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UBC Theses and Dissertations

Laser induced perturbation in a plasma Baldis, Hector Alberto 1971

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LASER INDUCED PERTURBATION IN A PLASMA by HECTOR A. BALDIS L i c e n c i a d o , U n i v e r s i d a d N a c i o n a l de C o r d o b a , 1964 M.Sc., U n i v e r s i t y of B r i t i s h C o l u m b i a , 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS- FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the D e p a r t m e n t of Phys i cs We a c c e p t t h i s t h e s i s as c o n f o r m i n g to t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA . A p r i 1 , 1971 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 a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s l v C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . -D e p a r t m e n t o f T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8 , C a n a d a ABSTRACT The i n t e r a c t i o n between a 2 0 MW Q-switched ruby l a s e r pu l se and a p a r t i a l l y i o n i z e d argon plasma has been s t u d i e d e x p e r i m e n t a l l y . When the focused l a s e r pu lse i s f i r e d i n t o the plasma', a t r a n s i e n t emiss ion from the plasma may be observed both in the continuum and l i n e e m i s s i o n . From measurements of the abso lu t e i n t e n s i t i e s of t h i s t r a n s i e n t r a d i a t i o n , e s t ima tes have been made of the popu-l a t i o n d e n s i t y of the e x c i t e d atoms and of the e l e c t r o n d e n s i t i e s . The S tark broadening of the Ar II l i n e s has a l s o been measured to ob t a i n the e l e c t r o n d e n s i t y in the t r a n s i e n t plasma and data ob ta ined in t h i s way are c o n s i s -t en t with those ob ta ined from the continuum r a d i a t i o n . Dur ing the time when the l a s e r l i g h t i s i n c i d e n t on the plasma the Ar II l i n e s show a s t rong asymmetry which d i s -appears q u i c k l y a f t e r the l a s e r pu lse has t e r m i n a t e d . Th i s asymmetry can be e x p l a i n e d in terms of the e l e c t r o n d e n s i t y g r a d i e n t p resen t in the expanding per tu rbed p lasma. i i i TABLE OF CONTENTS Page ABSTRACT. , i i TABLE OF CONTENTS i i i LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . v ACKNOWLEDGMENTS vi i i 1 CHAPTER I - INTRODUCTION . . . . . . . . . . 1 I-a I n t r o d u c t i o n to the p resen t exper iment . . 2 I-b An o u t l i n e of the t h e s i s 3 CHAPTER II - APPARATUS I l-a The plasma j e t . . . 5 11-b The l a s e r 9 II-c The d e t e c t i o n system 1° CHAPTER III - OBSERVATIONS AND RESULTS . . . 1 4 -111- a S p e c t r a l de t e rm ina t i on of the parameters of the plasma j e t . . . . . . . . . . . 15 111-b Genera l f e a t u r e s of the pe r tu rbed plasma . 22 111-c Expansion of the per tu rbed p lasma. . . . . 32 111-d The p o p u l a t i o n of e x c i t e d s t a t e s of Ar . . 3 4 111-e E l e c t r o n d e n s i t y from continuum emiss ion . 37 I l l - f L ine shape.of . Ar II l i n e s . . . . . . . . . 4 5 i v Page CHAPTER IV - ENERGY ABSORPTION FROM A LASER BEAM. . . . 54 IV-a I n t r o d u c t i o n . . . . . . . . . 54 IV-b Inverse bremsstrah-1 ung a b s o r p t i o n coe f f i c i en t . . . . . 55 IV-c P h o t o i o n i z a t i o n a b s o r p t i o n c o e f f i c i n e t . . 57 IV-d Energy absorbed by the p lasma. 62 IV-e Non l i nea r e f f e c t s due to the l a s e r beam. . 68 CHAPTER V - DISCUSSION AND CONCLUSIONS 70 BIBLIOGRAPHY. . . . . . . . . . . . . . . 7 7 V LIST OF FIGURES Page F igu re 1 - Exper imenta l arrangement . 6 F igu re 2 - The plasma j e t . 7 F igu re 3 - S y n c r o n i z a t i o n of the Q-switch and the choppi ng wheel . 12 F igu re 4 - Compos i t ion of the plasma j e t at a tmospher i c p r e s su re as a f u n c t i o n of the e l e c t r o n energ'y 19 F igu re 5 - Rad ia l d i s t r i b u t i o n of e l e c t r o n and neu t r a l number d e n s i t i e s in the plasma j e t at 19 „_ ^ u „ , . „ „ j. i, „ J _ 9 0 j. L. min uuuvc U I I C ^ U U I I C M ^ . • • • • • • • . • ~ ~ F igu re 6 - Rad ia l d i s t r i b u t i o n of some e x c i t e d s t a t e s of Ar I and Ar II . 21 F igu re 7 - O s c i l l o s c o p e t r a ce s of a l a s e r p u l s e , the continuum r a d i a t i o n at 5000 A, and the Ar II 4806 A l i n e . 2 3 F igu re 8 - O s c i l l o s c o p e t r a ces of Ar II 4806 A l i n e at d i f f e r e n t l o c a t i o n s of o b s e r v a t i o n in the plasma 2 3 F igu re 9 - I n t e n s i t y of continuum emiss ion at 5000 A a long the j e t ax i s . . . . . . 26 F igu re 10 - T r a n s i e n t emiss ions from the plasma at the cen t r e of the pe r tu rbed r eg ion 27 vi - Page F igu re 11 - I n t e n s i t y in the Ar II 4806 A l i n e em iss ion v s . degree of p r e - i o n i z a t i o n 28 F igu re 12 - I n t e n s i t y , in the Ar II 4806 A l i n e em iss ion v s . l a s e r power d e n s i t y 29 F igu re 13 - Increment in the continuum emiss ion at 5000 A v s . degree of p re- i oni z a t i on 30 F igu re 14 - V i s i b l e spectrum of the increment in the continuum emiss ion . 31 F igu re 15 - Diameter of the pe r tu rbed plasma as a f u n c t i o n of t i m e . . . . . 33 F i gu re 16 - P o p u l a t i o n d e n s i t y of f ou r Ar II energy l e v e l s v s . energy o f the l e v e l s 36 F i gu re 17 - E l e c t r o n number d e n s i t i e s at the cen t re of the pe r tu rbed plasma as a f u n c t i o n of t ime , ob ta ined from continuum abso lu t e i n t e n s i t i e s and from Ar II l i n e widths 43 F igu re 18 - E l e c t r o n number d e n s i t y ac ross the pe r tu rbed r eg i on . / . . . . . . . . . 4 4 F igu re 19 - E f f e c t of the i n s t rumen ta l broadening on the observed width of a l o r e n t z i a n l i n e . . . . . 4 ^ F i gu re 20 - T h i r d moment of Ar II 4880 A l i n e shape as a f u n c t i o n of time . . . . . . . . . . . . ^ 9 F igu re 21 - Shape of Ar II 4880 A l i n e at t=10 nsec . . . . 5 1 Page F igu re 22 - Shape of Ar II 4880 A l i n e at t=30 nsec . . . . 52 F i gu re 23 - Shape of Ar II 4880 A. l i n e at t=100 nsec . . . 53 F i gu re 24 - Power absorbed by the plasma by p h o t o i o n i z a t i o n and by i n v e r s e bremsst rah lung from a 0.9 j o u l e s l a s e r pu lse . . 64 F i gu re 25 - Energy absorbed by the plasma from a 0.9 j o u l e s l a s e r p u l s e . . . .65 v.i i i ACKNOWLEDGEMENTS I wish to express my most s i n c e r e a p p r e c i a t i o n to Dr. R. A. Nodwell f o r h is guidance and encouragement du r i ng the course of the exper iment . I would a l s o l i k e to thanks Dr. J . Meyer f o r h e l p f u l sugges t i ons and suppor t du r i ng Dr . Nodwe l l ' s l e a v e . Thanks are a l so due to Dr. F. L. Curzon f o r h is h e l p f u l sugges t ions in the p r e s e n -t a t i o n of t h i s t h e s i s . I would l i k e to acknowledge the t e c h n i c a l a s s i s t -ance of Mess r s . D. G. Sie.berg and J . A. Zang.aneh as wel l as the members of the Phys i c s machine shop s t a f f , i n p a r t i c u l a r to Mr. J . Bosma. I am a l s o indebted to Mr. Mike Wu f o r h is a s s i s t a n c e du r ing the l i n e shape measurements. It has-been a p l easu re being a s s o c i a t e d with the Plasma Phys i c s g roup , and in p a r t i c u l a r I am indebted to Mess r s . B. L. S t a n d f i e l d , R. N. Mor r i s and D. Camm f o r t h e i r f r i e n d s h i p and s t i m u l a t i n g d i s c u s s i o n s . Th i s work i s supported by a grant from the Atomic Energy Con t ro l Board of C a n a d a . - , 1 Chapter I INTRODUCTION Th i s t h e s i s d e s c r i b e s an exper imenta l i n v e s t i g a -t i o n of the p e r t u r b a t i o n of a p a r t i a