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UBC Theses and Dissertations

Diagnostics in a high density Z pinch plasma Hilko, Brian Kent 1981

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DIAGNOSTICS IN A HIGH DENSITY Z PINCH PLASMA by Brian K. Hilko B.Sc, University .of Waterloo, 1974 M.Sc, University of B r i t i s h Columbia, 1977 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of Physics) We accept t h i s thesis as conforming to the required standards THE UNIVERSITY OF BRITISH COLUMBIA © Brian Hilko, 1981 May 1981 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 advanced degree a t 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 , I agr 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 agree 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 department o r by h i s o r h e r 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 p e r m i s s i o n . BRIAN HILKO Department o f PHYSICS 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 2075 Wesbrook P l a c e V ancouver, Canada V6T 1W5 ^ ^ NOVEMBER 27, 1981. Date DE-6 (2/79) ABSTRACT A Z-pinch plasma, suitable for the study of C0 2 laser-plasma i n t e r -a c t i o n m e c h a n i s i m s , i s t h o r o u g h l y d i a g n o s e d u s i n g a number o f non-perturbing, o p t i c a l probe techniques. Simple streak and shadow methods g i v e an important p r e l i m i n a r y view of the s p a t i a l d i s t r i b u t i o n and r a d i a l dynamics of plasma during the high compression phase. The electron d e n s i t y and temperature are d e t e r -mined as a function of time by s p e c t r a l l y r e s o l v i n g the i o n f e a t u r e of Thomson scattered ruby laser l i g h t . Peak electron d e n s i t i e s well i n excess of 1 x 1 0 1 9 cm--* a n d temperatures near 50 eV are observed. Complementing the scattering r e s u l t s , holographic interferometry i s performed to examine both the temporal and s p a t i a l v a r i a t i o n of electron density. The diagnostics used are well suited to the examination of moder-at e l y dense, hot plasma and have been developed s p e c i f i c a l l y f o r a p p l i c a -t i o n i n our laser-plasma i n t e r a c t i o n studies. - i i -TABLE OF CONTENTS P a g e ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i i CHAPTER 1 INTRODUCTION 1 CHAPTER 2 THE Z-PINCH APPARATUS 5 CHAPTER 3 STREAK AND SHADOWGRAM PHOTOGRAPHY 12 3.1 Introduction 12 3.2 Experimental Method 14 3.3 Streak and Shadowgram Pictures 16 3.4 The Plasma Diameter vs Time 23 3.5 Electron Density from Ray Refraction 26 3.6 Conclusion to the Photographic Study . ^  . . . 33 CHAPTER 4 ELEMENTS OF THOMSON SCATTERING 35 4.1 Introduction 35 4.2 D i s t i n c t i o n Between Electron and Ion Features . 36 4.3 Advantage of the Ion Feature 46 CHAPTER 5 DESCRIPTION OF THE SCATTERING EXPERIMENTS 51 5.1 Introduction 51 5.2 Arrangement of the Scattering Geometry . . . . 54 5.3 Overall Layout of Experiment 59 5.4 C a l i b r a t i o n of the O p t i c a l System 65 CHAPTER 6 SCATTERING OBSERVATIONS AND RESULTS 70 6.1 Introduction 70 6.2 Discussion of the Spectra 70 6.3 Plasma Parameters for the Z-Pinch 79 CHAPTER 7 INTERFEROMETRIC DETERMINATION OF ELECTRON DENSITY . 86 7.1 Introduction 86 7.2 Double Exposure Holographic Method 87 7.3 The Plasma Refractive Index 91 7.'4 Formation of the Fringe Pattern 92 7.5 The Problem of Imaging 97 - i i i -TABLE OF CONTENTS (Cont'd) Page CHAPTER 8 LAYOUT OF THE INTERFEROMETRIC EXPERIMENT 106 8.1 Introduction 106 8.2 Cavity Dumping of the Laser O s c i l l a t o r 106 8.3 Optics of the Beam Paths 109 8.4 Recording and Post Exposure Processing . . . . I l l CHAPTER' 9 RESULTS FOR THE Z-PINCH PLASMA 113 9.1 General Features of the Interferograms . . . . 113 9.2 Data Processing 118 9.3 Plots of the Electron Density P r o f i l e 120 CHAPTER 10 CONCLUSION AND SUGGESTIONS 126 REFERENCES 130 APPENDIX A Triggering of the Discharge 133 - i v -LIST OF TABLES Table page I Basic Parameters of the Z-Pinch Discharge 6 II Numerical Estimates for the Thomson Scattering System . 57 III Radial Speeds from the Scattering Spectra 74 - v -LIST OF FIGURES Figure Page 1(A) Photograph of the Z-Pinch Apparatus 7 1(B) A Cross-Sectional View of the Ports 7 2 Voltage and Current Traces for the Discharge C i r c u i t . 10 3 Schematic of the Shadowgram Experiment 15 4 Streak Photographs of the Pinch Phase 18 5 Shadowgram Pictures 19 6 Formation of Contrast i n On-Axis Images 22 7(A) Plasma Diameter vs Time from Streak Photographs . . . . 25 7(B) Shadowgram Results for the Plasma Diameter 25 8 Ray Path i n an Axisymmetric Plasma 28 9 Deflection Curve for the Plasma at Maximum Compression. 32 10 A 'Typical' Scattered Spectrum 40 11 Comparative Spectral Brightness of Electron and Ion Features 49 12 Geometry for the Thomson Scattering Measurements . . . 55 13 Layout of the Scattering Experiment 60 14 D e t a i l s of the Scattering Volume 69 15 Examples of Observed Spectra 71 16 Refraction E f f e c t s i n the Backscatter C o l l e c t i o n Optics 77 17 Plasma Temperature Results . . . . . 80 18 Electron Density Results 82 19 I l l u s t r a t i o n of the Double Exposure Method 88 20 The Plasma Refractive Index vs. Electron Density . . . 93 21 A Ray Path Without Refraction 95 22 Imaging i n a Strongly Refracting Plasma ,99 23 Errors Introduced i n an Interferogram by Assuming Str a i g h t Line Paths 104 - v i -LIST OF FIGURES (Cont'd) Fig ure Page 24 O s c i l l a t o r and Amplifier Sections of the Cavity Dumped Laser . . 107 25 Optics of the Interferometry Experiment . . . . . . . . 110 26 Samples of the Interfercg rams Obtained Near Peak Compression 114 27 I l l u s t r a t i o n of the Region for which Interferograms were Analyzed 116 28 The Plasma D i s t r i b u t i o n During the Pinch Phase . . . . 122 29 Comparison of the Interferometric and Scattering Measurements . . . . . . . . . . . . . . . . . . . . . 124 A-1 Biasing and Main Gap Trigger C i r c u i t s 133 A-2 D e t a i l s of the Pre-Ionization 134 - v i i -ACKNOWLEDGEMENTS As part of a l a r g e e x p e r i m e n t a l p r o j e c t , I have had the g r e a t pleasure of working alongside a number of fine people. I wish to express my sincere a p p r e c i a t i o n and thanks to Dr. Jochen Meyer f o r h i s a i d and supervision throughout t h i s p r o j e c t . Dr. G. Albrecht, H. Houtman, Dr. C.J. Walsh and A. Cheuck have been u n s e l f i s h and continual sources of hel p and encouragement. My stay at U.B.C. would not have been possible without the f i n a n -c i a l assistance of the Plasma Physics Group. This work has been supported by a grant from the National Science and Engineering Research C o u n c i l of Canada. - v i i i -CHAPTER 1 INTRODUCTION This thesis reports a s e r i e s of diagnostic experiments t h a t have been s p e c i f i c a l l y developed i n conjunction with, and as part of, an ongoing i n v e s t i g a t i o n of laser-plasma i n t e r a c t i o n mechanisms. T h e r e f o r e , i n t h i s i n t r oduction, some consideration w i l l be given to the experiment as a whole i n order to place the objectives of t h i s t h e s i s work i n t o f u l l p erspec-t i v e . The peak compression phase of a Z-pinch discharge i n Helium i s the target plasma, into which a high power CO2 laser beam i s focussed. High i n t e n s i t y laser l i g h t can couple to the plasma v i a a number of d i f f e r e n t V-non-linear processes (Siebe, 1974; Milroy e t . a l . , 1979). The e f f e c t s of the laser on the plasma depend strongly on the l o c a l temperature and d e n s i t y d i s t r i b u t i o n of the target. As well, many of the c o u p l i n g processes can (and often do) occur simultaneously. The experiments that are underway at t h i s laboratory w i l l attempt to i s o l a t e and study the fundamentally d i f f e r -ent processes of laser-plasma i n t e r a c t i o n s . The following d i s c u s s i o n w i l l i ndicate that the Z-pinch plasma i s very well suited to such an endeavour. In many sim i l a r experiments, the target plasma i s c r e a t e d during the e a r l y portions of the incident laser pulse (Grek e t . a l . , 1978; J a c k e l e t . a l . 1976; Milroy e t . a l . , 1979). In these cases, however, i t i s d i f f i -c u l t to divorce the processes of plasma formation and l a s e r - p l a s m a i n t e r -action. Therefore, i t seems more desirable to study the i n t e r a c t i o n s using a target plasma, which has been pre-formed, and whose i n i t i a l c o n d i t i o n s can be established independently of the laser pulse. In a Z-pinch discharge, the progression of plasma c o l l a p s e w i l l make av a i l a b l e a wide range of plasma conditions. The plasma parameters, such as density, temperature, and corresponding g r a d i e n t s , vary reproduc-i b l y as functions of radius and time. As w e l l , the plasma c o n d i t i o n s i n - 1 -the Z-pinch change on a time scale which i s long compared to the i n c i d e n t laser pulse. Hence, the Z-pinch plasma may be used as a target of varying but c o n t r o l l e d and predictable parameters. I f the plasma c o n d i t i o n s are well known before hand, one can hope to study the laser-plasma i n t e r a c t i o n process i n d e t a i l . I t i s , t h e r e f o r e , very important to e s t a b l i s h the i n i t i a l conditions for the i n t e r a c t i o n s t u d i e s . T h i s has been done, and the r e s u l t s of this thesis constitute a thorough and d e t a i l e d experimental evaluation of the Z-pinch plasma parameters, prior to i r r a d i a t i o n with the CO2 l a s e r . The primary subject here i s o p t i c a l d i a g n o s t i c s of the Z-pinch using ruby l a s e r l i g h t , but, the u n d e r l y i n g emphasis i s on d i a g n o s t i c methods that are d i r e c t l y a p p l i c a b l e to the i n t e r a c t i o n s t u d i e s . As a r e s u l t , i t w i l l not be possible to avoid periodic discussions of the i n t e r -action experiments, though such occurrences have been minimized and kept b r i e f . Since the coupling mechanisms of i n t e r e s t occur near the c r i t i c a l density, n c for the incident CO2 laser l i g h t ( n c = 1 x 1 0 1 9 electrons cm - 3) the diagnostics must, in p a r t i c u l a r , be suited to plasma having an electron density which covers the range above and below n c . In the course of t h i s presentation, i t w i l l become c l e a r t h a t the a c t u a l d e f i n i t i o n of a high density plasma depends a g r e a t d e a l on the p a r t i c u l a r d i a g n o s t i c being considered. What may be the l i m i t a t i o n of one experiment can be the j u s t i -f i c a t i o n for another. Four separate experiments have been performed: streak and shadowgram photography, Thomson scat t e r i n g , and holographic i n t e r f e r o -metry. The remainder of this introduction outlines the subject material of this thesis and previews the experiments to be presented. Chapter 2 gives a d e s c r i p t i o n of the Z-pinch apparatus and reviews established c h a r a c t e r i s t i c s of the discharge. The plasma temperature and density during the pre and post pinch phases of the d i s c h a r g e have been c a r e f u l l y measured (Houtman, 1977) using spectroscopic methods. However, - 2 -during peak compression, the plasma emits o n l y continuum r a d i a t i o n and spectroscopy could not be used. In Chapter 3, two r e l a t i v e l y simple d i a g -nostics are p r e s e n t e d , s t r e a k and shadowgram photography, both taking advantage of the h i g h plasma d e n s i t y . The r e s u l t i n g p i c t u r e s g i v e an important preliminary view of d e t a i l s of the plasma structure and dynamics during a l l stages of the on-axis c o l l a p s e . The remainder of this thesis i s devoted to d e t a i l e d measurement of the plasma temperature and density using the methods of Thomson s c a t t e r i n g of ruby l a s e r l i g h t and h o l o g r a p h i c interferometry. Thomson scattering examines the plasma at the microscopic l e v e l by looking at f l u c t u a t i o n s i n the p a r t i c l e density, i . e . plasma waves. Us u a l -l y , scattering from electron plasma waves i s observed. However, Chapter 4 shows that with scattering methods, a high d e n s i t y plasma i s most e a s i l y investigated by scattering from ion acoustic f l u c t u a t i o n s , a technique not often considered as a diagnostic t o o l . Chapter 5 discusses the arrangement of the scattering geometry and describes the experiment i n d e t a i l . The geometry has been chosen to serve a two-fold purpose, namely, the measure-ment of thermal f l u c t u a t i o n l e v e l s g i v i n g the plasma temperature and density, and, extension of the experiment to examine induced or enhanced f l u c t u a t i o n s which are expected to occur with the i n t r o d u c t i o n of the C0 2 l a s e r . The scattering observations and r e s u l t s are presented i n Chapter 6. Complications i n the technique, a r i s i n g from the high plasma d e n s i t y , are also pointed out. At the macroscopic l e v e l , holographic interferometry measures the index of r e f r a c t i o n , a bulk plasma property that i s related i n a simple way to the electron density. Some basic p r i n c i p l e s of t h i s technique are given i n Chapter 7, but the main c o n s i d e r a t i o n w i l l be f o r the e f f e c t s of r e -f r a c t i o n . The f i r s t portion of Chapter 8 describes the generation of short d u r a t i o n d i a g n o s t i c p u l s e s through c a v i t y dumping of the r u b y l a s e r o s c i l l a t o r . This e f f o r t advances the diagnostics towards time s c a l e s more - 3 -appropriate to the i n t e r a c t i o n studies. The remainder of Chapter 8 com-pletes the presentation of the experimental arrangement for interferometry. A few i n t e r f e r eg rams are shown i n Chapter 9 along with the f i n a l data. The interferometry has given a f u l l view, both temporally and s p a t i a l l y , of the electron density d i s t r i b u t i o n i n the pinched plasma column. In d i v i d u a l l y , each of the diagnostic experiments i s i n s u f f i c i e n t to g i v e a complete picture of the high temperature, high d e n s i t y phase of t h i s Z-pinch plasma. Together though, t h i s series of experiments has been well-suited to providing complementary and c o r r o b o r a t i v e measurements of the plasma p r o p e r t i e s . I t has been found t h a t the p i n c h phase of t h i s discharge produces a plasma which ( i ) varies i n electron density from n e << 1 0 ^ 8 cm - 3 to n e = 6 x 1 0 ^ cm - 3, ( i i ) reaches a maximum temperature T = 50 eV, and ( i i i ) i s contained i n a c y l i n d r i c a l volume that ranges i n diameter from a few millimeters to less than one millimeter. The plasma parameters do not change s i g n i f i c a n t l y on a time s c a l e of a few nanoseconds. The d i f f e r e n t diagnostic methods agree, i n the case of o v e r l a p , to t y p i c a l l y within 40% while s h o t - t o - s h o t v a r i a t i o n s i n the e x p e r i m e n t a l data are t y p i c a l l y less than 2 0 % . Hence, t h i s t h e s i s shows t h a t the Z-pinch i s a very suitable target plasma for C 0 2 laser-plasma i n t e r a c t i o n experiments since the C O 2 laser finds already a f u l l y ionized plasma with well esta-blished c h a r a c t e r i s t i c s . The f i n a l chapter of t h i s thesis presents a b r i e f summary of the important features of both the plasma, and the diagnostic experiments. As well, some consideration w i l l be given to the a p p l i c a t i o n of these methods i n the i n t e r a c t i o n studies. - 4 -CHAPTER 2 THE Z-PINCH APPARATUS The Z-pinch discharge used throughout the investigations presented i n t h i s report i s a constant and major component of the i n t e r a c t i o n experi-ments. This chapter i s not intended to provide a complete a n a l y s i s of the Z-pinch, but rather to review established c h a r a c t e r i s t i c s (Houtman, 1977) and provide a background f o r the remainder of t h i s work. In order to supplement the following discussions, Table I g i v e s the b a s i c parameters and operating conditions of the discharge while the photograph of F i g u r e 1 shows the apparatus which has been assembled for i n t e r a c t i o n and diagnostic experiments. The discharge chamber i s constructed i n a c y l i n d r i c a l l y symmetric manner using a pyrex vacuum vessel 10.2 cm inside diameter. Electrodes are made from copper d i s c s of the same diameter and have an a x i a l separation of 35.6 cm. Brass wire mesh i s wrapped about the v e s s e l e x t e r i o r to form a co - a x i a l r e t u r n conductor. The d i s c h a r g e i s formed i n a c o n t i n u o u s l y flushed helium atmosphere that i s maintained at 1.2 torr pressure. The energy storage bank consists of six 14 uF capacitors which are charged i n p a r a l l e l to 11.5 kV. D i r e c t l y atop each c a p a c i t o r i s a spark gap switch. When these so-called 'main gaps' are triggered, the capacitors are discharged i n p a r a l l e l through the Z-pinch. Tn order to minimize the t o t a l inductance of the c i r c u i t , the current from each capacitor i s t r a n s -ported to the Z-pinch anode through 5, e l e c t r i c a l l y p a r a l l e l , 16 ohm high voltage transmission cables. There i s a t o t a l of 30 such cables, a l l these being of equal length. The discharge i s i n i t i a t e d i n the f o l l o w i n g manner. A 'master' spark gap i s used as the common element f o r seven separate t r i g g e r c i r -c u i t s . Six of the c i r c u i t s are i d e n t i c a l and these supply the t r i g g e r pulses for the s i x main spark gaps. The main gaps are triggered s i m u l t a n -eously. The Z-pinch anode receives the seventh t r i g g e r p u l s e , such t h a t , a t the same time the main gaps are triggered, a low density glow d i s c h a r g e - 5 -TABLE I BASIC PARAMETERS OF THE Z-PINCH DISCHARGE Vacuum vessel pyrex g l a s s , 10.2 cm I.D. 11.4 cm O.D. Electrode separation 35.6 cm F i l l i n g gas 1.2 torr Helium, 3.9 x 1 0 1 6 atoms per cm 3 @ 24°C Capacitor bank 84 uF Charging voltage 11.5 kV Ringing frequency 86 kHZ Available energy 5.6 k J Time of maximum compression 1.9 us Bank energy remaining @ 1.9 vs 2.7 kJ - 6 -ARM Fig ure 1 (A) Photograph of the Z-pinch apparatus. (B) A c r o s s - s e c t i o n a l view of the ports. f i l l s the chamber. This provides for pulsed p r e - i o n i z a t i o n of the plasma. Appendix A contains some a d d i t i o n a l d e t a i l s concerning the t r i g g e r c i r -c u i t r y and timing. With p r e - i o n i z a t i o n , the d i s c h a r g e can be i n i t i a t e d with a j i t t e r of less than 10 ns. The important point to be made here i s that p r e - i o n i z a t i o n of the plasma has been e s s e n t i a l f o r the c o o r d i n a t i o n of plasma and diagnostic events. A l l the diagnostic studies of th i s report have been performed i n the r a d i a l d i r e c t i o n with the c y l i n d e r a x i s o r i e n t e d h o r i z o n t a l l y (see Figures 1 and 3). Midway between the electrodes and diagonally opposing one another are two diagnostic ports. These ports were made by d r i l l i n g holes i n both the pyrex vessel and return conductor. Two more i d e n t i c a l holes are d r i l l e d i n the v e r t i c a l d i r e c t i o n for incident and transmitted CO2 laser l i g h t . The C0 2 laser beam i s also focused into the plasma i n the r a d i a l d i r e c t i o n , and, l i k e the diagnostic ports, midway between e l e c t r o d e s . In other words, the l i n e - o f - s i g h t through the diagnostic ports i s a horizontal diagonal of the discharge vessel while the CO^ laser beam w i l l t r a v e l along a v e r t i c a l diagonal of the vessel. These two diagonals are coplanar. The h o l e s t h a t were d r i l l e d through the v e s s e l and mesh a r e , res p e c t i v e l y , 1.9 cm and 3.7 cm i n diameter. The holes i n the brass mesh constitute only 10% of the t o t a l length of the plasma column whereas four such holes represent about 40% of the circumference of the r e t u r n conduc-tor. Note here that the access ports w i l l introduce p e r t u r b a t i o n s i n the plasma column. T h e r e f o r e , i n the v i c i n i t y of these h o l e s , r o t a t i o n a l symmetry of the plasma column i s not guaranteed. Two side-arms are h o r i z o n t a l l y mounted at the diagnostic ports and sealed to the vessel with o-rings (Figures 1 and 3). Windows and l e n s e s , etc., are mounted on the side-arm end pl a t e s . The C0 2 l a s e r beam enters the - 8 -discharge chamber v i a an L-shaped f o c u s s i n g channel. T h i s channel i s mounted on the d i s c h a r g e v e s s e l a t the top v e r t i c a l h o l e , as shown i n Figure 1. A 50 cm f o c a l length s a l t lens i s used as the air-vacuum i n t e r -face. A copper mirror, mounted inside the vacuum channel, steers the (con-verging) C O 2 laser beam into the discharge chamber. O p t i c a l components are removed from the immediate discharge v i c i n i t y and suffer only minor damage due to the d e p o s i t i o n of the d e b r i s t h a t i s generated during the d i s -charg e. The discharge current, I ( t ) was measured using a s m a l l Rogowski c o i l pick-up located i n a region near the anode where magnetic f i e l d s due to the discharge current could be sampled. The primary measurement here i s a changing magnetic flux inducing a c o i l c u r r e n t p r o p o r t i o n a l to d l / d t . Passive i n t e g r a t i o n provides d i r e c t oscilloscope d i s p l a y of the main d i s -charge current. A sample of the complete c u r r e n t t r a c e and an expanded portion of d l / d t are shown i n Figure 2 . Also, Figure 2 gives the capacitor voltage V c ( t ) as measured at one of the spark gaps. The voltage drop across the plasma column i t s e l f was not measured. Therefore, only charge drainage from the capacitor bank was determined. Passive elements i n the discharge c i r c u i t c o n t r o l early stages of the r i s i n g current pulse. As compression proceeds, the inductance of the plasma column i t s e l f increases and begins to dominate the c i r c u i t p a r a -meters. The reduction or dip i n current approximately 2 us after discharge i n i t i a t i o n , occurs at maximum compression. In the expanded d l / d t t r a c e , the current dip, and hence, the maximum compression or pinch phase, can be e a s i l y i d e n t i f i e d . Since t h i s moment of maximum compression i s c l e a r l y evident i n the d l / d t s i g n a l , the time at which d l / d t i s zero w i l l be used as the time reference for a l l diagnostics presented i n t h i s t h e s i s . - 9 -Vc 15 4. Figure 2 Voltage and current traces for the discharge c i r c u i t . - 10 -Characterization of the discharge dymanics and plasma c o n d i t i o n s began with the measurements of Houtman (1977). The experiments d e s c r i b e d therin included end-on framing camera studies and electron temperature and density determinations from s p e c t r a l l i n e broadening measurements. These experiments g i v e a complete and d e t a i l e d d e s c r i p t i o n of the collapse phase, i . e . times p r i o r to the dip i n c u r r e n t . Accurate measurement of plasma parameters and r a d i a l dynamics d u r i n g the h i g h compression phase were, unfortunately, not p o s s i b l e . Indications were that the pinched plasma had electron temperatures and d e n s i t i e s i n the range of 40 eV and 8.0 x 10 18 cm - 3 r e s p e c t i v e l y , with a minimum luminous radius of the order of 5 mm. These estimates represent a starting point for the present work i n which i t i s intended to extend measurements to time and size scales r e l e v a n t to the pinch phase of the discharge. - 11 -CHAPTER 3 STREAK AND SHADOWGRAM PHOTOGRAPHY 3.1 In t r eduction The experiments d e s c r i b e d i n t h i s c h a p t e r were i n t e n d e d to examine, i n as simple a way as possible, basic features of the plasma d i s -t r i b u t i o n during the time of maximum on-axis compression. This phase of the pinch has not been investigated with s u f f i c i e n t s p a t i a l or temporal r e s o l u -t i o n to observe d e t a i l s of either the plasma structure or motion. In t h i s respect, the present experiments are a s i g n i f i c a n t improvement and exten-sion of e a r l i e r work. The important parameter determined here i s the plasma r a d i u s as a function of time, r ( t ) , near the time of maximum compression. Changes i n the r a d i u s g i v e the v e l o c i t i e s v = d r / d t a s s o c i a t e d w i t h the plasma collapse and subsequent expansion. Because z-pinch plasmas are notoriously unstable to several magnetohydrodynamic perturbations (e.g.: see Artsimo-vich, 1964), the pinch phase can be expected to terminate i n some h i g h l y unstable manner. Irregular disrupt i o n of the plasma column has been c l e a r l y seen i n these measurements. This observation e s t a b l i s h e s the time during which the plasma i s s u f f i c i e n t l y well behaved to serve as a t a r g e t plasma for i n t e r a c t i o n studies. Two r e l a t i v e l y simple techniques are employed, streak and shadow-gram photography. Both of these depend on a high plasma density f or t h e i r a p p l i c a t i o n . The streak photographs g i v e an image of the plasma from s e l f -emitted r a d i a t i o n . Throughout the v i s i b l e region of the spectrum, a high temperature ionized gas produces e l e c t r o n - i o n bremsstrahlung r a d i a t i o n (Zel'dovich, 1966) with an i n t e n s i t y that i s only weakly dependent on the plasma temperature. However, because the i n t e n s i t y of the bremsstrahlung r a d i a t i o n depends on the frequency of electron-ion c o l l i s i o n s , the plasma emission c o e f f i c i e n t w i l l be proportional to the product of the e l e c t r o n ~ 12 " and ion number d e n s i t i e s , or, simply, n e^, n e being the electron density. Intensity v a r i a t i o n s i n the streak photographs w i l l t h e r e f o r e r e f l e c t the d i s t r i b u t i o n of electron density. For the shadow method, the plasma i s c o n s i d e r e d an e s s e n t i a l l y transparent object with the v a r i a t i o n i n electron d e n s i t y r e p l a c e d by i t s equivalent r e f r a c t i v e index d i s t r i b u t i o n . The plasma i s then i l l u m i n a t e d with a s p a t i a l l y uniform and c o l l i m a t e d beam of l i g h t . Upon passage through the plasma, portions of the beam are deflected from t h e i r o r i g i n a l path, the d e f l e c t i o n angle being proportional to the g r a d i e n t s i n r e f r a c -t i v e index that must be traversed (Barnard, 1975). Since the incident beam has an i n i t i a l l y uniform i n t e n s i t y d i s t r i b u t i o n , those regions of the plasma that are d e f l e c t i n g incident l i g h t w i l l show up a r e d u c t i o n i n the t r a n s -mitted beam i n t e n s i t y . In t h i s sense then, a photograph of the transmitted beam represents the plasma's shadow. From a more g e n e r a l p o i n t of view, the technique may be termed r e f r a c t i o n contrast imaging. The method i s of course quite s i m i l a r to the way i n which one can observe small bubbles or imperfections embedded in ordinary window panes. In keeping with the s i m p l i c i t y of these techniques, only the above b r i e f d e s c r i p t i o n of the methods has been given. With these d e s c r i p t i o n s , the experimental arrangement ( S e c t i o n 3.2) can be shown, and the b a s i c observations pertaining to the size and structure of the pinch phase can be interpreted. Then, i t w i l l be worthwhile to g i v e a b e t t e r i n d i c a t i o n of how the shadowgram method used here r e l a t e s to more g e n e r a l r e f r a c t i o n contrast imaging techniques. Following t h i s , numerical r e s u l t s are g i v e n for the plasma parameters obtained from this photographic study. S e c t i o n 3.4 uses the s t r e a k p i c t u r e s and a simple snow-plow model o f plasma collapse i n order to estimate the electron density. Section 3.5 c o n s i d e r s the shadowgrams i n more d e t a i l . In p a r t i c u l a r , some s t r u c t u r e i n the shadow images are the r e s u l t of interference e f f e c t s produced through the - 13 -use of a coherent probe beam. Such i n t e r f e r e n c e e f f e c t s have led to a second, independent estimate of the electron density. I t w i l l be seen that the streak and shadow techniques are q u i t e complementary i n nature. Each can provide a c l o s e look at plasma motion during the p i n c h phase. As w e l l , they both g i v e an i n d i c a t i o n of the s p a t i a l d i s t r i b u t i o n of electron density. Though the i n f o r m a t i o n i n t h i s regard i s more q u a l i t a t i v e i n nature, these experiments have g i v e n f a i r l y reasonable estimates of the electron density. 