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A two directional study of scattering of ruby laser light from a plasma jet Godfrey, Lawrence Allan 1973

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A TWO DIRECTIONAL STUDY OF SCATTERING OF RUBY LASER LIGHT FROM A PLASMA JET by LAWRENCE ALLAN GODFREY B . S c . , 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 , 1971 A THESIS PRESENTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e D e p a r t m e n t o f P h y s i c s We a c c e p t t h i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA September, 1973 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. 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 purposes may be g r a n t e d by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t c o p y i n g or p u b l i c a t i o n 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 not be a llowed without my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT A two channel system is used to study, simul- taneously in two d i r e c t i o n s , the scattering of ruby laser l i g h t from a plasma j e t . The experimental scattering spectrums compare well with theoretical predictions for scattering from an i n f i n i t e homogeneous thermal plasma. The fluctuations in the integrated spectrums for the two directions are shown to be p o s i t i v e l y c o r r e l a t e d , as well as to be too large to be accounted for by known sources of f l u c t u a t i o n . Changes in the plasma parameters, electron density and temperature, are ruled out as the source of the extra f l u c t u a t i o n s . i i i TABLE OF CONTENTS Paoje ABSTRACT i i TABLE OF CONTENTS i i i LIST OF FIGURES v ACKNOWLEDGEMENTS v i i Chapter I INTRODUCTION 1 Chpater II THEORY 3 A. Summary of Scattering Theory . 3 B. Determining Electron Density and Temperature from Experimental Scattering P r o f i l e s 7 C. Theoretical Calculation of Scattering Signal Dependence on Fluctuations in Electron Density and Temperature. 9 Chapter III EXPERIMENTAL APPARATUS . . . . . . 14 A. The Plasma Jet 14 B. The Ruby Laser 17 C. The Detecting System . . . . . 20 Chapter IV EXPERIMENTAL RESULTS AND DISCUSSION 23 A. Scattering P r o f i l e s and Determina- tion of N and T . . . . . . . . . . . . 24 e e i v Page B. Experimental Correlation and Standard Deviation 31 C. Estimation of Known Fluctuations . . . . 33 D. Discussion 36 Chapter V CONCLUSION 43 A. Conclusions 43 B. Suggestions for Further Study 44 BIBLIOGRAPHY 45 APPENDIX A Alignment Procedure 47 V I LIST OF FIGURES Figure Page II -1 Scattering of Plane Electromagnetic Radiation from a Plasma 6 11-2 Monochromator Transmission Function - Wide Passband 12 II- 3 Theoretical Dependence of Scattered Signal on Ng and/or T g Changing 13 III — 1 Experimental Arrangement 15 111 - 2 Schematic of the Plasma Jet 16 III- 3 Plasma Jet Power Supply C i r c u i t 18 III- 4 Laser Monitor C i r c u i t . 18 IV- 1 Monochromator Transmission Function - Narrow Passband 25 IV-2 Typical Oscillograms 26 IV-3 Theoretical F i t to Experimental Data for Forward Scattering 29 IV-4 Theoretical F i t to Experimental Data for Backward Scattering. . . . . . . . . . . . . . 30 IV-5 Comparison of Experimental Variations in Scattering Signal to Calculated V a r i a - tions Due to Changing N 39 v i Fi gure Page IV-6 Comparison of Experimental Variations in Scattering Signal to Calculated Variations Due to Changing T 40 v i i ACKNOWLEDGEMENTS I would l i k e to thank Dr . R.A. Nodwell f o r h i s adv ice and encouragement dur ing t h i s exper iment . My thanks a l s o go to Dr. H. B a l d i s f o r h i s many h e l p f u l h i n t s , to Mr. D. S ieburg and Mr. J . Aazam-Zanganeh f o r t h e i r t e c h n i c a l a s s i s t a n c e , and to Dr . M. C h u r c h l a n d , Mr. Gary A l b a c h , and other members of the Plasma P h y s i c s Group f o r t h e i r d i s c u s s i o n s of t h i s exper iment . 1 Chapter I INTRODUCTION The experimental results for scattering of e l e c t r o - magnetic radiation from free electrons in a plasma have, in general, been in good agreement with theoretical pre- d i c t i o n s . However, there have been many examples of deviations from theoretical p r e d i c t i o n s , usually involving enhancements in the scattering spectrum in the region of the frequency s h i f t corresponding to the plasma frequency, a) , or at multiples of 1/2 w (Gerry and Rose,^ Evans et al.3 Ringler and Nodwel1, 3 ' 4 » 5  Churchland 6 ). Another p o s s i b i l i t y of anomalous scattering was noted by D. H. Baldis while scattering laser l i g h t from a plasma j e t . The observed standard deviation of the scattered signal appeared to be too large to be accounted f o r by photon s t a t i s t i c s and other known sources of f l u c t u a t i o n s . It was suggested some non-thermal c h a r a c t e r i s t i c of the plasma could produce the extra observed f l u c u a t i o n . This experiment was performed to investigate the fluctuations in scattering s i g n a l , to determine i f 2 these fluctuations can be accounted for by known sources, and to try to determine another source of f l u c t u a t i o n i f they cannot. For this purpose, a two channel system was adopted. This allowed not only the study of the scattered signal simultaneously in two d i r e c t i o n s , but also the study of the correlation of the two scattered s i g n a l s . The shape of the scattered spectrum was c a r e f u l l y measured to determine the plasma parameters, electron density (Ng) and electron temperature ( T g ) . Then the integrated scattering spectrum was observed in order to measure the fluctuations in the scattered l i g h t for the two d i r e c t i o n s , as well as the c o r r e l a t i o n between the two s i g n a l s . Chapter II gives a b r i e f summary of scattering theory for a homogeneous i n f i n i t e