l l y i o n i z e d argon plasma under the i n f l u e n c e of the focused beam of a ruby l a s e r p u l s e . P e r t u r b a t i o n s in the r a d i a t i o n from a plasma due to a pu l se from a l a s e r have been r epo r t ed p r e v i o u s l y in the l i t e r a t u r e (Thompson and F i o c c o , 1963, L i d sky e t . al . , 1964 , Thompson, 1964 , Nodwell and Van der Kamp, 1968) but a s y s t ema t i c exper imenta l s tudy of the phenomena has not been c a r r i e d ou t . There have been s e ve r a l r e p o r t s in r ecen t yea rs of the exper imenta l and. t h e o r e t i c a l s t u d i e s in which a plasma is c r ea t ed by a high i n t e n s i t y l a s e r beam i n c i d e n t upon a s o l i d , l i q u i d or gas (Meyerand and Haught, 1963, Z e l ' d o v i c h and R a i z e r , 1965, De M i c h e l i s , 1969) , on the subsequent hea t ing of the plasma by the a b s o r p t i o n of the beam ( R a i z e r , 1965, De M i c h e l i s , 1969) , and on the e f f e c t of the h igh i n t e n s i t y beam on the a b s o r p t i o n c o e f f i c i e n t of the plasma (Rand, 1964, Genera lov e t . a l . , 1968, 1969, 1970) . In the exper iment we r e p o r t here we s t a r t wi th a plasma of a 2 predete rmined degree of p r e - i o n i z a t i o n and we study the changes in the emiss ion from the plasma due to the presence of a high power focused l a s e r beam. The m o t i v a t i o n f o r t h i s exper iment has been two-f o l d . F i r s t l y , the spectrum of the r a d i a t i o n from a l a s e r beam s c a t t e r e d by a plasma p rov ides i n f o r m a t i o n about the s t a t e of the plasma and the techn ique has been used s u c -c e s s f u l l y to determine e l e c t r o n and ion d e n s i t y and temper-a tu re in plasmas (Evans , 1969) . Th i s d i a g n o s t i c t echn ique o f f e r s good s p a t i a l and temporal r e s o l u t i o n . But a l i g h t wave p ropaga t i ng through a plasma may not on ly be s c a t t e r e d , but may a l s o be abso rbed , thus mod i f y ing the c o n d i t i o n s in the p lasma. A d e t a i l e d exper imenta l i n v e s t i g a t i o n of the p e r t u r b a t i o n e f f e c t i s e s s e n t i a l to a c cu ra t e i n t e r p r e t a t i o n of s c a t t e r i n g expe r imen t s . Secondly i t i s f e l t tha t a de t a i1ed q u a n t i t a t i v e examinat ion of the p e r t u r b a t i o n of the plasma due to the l a s e r pu lse w i l l he lp to c l a r i f y the e x c e e d i n g l y complex phenomena o c c u r r i n g in l a s e r p r o -duced plasma exper iments .-I-a I n t r o d u c t i o n to the p resen t exper iment . In the exper iment presented here we have i n v e s t i -' gated the p e r t u r b a t i o n of a plasma under the i n f l u e n c e of ) a focused ruby l a s e r beam. When the high power l a s e r l i g h t pu l se i s f i r e d i n t o the p lasma, a change in the l i g h t emiss ion from the plasma may be obse r ved . An i n c r e a s e 3 occurs both in the continuum and in the l i n e r a d i a t i o n from the p lasma. The t r a n s i e n t r a d i a t i o n may l a s t f o r s e ve r a l m ic roseconds a l though the l a s e r pu lse l a s t s on l y 50 nsec . Fu r the r one observes tha t the volume of the pe r tu rbed plasma i s expanding in s i z e , hence the l a s e r i s a f f e c t i n g a much l a r g e r volume of the plasma than the o r i g i n a l volume of the focused beam. From measurements of the a b s o l u t e i n t e n s i t i e s of^the t r a n s i e n t r a d i a t i o n , es t imates may be made of the p o p u l a t i o n d e n s i t y of the e x c i t e d atoms and of the e l e c t r o n d e n s i t i e s . The S tark broaden ing of s p e c t r a l l i n e s a l s o may be used to ob t a i n the e l e c t r o n d e n s i t y of the t r a n s i e n t p lasma. In the exper iment we have conduc t ed ,bo th- these measurements have been made in a pe r tu rbed argon plasma and c o n s i s t e n t r e s u l t s have been o b t a i n d . Dur ing the time tha t the l a s e r l i g h t pu lse i s i n c i d e n t on the plasma the Ar II l i n e s show a s t rong asymmetry which d i s appea r s q u i c k l y a f t e r the l a s e r pu lse c e a s e s . Th i s asymmetry can be e x p l a i n e d in terms of the e l e c t r o n d e n s i t y g r a d i e n t s p resen t in the expanding per tu rbed p lasma. . I-b An O u t l i n e of the t h e s i s . The d e s c r i p t i o n of the exper imenta l apparatus used in t h i s work i s presented in Chapter II. The d e s c r i p -t i o n of the apparatus has been d i v i d e d i n t o three main p a r t s : 4 the p r o d u c t i o n of the p lasma, the l a s e r used to pe r tu rb the p lasma , and the d e t e c t i o n and r e c o r d i n g of s i g n a l s . S ince most of the equipment used dur ing the course of the exper iment i s f a i r l y s tandard in t h i s type of r e s e a r c h , on ly a b r i e f d e s c r i p t i o n i s p r e s e n t e d . Chapter III i s devoted to the o b s e r v a t i o n s and r e s u l t s . These are presented in d e t a i l and a d i s c u s s i o n of some of the r e s u l t s are i n c l uded p a r a l l e l to t h e i r p r e s e n t a t i o n . The d e t e r m i n a t i o n of the degree of pre-i o n i z a t i o n of the plasma i s a l so i n c l uded in t h i s c h p a t e r . In Chapter IV the mechanism of energy a b s o r p t i o n from the l a s e r beam by the plasma i s p r e s e n t e d . C a l c u l a -t i o n s of the amount of energy absorbed based on the e x p e r i -mental d e t e r m i n a t i o n of the e l e c t r o n d e n s i t y are a l s o p resented and d i s c u s s e d . F i n a l l y , Chapter V p resents the d i s c u s s i o n of some aspec ts of the r e s u l t s tha t have been o b t a i n e d . The c o n c l u s i o n s of the present work as wel l as sugges t i on f o r f u t u r e work are presented at the end of the c h a p t e r . 5 Chapter II APPARATUS The purpose of t h i s chapte r i s to d e s c r i b e the apparatus used in the exper iment . The d e s c r i p t i o n w i l l be d i v i d e d in th ree p a r t s : the p roduc t i on of the plasma ( S e c t i o n 11 - a) , the l a s e r u n i t used to per tu rb the plasma ( S e c t i o n 11 -b) „ and the d e t e c t i o n system ( Sec t i on 11 - c ) . 11 - a The plasma j e t . The exper imenta l arrangement i s shown in F i gu re 1 and a schemat ic diagram of the plasma j e t used to p r o -duce the argon plasma is shown in F igu re 2. The v e r t i c a l ax i s of the plasma j e t i s p e r p e n d i c u l a r to the plane of F i gu re 1. The plasma j e t i s operated at a tmospher i c p r e s su re thus e l i m i n a t i n g the need of c o n t a i n e r wa l l s or windows,, and produces a s teady s t a t e plasma of h igh e l e c -t ron d e n s i t y and good r e p r o d u c i b i l i t y . For the c o n s t r u c -t i o n d e t a i l s and o p e r a t i o n of a plasma j e t s e e ( M o r r i s , 1968) . The power supp ly of the j e t c o n s i s t of a c u r r e n t t r ans fo rme r and of a 36 v o l t b a t t e r y bank. The t r ans fo rmer i s used to keep the j e t running .at low c u r r e n t (30 Amp 6 MONOCHROMATOR GLASS PLATE RUBY LASER Cu S O4 C E L L PHOTOMULTIPLIER 1 — — LASER MONITOR CONSTANT DEVIATION PRISM LASER DUMP SLIT AND CHOPPING WHEEL MONOCHROMATOR PHOTOMULTIPLIER FIGURE 1 Exper imenta l a r r a n g e m e n t . T h e ax i s of c y l i n d r i c a l symmetry of the plasma j e t i s p e r p e n d i c u l a r to the p lane of the • •••• • d i ag r am .