V cm"1 g) h) A _ .  _ „ . _ * . i ... • J . j j H- {  cm -1 pressure 0 . 3 torr - bank 2 kV - sweep 1yus g) V(driver) - V(ground) - ver t i c a l scale 2 0 0 V cm"1 h) V(electrode) - V(driver) - vertical scale 2 0 0 V cra"1 Fig. IV-8. Shock Tube Potentials -81-T r a c e s c) t o h) show t h a t when t h e p r e s s u r e i s v a r i e d , w h i l e m a i n t a i n i n g c o n s t a n t i n i t i a l bank v o l t a g e , p u l s e shape and d u r a t i o n may v a r y b u t t h e maximum p u l s e a m p l i t u d e r e m a i n s c o n s t a n t . O t h e r e x p e r i m e n t s showed t h a t t h e p o t e n t i a l d i f f e r e n c e between t h e d r i v e r and g r o u n d was t h e same as t h a t between t h e r i n g e l e c t r o d e and ground a f t e r some i n i t i a l i n t e r v a l . A c o m p a r i s o n o f waveforms i n d i c a t e d t h a t t h e same p o t e n t i a l d i f f e r e n c e o c c u r r e d a t t h e same t i m e t h a t t h e d r i v e r t o r i n g p o t e n t i a l d i f f e r e n c e became z e r o . The r i n g e l e c t r o d e was f o u n d t o r e m a i n n e g a t i v e w i t h r e s p e c t t o ground b y a t l e a s t i i V f o r o v e r 500 u s . However, t h e d r i v e r p o t e n t i a l became z e r o w i t h r e s p e c t t o ground ( t o w i t h i n 0.1 V) i n l e s s t h a n £0 u s . IV-10 Bank P o l a r i t y R e v e r s a l A f o i l c y l i n d e r I i " long.was p l a c e d a r o u n d t h e shock t u b e ' s e x t e r n a l s u r f a c e j u s t downstream o f t h e r i n g e l e c t r o d e . T h i s f o i l showed t h e same p o t e n t i a l v a r i a t i o n a s t h e r i n g e l e c t r o d e b u t a t a r e d u c e d a m p l i t u d e . The same e x p e r i m e n t a l c o n d i t i o n s as were u s e d t o o b s e r v e shock tube p o t e n t i a l s w i t h r e s p e c t t o ground were m a i n t a i n e d . F o r t r a c e s a) and b) o f F i g . I V - 9 , t h e bank was c h a r g e d i n t h e n o r m a l way, n e g a t i v e w i t h r e s p e c t t o g r o u n d . R e v e r s i n g t h e p o l a r i t y o f t h e bank w i t h r e s p e c t t o ground w h i l e k e e p i n g a l l o t h e r p a r a m e t e r s c o n s t a n t r e s u l t e d i n t r a c e s c) and d ) . Thus we see t h a t t h e r e v e r s a l o f t h e bank p o l a r i t y c a u s e d t h e p o l a r i t y o f t h e o b s e r v e d p o t e n t i a l s t o be r e v e r s e d and t h a t t h e waveforms were o t h e r w i s e unchanged. pressure 1 torr - bank 2 kV - sweep 1 ;bs cm" a) V(ground) - ^(cylinder) - vertical scale 2 0 0 V cm"' b) V(driver) - V(electrode) - ve r t i c a l scale 2 0 0 V cm' pressure 1 torr - bank 2 kV - sweep 1 us cm c) V(ground) - V(cylinder) - vertical scale 200 V cm"l d) V(driver) - V(electrode ) - vertical scale 2 0 0 V cm" .Fig . i y - 9 . Bank Polarity Reversal ^_ -83-I Y - 1 1 I v s I , Gas Impedance and D r i v e r L u m i n o s i t y o O b s e r v a t i o n o f I was made u s i n g a 20 t u r n p i c k - u p c o i l . O m i t t i n g t h e d e l a y u n i t , t h e t r i g g e r u n i t was m a n u a l l y a c t i v a t e d . The o s c i l l o -scope was t r i g g e r e d b y t h e i n p u t t o t h e t y p e K p l u g - i n u n i t . T r a c e a ) , F i g . I V - 1 0 , shows t h e o b s e r v e d waveform. B y f e e d i n g a 30 t u r n p i c k - u p c o i l o u t p u t v i a RG/5>8U c a b l e t o t h e i n t e g r a t o r a t t h e i n p u t o f a t y p e L p l u g - i n u n i t , t h e waveform o f I was o b s e r v e d . The shock tube was o p e r a t e d as i n s e c t i o n IV-6 and t h e r e s u l t -i n g s i g n a l i s shown i n t r a c e b) and on a l o n g e r t i m e base i n t r a c e c ) , o where i t i s compared t o t h e I waveform, t r a c e d ) . We note t h a t I f s waveform has s h o r t e r r i s e t h a n f a l l t i m e , h as a p e r i o d o f about 32 u s f r o m t h e f i r s t q u a r t e r c y c l e and about hh us f r o m t h e r e m a i n d e r o f t h e t r a c e , and i s i n s e n s i t i v e t o p r e s s u r e and gas t y p e v a r i a t i o n s . T r a c e b * i n d i c a t e s t h e r i s e o f d r i v e r l u m i n o s i t y i n t h e s e n s i t i v i t y range o f t h e 931 p h o t o m u l t i p l i e r t u b e . a) • • • I • M M B I s m m m WW* Ml mm m m m m m p r e s s u r e 10 t o r r a r g o n - bank 2 kV - sweep £ u s cm' a) I - v e r t i c a l s c a l e 1 V cm -1 F i g . I V - 1 0 , I v s I 5 Gas Impedance and D r i v e r L u m i n o s i t y p r e s s u r e 90 m t o r r a i r - bank 0.9 kV - sweep 2 Jis cm* b) I - v e r t i c a l s c a l e 0.01 V cm""-1-b*) p h o t o m u l t i p l i e r l o o k i n g a t d r i v e r d i s c h a r g e v e r t i c a l s c a l e 1 V cm" 1 pressure 0.1 mtorr a i r - bank 0.9 k V - sweep 10 p.s cm" c) I - v e r t i c a l scale 0.05 V oft d) I - vertical scale 1 V cm F i g . IV-10. I v s I y G a s Impedance and D r i v e r L u m i n o s i t y p r e s s u r e 75 m t o r r a i r - bank 2.4 kV - sweep 10 p.s cm e) two w i r e probe a t 188 c m — R = 10 k j l - v e r t i c a l s c a l e 0.5 V c m ~ l f ) two w i r e probe a t 50.2 cm - R — 10 k _ f L , - v e r t i c a l s c a l e 10 V c m ~ l g) h) p r e s s u r e 75 m t o r r a i r - bank 2.4 kV - sweep 10 ; i s cm"" 1 g) two w i r e probe a t 188.0 cm - R =- 10 k XI - v e r t i c a l s c a l e 0.5 V c m " ! h) two w i r e probe a t 50.2 cm - R c 0.1 k J l - v e r t i c a l s c a l e 1 V c m * l F i g . IV - 1 0 . I v s I , Gas Impedance, and D r i v e r L u m i n o s i t y -86-Gas impedance was o b s e r v e d b y t h e two w i r e p r o be c i r c u i t o f F i g . . 1 7 - 1 1 . A l l components were i n s u l a t e d from,L-.teiPSRielded b y , t h e p r o be c a r r i a g e and t e r m i n a l u n i t . t y p e 7 1 two w i r e probe - C D P6000 p r o b e s t o t y p e G p l u g - i n u n i t s 227 F i g 17-11. Two W i r e P r o b e C i r c u i t U s i n g R = 10 k l ~ l i n e a c h probe c i r c u i t , t r a c e s e) and f ) , F i g . 17-10, were o b t a i n e d . Upon c h a n g i n g R i n t h e p r o be c i r c u i t n e a r e s t t h e d r i v e r t o 0.1 , w h i l e m a i n t a i n i n g R = 10 k_£L i n t h e o t h e r c i r c u i t t r a c e s g) and h) were o b t a i n e d . We n o t e t h a t t h e impedance o f t h e two w i r e probe changed w i t h t h e same r i s e t i m e and p e r i o d , kh ps, as t h e I waveform. F u r t h e r m o r e , R may i n f l u e n c e t h e waveform and s e v e r a l o s c i l l a t i o n s n o t d e t e c t e d b y t h e p i c k - u p c o i l seem t o have o c c u r r e d . The p o l a r i t y o f t h e two w i r e p r o be s i g n a l d i d n o t change. 17-12 L i F and Q u a r t z Windows W i t h t y p e 71 two w i r e p r o b e s a t p o s i t i o n s 50.2 and 88.0 cm, t h e -87-shock tube was operated as i n section IV-6. The probe cir c u i t of Fig. IV-11 was used with R ==• 10 k l L i n each c i r c u i t . Measurements were made without a window and with LiF and quartz windows 3.3 mm thick, at 165.8 cm. The probe current was found to be insensitive to argon pressures from 65 to 120 mtorr and i n i t i a l bank voltages from 2 to 3 kV. However, marked current changes accompanied voltage changes below 2 kV. From the results at pressures around 85 mtorr and voltages around 2.2 kV the probe current was found to be 1.2 mA without a window, 0.2 mA with a LiF window, and 25 uA with a quartz window. However, the pulse shape was not affected by the windows. The two wire probe signals were found to have the same rise and f a l l times (10 to 90%) as the bank cur-rent pulse, Fig. IV-10. The maximum amplitude of the second, third, and fourth probe current peaks were about 5/8, 1/4, and 1/10 that of the f i r s t peak respectively. Since the period was about 44 ps,the probe signal l i f e time was 34.2 - 6.0 jas. IV-13 Wire Mesh Electrode Wire mesh, 12 wires to the inch, was inserted into the opening of a brass ring electrode at h9•9 cm. Capacitative ring probes were positioned at 29.8 and 84.7 cm. The ring potentials were monitored as described i n section IV-4 and the shock tube operated as i n section IV-11. The capacitative ring signals were found to be independent of whether the ring electrode contained the mesh (traces a and b Fig. IV-12) or did not contain i t (traces c and d). No effect was produced by earthing the ring through 170 cm of copper braid, when either a 2 nF condenser or a -88-300 V b a t t e r y ( b o t h p o l a r i t i e s ) was i n s e r t e d between t h e end o f t h e b r a i d and t h e r i n g . T h i s was n o t t h e c a s e when t h e r i n g was d i r e c t l y c o n n e c t e d t o t h e b r a i d . The change o c c u r r e d d u r i n g t h e f i r s t 10 ^ s o f o p e r a t i o n , as i s i l l u s t r a t e d b y t r a c e s e) t o h ) . S m a l l e r changes were p r o d u c e d b y p u t t i n g between t h e b r a i d and t h e r i n g r e s i s t a n c e s o f 100 -0 . and 10. JfL. , and a 0.5 pF c o n d e n s e r . W i t h a 1 0 X L r e s i s t o r t h e c a p a c i t a t i v e r i n g s i g n a l a t 8)4.7 cm was 30$ o f t h e v a l u e o b t a i n e d w i t h t h e f l o a t i n g r i n g . The maximum c u r r e n t t h r o u g h t h e r e s i s t o r was 1.5 A. 1 7 - l U A p p l i e d F i e l d s A. E l e c t r i c F i e l d -U s i n g a 300 V b a t t e r y t h e grounded mesh e l e c t r o d e a t L9.9 cm was b i a s e d p o s i t i v e w i t h r e s p e c t t o a n o t h e r r i n g e l e c t r o d e a t 33.8 cm. W i t h t h i s change, t h e c a p a c i t a t i v e r i n g s i g n a l s m a n i f e s t e d o n l y t h e e f f e c t o f t h e grounded mesh, as d i s c u s s e d above. B. M a g n e t i c F i e l d H o r s e s h o e magnet p o l e s were a l i g n e d p a r a l l e l t o t h e shock t u b e a x i s on i t s o u t s i d e s u r f a c e a t t h e p o s i t i o n 60 cm. The m a g n e t i c f i e l d v a r i a -t i o n a c r o s s t h e shock t u b e d i a m e t e r was a p p r o x i m a t e l y 0.1 T. Between t h e p o l e s was p l a c e d a t h r e e t u r n p i c k - u p c o i l ( P a i n and Smy I960) formed b y w r a p p i n g RG 58/U c a b l e around t h e o u t s i d e o f t h e shock t u b e . One end o f t h e o u t e r s h i e l d was grounded t o e l i m i n a t e e l e c t r o s t a t i c p i c k - u p . The p i c k - u p c o i l ' s o u t p u t v o l t a g e was measured by c o n n e c t i n g i t s ends t o P6000 p r o b e ' s c e n t r a l c o n d u c t o r s and t h e n c o n n e c t i n g t h e p r o b e s t o t h e i n p u t s o f a t y p e G d i f f e r e n t i a l a m p l i f i e r . No e f f e c t was p r o d u c e d i n t h e c a p a c i t a t i v e r i n g s i g n a l s and any i n d u c e d v o l t a g e i n t h e p i c k - u p c o i l was l e s s t h a n 0.1 V. 89-pressure 1 t o r r argon - bank 2 kV - sweep 0.5 jus cm a) capacitative r i n g at 29.8 cm - v e r t i c a l scale 20 V cm' b) capacitative ring at 81*.7 cm - v e r t i c a l scale 20 V cm" pressure 1 torr argon - bank 2 kV - sweep 5>us cm" c) capacitative ring at 29*8 cm - v e r t i c a l scale 20 V cm" d) capacitative ring at 84.7 cm - vertical scale 20 V era" Fig. IV-12. Effect of Wire Mesh Electrode  •90 e) f) p r e s s u r e 1 t o r r a r g o n - bank 2 kV - sweep 0.5 ps cm" 1 e) c a p a c i t a t i v e r i n g a t 29.8 cm - v e r t i c a l s c a l e 20 V cm f) c a p a c i t a t i v e r i n g a t 8IL»7 cm - v e r t i c a l s c a l e 20 V cm p r e s s u r e 1 t o r r a r g o n - bank 2 cV - sweep $ ps cm g) c a p a c i t a t i v e r i n g a t 2 9 . 8 cm - v e r t i c a l s c a l e 2 0 V cm h) c a p a c i t a t i v e r i n g a t 8 U . 7 e n - v e r t i c a l s c a l e 2 0 V cm' F i g . I V - 1 2 . ' E f f e c t o f W i r e Mesh E l e c t r o d e _ -91-IV-15 V a r i a t i o n o f P r o b e P o s i t i o n P e r p e n d i c u l a r t o t h e Shock Tube A x i s A t y p e I I I two w i r e probe a t 50.2 cm was moved t o v a r i o u s p o s i t i o n s p e r p e n d i c u l a r t o t h e shock t u b e a x i s , by means o f a probe c a r r i a g e and a s i d e t u b e . The t i m e t h a t t h e probe v o l t a g e v a r i e d f r o m i t s i n i t i a l v a l u e o f 27 V, i n d i c a t i n g a change i n gas impedance, was measured. The shock t u b e was o p e r a t e d as i n s e c t i o n IV-6 , w i t h 15 m t o r r o f a i r as t h e w o r k i n g gas and an i n i t i a l bank v o l t a g e o f 0.1* kV. F i g . IV-13 shows a p l o t o f t h e l o g a r i t h m o f t h i s t i m e a g a i n s t t h e d i s t a n c e o f t h e f r o n t edge o f t h e probe c a p s u l e f r o m t h e shock t u b e a x i s . P o i n t s t o t h e l e f t o f 0 cm on t h e g r a p h c o r r e s p o n d t o a p o s i t i o n n e a r e r th e p r o b e c a r r i a g e . We o b s e r v e t h a t w h i l e t h e c a p s u l e ' s f r o n t edge i s w i t h i n | cm of t h e shock t u b e a x i s , t h e v a r i a t i o n i n r e s p o n s e t i m e i s s m a l l . However, i n c r e a s i n g t h i s d i s t a n c e t o 1 cm c a u s e s an i n c r e a s e i n r e s p o n s e t i m e o f o v e r 50$. Two w i r e probe measurements a t somewhat g r e a t e r p e r p e n d i c u l a r d i s -t a n c e s f r o m t h e shock t u b e a x i s were d i s c u s s e d i n s e c t i o n IV-6 . F o r c o m p a r i s o n p u r p o s e s a s i m i l a r p l o t o f t h e s e measurements i s d e p i c t e d i n F i g . I V - l l * . I n s t e a d o f a i r , however, t h e w o r k i n g gas was a m i x t u r e o f 60 m t o r r o f a i r and 120 m t o r r o f a r g o n . IV-16 188 cm P r o b e ' s Response v s 50 cm P r o b e ' s P o s i t i o n The 188.0 cm p r o b e ' s r e s p o n s e t o changes i n gas impedance was s t u d i e d as a f u n c t i o n o f t h e 50.2 cm probe's p o s i t i o n p e r p e n d i c u l a r t o t h e shock t u b e a x i s . The e x p e r i m e n t a l c o n d i t i o n s were t h e same as t h o s e o f s e c t i o n IV-15. Type I p r o b e s were u s e d . -92= 6 U l n ( t ) 3 \ us 2 1 \ I 2 1 0 1 2 (cm) probe p o s i t i o n p e r p e n d i c u l a r t o shock t u b e a x i s F i g . 17-13. P r o b e ' s Response Time v s P e r p e n d i c u l a r P o s i t i o n 10 8 - \ 6 -I n t ( p ) 3 2 1 -1 1 1 1 1 1 1 8 7 6 5 U 3 2 (cm) probe p o s i t i o n p e r p e n d i c u l a r t o shock t u b e a x i s • P i g . rv- iU. P r o b e ' s Response Time v s P e r p e n d i c u l a r P o s i t i o n -93-The p l o t o f measured v a l u e s o f t h i s r e l a t i o n i s g i v e n i n F i g . 17 - 1 5 . We note t h a t t h e 50.2 cm probe a f f e c t s t h e r e s p o n s e t i m e o f t h e 188 . 0 cm probe a t d i s t a n c e s g r e a t e r t h a n 0.5 cm f r o m t h e shock t u b e a x i s . 17-17 The 188.0 cm P r o b e ' s Response Time vs I t s P e r p e n d i c u l a r  D i s t a n c e t o t h e Shock Tube A x i s M a i n t a i n i n g t h e shock t u b e o p e r a t i o n o f s e c t i o n 17 - 1 6 , t h e 50.2 cm probe c a p s u l e ' s f r o n t edge was p l a c e d on t h e shock t u b e a x i s . The 188 cm p r o b e 1 s r e s p o n s e time as a f u n c t i o n o f i t s p e r p e n d i c u l a r d i s t a n c e f r o m t h e shock t u b e a x i s i s p l o t t e d i n F i g . 17 - 1 6 . We n o t e a s i m i l a r v a r i a t i o n t o t h a t f o u n d f o r t h e 50.2 cm probe b u t t h e i n c r e a s e i n r e s p o n s e t i m e w i t h d i s t a n c e f r o m t h e a x i s i s much g r e a t e r i n t h i s c a s e . 17-18 50.2 and 188 . 0 cm P r o b e s Moved S i m u l t a n e o u s l y P e r p e n d i c u l a r  t o t h e Shock Tube A x i s U s i n g t h e same e x p e r i m e n t a l c o n d i t i o n s o f s e c t i o n 17 - 1 6 , t h e p e r -p e n d i c u l a r p r o be p o s i t i o n s were v a r i e d such t h a t b o t h p r o b e s were always t h e same d i s t a n c e f r o m t h e shock t u b e a x i s . S t a r t i n g w i t h a base p r e s s u r e o f 15 m t o r r ( p r o b a b l y a i r ) a r g o n was added t o g i v e f u r t h e r w o r k i n g p r e s -s u r e o f 17 m t o r r , 1 . 2 t o r r , and 9.1 t o r r . The r e s u l t s showed t h a t , e x c e p t f o r 9.1 t o r r , minimum probe r e s p o n s e t i m e o c c u r r e d when t h e probe w i r e s s t r a d d l e d t h e shock t u b e a x i s . A t 9.1 t o r r , t h i s minimum o c c u r r e d w i t h t h e probe c a p s u l e ' s f r o n t edge on t h e shock t u b e a x i s . G r e a t e r r e s p o n s e t i m e changes accompanied p o s i t i o n changes as t h e p r e s s u r e was i n c r e a s e d . F u r t h e r m o r e , t h e s i g n a l shape v a r i e d w i t h p r e s s u r e s u c h t h a t d e t e r m i n a t i o n of r e s p o n s e t i m e a t h i g h p r e s s u r e s was d i f f i c u l t . -91*-10 8 188 cm 6 probe's response h / 3 * 2 1 I I I 1 1 1 1 2 1 0 1 50.2 cm probe's position perpendicular to the shock tube axis Fig. 17-15. 188 cm Probe's Response vs 50 cm Probe's Position 10 8 1 188 cm \ probe's 6 \ response Q « ) U 3 i _ \ i 2 i i i i 1 I I  • 2 1 0 1 50 cm probe's position perpendicular to shock tube axis Fig. 17-16. 