plasma. A method, due to Kegal, of determining the electron density and tempera- ture from scattering p r o f i l e s is presented, as well as the theoretical dependence of the scattering signal on Ng and T . e Chapter III is devoted to a description of the experimental apparatus. Chapter IV describes the experi- mental method and r e s u l t s . A discussion of the results i s also presented in Chapter IV. The conclusion is given in Chapter V, and a detailed description of the alignment procedure i s presented in Appendix A. 3 Chapter II THEORY A. Summary of Scattering Theory The theory of scattering of l i g h t from free electrons in a plasma has been derived by many authors 7 8 (for example see Saltpet e r , Rosenbluth and Rostoker ) , so only a br i e f summary i s given here. The theory i s based on the c l a s s i c a l approach; that is electromagnetic radiation incident on the plasma causes the free electrons to be accelerated, which in turn causes the electrons to radia t e . The i n t e n s i t y of the scattered radiation from the electrons is equal to the ensemble average of the e l e c t r i c f i e l d vectors from a large number of electrons. The r e l a t i v e positions of the electrons w i l l r esult in d i f f e r e n t phase s h i f t s of the e l e c t r i c f i e l d vectors; t h e i r r e l a t i v e v e l o c i t i e s , d i f f e r e n t frequency s h i f t s . Unless there is some spatial nonuniformity in the charge d i s t r i b u t i o n , the resultant scattered signal 4 w i l l be zero in a l l directions except p a r a l l e l to the incident wave vector. This nonuniformity can arise from the p a r t i c l e nature of the plasma resulting in density f l u c t u a t i o n s . The density fluctuations can be thought of as a combination of random thermal waves in the plasma Thus the laser l i g h t is scattered from random thermal waves in the plasma, and t h e i r frequency and spatial d i s t r i b u t i o n w i l l determine the shape of the scattering spectrum. It is also possible to have spatial charge d i s t r i b u t i o n nonuniformity due to macroscopic variations of electron density. The d i f f e r e n t i a l scattering cross section for scattering through an angle 6 is given by: a |jc-k_0 ,u)-w0j = f̂- | l - s i n 2 6 cos2<j> ^— S |k-ko ,w-w0 j where: r 0 i s the c l a s s i c a l radius of the electron 4> is the angle between the d i r e c t i o n of p o l a r i z a t i o n of the incident radiation and the scattering plane n0 is the average electron number density jc0 is the incident wave vector k i s the scattering wave vector 0) k-k0 ,w-o)c is the incident wave frequency is the scattering wave frequency is the spectral density d i s t r i b u t i o n . See F i g . 11-1 for the geometry of the laser l i g h t scattering The spectral density d i s t r i b u t i o n is given by the Fourier transform of the autocorrelation function of the electron density: k-k0 ,U-CL)0 = FT Cn(A,x) = J - V P J T/2 dt n. r+A ,t+x T/2 FT f ( r , t ) E J dr dt f ( r , t ) exp ( u - a)o ) t - (k-k 0) • r For a Maxwellian plasma th i s gives: k-k0,w-w< 27rn« l i - J L o l n - Gfi - G.| 2 6 FIG SCATTERING OF PLANE ELECTROMAGNETIC RADIATION FROM A PLASMA 7 where: s u b s c r i p t e r e f e r s to the e l e c t r o n s s u b s c r i p t i r e f e r s to the ions T i s temperature i s the mass of the p a r t i c l e i s Boltzman's constant = (m/2TT K T ) * exp(- X 2) ( m e / 2 K T e ) 2 ( w - o ) o ) / | i _ k c m i T e m e T i G =-a 1 - 2 x exp(-X ) e x p ( - t 2 ) d t + i TT x exp -X a. 4TT n Qe / I i i a i rZ T « a. B. Determining E l e c t r o n D e n s i t y and Temperature from Experimental S c a t t e r i n g P r o f i l e s In g e n e r a l , when S (k_-k_0 ,w-u)0) i s p l o t t e d as a f u n c t i o n of X. or X , or p r e f e r a b l y as a f u n c t i o n of logio(AX),AX = X - X o , with a e » N e > T e > and T. as parameters, 8 there is an ion feature and an electron feature. The ion feature is very close to the central laser frequency and is usually d i f f i c u l t to in v e s t i g a t e . The electron feature can be used to determine the electron density and tempera- ture. The shape of the electron s a t e l i t e , when normalised to i t s maximum and plotted as function of log(AX), is completely determined by the parameter a: changes in ^ e  a n c ' ̂ e that keep the same a merely serve to s h i f t the spectrum along the log(AX) a x i s . Using this p r i n c i p l e i t i s possible to determine Ng and T g from the scattering 9 spectrum in the following manner, due to Kegal. A standard set of theoretical graphs is drawn for d i f f e r e n t a of S (k-k D ,w-u) 0 )/S m, v versus logio(AX), — max keeping Te,T.,6,<j> constant, with T. = T , and changing Ng as required. Then the experimental graph of the scattered s i g n a l , normalised to the incident radiation and the maximum scattering s i g n a l , versus logio(AA) is compared to the theoretical p l o t s . Once the theoretical graph is found that has the same shape as the experimental graph ( i . e . the experimental a is determined) the electron temperature and density can be calculated using the s h i f t A. A is the amount that the theoretical graph must be moved along the logio(AX) axis of the experimental graph so that the two graphs coincide. The electron density and temperature are then given by: 9 l o g 1 0 T e x = l o g i 0 T s t + 1og x 0[Vin 2 (8 s t/2) j logj s i n 2 ( 6 e x / 2 ) + 2A l o g 1 0 Np = l o g 1 0 N + 2A ex  e s t where the subscripts ex and st refer to the experimental and standard values r e s p e c t i v e l y . A s l i g h t change was made from Kegal's method to f a c i l i t a t e f i t t i n g actual experimental r e s u l t s . In the theoretical p r o f i l e s , the maximum value is well defined. However, in experimental results the true maximum is seldom