- •• - • •• 7 — 0 4.5 mm ANODE FIGURE 2 The plasma j e t . -8 t y p i c a l ) to min imize e l e c t r o d e damage. Because of the remain ing v o l t a g e r i p p l e on the r e c t i f i e d output of the t r a n s f o r m e r , the j e t i s powered with the ba t t e r y bank whenever a measurement i s performed on the p lasma. For t h i s purpose a c u r r e n t of 300 Amp i s employed. A r e s i s t o r bank i s used i n s e r i e s with the power supp ly to s t a b i l i z e the a r c . The c u r r e n t i s determined by measuring the vo l t age ac ross a 0.25 mSl shunt . The c u r r e n t passes between the thor ium tungsten tapered cathode and the copper r i n g anode. Both e l e c t r o d e s are water c o o l e d . Argon gas i s caused to f low from a chamber su r round ing the cathode out through the hole in the cen t r e of the anode thus forminy a smal l j e t above the anode. The gas f low i s 4.7 l i t e r / m i n . The l a s e r beam i s focused in the plasma at a d i s t a n c e from 2 to 10 mm above the anode. By f o c u s i n g the l a s e r beam at d i f f e r -ent p o s i t i o n s above the anode, plasmas of d i f f e r e n t i n i t i a l c o n d i t i o n s can be s t u d i e d . The i n i t i a l c o n d i t i o n s of the plasma can a l so be mod i f i ed by va r y ing the c u r r e n t in the j e t . An e l e c t r o n temperature between 11000°K and 16000°K wi th c o r r e s p o n d i n g e l e c t r o n number d e n s i t i e s be-1 ft - 3 1 7 -tween 3 x 10 cm" and 2 x 10" cm" i s o b t a i n e d . Th i s co r responds to a degree of i o n i z a t i o n between 10% and 60% r e s p e c t i v e l y . 9 11 -b The l a s e r . The ruby l a s e r i s a TRG model 104 A and p r o -duces a Q-switched 40 nsec pu lse with a maximun energy output of 1 j o u l e . The output i s r e p r o d u c i b l e to w i t h i n 10% over extended pe r i ods of c o n t i n u a l o p e r a t i o n i f the l a s e r i s f i r e d at r e g u l a r i n t e r v a l s not s h o r t e r than 40 seconds . The p lane of the e l e c t r i c vec to r of the l a s e r beam i s p a r a l l e l to the ax i s of the plasma j e t . The Q-swi tch ing i s performed with a r o t a t i n g pr ism with a speed of 30,000 rpm. ' The l a s e r beam i s focused wi th a l ens of 8 cm f o c a l l e n g t h w h i c h combined wi th the beam d iameter g i ves an f/10 f o r the convergent l a s e r beam. The f o c a l spot i s 0.02 cm in d iameter and a maximun power _ 9 d e n s i t y of 60 GVJ xnv *" i s o b t a i n e d . The d iameter of the f o c a l spot i s determined by the damage produced in a metal f o i l p l a ced at the f o c a l p l a n e . The power d e n s i t y i n c i -dent on the plasma i s v a r i e d by changing the c o n c e n t r a t i o n of copper su lpha te d i s s o l v e d in water in an a b s o r p t i o n c e l l p l a ced between the l a s e r and the p lasma. A r e f l e c t i n g g l a s s p l a t e mounted at the Brewster angle i s p laced between the l a s e r and the plasma and r e f l e c t s a smal l f r a c t i o n of the - l i g h t on to a s o l i d s t a t e d iode to check the p u l s e - t o - p u l s e r e p r o d u c i b i l i t y of the l a s e r o u t p u t . The s o l i d s t a t e d iode i s a Hew le t t -Packa rd , pa r t number 5082-4220, b i ased at 100 v o l t s to o b t a i n a f a s t r i s e t ime . A r i s e t i m e < 1 nsec and a l i n e r o p e r a t i o n up to 2 v o l t s output s i g n a l were o b t a i n e d . The l a s e r l i g h t dump c o n s i s t s of a c e l l with a Brewster 10 angle en t rance window c o n t a i n i n g a concen t r a t ed s o l u t i o n of copper supha te . 11-c The d e t e c t i o n sys tem. The d e t e c t i o n system c o n s i s t s of monochromator, p h o t o m u l t i p i i e r and o s c i l l o s c o p e . The o p t i c a l ax i s of the c o l l e c t i n g lens i s p laced p e r p e n d i c u l a r to both the i n c i d e n t l a s e r beam and the ax i s of the plasma j e t . The l enses focus the monochromator ent rance s l i t i n t o the plasma and thus the s p a t i a l r e s o l u t i o n in the plasma i s determined by the width and the he igh t of t h i s ent rance s l i t . . The c o l l e c t i n g lens ( l ens A in F igu re 1) can be d i s p l a c e d l a t e r a l l y to scan the per tu rbed reg ion- in the p lasma. These d i sp l acements are moni tored by two d i a l mi c r o m e t e r s . -Because of the c o n f i g u r a t i o n of the e l e c t r o n d e n s i t y g r a d i e n t s in the plasma and of the c y l i n d r i c a l geometry of the f o c a l spot of the l a s e r , we want to o b t a i n good v e r t i c a l s p a t i a l r e s o l u t i o n in the plasma r a t h e r than h o r i z o n t a l r e s o l u t i o n . Then by r o t a t i n g the image of the narrow ent rance s l i t by 90°we can maximize the wavelength r e s o l u t i o n of the monochromator and ob t a i n s i m u l t a n e o u s l y good v e r t i c a l s p a t i a l r e s o l u t i o n in the plasma wi thout l o s i n g too much l i g h t . The l eng th of the s l i t i s then chosen to maximize the amount of energy c o l l e c t e d in the monochromator c o n s i s t e n t with h o r i z o n t a l s p a t i a l r e s o l u t i o n in the p lasma. The ape r tu re of the e x t e r n a l o p t i c s matches the ape r tu re of the monochromator ( f / 6 ) . 11 The g r a t i n g monochromator was b u i l t in our l a b o r a t o r y . I t i s used i n s i x t h o rder wi th a d i s p e r s i o n of 3.8 A/mm and a t h e o r e t i c a l r e s o l v i n g power of 180,000. A cons tan t d e v i a t i o n pr ism i s p laced in f r o n t of i t to i s o l a t e the o r d e r s . The p h o t o m u l t i p i i e r i s an RCA 7265 which when b iased with a t o t a l anode-to-cathode vo l t age of 3000 v o l t s gave the nominal r i s e time of 2.6 nsec . The r eg i on of l i n e a l o p e r a t i o n of the p h o t o m u 1 t i p i i e r have been determined wi th a se t of c a l i b r a t e d Kodak neu t r a l d e n s i t y f i l t e r s . The anode load i s 50ft to match the cab le impedance. The o s c i l l o s c o p e ( Tek t ron ix 585) with a p lug i n v e r t i c a l a m p l i f i e r . ( # 8 2 ) g ive a combined r i s e time of 4.4 nsec . S i g n a l s were recorded on P o l a r o i d f i l m type 410 at a sweep speed of 50 nsec per d i v i s i o n and measured l a t e r with the help of a m a g n i f i e r . In o rde r to cut down the average anode c u r r e n t of the p h o t o m u l t i p i i e r due to the d i r e c t l i g h t from the plasma j e t we use a chopping wheel r o t a t i n g at 1725 rpm a l l o w i n g the p h o t o m u 1 t i p i i e r to be exposed f o r on l y 300usec du r ing each r o t a t i o n . Th i s a l lows us to work at a h ighe r i ns tan taneous anode cu r r en t thus i n c r e a s i n g the s i g n a l - t o - n o i s e r a t i o . The chopping wheel c o n s i s t s of a r o t a t i n g d i s k with two c i r c u l a r ape r tu res with d iam-e t e r s of 0.65 cm and 0.3 cm r e s p e c t i v e l y l o c a t e d at 7 cm and 8 cm r e s p e c t i v e l y from the cen t re of the d i s k (the l o c a t i o n of the second ho le is i r r e l e v a n t ) . The 12 reference light pulse photo diode amplifier magnetic head pulse V trigger voltage gate scr c i rcu i t tr igger transform. F I G U R E 3 Syncron i z a t i on of the Q-swi'tch and t h e c h o p p i n g whee l .