188 cm Probe's Response vs Its Position -95-IV-19 P r e c u r s o r vs Shock P h o t o m u l t i p l i e r S i g n a l s U s i n g t h e shock t u b e as i n s e c t i o n IV-2, t h e t y p e I p h o t o m u l t i p l i e r u n i t r e s p o n s e t o p r e c u r s o r e f f e c t was compared t o t h e r e s p o n s e t o t h e shock h e a t e d g a s , as a f u n c t i o n o f p o s i t i o n a l o n g t h e shock t u b e . A l l measurements were c a r r i e d o u t w i t h 1 t o r r o f a r g o n as t h e w o r k i n g gas and an i n i t i a l bank v o l t a g e o f 2.0 kV. E a c h p h o t o m u l t i p l i e r u n i t o u t p u t was conveyed b y RG 58/U c a b l e t o a t y p e L p l u g - i n u n i t i n p u t w h i c h was s h u n t e d b y a 1 k-H- r e s i s t o r . A l l t h e u p p e r beam t r a c e s i n F i g . IV-17 were made u s i n g one p h o t o -m u l t i p l i e r u n i t and a l l t h e l o w e r beam t r a c e s w i t h a n o t h e r . T r a c e s a) t o d ) show t h a t t h e p r e c u r s o r s i g n a l r e m a i n s a l m o s t i n d e p e n d e n t o f p o s i t i o n , d e s p i t e l a r g e changes i n t h e s h o c k s i g n a l s . T r a c e s e) and f ) were t a k e n w i t h t h e e n t r a n c e s l i t o f the u n i t s b l o c k e d t o l i g h t so t h a t t h e s e t r a c e s i n d i c a t e d t h e e l e c t r i c a l p i c k - u p . T r a c e s g) and h) i n d i c a t e t h a t a l t h o u g h t h e p r e c u r s o r s i g n a l becomes v e r y s m a l l a f t e r about 50 j u s , i t may r e m a i n comparable t o t h e shock s i g n a l f o r much l o n g e r t i m e s . A n e x t r a e f f o r t was made t o d e t e c t p r e c u r s o r s i g n a l s a t a b out 50 cm a l o n g t h e shock t u b e u s i n g a i r a t p r e s s u r e s f r o m 2 t o 350 m t o r r . U s i n g t h e more s e n s i t i v e t y p e I I p h o t o m u l t i p l i e r c i r c u i t and an i n i t i a l bank v o l t a g e o f 1 kV, any s i g n a l was s m a l l e r t h a n an 0.1 V n o i s e s i g n a l f r o m t h e d i s c h a r g e . I t was c o n c l u d e d t h a t any p r e c u r s o r s i g n a l was l e s s t h a n an 0.1 V s i g n a l f r o m t h e bank d i s c h a r g e . TV-20 V a r i a t i o n o f C a p a c i t a t i v e P r o b e S i g n a l s w i t h P r o b e P o s i t i o n T r a c e s a) and b ) , F i g . IV-18, d e p i c t t h e c a p a c i t a t i v e r i n g s i g n a l s s i m u l t a n e o u s l y o b s e r v e d a t two d i f f e r e n t p o s i t i o n s a l o n g t h e shock t u b e . - 9 6 -- l p r e s s u r e 1 t o r r a r g o n - bank 2.0 kV - sweep 50 us cm' a) p h o t o m u l t i p l i e r u n i t a t 35-9 cm - v e r t i c a l s c a l e 0.2 V cm" 1 b) p h o t o m u l t i p l i e r u n i t a t 50.3 cm - v e r t i c a l s c a l e 0.2 V cm -1 p r e s s u r e 1 t o r r a r g o n - bank 2.0 kV - sweep 50 u s cm" c ) p h o t o m u l t i p l i e r u n i t a t 73*1 cm - v e r t i c a l s c a l e 0.01 V cm d) p h o t o m u l t i p l i e r u n i t a t 84.0 cm - v e r t i c a l s c a l e 0.1 V cm F i g . I V - 1 7 . P r e c u r s o r v s . Shock P h o t o m u l t i p l i e r S i g n a l s e) f) pressure 1 torr argon - bank 2.0 kV - sweep $0 )is cm" e) photomultiplier unit at 73.1 cm - ve r t i c a l scale 0.01 V cm f) photomultiplier unit at 8U.0 cm - vertical scale 0.1 V cm pressure 1 torr argon - bank 2.0 kV - sweep 100 /as cm"-1-g) photomultiplier at 73.1 cm - vertical scale 0.005 V cm*"1 h) photomultiplier unit at 8 4 .0 cm - vertical scale 0.01 V cm Fig . IV-17. Precursor vs Shock Photomultiplier Signals pressure 1 torr argon - bank 2.0 kV - sweep 2 jus cm a) capacitative ring at 29»8 cm - ve r t i c a l scale 50 V cm' b) capacitative ring at 85»5 cm - ver t i c a l scale 50 V cm' pressure 85 mtorr air - bank l.U kV - sweep 0.2 / i s cm c) capacitative loop at 190.5 cm - v e r t i c a l scale 10 V cm d) capacitative loop at 52.7 cm - vertical scale 20 V cm"-F i g . IV-18. Capacitative Probe Signals -99-pressure 130 mtorr a i r - bank 0.8 kV - sweep 0.5 /is cm"1 e) capacitative loop at 190.5 cm - vertical sweep 10 V cm' f ) capacitative loop at 52.7 cm - vertical scale 20 V cm" Fig. 17-18. Capacitative Probe Signals The shock tube was operated as i n section IV-2 and the i n i t i a l bank and gas conditions were 2.0 kV and 1 torr of argon respectively. Ring potentials were measured using P6000 probe central conductors and type K plug-in units. We note that the 29.8 cm probe's signal deviated from the base line f i r s t and that the potential rise of the 85.5 cm probe was not abrupt but quite gradual. Capacitative loop potentials with respect to the driver were measured i n the manner described i n section 17-9. The loops were axially positioned at 52.7 and 190.5 cm. The driver discharge was i n i t i a t e d by increasing the bank's voltage u n t i l the driver gas broke down. -100-We a g a i n n o t e t h e g r a d u a l r i s e o f p r o b e p o t e n t i a l and t h e v a r i a t i o n s accompanying changes o f p r e s s u r e and bank v o l t a g e . No d i f f e r e n c e s were d e t e c t e d between c a p a c i t a t i v e r i n g and c a p a c i t a -t i v e l o o p p r o be s i g n a l s . T.V-21 Time t a k e n by C a p a c i t a t i v e R i n g t o A t t a i n P o t e n t i a l V a r i a t i o n  P r o p o r t i o n a l t o I On s i g n a l s s i m i l a r t o t r a c e s a) and b) i n F i g . IV-18, measurements o f t h e t i m e t h a t t h e c a p a c i t a t i v e r i n g s t a r t e d t o m a n i f e s t p o t e n t i a l o v a r i a t i o n s p r o p o r t i o n a l t o I were made. The f o l l o w i n g d e f i n i t i o n o f t ^ was u s e d . L e t t h e maximum s l o p e o f t h e s i g n a l b e f o r e t h e I v a r i a t i o n be p r o j e c t e d ( d o t t e d l i n e A,B i n F i g u r e IV-19). S i m i l a r l y l e t t h e f i r s t p o r t i o n o f t h e t r a c e w h i c h e x h i b i t s v a r i a t i o n p r o p o r t i o n a l t o I be a l s o p r o j e c t e d ( d o t t e d l i n e C,D i n F i g . IV-19). The p r o j e c t i o n o f t h e i n t e r s e c t i o n o f t h e s e two l i n e s o n t h e a b s c i s s a d e f i n e s t h e t i m e t^.. The e x p e r i m e n t a l c o n d i t i o n s c o n s i s t e d o f t h e t u b e b e i n g o p e r a t e d as i n s e c t i o n IV-11, an i n i t i a l bank v o l t a g e o f 2.0 kV, and a r g o n gas I n i t i a l l y i n t h e shock t u b e a t p r e s s u r e s f r o m 0.3 t o 9.3 t o r r . F o r t h e measurements t a b u l a t e d i n T a b l e IV-1, t h e o s c i l l o s c o p e was t r i g g e r e d b y t h e bank's I . Measurements o f t-^ f r o m t h e s i g n a l s o f c a p a c i t a t i v e r i n g s a t 29.7 and 8I4..O cm as a f u n c t i o n o f shock t u b e gas p r e s s u r e a r e g i v e n i n t a b l e I V-1. IV-22 Vf, vs t t U s i n g C a p a c i t a t i v e R i n g P r o b e s I n F i g . I V - 1 9 , l e t t h e i n t e r s e c t i o n o f A,B and C,D be p r o j e c t e d onto t h e o r d i n a t e . T h i s i n t e r s e c t i o n w i t h t h e p r o b e p o t e n t i a l a x i s d e f i n e s V^. -101-F i g . 17-19» D e t e r m i n a t i o n o f t ^ and 7-t *—*——~—-————————r. — , ^  [ri-n rl l|1 n HIIII i rm II IIi II WIIII • i II IIin mi II II iami  n m ^ — m — • W H L JJMIH TABLE 17-1 Times t h a t 29 and 8J4 cm C a p a c i t a t i v e R i n g P r o b e s E x h i b i t P o t e n t i a l 7 a r i a t i o n P r o p o r t i o n a l t o t h e D r i v e r P o t e n t i a l Bank 7olta'ge 2.0 k7 C a p a c i t a t i v e R i n g . P o s i t i o n (cm) Time ( t t ) (Us) A r g o n P r e s s u r e ( t o r r ) 29.7 2.05 ± 0.05 3.15 -" 0.0£ 3,»95'>.'OslO ' *t>;5 1.0 ± 0.05 3.0 - 0.05 9.0 - 0.05 9.3 * 0.5 84.0 1.U0 - 0.1 3.30 * 0.1 5.0 * 0.2 5.7 * 0.1 5.5 *o . 5 0.3 - 0.05 1.0 * 0.05 3.0 i 0.2 9.0 ± 0.5 9.3 * 0.5 -102. In F i g . IV-20 i s plotted V-^  against t-t obtained from traces taken using an i n i t i a l bank voltage of 2.0 kV and gas pressures from 0.3 to 9.3 torr of argon. -We note that a line through these points cuts the time axis at about 7.5 / L S . Measurements using an i n i t i a l bank voltage of 3 kV when plotted i n the same way also lead to a cut i n the time axis at about 7.5/is• -103-IV-23 Time for Ring Electrodes to Attain Driver Potential As discussed i n section IV-9 with sample traces, ring electrode potentials with respect to the driver were monitored. The times at which a ring at 96.3 cm attained the driver potential are given i n table IV-2 for various argon gas pressures and an i n i t i a l bank voltage of 2 kV. Similar measurements for a ring at h9*9 cm are also given using an i n i t i a l bank voltage of 3 kV and argon at 1 torr pressure. A l l these time measurements were made with respect to the leading edge of the bank current derivative which was used to trigger the oscilloscope sweep. The shock tube was operated as i n section IV-11. We note that the time decreased as the i n i t i a l bank voltage was increased and that the spread of points was sometimes greater than the measurement error of a single point, e.g. at 0.3 torr for the ring at U9.9 cm. After the i n i t i a t i o n of the driver discharge i t was found that the potential difference between two ring electrodes varied from zero and again returned to zaro at the end of some interval. This interval depended on the i n i t i a l bank voltage, the gas pressure, and the distance between the rings. The return to zero indicates that the ring furthest from the driver attained the driver potential. IV-2l| Six Inch Diameter Driver vs Three Inch Diameter Driver The time difference for two points along the shock tube to attain the same potential was measured for both a six and a three inch diameter glass cylinder i n the driver. Measurements similar to those described i n section IV-20 were made with the 6 inch diameter driver's -lOii-TABLE IV-2 Times that Ring Electrode Probes Attained Driver Potential Ring Probe Bank Voltage Time Pressure Position (kV) (us) (torr ) 33.8 cm 2 1.4 ± 0.1 0.3 i 0.05 2.9 t 0.1 1.0 t 0.05 2.7 ± 0.1 1.0 i o.o5 4.3 i 0.1 9.0 i 1.0 49.9 cm 2 1.7 i 0.1 0.3 t o.o5 2.4 1 0.1 0.3 i o.o5 3.1 i 0.1 1.0 ± 0.05 3.1 i 0.1 1.0 ± 0.05 3.3 ± 0.1 1.0 i o.o5 3.3 i 0.1 1.0 ± 0.05 4.6 ± 0.1 9.0 i 0.5 5.1 i 0.1 9.0 t 0.5 > 3 2.5 : 0.1 1.0 ± 0.05 2.6 r 0.1 1.0 ± 0.05 96.3 cm 2 3.0 1 0.1 0.3 t 0.05 3.9 i 0.1 1.0 i 0.05 6.3 ± 0.1 9.0 ± 0.5 -105-g l a s s c y l i n d e r r e p l a c e d b y a 3 - i n c h one o f e q u a l l e n g t h . No d i f f e r e n c e between t h e two c a s e s was o b s e r v e d f o r t h e i n t e r v a l f r o m u9.1 t o 96.1 cm i n t h e p r e s s u r e range 0.3 t o 1 t o r r . A l l measurements were made u s i n g a n i n i t i a l bank v o l t a g e o f 2.0. kV and a r g o n as t h e w o r k i n g gas e x c e p t a t 0.1 t o r r where a i r was u s e d . The measured p o i n t s a r e p l o t t e d i n F i g . IV - 2 1 . IV - 2 - ? R i n g Measurements U s i n g A p p l i e d P ' o t e n t i a l s F u r t h e r a t t e m p t s t o o b s e r v e A t a t h i g h e r p r e s s u r e s f o r t h e p o s i t i o n s h9'l and 96.1 cm p r o v e d i m p r a c t i c a l . The p o t e n t i a l d i f f e r e n c e between a r i n g a t one o f t h e s e p o s i t o n s and a n o t h e r 6 i n c h e s c l o s e r t o t h e d r i v e r became q u i t e s m a l l a t t h e s e i n c r e a s e d p r e s s u r e s . A more s e n s i t i v e d e t e c t o r o f changes i n gas c o n d u c t i v i t y was made b y c o n n e c t i n g a 300 o r 600 V b a t t e r y i n s e r i e s w i t h a 100 kl~L r e s i s t o r b etween r i n g s a t t h e above p o s i t i o n s and o t h e r r i n g s about 6 i n c h e s up-s t r e a m f r o m them. The p o t e n t i a l d i f f e r e n c e was s e t t o some v a l u e and changes i n t h i s i n i t i a l v a l u e l o o k e d f o r . These p o t e n t i a l d i f f e r e n c e v a r i a t i o n s were e x p e c t e d t o be due t o changes i n gas c o n d u c t i v i t y . The b e h a v i o u r o f t h e r i n g p a i r was much l i k e t h a t o f t h e two w i r e p r o be d i s -c u s s e d i n s e c t i o n I V - 6 . Measurements o f t h e t i m e d i f f e r e n c e , t h a t two p a i r s o f r i n g s a t d i f f e r e n t shock t u b e p o s i t i o n s d e t e c t e d changes i n gas c o n d u c t i v i t y , a r e p l o t t e d a g a i n s t gas p r e s s u r e i n F i g . IV - 2 1 . The shock t u b e was operated as i n S e c t i o n I V-2 w i t h an i n i t i a l bank v o l t a g e o f 2.0 kV. N i t r o g e n and a r g o n were u s e d i n t h e p r e s s u r e range 2 t o 100 t o r r . -106-Fig. IV-21. A t ' (ring pairs) vs IV-26 Methods of Applying Voltage Across Two Wire Probes Two methods were employed to apply voltage across the two wire probes. The f i r s t was used for voltages up to and including 136 V; the second for voltages from 137 V to 3 kV. Method 1 -' A modification of that shown i n Fig . IV-1|, this method consisted i n conveying, by means of RG £8/U cable central conductions, the battery's output or the output of a voltage divider across the battery to the probe positioner termination units. At the terminal unit, each central -107" c o n d u c t o r was c o n n e c t e d , i n s e r i e s w i t h a 100 MD. r e s i s t o r , t o one o f the p r o b e ' s w i r e s . Thus each probe was i s o l a t e d f r o m t h e a p p l i e d v o l t a g e s o u r c e b y 200 M i l and f r o m t h e o t h e r p r o be b y 400 M i l . The c a b l e ' s o u t e r c o n d u c t o r s e r v e d as a s h i e l d f o r t h e i n n e r c o n d u c t o r . Method 2 ' I n s t e a d o f t h e b a t t e r y , two 0 = 1,5 kV s u p p l i e s were u s e d . One s u p p l y d e l i v e r e d a p o s i t i v e v o l t a g e w i t h r e s p e c t t o ground and t h e o t h e r one a n e g a t i v e v o l t a g e . Thus w i t h b o t h s u p p l i e s s e t a t t h e same o u t p u t v o l t a g e , one o f t h e p r o b e ' s w i r e s would be b i a s e d p o s i t i v e w i t h r e s p e c t t o g r o und and t h e o t h e r w i r e n e g a t i v e w i t h r e s p e c t t o ground b y t h e same amount. 1M-0. r e s i s t o r s r e p l a c e d t h o s e o f 100 M i l . IV-27 Two W i r e P r o b e P r e c u r s o r I n v e s t i g a t i o n The t i m e d i f f e r e n c e f o r t h e d e t e c t i o n o f t h e p r e c u r s o r e f f e c t a t t h e shock t u b e p o s i t i o n s o f £0.2 and 188,0 cm was s t u d i e d as a f u n c t i o n o f i n i t i a l p robe v o l t a g e , , p r o b e t y p e , gas p r e s s u r e , and i n i t i a l bank v o l t a g e . U s i n g t y p e I I I p r o b e s , and an i n i t i a l p r o b e v o l t a g e o f 27 V, t h e t i m e d i f f e r e n c e between t h e p r e c u r s o r d e t e c t i o n a t t h e two shock p o s i t i o n s was measured as a f u n c t i o n o f i n i t i a l bank v o l t a g e . V a r i a t i o n f r o m t h e i n i t i a l p r o b e v o l t a g e was c o n s i d e r e d t o c o n s t i t u t e p r e c u r s o r d e t e c t i o n . The measurements o b t a i n e d f o r d i f f e r e n t p r e s s u r e s o f a i r a r e g i v e n i n t a b l e I V - 3 , F o r t h e s e measurements t h e shock t u b e was used as d e s c r i b e d i n s e c t i o n I V - 6 . P r o b e v o l t a g e s were m o n i t o r e d u s i n g t h e c i r c u i t o f F i g . IV-4j.» -108-TABLE IV-3 A t Using 27V Across a Two Wire Probe Pressure A t I n i t i a l Bank (mtorr) :- (us) Voltage (kV) 0.3 ± 0.1 2.00 ±. 0.1 0.1|0 i 0.05 1.0 t 0.1 0.60 i 0.05 0.9 ± 0.1 0.80 i 0.05 1.00 t 0.05 1.20 ± 0.05 o.5o ± 0.05 i . 6 o * o.o5 0.70 ± o.o5 2.00 t 0.05 1.51 1 2.2 i 0.1 0.U0 i o.o5 2.7 ± 0.1 0.50 ± 0.05 1.5 ± o . i o.8o i 0.05 1.30 + 0.07 1.00 i 0.05 1.50 + o.o5 i . 5 o i o.o5 1.20 i 0.05 1.60 i 0.05 1.10 i 0.05 2.00 i 0.05 1$ t 2 U.o i o . i o.Uo i o.o5 3.3 i 0.1 0.60 i 0.05 2.70 t 0.05 o.8o ± o.o5 2.ho t 0.05 l . o o t o.o5 2.35 i 0.05 1.20 1 0.05 1.85 i 0.05 l . U o t o.o5 i . 5 o i 0.05 i . 6 o ± 0.05 1.35 i o.o5 2.00 i 0.05 -109-TABLE IV-3 ( c o n t ' d ) P r e s s u r e ( m t o r r ) A t (Ms) I n i t i a l Bank V o l t a g e (kV) 30 + 5 2.10 i 0.05 i.8o ± o.o5 i.2o i 0.05 0.70 1 0.02 0.50 t 0.02 0.50 i 0.02 o.io ± «b;.o5 0.20 i 0.05 o.Uo ± o.o5 o.8o ± o.o5 "i.6o i o.o5 i.8o i o.o5 100 ± 10 iU.o± 0.5 7.2 - 0.2 5.1 ± o.i 3.55 ± o.i 3.05 ± 0.1 2.75 ± 0.05 o.io i o.o5 0.20 ± 0.05 o.Uo i o.o5 o.6o ± o.o5 o.8o ± o.o5 l.oo ± o.o5 160 ± 10 5.0 ± 0.2 3.o5 ± o.i 2.15 i 0.05 i.8o i o.o5 o.io t o.o5 0.20 - 0.05 o.Uo ± 0.05 o.5o t 0.05 420 ± 25 7.U i 0.1 U.3 1 0.1 3 . 