observed. This can result in incorrect normalisa- tion of the experimental r e s u l t s . To counteract t h i s , the v e r t i c a l axis was changed to a logio s c a l e , which allows small up and down s h i f t s when comparing the experi- mental and theoretical graphs. C. Theoretical Calculation of Signal Dependence on Electron Density and Temperature Since i t i s to be determined i f the experimental fluctuations are too large to be accounted for by known sources of f l u c t u a t i o n , a c a l c u l a t i o n must be performed 10 to determine the changes in the two scattering signals i f there are small changes in Ng and/or T . The mechanisms for shot-to-shot variation in N and T w i l l be discussed e e in the l a s t section of Chapter IV. The total signal detected by the photomulti- p l i e r w i l l be a convolution of the scattering spectrum and the transmission function of the monochromator. The instrument p r o f i l e can be determined experimentally, and depends on the wavelength setting and the width of the entrance and exit s l i t s . Let T(w) be the transmission function on the monochromator for a given frequency setting and exit and entrance s l i t s . The experimental signals are normalised to the incident r a d i a t i o n , and <j> = 9 0 ° , so we have P Scat k-k0 , O J - O ) < I, a S(k-k 0,w - t o o ) where  P 5 c a t is the scattered power, and I 0 is the incident i n t e n s i t y . Since we are not interested in absolute values, constants may be neglected, and the signal at the photo- m u l t i p l i e r is then given by: 11 + 00 PM Scat T(OJ)S k-k 0 ,u 3 - 0 ) o dw f o r the given monochromator s e t t i n g s . T h i s c a l c u l a t i o n was done f o r N = 2.07 x 1 0 1 6 e cm" 3, T e = 19,000 °K, and s c a t t e r i n g angles 49° 22' and 130° 32'. F i r s t N g was v a r i e d by ±50% from the value quoted above, while JQ was kept c o n s t a n t . Then T g was v a r i e d by ±50% while N g was kept c o n s t a n t . F i n a l l y both ^ e a n c ' ^ e were v a r i e d i n such a manner as to keep the same a. The monochromator had the t r a n s m i s s i o n f u n c t i o n shown i n F i g . 11-2, centred over the e l e c t r o n s a t e l l i t e peak f o r the forward d i r e c t i o n . The wavelength s e t t i n g o was 6972 A, the e x i t s l i t 2 mm wide and the entrance s l i t 400u wide. F i g . 11-3 shows the r e s u l t s of t h i s c a l c u l a t i o n ! 12 10 - (A) FIG 11-2 MONOCHROMATOR TRANSMISSION FUNCTION - WIDE PASSBAND a.«i 1 1 1 1 1 1 1 1 r 0.6 o.e 0.7 0.8 ae 1.0 1.1 J-2 1.3 L4 1.8 RELAT IVE C H A N G E IN P A R A M E T E R ( S ) FIG 11-3 THEORETICAL D E P E N D E N C E O F S C A T T E R E D S I G N A L O N N E A N D ^ R T E C H A N G I N G 14 Chapter III EXPERIMENTAL APPARATUS F i g . 111-1 is an i l l u s t r a t i o n of the experimental arrangement. Light from the ruby laser is focussed into the plasma j e t . Scattered l i g h t i s co l l e c t e d at 49° 28' and 130° 38' to the axis of the ruby laser and detected by a monochromator and photomultip!ier. A. The Plasma Jet The plasma j e t used in this experiment i s si m i l a r to that used by Chan 1 0  and B a l d i s 1 1  (see F i g . 111-2). For a complete description of the construction of a plasma 1 2 j e t see Morris. The j e t i s run with helium rather than argon since helium has considerably less continuum radiation than argon. Also the helium j e t i s much less 1 3 l i k e l y to be perturbed by the laser pulse (van der Kamp ) . The j e t is idled at low current, about 70 amps, with a M i l l e r model SRH 333s welding supply. When the laser is to be f i r e d , the current source is changed to a MONOCHROMATOF RUBY LASER FIG 111-1 EXPERIMENTAL ARRANGEMENT 16 FIG IU-2 SCHEMATIC OF ALL MATERIAL THE PLASMA JET , - 3/4 S C A L E B R A S S . E X C E P T W H E R E NOTED 1 7 48 v o l t , 240 amp-hour battery, and the current raised in six steps to 230 amps by p a r a l l e l i n g combinations of one ohm, 1000 watt r e s i s t o r s with the b a l l a s t r e s i s t o r ( F i g . 111-3). The large number of steps reduces the erosion of the water-cooled anode and cathode, thereby increasing the r e p r o d u c i b i l i t y of the j e t . The current is then adjusted exactly to 230±3 amps using a current and voltage regulated power supply (Trygon Electronics Model M36-30a). The j e t is allowed a few seconds to come to eq u i l i b r i u m , and then the laser i s f i r e d . The j e t current is monitored by measuring the voltage drop across a 10 _lf  ohm shunt with a d i g i t a l voltmeter (Dana 3800) which reads to the nearest tenth of a m i l l i v o l t . This gives a d i r e c t reading of the current: 1 mv = 10 amps. The shunt i s accurate to 1% and the v o l t - meter to 0.1 mv., so that the current could be set to o 230±3 A., but could be set to the same current from shot- to-shot to within 1 amp. The axis of the j e t is v e r t i c a l , and perpendicular to the monochromator and laser a x i s . B. The Ruby Laser A modified TRG Model 104 ruby laser is used in this experiment, capable of a 20 megawatt pulse with a 35 W E L D I N G S U P P L Y l — — r 1 0 1 a -A/W 1 Q V2o J L A A / V i a 1 <\AA.