-13 f i r s t ape r t u r e a l lows l i g t h from the plasma j e t to en te r i n t o the monochromator. The second ape r tu re i s used to produce a r e f e r e n c e pu lse from a photod iode to t r i g g e r the l a s e r at the time tha t the f i r s t ape r tu re i s a l i g n e d with the plasma j e t (see F igu re 1 ) . The r e f e r e n c e s i g n a l swi tchs on the t r i g g e r i n g c i r c u i t of the l a s e r power supp ly which would f i r e the l a s e r when the t im ing s i g n a l from the r o t a t i n g Q-switch a r r i v e s (see diagram of F igu re 3 ) . S ince the p e r i o d of r o t a t i o n of the Q-switch motor i s much s h o r t e r than the time i n t e r v a l du r ing which the l i g h t from the plasma en te r s the monochromator, the s y n c h r o n i z a t i o n works p e r f e c t l y in s p i t e of the random phase of the two r o t a t i o n s . A second d e t e c t i o n system with a wider wave-l eng th band pass i s used to moni tor the plasma and , p a r -t i c u l a r l y in the exper iments on the l i n e shapes , to moni tor the t o t a l l i n e i n t e n s i t y . A h a l f meter J a r r e ! ' A s h mono-chromator o f . f / 1 1 and a band pass of 5 A i s used f o r t h i s pu rpose . 14 Chapter III OBSERVATIONS AND RESULTS In t h i s chapte r the exper imenta l o b s e r v a t i o n s and r e s u l t s are p r e s e n t e d . The f o l l o w i n g s e c t i o n 111 - a dea l s with the s t a t e of the plasma p r i o r to the f i r i n g of the l a s e r p u l s e . A genera l p i c t u r e of the p e r t u r b a t i o n of the plasma when the . l a s e r i s - f i r e d is presented in s e c t i o n 111-b, where the o b s e r v a t i o n s on the expans ion of the pe r tu rbed r e g i o n . a r e a l s o i n c l u d e d . The p o p u l a t i o n of c* o n n n n v 1 ^ w r l ^ ^ -F A v* T T • r\ <n r~ U -> w o L. y-\ o v> n ri - — n •> /* A — w ^ i . i ^ » ^- * I _» \J t ( I t J. A * *J M J I I U V V, U C C II I I I U U J U t WV> o b t a i n some i n f o r m a t i o n about the s t a t e of e q u i l i b r i u m of the t r a n s i e n t plasma and they are presented in s e c t i o n 111 -c . The enhancement of the e l e c t r o n d e n s i t y has been determined us ing two independent methods. Measure-ments based on the abso lu t e i n t e n s i t y of the cont inuum r a d i a t i o n and on the Stark broadening of Ar II l i n e s are presented in s e c t i o n s 111 -d and 111-e r e s p e c t i v e l y . The asymmetric shape observed in the Ar II l i n e s i s a l s o p r e -sented i n . s e c t i o n I l l - e . . . . . . . 15 111 -a S p e c t r o s c o p i c d e t e r m i n a t i o n of the parameters of the  plasma j e t . The degree of i o n i z a t i o n of the plasma j e t be fo re the f i r i n g of the l a s e r (which I w i l l c a l l pre-i o n i z a t i o n ) has been ob ta ined s p e c t r o s c o p i c a l l y us ing the abso lu t e l i n e i n t e n s i t y of Ar I. These measurements have been performed under the assumpt ions tha t the plasma i s in l o c a l thermodynamic e q u i l i b r i u m (LTE) and tha t the plasma i s o p t i c a l l y t h i n . We have not determined to which ex ten t our p l a s m a . i s in LTE , but measurements performed by Freeman (1968) in an a tmospher i c argon j e t s i m i l a r to ours showed tha t the c o n d i t i o n s in the plasma were very near e q u i l i b r i u m . The assumption about the o p t i c a l t h i c k n e s s of the plasma i s a l s o r easonab le in our p lasma. Measurements performed by T o u r i n (1963) showed tha t the argon plasma produced in a plasma j e t at atmos-p h e r i c p r e s su re was t r u l y o p t i c a l l y t h i n i n the continuum r a d i a t i o n at wavelength s h o r t e r than 6500 A, a l though the plasma was o p t i c a l l y t h i c k at l onger wave length . The s e l f a b s o r p t i o n of atomic l i n e emiss ion i s more impor tan t and p lays a s i g n i f i c a n t r o l e in the d e t e r m i n a t i o n of emiss ion c o e f f i c i e n t s . The amount of s e l f a b s o r p t i o n depends on the t r a n s i t i o n and i n genera l i t v a r i e s f o r d i f f e r e n t 16 l i n e s . The work of Olsen (1963) in an argon arc shows tha t a l though some Ar I l i n e s are s t r o n g l y a b s o r b e d , the l i n e Ar I 6965 A i s p r a c t i c a l l y f r e e of s e l f a b s o r p -t i o n at e l e c t r o n d e n s i t i e s s i m i l a r to our p lasma. In o rde r to measure the degree of p r e - i o n i z a t i o n the d e t e c t i o n system i s c a l i b r a t e d f o r abso lu t e i n t e n s i t y measurements with a tungsten r ibbon lamp us ing f o r the e m i s s i v i t y of tungsten the va lues g iven by DeVos (1954) . The abso lu t e i n t e n s i t y of the l i n e Ar II 6965 A was measured ac ross the plasma and by numer ica l Abel un -f o l d i n g , the r a d i a l em iss ion p r o f i l e s were o b t a i n e d . T h i s em i s s i on p r o f i l e s y i e l d s the p o p u l a t i o n of the upper l e v e l s of the t r a n s i t i o n . I f the plasma i s assumed to be in l o c a l thermodynamic e q u i l i b r i u m , the Boltzmann equa t ion w i l l then r e l a t e t h i s p o p u l a t i o n to the t o t a l number d e n s i t y of atoms: " (P) = 9 ( P ) P X D n n CO T P kT (1) where n(p) i s the number d e n s i t y of atoms in the upper • (' l e v e l of the t r a n s i t i o n , g(p). the s t a t i s t i c a l weight of the l e v e l , n Q the t o t a l number d e n s i t y of atoms, 17 and U Q the p a r t i t i o n f u n c t i o n f o r the atom. The Saha equa t ion n i n e 2U i (T) (2ir m kT.) "12 U^TT exp I -AI O 0 kT (2) 2U. (T ) -07TT7 S(T) coup led with the equat ions f o r the t o t a l p ressu re n = kT(n . + n + n ) % i e o' ( 3 ) and wi th the c o n d i t i o n of charge c o n s e r v a t i o n e (n i - n e) = 0 ( 4 ) can then be used to ob ta in the number d e n s i t y of the d i f -f e r e n t components of the p lasma. In these equa t ions n^  and U.j(T) are the number d e n s i t y and the p a r t i t i o n f u n c t i o n of the i o n s , I the i o n i z a t i o n p o t e n t i a l f o r the atoms, and AI i s a smal l c o r r e c t i o n of the i o n i z a t i o n 0 p o t e n t i a l due to e l e c t r i c m i c r o f i e l d s in the p lasma. In equa t ions (2) to (4) the presence of a second s tage of 18 i o n i z a t i o n have been n e g l e c t e d . The reduced Saha f u n c t i o n S(T) has been c a l c u l a t e d and t a b u l a t e d f o r d i f f e r e n t va lues of T and d i f f e r e n t va lues of A I by Drawin and Felenbok o J ( 1965 ) , where va lues of A I q are a l s o g iven f o r d i f f e r e n t va lues of n . e Us ing equa t ions (1) to (4) we have c a l c u l a t e d the number d e n s i t y of e l e c t r o n s and n e u t r a l s , the e l e c t r o n t empe ra tu re , the degree of p r e - i o n i z a t i o n and the p o p u l a -t i o n of some e x c i t e d s t a t e s of the atoms and i o n s . The dependence of n g and n Q on the e l e c t r o n temperature i s shown in F i gu re 4 f o r the argon plasma j e t at a tmospher i c p r e s s u r e . The r a d i a l dependence of these v a r i a b l e s in the j e t are p resen ted in F igu re 5 and the p o p u l a t i o n of some e x c i t e d l e v e l s of Ar I and Ar I I are g iven in F i gu re 6. The p r o f i l e s of F igu re 5 co r respond to the plasma l o c a t e d at 3 mm from the anode of the plasma j e t , with a s e p a r a t i o n between cathode and anode of 9 mm. The r e s u l t s of F i gu re 5 are not very a c cu ra t e and e r r o r s may be as h igh as 25%, but they are- s u f f i c i e n t f o r the p resen t work. The d i f f e r e n t sources tha t c o n t r i b u t e to t h i s e r r o r a r e : t h e d e t e r m i n a t i o n of the temperature of the tungsten r ibbon lamp ( f 5%),. the u n c e r t a i n t y in the e m i s s i v i t y of tungs ten (t 2%)(DeVos, 1954) , s e l f a b s o r p t i o n in the plasma (< 5%) ( O l s e n , 1963) , r e p r o d u c i h i 1 i t y of the plasma j e t 19 ELECTRON ENERGY ( eV ) FIGURE 4 Compos i t ion of the plasma j e t at 1 atm.