8 * 0.1 3.3 i 0.1 o.2o ± o!o5 o.Uo ± 0.05 o.Uo ± 0.05 o.8o ± 0.05 920 ± 50 15.0 +o.5 9.6 ± 0.2 0.20 ± 0.05 o.Uo i 0.05 -no-In a similar way A t was obtained for other i n i t i a l probe voltages and the results are given i n tables IV-Ii t«p 17-8. For probe voltages of 109 V and higher Tektronix P6002 probes were used instead of the type P6000 probes used at the lower voltages. An i n i t i a l probe voltage of 2.5 7 gave the same results as 27 7 at a gas pressure of 15 mtorr but 0.28 7 increased the time difference slightly. ;-, .vi-The modifications to the type I probe were made to eliminate any p o s s i b i l i t y of direct photoionization of the gas between the probe wires. Probe 17 proved too insensitive so 'ft was modified to Probe 7. TABLE IV-h A t Using 547 Across a Two Wire Probe Pressure (mtorr) A t (ps) I n i t i a l Bank Voltage (k7) 30 i 5 2.55 t 0.07 1.05 i 0.07 0.60 ± 0.07 0.25 - 0.25 0. 70 ± 0.05 1. U0 ± 0.05 160 ± 10 1.95 i 0.07 1.00 ± 0.07 0.20 ± 0.05 o.uo ± 0.05 920 ± 5o 20.0 ± 0,5 6.6 i 0.2 0.20 ± 0.05 o.IiO/r 0.05 -111. TABLE 17-5 A t U s i n g 109 V A c r o s s a Two W i r e Probe. P r e s s u r e A t I n i t i a l Bank ( m t o r r ) (p) V o l t a g e (kV) 15 i 2 3.8 t 0.2 o.io + 0.05 3.2 ± 0 ,2 U.o ± 0.2 o.,7 ± 0.1 o.5o ± o.o5 0.7 i 0,1 0.75 ± 0.1 o.6o i 0.1 l . o o ± o.o5 0.7 ± 0.1 9.65 i 0.1 0.30 + o.o5 i . 5 o ± 0.05 0.30 ± o.o5 0.35 i o.o5 2.00 ± 0.05 -112= TABLE I V - 6 A t U s i n g 136 V A c r o s s a Two "Wire P r o b e Gas P r e s s u r e ( m t o r r ) A t ( u s ) I n i t i a l Bank V o l t a g e (kV) 2 + 1 U.20 ± 0.05 3.U0 ± 0.05 0.10 ± 0.05 0.75 ± 0.05 0.90 ± 0.05 0.50 ± 0.05 0.20 ± o.o5 o.Uo + 0.05 1.00 t 0.05 0.70 ± 0.05 1.50 ± 0.05 0.30 ± 0.05 o.55 ± o.o5 2.00 ± 0..05 ho ± 5 1.90 - 0.05 1.60 t 0.05 1.50 ± o„o5 0.10 ± 0.05. 1.10 ± 0.05 1.05 * 0.05 0.80 i 0.05 0.50 ± 0.05 0.50 ±0,05 o.Uo ± 0.05 0.28 ± 0.05 1.00 ± 0.05 0.28 ± 0.05 0.30 ± o.o5 0.20 ± 0.05 2.00 ± 0.05 70 ± 5 0.20 ± 0.05 0.10 ±-o.o5 0.10 ± 0.05 0.50 i 0.05 0.10 ± 0.05 1.00 ± 0.05 0.15 - 0.05 1.50 ± 0.05 0.15 ± 0.05 2.00 ± 0.05 -113-TABLE TV-7 A t Using 1 . 4 kV Across a Two Wire Probe Gas Pressure (mtorr ) A t (/is) I n i t i a l Bank Voltage (kV) 70 - 5 3.55 - 0.1 2.10 - 0.05 l . o o - 0.05 2.00 * 0.05 TABLE IV - 8 A t Using 1.6 kV Across a Two Wire Probe Gas Pressure A t I n i t i a l Bank (mtorr) O ) Voltage (kV) 12 ± 2 3.05 - 0.1 i 0.30 ± 0.05 1.55 * 0.05 i .oo ± o.o5 l .oo - o.o5 2.00 * 0.05 -114-17-28 Comparison ,of A i r , Argon and Helium Using type 7 probes, different gases were compared under the same experimental conditions as i n section 17 =-27. Changes i n probe sensi-t i v i t y with gas type and pressure were reduced by operating the probe just below the breakdown voltage. The probe voltage was set by increasing the probe voltage u n t i l a glow discharge occurred and then extinguishing the discharge, and re-adjusting the voltage to a value just below the breakdown value. After taking a shot a glow discharge usually remained between the probe wires which indicated the effectiveness of the adjustment made. The results are presented i n table 17-9. 17-29 Double Probe Measurements Density and temperature of the precursor electrons were estimated using the double Langmuir probe technique. The double probe's signal to noise ratio was improved by operating the shock tube as described i n section 17-20 and earthing the driver's back plate instead of the outer case of the bank as was done i n the previous sections. With a base pres-sure of less than 1 mtorr, argon at 90 mtorr had to be used to operate the bank at 2 k7. The £6.5 cm double probe signal triggered the oscilloscope. The type 71 two wire probe's voltage and current were determined by the c i r c u i t of Fig. 17^22. The voltage across R^  was determined from the oscilloscope trace. This voltage, when subtracted from the voltage across C, yielded the probe voltage, and when divided by the value of R^  yielded the probe*s current. Since the leakage resistance of C was much higher than R2, the voltage across C was determined from the measured battery -115-TABLE I V - 9 A t U s i n g J u s t B e l o w Breakdown V o l t a g e A.cross a Two W i r e P r o b e Gas P r e s s u r e ( m t o r r ) A t ( n s ) I n i t i a l Bank V o l t a g e (kV) A i r 5o ± 5 l . o o ± 0.05 o.5o t o.o5 o.5o t o.o5 1.10 ± 0.05 0.20 ± 0.05 o.5o ± o.o5 l . o o 1 o.o5 i.5o ± o.o5 80 ± 5 0.45 * o.o5 0.20 * 0.05 0.20 ± 0.05 o.5o * 0.05 l . o o * 0.05 2.00 i 0.05 120 ± 10 o.55 * o.o5 o.5o, ± o.o5 o.5o ± o.o5 o.5o * o.o5 l . o o ± o.o5 i.5o ± o.o5 U00 i 25 6.6 ±-o.i 4.0 ± o . i 3.8 ± o . i 0.20 - 0.05 o.4o ± o.o5 o.6o ±0.05 H e l i u m 300 ± 25 o.io ± o.o5 1.50 ±o.o5 1*20 ± 25 o.55 * o.o5 o.35 ± o.o5 0,25 A 0.05 0.30 ± o.o5 0.60 ± 0.05 i.8o ± o.o5 640 t 25 l . o o i 0.05 0.25 - o.,o5 o.6o ± 0.05 0.30 * o.o5 0.60 i 0.05 l . o o ± 0.05 A r g o n 80 t 5 o.6o ± o.o5 o.35 - o.o5 0.25 ± 0.05 0.20 i 0.05 o.6o * 0.05 i.5o ± o.o5 300 ± 25 6.8 ± o . i i .oo i o.o5 0.65 i 0.05 0.85 - 0.05 o.6o ±. o.o5 0.30 * 0.05 0.20 i 0.05 O.UO * 0.05 o.5o i o.o5 o.6o ± o.o5 o.8o i o.o5 525 i 25 0.20 * o.o5 0.20 * o.o5 0.20 ± 0.05 0.10 ± 0.05 0.20 ± 0.05 o.Uo ± o.o5 0.70 * o.o5 i.5o ± 0.05 -116-100 uF R . Type V I Two Wire Probe P6000 Tektronix probes - € 0 to G Unit i n oscilloscope v e r t i c a l amplifer F i g . IV-^22. Double Probe C i r c u i t Probe current (mA) 18. ® a /-* x R 3 - 1 k f l ® R 3 » 100 SL 12. «• / < / •< / X / 6. / 5 us 1 1 1 1 1 1 , 1 1 1 1 1 1 1 1 l -18 -12 -6 A 1 1 1 6 12 18 - 6-probe voltage ( V ) ® / © / -12-- ® " ' F i g . IVT-23. 56.5 cm Double Probe V - I Curve at 5 jus -117-voltage and the values of R-j_ and A l l the resistances used were within 2% of their rated values. Typical double probe traces are depicted i n Fig. IV-10, traces e) to h). The P6O0O probe capacities and the G amplifier balance had to be readjusted each time the oscilloscope's ve r t i c a l sensitivity was changed or the polarity of the applied probe voltage was reversed. Traces were obtained with C shorted for each sensitivity and each polarity. When double probe measurements were made at 56.5 cm, the 2 0 8 . 5 cm probe was used to check shot to shot reproducibility and vice versa. Care was taken to ensure that no current limiting was caused by the value of R-j. From traces of the f i r s t 50 us after the driver discharge excita-tion^ measurements of the voltage across R^ were made at 5, 10 and 30 yus. These values were then corrected using the corresponding measure-ment with C shorted. Thus each setting of the resistance values of the double probe c i r c u i t yielded a probe voltage and i t s corresponding current for the three times of interest. Points obtained i n this way enabled the construction of double probe V-I curves. V-I curves, for the specified times, are given i n Fig. IV - 2 3 to 28 for the 56.5 cm probe and i n Fig. IV -28 to 3 0 for the 2 0 8 . 5 cm probe. Measurements were then carried out on these V-I curves to detenrrine their slopes, the positive ion currents (I), and the electron current I e 2 « These values and the electron number densities and temperatures that were calculated from them using the methods of section II - 5 are given i n table IV-10. In the calculation of the electron number density ( n e ) , no correc-tion was made for the effect of sheath thickness. The area used was that of a probe wire (If x 0.01*0 x 2.5U x 0.5 cm 2). -118-probe current (mA) 1 2 . 6_ l i I i I i / / 1 / i /* ' — m / | * / • i -18 -12 -6 / ' 9* -6-© — « - 1 2 -' J ' 1 ' 1 6 12 18 probe voltage (V) j ! Fig. I V - 2 4 . 56.6 cm Double Probe VfI Curve at 10 p.s probe current (mA.) 6_ I I I I I 1 s 1 1 | 1 | 1 | 1 1 1 1 1 1 -18 -12 -6 -Q Q> g, * * ^ -6-6 12 18 probe voltage (v) Fig. IV - 2 5 . 56.5 cm Double Probe V-I Curve at 30 us -119-probe current (nA) 6 3 J--lcT -12 -6~ Z7r 5 us 6 12 18 probe voltage (V) Fig. IV-26. 208.5 cm Double Probe V - l Curve at 5 us probe current (mA) -18 "* -12 -3 -10 U£ 6 12 18 probe voltage (V) Fi g . IV-27. 208.5 cm Double Probe. V-I Curve at 10 us probe current (mft.) l 1 1 1 I 3 30 us i» if""" 1"" | | %~ i Lb 1 •<*> 1 --18 -12 -6 -3 6 12 probe voltage (V) 18 Fig. IV-28. 208.5 cm Double Probe V-I Curve at 30 us -120= TABLE 17-10 D o u b l e P r o b e R e s u l t s Time (/is) S l o p e (mA 7-1) I + ( n o r ) (raft.) I + ( r e v ) (mA) (mA) <l+> (mA) (§-)" (cm - 3 ) e (eV) 56.5 cm Probe 5 1.3 16 13.7 30.2 15.1 15.2 15.3 6.0 10 1.2 16.7 12.0 28.7 14.4 12.4 14.5 5.9 30 0.6 3.8 4.2 8.0 4.0 4.1 4.0 3.3 208.5 cm Probe 5 0.6 3.5 1.0 4.5 2.3 0.9 2.3 1.2 10 o.U 4 . 0 1.2 5.2 2.6 1.2 2.6 2.2 30 0.1 0.9 0.5 l . U 0.7 o.5 0.7 2.5 -121-CHAPTER V DISCUSSION OF RESULTS V - l C o m p a r i s o n o f P r e c u r s o r D e t e c t o r s V a r i o u s w o r k e r s have r e p o r t e d o b s e r v i n g a p r e c u r s o r e f f e c t under w i d e l y v a r y i n g e x p e r i m e n t a l c o n d i t i o n s w i t h d i f f e r e n t d e t e c t o r s . However, no c o m p a r i s o n o f t h e s i g n a l s o b t a i n e d f r o m t h e v a r i o u s d e t e c t o r s h a s , t o my knowledge, b e e n made. A. C a p a c i t a t i v e R i n g P o t e n t i a l v s P h o t o m u l t i p l i e r Output A s i s i l l u s t r a t e d b y t h e e x p e r i m e n t d e s c r i b e d i n s e c t i o n I V - 2 , t h e s i g n a l f r o m t h e c a p a c i t a t i v e r i n g .could be c o r r e l a t e d w i t h t h a t f r o m t h e p h o t o m u l t i p l i e r . D u r i n g t h e bank's d i s c h a r g e ( a b o u t 50 jus) b o t h d e t e c t o r s e x h i b i t e d a r e s p o n s e . The c a p a c i t a t i v e r i n g ' s p o t e n t i a l o s c i l l a t e d w i t h a maximum a m p l i t u d e o f about I4.O V and t h e p h o t o m u l t i p l i e r p r o d u c e d a n e g a t i v e p u l s e w i t h a maximum a m p l i t u d e o f t h e o r d e r o f I V . The r e s p o n s e o f t h e p h o t o m u l t i p l i e r commenced a p p r o x i m a t e l y a t t h e t i m e t h a t c a p a c i t a -t i v e r i n g ' s p o t e n t i a l a t t a i n e d i t s f i r s t maximum. - A t t i m e s l a t e r t h a n 50 p.s, b o t h t h e c a p a c i t a t i v e r i n g and t h e p h o t o -m u l t i p l i e r s i g n a l s were n e g a t i v e b y a b o u t 0.1 V. T h i s n e g a t i v e s i g n a l l a s t e d u n t i l t h e shock a r r i v a l w h i c h was up t o 500 / i s a f t e r t h e d r i v e r ' s d i s c h a r g e i n i t i a t i o n . The c a p a c i t a t i v e r i n g s i g n a l r e m a i n e d a p p r o x i m a t e l y c o n s t a n t d u r i n g t h i s i n t e r v a l b e f o r e t h e shock a r r i v a l b u t t h e p h o t o -m u i t i p l i e r s i g n a l decayed t o w a r d z e r o . B o t h t h e a m p l i t u d e and shape o f t h e s i g n a l v a r i e d w i t h p r e s s u r e . -122= Upon arrival of the shock front the capacitative ring signal became positive by about 0.2 V and gradually returned to zero after a time interval which was pressure dependent. The photomultiplier signal again became negative by an amount depending on the gas pressure and distance from the driver. Larger signals accompanied increases i n the pressure. The greater amplitude of the capacitative ring signal indicated greater sensitivity to the precursor effect than the photomultiplier.had. B. Pin Electrode vs Photomultiplier and Capacitative Ring Signals The experiment discussed i n section IV-3 shows that the pin electrode potential output varried i n the same way as the capacitative ring potential. A; direct comparison of the pin electrode potential variation with that of the capacitative ring, section 17-4, indicated that the pin electrode signal was about .20 times larger than the :capacitative ring signal at an argon-pressure of 1 torr. i: •:, C. Two Wire Probe The response time of a two wire probe (the time after driver, dis-charge i n i t i a t i o n that the voltage across the two. wire probe varied from i t s preset-value) was found to be dependent on the distance of the probe from the shock tube axis, the gas pressure, the i n i t i a l probe voltage, and. the amount of light reaching i t from the driver. I t i s therefore d i f f i c u l t to correlate the two.wire probe response time with other detector signals. D Comparison with Signals of Other Workers The amplitude of the positive capacitative ring signal observed i n this work was of the same order of magnitude as that observed by Weyman using a mechanical shock tube. The negative signal observed just before -123-t h e shock a r r i v a l b y Weyman (I960) was n o t o b s e r v e d i n t h i s work. T h i s s i g n a l i s p o s s i b l y dependent on shock s t r e n g t h and l u m i n o s i t y as was f o u n d b y G l o e r s e n (i960). A p h o t o m u l t i p l i e r r e s p o n s e d u r i n g t h e bank d i s c h a r g e was a l s o o b s e r v e d b y Schoen (1962). H i s d i s c h a r g e c o n s i s t e d o f a s i n g l e c u r r e n t p u l s e l a s t i n g about 80 / i s whereas t h e d i s c h a r g e o f t h i s work c o n s i s t e d o f s e v e r a l o s c i l l a t i o n s and l a s t e d f o r about 50 / i s , V r 2 O p t i c a l A s p e c t s o f t h e P r e c u r s o r A. O p t i c a l S i g n a l v s E l e c t r i c a l P i c k - u p P h o t o m u l t i p l i e r s i g n a l s were f o u n d t o be o n l y s l i g h t l y , i f a t a l l , a f f e c t e d b y e l e c t r i c a l p i c k - u p f r o m t h e bank d i s c h a r g e . A heavy b l a c k c l o t h o v e r t h e p h o t o m u l t i p l i e r ' s e n t r a n c e s l i t c a u s e d t h e r e s p o n s e t o b o t h t h e p r e c u r s o r and shock t o d i s a p p e a r . The l a r g e v a r i a t i o n o f p h o t o -m u l t i p l i e r r e s p o n s e t o changes i n p o s i t i o n a l o n g t h e shock t u b e and t o gas p r e s s u r e a l s o i n d i c a t e i n s e n s i t i v i t y t o p i c k - u p s i n c e t h e t i m e d e r i v a t i v e o f t h e bank c u r r e n t was p r a c t i c a l l y i n d e p e n d e n t o f t h e gas p r e s s u r e , B. P h o t o m u l t i p l i e r O b s e r v a t i o n s U s i n g an RCA 931 p h o t o m u l t i p l i e r t u b e r a d i a t i o n o f w a v e l e n g t h s between 300 and 700 nm was o b s e r v e d up t o 85 cm f r o m t h e d r i v e r i n 1 t o r r o f a r g o n and up t o 50 cm i n 3 t o r r o f a r g o n . The p h o t o m u l t i p l i e r u n i t s were a l i g n e d t o a c c e p t l i g h t e m i t t e d p e r p e n d i c u l a r t o t h e shock t u b e a x i s . On i n c r e a s i n g t h e gas p r e s s u r e f r o m 0.3 t o 3 t o r r , t h e r a d i a t i o n due t o t h e p r e c u r s o r e f f e c t i n c r e a s e d f r o m 1/20 t o 1/5 t h e maximum i n t e n s i t y o f t h e r a d i a t i o n f r o m t h e shock, w h i c h r e m a i n e d -12U-a p p r o x i m a t e l y c o n s t a n t . G r e a t e r r a d i a t i o n a t h i g h e r p r e s s u r e s c a n be c a u s e d b y t h e i n c r e a s e o f t h e a b s o r p t i o n c o e f f i c i e n t w i t h i n c r e a s e d p r e s s u r e . The p h o t o m u l t i p l i e r s i g n a l was more dependent on t h e e n v e l o p e o f t h e bank c u r r e n t t h a n t h e c u r r e n t i t s e l f . S i n c e t h e bank c u r r e n t l a s t e d f o r o n l y f>0/is, c o n t i n u i n g r a d i a t i o n t o 0,5 ms i n d i c a t e s t h a t t h e p r e c u r s o r e x c i t a t i o n was d e t e r m i n e d b y r a d i a t i o n f r o m h o t gas t h r o u g h -o u t t h e e n t i r e shock t u b e and d r i v e r . The l a c k o f any i n c r e a s e i n t h e r a d i a t i o n due t o t h e a p p r o a c h o f t h e shock f r o n t s u g g e s t s t h a t c o n -t r i b u t i o n s f r o m t h e shock i t s e l f t o t h e p r e c u r s o r e f f e c t a r e q u i t e s m a l l . Co P r e c u r s o r P r o d u c e d b y R a d i a t i o n I n s e r t i n g a L i F window between t h e d r i v e r and a two w i r e p r o b e c a u s e d t h e impedance o f t h e gas between t h e p r o b e ' s w i r e s t o i n c r e a s e t o 100 kTL as compared t o 8,3 k w i t h o u t t h e window. Assuming t h e gas c o n d u c t i v i t y p r o p o r t i o n a l t o t h e a b s o r b e d r a d i a t i o n , 92% o f t h e i o n i z a t i o n i s a t t r i b u t e d t o r a d i a t i o n f r o m t h e d r i v e r o f w a v e l e n g t h s l e s s t h a n 160 nm (160 nm b e i n g t h e w a v e l e n g t h f o r $0% t r a n s m i s s i o n b y t h e L i F ) . A s i m i l a r measurement u s i n g a q u a r t z window i n d i c a t e d t h a t 99% o f t h e i o n i z a t i o n was due r a d i a t i o n o f w a v e l e n g t h s l e s s t h a n 200 nm. S i n c e t h e windows were s e a l e d t o t h e shock t u b e w a l l t h e s e measure-ments r u l e o u t t h e p o s s i b i l i t y t h a t t h e p r e c u r s o r was due t o some shock phenomenon o r t o p a r t i c l e s f r o m t h e d r i v e r . D. E s t i m a t i o n o f D r i v e r Temperature Assuming i o n i z a t i o n d i r e c t l y - . p r o p o r t i o n a l t o t h e number o f p h o t o n s e m i t t e d b y t h e d r i v e r , a b l a c k b o d y t e m p e r a t u r e o f 1,1 eV i s r e q u i r e d t o have 92% o f t h e e m i t t e d p h o t o n s w i t h w a v e l e n g t h s l e s s t h a n 160 nm. -125-S i m i l a r l y a temperature of 1 . 2 eV i s required to have 99% of radiated photons with wavelengths less than 2 0 0 nm. This estimate i s very crude since the i o n i z a t i o n i s also dependent on the absorption c o e f f i c i e n t and the i o n i z a t i o n e f f i c i e n c y of an absorbed photon which can vary, greatly with changes i n wavelength. E. Comparison with Other Investigations Voorhies and Scott ( 1 9 ? 