—I Wv- 10 V 2 n J E T DHL F I G 111-3 P L A S M A J E T P O W E R S U P P L Y C I R C U I T P H O T O D I O D E 1 0 0 V m L I •TO O S S I L O S C O P E 1 o.oi pf J> 5 0 n C E R A M I C T F I G 111-4 L A S E R M O N I T O R C I R C U I T 19 nsec width at half i n t e n s i t y . The laser is Q-switched with a corner r e f l e c t i n g prism, rotation at 30,000 rpm. The front mirror of the laser cavity has 40% r e f l e c t i v i t y o at 6943 A. The glass ruby rod holders have been modified s l i g h t l y to accept a 3/8 inch diameter rod rather than the o r i g i n a l 10 mm. diameter rod. The 3 inch long ruby rod and one flash tube are a i r cooled. The capacitor bank contains 1000 joules at about 900 v o l t s . The laser l i g h t is focussed into the plasma and then absorbed in a copper sulphate solution l i g h t dump with an entrance window at the Brewster angle. The e l e c t r i c vector of the laser l i g h t is perpendicular to the scattering plane (<j> = 9 0 ° ) . The laser i s monitored by r e f l e c t i n g some of the laser l i g h t from a thin glass p l a t e , placed at the Brewster angle between the laser and the plasma, on to a s o l i d state photodiode. The diode, a Hewlett-Packard part #5082-4220, is biased at 100 volts to give a fa s t risetime (less than 1 nsec), and l i n e a r i t y up to 10 v o l t s . S u f f i c i e n t neutral density f i l t e r s are placed in front of the photodiode to keep i t operating in i t s l i n e a r region (actual signals about 0.5 v o l t s ) . F i g . 111-4 shows the c i r c u i t for the laser monitor. 21 the detecting system is very c r i t i c a l , . a detailed descrip- tion of the alignment procedure is presented in Appendix A. There are several obvious advantages of this optical delay system over a two monochromator, two photo- m u l t i p l i e r system. F i r s t , of course, is the convenience of having only one monochromator and photomultipiier as well as the reduced expense. Also, there is no problem of c a l i b r a t i n g the two monochromators so that they are analyzing the same wavelength, or have the same transmission function. There is no problem of d i f f e r e n t spectral sen- s i t i v i t i e s of two d i f f e r e n t photomultipiiers . The d i s - advantages are the very c r i t i c a l alignment and the high loss in the delay section (35%). The 35% loss i s not unreasonable considering 4% loss each time the scattered l i g h t enters or leaves lens C, and possible 10-20% loss on r e f l e c t i o n from the alluminum coated mirror. The grating monochromator, b u i l t in our labora- t o r y , is used in 5th order with l i n e a r dispersion of about o 4.5 A/mm, and a theoretical resolving power of about 30,000. A Kodak f i l t e r #29 is used to i s o l a t e the orders. The c o l l e c t i n g lenses are stopped to match the monochromator speed f/6. For a complete description of the monochromator 14 see VahAndel . Two photomultipiiers were used. A high gain tube, RCA 7265, was mainly used which had a S-20 response 22 o and nominal quantum e f f i c i e n c y of 3% at 6943 A. A RCA 31034 was also used, which had an extended response in the red due to i t s GaAs photocathode surface. Its quantum e f f i c i e n c y of 16% should give an improvement in signal to noise of about a factor of 3 over a photomultipiier with a S-20 response. The RCA 7265 was operated at 2200 v o l t s , and the RCA 31034 at 1900 v o l t s . A dual beam o s c i l l o s c o p e , Tektronix 551, with type L plug in units is used to record the signals from the photomultipiier and laser monitor. The traces are recorded on Polaroid type 410 f i l m . The combined r i s e - time of the oscilloscope and plug in units is about 15 nsec, wich serves to integrate the signal s l i g h t l y and improve the signal to noise. To help to reduce the stray l i g h t , the detection system from lens B to the monochromator is encased in a l i g h t proof tube, and the laser is covered except for an exit hole for the laser l i g h t . 23 Chapter IV EXPERIMENTAL RESULTS AND DISCUSSION The purpose of this chapter is to present and discuss the experimental r e s u l t s . F i r s t , the scattering p r o f i l e s and the determination of the electron density and temperature are given. Then the results for the corr e l a t i o n and standard deviation of the forward and backward scattering signals are presented. An estimate of the fluctuations due to d i f f e r e n t sources is made and then the results are discussed. For a l l the experimental work, the following conditions apply. The j e t was positioned so that the focal volume was centred 14.8 mm above the t i p of the cathode, 1.8 mm above the anode. Also the scattering angles were 49° 22' in the forward d i r e c t i o n s , 130° 38' in the backward d i r e c t i o n . The j e t current was 230 amps and the helium flow rate was 32 cubic feet per hour. Except where noted, the RCA 7265 photomultipiier was used. 24 A. Scattering P r o f i l e s and Determination of N and T 2 : e e So that work could be done with a plasma of known parameters, the scattering p r o f i l e s and electron density and temperature were determined. For this purpose, the monochromator exit s l i t was set to 400u wide to match the entrance s l i t , r e s u l t i n g in a triangular instrument o p r o f i l e , 1.8 A half-width, as i l l u s t r a t e d in F i g . IV-1 . A run consisted of scanning the spectrum at least four times, o with one scan composed of a shot every 1.8 A from about 6955 A to 7000 A. The oscillograms were then analyzed in a manner such that the electron density and temperature could be obtained as described in Chapter I I . F i g . IV-2a shows a typic a l oscillogram. The maximum heights of the scattered signals were measured and normalised to the height of the laser monitor s i g n a l . The measurements for each wavelength were then averaged and standard deviations about the mean clac u l a t e d . The means were then normalized to the maximum average s i g n a l , and a graph of the logio of this normalised signal versus logio(AX) was made. This experimental plot was then compared to a set of theoretical graphs for 1Q = 16,000 ° K , e t = 1 3 5° , a = 0.8 to 1.2 and 1.8 to 2.2 in steps of 0.05, so that a, N . T could be determined as described in e e Section II B. - 4 - 2 O 2 AX (Al FIG IV-1 MONOCHROMATOR TRANSMISSION FUNCTION - NARROW PASSBAND a. NARROW EXIT SLIT RCA 7265 PM TUBE "1 t 1 b. WIDE EXIT SLIT RCA 7265 PM TUBE 20mV/ d i v J