-20 r~ r — — i r —i i i i__ i i i 0.15 0.10 0.05 0 0.05 0.10 0.15 RADIUS'. ( cm ) j . FIGURE 5 Rad ia l d i s t r i b u t i o n of e l e c t r o n and neu t r a l number d e n s i t i e s in the plasma j e t at 12 mm above the ca thode .-21 RADIUS ( cm ) FIGURE 6 Rad ia l d i s t r i b u t i o n of some e x c i t e d s t a t e s of Ar I and Ar II.-2 2 (+ 3%), and e r r o r s due to the numer ica l u n f o l d i n g procedure (<10% ) ( Bockas ten , 1961). 111-b Genera l f e a t u r e s of the per turbed p lasma. Be fore the l a s e r pu lse i s f i r e d i n t o the p lasma , most of the l i g h t emi t ted by the plasma c o n s i s t s of cont inuum and Ar I l i n e r a d i a t i o n . We can a l s o observe some Ar II l i n e emiss ion but very weak ly . A l though the degree of p r e - i o n i z a t i o n is high (up to 60%) most of the Ar II ions are in the ground s t a t e . The p o p u l a t i o n s of some e x c i t e d Ar II ions are shown in F i g u r e 6. When the l a s e r l i g h t pu lse i s f i r e d i n t o the plasma a t r a n s i e n t r a d i a t i o n with d u r a t i o n of a few mic roseconds i s observed in the continuum and in the l i n e emiss ion from the p lasma. T y p i c a l p h o t o m u 1 t i p i i e r s i g n a l s are shown in F igure 7 compared to a l a s e r pu l se from the p h o t o d i o d e . The de lay between the l a s e r pu lse g iven by the d iode and the t r a n s i e n t plasma r a d i a t i o n i s due to the t r a n s i t time of the p h o t o m u l t i p i i e r . We observe a smal l dec rease in the Ar I emiss ion f o r a few microseconds a f t e r the f i r i n g of the l a s e r , but the r a t i o of t h i s decrease to the i n t e n s i t y of the l i n e i s so smal l due to the Targe emiss ion from the ambient plasma su r round ing the per tu rbed r e g i o n , tha t i t makes 23 a) A . t, ,i • i i i y m J b ) A j • f t V 1 A. c) 4 « + it** M S CO o ^ d E + u — CO Q O + CO P O < U CO f— Q rr O l u ' > CD O d 0 250 5 0 0 TIME ( nsec ) FIGURE 7 O s c i l l o s c o p e t races, of a l a s e r pu lse ( a ) , the continuum r a d i a t i o n at 5000 A ( b ) , and the Ar 1 1 4806 A l i n e (c ) . -0 — i l — tftffu i IA 4 » V i A. r rt i TIME ( psec) FIGURE 8 O s c i l l o s c o p e t r a ces of Ar II 4806 A l i n e at d i f f e r e n t l o c a t i o n s of o b s e r v a t i o n in the p lasma. The foca 1 spot of the l a s e r i s 0.02 cm in diam- . e te r and i s cen te red at 0. 2 4 q u a n t i t a t i v e measurements i m p r e c i s e . We have not at aay t ime observed any of the Ar III 1 ines ' a va i1ab l e to us w i t h i n the f r equency pass band of our o p t i c a l d e t e c t i n g sys tem. If we now scan a long the v e r t i c a l ax i s of the plasma j e t we observe tha t the t r a n s i e n t r a d i a t i o n has a d i f f e r e n t time behav io r at d i f f e r e n t p o s i t i o n s , and the maximum i n t e n s i t y occurs with a de lay that i n c r e a s e s the f u r t h e r we get from- the f o c a l spot of the l a s e r . Th i s can be observed in F igu re 8 where a set of t y p i c a l phcto-m u l t i p l i e r t r a ce s are d i s p l a y e d . Each t r a ce cor respond to a d i f f e r e n t p o s i t i o n in the p lasma, keeping the l a s e r beam focused at a f i x e d pi ace ( p o s i t i o n 0 in F igure 8 ) . Th is sugges ts tha t the p e r t u r b a t i o n produced in the plasma a f f e c t s a much l a r g e r r eg ion than the volume of the f o c a l s p o t . In o the r words , there i s a p e r t u r b a t i o n f r o n t tha t moves away from the f o c a l spot i n c r e a s i n g c o n s i d e r a b l y the volume of the pe r tu rbed r eg ion du r ing the o b s e r v a t i o n t ime . Measur ing the i n c r e a s e in r a d i a t i o n at p rede te rmina te t imes we can get c ross s e c t i o n of t h i s pe r tu rbed r eg ion as a f u n c t i o n of t ime . The graph in F i gu re 9 i l l u s t r a t e s the v a r i a t i o n of the i n t e n s i t y of the continuum r a d i a t i o n a long the ax i s of the plasma at d i f f e r e n t t imes a f t e r the f i r i n g of the l a s e r . The time o r i g i n i s taken at the peak of the l a s e r pu l se f o r a l l our r e s u l t s . 25 • The observed i n t e n s i t i e s ac ross the pe r tu rbed plasma as shown in F i gu re 9 can be conver ted i n to r a d i a l em i s s i on p r o f i l e s by Abel u n f o l d i n g . Th i s u n f o l d i n g i s a ccomp l i shed on l y ac ross the pe r tu rbed reg ion and not a c ross the e n t i r e p lasma. The r e s u l t s ob ta ined f o r the cont inuum and Ar II emiss ions at the cen t r e of the f o c a l spot are shown in F i gu re 10. The procedure of obse r v i ng at d i f f e r e n t p o s i t i o n s ac ross the per turbed r eg i on and l a t e r u n f o l d i n g to o b t a i n the emiss ion at the c en t r e or any o the r p o s i t i o n of the per tu rbed plasma was f o l l owed each time tha t an abso lu t e i n t e n s i t y measurement was pe r fo rmed . The dependence of the maximum t o t a l i n t e n s i t y of the Ar 11 4806 A l i n e upon the degree of p r e - i o n i z a t i o n and on the l a s e r power d e n s i t y are shown in F i gu res 11 and 12 r e s p e c t i v e l y . The dependence of the increment of the continuum emiss ion on the degree of p r e - i o n i z a t i o n i s shown in F i gu re 13 f o r th ree d i f f e r e n t l a s e r energy d e n s i t i e s . One sees tha t the i n f l u e n c e of the l a s e r energy d e n s i t y on the t r a n s i e n t emiss ion of the continuum is s t r o n g l y dependent on the degree of p r e- i on i z a t i on . At low pre-i o n i z a t i o n i t i s a n o n l i n e a r f u n c t i o n of the l a s e r energy d e n s i t y . Only in t h i s case of low p r e - i o n i z a t i o n i s a g r e e -ment ob ta ined with p rev ious r e s u l t s (Nodwell and Van der Kamp, 1968) where i t was found tha t the p e r t u r b a t i o n in the 2.0 2 6 1.5 1.0 JET FLOW IX I \ ' \ / \ / \ / \ ® ® I i " / / @ \ i ; i \ / , X \ I t » v / m i \ i / » v i f \ \ •7 r / * • • \ \ I x V \ V 0 | i : i • i -0.8 -0.4 0 0.4 0.8 POSITION IN THE P L A S M A (mm) FIGURE 9 I n t e n s i t y of continuum emiss ion at 5000 A a long the j e t ax i s at t =-10 nsec (0 ) , t = 10 nsec ( © ) , t = 30 nsec ( V ) , and t = 100 nsec (+).-27 TIME ( nsec ) FIGURE 10 T r a n s i e n t emiss ions from the plasma at the cen t re of the pe r tu rbed r e g i o n . -28 FIGURE 11 I n t e n s i t y in the Ar II 4806 A l i n e emiss ion v s . degree of p r e - i o n i z a t i o n . -29 10 20 30 40 LASER POWER DENSITY CGW cm~2 ) Intens i ty vs . FIGURE 12 in the Ar II 4806 A l a s e r power d e n s i t y . l i n e emiss ion I -»-» E ro i E o CO u i-2.0 1.5 1.0 0.5 0 0 30 9 A o 40 GW c r r r 2 V 20 GW cm-2 © 10 GW c m " 2 V X7 V 4 1 10 20 30 4 0 50 60 DEGREE OF PRE-IO NIZATIO N (%) FIGURE 13 Increment in the continuum emiss ion at 5000 A v s . degree of p r e - i o n i z a t i o n . -31 4.5 v CO I u 3.0 O < < or 2 1-5 Z> Z h-z O o o t = 5 nsec ® t = 50 nsec T 0 4000 5000 WAVELENGTH ( A ) 6 0 0 0 FIGURE 14 V i s i b l e spectrum of the increment in the continuum e m i s s i o n . -32 cont inuum emiss ion from the plasma showed very l i t t l e i n c r e a s e up to a l a s e r power of 20 MW, but tha t i t i n c r e a s e d r a p i d l y beyond t h i s power. At high pre-i o n i z a t i o n s , near the maximum e l e c t r o n d e n s i t y o b t a i n -ab l e in Ar at a tmospher i c p r e s s u r e , the change in the cont inuum emiss ion does not depend a p p r e c i a b l y on the l a s e r power. The t r a n s i e n t continuum emiss ion has been observed over the e n t i r e v i s i b l e spectrum (see F igu re 14 ) . 