3.2 Experimental Method The experimental arrangement for both techniques can be d e s c r i b e d with the aid of Figure 3. For shadowgrams, the beam of a Q-switched ruby i laser (500 mJ i n 20 ns) i s passed through a x10 expander and s p a t i a l f i l t e r combination to produce a collimated beam approximately 8 cm i n diameter. Only the ce n t r a l 2 cm portion of the expanded beam i s used to i l l u m i n a t e the plasma, thus providing for a s t r i c t l y uniform i n t e n s i t y d i s t r i b u t i o n i n the incident beam. The transmitted beam i s observed i n a plane which i s located some distance beyond the plasma, e.g., i n the o b j e c t plane i n d i -cated i n Figure 3. The plasma shadow, as i t appears i n the o b j e c t plane, i s then imaged onto polaroid f i l m using lens L. A cardboard box p r o t e c t s the f i l m from ambient exposure. D i r e c t plasma l i g h t i s reduced to n e g l i g i -ble l e v e l s by imaging through a Kodak g e l a t i n f i l t e r (#92) which cuts out o a l l l i g h t with wavelengths below about 6400 A. A d d i t i o n a l l y , g e l a t i n neutral density f i l t e r s were used to adjust' the exposure due to the ruby la s e r . In obtaining the shadow p i c t u r e s , the d i s t a n c e from the plasma axis to the image plane was held f i x e d . However, the d i s t a n c e from the plasma to the object plane could be varied by changing the p o s i t i o n of lens L (Figure 3). By observing the plasma shadow i n d i f f e r e n t o b j e c t p l a n e s , - 14 -r 1 image plane , gelatin filters feE3 -7-polaroid vacuum side-arm with entrance window ruby laser object plane plasma or Figure 3 Schematic of the shadowgram experiment, o b j e c t planes l e s s than 43 cm from the plasma are c o n t a i n e d w i t h i n the vaccun vessel. The distance from plasma to image plane i s approximately 350 cm. - 15 -some d i s c r i m i n a t i o n can be made between those regions of the plasma that are responsible for either large or small angular d e f l e c t i o n s . For example, when the object plane i s located c l o s e to the plasma a x i s , the i n c i d e n t rays that suffer only small d e f l e c t i o n s w i l l not have diverged s u f f i c i e n t l y to contribute to the image contrast. In t h i s case then, the s i z e of the shadow w i l l r e f l e c t the extent of the s t r o n g l y r e f r a c t i n g r e g i o n s of the plasma. On the other hand, i f the shadow i s observed i n very d i s t a n t object planes, the weakly r e f r a c t i n g regions w i l l also become apparent. Samples of the plasma shadow seen i n d i f f e r e n t o b j e c t planes w i l l be presented s h o r t l y . Streak photographs have been obtained i n a more s t r a i g h t forward manner. Returning to Figure 3, i n order to take streak p i c t u r e s , the ruby laser i s not used, g e l a t i n f i l t e r s are removed, and a 4 mm wide v e r t i c a l s l i t replaces the polaroid f i l m . The schematic lens L (now a four element system of imaging and image t r a n s p o r t l e n s e s ) i s arranged to image the plasma axis h o r i z o n t a l l y across the s l i t with a t o t a l magnification of x7. Plasma l i g h t transmitted through the s l i t i s viewed using a TRW model 1D image converter camera. The camera records a streaked image of the plasma on polaroid f i l m . The picture thus obtained gives a radius vs time p l o t of the plasma s e l f - l u m i n o s i t y . 3.3 Streak and Shadowgram Pictures This section gives a f u l l view of the pinch phase from photographs obtained with both streak and shadow techniques. The d e s c r i p t i o n here i s q u a l i t a t i v e , but serves to i l l u s t r a t e basic features of the p i n c h as w e l l as the correspondence between the two methods. Section 3.4 g i v e s measure-ments of the plasma diameter and shows t h a t t h i s correspondence can be quite good. - 16 -Figure 4 presents a composite of the observed streak photographs. Each of the three frames shown were obtained from separate f i r i n g s of the discharge. Between shots, the exposure window of the s t r e a k camera was translated with respect to the pinch time. As a reminder, the time axis i s referenced to the zero-crossing of d l / d t , as indicated i n Figure 2, so that d l / d t = 0 at time t = 0. The bright v e r t i c a l l i n e at the beginning of each frame i s an overexposed image of the s l i t . ( T h i s image r e s u l t s from a 'hesitation' i n the ramp voltage that i s applied to the d e f l e c t i o n p l a t e s of the image c o n v e r t e r tube.) Based on the s l i t image, i t i s easy to determine that the temporal r e s o l u t i o n i s approximately 5 ns. At early times t < -100 ns a d i f f u s e and weakly luminous plasma s h e l l can be seen moving r a d i a l l y inwards. Incoming plasma converging on axis i s compressed, and the bremsstrahlung emission increases s i g n i f i c a n t -l y , beginning at about t = -80 ns. The on-axis plasma therefore has a much higher density than the surrounding s h e l l . The high i n t e n s i t y ( i . e . high density) region continuously grows i n diameter as plasma accumulates on a x i s . Later than approximately t = +100 ns, the c l a r i t y and symmetry of the plasma boundary d e t e r i o r a t e s . T h i s i s presumed to correspond to a d i s r u p t i o n of the plasma column due to i n s t a b i l i t i e s . The features of the pinch phase mentioned above, namely, ( i ) an e a r l y time, incoming s h e l l , ( i i ) a high d e n s i t y plasma core on a x i s , surrounded by a low d e n s i t y r e g i o n , and, ( i i i ) break-up of the plasma column, can also be c l e a r l y seen i n the shadowgram p i c t u r e s . Figure 5 presents a sampling of some t y p i c a l shadowgram p i c t u r e s that were recorded. The c i r c l e of exposure i s a p r o j e c t i o n of the p i n c h vessel holes. These holes have a diameter of 1.9 cm and serve as a r e f e r -ence for image magnification. A l s o i n F i g u r e 5, the Z-axis of the d i s -charge chamber i s shown. Now, the plasma can be viewed i n both the r a d i a l and a x i a l d i r e c t i o n s , and, i n a l l the p i c t u r e s of F i g u r e 5, the plasma appears well aligned on the geometrical axis of the discharge vessel. " 17 ~ -300 -200 -100 0 +100 +200 Time [ns] Figure 4 Streak photographs of the p i n c h phase. Each frame spans a 200 ns time i n t e r v a l . - 18 -Fig ure 5 Shadowgram pi c t u r e s . The exposure time and d i s t a n c e from plasma to object plane are: (A) -70 ns, 32 cm; (B) +110 ns, 7 cm; (C) -20 ns, 32 cm; and (D) -30 ns, 7 cm. The outer boundary of the plasma i s , for example, indicated by the arrow i n picture (A). The exposure of Figure 5(A) was taken at time t = -70 ns, j u s t as the incoming plasma reaches the axis (see Figure 4 ) . s i n c e the plasma i s only weakly r e f r a c t i n g at these times, a large plasma to object plane d i s -tance of 32 cm was usea i n order to o b t a i n good c o n t r a s t i n the image structure. While testing the o p t i c s , various index of r e f r a c t i o n d i s t r i b u -tions were photographed, including a g l a s s rod or tube, a gas stream, etc. The br i g h t on-axis exposure of Figure 5(A) i s i n d i c a t i v e of an object whose r e f r a c t i v e index decreases with i n c r e a s i n g r a d i u s . Consequently, the on-axis plasma must have a lower e l e c t r o n d e n s i t y than the immediate surroundings. As well, the outermost boundary of the refracting region can be seen. Figure 5(A) therefore does confirm t h a t incoming plasma has a d i f f u s e though d e f i n i t e s h e l l structure. Late times are shown i n a somewhat lucky photograph, Figure 5 ( B ) . The exposure was taken at t = +110 ns and the o b j e c t plane i s 7 cm o f f ax i s . This photograph dis t i n g u i s h e s quite dramatically between the plasma structure before and after the pinch column has broken up. Development of the high density plasma core i s i l l u s t r a t e d i n the shadowgrams of Figures 5(C) and (D). These pictures were taken a t almost i d e n t i c a l times (t = -20 ns and -30 ns r e s p e c t i v e l y ) , though i n d i f f e r e n t object planes (32 cm and 7 cm r e s p e c t i v e l y ) . The dark column of F i g u r e 5(D) i s produced by rays d e f l e c t e d from the c e n t r a l dense plasma c o r e . Small ray d e f l e c t i o n s become apparent i n a much more d i s t a n t o b j e c t plane, Figure 5(C) where the shadow diameter corresponds i n size to the surround-ing low density plasma. Having had a look at the plasma shadow i n o f f - a x i s image p l a n e s , i t i s worthwhile here to indi c a t e how the pictures appear when the plasma axis i t s e l f i s imaged. Doing t h i s w i l l lead to a basic d i s t i n c t i o n between the shadow method used here and the usual, and possibly more fam i l i a r tech-nique of Schlieren photography. However, the following discussion does not - 20 -presume to replace the expert analysis of the s u b t l e t i e s of r e f r a c t i o n contrast imaging, i . e . : Holder, 1 9 6 3 . If the plasma axis and object plane are coincident (see Figure 3 or 6 ( A ) ) , the shadowgrams show a n o t i c e a b l e though very weak v a r i a t i o n i n exposure due to rays missing the f i r s t c o l l e c t i o n l e n s . T h i s lens views the pinch axis with an F/# of 1 4 implying a maximum d e f l e c t i o n angle of 2 . 2 ° . When imaging the plasma a x i s , exposure v a r i a t i o n s occur mainly within 50 ns of maximum compression and appear j u s t inside the boundary of the high density core where density gradients, and hence ray d e f l e c t i o n s , are l a r g e s t . Now, when plasma i s not present, the photographs of Figure 5 would of course be uniformly exposed f o r a l l o b j e c t planes s i n c e the i n c i d e n t i l l u m i n a t i o n i s uniform. If plasma i s present, and the object plane c o i n -cides with the plasma a x i s , the f i l m would again be u n i f o r m l y exposed. T h i s l a t t e r case r e q u i r e s t h a t two c o n d i t i o n s be f u l f i l l e d . ( i ) The imaging optics must have a s u f f i c i e n t l y small F/# to c o l l e c t a l l r e f r a c t e d l i g h t , and, ( i i ) the r e f r a c t e d rays do not d i v e r g e a p p r e c i a b l y w i t h i n distances comparable to the plasma r a d i u s . F i g u r e 6 and the f o l l o w i n g d i s c u s s i o n w i l l help to i l l u s t r a t e the d i f f e r e n c e between c o n d i t i o n s ( i ) and ( i i ) . When condition (i) only i s not s a t i s f i e d , exposure v a r i a t i o n s are due p r i m a r i l y to v i g n e t t i n g by some aperture i n the imaging system. Figure 6 ( A ) shows such a s i t u a t i o n where a l l rays d e f l e c t e d by more than some minimum angle are l o s t at the imaging len s T h i s corresponds to Schlieren photography where the o b j e c t i t s e l f i s imaged and l i m i t e d F/# viewing replaces the r o l e of a k n i f e edge or g r i d , e t c . , i n e l i m i n a t i n g s p e c i f i c angular d e f l e c t i o n s . In turn, /the d e f l e c t i o n angles are d e t e r -mined by the r e f r a c t i v e index g r a d i e n t s t h a t are t r a v e r s e d . T h e r e f o r e , Schlieren systems are s e n s i t i v e to Vu, U being the r e f r a c t i v e index. ~ 21 " object plane imagei plane object plane Fig ure 6 Formation of c o n t r a s t i n on-axis images. R e f r a c t e d rays can be (A) vignetted and/or (B) divergent. - 22 -In contrast, when a l l refracted l i g h t i s c o l l e c t e d , but c o n d i t i o n ( i i ) above i s not s a t i s f i e d , then exposure v a r i a t i o n s w i l l occur when r e f r a c t i o n produces a l o c a l spreading or divergence of the i n c i d e n t l i g h t . Figure 6(B) depicts a uniform i n t e n s i t y incident beam as a s e t of e q u a l l y spaced ray paths. In the object plane, the rays are c l e a r l y not e q u a l l y spaced. In t h i s case then, a non-uniform d e f l e c t i o n angle, that i s , V 2y determines the image structure. The shadow method i s not r e s t r i c t e d to image planes containing the r e f r a c t i n g object. In f a c t , the object (plasma) boundaries are more w e l l defined i n the shadow when o f f - a x i s planes are imaged. The shadow (as opposed to Schlieren) method has been appropriate here since i t was intend-ed to e s t a b l i s h the plasma dimensions during the pinch phase. 3.4 The Plasma Diameter vs Time In order to quantify the observations of this photographic study, two p l o t s of the plasma diameter D(t) are given i n t h i s section. The streak and shadowgram pictures have been analyzed separately. Comparison of the r e s u l t s w i l l show the close correspondence between the information obtained with e i t h e r technique. As well, based on these p l o t s , a simple estimate of the electron density at maximum compression i s given. Figure 7(A) gives the data obtained from eight streak frames. The diameter of the high density core, denoted by crosses, was c l e a r l y marked i n the photographs. The outer boundary of the s h e l l , shown as d o t s , was not so well defined and was estimated to be j u s t at the outer edges of the weakly luminous regions. V e l o c i t i e s a s s o c i a t e d with the s h e l l and core were determined for each frame, independent of the diameter measurements since measurement of the speed w i l l not depend on l o c a t i n g the boundaries p r e c i s e l y . The s o l i d l i n e s i n Figure 7 have slopes given by: - 23 -dD/dt ( s h e l l ) = -1.97 ± 0.27 x 10 6 cm s _ 1 dD/dt (core) = +2.14 + 0.11 x 10 6 cm s _ 1 and were positioned on the p l o t to g i v e the best v i s u a l f i t to the data points. Measurements made on approximately t h i r t y shadowgrams r e s u l t e d i n the p l o t of Figure 7(B). As i n d i c a t e d p r e v i o u s l y (see F i g u r e s 5(C) and 5(D)), shadow pictures taken with the image plane 7 cm o f f - a x i s i s o l a t e the highly r e f r a c t i n g core while p i c t u r e s i n the 32 cm plane d e l i n e a t e the region occupied by low d e n s i t y plasma. Diameters are taken to be the ( r a d i a l ) extent of the unexposed r e g i o n s , though, s i n c e the diameter i s s l i g h t l y z-dependent, some v i s u a l averaging was done. Because of t h i s averaging, the core and s h e l l diameters are estimated to be u n c e r t a i n to +_ 0.3 mm and + 0.5 MI r e s p e c t i v e l y . . Comparison of these two p l o t s i s to be made on the b a s i s of the s o l i d l i n e s . Those drawn on Figure 7(A) have been transferred e x a c t l y , i n p o s i t i o n and slope, to Figure 7 ( B). The l i n e s were determined from the streak measurements only, but are judged to f i t both s e t s of data e q u a l l y well. Given the s i z e of the plasma, the e l e c t r o n d e n s i t y can be e s t i -mated using a 'snow-plow' model of the z-pinch ( L e o n t o v i c h , 1957). One assumption of t h i s model i s that a l l gas c o n t a i n e d w i t h i n the d i s c h a r g e vessel i s swept-up and c o n f i n e d to a c y l i n d e r having a r a d i u s r which decreases as c o n s t r i c t i o n proceeds. The plasma density therefore increases i n d i r e c t proportion to the volumetric compression r a t i o . This assumption i s quite good and has often been used as a c r o s s - c h e c k f o r other d e n s i t y d i a g n o s t i c s . With t o t a l sweep-up, the maximum density achieved w i l l occur when the plasma radius i s minimum. Figure 7 i n d i c a t e s that the minimum r a d i u s - 24 " -200 -100 0 *100 time (ns) Figure 7(A) Plasma diameter vs time from streak photographs. - 200 -100 0 -100 time (ns) Figure 7(B) Shadowgram r e s u l t s for the plasma diameter. - 25 -r m i s , at most, approximately 2.5 mm. The d i s t r i b u t i o n of plasma for r < r m w i l l be assumed uniform. If the average i o n i z a t i o n i s Z, then the electron density i s given simply by n e = Z n D ( R / r m ) 2 . [1] The i n i t i a l conditions p r i o r to f i r i n g the discharge are the inner radius of the vessel, R = 5.08 cm and f i l l density n Q = 3.90 x 1 0 1 6 helium atoms per cm 3 (see Table I ) . At the minimum radius, i o n i z a t i o n i s assumed complete, so Z = 2. With these numbers, equation [1] p r e d i c t s an average e l e c t r o n density of: n e = 3.2 x 1 0 1 9 cm - 3 at r m . This density i s considerably higher than the o r i g i n a l estimates of Houtman, but the minimum plasma r a d i u s was not w e l l e s t a b l i s h e d at t h a t time. The high density predicted by equation [1] i s f u l l y supported i n the next section where electron density estimates are made by an e n t i r e l y d i f f e r e n t method. 3.5 Electron Density from Ray Refraction Here, the shadowgrams are re-examined through an a n a l y s i s of r a y d e f l e c t i o n s . The r e s u l t w i l l be an estimate for the electron d e n s i t i e s i n - 26 -both the core plasma and surrounding low density region. F i r s t though, i n order to define the qu a n t i t i e s that need to be determined from the shadow pic t u r e s , ray bending i n a c y l i n d r i c a l l y symmetric r e f r a c t i v e index d i s t r i -bution i s considered. The electron d e n s i t y d i s t r i b u t i o n i n the plasma i s assumed to (. depend only on the r a d i a l coordinate r and i s replaced everywhere by i t s equivalent r e f r a c t i v e index: y ( r ) = ( 1 - n e / n C ) V 2 . R [ 2 ] The r e f r a c t i v e index depends on the wavelength of the probe beam through n c, the c r i t i c a l or cut-off density. At ruby laser wavelengths n c = 2.3 x l O ^ cm~3. The plasma i s confined to be within a cylinder of radius r Q , outside of which, V = u = 1 . o The probe beam i s collimated and travels p a r a l l e l to the x - a x i s . Figure 8 depicts the path of one ray, incident on the plasma at h e i g h t y. In c y l i n d r i c a l c o o r d i n a t e s , the ray t r a j e c t o r y w i l l be g o v e r n e d by Bouguer's formula (Born, 1975) where the so-called impact parameter i s p = u y = y. - 27 -f y Figure 8 Ray path i n an axisymmetric plasma. - 28 -When r > r Q , the ray w i l l t r a v e l a s t r a i g h t l i n e path since the r e f r a c t i v e index i s constant. Within the object (plasma) the ray w i l l be deflected from i t s o r i g i n a l path. I f n e decreases with increasing r, then the path w i l l be as indicated i n Figure 8. Upon e x i t i n g the plasma, the ray w i l l have suffered a net angular deviation ty. Using equation [ 3 ] , i t i s easy to see that: 0 0 aKy) = TT-2/(d8/dr)dr , [4] T S where r g i s the stationary point, determined from Bouger's formula as the radius for which d r / d t = 0. P a r e n t h e t i c a l l y , i t should be noted t h a t equation [3] should begin with a +/- sign to c l a r i f y the f a c t t h a t dr/d6 changes sign at r s . The quantity that can be d i r e c t l y measured with shadow or Schlieren methods i s the angular d e f l e c t i o n determined by equation [4]. Given an object with a s p e c i f i e d r e f r a c t i v e index d i s t r i b u t i o n , enables one to ca l c u l a t e a d e f l e c t i o n curve ijj(y) t h a t w i l l c h a r a c t e r i z e the d i s t r i b u t i o n . C o n v e r s e l y , by knowing ty(y) , u(r) can be found. Completely s p e c i f y i n g u(r) r e q u i r e s t h a t the impact p a r a m e t e r (s) y corresponding to each v a l u e of ty be measured. E x p e r i m e n t a l l y , t h i s demands a considerably more sophisticated arrangement (e.g.: K o g e l s c h a t z , 1972) than the c u r r e n t shadowgram experiments. However, the shadow pictures a v a i l a b l e have allowed e x t r a c t i o n of a u s e f u l , though somewhat crude d e f l e c t i o n curve. The important information to be obtained from the d e f l e c t i o n curve i s the maximum dev i a t i o n angle \b as shown i n the curve of F i g u r e 8. - 29 -Shmoys (1961) and Keilmann (1972) have performed d e t a i l e d c a l c u l a t i o n s of i|;(y) using a v a r i e t y of f u n c t i o n a l forms f o r the plasma d i s t r i b u t i o n n e ( r ) . The functions chosen for n e ( r ) are a l l well behaved. The density i s maximum on axis and decays monotonically to zero at r Q . There were no sharp d i s c o n t i n u i t i e s i n either n e ( r ) or dn e/dr. A l l of their d e f l e c t i o n curves, though d i f f e r e n t i n d e t a i l , could be approximated by a s i n g l e curve, the form of which i s indicated i n Figure 8. The r e s u l t s of Shmoys and K e i l -mann1 s c a l c u l a t i o n s are that, to within an uncertainty of about 35%, *max " U 0 n e C r = °) / n c ' [ 5 ] Equation [5] w i l l be used to obtain the desired electron density estimates. The following considerations i l l u s t r a t e how the shadowgrams were analyzed. C e r t a i n l y some bounds can be put on the d e f l e c t i o n angle j u s t from a knowledge of the shadow radius i n a given object plane. For example, at about t = +30 ns, the high density core has a shadow radius of 1.6 mm i n an object plane 7 cm from the plasma. Therefore, i t should be safe to say that the maximum d e f l e c t i o n angle i s at l e a s t 23 mrad and occurs for an impact parameter no greater than 1.6 mm. S i m i l a r l y , observations i n both the 7 cm and 32 cm plane p l a c e bounds on the d e f l e c t i o n angle for rays passing through the low density s h e l l region. A second way used to obtain d e f l e c t i o n angle data depends on the f a c t that the probe beam i s coherent. Returning to the shadow photographs themselves, p a r t i c u l a r l y Figure 5(C), i t i s clear that the image s t r u c t u r e near the plasma boundary i s dominated by a number of well defined f r i n g e s . These fringes r e s u l t from the interference between undeviated rays passing - 30 -outside the plasma boundary, and r e f r a c t e d rays which pass thorugh the edges of the plasma. Notice also that the f r i n g e spacing decreases with increasing distance from the axis i n d i c a t i n g t h a t the r e f r a c t e d rays are being deflected by uniformly increasing angles. Given, as i n Figure 8, the t y p i c a l form of a d e f l e c t i o n curve, the above i n t e r p r e t a t i o n of fringes i s considered s u b s t a n t i a l l y c o r r e c t . In order to obtain data points for the d e f l e c t i o n curve, the d i s t a n c e d bet-ween adjacent interference minima i s measured. This g i v e s the d e f l e c t i o n angle: ty = s i n " 1 (X/d) a X/d associated with the ray producing a p a r t i c u l a r f r i n g e . R e f e r r i n g to the coordinate system of Figure 8, the object plane w i l l be l o c a t e d at a d i s -tance x = 1 from the plasma. In the object p l a n e , the f r i n g e appears at height y'. With t h i s (measured) i n f o r m a t i o n , e x t r a p o l a t i o n back to the y-axis gives the impact parameter: y = y' of the ray deflected by ty . Using the above arguments, shadowgrams taken a t t = +30 ns were analyzed. The time chosen for t h i s e x e r c i s e corresponds to the minimum radius of collapse. The r e s u l t i n g d e f l e c t i o n curve i s shown i n F i g u r e 9. The data points were determined by fringe analysis of shadowgrams recorded i n object planes 32 cm ( c i r c l e s ) and 7 cm (squares) from the plasma. The maximum d e f l e c t i o n angle for the core and s h e l l components of the plasma should be contained r e s p e c t i v e l y w i t h i n the upper and lower r e c t a n g u l a r regions. These bounds were determined simply from the shadow diameters i n the two object planes. - 31 -30 0 1 2 3 y (mm) Figure 9 D e f l e c t i o n curve for the plasma at maximum compression. - 32 -Because the data i s rather sketchy, c r i t i c a l examination of the shape of the d e f l e c t i o n curve would be u n j u s t i f i e d . The s o l i d l i n e i n Figure 9 has been included only to represent a p l a u s i b l e f i t to the data. Since i t i s clear that the pinched plasma has a d e f i n i t e two com-ponent structure, i t i s not hard to imagine that Figure 9 can be composed by the superposition of two s i m i l a r d e f l e c t i o n curves, each scaling d i f f e r -e n tly i n radius and height. Both curves, and therefore both components of the plasma, can be characterized by e q u a t i o n [ 5 ] , Taking i f o r the max s h e l l and core plasmas as 5 mrad and 25 mrad re s p e c t i v e l y , and n c for ruby laser l i g h t , g i v e s : n e ( s h e l l ) = 1.1 x 1 0 1 9 cm - 3 n e (core) = 6.0 x 1 0 1 9 cm - 3 Even with the p e s s i m i s t i c view of an uncertainty of a factor of two, these figures agree well with the average density estimated from equation [ 1 ] , based on a snow plow model of plasma compression. 