9 ) also observed precursor excitation that varied as the bank current. However, they did not specify i f the var i a t i o n was simi l a r to the periodic behaviour or to the envelope as found i n t h i s investigation. No other worker seems to have observed the sl i g h t amount of ex c i t a t i o n that existed even after the bank current had died out. Since t h i s e x c i t a t i o n had a much longer l i f e time, there seems to be contributions from both the hot spark discharge and the hot gas remaining a f t e r the bank current cessation. The-large precursor accompanying the bank current discharge reported by Schoen et a l ( 1 9 6 2 ) i s i n accord with the results of t h i s investiga-t i o n . The measurements using windows confirm Klingeriberg 1 s results (Vlth I n t . Conf. Abstracts) using microwave equipment. V°3 E l e c t r i c a l Aspects of the Precursor A. Precursor vs Pick°up The capacitative r i n g , r i n g electrode, and pin electrode probes showed a potential v a r i a t i o n proportional to the time derivative of the bank current, I . However, t h i s signal was not attributed to e l e c t r i c a l pick-up. A capacitative ri n g wrapped around the shock tube showed a - 1 2 6 = much larger potential v a r i a t i o n than a similar ring touching the tube's side. This suggests, that the potential v a r i a t i o n of the ring was due to capacitative coupling with the shock tube gas rather than to pick-up. A time delay, before the probes exhibited the potential v a r i a t i o n , further supports t h i s suggestion. This time delay was both gas pressure and shock tube position dependent0 B„ Precursor vs I and I Pi n electrodes, at diametrically opposite positions i n the shock tube w a l l , connected i n series with a battery and r e s i s t o r indicated that the shock tube gas impedance decreased during the bank's discharge. The rate that the gas impedance decreased was pressure dependent, being lower at higher pressures. The impedance change i s complicated by the fact that the driver discharge i s also pressure dependent (see appendix). Further evidence to connect the precursor i o n i z a t i o n with the bank current was provided by the measurements of double probe current. The current was found to be approximately proportional to the bank current squared. The probe.current was about \ i t s value at maximum bank current when the bank current f i r s t became zero a f t e r the discharge i n i t i a t i o n . This supports the long l i f e t i m e precursor e x c i t a t i o n as observed with the photomultipliers. The. plot of vs t t i n F i g . IV-20 suggests that the gas po t e n t i a l , as observed with a capacitative ring, probe, varies as the driver potential with respect to ground ( i . e . I I where L i s the bank lead inductance). The capacitative r i n g potential v a r i a t i o n proportional to I occurred following a time delay of less than 10 /is after the bank current discharge -127-i n i t i a t i o n . A n i n c r e a s e o f p r e s s u r e c a u s e d a l o n g e r t i m e d e l a y and a more g r a d u a l r i s e o f t h e r i n g p o t e n t i a l . F o r any one p r e s s u r e , p o s i t i o n s c l o s e r t o t h e d r i v e r showed a s m a l l e r t i m e d e l a y and a more g r a d u a l p o t e n t i a l r i s e t h a n p o s i t i o n s f u r t h e r away. R a d i a t i o n f r o m t h e c a t h o d e t r i g g e r s p a r k was f o u n d t o a f f e c t t h e gas c o n d u c t i v i t y and may have c o n t r i b u t e d t o t h e gas p o t e n t i a l r i s e . -The shock t u b e gas p o t e n t i a l change c a n be u n d e r s t o o d i n terms o f t h e t r a n s m i s s i o n l i n e m odel. I n F i g . V - l a r e p l o t t e d p o i n t s f r o m t h e p o t e n t i a l r i s e o f t r a c e e ) , F i g . I V-6. P o i n t s f r o m t r a c e k) of t h e same f i g u r e have b e e n p l o t t e d i n F i g . V-2. We now d i s c u s s t h e manner i n w h i c h t h e t h e o r e t i c a l c u r v e s were o b t a i n e d . The measured e l e c t r o n d e n s i t y v a r i e d a s : t h e bank c u r r e n t s q u a r e d ( i . e . s i n ^ i O g t ) . T h i s v a r i a t i o n i s c o n s i s t e n t w i t h t h a t p r e d i c t e d b y t h e h i g h t e m p e r a t u r e a p p r o x i m a t i o n t o t h e b l a c k body r a d i a t o r ( s e e e q u a t i o n s A7 and A l l i n a p p e n d i x A ) . The o b s e r v e d v a r i a t i o n i s n o t c o n s i s t e n t w i t h t h e l o w t e m p e r a t u r e a p p r o x i m a t i o n ( A 9 ) , s i n c e i t p r e d i c t s t h a t t h e p h o t o n i n t e n s i t y w i l l i n c r e a s e b y a f a c t o r o f 100 i n t h e i n t e r -v a l between 6.5 p.s and 7«3> ps, when t h e bank c u r r e n t i s a maximum. A n e f f e c t i v e t e m p e r a t u r e o f about 10 eV o r h i g h e r must be a s c r i b e d t o t h e d r i v e r gas t o be c o n s i s t e n t w i t h t h i s a p p r o x i m a t i o n , s i n c e t h e window measurements i n d i c a t e d t h a t the i m p o r t a n t i o n i z i n g w a v e l e n g t h s a r e o f t h e o r d e r o f 100 nm. . The d i s c r e p a n c y between t h i s t e m p e r a t u r e and t h a t e s t i m a t e d i n s e c t i o n V-2D i s not, s u r p r i s i n g c o n s i d e r i n g t h e a p p r o x i m a t i o n s made i n t h a t s e c t i o n . - 1 2 8 -6 0 . 3 / t h e o r e t i c a l curve ho. i t -experimental points / capacitative / r i n g p =• 0 . 3 t o r r voltage (V) 2 0 1 2 — , 1 1 , 3 h 5 6 time a f t e r i n i t i a t i o n of discharge (us) F i g . V - l . Rise to f v a r i a t i o n of trace e), F i g . IV-6 time a f t e r i n i t i a t i o n of discharge (us) F i g . V-2. Rise to I v a r i a t i o n of trace k ) , F i g . IV-6 -129= U p o n m a k i n g t h i s a p p r o x i m a t i o n t o ( 1 7 ) we may w r i t e (A12) a s N 0 ( " J i t o V-2) - c o n s t p~ V g s i n 60 g t exp(-2at) ( V - l ) I n t e g r a t i n g t h i s e x p r e s s i o n w i t h r e s p e c t t o t i m e y i e l d s | N 0 ( -J x t o d t = f ( t ) (V-2) where (A£) h a s b e e n u s e d t o d e t e r m i n e t h e v a r i a t i o n w i t h t h e e x p e r i m e n t a l p a r a m e t e r s a n d f ( t ) i s g i v e n b y f oo2 f ( t ) s ^ o - < — ( l ~ e " 2 a t ) - ( a sin60 Rt - w R c o s w g t ) x 2<a2+wJ;) ( 2 a x s i n W g t exp(-2at) V (V-3) a ^ B 2 2 a^ + ti> B t i f 60gt and 2at a r e « 1. ( V - u ) A p l o t o f f ( t ) f o r t h e e x p e r i m e n t a l v a l u e s o f a a n d 60 g i s g i v e n i n F i g . ' A p p - 2 o f t h e a p p e n d i c e s . F o r f i x e d z a n d p r e s s u r e p , e q u a t i o n (I4.-8) o f c h a p t e r I I i n d i c a t e s t h a t t h e p o t e n t i a l a t a p o i n t a l o n g t h e s h o c k t u b e s h o u l d v a r y a s V ( t ) o< c o s ( 0 ) g t ) e x p ( c o n s t p " 1 f ( t ) - t / l O . i i ) (V-5) C o s £0gt a n d t/10.lj. a r e due t o t h e b o u n d a r y c o n d i t i o n s t h a t V ( z , t ) must s a t i s f y , n a m e l y V ( 0 , t ) - c o s c o ^ t e x p ( = t / l O.U). T h i s i s t h e -130-v o l t a g e a c r o s s t h e l e a d f r o m t h e d r i v e r t o ground ( L l ) . U s i n g t h i s e x p r e s s i o n t h e t h e o r e t i c a l c u r v e s i n F i g . V - l and V-2 were c a l c u l a t e d f r o m t h e e x p e r i m e n t a l points„ From t h e e x p e r i m e n t a l p o i n t s o f F i g . V - l t h e c o e f f i c i e n t o f f ( t ) was 3 6 . 2 ± U»3 and t h e p r o p o r t i o n a l i t y , c o n s t a n t was 1 . 3 U i 0.1*5. T h i s v a l u e o f t h e c o e f f i c i e n t o f f ( t ) was a r r i v e d a t b y d e t e r m i n i n g i t f r o m f o u r s e t s o f two e x p e r i m e n t a l p o i n t s and t a k i n g t h e a r i t h m e t i c a v e r a g e . The e r r o r q u o t e d i s t h e r o o t mean square e r r o r assuming t h a t t h e f o r m u l a ( Z di/(n-D >* <v~6) c a n be u s e d , where d^ i s t h e d e v i a t i o n f r o m t h e mean. U s i n g t h e e x p e r i -m e n t a l d a t a o f F i g . V-2, t h e c o e f f i c i e n t o f f ( t ) was f o u n d t o be 5.56 ± 0.81 and t h e p r o p o r t i o n a l i t y c o n s t a n t was 0.55 - 0.11. T h e o r e t i c a l l y t h e p r o p o r t i o n a l i t y c o n s t a n t s h o u l d be i n d e p e n d e n t o f t h e gas p r e s s u r e and s h o u l d be t h e same f o r t h e two c a s e s . F u r t h e r m o r e , t h e c o n s t a n t i n t h e e x p o n e n t i a l o f (V-5) s h o u l d be p r e s s u r e i n d e p e n d e n t . E v e n though t h e c o n s t a n t s do n o t agre e w i t h i n e x p e r i m e n t a l e r r o r , t h e shape o f t h e c u r v e r e q u i r e d t o f i t t h e e x p e r i m e n t a l p o i n t s i s p r e d i c t e d b y t h e t h e o r e t i c a l model. The i o n i c c o n t r i b u t i o n t o t h e gas c o n d u c t i v i t y c o u l d be n e g l e c t e d because t h e m o b i l i t y o f e l e c t r o n s i n a r g o n i s about 250 t i m e s t h a t o f t h e i o n s (Brown 1959). The a p p r o x i m a t i o n R I » L I i s v a l i d when t h e r e s i s t -ance p e r u n i t l e n g t h i s l a r g e r t h a n 20 miT , assuming t h a t t h e c u r r e n t changes i n about 1 p s and t h a t t h e dominant i n d u c t a n c e i s t h e s e l f •131-inductance of the gas conductor (about 20 nH). For characteristic times of 1 us and a capacitance to ground of 1 pF per cm, the approxi-mation GV » GV i s v a l i d when the resistance to ground i s greater than 1 M i l . Using the value of B from the graph of Fig. V-3 and ( k ) estimated i n section 3L, we see that the approximation B >) (k) i s valid for pressures less than about 1 torr, C . Driver potential vs Shock Tube Gas Potential When the shock tube gas attains the driver potential we should expect the relation V(0,t) = V(a,t) (V-7) to be v a l i d . Combining this condition with equation (u-8) of chapter II and (V-2) the experimental parameters should satisfy the condition 2 -1 Bz ~ const 7 B p f ( t ) (V-8) Using this relationship and the capacitative ring data of table 2 —1 IV-1, a plot of ring position vs const V Q p~ f(t) i s given'in Fig. V-3. .A similar plot for the ring electrode data of table IV-2 i s also presented i n this figure. The errors were estimated assuming formula (V-6) to hold. We see that to within experimental error a l l the points f a l l on a straight line through the origin. . Thus the capacitative ring and the ring electrode probes gave compatible results. From the coefficient of f ( t ) , obtained from section B, and the slope of the graph of F i g . 7-3, B was estimated to be fj.fj 10~ 2 cm"1. -132-x ring electrode measurements O capacitative ring measurements const v l p - 1 f(t) Fig. V-3. Position from Driver vs. Const. V_ p" 1 f(t) - 1 3 3 -D . A p p l i e d F i e l d s T h e l a c k o f a n y a p p l i e d f i e l d e f f e c t i n d i c a t e d t h a t t h e p r e c u r s o r was n o t due t o a f l o w o f c h a r g e d p a r t i c l e s f r o m e i t h e r t h e d r i v e r o r t h e s h o c k f r o n t . E . S c r e e n E l e c t r o d e A s c r e e n e l e c t r o d e i n t h e s h o c k t u b e b e t w e e n a c a p a c i t a t i v e r i n g p r o b e a n d t h e d r i v e r d i d n o t a f f e c t t h e r i n g ' s s i g n a l u n l e s s i t was g r o u n d e d b y a s m a l l . i m p e d a n c e ( 1 0 ) . T h i s i n d i c a t e d t h a t t h e p r e -c u r s o r was n o t due t o a f l o w o f e l e c t r o n s f r o m t h e d r i v e r a n d t h a t t h e i m p e d a n c e b e t w e e n t h e d r i v e r a n d g r o u n d a f f e c t s t h e d e t e c t o r s i g n a l . T h i s i s c o n s i s t e n t w i t h t h e d i s c u s s i o n i n t h e p r e v i o u s s e c t i o n s . F„ S h o c k T u b e P o t e n t i a l s w i t h R e s p e c t t o G r o u n d T h e r e s u l t s o f s e c t i o n I V ° 9 s u p p o r t t h e c o n c l u s i o n o f t h e a b o v e s e c t i o n . A f t e r a s h o r t t i m e i n t e r v a l ( 1 0 u s ) , t h e g a s a t a p o i n t i n t h e s h o c k t u b e became e q u a l t o t h e d r i v e r p o t e n t i a l t o w i t h i n a few v o l t s . T h e g a s t h e n s t a y e d a t t h e d r i v e r p o t e n t i a l . G . B a n k P o l a r i t y R e v e r s a l R e v e r s a l o f t h e b a n k " s p o l a r i t y c a u s e d t h e p o l a r i t y o f a c a p a c i -t a t i v e p r o b e s i g n a l t o r e v e r s e . T h u s t h e c o n c l u s i o n s o f s e c t i o n s 3E a n d 3F were a g a i n s u p p o r t e d . H . T r a n s v e r s e V a r i a t i o n T h e f a c t t h a t t h e two w i r e p r o b e c o n t i n u e d t o r e s p o n d as t h e d i s t a n c e p e r p e n d i c u l a r t o t h e s h o c k t u b e a x i s was i n c r e a s e d c o u l d h a v e b e e n due t o e i t h e r e l e c t r o n s d i f f u s i n g i n t o t h e s i d e t u b e o r t o r a d i a t i o n f r o m t h e e x c i t e d gas f r o m t h e m a i n t u b e i n t o t h e s i d e t u b e . T h e s h o c k f r o n t a r r i v e d l o n g a f t e r t h e i o n i z a t i o n change was d e t e c t e d so i t s e f f e c t was n o t r e l e v a n t . =134= A s s u m i n g t h a t t h e two w i r e p r o b e r e s p o n d s when t h e e l e c t r o n d e n s i t y -exceeds some minimum v a l u e , e q u a t i o n (1-13) o f c h a p t e r I I p r e d i c t s t h a t t h e r e s p o n s e t i m e o f t h e probe s h o u l d v a r y as t h e square o f t h e d i s t a n c e f r o m t h e shock t u b e a x i s . The graphs o f F i g , IV-13 and IV-14 show t h a t t h i s r e l a t i o n s h i p , v a l i d f o r a d i f f u s i o n p r o c e s s , i s n o t f o l l o w e d . The r e l a t i o n s h i p i s t h a t t h e l o g a r i t h m o f t h e r e s p o n s e t i m e i s p r o p o r t i o n a l t o t h e d i s t a n c e f r o m t h e shock t u b e a x i s . T h i s r e l a t i o n s h i p c a n be u n d e r s t o o d i n terms o f t h e r a d i a t i o n m o d e l. E q u a t i o n (2-5) when combined w i t h t h e h i g h t e m p e r a t u r e a p p r o x i m a t i o n f o r N0( lJ 2 t o Z^2) ( A 1 2 ) , p r e d i c t s t h a t t h e number o f ph o t o n s a b s o r b e d p e r u n i t l e n g t h a t p o s i t i o n z and t i m e t i s r e l a t e d t o t h e e x p e r i m e n t a l p a r a m e t e r s b y NZ( V 1 t o l) 2) =• c o n s t Vg p ^ s i n 2 GJ g t exp (=2at - k ^ V ^ ) (V~9) As s u m i n g t h a t t h e number o f ph o t o n s r a d i a t e d i n t o t h e s i d e t u b e f r o m t h e gas i n t h e shock tube i s p r o p o r t i o n a l t o t h e number o f ph o t o n s a b s o r b e d b y t h e gas i n t h e shock t u b e , we may s a y t h a t t h e number o f ph o t o n s a b s o r b e d b y t h e gas i n t h e s i d e t u b e between "Z^ and lJ 2 i s r e l a t e d t o t h e e x p e r i m e n t a l p a r a m e t e r s b y Ni( V T_ t o V 2 ) rA V 2 p " 1 s i n 2 U J B t e x p ( - 2 a t - k V± j) z - k ^ ^ g X ) (V-10) where x i s t h e d i s t a n c e f r o m t h e shock t u b e a x i s t o t h e p o i n t o f o b s e r -v a t i o n i n t h e s i d e t u b e . F o r s m a l l t ( i . e . 