L_l 100 mV/. I l - P M I I I 4 I 'div C. WIDE EXIT SLIT RCA 31034 PM TUBE FIG IV-2 TYPICAL OSCILLOGRAMS X = 6972. ICOnsec^jy 27 For scattering in the forward d i r e c t i o n , a was found to be 2.0. The electron density and temperature were: T = 19,000 °K e N = 2.07 x 10 1 6  cm" 3 e The sources of error for determining the plasma parameters in this fashion are the uncertainty in determining a and in determining the s h i f t A. An estimate was made of the error by measuring the s h i f t s for a obviously too large and too small (2.05 and 1.95 respectively) and cal c u l a t i n g the electron temperature and density from these s h i f t s . This gave the average deviations: Ne = (2.07 ± 0.13) x 10 1 6  cm- 3 T e = (19,000 + 200) °K . The scattering p r o f i l e for the backward d i r e c - tion has a broad, Gaussian-like shape, c h a r a c t e r i s t i c of a $ 1. For low a, a wide range of a's give acceptable f i t s to the experimental r e s u l t s , so that i t is d i f f i c u l t to obtain accurate values for a, N e, T g from the scattering p r o f i l e s . The results obtained are: a = 0.95 ± 0.15 T e = 15,700 ± 3,500 °K Ne = 2.0 ± 0.4 x 10 1 6  cm- 3 . 28 The errors quoted above, determined in the same manner as for the forward d i r e c t i o n , r e f l e c t the i n s e n s i t i v i t y of the spectrum to Ng and T . However the values for electron density and temperature for the two directions and s e l f - c o n s i s t e n t . F i g . IV-3 and F i g . IV-4 show the experimental results for the scattering spectrums, along with the theoretical graphs of S(k-k 0 ,w-a)0 ) / s m a x using Ng and T g as determined from the scattering p r o f i l e for the forward d i r e c t i o n . It should be noted that the scattering angles, geometrically measured using the entrance aperture at the monochromator, the hole in the j e t anode, and the middle of the front mirror of the laser cavity as r e f e r - ence points, were 46° 25' and 133° 35'. However the presence of the focussing lens D can change the incident angle of the laser beam. The angles are d i f f i c u l t to measure with lens D affe c t i n g the incident r a d i a t i o n , so that the angle was determined to be that angle that gave good theoretical f i t s to the experimental data for both forward and backward scattering p r o f i l e s . These angles, 49° 22' and 130° 38', when used for other experi- mental runs, also gave good theoretical f i t s to the two p r o f i l e s , indicating that these were the proper scattering angles. 29 FIG IV-3 THEORETICAL FIT TO EXPERIMENTAL DATA FOR FORWARD SCATTERING 30 1.21- 1.0 0.8 >- V) Z' - 0.6 a < s CC O z o cf 0.4 0.2 0.0 I EXPERIMENTAL POINTS THEORETICAL FIT FOR 6 = 130° 38" N e = 2J07 x i o l a c m ' 3 T E = 19.000 °K 1.0 1.2 1.4 1.6 U8 LOG (ax(A)) F IG IV-4 THEORETICAL FIT TO E X P E R I M E N T A L DATA FOR BACKWARD SCATTERING 2.0 31 B. Experimental Correlation and Standard Deviation Once the plasma parameters were determined, the c o r r e l a t i o n between the backward and forward signals was studied, as well as the standard deviation of the two s i g n a l s . For this purpose, the monochromator exit s l i t was widened to 2.0 mm. This resulted in an instrument p r o f i l e shown in F i g . 11-2. The larger s l i t increased the total number of photons incident on the photomultipiier, and therefore reduced the shot noise. The monochromator was set so that the transmission function was centred on the electron s a t e l l i t e found in the forward scattering o spectrum. Because of the 10 A wide instrument p r o f i l e , e s s e n t i a l l y a l l of the s a t e l l i t e was observed. A series of at least 20 shots were f i r e d , with a one-minute wait between shots. The one minute was necessary for the cooling of the l a s e r , as well as making the power output more s t a b l e . F i g . IV-2b shows a typical oscillogram. The height of the maximum of the forward and backward signals were measured and normalised to the height of the laser monitor s i g n a l . The means and standard deviations were then c a l c u l a t e d . The c o e f f i c i e n t of cor- r e l a t i o n between two variables X and Y is defined as: 32 KX-X.MY-Y^ i P " [I(X-X.) 2(Y-Y i) 2] i i where J means the average value of X, and X̂  is the i t h measurement of X. Because only the quantities (X-X..) are used, i t is unnecessary to subtract the stray l i g h t , approximately constant, from the observed s i g n a l s . The presence of stray l i g h t w i l l , however, contribute to the standard deviations of the s i g n a l s . The contribution to the photomultipiier signal made by the stray l i g h t was corrected for when ca l c u l a t i n g the mean scattering signal . A typical experimental result gave a c o e f f i c i e n t of c o r r e l a t i o n of +0.85 for 25 shots. If the two signals were not co r r e l a t e d , there would be less than 1/2% chance of getting a c o e f f i c i e n t of c o r r e l a t i o n equal to or larger than t h i s . For a l l the runs, the c o e f f i c i e n t of cor r e l a t i o n was p o s i t i v e , with less than 10% chance of obtaining p equal to or larger than that observed. The standard deviations of the forward and backward signals were usually about 12-16% and 16-20% r e s p e c t i v e l y . Great care was taken to make the plasma condi- tions the same from shot-to-shot. The helium flow rate was set at the beginning of a run and never changed. 