3.6 Conclusion to the Photographic Study The experiments that have been presented i n t h i s chapter were i n -tended to g i v e a closer view of the plasma pinch phase than had p r e v i o u s l y been obtained by Houtman. This has been done using photographic techniques that have been ( i ) r e l a t i v e l y simple to implement, ( i i ) p a r t i c u l a r l y a p p l i -cable to plasmas of high electron density, and ( i i i ) capable of p r o v i d i n g adequate s p a t i a l and temporal r e s o l u t i o n . Primary aspects of the plasma dynamics and evolution of the e l e c -tron density structure have been determined by measuring the plasma d i a -meter as a function of time. Estimates f o r the e l e c t r o n d e n s i t y during - 33 -maximum compression have been made with r e a s o n a b l e a c c u r a c y . The peak plasma d e n s i t i e s achieved are well i n excess of the c r i t i c a l d e n s i t y f o r C0 2 laser l i g h t , namely, 1.0 x 1 0 1 9 cm - 3. i n this respect then, the pinch phase i s quite suitable for laser-plasma i n t e r a c t i o n experiments. Q u a l i t a -t i v e l y , the density structure during c o l l a p s e i s smooth and w e l l behaved for approximately 200 ns, aft e r which, the pinched column breaks up i n an i r r e g u l a r and unpredictable manner. This concludes the i n i t i a l observations of the p i n c h phase. The photographic study represents an important e x t e n s i o n of e a r l i e r work and w i l l prove v i t a l to the i n t e r p r e t a t i o n of subsequent experiments. The following few chapters constitute the second portion of this work, namely, accurate determination of the plasma d e n s i t y and temperature during the pinch phase using Thomson scattering of ruby laser l i g h t . - 34 -CHAPTER 4 ELEMENTS OF THOMSON SCATTERING 4.1 Introduction Thomson scattering by plasma f l u c t u a t i o n s i s a very common method for measuring temperature and density. Several good reviews of the subject have been published (Kunze, 1968; Evans, 1969; D e S i l v a , 1970) and these g i v e a complete d e s c r i p t i o n of the theory and t e c h n i q u e s o f Thomson s c a t t e r i n g . The analysis presented i n these reviews has remained r e l a t i v e l y unchanged to the present time. T h i s chapter w i l l not attempt d e t a i l e d derivations pertaining to the theory of electromagnetic wave s c a t t e r i n g i n plasmas. However, r e s u l t s of the theory w i l l be used to d e f i n e the b a s i c aspects and parameters of Thomson s c a t t e r i n g t h a t are important f o r the current Z-pinch diagnostics. In plasmas, the Coulomb forces acting between p a r t i c l e s a l l o w f o r a wide v a r i e t y of wave phenomenon. As a consequence, the frequency or wavelength spectrum of l i g h t scattered from plasma p a r t i c l e f l uctuations i s r i c h i n structure and d e t a i l . Although only scattering from e l e c t r o n s i s s i g n i f i c a n t , strong Coulomb coupling between electrons and ions can r e s u l t i n s c a t t e r i n g which i s dominated by, and c h a r a c t e r i s t i c o f , the i o n d i s t r i b u t i o n . The f i r s t section of this chapter discusses the d i s t i n c t i o n bet-ween the so-called electron and ion features of the spectrum of s c a t t e r e d l i g h t . Separation of the t o t a l spectrum i n t o two d i s t i n c t components stems from the two basic types of f l u c t u a t i o n s t h a t occur i n plasmas, namely, ele c t r o n plasma waves and ion acoustic waves. The usual Thomson scattering method examines the electron feature. However, i n the experiments to be presented, only the ion component of the spectrum i s observed. A p p l i c a t i o n of Thomson scattering to the c u r r e n t i n v e s t i g a t i o n i s t h e r e f o r e , q u i t e - 35 -u n c o n v e n t i o n a l i n the sense t h a t d e t a i l s of the i o n f e a t u r e a r e not normally observed or even considered for routine diagnostic purposes. The second portion of t h i s chapter w i l l demonstrate t h a t the i o n f e a t u r e i s p a r t i c u l a r l y u s e f u l f o r determining plasma p a r a m e t e r s i n moderately hot, dense environments such as the c u r r e n t Z-pinch plasma. This conclusion w i l l r e s u l t from a comparison of the r e l a t i v e s p e c t r a l brightness of e l e c t r o n and i o n f e a t u r e s . The emphasis w i l l be on the a b i l i t y to d e t e c t s c a t t e r e d l i g h t over and above the l e v e l of plasma bremsstrahlung emmission. Background l i g h t l e v e l s w i l l increase with n g2 whereas the i n t e n s i t y of s c a t t e r e d l i g h t i n c r e a s e s o n l y l i n e a r l y with n e . At plasma d e n s i t i e s where the electron feature i s completely masked i n background l i g h t , the ion feature may be e a s i l y d e t e c t a b l e , and t h e r e f o r e represent an important extension of the u s e f u l n e s s of Thomson s c a t t e r i n g d i a g n o s t i c s . 4.2 D i s t i n c t i o n Between Electron and Ion Features The s p e c t r a l d i s t r i b u t i o n , t h a t i s , the i n t e n s i t y vs frequency dependence of l i g h t scattered from a plasma i s given by the so-called shape factor S(k, u ) . This function i s defined through the d i f f e r e n t i a l c r o s s -section per u n i t volume: & " V e S ( k » a ) ' Here, n e i s the average electron density. The scattering properties of a - 36 -single electron are contained i n the Thomson c r o s s - s e c t i o n , a . Though not e x p l i c i t l y shown, 0 a l s o c o n t a i n s the u s u a l angular dependence of e l e c t r i c dipole r a d i a t i o n . (By v i r t u e of i t s much larger mass, s c a t t e r i n g from ions i s neglected). The scattering properties of the whole system of interacting p a r t i c l e s i s described by S ( k , o j ) . C o n s e r v a t i o n of momentum determines the wavevector TT = k - k , with k,-. and k a being the wavevectors o s ° fa for incident and scattered l i g h t r e s p e c t i v e l y . Wavevector k s e l e c t s the s p a t i a l component of density f l u c t u a t i o n s which contribute to the scattered s i g n a l of the frequencies co = + | C0Q - C0s| (conservation of energy). The complete frequency and wavevector dependence of the scattering cross-section for plasmas has been calculated i n d e t a i l by several authors, (e.g. Salpeter, 1960; Salpeter, 1963 or Rosenbluth, 1962). Salpeter (1960) has shown that the shape factor S(k,to) may be w r i t t e n as the sum of two separate components, S(k,aO = Se(k,a>) + S i ( k , c o ) , [ 6 ] where the subscripts refer to the electron and ion features of the p r o f i l e . This separation emphasizes the two d i f f e r e n t types of plasma waves that may be investigated by scattering techniques. The following d e s c r i p t i o n w i l l i s o l a t e the basic d i f f e r e n c e between electrons which scatter into these two components of the spectrum, namely, the apparent electron i n e r t i a . The electron feature r e s u l t s from scattering off electron Langmuir waves. These are l o n g i t u d i n a l , e l e c t r o s t a t i c f l u c t u a t i o n s i n the d e n s i t y of electrons only. Perturbations i n the electron d e n s i t y which produce a charge separation w i l l set-up an e l e c t r i c f i e l d fiU and t h i s f i e l d provides the restoring force for o s c i l l a t i o n . Electrons of course, can respond very r a p i d l y to 6E compared with the r e l a t i v e l y massive ions. Ions can t h e r e -fore be considered immobile and the electron motion i s completely decoupled - 37 -from the background of p o s i t i v e ions (except in so far as the ions ensure e l e c t r i c a l n e u t r a l i t y over the plasma volume). Consequently, e l e c t r o n Langmuir f l u c t u a t i o n s are of the high frequency type and the e l e c t r o n feature cannot be expected to give information on the ion motions. The ion feature i s the r e s u l t of scattering from e l e c t r o n s which are t i e d (via Coulomb forces) to the i o n motions. The i n e r t i a of these electrons w i l l now be determined by the i o n mass so t h a t c h a r a c t e r i s t i c frequencies i n the ion feature are much lower than those f o r the e l e c t r o n feature. Ion acoustic f l u c t u a t i o n s , though analogous to the more f a m i l i a r low frequency sound waves, are a l s o e l e c t r o s t a t i c o s c i l l a t i o n s (Chen, 1974). In response to perturbations in the ion density, electrons attempt to preserve l o c a l e l e c t r i c a l n e u t r a l i t y by moving together with the i o n s . However, not a l l electrons contribute to neutralizing the e l e c t r i c f i e l d s produced by the ion disturbance. It i s the r e s i d u a l e l e c t r i c f i e l d t h a t maintains the ion o s c i l l a t i o n . The magnitude of the residual f i e l d depends on the number of high energy' electrons which do not p a r t i c i p a t e i n s h i e l d -ing , and, t h i s i n turn i s determined by the d i s t r i b u t i o n of e l e c t r o n v e l o -c i t i e s . Therefore, a f u l l d e s c r i p t i o n of the ion f e a t u r e w i l l c o n t a i n parameters of both electron and ion d i s t r i b u t i o n s . The basis of equation [6] for separating the spectrum of scattered l i g h t into electron and ion features i s , of course, the large d i s p a r i t y i n frequency s c a l e s which r e s u l t s from the d i f f e r e n c e i n the e l e c t r o n ' s apparent i n e r t i a . In a simple view of the electron term, the electrons can be considered uncorrelated. ( C l e a r l y , t h i s i s not the g e n e r a l case s i n c e c o r r e l a t i o n s are required for the existence of plasma waves. The c o n d i -tions under which c o r r e l a t i o n e f f e c t s can be ignored w i l l be presented s h o r t l y , when the spectra are described i n more d e t a i l ) . If the e l e c t r o n s are also randomly d i s t r i b u t e d i n space, the e l e c t r o n d e n s i t y w i l l have s p a t i a l f l u c t u a t i o n s t h a t are s t a t i s t i c a l l y i ndependent. Then, the - 38 -scattered i n t e n s i t y , at a given frequency s h i f t , w i l l be p r o p o r t i o n a l to the number of electrons that have a v e l o c i t y corresponding to t h i s Doppler s h i f t e d frequency. I f the e l e c t r o n v e l o c i t i e s a r e d e s c r i b e d by a Maxwellian d i s t r i b u t i o n , the s c a t t e r e d spectrum w i l l j u s t be a Gaussian p r o f i l e with a width determined by the mean thermal speed of electrons. In a very s i m i l a r way, the ions can be considered to behave i n d e p e n d e n t l y of one another. Those e l e c t r o n s t h a t c l o s e l y f o l l o w the i o n motions w i l l produce a scattered spectrum that r e f l e c t s the v e l o c i t y d i s t r i b u t i o n of the ions. Based on the simple d e s c r i p t i o n above, i t i s easy to see t h a t the electron and i o n f e a t u r e s w i l l have s p e c t r a l widths determined by the respective electron and ion thermal v e l o c i t i e s . The width of the e l e c t r o n feature w i l l therefore be larger than that of the ion component by a factor of the order of: v/v. = (m./m ~)h • e 1 v i ' eJ 2 [7] For example, v e / v i = 86 i n a f u l l y ionized equilibrium helium plasma. Such a large discrepency i n frequency scaling has serious consequences i n terms of experimental a p p l i c a t i o n . This w i l l be d i s c u s s e d f u r t h e r i n S e c t i o n 4.3. The simple estimate above p r e c l u d e s the p o s s i b i l i t y of d e n s i t y f l u c t u a t i o n s t h a t are produced by the c o l l e c t i v e e x c i t a t i o n of plasma waves. Nonetheless, i n spite of such complications, equation [7] remains a very reasonable r e p r e s e n t a t i o n of both the source and magnitude of the r e l a t i v e widths of electron and ion features. Figure 10 shows what a more t y p i c a l scattered spectrum might look l i k e . C e r t a i n l y t h i s spectrum cannot be d e s c r i b e d by a G aussian. The appearance of resonant structure i s quite evident. The remainder of t h i s - 39 --4—» "E >» t-O c lo *_ a x - 4 2 H 1 FIGURE 10 A ' t y p i c a l ' scattered spectrum. Frequency scales are normalized to e i t h e r the electron or ion thermal v e l o c i t i e s , x = »/kv^. Note the r e l a t i v e i n -t e n s i t y scales. - 40 -s e c t i o n w i l l d i s c u s s t h i s ' t y p i c a l ' spectrum i n d e t a i l . In order to i n i t i a t e t h i s discussion, the f r a c t i o n of the t o t a l amount of s c a t t e r e d l i g h t t h a t w i l l appear i n e i t h e r the e l e c t r o n or i o n f e a t u r e w i l l be written down. The d i s t r i b u t i o n of s c a t t e r e d l i g h t i s determined by the frequency integrated shape factors (Evans, 1969) S e ( k ) = /Se(k,£o)dco = O a 2 ) " 1 [8] s, oo ( l + a 2 ) [ l + a 2 ( l + Z T e / T . ) ] These are c a l c u l a t e d assuming the e l e c t r o n and i o n d i s t r i b u t i o n s are Maxwellian, but at d i f f e r e n t temperatures. The degree of i o n i z a t i o n i s Z. The most important parameter here, which determines the type of scattered spectrum observed i s the c o r r e l a t i o n or scattering parameter, a = CkA D)-> [ 9 ] This i s the r a t i o of two c h a r a c t e r i s t i c lengths. The d e n s i t y f l u c t u a t i o n which sc a t t e r s incident l i g h t has a wavelength X = 2ir/k and t h i s determines the distance over which p a r t i c l e c o r r e l a t i o n s w i l l be i n v e s t i g a t e d . In turn, X i s determined e n t i r e l y by the experimenter through c h o i c e of the wavelength of incident l i g h t , and arrangement of the s c a t t e r i n g geometry". The Debye shielding length for electrons, XD = ^o^/^V1"2 C m k s ) i s fixed by the plasma conditions, i . e . the electron temperature T e, and - 41 -density n e . The Debye length represents the distance over which a l o c a l perturbation i n the charge d e n s i t y can be e f f e c t i v e l y s h i e l d e d from the r e s t of the plasma by the a t t r a c t i o n (or r e p u l s i o n ) o f n e i g h b o u r i n g charges. In order to get some idea of how c o r r e l a t i o n e f f e c t s i n f l u e n c e the frequency spectrum of scattered l i g h t , consider f i r s t only the electron feature where the spectral shape i s completely determined by alpha. The simplest i l l u s t r a t i o n i s found i n the l i m i t a << 1 where in c i d e n t l i g h t i s scattered from density f l u c t u a t i o n s whose scalelength k - 1 i s much less than the Debye l e n g t h . Here, the long range nature of the Coulomb f i e l d i s not apparent. Of course, the p a r t i c l e s do i n t e r a c t v i a t h e i r e l e c t r i c f i e l d s . However, over distances small compared to the Debye length, the net e f f e c t of i n t e r a c t i o n s i s to produce a l o c a l l y random d i s -t r i b u t i o n of charges . The scattering i s the same as would be obtained from t o t a l l y independent electrons. Because the electrons behave independently i n t h i s l i m i t , the t o t a l scattered i n t e n s i t y i n the ion feature approaches zero, while S e(k) -»- 1 (see equations [8]). The t o t a l scattering cross-section becomes da/dfi = n a . The frequency spectrum w i l l be Gaussian i n shape corresponding to a Maxwellian d i s t r i b u t i o n of electron v e l o c i t i e s . This s i t u a t i o n was described e a r l i e r i n the discussion leading to e q u a t i o n [7]. Only T e, the electron temperature may be measured from the shape. In order to obtain n e , the t o t a l i n t e n s i t y of r a d i a t i o n scattered i n t o the detection system must be determined. ( C a l i b r a t i n g the s c a t t e r e d s i g n a l d i r e c t l y i n terms of electron density i s e a s i l y done by Rayleigh scattering from neutral gases. This procedure i s described i n the next chapter). - 42 -The long range nature of the Coulomb f o r c e becomes apparent as alpha approaches and exceeds unity. Then, the f l u c t u a t i o n s t h a t produce scattering have wavelengths the order of or g r e a t e r than a Debye l e n g t h . Scattering from these f l u c t u a t i o n s w i l l e x h i b i t the c o o p e r a t i v e behaviour of electrons and the spectra w i l l be determined by the p r o p e r t i e s of the plasma waves. The most dramatic example i s found i n the l i m i t of a >> 1 or k - 1 >> Xp. The electron feature consists of two narrow spik e s or s a t e l l i t e s centered about the ion l i n e and s h i f t e d by a frequency approximately equal to the electron plasma frequency, w p = ( e 2 n e / e 0 m e ^ • ( m k s ) [10] (Figure 10 shows the electron s a t e l l i t e s are reasonably well developed even at modest values of alpha)-. These long wavelength f l u c t u a t i o n s propagate with a large phase v e l o c i t y . The perturbation f i e l d 6E t a s s o c i a t e d with these f l u c t u a t i o n s , moves r a p i d l y through the plasma. Slow moving e l e c -trons see 6E as a high frequency f i e l d and do not have time to respond. However, electrons which are moving with the phase v e l o c i t y of the wave w i l l r e a d i l y p a r t i c i p a t e i n the o s c i l l a t i o n . Scattering off these f l u c t u a -tions w i l l r e s u l t i n Doppler s h i f t s corresponding to the phase v e l o c i t y of the wave. Thus, at large alpha, the f l u c t u a t i o n that produces s c a t t e r i n g i s a normal mode of e l e c t r o s t a t i c plasma o s c i l l a t i o n . The width of the e l e c -tron s a t e l l i t e s i s small compared to t h e i r frequency, a feature c h a r a c t e r -i s t i c of a natural o s c i l l a t i o n experiencing o n l y weak damping . L o c a t i n g these spikes w i l l g i v e an accurate measure of the e l e c t r o n d e n s i t y , but information on the electron temperature i s l o s t . However, the u s e f u l n e s s of the e l e c t r o n f e a t u r e f o r l a r g e alpha i s somewhat l i m i t e d s i n c e , as - 43 -equations [8] show very l i t t l e scattered l i g h t w i l l be contained i n these resonance l i n e s . The reason that the cross-section for scattering i n t o the electron feature decreases with increasing alpha can be understood as f o l l o w s . At large alpha, the phase v e l o c i t y of el e c t r o n plasma waves g r e a t l y exceeds the mean thermal speed of the electrons. Because of the nearly f r i c t i o n l e s s nature of the electron f l u i d , the f l u c t u a t i o n amplitude w i l l be determined by only those electrons with v e l o c i t i e s comparable to the phase v e l o c i t y of the wave. As alpha increases, the phase v e l o c i t y moves farther and farther i n t o the wings of the electron v e l o c i t y d i s t r i b u t i o n , so t h a t fewer and fewer electrons are able to p a r t i c i p a t e i n the o s c i l l a t i o n . An example of the s p e c t r a l shape corresponding to i n t e r m e d i a t e values of alpha, i . e . a ^ 1 i s shown i n Figure 10. The important aspect to note i s that the electron feature depends only on the parameters of the elec t r o n d i s t r i b u t i o n , n e and T e through a • The.shape of the ion feature i s also e n t i r e l y determined by a single parameter B , defined by: 32 - - S £ _ C Z T / T . ) . M i ] 1-HX2 6 Parameters of both electron and ion d i s t r i b u t i o n s are now present. S i m i l a r -i t y with the el e c t r o n f e a t u r e can be emphasized i f the Debye s h i e l d i n g length for ions i s defined, XD. = (e oKT./Ze 2n e)32 (inks). . This allows a d i s t i n c t i o n to be made between a = a * given i n equation [9], e and the corresponding parameter, - 44 -a. = a ( Z T e / T . ) % Then, the shape parameter $ for the ion l i n e becomes, B = a . ( l + c t 2 ) " % . When alpha i s small, 3 = i s also small and the ion l i n e has a s p e c t r a l shape which i s approximately Gaussian. The ions behave n e a r l y independent of one another so the s p e c t r a l width i s c h a r a c t e r i z e d by a Maxwellian d i s t r i b u t i o n of ion v e l o c i t i e s . Of course, a = o corresponds to scattering from t o t a l l y independent electrons and the i o n f e a t u r e d i s -appears, S^(k) = 0. However, the ion l i n e begins to be a s i g n i f i c a n t com-ponent of the spectrum as alpha exceeds a value of about 0.2. At large a , the l i m i t i n g value of 8 i s (Z T e / T i ) 1 / 2 . The sharp s a t e l l i t e s that appear i n the electron feature for a » 1 only develop i n the ion feature when Z T e / T i >> 1 (making B l a r g e ) . Ion acoustic f l u c t u a -tions are normally h e a v i l y damped o s c i l l a t i o n s and t h e r e f o r e produce a broad s c a t t e r e d spectrum, corresponding to modest values of beta (see Figure 10, for example). Under non-equilibrium plasma conditions (T e >> T^) ion waves are only weakly damped and d i s t i n c t i o n s a t e l l i t e s appear at Doppler s h i f t s determined by the ion acoustic speed, [12] C s - (ZKT/m.)!* . - 45 -When the ion feature does d e v e l o p a sharp resonance s t r u c t u r e , the i o n waves that produce the scattering have a phase v e l o c i t y C s which g r e a t l y exceeds the average thermal v e l o c i t y of the i o n s . As the phase v e l o c i t y moves farther i n t o the wings of the ion v e l o c i t y d i s t r i b u t i o n , there are fewer and fewer p a r t i c l e s contributing to the f l u c t u a t i o n amplitude. Hence, i n complete s i m i l a r i t y with the e l e c t r o n f e a t u r e , the s c a t t e r i n g c r o s s -section Sjjk) decreases with increasing beta when 3 >> 1. This implies not only large alpha, but also Z T e / T i >> 1. However, i n high density plasmas, ele c t r o n - i o n thermalization i s rapid and g e n e r a l l y , one would not expect extremely large deviations from equilibrium. If Z T e / T i < 20, equation [12] w i l l o n l y a p p r o x i m a t e l y l o c a t e the i o n resonance ( R o s e n b l u t h , 1 962; Barnard, 1980). The above d i s t i n c t i o n between electron and i o n f e a t u r e s has been ne c e s s a r i l y b r i e f . A d e t a i l e d d e s c r i p t i o n of the s u b t l e t i e s of Thomson scattering and plasma wave theory i s well beyond the scope of t h i s t h e s i s . In terms of experimental a p p l i c a t i o n , one important p o i n t to be e x t r a c t e d from the previous discussion i s contained i n equation [7] or equations [10] and [12], where the electron and ion mass determine the r e l a t i v e s p e c t r a l widths. This d i f f e r e n c e i s examined further i n the following section. 