2 a t yCd-Q1^ ^ 1) and c o n s t a n t z , V g , and p we may w r i t e t h a t x and t a r e r e l a t e d t o M 1, -135' the t o t a l number of photons absorbed at x per unit length, by N' *< t 2 exp(-kx) ( V - l l ) where k i s some average absorption c o e f f i c i e n t . For a detector that responds when the electron density i s above some minimum value and assuming that the electron density i s proportional to the radiation absorption we expect the parameters x and response time t , for v a r i a t i o n of the probe po s i t i o n , to be related by This i s the relationship exhibited by the graphs of F i g . IV-13 and IV-14. We therefore conclude that the i o n i z a t i o n i n the side tube i s due to absorption of ra d i a t i o n from the excited gas i n the shock tube. Using equation (V-13) and measuring the slopes of the graphs k was estimated. .From F i g , IV-13 the value of k was 2„1 and from IV-14 i t was 0.62. Using equation (2-2) of chapter I I , the average absorption c o e f f i c i e n t was 4300 Mb from F i g . IV-13 and 104 Mb from F i g . IV-lU. Both these values are higher than the maximum experimental value f o r a single wavelength ( ^ 35 Mb.Rustgi 1964). A higher value can be expected f o r two reasons: 1) as x increases the effective volume of t exp(-kx) s. const (V-12) On taking the logarithm we get that 2 In t = kx + const (V-13) -136-the radiator, as seen by the gas i n the side tube, decreases and 2) unless t <C 7 us, the above approximation leads to a higher value of k than the true value. The higher value of the cross section from the graph of Fig, IV-13 i s i n accord with reason 1). I . Longitudinal Variation Assuming a detector that responds when the electron density i s greater than; some minimum value, and that the electron density i s pro-portional to the absorbed radiation, equation (V-9) predicts that the response time of the detector t should be related to the experimental parameters V B, p, and z by 2 - 1 2 Vg p sin D ^ t exp(-kz-2at) =. const (V-lU) Upon taking the square root of (V-lI*) and assuming at (<^€Ugt « 1, we may write V t tt const p2 exp(kz) (V-l£) B z We would expect A t, the difference i n time that probes at two positions z 2 , z-j_ respond, to be related to the parameters by V B A t = const p2 jj3xp(kz 2) - expCk^) j (V-l6) Therefore for constant z 2 and z-j_ we should expect to find Vfi A t constant for any one pressure and to increase with an increase i n pressure. Applying (V-l6) to the data of table IV-3 shows that V ^ A t i s D approximately constant for any one pressure. Deviations are larger -137-when A t i s large but the approximate formula i s not v a l i d for times of the order of 5 us. The expected increase of V g A t with an increase i n pressure was not always adhered to. The observed variation could be due to changes i n the probe sensitivity with pressure and to the state of the probe wire surfaces. In Fig, V-U the average value of Vg A t has been plotted against the logarithm of the gas pressure. Also plotted i n this graph are points obtained using the data of tables IV-4 and IV-8 for other probe voltages. The points obtained using the higher probe voltages suggest that any increase of Vg ^ 1 with pressure could be masked by change of probe characteristics with pressure. However, the measurements do indicate that the precursor ionization i s not some shock phenomenon. Any abrupt change in the gas ionization should be insensitive to probe voltage changes. Formula (V-6) was used to calculate the error i n Vg A t and the pressure error was that due to reading the vacustat. These measurements indicate that any limiting precursor velocity i s greater than 1/20 the speed of li g h t . From this we conclude that precursor ionization i s due to the absorption of radiation from the driver. This supports the conclusions of the previous sections. J . Driver Geometry Variation The data of Fig. IV-21 indicates that there was no detectable difference between the three inch and the six inch diameter drivers. This suggests that the radiator's effective volume was considerably smaller than the total driver volume. -138-1.0 _ 10 -1 I n p (torr) CZ1 lCT* _ 10 ,-3 TO o Legend 3 1 27 V 54 V 109 V 136 V 1.4 kV 1.6 kV 10' rh 1 2 3 4 <VB A t ) (00.2 - 188.0 cm) (kV jxs) F i g . V -4 . (vB A t) vs In p - 1 3 9 -K. Precursor Electron Temperature Since the f i r s t bank current maximum occurs approximately 7.5jxs a f t e r the discharge i n i t i a t i o n , the measurements at 5 and 10 /xs should give approximately the same value for the electron temperature, i f 2 the radiation i s approximately proportional to I . I f the radiation rate varies slower than the discharge period then t h i s would hot be the case. The difference between the two values at 208 cm i s thought to be due to experimental error. .Since the electron temperature was quite high and the gas did not glow i t seems probable that no equilibrium existed between the electrons and the other types of p a r t i c l e . Probe studies are s t i l l subject to many d i f f i c u l t i e s (Loeb 1955) so that quantitative data should be regarded with some degree of caution. L. Precursor Electron Density The electron number density during the second current pulse was about l/k that of the f i r s t current pulse. Thus the number density showed the same time v a r i a t i o n as the current. Since the double probe traces showed the same time v a r i a t i o n as the current except for the p o l a r i t y reversal, i t seems that the electron density was proportional to the magnitude of the current. This suggests that r a d i a t i o n from the driver was due to arc heating of the gas rather than any cathode or anode phenomenon. These results are i n agreement with the measurements made using capacitative probes and reversing the bank p o l a r i t y . I t i s d i f f i c u l t to check the assumptions made i n the density deter-mination. The assymetry of the V-I curves suggest that the probe wires were not i d e n t i c a l . Since the gas was only about 0 . 1 $ ionized i t i s reasonable to assume that the gas molecules or atoms were only singly ionized. The effect of the sheath thickness was ignored as this thickness - l l | 0 -was not measured. The sheath effect would enlarge the effective probe area and thus reduce the measured electron density. In any case the quoted electron density should only be considered as an order of magni-tude estimate. I t i s not possible to be more certain than this using the technique at i t s present state of refinement. Upon averaging the 5 and 10 JUS densities, we see that the electron density at 56.5 cm i s 5»9 times greater than the density at 208.5 cm. The ratio i s less than the ratio of the square of the positions. This suggests ionization by photoabsorption rather than some interaction between radiation and the shock tube wall, which should vary more with position. Furthermore the process seems one dimensional justifying this assumption i n chapter I I . The variation i n electron density infers that the average absorption coefficient i s 93 per cm at standard temperature and pressure and that the source must be capable of radiating more than lO 1 ^ photons for ionization,, For B >^)> <fk. we require p 1 torr. M. Comparison of Gases From the graph of Fig. TV-21, we see that A. t for nitrogen was generally larger than for argon. This does not necessarily mean that nitrogen absorption was greater. Besides radiation absorption one must also consider the change i n driver conditions with gas as well as the detector sensitivity changes. One might expect the delay times for argon to be smaller than those for nitrogen, since argon's sparking potential i s lower than nitrogen's. Furthermore, nitrogen has lower pd value than argon (Cobine 1958, p.165)• There does not seem to be any difference among the gases and the increase with pressure was negligible over an order of magnitude of pressure. The In Fig. V-5 i s a plot of for the data of table IV-9. - u a -large value for a i r at 0.1*2 torr i s not thought to be significant because of the large . A. t used to compute i t . The computational method of section I was used. Since the probe voltage used was just below the breakdown value, there should be no effect due to changes i n probe sensitivity. This means that the only significance one can safely give to the points i n Fig. IV-21 i s that precursor ionization occurs up to pressures of 100 torr. N. Comparison with Other Investigations I t i s d i f f i c u l t to compare these results with those of other workers. The work of this thesis indicates that precursor ionization i s primarily due to the discharge i n the driver. The electric aspects of precursor investigations have been carried out i n mechanical shock tubes and there-fore under different experimental conditions. The observed electron densities are of approximately the same order of magnitude as those observed by others using microwave techniques. No other double probe investigation of the precursor effect, to the best of my knowledge, exist i n the literature to date. Therefore the estimated electron temperature cannot be checked against another report. The results obtained using applied electric fields corroborate those obtained using the magnetic f i e l d . Similar experiments with magnetic fields are reported i n the literature (see appendices) and a l l indicate that the fast precursor i s not effected by the f i e l d s . Similar effects to those reported i n this thesis resulting from con-necting points along the shock tube to ground were reported by Barach and Sivinski (l°6l*). They were primarily interested i n the resulting increase i n shock speed. -1U2-Injp (torr) 10 -2 ffi Legend axr r x ~ i helium / I i i argon / probe voltage just below breakdown 1 2 3 <VB A t ) (Wjj.iT1) F i g . V-5. ( V B A t ) vs In p f o r a i r , He, and Ar -UO-It i s f e l t that the experimental discharge parameters, especially the discharge period and current amplitude, are very important i n deter-mining the magnitude and rise of precursor electron density. Therefore a useful comparison with the work i n the literature i s not possible since these parameters have not been specified i n sufficient detail. The results of this work are not compatible with those of Klingen-berg (63) who found that the electron density was inversely proportional to the i n i t i a l bank voltage and proportional to the square root of the gas pressure. The results obtained using windows contradict the hypothesis that the precursor might be due to a fast hydrodynamic wave (Fowler 1962) or to particles either charged or uncharged escaping from the shock front (Weyman i960, Pipkin I96I). The electron density was much larger than that found by Weyman under different experimental conditions. Weyman's method, while perhaps useful i n the case of diffusion processes, i s not applicable for radiation absorption. This method leads to a signal, that i s proportional to difference between the ion and electron density.and should not give any result i f the electron density i s equal to the ion density. Observation of an ultraviolet continuum radiation from e l e c t r i c a l sparks has already been reported i n the literature (Tanaka 1955, Roth 1959). - l l i U -GHAPTER V I CONCLUSIONS P r e c u r s o r i o n i z a t i o n i n an e l e c t r o m a g n e t i c shock t u b e was d e t e c t e d w i t h L a n g m u i r d o u b l e p r o b e s , c a p a c i t a t i v e r i n g , r i n g e l e c t r o d e and p i n e l e c t r o d e p r o b e s . The l i g h t e m i t t e d b y t h e e x c i t e d gas was o b s e r v e d w i t h a p h o t o m u l t i p l i e r , b u t t h i s d e t e c t o r was l e s s s e n s i t i v e t h a n t h e e l e c t r i c p r o b e s . Measurements u s i n g a p p l i e d e l e c t r i c and magnetic f i e l d s and a s c r e e n e l e c t r o d e showed t h a t t h e p r e c u r s o r e f f e c t was n o t due t o c h a r g e d p a r t i c l e s f r o m t h e d r i v i n g d i s c h a r g e . O b s e r v a t i o n s u s i n g q u a r t z and l i t h i u m f l u o r i d e windows t o i s o l a t e t h e d r i v i n g d i s c h a r g e s u p p o r t e d t h i s c o n c l u s i o n and a l s o i n d i c a t e d t h a t t h e p r e c u r s o r was n o t due t o a f a s t shock wave. More t h a n 99% of t h e i o n i z a t i o n i s due t o a b s o r p t i o n o f r a d i a t i o n o f w a v e l e n g t h s l e s s t h a n 200 nra. Lan g m u i r d o u b l e p r o b e measurements showed t h a t t h e gas i s about 0.1$ i o n i z e d , and t h a t t h e e l e c t r o n s a r e n o t i n t h e r m a l e q u i l i b r i u m w i t h t h e r e s t o f t h e g a s . I t was a l s o f o u n d t h a t t h e w a l l e f f e c t s were n e g l i g i b l e . The p r e c u r s o r i o n i z a t i o n c o n s i s t e d o f a main component t h a t v a r i e d as t h e square o f t h e d i s c h a r g e c u r r e n t ( l a s t i n g 50 u s ) and a s m a l l e r component l a s t i n g about 0.5 ms. P h o t o m u l t i p l i e r measurements i n d i c a t e d t h a t t h e i o n i z a t i o n f r o m t h e shock f r o n t i s n e g l i g i b l e . The t i m e i n t e r v a l between d e t e c t i o n o f i o n i z a t i o n a t two d i f f e r e n t -145-s t a t i o n s was t h e same f o r a i r , h e l i u m and a r g o n . The e f f e c t p r o p a g a t e d w i t h a speed g r e a t e r t h a n 1/20 t h e speed o f l i g h t . I o n i z a t i o n c o u l d be d e t e c t e d i n a s i d e t u b e p r i o r t o t h e a r r i v a l o f t h e shock f r o n t . T h i s has n o t been o b s e r v e d b y o t h e r w o r k e r s , p r e s u m a b l y due t o t h e l o w e r s e n s i t i v i t y o f t h e i r p r o b e s . C a p a c i t a t i v e r i n g , r i n g e l e c t r o d e , and p i n e l e c t r o d e p r o be measure-ments showed t h a t , f o l l o w i n g some t i m e i n t e r v a l a f t e r t h e d i s c h a r g e i n i t i a t i o n , t h e shock t u b e gas p o t e n t i a l became e q u a l t o t h e d r i v e r p o t e n t i a l . The dependence o f t h e p r e c u r s o r e f f e c t on t h e e x p e r i m e n t a l p a r a m e t e r s c a n be u n d e r s t o o d b y c o n s i d e r i n g t h e d r i v e r t o a c t as an i n f i n i t e s l a b b l a c k b o d y r a d i a t o r whose t e m p e r a t u r e i s a b out 10 eV. The b e h a v i o u r o f t h e shock t u b e gas p o t e n t i a l a g r e e d w i t h a t h e o r y t r e a t i n g t h e shock t u b e as a t r a n s m i s s i o n l i n e w i t h a t i m e dependent r e s i s t a n c e p e r u n i t l e n g t h . The r e s i s t a n c e was assumed t o v a r y p r o p o r t i o n a l l y t o a b s o r p t i o n o f r a d i a t i o n f r o m t h e d r i v e r . A u s e f u l c o m p a r i s o n w i t h the work o f o t h e r s i s n o t p o s s i b l e a t p r e s e n t s i n c e t h e p e r t i n e n t p a r a m e t e r s have n o t been g i v e n i n s u f f i c i e n t d e t a i l . F u r t h e r work i s n e c e s s a r y t o d e t e r m i n e whether o r n o t o b s e r v a -t i o n s u n d e r d i f f e r e n t e x p e r i m e n t a l c o n d i t i o n s c a n be e x p l a i n e d b y t h e p r o p o s e d t h e o r e t i c a l m o d e l . A c heck o n t h e p o i n t s o u r c e a p p r o x i m a t i o n , d i s c u s s e d i n t h e a p p e n d i c e s , w o u l d be u s e f u l . More d e t a i l e d i n f o r m a t i o n on t h e i m p o r t a n t r a d i a t i o n w a v e l e n g t h s w o u l d l e a d t o a b e t t e r u n d e r -s t a n d i n g o f t h e e n e r g y t r a n s f e r mechanisms. Such i n f o r m a t i o n w o u l d e n a b l e a more r e f i n e d t h e o r e t i c a l i n t e r p r e t a t i o n o f t h e r e s u l t s . Such an i n t e r p r e t a t i o n s h o u l d t a k e i n t o a c c o u n t t h e p r e c u r s o r component w i t h t h e 0.5 ms l i f e t i m e . -146= APPENDICES A. Black Body Radiation Consider radiation from a hot gas under the following assumptions! 1) Energy i s supplied to the gas by a damped sine wave current and this energy i s then radiated. The current i s obtained by discharging a condenser. 2) About 10$ of the i n i t i a l condenser energy i s dissipated i n the gas. 3) The energy i s dissipated into a fixed volume of gas, independent of the experimental parameters. 4) The gas may be considered ideal to determine the number of molecules per unit volume. 5) A l l the energy delivered to the molecule raises i t s effective temperature. 6) The gas acts as a black body radiator. Using assumption 1) we write that the energy radiated per unit time i s that supplied by the condenser at time t, per unit time, which i s Vg U 0 s i n 2 CJ B t e = 2 a t (Al) where OJ g i s the angular frequency of the discharge ci r c u i t , and a i s the current damping constant. -11*7-Using assumption 2 ) , U Q may be detenrriLned by equating the time integral of (Al) to the appropriated fraction of the i n i t i a l bank energy, thus 2 f 2 - 2 a t C VB , , VB U o S i n W B * e d t " - i b " ( A 2 ) Upon performing the integration we get W a 2 t ^ ) £ J o u l s / ( k y ) 2 (A3) Assumption 1*) enables the number density of molecules to be written as ( ° 760 T ( h U ) g Equating the energy supplied to the gas, divided by the number of gas particles, to the average particle temperature times k, gives using (Al) and (AU) 760 U 0 V B sin Li B t e~ 2 a t = 1 2 . 2 . - 2 a t _ t k t . kT - - £ " J • T — A p V B sin U)Qt e T ( A $ ) 273 n 0 p V g where k is Boltzmann's constant T is the temperature of the radiating gas U 0 is a constant of the apparatus given by (A3) no is Loschmidt's constant p i s the gas pressure in torr - 1 U 8 -V i s the volume of the radiating gas T g i s the gas temperature before the discharge i n i t i a t i o n " Considering the gas to be a black body radiator, then under conditions of thermal equilibrium the number-.of photons emitted with frequency ^ to 2> •+ d~2J i s given by (Kittel p.lOlj) n(zJ ) - 8TTV" h V /kT n e ' = 1 (A6) where V' i s the radiator's volume. The to t a l number of photons emitted i n the frequency range TJ-^ to i) 2 i s obtained from (A6) by expanding the denominator i n a binominal expansion and integrating term to term. The result of t h i s integration i s 'hz^/kT • 2 , /kT 4 c , 18TTV' ~ 3 ~ i - l i + 1 O O n-1 n J C T \ 2 / kT\ 3 +2 $4 n n (A7) =nh When h l ^ » kT we may approximate (A7) by „/ , ^ • g n^' ^ / ^ l / ^ / . i v2 "hi^/kT * . 2\ (A8) -11+9= N ( ^ 2 ) = ~ 3 ~ T g -8 T r V' i v ' s i n ^ B t e " 2 a M ^ e hVjp e 2 at L-T A.vf s i n 2 c O R t g B B ] I 2 a t -1 h ^ 2 P e T g 1 2 2 +. -' A V B s i n o>Bt (A9) Equation (A9) indicates that the number of photons radiated i s very small except when s i n w ^ t i s large. When hV « kT we may approximate (A7) by 8TTV N(V-L to V 2 ) - — V2 ^ d V hV (A10) Upon performing the inte g r a t i o n , (A10) becomes N ( v ' 1 to V 2 ) = 8T/V< kT f . 