33 The c u r r e n t was r e s e t to the same va lue to w i t h i n l e s s than 1/2%. Two methods were used to operate the j e t dur ing a r u n . The j e t was u s u a l l y i d l e d at about 70 amps as b e f o r e , and then the c u r r e n t r a i s e d to 230 amps. However runs were a l s o made wi th the c u r r e n t mainta ined at 230 amps. Both methods produced the l a r g e p o s i t i v e p. The RCA 31034 p h o t o m u l t i p i i e r was a l s o t r i e d . F i g . IV -2c shows the improvement i n s i g n a l to n o i s e , but I the standard d e v i a t i o n s of the s i g n a l s a c t u a l l y were only reduced by one or two per c e n t . Th is i s because there are o ther l a r g e sources of e r r o r which o v e r r i d e the improvement i n S/N. The c o e f f i c i e n t of c o r r e l a t i o n remained at i t s high p o s i t i v e v a l u e . C. E s t i m a t i o n of Known F l u c t u a t i o n s To see i f the s c a t t e r i n g s i g n a l s as measured i n S e c t i o n IV B. have more f l u c t u a t i o n s than can be e x p e c t e d , es t imates of the s i z e of f l u c t u a t i o n s from d i f f e r e n t sources were made. The sources cons idered were: shot no ise due to the smal l number of p h o t o e l e c t r o n s , f l u c t u a - t i o n s due to the continuum r a d i a t i o n , f l u c t u a t i o n s due to v a r i a t i o n s i n s t r a y l i g h t , and e r r o r i n measurement of the s i g n a l h e i g h t s . I 34 To estimate the shot noise, the total number of photoelectrons had to be determined. The area under the curve of a signal from the photomultipiier is n times the area attributed to one photoelectron, where n is the total number of photoelectrons emitted from the photocathode surface. Thus i f the size of the signal of one photoel ectron can be determined, then the total number of photoelectrons can be estimated. There are two main d i f f i c u l t i e s in deter- mining the signal from one photoelectron. F i r s t , the signal is very small, less than 5 mv in height at the photomul t i p i i e r voltage used. Secondly, i t is d i f f i c u l t to know whether or not the signal observed is due to a single photoelectron, to more than one, or due to an electron emitted from one of the dynodes. Inspite of these d i f f i c u l t i e s i t was f e l t that this method was the most dir e c t way of getting a good estimate of the number of photoelectrons. The manufacturer's s p e c i f i c a t i o n s for the gain of the photomultipiier tube cannot be used for a good estimate, since there are such large variations in gain from tube to tube. The signal from one photoelectron was determined in the following manner. The monochromator was set to o 100 A from the ruby laser wavelength so that the p r o b a b i l i t y of more than one photon being detected by the photomultip!ier 35 was small. When the laser was f i r e d , the photomultipiier signal was usually f l a t , but occasionally there appeared a small s i g n a l . The position of the signal along the time axis v a r i e d , but the area of the signal remained constant. The triangular pulse was approximately 20 nsec wide at i t s base, and 2 mv high. Using this area i t was then possible to estimate the number of photo- electrons in any photomultipiier signal as stated above. o For the case of a 10 A bandpass situated on the electron s a t e l l i t e as described in Section IV B, i t was estimated that there were 400 photoelectrons in the forward d i r e c t i o n s i g n a l , and 300 in the backward. This would give a contribution of 5% and 6% to the standard deviations of the two signals r e s p e c t i v e l y . The existence of continuum radiation causes fluctuations in the baseline of the signal from the photomultipiier, and therefore contributed to the f l u c - tuations in the scattering s i g n a l s . An estimation of this contribution was made by considering that part of an oscillogram which has no scattering s i g n a l . Fifteen measurements were taken, one every 20 nsec over a 300 nsec range, of the position of the baseline from a horizontal g r a t i c u l e l i n e . The standard deviation of this measurement was then compared to the average height 36 of the s c a t t e r i n g s i g n a l s . The standard d e v i a t i o n s of the b a s e l i n e was found to be about 5% and 8% of the forward and backward s c a t t e r i n g s i g n a l s r e s p e c t i v e l y . The s t r a y l i g h t was assumed to o r i g i n a t e from o the l a s e r l i g h t at 6943 A e n t e r i n g the monochromator. Thus the s t r a y l i g h t was p r o p o r t i o n a l to the i n c i d e n t r a d i a t i o n . A f t e r the s t r a y l i g h t s i g n a l was normalised to the l a s e r monitor s i g n a l , i t had a standard d e v i a t i o n of about 20%. Since the forward and backward s i g n a l s were comprised of about 3% and 5% s t r a y l i g h t , the s t r a y l i g h t would c o n t r i b u t e about 1/2% and 1% to the standard d e v i a t i o n s of the forward and backward s c a t t e r - ing s i g n a l s . The heights of the s i g n a l s on the o s c i l l o g r a m s were measured using a xlO magnifying g l a s s with an estimated e r r o r of 2%. The t o t a l estimated standard d e v i a t i o n of the s c a t t e r i n g s i g n a l s , adding the square of the i n d i - v i d u a l estimates and t a k i n g the s q u a r e - r o o t , are 8% and 11% f o r the forward and backward s c a t t e r i n g s i g n a l s r e s p e c t i v e l y . D. D i s c u s s i o n The s c a t t e r i n g p r o f i l e s are i n e x c e l l e n t agree- ment with t h e o r e t i c a l p r o f i l e s f o r T g = 19,000 °K, 37 Ng = 2.07 x 10 1 6  cm" 3 , and e = 49° 22', 130° 38'. The temperature i s s l i g h t l y higher than reported previously, (van der Kamp, 13  Chan, 1 0  Stansfield , 1 5  B a l d i s , 1 1 1 2 Morris ) , but is within error of the values quoted by van der Kamp and Morris. The electron density is com- parable to that reported e a r l i e r . The total estimated standard deviation of the two scattering signals are both less than 3/4 of the actual standard deviations. The estimates are very rough, and the total deviation could be 2 or 3% low, but they are s t i l l much less than the observed deviations. It was found that the fluctuations in the two scattering signals are highly c o r r e l a t e d . If the fluctuations originated from shot noise, continuum r a d i a t i o n , and stray l i g h t alone, one would expect the fluctuations to be independent. The fact that the fluctuations are too large and are correlated indicates that there must be at least one other source of f l u c t u a - t i o n , about 12% in magnitude and p o s i t i v e l y correlated for the two d i r e c t i o n s . One might propose that i f the electron density and/or temperature changed from shot-to-shot, then this might produce the required v a r i a t i o n in s i g n a l . 