4.3 Advantage of the Ion Feature Since s c a t t e r e d l i g h t must be d e t e c t e d over the thermal s e l f -emission of the plasma, the major advantage of the ion feature i s i t s high s p e c t r a l brightness. That i s , the high scattered power per u n i t frequency i n t e r v a l . To compare the r e l a t i v e i n t e n s i t i e s of the two s p e c t r a l compon-- 46 -ents, the portion of scattered l i g h t appearing i n e i t h e r the e l e c t r o n or ion feature may be considered u n i f o r m l y d i s t r i b u t e d over the r e s p e c t i v e frequency i n t e r v a l s , Aco = g(ct)kv 6 [13] AO). = g(B)kv. . The factors g i n equations [13] have been introduced to allow for the f a c t that scattered l i g h t may be quite non-uniformly d i s t r i b u t e d . In p a r t i c u l a r , for large alpha or beta, sharply defined resonance structure can appear and g << 1 . At very small values of the s c a t t e r i n g parameter, the s p e c t r a l shape approaches a Gaussian f u n c t i o n , g(0) = l n 2, and equations [13] specify the hal f width at half maximum. As well, equations [13] s p e c i f y a common scattering vector k so th a t comparison w i l l be made for a g i v e n , though a r b i t r a r y , scattering geometry. The s p e c t r a l i n t e n s i t y of the ion feature, r e l a t i v e to the e l e c -tron feature can therefore be defined as: S.OOAu l e 1 = S (k)Ao>. e i Using equations [8] and the frequency i n t e r v a l s from equations [13] gives T _ g(oO j V i f Za" *<B> I Vet i + a 2 ( i + Z T n.) [ 1 4 ] e I - 47 -Equation [14] i s presented g r a p h i c a l l y i n F i g u r e 11 where the plasma has been assumed to be an equilibrium helium plasma: Z = 2, T e = T^. As alpha increases from zero, the f r a c t i o n of scattered l i g h t contained i n the ion l i n e i n c r e a s e s with alpha l i k e a1* . The two f e a t u r e s have comparable brightness ( I = 1) at a = 0.28. At a = 1, the ion l i n e i s 43 times brighter than the e l e c t r o n f e a t u r e . At l a r g e r a l p h a , the narrow electron resonance structure begins to appear and the spectral i n t e n s i t y of the electron feature increases. The width of the e l e c t r o n resonance i s determined by the amount of damping experienced by e l e c t r o n plasma waves. To evaluate equation [14] for l a r g e a l p h a , account must be made of both Landau damping and c o l l i s i o n a l damping contributions to the s p e c t r a l width (Evans, 1969). Landau or c o l l i s i o n l e s s damping decreases e x p o n e n t i a l l y with i n -creasing alpha and the s p e c t r a l i n t e n s i t y of the electron resonance corres-pondingly increases. However, the s p e c t r a l width cannot decrease i n d e f i n -i t e l y since, ultimately, the frequency of electron-electron c o l l i s i o n s w i l l determine the rate of energy d i s s i p a t i o n from the wave. C o l l i s i o n a l c o n t r i -butions to the s p e c t r a l width can be expressed i n terms of N = X sn > the D D e number of p a r t i c l e s i n a Debye cube. Equation 14 corresponds to the c o l l i -s i o n l e s s case, that i s , N D approaching i n f i n i t y . However, Figure 11 also i l l u s t r a t e s how N D a f f e c t s the r e l a t i v e brightness. The conclusion to be drawn from Figure 11 i s that the i o n l i n e i s indeed the most intense feature of the s c a t t e r e d spectrum over v i r t u a l l y the e n t i r e range of the scattering parameter alpha. Because of the ease of detection, the ion f e a t u r e f i n d s i t s most important a p p l i c a t i o n i n plasmas of r e l a t i v e l y high electron d e n s i t y where - 48 -100 -i i — i i i r 10 :ness e bright / i Ion Feature > ^ — *-> a / i Electron Feature 0.1 .1 i i i i 1 \ 1 2 4 6 alpha Figure 11 Comparative s p e c t r a l b r i g h t n e s s of e l e c t r o n and i o n features. A r e l a t i v e b r i g h t n e s s g r e a t e r than u n i t y i n d i c a t e s t h a t the s p e c t r a l b r i g h t n e s s o f the i o n f e a t u r e exceeds t h a t of the e l e c t r o n f e a t u r e (see equation 14). - 49 -bremsstrahlung emmission i s large. The c l a s s i c a l e x p r e s s i o n ( Z e l ' d o v i c h , 1966) for the s p e c t r a l brightness of electron-ion bremsstrahlung, J B has the dependence: n 2 J D « — exp(-hv/KT) . At o p t i c a l frequencies hv » 2 eV > the exponental f a c t o r i s v i r t u a l l y constant for a l l plasmas having temperatures (T e = T^ = T) more than a few eV. The t o t a l amount of scattered l i g h t however, i s l i n e a r l y p r o p o r t i o n a l to the density and i s contained i n the i n t e r v a l Aw « k(KT) 2. The c o r r e s -ponding s p e c t r a l brightne ss of scattered l i g h t , Jg w i l l behave l i k e , n T e J « — r • 5 k T 2 The k~ 1 dependence i n J s shows that scattering from slow fluctuations with small k w i l l lead to b r i g h t scattered spectra. Forming the r a t i o : J s / J B " < kV _ 1 shows that, roughly independent of the temperature, the higher the plasma density, the more d i f f i c u l t i t i s to i n t e r r o g a t e with s c a t t e r i n g t e c h n i -ques. Therefore, at high plasma d e n s i t i e s , advantage must be taken of the brightness of the ion feature. - 50 -CHAPTER 5 DESCRIPTION OF THE SCATTERING EXPERIMENTS 5.1 Introduction This chapter describes i n d e t a i l the e x p e r i m e n t a l arrangements that were used for Thomson scattering i n the Z-pinch plasma. I t i s worth mentioning here that, i n spite of the d i s c u s s i o n s from the l a s t c h apter, the scattering experiments f i r s t attempted to investigate the electron fea-ture. I f i t c o u l d be d e t e c t e d , the e l e c t r o n f e a t u r e would serve as a cross-check on the plasma parameters obtained from the i o n f e a t u r e . How-ever, because of the very high l e v e l s of bremsstrahlung emission, signal to noise r a t i o s i n the electron feature were p r o h i b i t i v e l y low. As w i l l be seen l a t e r , the ion feature did not suffer from this l i m i t a t i o n . The f i r s t s e c t i o n of t h i s chapter shows the two separate geo-metries that were used to examine s c a t t e r i n g from i o n a c o u s t i c f l u c t u a -t i o n s . An analysis of the geometries w i l l d i s t i n g u i s h between the two scattering systems while a few numerical estimates w i l l help to i l l u s t r a t e some of the c h a r a c t e r i s t i c s and parameters of the i o n f e a t u r e t h a t were mentioned i n the previous chapter. The following c o n s i d e r a t i o n s i n d i c a t e why two separate scattering systems were chosen and that, i n f a c t , the pre-sent diagnostic experiments are intimately related to the C O 2 laser-plasma i n t e r a c t i o n experiments. One of the primary i n t e r e s t s i n laser-plasma i n t e r a c t i o n e x p e r i -ments i s the study of non-linear parametric processes which, among o t h e r s , includes stimulated Raman or B r i l l o u i n s c a t t e r i n g . A complete d e s c r i p t i o n of these processes can be found elsewhere (e.g.: Chen, 1974; Siebe, 1974). These processes are scattering i n s t a b i l i t i e s which are produced with v e r y high i n c i d e n t laser i n t e n s i t i e s . The e a s i e s t i n s t a b i l i t y to e x c i t e , and - 51 -therefore most important, i s the B r i l l o u i n mode, whereby the CO2 laser i s s c a t t e r e d by and enhances an i o n a c o u s t i c wave. ( S t i m u l a t e d Raman scattering involves the electron Langmuir wave). At the expense of some of the incident laser energy, plasma waves can be excited to amplitudes which are many orders of magnitude above the normal thermal l e v e l of plasma f l u c t u a t i o n s . As w e l l , the most u n s t a b l e flu c t u a t i o n s are those which scatter the CO laser beam d i r e c t l y back onto 2 i t s e l f so that the enhanced plasma f l u c t u a t i o n s w i l l have a wavelength ^ = 12. The CO2 laser-plasma i n t e r a c t i o n experiments w i l l therefore generate s p e c i f i c , long wavelength, and highly non-thermal f l u c t u a t i o n s i n the plasma density. One of the Thomson s c a t t e r i n g geometries has been arranged to d i r e c t l y examine the properties of such enhanced f l u c t u a t i o n s through the scattering of ruby laser l i g h t . In order to do t h i s , the wavevector for Thomson scattering must be matched, i n both magnitude and d i r e c t i o n , with the wavevector of the f l u c t u a t i o n induced by CO2 l a s e r . This i n turn re-quires that scattered ruby laser l i g h t be observed at very s m a l l forward angles. Also, i n order to c o r r e l a t e the stimulated processes with the plasma parameters, one would l i k e to have a simultaneous measurement of the plasma temperature and density i n the i n t e r a c t i o n volume. Thi s can be done by measuring the spectrum of the thermal l e v e l of density f l u c t u a t i o n s . There-r fore, a second Thomson s c a t t e r i n g geometry i s arranged to s c a t t e r from density f l u c t u a t i o n s that are determined only by the thermal p r o p e r t i e s of the plasma and are t o t a l l y u n c o r r e l a t e d with the s t i m u l a t e d s c a t t e r i n g processes (except in as much as the C0 2 laser may change the l o c a l thermal - 52 -p r o p e r t i e s ) . The second Thomson s c a t t e r i n g geometry t h e r e f o r e looks at short wavelength fl u c t u a t i o n s i n the extreme back scatter d i r e c t i o n . For the present purpose of e s t a b l i s h i n g the plasma c o n d i t i o n s p r i o r to introducing the C0 2 l a s e r , both scattering systems are used to observe the thermal l e v e l of ion f l u c t u a t i o n s . The plasma parameters mea-sured from scattered spectra are the electron density from the i n t e n s i t y of scattered l i g h t , and the ion temperature from the s p e c t r a l d i s t r i b u t i o n . Even though i t w i l l be assumed throughout that the electron and ion temper-atures are equal, i t i s important to r e i t e r a t e that the s p e c t r a l width of the ion feature i s determined by the d i s t r i b u t i o n of ion v e l o c i t i e s . As a r e s u l t of t h i s , many d e t a i l s of the s c a t t e r i n g geometry and d e t e c t i o n systems w i l l be dominated by the r e l a t i v e l y h i g h r e s o l u t i o n c a p a b i l i t i e s needed to examine the ion feature. I t w i l l be seen s h o r t l y t h a t o n l y the back-scatter spectrum has a wavelength spread t h a t i s wide enough (a few angstroms) to be resolved e a s i l y . The f i n a l section of t h i s chapter d e s c r i b e s c a l i b r a t i o n of the s e n s i t i v i t y of the detection systems by R a y l e i g h s c a t t e r i n g from n e u t r a l gases. C a l i b r a t i o n i s required i n order to determine the electron d e n s i t y . When scattering i n t o the e l e c t r o n f e a t u r e , t h i s procedure i s o f t e n not necessary since the spe c t r a l shape, determined by alpha, i s quite s e n s i t i v e to both the electron temperature and d e n s i t y . Then, measurement of the width and shape can be used to determine n e and T. However, the shape of the ion feature, determined by the bet a , i s p a r t i c u l a r l y i n s e n s i t i v e to either plasma parameter (see equation [11]). Therefore, c a l i b r a t i o n of the detection systems w i l l be necessary for density measurements which u t i l i z e the ion feature. - 53 -5.2 Arrangement of the Scattering Geometry Orientation of the plasma with r e s p e c t to the wavevectors f o r Thomson scattering i s shown i n Figure 12. With reference to Figure 12, the f o l l o w i n g d e s c r i p t i o n w i l l g i v e an i n d i c a t i o n of some of the numbers involved and help to c l a r i f y how the scattering systems are arranged. What can be expected i n terms of the spe c t r a l d i s t r i b u t i o n of s c a t t e r e d l i g h t w i l l a l s o be given. When plasma parameters are required i n c a l c u l a t i o n s , the i n i t i a l estimate of Houtman i s used for the maximum plasma temperature while the maximum density i s taken from the es t i m a t e s made i n Chapter 3, i . e . : n e = 4 x 1 0 1 9 cm - 3 T = 40 eV. The wavevector of the density f l u c t u a t i o n producing s c a t t e r i n g i s ^x = ^o ~ ^xs* 'J^ie double subscripting here and i n Figure 12, distinguishes between forward, x = f and backward, x = b s c a t t e r i n g d i r e c t i o n s . The incident ruby laser beam has k Q = |k0|= 2 IT/6943 A or kg = 9.05 x 10 4 cm - 1. Because scattered l i g h t i s only s l i g h t l y s h i f t e d from the i n c i d e n t l a s e r wavelength k Q = k x s to a very good approximation so that k x = 2k Q s i n (6 x/2) i s determined s o l e l y by the angle e x between in c i d e n t and scattered beam d i r e c t i o n s . For the forward scattering system, kf l i e s p a r a l l e l to the plasma axis and 0^ = 7.5°. This angle i s determined by the requirement that the B r i l l o u i n process be interrogated: k f = 2 k C 0 : ) = 1.19 x 10 4 cm - 1. - 54 -FIGURE 12 Geometry for the Thomson Scattering Measurements - 55 -Backscattered l i g h t i s detected in the a n t i p a r a l l e l d i r e c t i o n having 6^ = 172.5° with k^ = 1.81 x 10 5 cm - 1. The f l u c t u a t i o n s observed in backscatter w i l l propagate i n the r a d i a l d i r e c t i o n , p e r p e n d i c u l a r to both the plasma axis and k f . As mentioned i n the introduction, the k-vector arrangement has been chosen with the i n t e r a c t i o n experiments i n mind. Re f e r i n g back to the p r e v i o u s c h a p t e r , the s p e c t r a l w i d t h Ato a kv. can be estimated using the above k-vectors and a plasma tem-l i perature of 40 eV. (As a matter of convenience, the widths w i l l be expres-sed in wavelength u n i t s . The conversion i s e a s i l y done since the frequency s h i f t s to. = co - to = dto are small, and incident l i g h t , at frequency i o s o to = k c , , w i l l appear sh i f t e d according to: dto = cdk = to dX/X » c ° o o o being the speed of l i g h t i n vacuum.) For the backward s c a t t e r i n g system, the ion feature can be expected to have a FWHM of approximately 6.0 A at maximum plasma compression, while the spectrum i n forward d i r e c t i o n w i l l be o narrower by the factor k f s / k b s , making the width only about 0.4 A. The above c a l c u l a t i o n s , along with others such as the plasma Debye length and relevant s c a t t e r i n g parameters, are q u i t e straightforward . Table II gives a summary of numerical estimates for a few of the important parameters used to d e s c r i b e the plasma and the two s c a t t e r i n g systems. Though these estimates are only representative of peak compression, they do serve to point out p a r t i c u l a r l y t h a t , i n high d e n s i t y plasma, alpha i s large while N D i s small. Comparing the relevant numbers from Table II with Figure 11 r e i n f o r c e s the fa c t that only the ion feature w i l l be d e t e c t a b l e i n the current scattering experiments. Since the objective of these experiments i s to determine what the plasma parameters are during a l l stages of the high compression phase and therefore e s t a b l i s h i n i t i a l conditions for the i n t e r a c t i o n s t u d i e s , both - 56 -TABLE II Numerical Estimates for the Thomson Scattering Systems Z-pinch plasma parameters: helium, Z = 2 (at peak compression) n e = 4.0 x 1 0 1 9 cm - 3 T e = T i = T = 40 eV Vj_ = 4.3 x 10 6 cm s e c - 1 X D = 7.4 x 10~ 7 cm N D = 16 Ruby laser scattering parameters: 0) o = 2.72 x 1 0 1 5 s e c - 1 k Q = 9.05 x 10 4 cm - 1 X = 6943 A o Forward Backward 6 7.5 172.5 (deg. k 1.2 x 10 4 1.8 x 10 5 (cm - 1 AXFWHM 0 , 4 0 6 , 0 ( A ) a 112 7.5 3 . 1.4 1.4 - 57 -scattering systems are used only to measure the unperturbed thermal pro-p e r t i e s of the Z-pinch. I t i s unfortunate that the scattering d i a g n o s t i c s has not been used to make measurements with the C02 laser incident i n the plasma. The reasons for t h i s stem from the two p r i n c i p l e f a c t o r s , the f i r s t of which i s a circumstance e s s e n t i a l l y h i s t o r i c a l i n nature. O r i g i n a l l y , the set-up for these laser/plasma i n t e r a c t i o n e x p e r i -ments (Albrecht, 1979) had the CO2 laser beam introduced a x i a l l y into the plasma. Parametrically enhanced f l u c t u a t i o n s would therefore propagate i n the a x i a l d i r e c t i o n and could be interrogated with the forward s c a t t e r i n g arrangement shown i n Figure 12. Such a configuration, however required that the CO2 laser beam propagate almost p a r a l l e l to, and h a l f the length of the plasma column. Although many f o c u s s i n g schemes attempted to e l i m i n a t e severe r e f r a c t i o n e f f e c t s , i t was v i r t u a l l y impossible to introduce the CO2 laser l i g h t a x i a l l y so that the i n t e r a c t i o n volume and d i a g n o s t i c volume had s u f f i c i e n t overlap without dramatically al t e r i n g the plasma c h a r a c t e r -i s t i c s . The i n t e r a c t i o n geometry has since been changed to have the CO2 laser incident r a d i a l l y into the plasma as was described i n Chapter 2. The second, and main reason for Thomson scattering without i n t r o -duction of the CO2 laser l i g h t i s a d i r e c t r e s u l t of the quite general ex-perimental d i f f i c u l t i e s of any scattering experiment. In p a r t i c u l a r , the detection system must have s u f f i c i e n t r e s o l u t i o n c a p a b i l i t i e s to see the o shape of the ion feature. A s p e c t r a l width of 6.0 A corresponding to the expected backscatter spectrum i s of course not l a r g e , but i s w e l l w i t h i n the r e s o l u t i o n range of t y p i c a l monochromators. The forward s c a t t e r i o n - 58 -feature i s considerably narrower making r e s o l u t i o n of t h i s spectrum with conventional techniques a much more d i f f i c u l t problem. S c a t t e r i n g with s p e c t r a l r e s o l u t i o n i s therefore only attempted i n the b a c k s c a t t e r system where the proposed detection system can be used and the d i f f i c u l t i e s of extending the method to higher r e s o l u t i o n experiments can be examined. Non-resolved measurements of the forward s c a t t e r i n t e n s i t y are r e l a t i v e l y e a s i e r to perform and can be done s i m i l t a n e o u s l y with the backscatter measurements. Data obtained i n forward s c a t t e r w i l l be a valuable cross-check of the r e s u l t s obtained from the a n a l y s i s of back-scattered l i g h t . Having discussed the s a l i e n t f e a t u r e s of the s c a t t e r i n g v e c t o r s and t h e i r geometrical arrangement, the remainder of the scattering e x p e r i -ment w i l l now be described. 5.3 O v e r a l l Layout of Experiment The f u l l arrangement of the two scattering systems i s shown i n the semi-schematic diagram of F i g u r e 13. The o r i e n t a t i o n of the d i s c h a r g e vessel with side arms and viewing ports, e t c . , w i l l be r e c a l l e d from the e a r l i e r d e scriptions of Chapters 2 and 3. The incident l i g h t source i s a conventional Q-switched ruby l a s e r o s c i l l a t o r i n combination with a single a m p l i f i c a t i o n stage. Because the scattered spectra are r a t h e r narrow, i t i s of i n t e r e s t to c o n s i d e r the s p e c t r a l d i s t r i b u t i o n of incident l i g h t . The o s c i l l a t o r c a v i t y has a 100% r e a r r e f l e c t o r and the output coupler i s a 66% r e f l e c t i n g , m u l t i p l e s u r f a c e Fabry-Perot e t a l o n . The etalon provides for some l o n g i t u d i n a l laser mode s e l e c t i o n . The etalon has o o a measured mode spacing of 0.37 A, each mode being l e s s than 0.06 A i n width. The mode spacing, however, i s somewhat less than the g a i n narrowed width of the laser flourescence l i n e . Consequently, the laser output has a - 59 -b FIGURE 13 Layout of the scattering experiment. - 60 -wavelength d i s t r i b u t i o n consisting of s e v e r a l narrow s p i k e s separated by the etalon mode spacing. Usually, only one or two l o n g i t u d i n a l modes of the etalon are present, but often, one or two s l i g h t l y o f f - a x i s modes a l s o appear i n the output spectrum. T h i s s t r u c t u r e i n the l a s e r spectrum i s o always contained within less than a 0.6 A i n t e r v a l . However, the scattered o spectrum i n the forward d i r e c t i o n i s expected to be much less than 1A wide (see Table I I ) . Therefore, s p e c t r a l l y resolved measurements of the forward scatter ion feature w i l l require consistent i s o l a t i o n of a s i n g l e e t a l o n mode. In backscatter, the wavelength d i s t r i b u t i o n of i n c i d e n t l i g h t i s s u f f i c i e n t l y small and can be ignored as being a s i g n i f i c a n t c o n t r i b u t i o n to the width of the scattered spectrum. Power l e v e l s i n the incident beam are t y p i c a l l y about 300 MW, or 6 joules i n a 20 ns FWHM pulse. In order to minimize the amount of s t r a y laser l i g h t entering the detection o p t i c s , the e n t i r e l a s e r and i n c i d e n t beam path i s housed i n a l i g h t t i g h t arrangement of boxes and tubes. Also, immediately p r i o r to i n t r o d u c i n g the beam i n t o vacuum, i t i s focussed through a helium flushed s p a t i a l f i l t e r i n g pinhole. Helium gas i s used to reduce the p o s s i b i l i t y of laser breakdown sparks at the p i n h o l e (Morgan, 1975). F i l t e r i n g the beam helped eliminate spurious o f f - a x i s l a s i n g modes which were found to contribute s i g n i f i c a n t l y to s t r a y l i g h t l e v e l s . The 'cleaned' beam i s then focussed onto the pinch axis to a spot diameter of approximately 0.25 mm. Incident l i g h t which i s t r a n s m i t t e d through the plasma i s co l l e c t e d i n a Rayleigh horn beam dump, intended to absorb com-p l e t e l y a l l unscattered r a d i a t i o n . The forward scatter beam path consists of a series of m i r r o r s and lenses which transport the scattered beam and image the s c a t t e r i n g volume onto the entrance s l i t of a Spex 3/4 meter f o c a l length monochromator. The ion feature though i s not s p e c t r a l l y r e s o l v e d so the monochromator a c t s only to f i l t e r out background l i g h t from the plasma. E x i t s l i t s are set to o transmit only a 7 A wide band, centered on the l a s e r wavelength. Beyond - 61 -the e x i t s l i t , a low l o s s o p t i c a l f i b e r bundle c o l l e c t s and t r a n s p o r t s l i g h t to a photomultiplier. O s c i l l o s c o p e t r a c e s of the p h o t o m u l t i p l i e r output are photographed g i v i n g a temporal r e c o r d of the l i g h t t h a t i s c o l l e c t e d . Such power measurements p r o v i d e a d d i t i o n a l d i s c r i m i n a t i o n against plasma l i g h t since s c a t t e r e d l i g h t i s p r e s e n t o n l y f o r the 20 ns duration of the l a s e r p u l s e . On t h i s time s c a l e , the average l e v e l of plasma background l i g h t does not change s i g n i f i c a n t l y and background l i g h t e s s e n t i a l l y appears as an a d d i t i o n a l b i a s or b a s e l i n e on the s c a t t e r e d s i g n a l . (The l i m i t a t i o n here i s due to f l u c t u a t i o n s i n the b a s e l i n e t h a t r e s u l t from shot noise i n both the photomultiplier and i n the e m i s s i o n of photons by the plasma. Scattered l i g h t must s t i l l be d e t e c t e d over and above such s t a t i s t i c a l f l u c t u a t i o n s . ) In backscatter, the d e t e c t i o n system i s designed to r e c o r d the f u l l s p e c t r a l d i s t r i b u t i o n of scattered l i g h t on s i n g l e shot of the ruby l a s e r . Much of the complexity of the backscatter o p t i c a l system i s based on matching the c o l l e c t i o n and dispersion optics to the detector character-i s t i c s . The detector i s an O p t i c a l Multichannel Analyser (abbreviated OMA) produced by Princeton Applied Research Corp. (model 1 2051 d e t e c t o r head with model 1204 A e l e c t r o n i c control console). The OMA i s e s s e n t i a l l y an extremely sophisticated e l e c t r o n i c image converter camera, t h i s p a r t i c u l a r model having two stages of image a m p l i f i c a t i o n . D e t a i l s of the d e s i g n and operation of the OMA can be found i n the i n s t r u c t i o n manuals av a i l a b l e from PAR Corp. For a discussion of the backscatter o p t i c s , o n l y the f o l l o w i n g b r i e f d e s c r i p t i o n i s given. An o p t i c a l image on the detector head photocathode i s segmented i n t o a l i n e a r array of 500 channels, each corresponding to a 0.025 mm wide by 5.0 mm high portion of the photocathode. The f u l l a c t i v e portion of the target area i s 12.5 mm by 5.0 mm. A m p l i f i e d p h o t o e l e c t r o n s i g n a l s are c o l l e c t e d during a 768 ys "on" time, a f t e r which, the accumulated signal in each channel i s d i g i t i z e d and stored i n memory. For any given channel, one ~ 62 " d i g i t a l count corresponds to the accumulated e f f e c t of approximately 20 v i s i b l e photons in c i d e n t on the photocathode. (The quantum e f f i c i e n c y of the photocathode i s 60%). Two aspects of the d e t e c t o r are of importance here. F i r s t , the f i n i t e width of each detector channel r e q u i r e s t h a t the OMA s p a t i a l r e s o l u t i o n be matched with that of the d i s p e r s i o n instrument for optimum s p e c t r a l r e s o l u t i o n . Secondly, since o p t i c a l input to the OMA i s accumulated, i . e . : time integrated, d i s c r i m i n a t i o n between s c a t t e r e d l i g h t and plasma background must be made on the basis of energy rather than power. Dispersion of the spectrum i s provided using a second Spex 3/4 m f o c a l length monochromator equipped with a 1200 line/mm g r a t i n g , blazed i n o 1st order for 7000 A. The monochromator has a c o l l e c t i o n r a t i o of F/7.5 and o a r e c i p r o c a l dispersion of 10 A/mm. The entrance s l i t was set at 0.012 mm wide by 0.350 mm h i g h . Imaging 1:1 a t the e x i t plane g i v e s a s p e c t r a l o r e s o l u t i o n i n t e r v a l of 0.12 A FWHM. Additional external optics, consisting of a x5 microscope objective and a beam t r a n s p o r t l e n s , images the mono-chromator e x i t plane onto the OMA head with a t o t a l magnification of x10.5. The monochromator entrance s l i t therefore covers 75% of the height of 5 OMA o channels. The maximum r e s o l u t i o n with t h i s arrangement i s 0.12 A (0.024 o A/channel). This matching i s not q u i t e o p t i m a l s i n c e the width of the monochromator entrance s l i t used i s s l i g h t l y more than twice the d i f f r a c -t i o n limited c a p a b i l i t i e s of the instrument. Also, the OMA has a s p a t i a l r e s o l u t i o n of 3 channels FWHM, t h i s l i m i t a t i o n being due to e l e c t r i c a l c r o s s - t a l k between adjacent OMA channels. For the b a c k s c a t t e r spectrum, attention to fine d e t a i l s of the matching i s unimportant s i n c e Table II indic a t e s that the system described above has more than adequate r e s o l u -t i o n . However, th i s system may not have s u f f i c i e n t r e s o l u t i o n to examine the spectrum of forward s c a t t e r e d l i g h t . T h e r e f o r e , the b a c k s c a t t e r arrangement attempts to p r o v i d e a t l e a s t a near l i m i t a t i o n t e s t of the detection system. " 63 " Discrimination against plasma l i g h t i s v i t a l since bremsstrahlung i s emitted over the several microsecond time i n t e r v a l of the discharge com-pared with the 20 ns duration of scattered l i g h t . The OMA has an e l e c t r i -c a l gating mode which permits l i g h t to be detected only for the duration of a user supplied voltage pulse. However, for short gating pulses there are d i s t o r t i o n s i n the e l e c t r o n i c imaging stages which s e v e r e l y degrade the re s o l u t i o n c a p a b i l i t i e s of the instrument (Simpson, 1977; Albrecht, 1978). The OMA i s therefore used i n the continuous recording (or 'real time') mode and an e l e c t r o - o p t i c shutter performs the g a t i n g f u n c t i o n . The s h u t t e r operates i n the following simple way. Backscattered l i g h t i s passed through the s e r i e s combination of p o l a r i z e r , pockels c e l l , and crossed p o l a r i z e r . The po c k e l s c e l l i s a double c r y s t a l , KD*P u n i t having a half-wave voltage of 2.2 kV and p o l a r -i z e r s are of the Glan-Thomson type. The f i r s t p o l a r i z e r takes advantage of the l i n e a r p o l a r i z a t i o n of the ruby l a s e r beam by passing a l l s c a t t e r e d l i g h t and rejecting one-half of the plasma emission. Now, when the pockels c e l l i s not activated, the p o l a r i z a t i o n of l i g h t t r a n s m i t t e d through the c e l l i s not altered and therefore w i l l be blocked by the second p o l a r i z e r . If the pockels c e l l i s supplied with i t s half-wave voltage, l i g h t e n t e r i n g the c e l l w i l l e x i t with the plane of p o l a r i z a t i o n r o t a t e d by 90°. Then, the second p o l a r i z e r w i l l be transmitting. For gating purposes, a k r y t r o n triggered, cable discharge c i r c u i t i s used to generate a 2.2 kV, square wave voltage pulse of 100 ns duration. The gate pulse i s centered i n time on the inc i d e n t laser pulse. Plasma emission occurring o u t s i d e t h i s time i n t e r v a l i s suppressed. In order to obtain a good on-off contrast r a t i o with t h i s o p t i c a l gating method, l i g h t passing through the polarizer/pockels c e l l arrangement must be accurately c o l l i m a t e d . A 50 cm f o c a l l e n g t h lens c o l l e c t s the scattered l i g h t (F/16 c o l l e c t i o n cone) and images the s c a t t e r i n g volume onto a f i e l d l i m i t i n g pinhole. Scattered l i g h t i s transmitted through the " 64 " pinhole and then collimated. This collimated beam i s passed through the shutter and then refocussed onto the monochromator entrance s l i t . (Overall, the entrance s l i t i s imaged onto the plasma a x i s with X0.71 m a g n i f i c a -t i o n ). With perfect c o l l i m a t i o n , the on - o f f c o n t r a s t r a t i o can exceed 1000:1 , but the observed cont r a s t i s about an order of magnitude lower. The e f f e c t of poor contrast has been very important because of the r e l a t i v e time s c a l e s i n v o l v e d . T h i s can be understood by making the f o l l o w i n g observations. Plasma l i g h t and scattered l i g h t w i l l of course be col l e c t e d during the shutter's 100 ns on time. Also, because the OMA time integrates, plasma emission w i l l r e g i s t e r (as leakage l i g h t ) for the f u l l d u r a t i o n of the discharge, namely, a few microseconds. The o v e r a l l e f f e c t f o r these experiments i s that, by using the o p t i c a l shutter, plasma background l e v e l s are reduced only by approximately a factor of 10. However, i t w i l l be seen that t h i s has been s u f f i c i e n t to give very good s i g n a l to noise r a t i o s i n the scattered spectra. 