111-c Expans ion of the pe r tu rbed p lasma. The p e r t u r b a t i o n expands away from the l a s e r focus wi th a v e l o c i t y which is s eve ra l t imes tha t of the speed of sound in the medium. The d i f f e r e n c e between the v e l o c i t i e s of the up-f low ing and down-flowing f r o n t s as observed in the l a b o r a t o r y frame of r e f e r e n c e , g i ves app rox ima te l y twice the v e l o c i t y of the stream f low ( approx imate l y 700 m s e c " 1 ) . Th i s assumes tha t the p ropaga t i on v e l o c i t y of the f r o n t r e l a t i v e to the stream f low i s the same in both d i r e c t i o n s . The d iameter of the pe r tu rbed plasma as a f u n c t i o n of time i s p l o t t e d in F i gu re 15. The v e l o c i t y of the f r o n t v a r i e s wi th time and at t=20 n s e c , near the end of the l a s e r p u l s e , the v e l o c i t y of the r a d i a l l y expanding f r o n t i s 6300 m s e c " 1 . S ince the speed of sound in the p r e - i o n i z e d plasma i s app rox ima te l y 1700 m s e c " 1 , t h i s expanding f r o n t moves with a Mach number of 3 .7 . As the 3 3 20 4 0 6 0 TIME (nsec ) 100 FIGURE 15 Diameter of the pe r tu rbed plasma as a f u n c t i o n of t ime . _ 2 The i n c i d e n t l a s e r power d e n s i t y i s 40 GW cm . The v e r t i c a l bars r ep r e sen t a t y p i c a l s tandard d e v i a t i o n of • of the mean of e i g h t r e a d i n g s . -3 4 p e r t u r b a t i o n expands i n to the ambient plasma i t i s s t r o n g l y a t t enua ted l i m i t i n g the o b s e r v a t i o n s to a maximum d i s t a n c e of 0.08 cm from the f o c a l s p o t . 111-d The p o p u l a t i o n of e x c i t e d s t a t e s of Ar II. . The p o p u l a t i o n d e n s i t y of some e x c i t e d s ta tes-of Ar II ions have been determined from measurements of the a b s o l u t e i n t e n s i t y of the e m i t t i n g l i n e . If the p o p u l a t i o n s of these e x c i t e d s t a t e s are known to have a d i s t r i b u t i o n near a Boltzmann e q u i l i b r i u m d i s -t r i b u t i o n , an es t imate of the e x c i t a t i o n temperature cou ld g i ve an idea of the e l e c t r o n tempera tu re . The t o t a l energy r a d i a t e d per un i t s o l i d angle in a t r a n s i t i o n from l e v e l p to l e v e l q in an o p t i c a l l y t h i n plasma i s (Cooper , 1966) n p ( x , t ) dx " (5) where n i s the upper l e v e l p o p u l a t i o n d e n s i t y and A„ „ P p,q i s the t r a n s i t i o n p r o b a b i l i t y f o r the t r a n s i t i o n . A d e t e r m i n a t i o n of I ( t ) in abso lu t e u n i t s w i l l in p r i n c i p l e y i e l d the t o t a l number d e n s i t y of ions e x c i t e d in s t a t e p, i n t e g r a t e d a long the l i n e of s i g h t . Using equa t ion I'(t) = P- A v ; 4TT p,q ( 5 ) , the p o p u l a t i o n s at the cen t re of the l a s e r focus of the upper l e v e l s of f ou r Ar 11 l i n e s have been obta ined as a f u n c t i o n of time from the observed i n t e n s i t i e s I ( t ) . The Abel u n f o l d i n g has been performed n u m e r i c a l l y us ing the c o e f f i c i e n t s g i ven by Bockasten (1961) . Th i s u n f o l d -ing i s performed under the assumption tha t the expans ion of the pe r tu rbed plasma has a c y l i n d r i c a l symmetry. Th i s i s a r easonab le assumpt ion to make in view of the u n i f o r m -i t y of the e l e c t r o n d e n s i t y p r i o r to the f i r i n g of the l a s e r in the r eg ion of the p e r t u r b a t i o n (see F igu re 5 ) . To measure I ( t ) the e x i t s l i t of the monochromator was opened to admit most (> 95%) of the l i n e i n t e n s i t y to the p h o t o m u l t i p i i e r . The d e t e c t i o n system i s c a l i b r a t e d f o r a b s o l u t e i n t e n s i t y measurements with a tungsten r ibbon lamp us ing f o r the e m i s s i v i t y of tungsten the va lues g iven by DeVos (1954) . The t r a n s i t i o n p r o b a b i l i t i e s Ap have been ob ta ined from Olsen (1963) . The l o g a r i t h m i c p l o t of the p o p u l a t i o n s d i v i d e d by the s t a t i s t i c a l weight of the l e v e l s are shown in F igu re 16, where a s t r a i g h t l i n e would co r respond to a Boltzmann e q u i l i b r i u m d i s t r i b u t i o n among the l e v e l p o p u l a t i o n s . The d i s t r i b u t i o n ob ta ined at t = 100 nsec i s very c l o s e to a Boltzmann d i s t r i b u t i o n with kT = 1.7 e V but the d i s t r i b u t i o n at e a r l i e r t imes i s c l e a r l y not in e q u i l i b r i u m . Any d e t e r m i n a t i o n of the e l e c t r o n temperature us ing l i n e emiss ion du r i ng the time 10 12 i E u Q. cn \ QL 2 1011 10 10 19 < < o t = 30 nsec t = 10 nsec t= 0 nsec ° t =100 nsec - < < < CO 00 O ID 00 CO CO < t = -10 nsec 2 0 E p ( eV ) 21 22 FIGURE 16 P o p u l a t i o n d e n s i t y of f ou r Ar II energy l e v e l s v s . energy of the l eve l s . . The p o p u l a t i o n s are d i v i d e d by the s t a t i s t i c a l weight of the l e v e l . -3 7 tha t the l a s e r pu l se i s p resen t would o b v i o u s l y g i ve e r roneous r e s u I t s . Ill.-e E l e c t r o n d e n s i t y from continuum e m i s s i o n . The cont inuum emiss ion a r i s e s from both f r e e -f r e e and f ree-bound t r a n s i t i o n s and i s a f u n c t i o n of e l e c t r o n number d e n s i t y and e l e c t r o n tempera tu re . S ince in the v i s i b l e r eg ion of. the spectrum the temperature dependence i s r a t h e r weak, an abso lu t e measurement of the cont inuum emiss ion may t h e r e f o r e be used to determine the product of e l e c t r o n and ion d e n s i t i e s i n t e g r a t e d a long the l i n e of s i g h t ; the s p a t i a l dependence of the product rt f \r • f • ^ * r , ^ v "t" ^  ^ \ i 4- l-> o v> /-> rl ^ + A » " v. A Kw c- "1 « i *-> 1 1 -j \ A j l. y I I ^ ^ /\ j U / IllWJf UIICII t-/V- 14 C. U U I III I H C U U J o p u u i u i U I I ~ f o l d i ng . F r e e- f r ee t r a n s i t i o n s , or b r emss t r ah lung , i s the r a d i a t i o n emi t ted from a f r e e e l e c t r o n moving in an e x t e r n a l f i e l d . In the process the e l e c t r o n l o ses pa r t of i t s k i n e t i c energy and slows down. The c ross s e c t i o n f o r t h i s t r a n s i t i o n i s ob ta ined from c l a s s i c a l e l e c t r o d y n a m i c s by s o l v i n g the mechanica l problem of motion of an. e l e c t r o n in a h y p e r b o l i c o r b i t around an i o n . i . • As a r e s u l t of f r e e - f r e e t r a n s i t i o n s the energy emi t ted in the f r equency i n t e r v a l dv per u n i t volume per u n i t time i n t o the element of s o l i d angle dfi i s g i ven by ( F i nke l nbu rg and P e t e r s , 1957) 3 8 f f 16TT: j ' ' dvdft = v 3 /3" m c 3 2TT rn kT e e exp hv kT (6) x n. n dvdft i e where Z i s the e l e c t r i c charge of the i o n , T g the tem-pe ra tu re of the e l e c t r o n s , n^  and n g the number d e n s i t i e s of ions and e l e c t r o n s r e s p e c t i v e l y , and v the f r equency of the emi t ted r a d i a t i o n . In o rde r to app ly t h i s equa t ion to a t r a n s i e n t non-homogeneous p lasma, we have to i n c l u d e the time and s p a t i a l dependence of n^  , n g and T g . Then , an i n t e g r a -t i o n a long the l i n e of s i g h t should be performed to g i ve the t o t a l c o n t r i b u t i o n to the emi t ted r a d i a t i o n . We then o b t a i n j ^ f ( t ) dvdfi = 1 6-rre1 3/3" rn c 3 e 2iTm. exp hv k T e ( x , t ) X k T e ( x , t ) n. j (x,t ) n ( x , t ) dx dv dfl ( 7 ) 3 9 Let. us c o n s i d e r next the c o n t r i b u t i o n to the c o n -t inuum r a d i a t i o n from f ree-bound t r a n s i t i o n s . T h i s i s c a l -c u l a t e d in a s i m i l a r way as the c o n t r i b u t i o n from f r e e - f