2 4] ( A l l ) ( A l l ) and (A5) combine as N ( v ' 1 to -J2) * i t i l l iS A V 2 8 i n 2 ( c 0 B t ) T g 9 X p ( - 2 a t ) ( V 22 - V x 2 ) ,3 h p (A12) Typical experimental vlaues f o r the work reported i n t h i s thesis are: -2 „i . a s 1.56 10 us (estimated from double probe current decay values) UJg = 0.11+3 us" 1 - l 5 0 ° V_ - 2 k? D C - U50 uF V * 50 cm (as estimated from Kerr c e l l photos of the discharge) 3 V = 20 cm (also from Kerr c e l l photos) p = 0 . 1 torr T g ~- 2 9 3 ° K ^ = 1 . 9 to 15 x l O 1 ^ Hr* lz kT = 1 .1 eV from the measurements with windows Using these values we get that U = 1.1*0 joulea/(kV) 2 o kT = 170 eV (from A5) A = 8.1*8 1 0 " 1 9 N( ( 1 . 9 to 15) x l O 1 ^ THz) - 3 . 9 l O 1 ^ (using kT = 1.1 eV) = 2 . 2 1 0 2 1 (using kT = 170 eV) * The frequency ranged lower limit was established by the window measurements and the upper limit was estimated from the average absorption coefficient as calculated from the electron number density and the tables of absorption coefficient vs wavelength (Allan 1 9 6 3 ) . We note that the driver temperature as estimated from window measurements i s about ^% that expected from the energy input and equation A5. B. Kerr C e l l Photographs To determine the variation of the driver discharge with pressure, Kerr c e l l photographs were taken at various time intervals after the discharge i n i t i a t i o n . In Fig. App-1 are shown photographs taken -1*1-at 0.1, 1.0, and 10 torr of argon. A l l photographs were taken using the shock tube as i n section IV-2. One channel of the delay unit was used to trigger the oscilloscope and the bank; a second to trigger the Kerr c e l l . The photographs show that the discharge i s both time and pressure dependent. An i n i t i a l bank voltage of 2 kV was used for a l l measurements. Photographs were also taken with the driver not triggered. These photos differed from the triggered driver case i n two ways. The i n i t i a l discharge to the front driver plate was absent and the apex of the advancing cone of luminous gas was blunter. Photographs taken with the inside of the glass cylinder lined with brass gauze were identical to one taken without the brass gauze. Do Survey of Experimental Work on Precursors There i s a dichotomy of precursor effects. One precursor extends only a short distance ahead of the shock front and moves at the same velocity or just s l i g h t l y faster. The second type moves much faster than the f i r s t and i n fact seems to appear throughout the shock tube simultaneously. a)•The low speed precursor (type I) 1. Apparatus and operating conditions. Precursors of this type were observed.by Schreffler and Christian (19*U) i n a variety of gases at atmospheric pressures the pure gases He, A, and Clj the molecular gas SF^j and the mixtures of air , butane propane, $0% . Af. - $0% Ng. The shock tube consisted of a solid explosive (a mixture of TNT and RDX) driver made into a block having a square face 8" per side and a - 1 * 2 - n L J ! f 1 # 5 us - 0 # 1 torr 2 . £ us - 0 . 1 torr A-2 , 0 us - 1 . 0 torr 3 . 2 us - 1 . 0 torr k*S us - 1 . 0 torr • f ML 1 . * us - 1 0 t o r r 3 . * us - 1 0 t o r r F i g . App - 1 . K e r r C e l l P h o t o g r a p h s o f D r i v e r D i s c h a r g e -153-'CO 5 8 } 9 {— ( l - e " 2 a t ) - (a s i n COBt •+ 2 ( a 2 - f - « 2 ) L 2a f ( t ) 2 k 6 ' 8 10 time (us) . . ^ ^ r m ^ l l m m M ^ M ^ ^ ^ _ ., . iM-n^ Minunmni'i it- m i F i g . App-2. Pl o t of f ( t ) vs t thickness of 2". This driver operated into two types of t e s t sections 1) a cardboard tube 8" i n diameter and 16" long with a 1 m i l Dural f o i l over one end, and 2) a l u c i t e box 5" x 5" x 16" having walls 1/8" thick. The apparatus of Jahn and Grosse consisted of a driver made from a brass pipe 3' long and having an i n t e r n a l diameter of 1-3/8". The driver was designed to burst a diaphram when f i l l e d with helium at a pressure of 28.6. atms. The high pressure driver gas was then allowed to expand into a brass pipe having the same diameter and a length of 5 m. At the end of the 5 m section of pipe was. a further 1.3 m long section where the observations took place. A mach 4.2*. shock i n 10 t o r r of nitrogen was obtained at the end of the 5 m section. The apparatus used by Weyman to observe precursors ahead of Mach 8=12 shock waves i n argon at pressures of k to 6 t o r r was described by the author as a conventional pressure driven shock tube having a low pressure section made from 1.5 cm diameter glass. Gloersen also used a pressure driven shock tube,. The driver was a 2" diameter st e e l section, 7" long. The brass diaphram was designed to rupture when the driver was f i l l e d with helium to a pressure of U-8 Ktorr. Xenon at pressures of 1 and 1.3 t o r r was used i n the low pressure section. Shock speeds of mach 9 and 11 were obtained. A report of the f i r s t type of precursor using an electromagnetic apparatus was made by Groenig who used an inverted pinch discharge chamber as described by Liepmann. Although Liepmann does not give many deta i l s of the apparatus he does state that the bank capacitance was 15 uF and the system had an i n i t i a l current r i s e of 130 kA us" 1. Groenig states that the discharge chamber was operated at an i n i t i a l argon pressure -155' of .0 .1 torr and that the bank was charged to an i n i t i a l voltage of 12 kV. Charvet also used an electromagnetic device. His driver's shape was that of a truncated cone. The positive electrode was at the apex and at the base was a conducting ring that served as the cathode. The height of the cone was 17 cm and at the base the diameter was 7.3 cm which was also the diameter of the shock tube. The bank consisted of two Tobe 15 uF condensers normally operated at 18 kV, The driver c i r c u i t inductance including the bank was 600 nH and the measured ringing fre-quency 120 kHz. This system was capable of producing a maximum current of L4o kA. The apparatus was operated using a i r at an i n i t i a l pressure of 0 . 1 to 0 .2 torr. 2. Results. Schreffler and Christian found from their framing camera photos of'the shock front evaluation and i t s precursor that the precursor intensity increased when the shock front intensity increased. Furthermore both the shock and precursor luminosity became undetectable throughout the shock tube simultaneously. The precursor disturbance along the wall of the shock tube was similar to t hat found along the surface of rods placed on the axis of the shock tube. Mechanically shielding the hot exploding gases of the driver from the shock heated gas did not eliminate the precursor. A spectrogram of the gas close to the wall, and ahead of the shock showed only a trace of the wall material. P a r t i a l l y blocking the tube at a position down stream from the driver caused the gas at the front of the block to become luminescent before the arrival of the shock front and the precursor to be strongly attenuated i n the region behind the block. Schreffler and Christian observed that the precursor velocity i n -156= argon was about 10 km s as compared to a shock v e l o c i t y of 8 km s . Weyman found that i n argon (at a lower i n i t i a l pressure) the v e l o c i t y of the precursor was 10 km s™ 1 as compared to a shock v e l o c i t y of h km s""*". Gloersen, working with an i n i t i a l pressure of 1 t o r r , observed a Xenon precursor v e l o c i t y of Iu5 km s _ 1 and a shock v e l o c i t y of 1,7 km s~""* at the same pos i t i o n . 50 cm further down stream the precursor v e l o c i t y was 2 ok km s" 1 and the shock v e l o c i t y was 1.7 km s ""*. Changing the pressure to 1.3 t o r r while maintaining the same mach number, Gloersen found that at the position nearest the driv e r both the precursor and the shock had a v e l o c i t y of 1.5 km s" 1. At the pos i t i o n 50 cm down stream the precursor v e l o c i t y was 2.5 km s" 1 and the shock v e l o c i t y was 3.5 km s"*1. Schre f f l e r does not give any det a i l s about the s e n s i t i v i t y of the framing camera that he used to observe luminescent precursors. I t was quite probable that the gas was considerably ionized before a luminous precursor could be detected. This was demonstrated when a block was used to p a r t i a l l y stop up the shock tube since the gas i n front of the block became luminous before the a r r i v a l of the luminous shock f r o n t and precursor. Weyman, by comparing the signal he obtained from c o i l s with a ferroxcube core to the signal from the same c o i l s due to an a.c. current through a wire on the shock tube axis, concluded that net charge density was 10? cm~30 To arrive at t h i s value he assumed that the precursor was a cloud of electrons moving at the precursor v e l o c i t y . Gloersen t r i e d using the same method i n the case of his own precursors and came to the conclusion that the method was only good for densities of 10° cm ' or l e s s , whereupon he l e t the matter r e s t . -1*7-Groenig, by comparing the current of his measuring diode when a f i e l d (lkG) was applied to the section of tubing between the discharge apparatus and the sensing apparatus with the current of the same diode when the f i e l d was not applied, concluded that the electron density was about 10^ cm~^. Jahn and Grosse using a test section of rectangular dimensions kn x 3/8" found large precursor leaders on the shock front at the w a l l boundaries. The observations were carried out using an interferometer,, Wevman observed that the gas i n the shock tube became negative with respect to ground before the a r r i v a l of the shock front. As the distance from the driver increased the slope of the pot e n t i a l f a l l became more gradual and the duration of the negative pulse became longer. The a r r i v a l of the shock front, as determined by means of a photomultiplier, caused the p o t e n t i a l to r e t u r n to the base l i n e while the driver slug of gas caused i t to go negative again. This potential v a r i a t i o n was observed using a capacitative r i n g made by wrapping a wire 1/32" i n diameter around the outside of the glass tube and monitor-ing i t s p o t e n t i a l with respect to ground with the input probe of a Tektronix oscilloscope. The input c i r c u i t of the probe was equivalent to a 20 M SL r e s i s t o r i n p a r a l l e l with an 8pF condenser. Gloersen used capacitative rings made from brass shims 2 mm wide grounded, v i a 1 M,fL r e s i s t o r s , to the cold water pipe. At an i n i t i a l pressure of 1 t o r r , a mach 9 shock exhibited the same type of precursor observed by Weyman, Increasing the mach number to 11 while maintaining the i n i t i a l pressure resulted i n the loss of the negative dip before the a r r i v a l of the shock. For mach 9 and an i n i t i a l pressure of 1.3 t o r r -158-the precursor before the shock became positive instead of negative as found with the lower pressure at t h i s mach number. Groenig, observing the number of electrons i n a side chamber to the discharge chamber, found that the number of electrons increased when the shock reached the walls of the discharge chamber,. The pressure i n the side chamber was maintained at 1 mtorr as compared to 0»1 t o r r i n the discharge chamber. Charvet observed that the signal from the shock was preceded by a signal of 5 p.s duration and that the time i n t e r v a l between the short duration s i g n a l and the shock increased as the point of observation became further from the d r i v e r , b) High speed precursor (type I I ) 1. Apparatus and operating conditions. In the l i t e r a t u r e to date the only discussion of the high speed precursor by a worker using a mechanical shock tube seems to be that of Gloersen. There are also some indications of t h i s type of precursor i n the sample traces of Weyman's report„ Gloersen observed the high speed precursor effect under the same experimental conditions as the low speed precursor. The f i r s t report of precursors i n an electromagnetic shock tube was that of Voorhies and Scott ( 1 9 5 9 ) T h e y used a shock tube of s i m i l a r design to that of Josephson as did a number of other workers (Charvet 1963, Fowler and Hood 1962 s Gerardo et a l 1963). The apparatus of Voorhies when operated at an i n i t i a l bank voltage of 21kV was capable of producing a peak current of 0.2 MA when the gas i n the shock tube was a mixture of 90$ D 2 and 10$ He at an i n i t i a l pressure of 0.15 t o r r . The shock v e l o c i t y at the point of observation was 50 km s^ 1. The dimensions of the tube were not given. Charvet's apparatus and operating conditions are discussed i n the section on low v e l o c i t y precursors. Gerardo's driver d i f f e r e d from that of Josephson i n that i t s geometry was not conical but c y l i n d r i c a l . A pyrex tube having an inside diameter of 0.8 inches was used. The bank consisted of low inductance capacitors of rated working voltage 20 kV and t o t a l capaci-tance lk.5jiF, The experimental gases were argon and neon at i n i t i a l pressures of 1 to 5> t o r r . Mach numbers of h to l i * were produced under these conditions. What presumably was an improved version of the apparatus of Fowler and Turner, reported i n 19*, was used by Fowler & Hood. Their apparatus generated a column of dr i v e r gas 1 m long that could produce shock speeds of mach 1*0 i n a tube $0 mm i n diameter, when an i n i t i a l bank voltage of only 10 kV was used. They used argon and hydrogen at i n i t i a l pressures from 0.1 to 1 t o r r . The apparatus used by Schoen et a l . and by Mahaffey et a l . con-sis t e d of a dr i v e r that had a funnel shaped electrode and a c o a x i a l l y positioned rod electrode at i t s apex. The funnel base opened out into a pyrex shock tube with an i n t e r n a l diameter of 6". The working gas was argon at i n i t i a l pressures from 0.1 to 1 t o r r . The apparatus used by McLean et a l . was the same as that used f o r e a r l i e r work (McLean et a l I960). I t consisted of a T-tube driver that operated into a quartz shock tube 3 cm i n diameter and 30 cm long. The gas used was helium at an i n i t i a l pressure of 1 t o r r . The driver was operated with a capacitance of 0.6*JJF charged i n i t i a l l y to l±2 kV. Groenig's discharge chamber i s described above i n the section on low v e l o c i t y precursors. Jones used the exploding wire technique and -160-fed energy into 6.8 m i l copper wire h cm long at the rate of 180 J cm" . The wire was exploded i n a chamber with a i r , argon, nitrogen, or helium at pressures from 50 to 5>00 t o r r . The electrodeless 0-pinch technique was used by Russel et a l . and by Quinn & Bodin. Russel et a l . worked with the discharge machine at AWRE known as MIDGE. A capacitor bank of 2 /iF, i n i t i a l l y charged to 30 kV, was discharged through a copper plate loop wrapped around a quartz tube 7.6 cm i n diameter. The loop's width was 7»5 cm. Argon and deuterium at i n i t i a l pressures of 5 mtorr to 1 t o r r were used. .Quinn & Bodin described t h e i r apparatus as a 20 kJ bank operating at 15 kV 0 The bank was discharged i n t o a pinch c o i l , wrapped around a square perspex tube of cross section 19 cm x 10 cm. I n i t i a l deuterium pressures from 0.1 to 0.5 t o r r were used. 2. Results. Gloersen found that when the shock (mach 11 - 1 torr ) became luminous a precursor signal seemed to appear throughout the shock tube. This precursor, which appeared with the. shock luminosity onset, was only observed at maximum shock speed. Capacitative ring signals d i f f e r e d from those of the brass end plate. The ring signals seemed to be approximately the derivative of the end plate si g n a l . •Voorhies and Scott observed the 587.6 nm l i n e of helium and found that the precursor ex c i t a t i o n i n t e n s i t y was about 90$ that of the shock. They also stated that the precursor i n t e n s i t y varied with the bank current and that the precursor and current time variations were the same. Looking at a sp h e r i c a l l y shaped rod end down stream from the driver with a streak camera Charvet found that the gas i n front of the rod became luminous for a few us after the i n i t i a t i o n of the discharge and •161-then remained dark t i l l the shock front's a r r i v a l . This observation was made using an i n i t i a l a i r pressure of 0.1 t o r r and an i n i t i a l bank voltage of 10 kV. Using an i n i t i a l neon pressure of 1± t o r r and 12 kV bank voltage, Gerardo et a l . found that the microwave trans-m i s s i b i l i t y , 15 cm from the discharge chamber, dropped for 2 ^ i s at about 1^us after the discharge i n i t i a t i o n and again at 21^us when the shock arrived. I t was also found that the electron density dropped 13 —3 1 ? —^ from 10 cm~-% at 12 cm from the discharge chamber, to 10 cm J at 2k cm from the discharge chamber. These observations were made at maximum bank current. The number density decrease with distance from the driver was a function of both the i n i t i a l neon pressure and the i n i t i a l bank voltage. Fowler and Hood found the same luminous precursor effect for both argon and hydrogen. At 2 m from the dri v e r , Schoen et a l . observed maximum precursor signal amplitude when the bank voltage became minimum. 