5.4 C a l i b r a t i o n of the O p t i c a l Systems A c a l i b r a t i o n of the detection s e n s i t i v i t y must be performed i n order to determine electron d e n s i t i e s from observed scattered i n t e n s i t i e s . Therefore, before showing some of the plasma scattering s p e c t r a , c a l i b r a -t i o n by Rayleigh scattering i s d i s c u s s e d . In the p r o c e s s , an important l i m i t a t i o n of the current geometry w i l l be pointed out. The frequency integrated d i f f e r e n t i a l scattering c r o s s - s e c t i o n i s relat e d to the electron density ng by: da/dfi = n a S.fk) . e e I V J r \ - 65 -D i r e c t a p p l i c a t i o n of t h i s r e l a t i o n s h i p requires an absolute c a l i b r a t i o n of the complete imaging and detection system, a very d i f f i c u l t i f not imposs-i b l e procedure to implement with r e l i a b i l i t y . The g e n e r a l p r a c t i c e i s to perform a r e l a t i v e c a l i b r a t i o n by Rayleigh s c a t t e r i n g o f f n e u t r a l g a s e s . This form of c a l i b r a t i o n can be done as follows. ed to a number density, n Q of molecules with known Rayleigh cross-section Oft . Scattering o f f t h i s gas produces a s i g n a l P R which, when normalized to the i n c i d e n t laser i n t e n s i t y , can be expressed as A l l molecules contributing to P R are contained in the scattering volume V R. The unspecified factor f contains a l l properties of the system t h a t remain i d e n t i c a l f o r both Thomson and R a y l e i g h s c a t t e r i n g experiments. For example, f a c t o r s such as: s o l i d angle of c o l l e c t i o n , throughput of imaging components, dis p e r s i o n instruments or detectors, etc., would a l l be i n c l u d -ed i n f. Using e x a c t l y the same system f o r Thomson s c a t t e r i n g g i v e s a s i m i l a r expression for scatter i n t o the ion feature, Given the present scattering system, the discharge vessel i s f i l l -n o S . ( k ) V ^ f . e e i J T Forming the r a t i o P - P / P R and solving for the electron density, n e g i v e s : n e [15] - 66 -where the factor i n square brackets i s j u s t the c a l i b r a t i o n c o n s t a n t f o r the detection system. Given S^(k), the electron density may be determined simply by com-paring the plasma scattering signals with those obtained by scattering from a known pressure of c a l i b r a t i o n gas. Many gases can be used for c a l i b r a t i o n purposes (George, e t . a l . , 1965; D e S i l v a , 1970) the most common being nitrogen where a /a = 3.65 x 102. Assuming for the moment that V R = R e V T and Si(k) = 1 then scattering from 110 torr of N 2 w i l l give the same t o t a l s i g n a l as a plasma with n g = 1.0 x 1 0 1 6 cm - 3. I t should be noted that Rayleigh scattered l i g h t has a bandwidth which i s very small, being determined from Doppler broadening by molecules i n a room temperature gas. T h e r e f o r e , measurements must be made at the laser wavelength. Even at zero gas pressures, laser l i g h t can be accident-a l l y scattered i n t o the detection system giving a constant l e v e l of s t r a y l i g h t which w i l l be added to the R a y l e i g h s i g n a l . When s t r a y l i g h t i s present, the true Rayleigh s i g n a l i s determined by examing the li n e a r v a r i -ation of scattered i n t e n s i t y with gas p r e s s u r e . E x t r a p o l a t i o n to zero pressure w i l l reveal the stray l i g h t l e v e l . Measurement of the electron density using equation [15] does r e -quire a knowledge of S^(k) and hence of alpha. For both scattering systems, Table II shows a >>1 and therefore S^(k) approaches the constant value Z/(1+ZT e/T£) = 2/3. Apart from the discrepancy i n volume then, equation [15] i s e s s e n t i a l l y independent of alpha, giving a quite simple determina-ti o n of n e . - 67 -In many circumstances, e q u a t i o n [15] can be f u r t h e r s i m p l i f i e d since the two volumes V R and V T are i d e n t i c a l and can be incorporated into the cancelled factor f. However, for the c u r r e n t experiment t h i s i s not the case. Figure 14 shows the scattering volume i n d e t a i l . This figure i s to be viewed i n conjunction with the wavevector diagram of Figure 12. The i n c i d e n t beam i s focussed to a diameter d = 0.25 mm on the plasma a x i s . Imaging the monochromator entrance s l i t s a t a shallow 7.5° angle with respect to k Q produces a rather long region of overlap from which scattered l i g h t w i l l be c o l l e c t e d . With the geometry of F i g u r e 13, the s c a t t e r i n g volume i s determined to have a length, normal to the plasma axis of L = 1.9 mm. Recalling the streak or shadow photographs, the diameter of the high density plasma core i s s i g n i f i c a n t l y s m a l l e r than the s c a t t e r i n g volume during portions of the pinch phase. Two important aspects of the scattering system should therefore be kept i n mind when viewing and analyzing scattered s i g n a l s . F i r s t l y , when equation [15] i s used to c a l c u l a t e electron d e n s i t i e s , the r e l a t i v e volumes V R / v T must be estimated and t h i s i s taken to be d i r e c t l y proportional to the respective lengths of the scattering volumes, L ^ / L i j i . Using Figure 14, 1^ i s f i x e d at 1.9 inm. As long as the plasma diameter i s larger than t h i s , L J J = L T . Otherwise, Lrp i s measured from streak photographs as the b r i g h t core diameter. The second, now obvious point, i s that along the viewing d i r e c -t i o n there i s considerable lack of s p a t i a l r e s o l u t i o n . Parameters d e t e r -mined from scattered l i g h t w i l l therefore be average values f o r the high density plasma core. " 6 8 " FIGURE 14 D e t a i l s of the scattering volume - 69 -CHAPTER 6 SCATTERING OBSERVATIONS AND RESULTS 6.1 In t r eduction Some aspects of the scattering experiments were not quite expected and lead to a few questions about the i n t e r p r e t a t i o n of observed s i g n a l s . The f i r s t section of t h i s chapter presents a sampling of the raw s p e c t r a l data to show the type of information t h a t was o b t a i n e d . Answers to the questions that arose w i l l g i v e better i n s i g h t i n t o the shock wave nature of the plasma structure a t p i n c h time. As w e l l , i t w i l l be seen t h a t the e f f e c t s of r e f r a c t i o n can enter i n t o consideration i n rather a s u b t l e way. A complete i n t e r p r e t a t i o n of the data w i l l be seen to r e l y h e a v i l y on the e a r l i e r streak and shadowgram observations. The f i n a l section of t h i s chapter concludes the scattering experi-ments by p r e s e n t i n g the e l e c t r o n temperature and d e n s i t y measurements obtained for the f u l l duration of the pinch phase. The data c o n f i r m and extend the r e s u l t s of previous experiments on t h i s Z-pinch. The d e n s i t y measurements are compared with the e s t i m a t e s made i n Chapter 3, and, i n p a r t i c u l a r , with the snow-plow model of plasma collapse. 6.2 Discussion of the Spectra A few backscatter spectra are reproduced i n F i g u r e 15. Each of the spectra was recorded on a single shot of the ruby l a s e r . These t r a c e s d i s p l a y the f u l l 500 channel OMA r e c o r d s . The h o r i z o n t a l s c a l e spans a t o t a l wavelength i n t e r v a l of 12 A, though note that the scale i s i n v e r t e d , wavelength increasing l i n e a r l y to the l e f t . The top spectrum, Figure 15(A) i s a c a l i b r a t i o n shot showing Rayleigh s c a t t e r i n g from 1/2 atmosphere of nitrogen gas. Laser mode structure due to the o s c i l l a t o r output e t a l o n i s - 70 -(A) 1/2 atmosphere N2 IB) n p = 0.6 x 1 0 1 8 cm* 3 T e= 22 eV t =-160 ns (C) n~ = 1.6 x 1 0 1 9 cm' 3 T e= 28 eV t = • 40 ns (D) ne= 3.3 x 1 0 1 8 cm" 3 T e = 6.3 eV t = *310 ns FIGURE 15 oobserved spectra. The f u l l i n t e r v a l displayed h, with wavelength increasing to the l e f t . - 71 -evident. For t h i s shot, there were only two l o n g i t u d i n a l modes p r e s e n t , with the modes separated by 0.37 A. The remaining three spectra are plasma scattering events, each l a b e l l e d a c c o r d i n g to the o b s e r v a t i o n time and computed temperature and density. Spectra 15(A) and 15(B) are d i s p l a y e d with approximately equal s e n s i t i v i t i e s i n the v e r t i c a l d i r e c t i o n . Compared to the c a l i b r a t i o n shot, 15(B) shows s t a t i s t i c a l f l u c t u a t i o n s of the b a s e l i n e which are now more severe since plasma background l i g h t i s also recorded. As well the plasma density i s low and b a s e l i n e f l u c t u a t i o n s make f o r a r a t h e r i l l - d e f i n e d s p e c t r a l shape. However, Thomson scattered l i g h t i s c l e a r l y present. The bottom two spectra i n Figure 15 show that higher density plasma g i v e q u i t e strong scattered s i g n a l s , well i n excess of the noise l e v e l s . In order to i l l u s t r a t e one c o m p l i c a t i o n t h a t can a r i s e when Thomson scattering from high density plasma, the f i r s t o b s e r v a t i o n to be discussed i s concerned with the l e v e l of s t r a y l i g h t appearing i n both forward and backward scattering detection systems. For the series of c a l i -b r ation shots, Rayleigh scattering was measured as a function of f i l l pres-sure i n order to ascertain the detection s e n s i t i v i t y along with the s t r a y l i g h t l e v e l s (see Section 5.4). In backscatter, there was no measurable stray l i g h t . In forwardseatter, stray l i g h t was present, and only amounted to scattering from an equivalent electron density of 7 x 10 1^ cm - 3. This l e v e l of stray l i g h t i s well below the electron d e n s i t i e s of i n t e r e s t and, though accounted for i n the a n a l y s i s , i t was not a s i g n i f i c a n t contribution to plasma scattering signals during most of the pinch phase. However, around the time of maximum compression the f o r w a r d scattering signals would show unpredictable shot to shot v a r i a t i o n s ( f o r fixed timing) of as much as six orders of magnitude above expected thermal scattering l e v e l s . Large amounts of s t r a y l i g h t a l s o appear i n back-- 72 -scattered spectra, though only when the forward scatter signals are g r e a t l y enhanced. Figure 15(C) gives an example of t h i s circumstance. The narrow spike superimposed on top of the scattered s i g n a l i s stray l i g h t . Like the Rayleigh scattered s i g n a l i n Figure 15(A), stray l i g h t i s unbroadened and appears at the laser wavelength. Figure 15(B) and (D) show no stray l i g h t , consistent with the N 2 c a l i b r a t i o n . These observations are of course e x p l a i n e d by noting t h a t the a p p l i c a b i l i t y of a shadowgram technique depends on ray bending. The angu-l a r d e f l e c t i o n estimates made e a r l i e r do i n d i c a t e t h a t the i n c i d e n t ruby laser l i g h t can be deflected to such an extent that transmitted l i g h t w i l l be inadequately absorbed by the beam dump. Considering t h a t the i n c i d e n t beam power i s at the megawatt l e v e l while s c a t t e r e d l i g h t i s measured at the photon l e v e l , i t i s easy to see t h a t even s l i g h t l y i n e f f i c i e n t beam dumping can lead to serious stray l i g h t problems. The l a r g e enhancements of forward scattered l i g h t and correlated appearance of stray l i g h t i n the back scatter spectrum have t h e r e f o r e been a t t r i b u t e d to high l e v e l s of stray l i g h t brought about by r e f r a c t i o n of the in c i d e n t laser beam. A second aspect of the spectra to n o t i c e i s t h a t the middle two spectra of F i g u r e 15 appear n o t i c a b l y red s h i f t e d with r e s p e c t to the inci d e n t laser wavelength. I t w i l l be r e c a l l e d , from the wavevector geo-metry of Figure 12, that the backward d i r e c t i o n d e t e c t s s c a t t e r i n g from density f l u c t u a t i o n s which propagate i n the r a d i a l d i r e c t i o n . Therefore, a net displacement of the spectrum gives an i n d i c a t i o n of the average r a d i a l speed of plasma contained within the scattering volume. Radial v e l o c i t y e s t i m a t e s based on a net Doppler s h i f t of the spectra are not very accurate since the s h i f t s are much sm a l l e r than the width of the spectra, and, p r i m a r i l y because the s h i f t s observed are of the same magnitude as shot-to-shot f l u c t u a t i o n s i n the wavelength of i n c i d e n t l i g h t . (For some spectra l i k e 15(C), stray l i g h t has aided as a wavelength - 7 3 -reference). As well, only a l i m i t e d number of shots were made at e a r l y times when the red s h i f t s were s i g n i f i c a n t . N onetheless, the s h i f t s are s i g n i f i c a n t and Table III presents the r a d i a l v e l o c i t y measurements, dr/dt, as they could be extracted from the a v a i l a b l e scattering data. TABLE I I I Radial Speeds from the Scattering Spectra Time (ns) dr/dt (x 10 6 cm s e c - 1 ) -150 -3.2+1.6 -50 < t < 0 -0.9+0.4 t > 0 0 The above measurements can be considered along with the streak and shadowgram r e s u l t s presented i n Chapter 3. Most n o t a b l y , the f i r s t two e n t r i e s i n Table III show t h a t the s c a t t e r i n g volume, l o c a t e d near the plasma axis, sees r a d i a l speeds that d i f f e r with time. The outer boundary of the plasma (see Figures 7(A) and 7(B)) moves inward with an a p p r o x i -mately uniform speed, which i s roughly equal to the second e n t r y i n Table I I I . At somewhat e a r l i e r times, plasma near the a x i s i s t r a v e l l i n g s i g n i f i c a n t l y f a s t e r . This d i f f e r e n c e i n plasma speed near the a x i s i s at l e a s t q u a l i t a t i v e l y consistent with a d e s c r i p t i o n of the pinch e f f e c t t h a t includes the formation of shock waves ( A l l e n , 1957). The d i f f e r e n c e i n speed can be understood as follows. The magnetic forces driving plasma inward act much l i k e a p i s t o n driven i n t o a gas f i l l e d tube. Compressed plasma, c o l l e c t e d up by, and moving inward with t h i s magnetic piston, can be preceded by a shock wave t r a v e l l i n g inward f a s t e r than the bulk of the plasma l o c a t e d near the - 74 -p i s t o n . The shock front therefore reaches the axis sooner than the bulk of the plasma. Since the scattering volume i s located near the plasma a x i s , the net Doppler s h i f t a t e a r l y times i s i n t e r p r e t e d as i n d i c a t i n g the appearance of the shock front, while, s h o r t l y a f t e r w a r d s , slower plasma, accumulated at the piston, would enter the s c a t t e r i n g volume. R a d i a l l y d i r e c t e d motions would eventually be thermalized and no net Doppler s h i f t would be evident, as the f i n a l entry i n Table III i n d i c a t e s . This view of the pinch phase could have been alluded to i n Chapter 3 when the streak pictures (Figures 4 or 7) were discussed. Development of a two component structure i n the plasma column i s a l s o i n d i c a t i v e of the shock wave nature of plasma col l a p s e . In p a r t i c u l a r , the p r e c u r s o r shock converging on axis i s what i n i t i a t e s formation of the high d e n s i t y plasma c o r e . However, the photographic experiments do not measure p a r t i c l e v e l o c i t i e s d i r e c t l y . In combination with Chapter 3, the Doppler s h i f t data can be explained q u a l i t a t i v e l y , but, the s c a t t e r i n g experiments l a c k the s p a t i a l r e s o l u t i o n required to make quantitative e v a l u a t i o n s of the shock structure. The f i n a l point of discussion i n t h i s section concerns again the net wavelength s h i f t appearing i n the backscatter spectra. A question about the average Doppler s h i f t a r i s e s , not from the presence of a red s h i f t , but from the absence of a blue s h i f t . Presumably, i f the scattering volume i s symmetrically located on the plasma axis, scattered l i g h t should be observ-ed from both 'sides' of the plasma. The region of plasma nearest the laser and backscatter optics w i l l be moving away from the i n c i d e n t beam g i v i n g r i s e to the observed red s h i f t . Beyond the a x i s , plasma c o l l a p s i n g r a d i a l l y inward w i l l i n f a c t be moving towards the i n c i d e n t beam. Hence, one would expect not only red s h i f t e d spectrum, but a l s o a s i m i l t a n e o u s blue s h i f t e d one, the t o t a l spectrum showing symmetry about the ruby wave-- 75 -length. One p l a u s i b l e explanation for the absence of a blue s h i f t e d com-ponent w i l l be put forward i n terms of r e f r a c t i o n . Before doing so though, i t i s worth indicating why r e f r a c t i o n e f f e c t s were consi d e r e d a p l a u s i b l e explanation. As has already been shown by shadowgrams and, from the d i s c u s s i o n of stray l i g h t there can be rather large d e f l e c t i o n s of ruby laser l i g h t by the plasma. F i g u r e 9 shows t h a t the angular d e f l e c t i o n s can exceed approximately 23 mrad or 1.3 degrees. In f a c t , during the course of the i n t e r f e r o m e t r i c measurements, i t was v e r i f i e d t h a t the sharp d e n s i t y gradients, existing near the core boundary, produce d e f l e c t i o n s i n excess of 3.5°. Nonetheless, i f i t i s accepted t h a t the maximum d e f l e c t i o n i s 1.3°, r e f r a c t i o n e f f e c t s w i l l be n e g l i g i b l e i f t h i s d e f l e c t i o n i s s m a l l compared to the acceptance angle of the b a c k s c a t t e r c o l l e c t i o n o p t i c s . However, t h i s i s not the case. Recalling the d i s c u s s i o n i n S e c t i o n 5.3, backscattered l i g h t i s c o l l e c t e d by a 50 cm f o c a l length lens which views the scattering volume with an F/# of 16. In other words, the c o l l e c t i o n cone has a half-angle of 1.8°. Therefore, the minimum d e f l e c t i o n angle i s quite comparable with the maximum acceptance a n g l e . The f o l l o w i n g d i s -cussion i l l u s t r a t e s how such a circumstance can lead to o n l y r e d - s h i f t e d spectra. Consider then that the scattering volume i s symmetrically l o c a t e d o n - a x i s and r e p r e s e n t s a l i n e source of l i g h t . The t o t a l amount of scattered l i g h t c o l l e c t e d by the backscatter optics w i l l be some i n t e g r a l over a l l the elemental c o n t r i b u t i o n s along the l i n e . F i g u r e 16 shows a c r o s s - s e c t i o n of the h i g h d e n s i t y core plasma and i n d i c a t e s how two symmetrically located portions of the l i n e would c o n t r i b u t e to the t o t a l s i g n a l . Also, i n Figure 16, the scattering volume has a l e n g t h which i s comparable to or larger than the core diameter. On the l e f t of the plasma axis, scattered l i g h t , o r i g i n a t i n g from plasma moving towards the incident beam, must r e - t r a v e r s e the plasma and " 76 " FIGURE 16 Refraction e f f e c t s i n the backscatter c o l l e c t i o n o p t i c s . - 77 -therefore be refracted away from the c o l l e c t i o n lens. This i s shown by the s o l i d l i n e i n Figure 16 and can be compared with the r a y t r a j e c t o r y g i v e n i n Figure 6. The dotted l i n e i n Figure 16, originating from the same point i n the plasma, shows the path of the same ray i f r e f r a c t i o n were neglected. The r e s u l t of r e f r a c t i o n then i s to decrease the e f f e c t i v e c o l l e c t i o n cone for t h i s region of the scattering volume. On the other hand, the corresponding element of the s c a t t e r i n g volume which i s closer to the lens produces the red s h i f t e d s p e c t r a l com-ponent and contributes to the s i g n a l with a c o l l e c t i o n cone t h a t i s i n -creased as a r e s u l t of r e f r a c t i o n . In a f i r s t approximation, the amount of l i g h t l o s t from the 'far' side of the scattering volume w i l l be gained from the near side so that the t o t a l amount of scattered l i g h t c o l l e c t e d remains f i x e d . However, with the i n c l u s i o n of r e f r a c t i o n e f f e c t s , one can see that i t i s possible for the plasma to produce a scattered s i g n a l that i s domin-ated by the c h a r a c t e r i s t i c s of the plasma nearest the c o l l e c t i o n lens. The e f f e c t s of r e f r a c t i o n are c o n s i d e r e d at l e a s t a p a r t i a l e x p l a n a t i o n f o r not seeing a blue s h i f t . The most l i k e l y reason f o r observing only r e d - s h i f t e d s p e c t r a i s t h a t there i s simply an e r r o r i n imaging the scattering volume symmetrically about the plasma a x i s . A l i g n -ment of the scattering system was accomplished by p l a c i n g a s m a l l p i n h o l e a t the precise geometrical l o c a t i o n of the a x i s of the d i s c h a r g e v e s s e l . The incident beam and monochromator entrance s l i t s were then imaged on the center of t h i s pinhole. However, considering that the scattering volume i s only 2 mm i n length, i t i s quite possible that the discharge i t s e l f was not so accomodating as to have the plasma axis correspond e x a c t l y to the geo-me t r i c a l axis of the v e s s e l . For i n s t a n c e , i f the plasma a x i s was d i s -placed from the center of the f o c a l volume, i n the d i r e c t i o n of the i n c i -dent beam, by 0.5 mm, s c a t t e r i n g from the f a r s i d e of the plasma would constitute only 25% of the t o t a l s i g n a l . - 78 -Apart from some of the u n c e r t a i n t i e s i n f u l l y e x p l a i n i n g the scattering observations, and, to the extent that the scattering experiments represent a r a d i a l l y averaged i n v e s t i g a t i o n of the plasma column, i t w i l l be seen i n the following section that the plasma parameters determined from scattering agree very well with previous independent measurements. 