r e e t r a n s i t i o n s but some comp lex i t y a r i s e s because one must c o n s i d e r now the complex, s t r u c t u r e of the ion or atom. In f r e e - f r e e c o l l i s i o n s one deal with e l e c t r o n t r a n s i t i o n s from one h y p e r b o l i c o r b i t to another one at a lower energy . Any f i n a l s t a t e i s p o s s i b l e p rov ided tha t the energy of the e l e c t r o n in the f i n a l s t a t e i s p o s i t i v e . But in f ree-bound t r a n s i t i o n s , or r e c o m b i n a t i o n , one has to cons i der t rans i.ti oris where the e l e c t r o n i s c ap tu red i n t o we l l de f ineaand f i n i t e number of l e v e l s . The c ross s e c t i o n depends then on the d e n s i t y of l e v e l s encountered w i t h i n a g i ven i n t e r v a l . To ob t a i n the emiss ion c o e f f i c i e n t the c a l c u l a t i o n s f o r a complex atomic sys tem, l i k e A r , are performed in two s t a g e s . The emiss ion c o e f f i c i e n t i s f i r s t ob ta ined f o r an hydrogen sys tem, and then the equa t ion i s m o d i f i e d to take i n t o account a more complex s t r u c t u r e . For t h i s purpose S c h l u t e r (1965) i n t r oduces two f a c t o r s , j^— and £, i n t o t h e ' e x p r e s i o n f o r the emiss ion c o e f f i c i e n t f o r hydrogen . The f a c t o r y/U . takes i n t o account the d i f f e r e n c e in atomic s t r u c t u r e between .the., compl ex atom and hydrogen . The second c o r r e c t i n g f a c t o r £ ( v , T ) , f i r s t i n t r oduced by Biberman and Norman (1960) , depends on' the e l ement , the f r equency v , and in genera l , on the temperature T . • The 40 r a d i a t i o n emi t ted by f ree-bound t r a n s i t i o n s in a complex atomic s t r u c t u r e such as Ar i s then g iven by j T D dvdft = v 3/3" m c 3 2ir rn k T e e 1 - exp hv kT X y J T ) ? ( v ,T ) n. n e dv d^ (8) where IK (T) i s the p a r t i t i o n f u n c t i o n f o r the ions and the f a c t o r [1 - exp(-hv/kT) ] accounts f o r the e f f e c t i v e decrease in a b s o r p t i o n caused by induced e m i s s i o n . Values of £ and y f o r Ar are g iven by Schiu.fjzr (1 968) . In the s p e c t r a l r eg i on of i n t e r e s t , the temperature dependence of £ ( v , T ) i s very smal l and £ can be assumed to be c o n s t a n t . Taken i n t o account the time and s p a t i a l dependence of the v a r i a b l e s n^  , n g and T g i n t o equa t ion (8) we g e t : j ^ b ( t ) dv d'R = 16 e' 3/3" m c 3 e k T e ( x , t ) 2irm. 1 -exp hv [ k T (x , t ) J ( 9 ) U (T (x , t ) 7 5 ( v , T e ( x , t ) ) n.. (x,t) n e (x,t ) dx dv do, 41 The t o t a l cont inuum em i s s i on i s . t h e n g iven by the sum of equa t i ons (7) and ( 9 ) : j v ( t ) - j j f ( t ) + j j b ( t ) 16 e" 3/3m c 3 2Trm, [k T p ( x , t ) . Y U(T) 1 -exp hv' kT f 1 U(T)) Y? J X n. . (x,t ) n ( x , t ) dx dv dfi (10) which g i v e s a r e l a t i o n between n { » ' n e » ^ "'and the t o t a l a b s o l u t e i n t e n s i t y : j . S ince the number d e n s i t y of Ar III i s very smal l in our plasma we can r e p l a c e the produc t n i * n e n e ^ " f u r t h e r m o r e , s i n c e equa t i on (10) i s on l y weakly dependent on the e l e c t r o n t e m p e r a t u r e , we can s t i l l use i t to de te rmine the e l e c t r o n d e n s i t y in s p i t e o f the f a c t t ha t we have not measured T „ . Because of t h i s weak e dependence on T g the u n c e r t a i n t y in the e v a l u a t i o n of n g i s r a t h e r s m a l l , even i f 1Q i s e s t ima ted on l y ve ry r ough l y As a lower l i m i t f o r T we take i t s va lue p r i o r to the f i r i n g o f the l a s e r . As an upper l i m i t we, take the va lue 42 tha t T g would have been reached i f a l l the energy absorbed by the plasma had gone i n t o trans1 at iona1 energy of the e l e c t r o n s . The u n c e r t a i n t y in n g so i n t r o d u c e d i s comparabl to the exper imenta l e r r o r (10%). The observed i n t e n s i t i e s j ^ ( t ) are Abel un fo lded n u m e r i c a l l y to o b t a i n the emiss ion as a f u n c t i o n of p o s i t i o n i n s i d e the p lasma. Measurements in abso lu t e va lue of the continuum emiss ion have been performed, in seve ra l d i f f e r e n t r eg ions of the spec t rum. The e l e c t r o n d e n s i t y ob ta ined from measure ment at the wavelength of 5000 A are p l o t t e d in F igure 17 as a f u n c t i o n of t ime . These va lues cor respond to the cen t re of the l a s e r f o c u s . The upper t r a ce cor respond to an e l e c t r o n temperature of 21 ,000 °.K(kT = 1.8eV) and the lower- t r a ce to 12,000 ° K ( k T = 1.1 eV ) . The s p a t i a l d i s t r i b u t i o n of the e l e c t r o n number d e n s i t y ac ross the pe r tu rbed reg ion is shown in F i gu re 18 at two d i f f e r e n t t imes dur ing the decay of the p lasma. An i n t e r e s t i n g f e a t u r e of the t r a n s i e n t continuum emiss ion i s i t s sharp peak near the maximum of the l a s e r pu lse (see F i gu re 7 ) . Th i s f e a t u r e i s observed at a l l f r e q u e n c i e s . . The reason f o r t h i s sharp sp i ke with r i s e t ime even f a s t e r than the r i s e of the l a s e r pu lse i s the n o n l i n e a r dependence of the continuum emiss ion on the e l e c t r o n d e n s i t y . Th i s sharp peak emiss ion near the max i -mum of the, l a s e r pu lse made i t i m p o s s i b l e to use l a s e r 43 ol i _ i : _ i : J I - 5 0 0 5 0 100 150 200 TIME ( nsec ) FIGURE 17 ' E l e c t r o n number d e n s i t y at the cen t re of the pe r tu rbed plasma as a f u n c t i o n of t ime , ob ta ined from continuum abso lu t e i n t e n s i t i e s ( s o l i d l i n e ) and from Ar II l i n e widths (0 ) .-44 10 L U 0 — j — t = 10 nsec t = 30 nsec -0.6 -0.3 POSITION IN 0 0.3 0.6 THE PLASMA (mm) FIGURE 18 E l e c t r o n number d e n s i t y ac ross the pe r tu rbed r eg ion determined from continuum i n t e n s i t y measurements at the wavelength of 5000 A .-45 s c a t t e r i n g as a d i a g n o s t i c t echn ique f o r measurements of t r a n s i e n t e l e c t r o n d e n s i t y dur ing the time tha t the l a s e r pu l se was p r e s e n t . I I I - f L i n e shape of Ar II l i n e s . The e m i t t i n g atoms, and ions in the plasma are pe r tu rbed by c o l l i s i o n s with other p a r t i c l e s . In the plasma j e t at a tmospher i c p r e s s u r e , the s t r o n g e s t i n t e r -a c t i o n i s due to e l e c t r i c f i e l d s produced by the e l e c -t rons and i o n s , which cause S tark broadening of the emi t ted s p e c t r a l l i n e . I f i n t e r a c t i o n wi th e l e c t r o n s i s the dominant S tark broaden ing mechanism, the emi t ted l i n e shape would have a L o r e n t z i a n shape with h a l f - h a l f width g i ven by (Cooper , 1966) w =.n (T e ) n e where the S tark Broadening parameter Q, i s g e n e r a l l y a s l ow l y v a r y i ng f u n c t i o n of the e l e c t r o n temperature T . By measur ing the l i n e width of these l i n e s one can o b t a i n the e l e c t r o n number d e n s i t y where the e m i t t i n g atoms are submerged. The l i n e shape of s e ve r a l Ar II l i n e s have been measured at s e ve r a l t imes du r ing and a f t e r the l a s e r p u l s e . To o b t a i n good s t a t i s t i c s no l e s s than 46 f i v e measurements have been taken at each of the 15 wave-lengths taken ac ross each l i n e . A t y p i c a l r e s u l t i s shown in F igu re 21 where the exper imenta l l i n e shape of Ar II 4880 A i s p l o t t e d f o r t = 10 nsec . To ob t a i n the a c tua l l i n e shape from the observed v a l u e s , these are deconvo lu ted with the i n s t rumen ta l p r o f i l e , which has