3.5 m from the driver of the same shock tube Mahaffey et a l . detected an electron density greater than 1 0 1 0 cvT^, McLean et a l . observed a 587.6 nm helium precursor which was about 2% as intense as the same radiation behind the shock front. Presumably both measurements were made at the same unspecified distance from the d r i v e r . The inten-s i t y of the precursor 587.6 nm helium l i n e that he observed i n the main tube was only about 1.5$ that of the shock i n t e n s i t y . Precursor i n t e n s i t y i n a side tube was found to be about 1/10 the i n t e n s i t y of the precursor i n the main tube. The distance from the shock tube axis was not specified. The pressure l i n e width was smaller than the shock l i n e width. Groenig found that the gas i n the v i c i n i t y of diode probes became ionized when the discharge was i n i t i a t e d . This i o n i z a t i o n was =162= not effected by the f i e l d as was a slow precursor. Jones, observing the transmission losses i n the gas of the discharge chamber, found that the r i s e times of the losses were longer f o r the higher pressures. Increasing a i r pressure by a factor of 10 also increased the time f o r h a l f transmission by a factor of 10. The transmission % decreased for an i n t e r v a l soon a f t e r the i n i t i a t i o n of the discharge, increased and decreased again more slowly l a t e r . The i n i t i a l decrease came about k ps a f t e r the s t a r t of the discharge f o r argon and helium and 10yis after the discharge i n i t i a t i o n f o r a i r and nitrogen. The i n i t i a l drop was found to be quite pressure sensitive, being higher f o r lower values of pressure. Russel et a l . found that deuterium i o n i z a t i o n was pressure depend-ent from 30 mtorr to 1 t o r r . At 1 t o r r i t was small, at 30 mtorr i t was undetectable, and at 0.1 t o r r i t was a maximum0 Between 10 mtorr and 0.2 t o r r argon i o n i z a t i o n was so high that i t did not f a l l below the monitoring apparatus saturation value i n the i n t e r v a l between the fast precursor and the a r r i v a l of the shock f r o n t . The r i s e and f a l l of the electron number density was found to depend on both gas type and gas pressure. Quinn and Bodin found that the time derivative of the electron number density f o r any given time decreased as the distance from the pinch c o i l increased. From the sample traces of Gloersen"s work the precursors he observed seemed to have had a speed of 50 km s = 1 or greater. McLean et a l . e s t i -mated that the precursor v e l o c i t y was 100 or more times greater than the unspecified shock v e l o c i t y . Fowler and Hood's rotating mirror experiments resulted i n the detection of argon precursors having a -163 speed of 2 Mm s at pressures from 0.1 to 0.5 t o r r . For a 1 t o r r pressure, the speed was 0.5 Mm s" 1. Schoen et a l . concluded frqm t h e i r photomultiplier observations that the precursor speeds were greater than 5 Mm s Quinn and Bodin found that the electron density along the tube rose to 1 0 1 2 cm"-* a t a speed of 80 km s" 1. This speed was found to be independent of the deuterium: pressure from 0.2 to 0.5 tOITo By using spaced t h i n conducting films on the inside of the shock tube Jahn and Grosse, assuming the gas between the films to be of uniform r e s i s t i v i t y , estimated that the charge density was about H i ~ 3 10 cm . B.y the method of microwave transmission d i f f e r e n t workers observed electron densities i n the range l O 1 ^ to. l O 1 3 cm"3. Mahaffey observed the lower value 3.5 m from the d r i v e r 0 Gerardo made obser-vations i n the range 10 to 10 J f o r distance of 12 to 2h cm from the dri v e r . Observations i n the same range were made by Jones, Russel (at 30 cm from the pinch c o i l ) , and by Quinn and Bodin at distances of 30 to 65 cm from the pinch c o i l . A report of Hollyer 1 1 s work was not obtainable so that information on h i s investigations had to be obtained from the reports of others, Gloersen found i t d i f f i c u l t to decide whether Hollyer observed either the fast or slow precursor or both. He claims that Hollyer observed precursors i n argon up to 0.5 m ahead of the shock and considered wa l l effects i n d e t a i l . Weyman revealed that Hollyer found precursors to t r a v e l further i n glass shock tubes than s t e e l ones. I n order to establish the presence of photoionization Hollyer looked for positive ions ahead of the shock. I n krypton he found them f o r mach numbers -164" greater than 12 but not i n argon. He concluded that photoemission from the walls was therefore the dominant mechanism. J.ahn and Grosse reported that Hollyer investigated the d i f f i c u l t i e s of using the Langmuir probe technique f o r transient discharges. c) Applied f i e l d s Magnetic f i e l d s of from 0.1 to 0.4 T have been applied to shock tubes i n which precursors were observed by a number of workers (Voorhies & Scott, Groenig, Mahaffey et a l 0 j ) Gerardo et a l 0 i , Fowler & Hood, and Gloersen). I n a l l cases i t was observed that the f i e l d had no observable effect on the observed precursor. From t h i s i t was concluded that the precursor was not due to a flow of electrons and that any electrons appearing i n the gas at any po s i t i o n are produced l o c a l l y . I t also follows that any electron interactions are short range. d) P o l a r i t y reversal Voorhies and Scott reversed the p o l a r i t y of the bank that energized t h e i r shock tube and found that t h i s produced no detectable change i n the observed precursor. e) P u r i t y and boundary c o r d i t i o n The work of S c h r e f f l e r and C h r i s t i a n showed that the shock tube w a l l strongly influenced the nature of t h e i r precursor. They found a precursor effect at the w a l l which started at some distance from the dr i v e r . For shock tube r a d i i of 2" or greater the point of the pre-cursor i n i t i a t i o n was the samej however the distance increased f o r tubes of smaller diameter. For example, i n argon i t was found that a reduction of diameter to 1" caused the distance to double. I t was further found =165-that the same type of disturbance could be observed at the boundary of a rod at the center of the tube. Rods of copper, b i r c h dowel, and threaded brass indicated that the disturbance v e l o c i t y was independent of the boundary composition. A stepped b a r r i e r at the w a l l showed that the w a l l disturbance became turbulent when the b a r r i e r thickness became UO i l l s . The work of Hollyer showed that precursors t r a v e l l e d much further i n glass tubes than i n steel ones. Jahn and Grosse found, using an interferometer, that the reflected shock had prominent precursor at the walls i n a rectangular tube 3/8" by It". Gloersen, using a l i g h t pipe and photomultiplier, studied the time difference between the i n i t i a l l i g h t spike attributed to impurities and the main luminosity pulse. He found that the time delay was independent of the density immediately behind the shock. The delay times i n the 2" tube were 2 times greater than those for a 1" diameter tube. The addition of as an impurity i f done i n small quantities decreased the delay time. No v a r i a t i o n resulted from using d i f f e r e n t supply b o t t l e s . I n i t i a l l i g h t spikes were enhanced by driving impurities from the wall by the application of a t e s l a c o i l . No special significance was a t t r i -buted to the factor of 2 occurring from the change i n diameter. I t was found that the addition of Q»2- mole % of Fe(CO)^ to the driver caused the delayed luminosity to be e n t i r e l y quenched and t h i s effect was also produced using benzene. In order to obtain reproducible results i t was found necessary to clean the shock tube walls between shots. This seems to indicate the possible importance of w a l l effects., as contrasted -166-with the results of S c h r e f f l e r who found that the w a l l composition was unimportant. The Xe used as the shock tube gas was considered e s s e n t i a l l y transparent to u l t r a v i o l e t r adiation and i n t e r a c t i o n with the walls or impurities was deemed a necessary part of the process. At s u f f i c i e n t concentration, a l l the energy i n the shock front can go into d issociation of any O2 impurities since oxygen~rare gas c o l l i s i o n cross sections are large. i Quinn and Bodin proposed a model that accounted for the i o n i z a t i o n of the gas i n t h e i r 0-pihch discharge as due to a combination of the processes of photoelectric emission from the shock tube walls and photo-i o n i z a t i o n . A study of the v a r i a t i o n of n e with time and distance from the driver permitted them to conclude that since the v a r i a t i o n with ambient gas pressure i s so i n s i g n i f i c a n t the w a l l s play an e s p e c i a l l y important r o l e , the dominant source of the i o n i z a t i o n i s photoelectron emission from the walls and that the most effec t i v e wave lengths seem to be 3> = 100 nm. f) Energy transfer mechanism Sch r e f f l e r and C h r i s t i a n concluded that the energy car r i e d forward by the precursor can be quite appreciable. An experiment i n argon (blocking the shock tube a f t e r some distance) indicated that when the shock front was no longer v i s i b l e to portions of the tube the precursor was quite attenuated i n these blocked portions. Since t h i s block was quite r i g i d , i t i s also possible that the b a r r i e r seriously interfered with the shock front properties so that blocking the r a d i a t i o n may not have been the only e f f e c t . Photographs of the luminosity suggest the p o s s i b i l i t y of shock front r a d i a t i o n . •167 Experiments by Hollyer indicated the absence of positive ions ahead of the shock i n argon. On t h i s basis, photons from the shock front might detach electrons from the w a l l which can then excite the shock front's gas molecules, giving r i s e to the lumination. Voorhies and Scott attributed the precursor they observed i n a He-Dg mixture to a % - t r a n s i t i o n . Their proposed energy transfer mechanism was that resonant photon absorption produces a 3 P state which i s changed to a state v i a a spin change due to c o l l i s i o n s . They found that the precursor varied as the bank current. Furthermore 20 eV electrons are required so that the driver seemed to be the source of the observed precursors,. The absence of any effect due to p o l a r i t y reversal and application of a f i e l d was taken as evidence against the p o s s i b i l i t y of the precursor being a cloud of energetic electrons from the driver. Weyman, on the basis of magnetic c o i l measurements, concluded that the precursor i s probably due to electron d i f f u s i o n from the shock fron t . He gave three reasons f o r t h i s hypothesis, the thermal v e l o c i t y of the electrons i s about 300 times that of the ions, the mean free path of 1 eV electrons i s very long due to Ramsauer e f f e c t , and the e l e c t r i c f i e l d except i n the immediate v i c i n i t y of the i o n i z a t i o n i s strongly three dimensional. Upon the basis of the detected presence of an u l t r a v i o l e t continuum radiation from rare gases (Tanaka V)S6S Roth 19*9) excited by e l e c t r i c a l discharges and shock waves, Gloers'en concluded that since u l t r a v i o l e t absorption by Xe i s very small, the precursor he observed was due to photoemission from the shock tube walls. I t i s also more probable that the sustaining mechanism f o r luminosity i s also due to the u l t r a v i o l e t =168-radi a t i o n since i t has a long l i f e time r e s u l t i n g from the fact that metastables decay through three body c o l l i s i o n s . Resonance radiation can be ruled out since i t s l i f e time i s very short. This u l t r a v i o l e t continuum radiation can also account for the rapid cooling of the shock heated gas s the occurrence of which i s borne out by the fact that Fe(CO)£ was not excited at the interface while small impurities at the shock front do get excited. By comparing, the rad i a t i o n from a point i n a shock tube with that from a side tube McLean et a l . found that the signal i n the shock tube was much greater than that i n the side tube i n d i c a t i n g that 90% of the precursor radiation came from the arc discharge and the rest possibly from the shock front. They also attributed the observed precursor to u l t r a v i o l e t radiation. Fowler and Hood on the basis of t h e i r studies with a rotating mirror camera postulated that precursors i n Ar and Hg could be caused by either radiation from the driver or heat conduction processes. Possible photon processes weres M* + M» — » M •+ e~ + KoEo h V + - M — > M -r 6* •+ K . E . Shoen et a l . (1962) also t e n t a t i v e l y designated u l t r a v i o l e t radia-t i o n as the cause of a precursor they observed. Other experimenters using a pinch c o i l d r i v e r attributed the cause of precursors to radiation from the center of the driv e r c o i l (Russel et a l . 1963, Quinn and Bodin 1963). Charvet concluded that the precursor s i g n a l he observed was not caused by l i g h t being transmitted along the glass of the shock tube s as •169-might have been observed with a photomultiplier, but was of an electro-magnetic nature and that the shock tube acted as a wave guide, g) Measuring apparatus Precursors have been studied by means of various types of measuring apparatus. We f i n d i t convenient to divide these various apparatuses into two groups, o p t i c a l and e l e c t r i c a l s depending on which aspect of the precursor i s most relevant to the measurement. 1. Optical. A framing camera was used by Sc h r e f f l e r and C h r i s t i a n for t h e i r study at atmospheric pressure. This was a 25 lens framing camera after Brixner (1952) and the frames were taken at inte r v a l s of 0.9 us. Jahn and Grosse found that most of the r e f l e c t i o n flows i n t h e i r apparatus were too bright to permit interferometric or Schlieren studies of the wave or density patterns. The use of the t h i n 3/8" section per-mitted t h i s measurement which was not possible with the c y l i n d r i c a l tube. Voorhies and Scott did t h e i r study of the 587.6 nra He l i n e with a 500 mm Jaco monochromator. Their radiation detector was a IP21 photo-m u l t i p l i e r . This instrument's resolution was 70 pm and the precursor l i n e h a l f width was also measured to be t h i s . Gloersen,using a f/8 Ebert spectrometer coupled with a standard image orthicon t e l e v i s i o n camera to increase the s e n s i t i v i t y by two or three orders of magnitude over that of a photographic plate, did not observe any precursor i n the spectral range .3 to .6 pn or at points along the spectrum to 1 p i using an infrared converter. The 587.6 nm l i n e of He was also observed,by McLean et a l . using an / /27 grating spectrograph with an 0.68 nm/mm resolution and photo-m u l t i p l i e r s of an unspecified type as radiation detectors. The precursor -170-was observed only after special e f f o r t s had been made to increase the signal to noise ratio„ .No de t a i l s of the camera used by Fowler and Hood were given. 2. E l e c t r i c a l sensors. Hollyer investigated the d i f f i c u l t i e s involved i n using conventional Langmuir probe techniques to measure electron d en s i t i e s i n shock heated gas<> Capacitative probes were used by Weyman and Gloersen. Weyraanlls probe consisted of 1/32" diameter wire wrapped around the outside of the shock tube,, The probe p o t e n t i a l with respect to ground was monitored using a Tektronix low capacity probe and a Tektronix 5*1 oscilloscope. A s i m i l a r probe used by Gloersen was made from 2 mm brass shim. The magnetic probe used by Weyman consisted of c o i l s wrapped around a ferroxcube core. An output of about. 