38 Mechanisms that might change N g and T g are v a r i a t i o n s i n the j e t c u r r e n t or gas flow r a t e , or perhaps changes i n p o s i t i o n of the plasma j e t flame due to e r o s i o n of the cathod or anode. The l a t e r would tend to i n c r e a s e or decrease both N and T at the same time. A s h i f t of e e more than 1 mm o f f the centre of the j e t would seem unreasonable: t h i s would produce a change i n N g and T f i 1 2 of 17% (Morris ). However, c a l c u l a t i o n s of S e c t i o n II-C show t h a t i f both N and T decrease by 20% then . e e J, i the s i g n a l i n the forward d i r e c t i o n should i n c r e a s e by H%, and i n the backward d i r e c t i o n , should decrease by 8 i % . These changes are too small as well as having negative c o r r e l a t i o n r a t h e r than p o s i t i v e . I t i s not obvious e x a c t l y the changes i n N g and T g r e s u l t i n g from changes i n the gas flow r a t e or j e t c u r r e n t . However, i f i t i s assumed that these or any other mechanism t h a t changes the plasma parameters leaves one of T g or N Q constant and changes the o t h e r , then t h i s cannot provide the e x t r a f l u c t u a t i o n s as i l l u s t r a t e d i n F i g . IV-5 and IV-6. F i g . IV-5 i s a t h e o r e t i c a l graph of the s i g n a l as f u n c t i o n of N g assuming T g constant at the experimental value of 19,000 °K, reproduced from S e c t i o n II C. The experimental p o i n t s p l o t t e d on t h i s graph were determined i n the f o l l o w i n g 39 24 r EXPERIMENT THEORY 0.8 0.8 IP 1.2 Ne/2.07x i o 1 6 cm"3 F I G IV-5 COMPARISON OF EXPERIMENTAL VARIATIONS IN SCATTERING SIGNAL TO CALCULATED VARIATIONS DUE 1.4 TO CHANGING N p 24 If) 2 2 2 0 18 BACKWARD >-cr < or i— cn or < co z OI t-z 16 14 12 FORWARD 1 i EXPERIMENT THEORY 10 0.8 0.8 1.0 1.2 Te/19,000 °K 1.4 1.6 FIG IV-6 COMPARISON OF EXPERIMENTAL VARIATIONS IN SCATTERING SIGNALS TO CALCULATED VARIATIONS DUE TO CHANGING T, e 41 manner. Assume that an increase in the signal in the backward dir e c t i o n from i t s average value as measured in Section III B is due e n t i r e l y to a change in N g. This new Ng can be read from the graph IV-5. Using t h i s new N g, the new theoretical signal in the forward di r e c t i o n can be determined. The actual experimental forward signal is plotted at the new N g, normalised so that the average forward signal is equal to the theoretical signal for T e = 19,000 °K , Ne = 2.07 x 10 1 6  cm - 3 . If the changes in signal are r e a l l y due to changes in N g, then the experimental points plotted as described should l i e about the theoretical curve for the forward d i r e c t i o n . As can be seen from the graph, this is not the case. The error bars drawn come from the estimate made in Section IV C for a l l known sources of e r r o r . A similar procedure was used to check i f the variations are due to changes in T g alone. This time the signal in the forward d i r e c t i o n was used to f i n d the new T g and then the experiment points were drawn for the backward dir e c t i o n ( F i g . IV-6). Again the theoretical curve and experimental points do not match up. The above calculations indicate that the extra deviation is probably not due to fluctuations in Ng and T . It might s t i l l be possible for N and T to be e  3 r  e e 42 changing in some s p e c i f i c way to give the required devia- t i o n s , but this does not seem reasonable because the variations in the calculated signal are too small unless very large changes (about 50%) are made in Ng and T . It would seem then that the plasma j e t has some non- thermal c h a r a c t e r i s t i c s which contribute to the standard deviation of the scattering s i g n a l , but are not so big as to cause large deviations from normal thermal s c a t t e r - ing p r o f i l e s . 43 Chapter V CONCLUSIONS A. Conclusions Scattering p r o f i l e s for scattering of ruby laser l i g h t from a plasma j e t were measured simultaneously in two directions using a two channel system with optical delay. The experimental data agrees very well with theoretical p r o f i l e s for scattering from and i n f i n i t e homogeneous thermal plasma with Ng = 2.07 x 10 1 6  cm - 3 , T g = 19,000 °K. The integrated scattering s i g n a l , measured o with 10 A wide monochromator trasmission f u n c t i o n , proved to have a standard deviation too large to be accounted for by known sources of f l u c t u a t i o n s . Also the i n t e - grated scattering signals for the forward and backward scattering angles had a large p o s i t i v e c o e f f i c i e n t of c o r r e l a t i o n . Theoretical calculations show that the extra, correlated fluctuations cannot originate from changes in Ng and T . Thus i t i s suggested that the plasma j e t has non-thermal properties that have only a small effect on normal thermal scattering of laser l i g h t from a plasma j e t . B. Suggestions for Further Study The dependence of the extra fluctuations and positive c o r r e l a t i o n on the scattering vector jc could be studied. It may be possible for the non-thermal effects to have a sharp dependence on k_ such as Ringler and Nodwell found for the total integrated i n t e n s i t y of laser l i g h t scattered from a magnetically s t a b i l i s e d , low pressure hydrogen arc where the total integrated int e n s i t y was found to be approximately twice the theo- r e t i c a l value at one p a r t i c u l a r jc vector, then dropped quickly to that predicted by theory as k_ was varied. A multichannel system might be adopted where the entire scattering spectrum can be found with one f i r i n g of the l a s e r . This would allow N and T to be 3  e e determined from shot to shot, and therefore make the experiment more independent from changes in experimental parameters. Such a multichannel system is only recently on the market. 