6.3 Plasma Parameters for the Z-Pinch R e s u l t s f o r the plasma parameters obtained from the Thomson scattering experiments are shown i n F i g u r e s 17 and 18. These g i v e the plasma temperature and electron density r e s p e c t i v e l y as a function of time during the pinch phase. Again, the time axis i s referenced to d l / d t = 0. The smooth curves drawn on each p l o t represent a v i s u a l approximation to the data points. Ion temperatures, F i g u r e 17, were determined using a computer aided v i s u a l f i t t i n g routine to compare the observed b a c k s c a t t e r s p e c t r a with t h e o r e t i c a l p r o f i l e s . The t h e o r e t i c a l shape f o r the i o n f e a t u r e i s c a l c u l a t e d using S a l p e t e r ' s (1963) approximation with Z = 2 f o r f u l l y ionized helium and T e = T^. Over the range of plasma parameters measured, electron-ion c o l l i s i o n times are i n the sub-nanosecond regime so i t i s quite v a l i d to assume equal electron and ion temperatures. When the shape of the backscatter spectrum i s well defined, as i n Figure 15(C) or (D), the f i t t i n g procedure allows the average ion temperature to be determined to an uncertainty of 10 - 20%. Below an electron density of approximately 1 x 1 0 1 8 cm - 3, the backscatter spectra show rather poor s i g n a l to noise r a t i o s (see Figure 15(B) for example). In these instances, temperature measure-ments become less accurate and are good to, at worst, about 40%. - 79 -FIGURE 17 Plasma temperature r e s u l t s . Measurements are from Thomson scattering i n the backward d i r e c t i o n (open c i r c l e s ) and l i n e to continuum r a t i o s (crosses). - 80 -For comparison, the data points drawn as crosses give temperature measurements from e a r l i e r work, (Houtman, 1977; A l b r e c h t , 1979; H i l k o e t . a l . , 1980). These estimates were based on the l i n e to continuum r a t i o o for the H e l l 4686 A emmission l i n e . Above 25 eV, t h i s s p e c t r a l l i n e i s e s s e n t i a l l y non-existent since the plasma i s f u l l y i o n i z e d . However, the spectroscopic data below 25 eV i s r e l i a b l e and agrees f a v o u r a b l y with the Thomson scattering r e s u l t s . T y p i c a l e r r o r bars have been i n d i c a t e d i n Figure 17. Electron density data, Figure 18, i s obtained from both forward (open squares) and backward (open c i r c l e s ) scattering experiments. Using the Rayleigh scattering c a l i b r a t i o n s , n e was computed from equation [15] with S^(k) = 2/3. As shown i n Figure 14, the scattering volume had an e s t i -mated length of 1.9 mm which, at times during maximum compression, exceeded the plasma diameter. When comparing Rayleigh and plasma scattering signals t h i s discrepancy i n c o l l e c t i o n volumes was accounted f o r . C o l l e c t i v e s c a t t e r i n g , i . e . : an ion feature i n the backward d i r e c -t i o n was not observed for d e n s i t i e s below 2 x 1 0 1 7 cm - 3. Density measure-ments at early times could be extended to < 1 0 1 7 cm"3 since the ion feature i n forward d i r e c t i o n s t i l l c o n t a i n e d s i g n i f i c a n t amounts of s c a t t e r e d l i g h t . During the h i g h compression phase, F i g u r e 18 shows a p p a r e n t l y spurious data points with n e > 1 0 2 0 cm - 3 which originate from the forward scatter data. These and other o f f scale points are due to the l a r g e s t r a y l i g h t enhancements discussed e a r l i e r . Accordingly, those measurements i n the forward d i r e c t i o n that i n d i c a t e e l e c t r o n d e n s i t i e s w e l l i n excess of 0 - 81 -FIGURE 1 8 Elec t r o n d e n s i t y r e s u l t s . Measurements are from Thomson scattering i n backward d i r e c t i o n (open c i r c l e s ) and forward d i r e c t i o n (open squares), and Stark brodening (crosses). The dotted l i n e shows the snow-plow model pre d i c t i o n for Z = 2. i - 82 -10^ u cm - 3 are not plotted i n Figure 18. Again, the f i r s t density measure-ments on t h i s Z-pinch were obtained s p e c t r o s c o p i c a l l y and are i n c l u d e d i n Figure 18 as crosses. (Like the s c a t t e r i n g geometry, the s p e c t r o s c o p i c experiments had been arranged to view the on-axis plasma i n a r a d i a l d i r e c -t i o n ) . The agreement between a l l three d e n s i t y d e t e r m i n a t i o n s i s q u i t e good. I t i s interesting to compare d e n s i t y measurements from Thomson scattering with the snowplow model of plasma collapse described i n S e c t i o n 3.4. Equation [1] s p e c i f i e s that the average electron d e n s i t y w i t h i n the plasma column i s determined by the column radius and assumes t o t a l sweep-up of the i n i t i a l f i l l gas. The dotted l i n e i n Figure 18 shows the predictions of equation [1] for f u l l y ionized helium with the outer r a d i u s as a func-t i o n of time taken from the streak and shadowgram p l o t s , F i g u r e 7(A) or 7(B). At peak compression, the scattering measurements and p r e d i c t i o n s from t o t a l sweep-up correspond completely because the averaging p r o p e r t i e s of the scattering system and the averaging properties of equation [1] a l s o correspond. However, pr i o r to peak compression, the plasma density on-axis i s considerably lower than an i n t e r n a l l y uniform d i s t r i b u t i o n p r e d i c t s . The r a d i a l d i s t r i b u t i o n of electron density i s of course not uniform. Both the s t r e a k and shawdowgram s t u d i e s show t h a t most of the gas t h a t i s swept-up by the magnetic f i e l d remains confined w i t h i n a r e l a t i v e l y t h i n s h e l l up u n t i l about t = -50 ns. Prior to t h i s time, the plasma d e n s i t y i n s i d e the s h e l l (that i s , near the axis) w i l l be comparatively low and the scattering experiments have more than adequate s p a t i a l r e s o l u t i o n to show t h i s c l e a r l y . The average e l e c t r o n d e n s i t y of the s h e l l i t s e l f w i l l c l o s e l y follow the dotted l i n e since at these times, the plasma r a d i u s i s s m a l l compared with the s i z e of the v e s s e l so the amount of gas t h a t - 83 -remains to be c o l l e c t e d up w i l l contribute l i t t l e to the e l e c t r o n d e n s i t y of the s h e l l plasma. This concludes presentation of the Thomson scattering d i a g n o s t i c s and the Z-pinch plasma parameters obtained by this method. The f o l l o w i n g discussion provides a b r i e f review of some of the important aspects of he current scattering experiments. The scattering r e s u l t s have v e r i f i e d previous s p e c t r o s c o p i c mea-surements of the plasma parameters obtained f o r the pre and p o s t - p i n c h phases of the d i s c h a r g e . Where s p e c t r o s c o p i c (and other) d i a g n o s t i c s attempted previously have f a i l e d , scattering from ion acoustic f l u c t u a t i o n s has proved to be a valuable method for extending measurement c a p a b i l i t i e s i n t o the high temperature, high d e n s i t y phase. The plasma d e n s i t y and density gradients are s u f f i c i e n t l y large to r e s u l t i n s i g n i f i c a n t r e f r a c -t i o n at the ruby laser wavelength. This has introduced some problems with stray l i g h t . S p e c t r a l l y resolved detection, as i n the backscatter system, can aid i n discriminating against stray l i g h t . However, i n order to resolve the thermal ion spectrum i n the forward d i r e c t i o n , more e f f i c i e n t beam dumping w i l l be required. Two v i t a l aspects of the scattering experiments have l i m i t e d the d e t a i l with which the high compression phase could be i n v e s t i g a t e d . F i r s t -l y , the current arrangement of the s c a t t e r i n g systems has r e s u l t e d i n a lack of high s p a t i a l r e s o l u t i o n . Consequently, the measurements have given only the average l i n e - o f - s i g h t plasma conditions whereas the plasma temper-ature, d e n s i t y and r a d i a l v e l o c i t y d i s t r i b u t i o n w i t h i n the s c a t t e r i n g volume can be quite non-uniform. Secondly, the temporal r e s o l u t i o n afforded by the q-switching process i s i n s u f f i c i e n t to i s o l a t e some of the more rapid changes that occur during the on-axis collapse. Though these l i m i t a -tions are present, the scattering experiments, combined with the streak and shadowgram study, have c o n t r i b u t e d g r e a t l y to diagnosing the c u r r e n t z-pinch plasma. - 84 " The f i n a l experiment of t h i s thesis work attempts to give a second independent measurement of the electron density with, as well, the s p e c i f i c g o a l of overcoming the temporal and s p a t i a l l i m i t a t i o n s of the s c a t t e r i n g experiments, thus providing a more d e t a i l e d view of the peak compression phase. " 85 ~ CHAPTER 7 INTERFEROMETRIC DETERMINATION OF ELECTRON DENSITY 7.1 In t r eduction With scattering methods, the plasma i s interrogated at the micro-scopic l e v e l v i a p a r t i c l e f l u c t u a t i o n s . Such a technique i s important f o r the i n t e r a c t i o n experiments since the C0 2 laser can be absorbed by coupling d i r e c t l y to s p e c i f i c f l u c t u a t i o n s . Effects of the C0 2 laser can also be observed at the macroscopic l e v e l since l o c a l i z e d d i s t u r b a n c e s w i l l even-t u a l l y decay i n some hydrcdymanic fashion. Therefore, i n the next stage of diagnostic i n v e s t i g a t i o n , the Z-pinch i s examined by measuring a macro-scopic plasma parameter, namely, the index of r e f r a c t i o n . T h i s has been done using double exposure holographic interferometry. The interferometric measurements have given a complete two dimensional view of the plasma e l e c -tron density d i s t r i b u t i o n . These experiments then not only complement the scattering r e s u l t s with an independent measurement of n e, but also dramati-c a l l y improve s p a t i a l r e s o l u t i o n . The f i r s t s e c t i o n d e s c r i b e s the major advantage of the double exposure holographic technique and why t h i s method was s e l e c t e d over more conventional ones. Next, a simple approach to the formation and i n t e r p r e t a -t i o n of the interference pattern w i l l be given. However, the remainder of t h i s chapter expresses a concern for the a p p l i c a b i l i t y of i n t e r f e r o m e t r i c techniques to high density plasma, or i n general, h i g h l y r e f r a c t i n g phase objects. The problem r e s u l t s from the a d d i t i o n a l phase d i s t o r t i o n s i n t r o -duced as a r e s u l t of curvature i n the ray paths. Though the c a l c u l a t i o n s presented w i l l show that r e f r a c t i o n e f f e c t s are not of primary importance - 86 -for the c u r r e n t Z-pinch d i a g n o s t i c s , i t has i n f a c t been important to v e r i f y t h i s . In p a r t i c u l a r , i t i s v i t a l to p o i n t out t h a t the c u r r e n t l y used imaging arrangment may not be adequate f o r the proposed i n t e r a c t i o n experiments. 7.2 Double Exposure Holographic Method Holographic interferometry covers a wide range of topics i n optics and photographic processing (e.g. C o l l i e r e t . a l . , 1971). A very recent and complete treatment of the theory, p r a c t i c e , and a p p l i c a t i o n of h o l o g r a p h i c interferometry can be found i n the text written by Charles M. Vest (1979). No attempt w i l l be made here to describe a l l aspects of the method, though relevant features of the techniques involved, as they apply to the c u r r e n t experiments w i l l be pointed out where appropriate. This f i r s t section i l l u s t r a t e s the basic idea of the double expo-sure procedure and points out the most important d i f f e r e n c e between conven-t i o n a l interferometry and the holographic method, namely, that the methods are r e s p e c t i v e l y d i f f e r e n t i a l i n space or, d i f f e r e n t i a l i n time. The con-sequences of t h i s d i f f e r e n c e w i l l a l s o be d i s c u s s e d and i t w i l l be seen that the double exposure h o l o g r a p h i c technique o f f e r s a g r e a t d e a l of f l e x i b i l i t y i n the study of transient events. The double exposure method i s i l l u s t r a t e d i n Figure 19 which shows nothing more than a schematic arrangement for recording and r e c o n s t r u c t i n g o f f - a x i s holograms of a transparent object. In Figure 19(a), the i n c i d e n t laser beam i s s p l i t i n t o two beams which t r a v e l d i f f e r e n t paths before being recombined, and the i n t e r f e r e n c e p a t t e r n i s recorded on a photo-g r a p h i c p l a t e . One wavefront, d e s i g n a t e d the r e f e r e n c e beam, has a s p a t i a l l y uniform (or at l e a s t simple) amplitude and phase d i s t r i b u t i o n . This beam i s used holographically to record the amplitude and phase d i s t r i -- 87 -( A ) R e c o r d i n g l a s e r b e a m object r e l a y s p l i t t e r o p t i c s ( B ) R e c o n s t r u c t i o n FIGURE 19 I l l u s t r a t i o n of the double exposure method. - 88 -bution of the second wavefront, the scene beam. Since the o b j e c t under consideration i s transparent, upon transmission through the o b j e c t , o n l y the phase d i s t r i b u t i o n of the scene wavefront i s a l t e r e d while the a m p l i -tude d i s t r i b u t i o n remains unchanged. The scene beam also contains some unspecified r e l a y o p t i c s . T h i s could be a simple o p t i c a l delay for matching the beam paths to the coher-ence length of the laser source, and/or a more complicated imaging arrange-ment allowing f o r say, m a g n i f i c a t i o n of the o b j e c t wavefront onto the pl a t e . Though not shown, the reference beam as well could contain s i m i l a r beam handling or magnification matching components. This system then i s used to record two d i f f e r e n t scene beams on the same photographic p l a t e . The f i r s t exposure records the wavefront of the scene beam when the object i s not present, while the second exposure i s made with the o b j e c t i n p l a c e . The two scene beams must t h e r e f o r e be recorded at d i f f e r e n t times. However, af t e r development and processing of the p l a t e , a single reference beam i s used to reconstruct both scene beams simultaneously, as i l l u s t r a t e d i n Figure 19(B). Now, int e r f e r e n c e between the two reconstructed wavefronts can be observed and recorded. The d i f f e r -ence between the (reconstructed) scene beams i s due only to the presence of the object since a l l else i n the scene beam path was i d e n t i c a l f o r both exposures. Examination of the two scene beams of Figure 19(B), from the point of view of the polaroid f i l m , would lead to the conclusion that the i n t e r -ference pattern originated from a c o n v e n t i o n a l M i c h e l s o n or Mach-Zender interferometer with a transparent, phase d i s t o r t i n g object i n one arm. In th i s sense then, the double exposure holographic technique j u s t d e s c r i b e d merely mimics a l l the usual i n t e r f e r o m e t r i c methods except tha t the two wavefronts of i n t e r e s t are permanently recorded through holography and can be viewed at l e i s u r e . The most important d i f f e r e n c e though i s t h a t the i n t e r f e r i n g wavefronts i n the double exposure method o r i g i n a t e , not from - 89 -d i f f e r e n t regions of space, but from d i f f e r e n t times. Conventional i n t e r -ferometry i s j u s t the opposite since the beams that i n t e r f e r e must be p r e -sent simultaneously but t r a v e l through d i f f e r e n t regions of space. In the following b r i e f discussion, the f l e x i b i l i t y allowed by the i n t e r f e r o m e t r i c studies which are d i f f e r e n t i a l i n time are pointed out through the example of the current laser/plasma i n t e r a c t i o n experiments. In the present experiment, the f i r s t exposure can be made before f i r i n g the Z-pinch discharge and the vessel contains low p r e s s u r e helium. The second exposure can then be taken at v a r i o u s times during the p i n c h phase. Each exposure w i l l l a s t only for the d u r a t i o n o f the l a s e r pulse, which must of course be short enough that the plasma appears as a s t a t i o n -ary object. The interference pattern produced w i l l be e n t i r e l y e q u i v a l e n t to that obtained i n say a Mach-Zender configuration where the plasma i s i n one arm of the interferometer and there i s a uniform r e f r a c t i v e index d i s -t r i b u t i o n i n the other arm. In t h i s instance then, a holographic record of the wavefronts might only be considered an advantage because i t allows some f l e x i b i l i t y for subsequent image processing. Using a short pulse laser for h o l o g r a p h i c i n t e r f e r o m e t r y allows for another possible exposure sequence. If i t i s arranged to have the time i n t e r v a l between exposures also very short, then both exposures could be obtained during the pinch phase. Then, only the change i n plasma conditions which occurred i n the time i n t e r v a l between exposures would be seen i n the reconstructed interference pattern. One could therefore completely i s o l a t e r a pid plasma motions from more s l o w l y v a r y i n g 'ambient' c o n f i g u r a t i o n s (Armstrong, 1977). As an example, a p p l i c a t i o n of such an arrangement w i l l be of p a r t i c u l a r importance i n i s o l a t i n g e f f e c t s of the CO2 laser i n the proposed i n t e r a c t i o n experiments since the CO2 laser pulse w i l l l a s t for the order of a nanosecond or l e s s , a time s c a l e over which the t a r g e t plasma i s e s s e n t i a l l y stationary. However, the most often cited example of - 90 -the temporal i s o l a t i o n advantage of double exposure holographic i n t e r f e r o -metry i s when the ambient c o n f i g u r a t i o n c o n t a i n s r a t h e r poor q u a l i t y o p t i c s , a circumstance which cannot be t o l e r a t e d w i t h c o n v e n t i o n a l methods. In any event, the above p o s s i b i l i t i e s a r i s e from the f a c t that the double exposure method i s d i f f e r e n t i a l i n time. For the present purposes, the f i r s t i n t e r f e r o m e t r ic measurements were intended to extend the s c a t t e r -ing r e s u l t s by examining the plasma configuration during maximum compres-sion, that i s , when the f i r s t exposure i s made before f i r i n g the discharge. For t h i s case, Section 7.4 g i v e s a simple a n a l y s i s of the formation and i n t e r p r e t a t i o n of the interference pattern. Before doing t h i s though, the following short section e s t a b l i s h e s some data f o r the plasma r e f r a c t i v e index as a function of electron density. 7.3 Plasma Refractive Index The basic plasma property that i s of i n t e r e s t f o r i n t e r f e r o m e t r y i n the index of r e f r a c t i o n which, i n i t s s i m p l e s t form (Jahoda, 1971) i s related to the electron density through equation [2]. y(r) = (1 - n e / n c ) V 2 The index of r e f r a c t i o n depends on the wavelength at which i t i s measured, through the c r i t i c a l density, n c , where: n c = 1.12 x 10 2 1X" 2 cm"3, i f the wavelength i s given i n microns. Using ruby laser l i g h t , n c =2.33 x 10 2 1 cm - 3. In terms of i n t e r f e r o m e t r i c measurements, the r e f r a c t i v e index d i f f e r s s i g n i f i c a n t l y from u n i t y when the e l e c t r o n d e n s i t y becomes the order of 1% n c . For comparison, the plasma r e f r a c t i v e index i s smaller than un i t y by about the same amount that ordinary a i r i s l a r g e r than u n i t y , a t an electron density of 0.05% n c . This provides a more or less quantitative d i s t i n c t i o n between high and low density plasma, the current Z-pinch being i n the former category. In what f o l l o w s l a t e r , the a c t u a l numbers i n v o l v e d may be o f i n t e r e s t , so, as a matter of convenience and r e f e r e n c e , F i g u r e 20 i s included here to show the plasma r e f r a c t i v e index at the wavelength of ruby laser l i g h t . 7.4 Formation of the Fringe Pattern This section gives a simple analysis of the generation and i n t e r -p r e t a t i o n of the interference pattern produced when the e f f e c t s of r e f r a c -t i o n are not important. As w i l l be seen l a t e r , r e f r a c t i o n e f f e c t s , as well as generating a good deal more mathematical complication, w i l l a l s o i n t r o -duce a more serious problem. The basic ideas presented here though w i l l remain unchanged when r e f r a c t i o n i s included. The pinch plasma i s assumed to have a symmetric e l e c t r o n d e n s i t y d i s t r i b u t i o n , n e = n e ( r ) which does not vary along the plasma column, i . e . : - 92 -FIGURE 20 The plasma r e f r a c t i v e index vs. electron density. - 93 -i n the z d i r e c t i o n . The plasma can therefore be replaced by i t s equivalent r e f r a c t i v e index d i s t r i b u t i o n according to equation [ 2 ] . In F i g u r e 2 1 , a c r o s s - s e c t i o n of the plasma column i s shown where V = u (r) i n s i d e a maximum radius of r Q . For r > r Q , u = u = 1 . o The plasma i s illuminated by a collimated beam, entering p a r a l l e l to the x-axis. Consider then the o p t i c a l pathlength of a ray i n c i d e n t at height y. The l i g h t ray i s assumed not to d e v i a t e from a s t r a i g h t l i n e path. Ray curvature due to r e f r a c t i o n e f f e c t s i s therefore ignored. As a f i r s t or reference exposure, plasma i s not p r e s e n t and the ray t r a v e l s an o p t i c a l path 1 = u (x n-x.) i n going from A to B. For O O B A the second exposure, the plasma i s i n place and the o p t i c a l path from A to B i s now 1-| , where l t = J u ( r j d x evaluated over the l i m i t s to X-Q. The path diff e r e n c e Al = 1 q - 1^, bet-ween reference and scene ray can be expressed a l t e r n a t i v e l y as a phase di f f e r e n c e A<f> = 2irAl/X or, more appropriately, i n terms of the number of wavelengths P = Al/X . (Lambda w i l l be co n s i s t e n t l y taken as the vacuum waveleng th.) N Upon reconstruction, the two wavefronts are present simultaneously and they w i l l i n t e r f e r e . The interference pattern that i s then produced w i l l d i s p l a y contours of constant P, interference maxima o c c u r r i n g when P i s i n t e g e r while h a l f - i n t e g e r P correspond to minima. In the f r i n g e pattern, the only d i r e c t l y measurable quantity i s the fringe number P. The desired pathlength information i s t h e r e f o r e obtained by simply counting f r i n g e s . Each fringe i s located i n the interference pattern and i d e n t i f i e d by i t s corresponding value of P. - 94 ->v-1 FIGURE 21 ray path without r e f r a c t i o n . - 95 -With the axisymmetric configuration of Figure 21 , i t i s clear that the f r i n g e number depends only on y X l r B P(y) - ( y o - y ( r ) ) d x , r 1 6 ] XA whereas the r e f r a c t i v e index i s a f u n c t i o n of the r a d i a l c o o r d i n a t e r . Equation [16] can be shown to be the Abel t r a n s f o r m r e l a t i o n s h i p between the observable function, P(y) and the l i n e i n t e g r a l of the desired function u ( r ) . Standard numerical routines (e.g. Fan, 1975) can then be used to Abel i n v e r t the i n t e r f erometric data to give the complete r a d i a l d i s t r i b u -t i o n u(r) and therefore ng(r). The analysis and equations leading to the d i s t r i b u t i o n of f r i n g e s P(y) i n the interference pattern i s not so s t r a i g h t forward i f ray r e f r a c -t i o n i s taken into account. In p a r t i c u l a r , Abel i n v e r s i o n i s no longer s t r i c t l y v a l i d s i n c e t h i s assumes e x p l i c i t l y t h a t the r a y p a t h s a r e s t r a i g h t l i n e s . However, without this assumption the u n f o l d i n g of i n t e r -ferometric data becomes an extremely lengthy and-complex procedure, and, i n f a c t , the data can be ambiguous enough to make interferometry an unsuit-able diagnostic. In the following section, the problem of ray r e f r a c t i o n i n an axisymmetric object i s outlined and the assumption of s t r a i g h t l i n e paths i s considered i n order to i l l u s t r a t e the care which must be taken when performing interferometry on highly r e f r a c t i n g objects. - 96 -7.5 The Problem of Imaging In order to help reduce the e f f e c t s of r e f r a c t i o n , wavefronts are recorded by using a lens or system of lenses to form an image of the object d i r e c t l y on the photographic p l a t e . T h i s i s of course a more or l e s s obvious approach to the problem of r e f r a c t i o n , depending on how the a c t u a l imaging process i s viewed. From the point of view of interferometry, o n l y the phase r e l a t i o n s h i p between reference and scene ray, at a given point i n the object, i s of i n t e r e s t . By producing an image of the o b j e c t , a lens acts to r e s t o r e the o r i g i n a l phase r e l a t i o n s h i p , i n d e p e n d e n t l y of the d i r e c t i o n s the two rays may have l e f t the o b j e c t p o i n t i n q u e s t i o n . One can then see the necessity of using some imaging element when r e f r a c t i o n cannot be neglected. The basic question to be considered i n this section can be s t a t e d as follows. Given an axisymmetric r e f r a c t i v e index d i s t r i b u t i o n , where, i n r e l a t i o n to the object, must the image plane be located i n order to neglect the e f f e c t s of r e f r a c t i o n when analyzing interferometric data? T h i s ques-t i o n i s c l e a r l y related to the present Z-pinch i n v e s t i g a t i o n , but i t i s of considerably more general i n t e r e s t . For example, i n v i r t u a l l y a l l l a s e r / plasma experiments the f o c a l volume of the laser i s c y l i n d r i c a l or c o n i c a l . The plasma contained i n the f o c a l volume can therefore be described i n an axisymmetric coordinate system. Equally important i s that such plasmas have high electron d e n s i t i e s and are therefore strongly r e f r a c t i n g objects. This question has been addressed, i n part, by Vest (1975) who has shown that ray curvature e f f e c t s can i n f a c t be n e g l e c t e d i f the plasma axis (the plane x=0 of Figure 21) i s imaged. Then, Abel i n v e r s i o n of the fringe data, based on the assumption of s t r a i g h t l i n e paths, w i l l y i e l d the cor r e c t d i s t r i b u t i o n u(r) to within a few percent. This r e s u l t was shown to be v a l i d even f o r very extreme cases of r e f r a c t i o n by axisymmetric objects. However, only the image plane l o c a t e d p r e c i s e l y on the a x i s of symmetry was examined. In order to o b t a i n a more complete p i c t u r e and - 97 -therefore gain a better understanding of the true l i m i t a t i o n s of Ve s t ' s r e s u l t s , i t was f e l t t h a t c o n s i d e r a t i o n should be g i v e n to other image planes, p a r t i c u l a r l y i n view of the f a c t that i t may not always be possible to know before hand where p r e c i s e l y the plasma w i l l be located. (Based on the e a r l i e r discussions of the Thomson scattering r e s u l t s , t h i s p o s s i b i l i t y has indeed shown i t s e l f to be quite r e a l i n the present d i a g n o s t i c e x p e r i -ments. ) In the following d e s c r i p t i o n i t w i l l be shown how v a r i o u s image planes have been analyzed. Figure 22 depicts again an axisymmetric r e f r a c t i v e index d i s t r i b u -t i o n u = u(r) extending to a radius R Q , beyond which the r e f r a c t i v e index i s unity. The probe beam i s collimated and enters from the l e f t , p a r a l l e l to the x-axis. A photographic p l a t e , used to r e c o r d the wavefronts, i s imaged into the object at the plane x = X£ m a - j e . In the presence of the object, one ray of the probe beam i s shown entering the d i s t r i b u t i o n at a height y = B and t r a v e l l i n g the r e f r a c t e d path CD. This ray leaves the o b j e c t a t an angle ^ with r e s p e c t to the x-axis. In the discussion of r e f r a c t i o n angles i n Chapter 3, the d i f f e r e n -t i a l ray path was given i n c y l i n d r i c a l coordinates by Bouguer's formula: i