1 mV was obtained from a mach 12 shocke Groenig attributed diode saturation currents of 200 pk to electron desnities of 10 cm = J. The diode consisted of a * m i l cathode inside a J(" diameter cylinder. The length of the diode was 3/li" o 8 mm microwave equipment was used by Russel et a l . , Quinn and Bodin, 12 13 and Gerardo et a l , to observe electron densities from 10 to 10 J cm J* Mahaffey et a l . made microwave measurements of densities from l O 1 ^ to 1 0 1 2 cm°3. . Charvet detected electromagnetic radiation with a V-antenna whose output was applied across a neon bulb. The l i g h t from the neon bulb was observed with a DARI0 *3 AVP photomultiplier. =171-E. .Survey of Theoretical Wqrk Several papers have been published to give an explanation of the observed precursor effects. Some have considered precursors as being due to the diffusion of electrons, others consider radiation from the shock front, and s t i l l others have considered radiation from the driver discharge i n the case of electromagnetically driven shock tubes. Let us therefore review the work under these headings, a) Diffusion In 196l, Pipkin published a paper i n which he considered the gas to stream i n one dimension through a region where i t was sl i g h t l y ionized. The fraction of ionization was assumed to be small as compared to one but large enough so that the Debye length was much smaller than the mean free path of the ions through the neutral gas. The electron mean free path was i n turn larger than the ion mean free path. Momentum was assumed to be only affected by a one dimensional e l e c t r i c a l f i e l d and the diffusion coefficient of the ion or electron with the neutrals. When compared with the experimental values for electron density, as found by Weyman i n I960, the predicted values are much smaller than those-observed. Pipkin observed that this might be due to the assump-tion about the electric f i e l d being only one dimensional. The ionization mechanism was not discussedo Wetzel i n 1962'again considered diffusion of electrons. He did not discuss the mechanism of the production of the electrons at the shock front. A model was proposed consisting of a source that moves with the shock velocity and has an electron number density n and a temperature T. The electrons from the model are assumed to have a =172= d i f f u s i o n constant D for d i f f u s i o n into the neutral gas ahe^d of the shock fro n t . By assuming that the probes used by Weyman responded only when the number density was above some minimum and p l o t t i n g a family of curves for di f f e r e n t minima, he found that the model pre-dicted the same behaviour for one of the curves as found by Weyman f o r variations with distance from the shock front. Pipkin again i n 1963 considered precursor i o n i z a t i o n including the modification of the e l e c t r i c f i e l d to the three dimensional case as he suggested i n I96I. The gas i n the shock'tube was considered to form a capacitor with ground and t h i s capacitor was assumed to have a re l a t i o n between the excess charge i n the gas (electrons) and the potential d i s t r i b u t i o n i n space. The potential d i s t r i b u t i o n along the axis of the tube gave r i s e to,the accelerating f i e l d . Both f i e l d and d i f f u s i o n effects on the electron d i s t r i b u t i o n are considered. Neglect-ing the pressure effect the f i e l d caused the electrons to have a sharp front that moved from the driv e r so that the distance was proportional to t 2 . The effect of d i f f u s i o n from the pressure gradient was to produce a low electron density d i s t r i b u t i o n ahead of the el e c t r o s t a t i c front5 thus destroying the sharp front, k spherical approximation was used to estimate the potential v a r i a t i o n ahead of the shock front. The theory gives the same shape for the i n i t i a l stages of the el e c t r o s t a t i c signals as observed by Weyman and a si m i l a r shape to the experimental values of the precursor v e l o c i t y 6 Schoen et a l . used two colminating s l i t s i n front of a photo-m u l t i p l i e r to observe t h e i r precursor. No information was given about the photomultiplier or i t s associated c i r c u i t s 0 -173-b) Shock front radiation The t h e o r e t i c a l treatment of the precursor effect from the point of view of radiation was f i r s t done by Biberman who considered a one dimensional shock front of i n f i n i t e area,, The r a d i a t i o n was assumed to be black body around the spectral region of the resonance l i n e s of the shock heated gas. Concentrations of excited atoms were considered rather than i o n i z a t i o n ahead of the shock. The following year, I960, L i n , who was interested i n estimating the effective r e f l e c t o r f o r microwaves when an object re-entered the atmosphere, considered radiation of a given frequency to have a character-i s t i c mean free path i n a given gas. The loss of a photon was considered to result i n the production of a single electron and the radiation was assumed to be i s o t r o p i c . The dominant mechanism i n the atmosphere was considered to be 0 2 absorption i n the wave length gamut 88 to 103 nm. From the i o n i z a t i o n cross section and the required electron density, fo r the s e n s i t i v i t y of the radar use, i t was calculated that the mean free path, f o r the radiation considered, was of the order of * m. I n a l a t e r paper by Wetzel he also seems to favour ra d i a t i o n instead of d i f f u s i o n as i n h i s e a r l i e r paper. He considered a one dimensional shock front to be replaced by a photon emitter that radiated according to the Planck radiation law's high frequency l i m i t . The effects of the absorption cross section and the i o n i z a t i o n cross section are discussed but no application to any experimental data i s made. The state of the gas ahead of the shock front was considered to be effected by the presence of both excited atoms and electrons by Lagar'kov and Yakubov i n 1963. They continued the work of Biberman taking account -174-of the effects of the shock tube diameter and the jpresence of meta-stables. Expressions were obtained f o r the concentrations of the excited atoms at diff e r e n t positions ahead of the shock, considering the numberof excited atoms to be due,, to radiation from the shock and the excited atoms i n other portions of the shock tube. Concentrations of the order of 10° x to 10 of the Boltzman concentration behind the shock are predicted. In the case of electrons i n argon the number of electrons expected ahead of the shock should be less than 10~-> times the number of neutrals. The amount varies with the speed of the shock wave and when the resultsof Weyman were considered- i n the l i g h t of the theory i t was concluded that photoionization could account f o r the measured electron density. The possible contribution from photoelec-tron emission from the walls was mentioned but not accounted f o r otherwiseo c) Radiation from the discharge The f i r s t publication that consideres precursor effects as due to radiation from the discharge i n an electromagnetic shock tube seems to be that of Gerardo et a l . i n l< ? 6 3 o They found that assuming the pre-cursor to be predominantly due to photoionization by soft X-rays r e a d i l y explained t h e i r experimental r e s u l t s . A time independent consideration was made mindful of the effects of gas and pressure, wave length, s o l i d angle and w a l l e f f e c t s , and the distance from the source. Allowance was also made for secondary electrons produced by photoabsorption of the primary radiation and by i n t e r a c t i o n of the primary radiation with the shock tube walls. From the experimental results i t was concluded that no electrons traveled any distance of significance to the theory and .175-that the i o n i z i n g r a d i a t i o n was from a narrow band of wave lengths (1 to k £)„ Because of the number of unknowns, no d e f i n i t e corrobora-t i o n of the theory was i n f e r r e d from t h e i r experimental data 0 I n order to explain t h e i r experimental r e s u l t s , Quinn and Bodin i n 1963 considered two models involving radiation from the pinch d i s -charge of t h e i r apparatus. At any point along the axis of the shock tube, the radiation present was assumed to have the same time v a r i a t i o n as the source and an exponential decay of i n t e n s i t y i n accordance with the mean free path concept. On the basis of experimental data of t h e i r work they could assume that time and s p a t i a l v a r i a t i o n were independent. Consideration of just photoionization predicted that:.the time rate of change of electron number density should f a l l o f f as the square of the distance. A consideration of photoemission indicated that the f a l l o f f should be inversely proportional to the cube of the distance from the source. Comparison of the two rates indicates that when the mean free path f o r absorption i s greater than the distance from the source one should expect photoemission to be the more probable of the two e f f e c t s . ,; The most recent treatment of precursor radiation i s that of P h i l l i p s i n I 9 6 1 4 0 He considers models a t t r i b u t i n g the precursor to black body radiation from the discharge and to the effect of the d i s -charge's f i e l d at some distance from the discharge. Wall effects and fluorescence were neglected and the point of observation was considered to be much further from the discharge than the shock tube radius. The radiation model predicted that the time rate of change of the electron number density was proportional to the number density of the neutrals -176-and inversely proportional to the square of the distance from the discharge region. The f i e l d model considered ionization build-up. due to far f i e l d effects predicted inverse variation with the sixth power of the distance from the discharge. The models could account for the reported time rate of change of electron number density but not the variations with pressure and.distance. F. Radiation Model - Point Source Radiator Consider radiation absorption subject'^to the following'.assumptions? 1) A point source radiates intensity I within a region d A about the wavelength A « 2) . The Lambert-Beer law of absorption holds. 3) I = I q (p, Vg s i n 2 ( o ; B t ) exp(-2at)). The source's intensity i s a function of i t s gas pressure and the e l e c t r i c a l energy dissipated i n i t by a condenser discharge. Vg i s the i n i t i a l condenser voltage s 60g i s the angular frequency of the discharge c i r c u i t , and a i s the damping constant. At some distance z from the source the intensity w i l l be reduced due to variation i n solid angle to -* =_ J£ZL (Fl) z A 4 T T z 2 The effect of absorption w i l l be to further reduce this intensity to V * °'k'hZ <n> -177= where k7y i s the absorption coefficient for radiation of wavelength 7\ « •From (F2) I t follows that The f i r s t term accounts for change i n intensity due to absorption and the second term for that due to change i n solid angle. •For processes that require I* to remain constant, equation ( F 3 ) z determines the relation that the experimental parameters should follow. I f assumption 3) i s valid, the condition may be written as (K^T 2 } JE°A( ' P , V2 s i n 2 ( ^ ) n t ) e" 2 a t); expt-k* z) = const. (?h) I f p,z remain constant, then from (Fa) we get that the energy input to the source must remain constant or Vfi sin (Wgt) e ~ a t ~ const. (F£) I f just the, distance from the source i s fixed, I z i s constant when the parameters are related by •=2at I 0 7 v ( P j V | . s i n 2 (wBt.) e ) = const. (F6) For processes that 'require I Z due to absorption to remain constant equation (FU) states that the variables should satisfy =k* z ^ O A 6 * = const.z ( F 7 ) -178= For processes requiring the contribution due to change i n s o l i d angle to remain constant, the parameters should be related by I e" k^ z =. const z 3 (F8) 07\ When k ^ z . « 1 we may approximate equations (F7) and (F8) by k A I Q 7 l ^ const z 2 ( F 9 ) and 3 I ^ const z (F10) OA S i m i l a r l y when k ^ z >j> 1 we may write f o r both (F7) and (F8) that I 0 ? v ^ const exp(-k f l z) ( F l l ) Thus one can distinguish which change i n i n t e n s i t y i s the more important using equations (F9) and (F10) provided that the condition k^ z 1 i s not satisfied,, G, Transmission Line - Point Source Radiator Assuming that the conductivity i s due to absorption of point source radiation and using (F3), we write the resistance per unit length as R(z,t) - R(t) z 2 exp(kz) (Gl) - 1 7 9 -Using equations (3-5) and (3-6) with (Gl) we obtain upon separat-ing the variables that w" ( z ) - (k+ | ) w(z) a m j ^ l = hB2 (G2) W(z) exp(kz) zd X(t) The solution f o r the time dependent part i s given by ( 3 - 7 ) o Putting k =. 0 (G2) becomes W' 5(z).- 2z~V(a) W.('B) = 0 -(03) which has the solution W(a) = const fez2)3^ X^C&a2) (Gh) where K i s the modified Bessel function of the. second kind defined as K (x) — — - 3 - £ f l W2k-> (x/2) 2*~P , ( a g ) arid has the properties K p ( x ) - > 2 P ° 1 (p-l)i x~P a s x - » 0 CTr/2x) 2 e" x as x — » x = (G6) -180-BIBLIOGRAPHY A l l e n , C. W. Astrophysical Quantities, 2nd Ed,i(The- Athlone Press), 1963. A l l i s , W. P. Phys. Today 1*, 22, 23 (1962). Barach, J . P. & S i v i n s h i , J . A. Phys. Fluids 7,:107* (1964). Biberman, L. M. & Veklenko, B. A. Soviet Phys. JETP 10, 117 (I960). Bishop, A. S. Project Sherwood. Doubleday & Co. Inc. (I960)j Phys. Today 17, 19 (1964). Boyd, R. L. F. Proc. Roy. Soc. A201, 229, 329. (19*0)| 6I1B, 79* (19*1). Brixner, B. Journal of the Society of Motion Picture & Television Engineers *9, *03. (19*2). Brown, S. C„ Basic. Data of Plasma Physics. M.I.T. Press (19*9). Charvet, Y. These d»Universite d»Aix, Marseille (1963). Cobine, J . D. Gaseous Conductors, Dover Publications (19*8)» Cormack, G, Ph«D. Thesis, U n i v e r s i t y of B r i t i s h Columbia (1963). Delcroix, J 0 L. Introduction to the Theory of Ionized Gases, Interscience (i960). •Fowler, R. G, & Hood, J . D, Phys. Rev. .128, 991 (1962). Gerardo, J . B., Hendricks, C. D. & Goldstein, Lo Phys. Fluids 6 , 1222 (1963). Gloersen, P. B u l l . Jtm. Phys. Soc. 4, 283 (19*9)§ Phys. Fluids 3, 8*7 (I960). Groenig, H. Phys. Fluids 6, 142 (1963). Hart, P. J . Phys. Fluids *, 38 (1962). -181-Hollyer, R. N. Applied Physics Laboratory Report, GM-903, John's Hopkins U n i v e r s i t y (19*7). Jahn, R. G., Gosse, F. A. Technical Report No. 13, LeHigh Un i v e r s i t y (19*9); Phys. Fluids 2, U69 (19*9). Jones, D. L . Phys. Fluid s *, 1121 (1962). Josephson, V., Hales, R. ¥. Phys. F l u i d s k9 373 "(1961). K i t t e l , C. Elementary S t a t i s t i c a l Physics, John Wiley & Sons, New York (19*8). kUngeriberg, H. VI I n t . Conf. Ion. Phen. Gases, Abstracts X-17j Z. Naturforschg. 18a, 1331 (1963). Lagar'kov, A. N., Yakubov, I . T. Optics & Spect. 14, 103 (1963). Liepmann, H. W,, Vlases, G. Phys. Fluids U, 927 (1961). L i n , S. C. Journal of Geophysical Research 67,.38*1 (I960). Loeb9 L. B. Basic Processes of Gaseous Electronics, U n i v e r s i t y of C a l i f o r n i a Press (19**). Mahaffey, D. W., Sanga, L. and Schoen, R. I . *th Annual Meeting of the American Physical Society (Plasma Div.) San Diego (1963). Margenau, H., Murphy, G. M. Mathematics of Physics & Chemistry, D 0 Van Nostrand Co. Inc. (19*6). McLean, E. A., Kolb, A. C , Giiem, H„ R» Phys. Fluids 4, 10** (1961). Pain, H. J.,.Smy, P. R. S. Journal of F l u i d Mechanics 9, 390' (I960). P h i l l i p s , N. J . Proc. Phys. S o c . §2» 27* (1964). P i p k i n , A. C. Phys. Fluids 4, 1298 (196l)| 6, 1382 (1963). Quinn, J . M. P., Bodin, H. A. B. VI I n t . Conf. Ion. Phen. Gases. Roth, W. Journal of Chemical Physics 31, 844 (19*9). Russel, J . A., Elphick, B. L. Alcock, M. W„, Daniel, jJ. Ao_Atomic — Weapons Research-Establishment Report 0-11/62 (1962). -182= Rustgi, 0. P. J . Opt. Soco Am, 5k, 464 (1964 )o Schoen, R. I . , Sanga, L, Horn, J.R. Boeing S c i e n t i f i c Research Laboratory's F l i g h t Sciences* Technical Memorandum No. 12 (1962). S c h r e f f l e r , R. G., Chr i s t i a n , R. H. J . A. P. 25, 32k &95k)* Tanaka, Y. J . Opt. Soc. Am. J J 5 , 710 (1955). Theophanis, G. JU Rev. S c i . I n s t . 31, U27 (i960). Thompson, W. B„ An Introduction to Plasma Physics, Pergamon Press 1962. V i e i l l e , P. Compte Rendus 129, 1228 (1899). Voorhies, H. G., Scott, F. R. Phys. Fluids 2, 576 (l959)j B u l l . Am. Phys. Soc. Ser. I I 4, 50 (1959). Weissler, G. L. Handbuch der Physik (Flllgge),.Vol. 21, Springer-Verlag (1956). Wetzel, L. Phys. Fluids 5, 82U (1962), Phys. Fluids 6, 750 (1963). Weyman, H. D. B u l l Am. Phys. Soc. (Troy) U, 283 (1959); Phys, Fluids 3, 5h5 (i960). Weyman, H. Do & Holmes, L. B. VI Int. Conf. Ion. Phen. Gases, A r t i c l e X - l . L i s t of Abbreviations used i n Bibliography B u l l . Am Physo S o c , B u l l e t i n of the American Physical Society. J . Opt. Soc. Am., Journal of the Optic a l Society of America. Optics & Spect., Optics and Spectroscopy - tra n s l a t i o n from the Russian. Proc. Phys. S o c , Proceedings of the Physical Society of London. P r o c Roy. S o c , Proceedings of the Royal Society. Phys. F l u i d s , Physics of F l u i d s . Phys. Rev., -The Physical Review. Phys. Today, Physics Today. Soviet Phys., Soviet Physics translations JETP. VI I n t . Conf. Ion. Phen. Gases, The VI International Conference on Ionization Phenomenon i n Gases at Paris 1 9 6 3 o Z. Naturforschg., Z e i t s c h r i f t fur Naturforschung. 

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