1 45 BIBLIOGRAPHY 1. Gerry, E.T. and Rose, D.J. 1 966. J. App1 . Phys. 37: 2715-2724. 2. Evans, D.E. et al. 1 966. Nature 2jJ_: 23-24. 3. Ringler, H. and Nodwell, R.A. 1969. Phys. L e t t . 29A: 151. 4. Ringler, H. and Nodwell, R.A. 1969. Phys. L e t t . 30A: 126. 5. Ringler, H. and Nodwell, R.A. 1969. Third Europ. Conf. on Contr. Fusion and Plasma Physics, Utrecht. 6. Churchland, M.T. 1972. Ph.D. Thesis, University of B r i t i s h Columbia. 7. Saltp e t e r , E.E. 1960. Phys. Rev. 1_20: 1528-1 535, 8. Rosenbluth, M.N. and Rostoker, N. 1962. Phys. Fluids 5: 776. 9. Kegal, W.H. 1965. Internal Report. I n s t i t u t fur Plasma Physik, IPP 6/34. 10. Chan, P.W. 1966. Ph.D. Thesis, University of B r i t i s h Columbia. 11. B a l d i s . H.A. 1971. Ph.D. Thesis, University of B r i t i s h Columbia. 12. Morris. R.N. 1968. Ph.D. Thesis, University of B r i t i s h Columbia. 46 13. van der Kamp, G.S.J.P. 1968. M.Sc. Thesis, University of B r i t i s h Columbia. 14. VanAndel , H.W.H. 1 966. Ph.D. Thesis, University of B r i t i s h Columbia. 15. S t a n s f i e l d , B.L. 1971. Ph.D. Thesis, University of B r i t i s h Columbia. 47 Appendix A ALIGNMENT PROCEDURE Because the alignment of the d e t e c t i n g system i s c r i t i c a l , a d e t a i l e d procedure i s given here. F i r s t a HeNe l a s e r i s a l i g n e d with the o p t i c a l a x i s of the monochromator, the beam going i n the e x i t s l i t which has been s e t to the r e q u i r e d width. Then, with the monochromator s e t to t r a n s m i t the l a s e r l i n e , two s t r a i g h t edges are placed 500u apar t over the 400u wide entrance s l i t so t h a t the r e c t a n g l e formed i s centred over the l a s e r beam. T h i s helps to d e f i n e the volume of the observed plasma. Next a f r o n t s u r f a c e m i r r o r i s placed 50 meters away so t h a t the l a s e r beam h i t s approximately i n the c e n t r e . The beam forms a d i v e r g i n g d i f f r a c t i o n p a t t e r n when i t leaves the monochromator, so i t i s 4 to 5 cm. wide at the m i r r o r . Because of t h i s , a stop was placed j u s t i n f r o n t of the m i r r o r t h a t has a s e r i e s of concen- t r i c c i r c l e s drawn on i t s f a c e , centred around a 1/8 48 inch diameter hole. This stop is placed so that the hole is in the centre of the d i f f r a c t i o n pattern, using the c i r c l e s as a guide. The res u l t is a small c i r c l e of l i g h t with some d i f f r a c t i o n rings being re f l e c t e d from the mirror. The mirror is then adjusted so that the refle c t e d c i r c l e is centred on the entrance rectangle of the monochromator. The lenses are now placed in their proper position along the axis of the detecting system with the aid of a telescope focussed to i n f i n i t y . The telescope is placed between the mirror and the expected position of lens C centred on the laser beam. Lens A is approximately centred on the laser beam and then adjusted so that the image of the entrance s l i t i s in the same plane as the cross hairs of the telescope. Thus the entrance s l i t - l e n s distance is equal to the focal length of lens A. Next lens B and C are positioned. Lens B is placed so that i t is about one focal length from the position of the plasma j e t . The placement is not too c r i t i c a l because of the adjustments on the j e t . Using the telescope again, lens C is placed so that the focal points of B and C coincide, which occurs when the image of the entrance s l i t is again in the same I 49 plane as the cross h a i r s . Stops are placed on the optical benches so that the lenses can be removed and replaced without changing th e i r position along the axis of the detection system. Next i s the adjustment of the horizontal and v e r t i c a l positions of the lenses. Because of the greatly diverging beam after passing through a l e n s , there is no good reference for positioning lenses B and C by themselves. Together, however, there is a good j reference beam since the only e f f e c t they have is to enlarge the beam by the r a t i o of the i r focal lengths. They are then aligned, with lens A removed, so that the laser beam is centred on both the aperture at the mirror and at the monochromator. Lastly lens A i s positioned so that the beam is centred on the stop at the mirror, with both B and C in place. The l a s t step is to stop down the lenses so that they match the monochromator speed f/6. With the stop at the mirror removed, and f/3 lenses, focal lengths 12, 12, 30 cm. for A, B, and C r e s p e c t i v e l y , the re f l e c t e d laser beam should cover a l l the area of the lenses and be centred on each. Because of the distance required, the f i r s t attempt at this experiment used three mirrors and f i v e r e f l e c t i o n s in the optical delay section to fold the l i g h t path. However, the extreme losses of this arrange- ment made i t i m p r a c t i c a l , so that i t was necessary to adopt a one mirror system.

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