X = | ( u 2 r 2 . B 2 ^ , [ 3 ] and the angular deviation can then be determined (Schreiber, et a l . , 1 973) as: R o iKB) = 2 c o s _ 1(B/R o) - 2 (dr/d0)- 1dr . r m The lower i n t e g r a t i o n l i m i t i s the i n f l e c t i o n point of equation [ 3 ] , where the d e r i v a t i v e i s zero. To avoid a d d i t i o n a l complications to th i s d e s c r i p -t i o n , i t w i l l be assumed that there i s only one such stationary point with-- 98 -FIGURE 22 Imaging i n a strongly r e f r a c t i n g plasma. - 99 -i n the d i s t r i b u t i o n . The equations presented here can be e a s i l y extended, i f desired, i n a piecewise fashion, to include more elaborate d i s t r i b u t i o n functions. Now, when the ray i n q u e s t i o n , namely the scene r ay, e x i t s the d i s t r i b u t i o n , i t t r a v e l s a s t r a i g h t l i n e path dy/dx = c o n s t . = tan . Extrapolating backwards, t h i s scene r a y i n t e r s e c t s the image plane a t a height y = B^. When the reference exposure i s taken, the object i s not pre-sent and the ray which w i l l i n t e r f e r e with the above scene ray i s j u s t that reference ray which also i n t e r c e p t the image plane at height y = B^. This reference ray i s shown i n Figure 22 t r a v e l l i n g p a r a l l e l to the x-axis along the path GEHF. The reference and scene rays of Figure 22 w i l l i n t e r f e r e according to t h e i r r e l a t i v e phase, or o p t i c a l path d i f f e r e n c e , a t the photographic p l a t e . To determine the path d i f f e r e n c e , c o n s i d e r f i r s t the scene r a y which, ins i d e the d i s t r i b u t i o n , t r a v e l s an o p t i c a l p a t h l e n g t h L g i v e n by the i n t e g r a l of u(r)ds from point C to point D. Here, ds i s an incremen-t a l arc segment along the refracted path. In c y l i n d r i c a l coordinates ( d s ) 2 = ( d r ) 2 + ( r d 9 ) 2 = ( d r ) 2 ( l + r 2 ( d 6 / d r ) 2 ) . Using equation [3] and the assumption that the d i s t r i b u t i o n i s symmetric about the stationary point g i v e s : R ° u 2 r d r . l 1 8 l r m The reference ray path to be compared with L i s found by f i r s t noting that both reference and scene rays can be considered i n phase at the points G and C r e s p e c t i v e l y . Secondly, on the e x i t s i d e of the d i s t r i b u -- 100 -t i o n , the curve through points D and H i s a c i r c u l a r arc ce n t e r e d at the apparent point of o r i g i n of the two rays. Through an i d e a l imaging system, both rays w i l l t r a v e l the same o p t i c a l path from D or H to the r e c o r d i n g f i l m . Therefore, the o p t i c a l path d i f f e r e n c e between the r e f e r e n c e and scene rays shown w i l l be: The interference pattern observed w i l l d i s p l a y contours of con-stant d e l t a , and the interferogram i s analyzed by simply counting f r i n g e s . For the experiment d e p i c t e d i n F i g u r e 22, the measured d i s t r i b u t i o n of fringes i n the image plane w i l l be c a l l e d M, where: M(y) = A(y)/X . [20] Because the r e f r a c t i v e index d i s t r i b u t i o n i s axisymmetric, M and d e l t a are indicated e x p l i c i t l y to be only a function of the y coordinate i n the image plane. I m p l i c i t l y though, M i s understood to be also a function of Ximage' the l o c a t i o n of the image plane. Given a s p e c i f i c r e f r a c t i v e index d i s -t r i b u t i o n , equations [3], and [17] to [20] allows the fringe f u n c t i o n M to be calculated for any desired image plane. The question being asked here can now be restated as follows. How does the observed function M(y) d i f f e r from the f r i n g e f u n c t i o n P(y) i n equation [16], where P(y) i s calculated on the assumption t h a t no r e f r a c -t i o n takes place? If P and M d i f f e r s i g n i f i c a n t l y , then Abel i n v e r s i o n of the observed data w i l l not y i e l d the c o r r e c t r e f r a c t i v e index d i s t r i b u -t i o n . As the equations i n v o l v e d are not v e r y amenable to a n a l y t i c a l i n v e s t i g a t i o n , they have been s o l v e d n u m e r i c a l l y , with the observed and assumed functions, P and M, being compared i n the following manner. - 101 -The image plane i s divided into N evenly spaced values of y, with the spacing given by y m a x / N , where: M (Y >. vmax> = 0. Depending of course on the image plane chosen, the observed f r i n g e p a t t e r n w i l l extend out to at l e a s t y m a x = R D. Also, for each of the N y-coordin-ates i n the observed pattern, the s t r a i g h t l i n e f r i n g e f u n c t i o n , P(y) i s c a l c u l a t e d . The measured and assumed f r i n g e p a t t e r n s are determined to d i f f e r by an amount: P(0) N I '{M(y.)-P(y.)} 2/N i = l [21] With the majority of the c a l c u l a t i o n s that were performed, sigma was essen-t i a l l y i n v a r i a n t for N > 10. However, for those r e s u l t s presented here, N = 50 was used to ensure a completely representative sampling. The normaliz-ati o n factor P(y = 0) = M(y = 0) , makes sigma independent of the a c t u a l s i z e of the r e f r a c t i v e index d i s t r i b u t i o n , so t h a t e q u a t i o n [21] can be used as a basis for comparing a large v a r i e t y of experiments. Several f u n c t i o n a l forms f o r the r e f r a c t i v e index d i s t r i b u t i o n were examined. As a t y p i c a l example, equation [21] w i l l be presented using the following parabolic function: y(r) = 1 - e ( l - r 2 ) , r < 1 [ 2 2 ] = 1 , r > 1 . Figure 23 d i s p l a y s several curves of c o n s t a n t sigma, g i v e n as a function of the r e f r a c t i v e index on-axis and the l o c a t i o n of the image - 102 -plane. The axis of symmetry for the object i s located at x = 0, as i n d i -cated i n Figure 22. Given the r e f r a c t i v e at r = 0, F i g u r e 23 shows t h a t the error introduced by assuming s t r a i g h t l i n e paths w i l l increase as the image plane i s moved in c r e a s i n g l y farther behind (x < 0), or i n front (x > 0) of the a x i s . As w e l l , f o r a p a r t i c u l a r maximum e r r o r , the allowed l a t i t u d e i n locating the image plane decreases very d r a m a t i c a l l y as the r e f r a c t i v e index begins to deviate from u n i t y . A not so extreme example (Sweeney, et a l . , 1976) might be that, i f , at y(r = 0) = 0.8, the average error i n the observed fringe pattern i s to be less than 5%, then the image plane must be located within the object with a p r e c i s i o n of b e t t e r than +_ 1/10 the diameter of the object. I t w i l l be noted a l s o t h a t i n F i g u r e 23, the apparent optimum image plane i s located j u s t i n front of the a x i s , at a s l i g h t l y p o s i t i v e value of x. However, the image planes being c o n s i d e r e d are the image locations i n vacuum. When the object i s in place, i t w i l l , i n the p r e s e n t case, act l i k e a diverging lens and displace the vacuum image more towards the a x i s . Thus, the combined e f f e c t of the 'plasma l e n s ' and e x t e r n a l lens r e s u l t s i n an image of the axis of symmetry. On the other hand, i f the object considered had a r e f r a c t i v e index always larger than 1, that i s , e < 0 i n equation [22] , the apparent optimum image plane would be s l i g h t l y negative. There are two aspects of equation [21], as presented i n Figure 23, which should be kept i n mind. F i r s t l y , Figure 23 i n d i c a t e s only the average error introduced i n the observed fringe pattern when i t i s assumed that the pattern has been generated by unrefracted rays. S p e c i f i c areas of a g i v e n fringe pattern w i l l show deviations that can be s i g n i f i c a n t l y more severe, p a r t i c u l a r l y i n regions where the gradients that must be traversed are very steep. Secondly, though the parameter sigma i s a natural choice for compar-ing the fringe patterns M(y) and P(y), c r i t i c a l examination of the s t r a i g h t l i n e path assumption must ultimately be performed on the d e s i r e d f u n c t i o n y ( r ) . However, from an experimental standpoint, the b a s i c o bservable i s only M(y). Since the Abel inversion process can be viewed as a weighted - 103 -image plane, x FIGURE 23 Errors introduced i n an interferogram by assuming s t r a i g h t l i n e paths. - 104 -i n t e g r a t i o n over the slope of the fringe, f u n c t i o n , i t may be more appro-p r i a t e to make comparisons based on the d e r i v a t i v e s of M and P, rather than on the functions themselves. The problem of imaging i n h i g h l y r e f r a c t i v e o b j e c t s i s a non-t r i v i a l one and has yet to be s o l v e d i n any g e n e r a l l y s a t i s f a c t o r y way. The c a l c u l a t i o n s that have been shown here do, however, give a better i n d i -cation of the l i m i t a t i o n s of interferometry as a d i a g n o s t i c f o r h i g h den-s i t y plasma. For the present Z-pinch diagnostics, the minimum r e f r a c t i v e index on axis w i l l be i n the range 0.99 to 0.98. Since the Z-pinch plasma has a s i z e the order of a few millimeters and can c u r r e n t l y be located with about t h i s p r e c i s i o n , Figure 23 shows that these in v e s t i g a t i o n s w i l l not be dominated by imaging considerations. The f o l l o w i n g chapter d e s c r i b e s i n d e t a i l the complete experimental arrangement used to perform i n t e r f e r o -metric measurements on the Z-pinch plasma. - 105 -CHAPTER 8 LAYOUT OF THE INTERFEROMETRIC EXPERIMENT i 8.1 Introduction The l i g h t source f o r producing i n t e r ferog rams i s again a ruby l a s e r . Operating the laser i n Q-switched mode produces exposure times i n the 20 to 30 ns range. However, the electron density can change s i g n i f i -c a n t l y over the duration of a Q-switched pulse so t h a t the plasma cannot always be considered stationary. The e f f e c t of plasma motion during an exposure w i l l be to smear out the interference pattern. Though i n t e r f e r o-metry was attempted with a Q-switched pulse, the r e s u l t s were not s a t i s -f a c t o r y . The f i r s t s e c t i o n i n t h i s chapter shows a simple ruby l a s e r o s c i l l a t o r that uses c a v i t y dumping generating much s h o r t e r l i g h t p u l s e s . The remainder of the chapter outlines many pertinent d e t a i l s of the r e s t of the experimental arrangement including the optics of the scene and r e f e r -ence beam paths as w e l l as photographic p r o c e s s i n g and r e c o n s t r u c t i o n data. 8.2 Cavity Dumping of the Laser O s c i l l a t o r The idea and theory of laser c a v i t y dumping was f i r s t presented by A. Vuylsteke (1963). Since then, many d i f f e r e n t arrangements have been used to extract short duration l i g h t pulses from a l a s e r c a v i t y (Siegman, 1973; Hamal, 1978). Here, a very simple scheme i s used and the e s s e n t i a l aspects of the procedure can be described with the aid of F i g u r e 24. The upper portion of t h i s figure shows the current arrangement of components i n the o s c i l l a t o r c a v i t y . The rear mirror i s 100% r e f l e c t i n g while the previously d e s c r i b e d etalon remains as a f r o n t mirror. PC1 and PC2 are p o c k e l s c e l l s and the p o l a r i z e r i s c a l c i t e i n a Glan-Thompson arrangement. Without PC2 p r e s e n t , - 106 -100% p o l . r u b y r o d e t a l o n FIGURE 24 O s c i l l a t o r and amplifier sections of the c a v i t y dumped l a s e r . - 107 -the c a v i t y appears as a conventional Q-switched o s c i l l a t o r . PC1 and the p o l a r i z e r provide the Q-switching ac t i o n . PC2 i s placed inside the c a v i t y and, with no v o l t a g e a p p l i e d , i t behaves merely as a p a s s i v e , f r e e l y transmitting component. I n i t i a l l y , the quarter wave r o t a t i o n voltage i s held on PC1 while the ruby rod i s pumped. At maximum inversion the voltage on PC1 i s dropped to zero, now rendering PC1 also f r e e l y transmitting. This i n i t i a t e s b u i l d -up of the Q-switched pulse. In Figure 24, the preferred p o l a r i z a t i o n inside the c a v i t y i s i n the plane of the page. However, when the photon d e n s i t y i n s i d e the c a v i t y i s maximum, the quarter wave voltage i s a p p l i e d to PC2. Photons which now double pass through PC2 w i l l have t h e i r p o l a r i z a t i o n rotated by 90° and be r e f l e c t e d or dumped by the p o l a r i z e r . The time i t takes to dump a l l l i g h t from i n s i d e the c a v i t y i s determined purely by the c a v i t y t r a n s i t time. If n i s the average r e f r a c -t i v e index, L the distance between f r o n t and r e a r m i r r o r s , and c i s the speed of l i g h t , then the ca v i t y dumped pulse w i l l have a t o t a l d u r a t i o n of t - 2 nL/c, approximately twice the mirror-to-mirror t r a n s i t time. Currently, nL =75 cm giving a pulse width of about 5 ns. T h i s i s a considerable improvement over the Q-switched pulse d u r a t i o n . However, the c a v i t y length need not l i m i t the pulse width since PC2 can be s u p p l i e d with a voltage pulse that i s s h o r t e r than the double t r a n s i t time. The s i m p l i c i t y of c a v i t y dumping makes i t q u i t e an a t t r a c t i v e method f o r generating pulses i n the 1 to 10 ns range. In order to extract high energy pulses by ca v i t y dumping one would norm a l l y c o n s i d e r r e p l a c i n g the e t a l o n with a second 100% r e f l e c t i n g mirror. The etalon here provides l o n g i t u d i n a l mode se l e c t i o n to improve the temporal coherence l e n g t h of the l a s e r . L i g h t coupled out through the etalon, though representing a s i g n i f i c a n t f r a c t i o n of the ava i l a b l e energy, i s simply rejected. - 108 -The lower portion of F i g u r e 24 shows the remainder of the ruby laser system, which i s simply a double pass amplifer s t age. The o n l y odd component here i s a second c a l c i t e p o l a r i z e r used to steer the beam through the a m p l i f i e r . The reason for t h i s i s one of e x p e r i m e n t a l convenience. The e n t i r e o p t i c a l system i s a l i g n e d using the beam o f a low power Helium-Neon l a s e r . In the c a v i t y dump d i r e c t i o n , l i g h t does not leave the f i r s t c a l c i t e p o l a r i z e r normal to the e x i t face. Consequently, the a l i g n -ment beam and ruby laser beam e x i t the o s c i l l a t o r c a v i t y at s l i g h t l y d i f f -erent angles. Dispersion data for c a l c i t e (Machewirth, 1979) shows t h i s d i f f e r e n c e to be approximately 0.05°. The second p o l a r i z e r compensates f o r the d i s p e r s i o n of c a l c i t e , allowing the whole experiment to be aligned with the He-Ne l a s e r . 8.3 Optics of the Beam Paths After leaving the a m p l i f i e r , the ruby laser has a beam diameter of approximately 2.5 mm. Natural d i v e r g e n c e over a 9 m path i n c r e a s e s the beam diameter to about 6 mm. A f i n a l x4 beam expander, with a f o c a l plane pinhole, i s used to f i l t e r and collimate the beam f o r i n t e r f e r o m e t r y . Figure 25 shows a p a r t i a l l y s i m p l i f i e d v e r s i o n of the remainder of the interferometer o p t i c s . Passing the beam through a 50% r e f l e c t i n g m i r r o r p r o v i d e s equal amplitude reference and scene beams. The scene beam i s d i r e c t e d r a d i a l l y i n t o the discharge vessel. A system of three lenses produces an image of the plasma axis on the photographic plate, with a t o t a l m a g n i f i c a t i o n of x3.5. The photographic plate i t s e l f i s housed i n a l i g h t t i g h t box i n d i c a -ted by the dotted rectangle i n Figure 25. The angular acceptance of the imaging o p t i c s i s l i m i t e d by l e n s L1 to a f u l l cone angle of 7.2° or F/8.0. In the reference arm, lens L2 focusses the reference beam through a s p a t i a l f i l t e r pinhole P1. The beam subsequently expands f r e e l y to s t r i k e ~ 109 " FIGURE 25 Optics of the interferometry experiment. 110 -the plate a t an angle of 5° w i t h r e s p e c t to the scene beam. Two other lenses i n the reference arm serve simply to i n v e r t t h i s beam so t h a t the recombined wave fronts have the proper s p a t i a l o r i e n t a t i o n with r e s p e c t to each other. Even with the provisions for beam f i l t e r i n g , the s p a t i a l coherence of the laser was not p a r t i c u l a r l y good. Lense L2 was chosen to expand the reference beam by e x a c t l y the same amount as the scene beam. Then, by adjusting mirror M1, both beams could be p r e c i s e l y overlaped on the p l a t e . Lack of s p a t i a l coherence was therefore not a problem. Considering temporal coherence, both beam paths are matched to within 5 to 10 mm over the 8.5 m distance from beam s p l i t t e r to p l a t e . This matching was s u f f i c i e n t to pro-duce good q u a l i t y f r i n g e s . 8.4 Recording and Post Exposure Processing The wave fronts are recorded on Kodak type 120-02 high r e s o l u t i o n holographic p l a t e s . This 0.006 mm thick emulsion has a contrast index bet-ween 4 and 6 (depending on development time) and r e q u i r e s an exposure of o about 300 ergs/cm 2 at 7000 A to produce a developed density D = 1.0. After both exposures are made, the p l a t e s a r e p r o c e s s e d i n the s t a n d a r d recommended fashion using D-19 for 5 minutes as the developer stage. Many of the photographic emulsions a v a i l a b l e f o r holography have high contrast, making them very s e n s i t i v e to v a r i a t i o n s i n exposure. Be-cause of t h i s , and since the ruby laser Intensity can f l u c t u a t e by 50% or more from shot to shot, exposures are bi a s e d towards the heavy s i d e to ensure that each shot gets f u l l y recorded. After development, the p l a t e s have a density usually ranging from 1 to 4. The f i n a l step b e f o r e r e c o n -s t r u c t i o n then i s to b l e a c h the emulsion using a simple, d r y , bromine vapour method (Graube, 1974). - 111 -The procedure of heavy over exposure and subsequent b l e a c h i n g i s quite standard i n h o l o g r a p h i c i n t e r f e r o m e t r y . T h i s i s because one i s interested i n producing high contrast fringes rather than recording l i n e a r -i t y . As well, bleached holograms have very high d i f f r a c t i o n e f f i c i e n c i e s (Chang, 1970). This g r e a t l y f a c i l i t a t e s both alignment of the r e c o n s t r u c -t i o n o p t i c s , and photographing of the interference pattern. When recording the holograms, the plate i t s e l f was imaged onto the plasma axis to eliminate r e f r a c t i o n e f f e c t s . In order to m a i n t a i n t h i s feature i n reconstruction, the interference pattern must be recorded a t an image of the pl a t e . Reconstructions of the wave fronts are obtained using helium-neon laser l i g h t and a simple, single lens imaging arrangement. The helium-neon laser serves as the o r i g i n a l r e f e r e n c e beam and the p l a t e i s illuminated from the emulsion side, as was done during the r e c o r d i n g pro-cess. Using only the f i r s t order transmitted l i g h t (corresponding to the o r i g i n a l scene beams), the pl a t e , and therefore plasma axis, i s imaged onto ordinary polaroid f i l m . High r e s o l u t i o n f i l m i s not required to record the interference pattern since the lens allows the plate image to be magnified as desired. - 112 -CHAPTER 9 RESULTS FOR THE Z-PINCH PLASMA 9.1 General Features of the Interfer eg rams This section presents a q u a l i t a t i v e i n t e r p r e t a t i o n and d i s c u s s i o n of the fri n g e patterns that were observed. The f i r s t exposure was made pr i o r to f i r i n g the discharge. The second exposure, made at var i o u s times during the pinch phase, i s again referenced i n time to the d l / d t t r a c e . A few reconstructed interference patterns are shown i n F i g u r e 26. The c i r -cular f i e l d of view represents the holes (1.9 cm diameter) i n the discharge v e s s e l . The z-axis of the discharge vessel corresponds to a l e f t to r i g h t diameter of these c i r c l e s . If the plasma had pe r f e c t c y l i n d r i c a l symmetry, the f r i n g e s would be s t r a i g h t l i n e s running p a r a l l e l to, and symmetrically centered about the d i s c h a r g e a x i s . T h i s i s c l e a r l y not the case here. Each p h o t o g r a p h d i s p l a y s quite a complex two dimensional structure. This lack of symmetry i s introduced i n t o the plasma column during the f o r m a t i v e stages of the discharge, when current i s flowing along the i n t e r i o r w a l l of the v e s s e l . In the v i c i n i t y of the access p o r t s , there i s of course the p h y s i c a l perturbation of the holes i n the v e s s e l . Along with t h i s , there i s a complex d i s t o r t i o n of the magnetic f i e l d configuration since there are also holes i n the outer return conductor. The interferometric experiments were performed using a vessel with four holes, two for the diagnostics and two for the CO2 l a s e r . In Chapter 2 i t was pointed out that these holes constitute a s i g n i f i c a n t f r a c t i o n of the circumference of the vessel so that complete r o t a t i o n a l symmetry of the plasma column was not expected. However, the s e v e r i t y of the d i s t o r t i o n s could not be predicted and there was some hope that the symmetry would not - 113 -F I G U R E 2 6 Samples of the interferograms obtained near peak compression. The observa-ti o n times are: (A) t = (B) t = (C) t = (D) t = -31 ns, -30 ns, -90 ns, and +85 ns. - 114 -be degraded to the extent seen i n Figure 26. For comparison, the shadow-gram photographs shown i n Figure 5 were obtained using a d i s c h a r g e v e s s e l having only the two diagnostic ports. With only two holes i n the v e s s e l , the plasma symmetry i s well preserved. Apart from the lack of symmetry, formation of the plasma from shot to shot i s quite reproducible. This i s best i l l u s t r a t e d i n F i g u r e s 26(A) and 26(B), which were both taken at i d e n t i c a l times t = -30 ns. In the low density regions, outside the plasma core, the fringes are broad and w i d e l y spaced. In these regions of the plasma, both fringe patterns are remarkably si m i l a r i n terms of spacing, number, and contour of the f r i n g e s . Interfero-metric measurement techniques are characterized by their high s e n s i t i v i t i e s so that, r e l a t i v e l y small v a r i a t i o n s i n the plasma d i s t r i b u t i o n would be apparent i n the fringe pattern. As a very rough guide, the average electron density changes by about 1 x 1 0 1 7 cm - 3 i n going from a maxima to the adja-cent f r i n g e minima. S i m i l a r i t i e s between the fringe patterns of Figures 26(A) and (B) extend i n t o the more dense regions of the plasma core. Though the f r i n g e s here are c l o s e l y spaced and d i f f i c u l t to see i n these reproductions, there i s a considerable degree of correspondence between s t r u c t u r a l d e t a i l s of the two interference patterns. Near the time of maximum compression (again F i g u r e s 26(A) and (B)), the interferograms often do not show a clear fringe pattern through-out the v i c i n i t y of the plasma a x i s . Lack of f r i n g e s near the a x i s i s p r i m a r i l y the r e s u l t of r e f r a c t i o n of the probe beam. Though i t remains true here that ray bending w i l l be compensated f o r s i n c e the i n t e r f e r i n g beams are recombined at an image of the plasma a x i s , the imaging system must be able to c o l l e c t a l l r e f r a c t e d l i g h t . The c u r r e n t o p t i c s has an acceptance cone of F/9 which i s not s m a l l enough to c o l l e c t those rays passing through the strongly r e f r a c t i n g regions of the core. - 115 -FIGURE 27 I l l u s t r a t i o n of the region for which interferograms were analyzed. - 1 1 6 -Though r e f r a c t i o n i s at l e a s t p a r t i a l l y r e s p o n s i b l e f o r missing f r i n g e s i n the core region, motional blurring may s t i l l be a c o n t r i b u t i n g f a c t o r . The following e s t i m a t e i n d i c a t e s t h a t the f r i n g e s can a l s o be smeared out during a 5 ns probe pulse. A ray t r a v e l l i n g through the plasma column can be assigned a fri n g e number P given by equation [16]. I f the ray t r a v e l s along a d i a -meter of the plasma, and, only the f i r s t order expansion of the r e f r a c t i v e index (equation [2]) i s used, P w i l l be given by: P = f ( n r / n c ) > [23] where n i s the average electron density within the column, radius r . Both n and r vary with time. Equation [1] suggests t h a t , i f the p a r t i c l e inventory i s fix e d , n and r do not change i n d e p e n d e n t l y of one another. When r decreases, n increases so that P tends to remain c o n s t a n t , though th i s c a n c e l l a t i o n e f f e c t i s not quite complete. Over an exposure time of At, the f r i n g e number w i l l change by AP. Assuming n and r are r e l a t e d according to eq u a t i o n [ 1 ] , t h e n , d i f f e r e n t i a t i n g equation [23] with respect to time r e s u l t s i n : X n  Kat } c Chapter 3 gi v e s dr/dt = 1 x 10^ cm s e c - 1 . As a worst case estimate, the maximum average electron density i s 4 x 1 0 1 9 cm - 3. Taking these figures with At = 5 ns gives AP 1.2. N e g l i g i b l e m o tional b l u r r i n g would r e q u i r e AP << 1. T h i s condition i s well s a t i s f i e d during much of the pinch phase. However, near maximum compression, the above estimate shows that the e f f e c t of a f i n i t e exposure time cannot be neglected as a possible factor contributing to the absence of well defined f r i n g e s . - 117 -At e a r l y times, as i n Figure 26(C), the plasma i s much less dense, and has correspondingly weak density gradients. Plasma motion and r e f r a c -t i o n are t h e r e f o r e c o m p l e t e l y n e g l i g i b l e and f r i n g e s can be observed throughout the plasma column. Figure 26(D) has been included for complete-ness and shows an interferogram that was taken well after peak compression. This photograph corresponds to the shadowgram of F i g u r e 5(B) where the plasma has blown apart i n a rather turbulent fashion. 9.2 Data Processing Quantitative analysis of the data requires t h a t the f r i n g e func-t i o n P(y) i n equation [16] be determined from the i n t e r f e r o g r a m s . Each interfercgram corresponding to a d i f f e r e n t time i n the p i n c h phase. Once found, P(y) was Abel inverted using the numerical routine described by Fan (1975), and the electron density d i s t r i b u t i o n n e ( r ) i s obtained. C l e a r l y though, complete analysis of each interference p a t t e r n i s quite a formidable task since ( i ) there are a very large number of f r i n g e s , ( i i ) the perturbations produced by the access ports have given an a d d i t i o n -a l z-dependence to the plasma d i s t r i b u t i o n , and ( i i i ) f o r much of the time i n t e r v a l observed, the complexity of the f r i n g e p a t t e r n near the plasma axis does not allow for an unambiguous assignment of f r i n g e numbers. For these reasons, the analysis has been li m i t e d to a single z coordinate, z Q and P(y, z = z Q) i s found as a function of time i n the pinch phase. Since the primary i n t e r e s t i s i n establishing the plasma d i s t r i b u t i o n f o r i n t e r -action studies, the coordinate z Q i s chosen to correspond with the f o c a l p o s i t i o n of the C0 2 l a s e r . The sketch of Figure 27 i s arranged to corres-- 118 -pond with the o r i e n t a t i o n of the interferograms of Figure 27. T h i s sketch locates the region of plasma for which data i s c o l l e c t e d . The i n t e r a c t i o n laser beam enters the f i e l d of view from the top of F i g u r e 2 7 w i t h the anode and cathode of the discharge being r e s p e c t i v e l y off to the r i g h t and l e f t of the frame. The y coordinate of each v i s i b l e maxima and minima along the scan l i n e i s recorded. Highly magnified r e c o n s t r u c t i o n s were made to a i d i n measuring the very c l o s e l y spaced fringes near the plasma core. A l l photo-graph dimensions are s c a l e d to r e a l space plasma c o o r d i n a t e s using the known image magnifications. The fringe f u n c t i o n s are then Abel i n v e r t e d with the assumption that, at l e a s t over the h a l f - d i a m e t e r r e g i o n of the plasma column that i s being measured, the plasma i s very n e a r l y axisym-metric. Though i t may not be very s a t i s f y i n g to make th i s assumption, the following discussion points out two, more important, sources of e r r o r . In order to s p e c i f y the r a d i a l p o s i t i o n of f r i n g e s , the l o c a t i o n of r = y = 0 i s r e q u i r e d . The plasma a x i s , r = 0 i s determined to be centered within the r e g i o n where the f r i n g e d e n s i t y i s h i g h . The b e s t judgement that can be made here i s that the o r i g i n , y = 0, i s u n c e r t a i n to no more than + 0.5 mm which corresponds to about + 2 mm i n the p i c t u r e s of Figure 26. The o r i g i n uncertainty enters into the u n f o l d i n g computations i n a rather complex way. However, for the r e s u l t s that w i l l be shown, the net e f f e c t i s p r i m a r i l y an uncertainty, by the same amount as g i v e n above, i n locating the r a d i a l coordinate axis with respect to the electron density d i s t r u b i t i o n , rather than an error i n the electron density i t s e l f . From a q u a l i t a t i v e point of view, t h i s e f f e c t i s to be expected s i n c e the i n v e r -sion i n t e g r a l i s mainly s e n s i t i v e to the d e r i v a t i v e , dP(y)/dy which i s i n v a r i a n t under t r a n s l a t i o n . The f r i n g e number P must also have a reference point corresponding to the outer boundary y = r D of the plasma where P ( r Q ) = 0. Far from the - 119 -a x i s , the fringes are widely spaced and appear to extend beyond the f i e l d of view. The boundary r D i s obtained by p l o t t i n g P(y) vs. y, with the h o r i -zontal axis being y. By extrapolating to large y, r Q and therefore P = 0, i s determined as the point where P(y) becomes hori z o n t a l l i n e . This proce-dure, amounts to simply terminating the d i s t r i b u t i o n a t some more or l e s s a r b i t r a r y , but large maximum r a d i u s , which was u s u a l l y estimated to be between 1.5 to 2 times the radius of the viewing ports. The precise choice of r Q was unimportant- since the absolute error introduced i s the order of 10 16 to 10 1 cm - 3 and i s quite i n s i g n i f i c a n t compared to the electron den-s i t i e s of i n t e r e s t , namely 10 18 to 1020 cm - 3. At t h i s point, the discussion of the interfercgrams may appear to be dominated by the uncertainties and assumptions r e q u i r e d to e x t r a c t the electron density d i s t r i b u t i o n . T h i s i s , i n p a r t , a consequence of the inherently high s e n s i t i v i t y of interferometry. The interfercgrams do indeed give a very d e t a i l e d picture of the plasma, but, i n the following s e c t i o n , a more quantitative view i s presented, and t h i s w i l l h e l p put the uncer-t a i n t i e s into better perspective. 9.3 Plots of the Electron Density P r o f i l e F i g u r e 28 shows the i n t e r f e r o m e t r i c r e s u l t s f o r the e l e c t r o n density n e ( r , t ) over the time i n t e r v a l -90 ns _< t <^  60 ns. At times l a t e r than about t = +50 ns, the plasma has broken-up and the f r i n g e p a t t e r n s cannot be analyzed (see Figure 26(D)). E a r l i e r than t = -90 ns, the plasma column has the combination of large radius and low d e n s i t y and produces a fringe pattern that extends well outside the f i e l d of view. This makes i t - 120 -d i f f i c u l t to extrapolate the fringe pattern to l a r g e r a d i i . I n f o r m a t i o n about the on-axis plasma density i s absent due to the l a c k of o bservable fringes near r = 0. The p r o f i l e s are extended from r = 0 to the f i r s t data point with a h o r i z o n t a l dashed l i n e i n order to i n d i c a t e the r e g i o n where fringes could not be measured with c e r t a i n t y . As well, these dashed l i n e s are i n d i c a t i v e of the accuracy with which the plasma axis could be defined. However, for the time i n t e r v a l shown, b u i l d - u p of the e l e c t r o n d e n s i t y within the plasma column i s well mapped out. Though the interferometric data appears somewhat sketchy, i t i s worthwhile here to r e c a l l the r e s u l t s of the Thomson s c a t t e r i n g measure-ments as presented i n Figure 18. The time span covered by the i n t e r f e r o -metric data of Figure 28 represents only the c e n t r a l 15% of the s c a t t e r i n g data. From t h i s point of view, i t i s c l e a r t h a t the c a v i t y dumped l a s e r system has provided a considerable improvement i n the temporal r e s o l u t i o n c a p a b i l i t i e s of these experimental i n v e s t i g a t i o n s . Such a large discrepancy i n time scales makes i t somewhat d i f f i c u l t to correlate the two experiments since, over the time span of the i n t e r f e r o m e t r i c d a t a , the s c a t t e r i n g r e s u l t s y i e l d only a few data points. Also, i n terms of s p a t i a l r e s o l u -t i o n , the scattering measurements represent r a d i a l l y averaged d e n s i t i e s , while the interferometric data would be expected to show higher peak den-s i t i e s . Nonetheless, the remainder of t h i s d i s c u s s i o n w i l l p r o v i d e some comparison of the interferometric data with previous r e s u l t s , and i t w i l l be seen that the correspondence i s quite good. A simple judgement of the r e l i a b i l i t y of the density p r o f i l e s can be made on the basis of an inventory of electrons. Before f i r i n g the d i s -charge, the t o t a l number of a v a i l a b l e e l e c t r o n s per u n i t l e n g t h , namely, 0.63 x 1 0 1 9 cm - 1, i s determined by the i n i t i a l f i l l conditions. Each of the electron density p r o f i l e s were integrated, assuming c y l i n d r i c a l symmetry, to find the t o t a l number of e l e c t r o n s measured to be w i t h i n the p i n c h column. An average of ten p r o f i l e s shows the number of e l e c t r o n s to be - 121 -6 e l e c t r o n d e n s i t y l*10 1 9 cm"3) FIGURE 28 The plasma d i s t r i b u t i o n during the pinch phase. - 122 -0.47 + 0.9 x 1 0 1 9 cm - 1, which accounts for 75% of the f i l l gas. Of course, not a l l the gas w i l l have been swept-up during the e a r l y implosion stage of the discharge. If 25% of the gas i s assumed to remain uniformly d i s t r i b u -ted within the chamber, the background electron density would be 2 x 10 1^ cm - 3. With the observation f i e l d l i mited to comparatively small r a d i i , t his background electron d e n s i t y i s somewhat below the p r e s e n t s e n s i t i v i t y . Therefore, a measured c o l l e c t i o n factor of 75% r e p r e s e n t s a lower bound. In view of t h i s , the inventory of electrons i s rather complete. Figure 29 g i v e s a comparison of the interferometric data with the Thomson scattering r e s u l t s . The open c i r c l e s i n t h i s figure show the e l e c -tron density measurements obtained from the scattering experiments plus one spectroscopic value at t = -80 ns. The i n t e r f e r o m e t r i c data i s shown as bars, but these bars require some explanation. Because the scattering experiments lack s p a t i a l r e s o l u t i o n i n the r a d i a l d i r e c t i o n , the density p r o f i l e s of Figure 28 were therefore r a d i a l l y averaged over the 2 mm length of the scattering volume. The upper l i m i t of the bars i n Figure 29 show the average density assuming that the scattering volume was symmetrically located on the plasma a x i s . However, r e c a l l i n g the d i s c u s s i o n i n s e c t i o n 6.2 concerning the n e t r e d s h i f t i n some scattered spectra, an attempt was made to see i f the i n t e r f e r o m e t r i c data would be more consistent with a scattering volume that had been d i s p l a c e d with respect to the plasma a x i s . The lower l i m i t of the bars i n F i g u r e 29 corresponds to averaging the d e n s i t y p r o f i l e s assuming the s c a t t e r i n g volume was displaced i n the r a d i a l d i r e c t i o n by 1 mm. Even though there does appear to be a tendency for the s c a t t e r i n g experiments to g i v e lower electron d e n s i t i e s , i f error bars were p l a c e d on the scattering data, they would be approximately + 30%. Consequently, any - 123 -ro 'E o x c .4 h 2 h -100 •100 time (ns) FIGURE 29 Comparison of the interferometric and scattering measurements. Open c i r c l e s show the Thomson s c a t t e r i n g r e s u l t s . The bars g i v e the corresponding measurements that were extracted from the density p r o f i l e s . - 124 -judgement concerning imaging i n the s c a t t e r i n g experiments would have tenuous j u s t i f i c a t i o n . Nonetheless, t h i s e x e r c i s e i n comparison i l l u s -t rates c l e a r l y and most i m p o r t a n t l y , t h a t , i f the d e n s i t y p r o f i l e s are averaged over the scattering volume, the i n t e r f e r o m e t r i c and s c a t t e r i n g measurements agree very c l o s e l y . On the other hand, i f the density p r o f i l e s are extrapolated to r = 0, the peak electron density on axis would be s i g n i f i c a n t l y higher (about a factor of two higher) than the scattering data shows. In p a r t i c u l a r , the peak density at maximum compression i s indicated to be 7 x 1 0 ^ cm - 3. Now, i n section 3.5, the shadowgram analysis provided an e a r l y e stimate of 6 x 1 0 1 9 cm - 3 for the on-axis density at maximum compression. Although such a c l o s e correspondence between these two values may be f o r t u i t o u s , the shadowgram experiment has proven to be a very reasonable estimator. - 125 -CHAPTER 10 CONCLUSION AND SUGGESTIONS This f i n a l chapter w i l l conclude the presentation of the e x p e r i -mental i n v e s t i g a t i o n s performed as part of t h i s thesis work. The following discussions w i l l consider b r i e f l y each of the experiments, with the aim of providing (i) a review of the s a l i e n t features of the high density Z-pinch plasma that have been observed, ( i i ) a summary of the d i a g n o s t i c e x p e r i -ments, with some c o n s i d e r a t i o n g i v e n to ( i i i ) t h e i r a p p l i c a t i o n to the laser/plasma i n t e r a c t i o n studies. The f i r s t two experiments, namely, the s t r e a k and shadowgram photography, were performed and intended as an i n t r o d u c t i o n to the pre-v i o u s l y unexplored high compression phase of t h i s Z-pinch d i s c h a r g e . To t h i s end, these i n i t i a l experiments have been g i v e n a c l e a r view of the evolution of the on-axis plasma by establishing the plasma s i z e , along with the basic structure and dynamics, as f u n c t i o n s of time during the p i n c h phase. The plasma structure i s characterized by two major components. A d i f f u s e plasma s h e l l , having r e l a t i v e l y low electron density (< 1 0 1 8 cm - 3), collapses to a minimum outer r a d i u s of 0.25 cm. The plasma on-axis i s shock compressed and heated to form the high d e n s i t y plasma c o r e . T h i s on-axis plasma develops from sub-millimeter dimensions and grows i n size as plasma from the s h e l l continues to accumulate and be compressed i n t o the core. These i n i t i a l experiments have had one very important f e a t u r e i n common: they are simple and easy to do. Here, with only modest a t t e n t i o n to experimental d e t a i l s , a wealth of q u a n t i t a t i v e i n f o r m a t i o n has been obtained. Refraction methods, such as the shadow photography, should not be overlooked as being well suited to the l a s e r / p l a s m a s t u d i e s . At very h i g h i n c i d e n t power d e n s i t i e s , the i n t e r a c t i o n r e g i o n i s known to be characterized by small scale structure and steep density gradients (Milroy, - 126 -e t . a l . , 1978; Itj, e t . a l . , 1979). With appropriate m o d i f i c a t i o n s , t e c h n i -ques based on r e f r a c t i o n can be very s e n s i t i v e probes of the i n t e r a c t i o n volume. For instance, through angular decomposition of the t r a n s m i t t e d probe beam, one can obtain d i r e c t information about the plasma s t r u c t u r e and shape without requiring any s p e c i a l (and often expensive) consideration for high s p a t i a l r e s o l u t i o n . From the Thomson scattering experiments, the plasma temperature was seen to range up to a maximum of 45 - 50 eV, and the e l e c t r o n d e n s i t y has been measured over a range of three orders of magnitude. The measured peak density, 4 x 1 0 1 9 cm - 3, was c l o s e l y corroborated by two independent estimates obtained from the streak and shadowgram observations. Complex numerical modelling of the plasma c o l l a p s e i n a Z-pinch discharge (Hain, e t . a l . , 1960) p r e d i c t s strong shock heating of the on-axis plasma. However, the plasma temperature has not been an e a s i l y a c c e s s i b l e parameter i n t h i s and s i m i l a r d i s c h a r g e s (e.g. S t e e l , e t . a l . , 1978). Spectroscopic measurements have proved to be i n a p p r o p r i a t e during peak compression (Houtman, 1977, Albrecht, 1979) because of the high temperature and density. Also, more r e c e n t attempts to examine t h i s Z-pinch using X-ray measurement techniques have proved inadequate because the plasma temperature i s too low. The s c a t t e r i n g experiments have t h e r e f o r e been v i t a l for establishing the plasma temperature during the p i n c h phase. As well, i t i s believed that these Thomson s c a t t e r i n g experiments r e p r e s e n t one of the few, i f not the f i r s t a p p l i c a t i o n of the i o n f e a t u r e as a routine diagnostic t o o l . The scattering experiments w i l l be of paramount importance for the i n t e r a c t i o n studies since they w i l l i n t e r r o g a t e the plasma a t the micro-scopic l e v e l . A l l of the parametric processes expected to occur (Drake, e t . a l . , 1974) have t h e i r signatures i n the frequency and/or wavevector spec-trum of the induced plasma f l u c t u a t i o n s . The s c a t t e r i n g experiments t h a t - 127 -have been presented were arranged to provide for high s p e c t r a l r e s o l u t i o n and s i n g l e shot recording of the e n t i r e low frequency f l u c t u a t i o n spec-trum. In the low frequency regime of scattered s p e c t r a , the problem of stray l i g h t can be a very important one. F i r s t l y , knowing that stray l i g h t i s introduced because of r e f r a c t i o n w i l l a i d i n arranging f o r more e f f i -c i e n t beam dumping. Also, the backscattered spectra of Figure 14 show that stray l i g h t can be i s o l a t e d from scattered l i g h t via s p e c t r a l r e s o l u t i o n . F i n a l l y , the ruby laser has r e c e n t l y been mod i f i e d to produce sub-nano-second duration diagnostic pulses. If the o p t i c a l g a t i n g method used i n the present scattering experiments i s correspondingly scaled i n time, stray l i g h t can be further discriminated against on the basis of time of f l i g h t . Therefore, with the means made ava i l a b l e by these experiments, s t r a y l i g h t should not present a serious problem for future s c a t t e r i n g i n v e s t i g a t i o n s using t h i s Z-pinch. At the macroscopic l e v e l , the interferometric i n v e s t i g a t i o n s have given a d e t a i l e d picture of the plasma d i s t r i b u t i o n . Q u a l i t a t i v e l y , the holes i n the discharge vessel and return conductor have degraded the l o c a l symmetry of the plasma column. Consequently, some u n c e r t a i n t y has been introduced into the analysis of the fringe patterns. However, because the perturbations appear i n an extremely r e p r o d u c i b l e manner, any e f f o r t to restore the plasma symmetry w i l l be time well spent i n providing for p r e c i -sion measurements of the density d i s t r i b u t i o n . I t i s well established that surface i n s t a b i l i t i e s develop on the plasma column as a r e s u l t of perturba-tions i n the shape of the vessel w a l l (Curzon e t . a l , 1964). I t should, therefore, be p o s s i b l e to adopt the methods ofCurzon et.al.and thereby produce a c y l i n d r i c a l p e r t u r b a t i o n which e f f e c t i v e l y overwhelms the azimuthal i r r e g u l a r i t y generated by the access ports . I t has been shown t h a t , even though r e f r a c t i o n e f f e c t s on the interferometric experiments are not n e g l i g i b l e , precise imaging was not an important requirement for examining the Z-pinch plasma i t s e l f . However, for the i n t e r a c t i o n experiments, the plasma r e g i o n of i n t e r e s t w i l l have - 128 -dimensions the order of, and smaller than, the CO2 laser f o c a l spot s i z e . This, i n turn, w i l l be s i g n i f i c a n t l y s m a l l e r than the dimensions of the plasma column. Then, imaging the i n t e r a c t i o n r e g i o n with the ac c u r a c y indicated by Figure 22 may not be p o s s i b l e , p a r t i c u l a r l y i n view of the ph y s i c a l l i m i t a t i o n s imposed by the size of the discharge vessel. (General-l y , high q u a l i t y imaging of s m a l l o b j e c t s r e q u i r e s p l a c i n g s h o r t f o c a l length optics close to the object - a s i t u a t i o n not a c c e p t a b l e here.) The most reasonable s o l u t i o n would be to avoid r e f r a c t i o n e f f e c t s by using f r e -quency doubled ruby laser l i g h t . The loss i n s e n s i t i v i t y of a f a c t o r of 2 can be e a s i l y t o l e r a t e d . The corresponding i n c r e a s e i n the c r i t i c a l density (a factor of 4) w i l l produce an enormous relaxation of the imaging requirements when the electron density i s below about 1 x 10 2^ cm - 3. F i n a l l y , by using the time d i f f e r e n t i a l nature of double exposure holography, short time scale v a r i a t i o n s i n the plasma density i n the CO2 laser i n t e r a c t i o n region can be completely i s o l a t e d from the unperturbed "background" plasma column. This was tested i n a very p r e l i m i n a r y way by photographing the plasma column i t s e l f , near peak compression, using a 12 ns inter-exposure separation. Though the plasma core does change over t h i s time i n t e r v a l , a l l fringes outside the core were completely eliminated from the interference p a t t e r n . C o n s i d e r a b l e improvements can be made along these l i n e s without a great deal of d i f f i c u l t y a n t i c i p a t e d . The i n v e s t i g a t i o n s that were presented i n t h i s t h e s i s have f u l -f i l l e d t h e i r intended functions. A thorough examination of the Z-pinch plasma c h a r a c t e r i s t i c s throughout the high d e n s i t y compression phase has given a complete data base of information on the i n i t i a l target conditions, p r i o r to i r r a d i a t i o n with the CO2 l a s e r . The experiments that were present-ed provide a sequence of micro and macroscopic diagnostic methods t h a t can be f r u i t f u l l y applied to a d e t a i l e d study of laser/plasma i n t e r a c t i o n s . - 129 -REFERENCES Albrecht, G.F., Ph.D. Thesis, U n i v e r s i t y of B r i t i s h Columbia, (1979). Albrecht, G.F.; Kallne, E. and Meyer, J . , Rev. S c i . Instrum., 49(12), 1637 (1978). A l l e n , J.E., Proc. Phys. S o c , B70, 24 (1957). Armstrong, W.T. and Forman, P.R., Appl. Optics 16(1), 229 (1977). Artsimovich, L.A., i n 'Controlled Thermonuclear Reactions' Ch. 6, (Gordon and Breach, 1964). Barnard, A.J. and Ahlborn, B., Am. J . Phys., 43(7), 573 (1975). Barnard, A.J. and G u l i z i a , C., Can. J . Phys., 58, 565 (1980). Born, M. and Wolf, E. , i n ' P r i n c i p l e s of O p t i c s ' , 5 t h E d i t i o n , 123 (Pergamon, 1975). Chang, M. and George, N., Applied Optics, 9 (3), 713 (1970). Chen, F.F., In 'Introduction to Plasma Physics', (Plenum, 1974). C o l l i e r , R.J., L i n , L.H. and Burchhardt, C.B., ' O p t i c a l Holography', (Academic, 1971). Curzon, F.L.; Hodgson, R.T. and C h u r c h i l l , R. J . , J . Nuclear Energy C, 6, 281 (1964). Desilva, A.W. and Goldenbaum, G.C., i n 'Methods of Experimental P h y s i c s ' E d i t e d by R.H. Lovberg and H.R. Griem, V o l . 9A, Ch. 3, 61 (Academic, 1970). Drake, J.F.; Kaw, P.K.; Lee, Y.C.; Schmidt, G.; L i u , C S . and Rosenbluth, M.N., Phys. F l u i d s , 17 (4), 778 (1974). Evans, D.E. and Katzenstein, J . , Rep. Prog. Phys., 32, 207 (1969). Fan, L.S. and Squire, W., Computer Phys. Commun., 10, 98 (1975). George, T.V.; Goldstein, L.; Slama, L. and Yokoyama, M. , Phys. Rev., 137 (2A), 369 (1965). Graube, A., Appl. Optics, 13 (12), 2942 (1974). Grek, B.; Martin, F.; Johnston, T.W.; Pepin, H.; M i t c h e l , G. and R h e a u l t , F., Phys. Rev. L e t t . , 41(26), 1811 (1978). Hain, K.; Hain, G.; Roberts, K.V.; Roberts, S.J. and Koppendor f e r , W. , 7, Naturforschg, 15 (A), 1039 (1960). - 130 -REFERENCES (Cont'd) Hilko, B., Meyer, J . , Albrecht, G. , and Houtman, H., J . Appl. Phys., 51 (9), 4693 (1980). Holder, D.W. and North, R.J., 'Schlieren Methods', Notes on Applied Science No. 31, (HMSO London, 1963). Houtman, H., M.Sc. Thesis, U n i v e r s i t y of B r i t i s h Columbia, (1977). Jackel, S.; Perry, B. and Lubin, M., Phys. Rev. L e t t . , 37(2), 95 (1976). Jahoda, F.C. and Sawyer, G.A., i n 'Methods of Experimental Physics', Plasma Physics, V o l . 9 (b), 1 (Academic, 1971). Keilmann, F., Plasma Physics 14, 112 (Pergamon, 1972). Kogelschatz, U. and Schneider, W.R., Applied Optics, 11 (8), 1822 (1972). Kunze, H.J., i n 'Plasma Diagnostics', 550 (North-Holland, 1968). Leontovich, M.A. and Osovets, S.M., J . Nuclear Energy I I , V o l . 4, 209 (1957). Machewirth, J.M., O p t i c a l Spectra, December (1979). Milroy, R.D.; Capjack, C.E.; McMullin, J.N. and James, C.R., Can. J . Phys., 57, 514 (1979). Morgan, C.G., Rep. Prog. Phys., 38, 621 (1975). Ng, A.; Salzmann, D. and Offenberger, A.A., Phys. Rev. Lett . , 43 (20), 1502 (1979). Salpeter, E.E., Phys. Rev., 120 (5), 1528 (1960). Salpeter, E.E., J . Geophys. Res., 68 (5), 1321 (1963). Schreiber, P.W.; Hunter I I , A.M. and Smith J r . , D.R., Plasma P h y s i c s , 15, 635 (1973). Shmoys, J . , J . Appl. Phys., 32 (4), 689 (1961). Siebe, J . , Phys. F l u i d s , 17 (4), 765 (1974). Siegman, A.E., IEEE J . Quantum Electron., QE-9, 247 (1973). Simpson, R.W. and Talmi, Y., Rev. S c i . Instrum., 48 (10), 1295 (1977). S t e e l , D.G.; Rocket, P.D.; Bach, D.R. and C o l e s t o c k , P.L., Rev. S c i . Instrum., 49 (4), 456 (1978). - 131 -REFERENCES (Cont'd) Sweeney, D.W.; Attwood, D.T. and Coleman, L.W., Appl. Optics, 15 (5), 1126 (1976). Rosenbluth, M.N. and Rostoker, N., Phys. F l u i d s , 5 (7), 776 (1962). Vest, CM., Appl. Opt., 14 (7), 1601 (1975). Vest, CM., 'Holographic Interferometry', (John Wiley & Sons, 1979). Vuylsteke, A.A., J . Appl. Phys., 34 (6), 1615 (1963). Zel'dovich, Y.B. and Raizer, Y.P., i n 'Physics of Shock .Waves and High-Temperature Hydrodynamic Phenomenon', V o l . 1, 258 (Academic, 1966). - 132 -APPENDIX A TRIGGERING OF THE DISCHARGE Detai l s of the design, construction and operation of the discharge c i r c u i t are well documented i n our laboratory (e.g.: Houtman, 1977). This appendix has been included here i n order to e s t a b l i s h the n e c e s s a r y docu-mentation of those changes to the c i r c u i t r y that were made by the p r e s e n t author. Figure A-1 shows one of the six main gap t r i g g e r c i r c u i t s . The master gap i s an e n t i r e l y c o - a x i a l arrangement, housing the s i x 2700 pF trig g e r capacitors. The p r e - i o n i z a t i o n c i r c u i t that was added to the master gap i s described v i a Figure A-2. Note that the Z-pinch anode has a 3 cm diameter hole i n the center i n order to accommodate the trigger e l e c t r o d e . With t h i s arrangement, and, at the current operating c o n d i t i o n s , the p r e -i o n i z a t i o n was s u f f i c i e n t to reduce the j i t t e r i n the main d i s c h a r g e from greater than 50 ns to less than 5 ns. to z-oinch T T Master gap FIGURE A-1 Biasing and main gap trigger c i r c u i t s . " 133 " 3 = lucite A .nylon •lb brass ring optical fiber PM tube main discharge pref lash - H h - 50 i 5 ns F I G U R E A-2 Description of the p r e - i o n i z a t i o n . - 134 -

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