been determined e x p e r i m e n t a l l y and has a width of 0.36 A. In F igu re 19 we have c a l c u l a t e d the expected l i n e width f o r an observed l i n e w i d t h , us ing the a c tua l l i n e shape of the ins t rument and assuming a L o r e n t z i a n shape f o r the s p e c t r a l l i n e . The i n s t rumen ta l l i n e shape i s not t r i a n g u l a r i n shape because of o p t i c a l a b e r r a t i o n s in the monochromator. The c o r r e c -t i o n f o r the i n s t rumen ta l width i s not very s i g n i f i c a n t because of the width of the observed l i n e s and a f f e c t s the r e s u l t s on ly when the l i n e s narrow du r i ng the decay of the p lasma. Every l i n e observed showed a s t rong asymmetry du r i ng the time tha t the l a s e r pu lse was p resen t (see F i gu re 21 ) . Immediately a f t e r w a r d s , the asymmetry d i s -appears q u i c k l y and the width of the l i n e reduces as the plasma decays . S ince a bas i c assumpt ion made in the d e t e r -m ina t i on of the e l e c t r o n d e n s i t y from the measurements of the l i n e width i s that the l i n e s are symmet r i c , we need to t e s t the l i n e f o r symmetry. As a measure of the asym-metry of the l i n e we c a l c u l a t e the skewness of the 47 0 0.3 0.6 0.9 1.2 1.5 ACTUAL LINE WIDTH ( A ) FIGURE 19 E f f e c t of the i n s t rumenta l broadening on the observed width of a L o r e n t z i a n l i n e . -48 d i s t r i b u t i o n of exper imenta l po in t s ac ross the l i n e us ing the t h i r d moment of the d i s t r i b u t i o n . A p l o t of t h i s skewness as a f u n c t i o n of time o f . t h e l i n e Ar II 4880 A i s shown in F i gu re 20. A f t e r the asymmetry has d i sappea red the va lue of n g i s ob ta ined as a f u n c t i o n of time from the width of the l i n e . F i gu re 20 shows tha t at l a t e r t imes the l i n e i s symmetr ic and t h e r e f o r e the e l e c t r o n d e n s i t y can be determined from the width of the l i n e us ing the S tark c o e f f i c i e n t determined by Roberts (1968) . The e l e c t r o n d e n s i t i e s so ob ta ined from the l i n e s Ar II 4806 A and Ar II 4880 A are p l o t t e d in F igu re 17. The l a r g e r e r r o r bars are due to c o n t r i b u t i o n s from the u n c e r t a i n t y in the width of the l i n e s and from the u n c e r t a i n t y in the S tark c o e f f i c i e n t s . The s tandard d e v i a t i o n s in these c o e f f i c i e n t s are 18% and 14% r e s p e c t i v e l y ( Robe r t s , 1968) and they r e p r e s e n t 50% of the s i z e of the e r r o r b a r s . i n F i gu re 17. The d e t e r m i n a t i o n of n g from continuum emiss ion i s a l s o p resented in F igu re 17 and a good agreement between the two methods i s o b t a i n e d . The asymmetry, observed in the l i n e s du r ing the t ime of the l a s e r pu lse has been a t t r i b u t e d to e l e c t r o n d e n s i t y g r a d i e n t s i n s i d e the pe r tu rbed r eg i on which are p resen t on ly du r i ng the time of the l a s e r p u l s e . Th i s asymmetry was in agreement with the s i gn of the known Stark s h i f t of the l i n e . By assuming the l i n e shape f o r FIGURE 20 T h i r d moment of Ar II 4880 A l i n e shape as a f u n c t i o n of t ime .-50 the Ar II l i n e emi t ted at any g iven po in t to be L o r e n t z i a n wi th a p p r o p r i a t e S tark c o e f f i c i e n t s of width and s h i f t f o r each e l e c t r o n d e n s i t y i n s i d e the pe r tu rbed r e g i o n , we have generated the expected l i n e shape by summing the c o n t r i b u t i o n s from d i f f e r e n t r eg ions of the plasma a long the l i n e of s i g h t . The s p a t i a l d i s t r i b u t i o n of the e l e c t r o n d e n s i t y du r i ng the time of the l a s e r can be ob ta ined from the cont inuum emiss i on measurements, as shown in F igu re 18. The s p a t i a l d i s t r i b u t i o n of the p o p u l a t i o n of the upper l e v e l of the t r a n s i t i o n has a l s o been taken i n t o account i n the c a l c u l a t i o n s . The so generated l i n e shapes are no rma l i zed and compared to the exper imenta l l i n e shapes . In F i g u r e s . 2 1 and 22 the c a l c u l a t e d l i n e shapes f o r Ar II 4880 A are compared to the exper imenta l po in t s at two subsequent t imes du r i ng the decay of the p lasma, immediate ! a f t e r the.maximun of the l a s e r p u l s e . E r r o r bars denote s tandard d e v i a t i o n s of the mean v a l u e . A good agreement i s found f o r l i n e s with e i t h e r blue or red s h i f t . In F i gu re 23 the l i n e shape f o r the same Ar II 4880 A i s p l o t t e d at 100 nsec l a t e r , du r ing the decay of the p lasma. The l i n e i s narrower and symmetr ic . 51 4873.0 4876 .5 4880 .0 WAVELENGTH ( A ) 4883 .5 FIGURE 21 Shape of Ar II 4880 A l i n e a t t = 10 nsec . The p r e d i c t e d shape ( s o l i d 1 i n e ) - i s computed based on the 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 ob ta ined from continuum e m i s s i o n . / 52 1 I 1 4873.0 4876 .5 4 8 8 0 . 0 4 8 8 3 . 5 WAVELENGTH ( A ) FIGURE 22 Shape of- Ar 1 1.4880 A l i n e at t•= 30 n s e c -53 4873.0 4876.5 48800 WAVELENGTH ( A ) 4883.5 FIGURE 23 Shape of Ar II 4880 A l i n e at t= 100 nsec 54 Chapter IV ENERGY ABSORPTION FROM A LASER BEAM IV-a I n t r o d u c t i o n In t h i s chapte r I would l i k e to d i s c u s s the a b s o r p t i o n of energy from the l a s e r p u l s e , when the beam i s f ocused i n t o a p lasma. Because the f r a c t i o n of energy absorbed i s r e l a t i v e l y smal l (see s e c t i o n 11-c) we have not been ab le to get a r e l i a b l e measure of the d i f f e r e n c e between the i n c i d e n t and t r a n s m i t t e d l a s e r beam in o rde r to determine the energy abso rbed . A l though we do not have an exper imenta l d e t e r m i n a t i o n of the amount of absorbed energy to compare w i t h , an es t imate of t h i s energy and a d i s c u s s i o n of the process of a b s o r p t i o n is of i n t e r e s t at t h i s po in t of the t h e s i s . When a l a s e r l i g h t beam i s f i r e d i n t o a plasma a f r a c t i o n of i t s energy i s l o s t from the beam. The plasma may s c a t t e r , r e f r a c t , and absorb d i f f e r e n t f r a c -t i o n s o f the l i g h t beam. O f t h e s e three p r o c e s s e s , the l a s t one i s the one which w i l l pe r tu rb the s t a t e of the ! p lasma. A b s o r p t i o n i s ach ieved in f r e e - f r e e t r a n s i t i o n s ( i n v e r s e b remss t rah lung )and in bound-free t r a n s i t i o n s ( p h o t o i o n i z a t i o n ) . A b s o r p t i o n due to resonance or l i n e 55 a b s o r p t i o n in bound-bound t r a n s i t i o n s does not take p l ace in a plasma when a l a s e r l i g h t beam from a ruby i s used . In the two f o l l o w i n g s e c t i o n s of t h i s chapte r the p rocesses of i n v e r s e b remss t rah lung and p h o t o i o n i z a -t i o n are d i s c u s s e d . In s e c t i o n IV-d the t o t a l energy absorbed i s c a l c u l a t e d and in s e c t i o n IV-e n o n l i n e a r e f f e c t s due to the presence of the high e l e c t r i c f i e l d of the l a s e r beam is d i s c u s s e d . The photon number den -s i t y i s the on ly p rope r t y o f . t h e beam that we are c o n -cerned w i t h , a l though the f o l l o w i n g d i s c u s s i o n would app ly to any l i g h t beam. The coherent p rope r t y of a l a s e r beam is c o n s i d e r e d on ly in s e c t i o n IV-e where n o n l i n e a r e f f e c t s are d i s c u s s e d . IV-b Inverse b remss t rah lung a b s o r p t i o n c o e f f i c i e n t . Th i s atomic process r e f e r s to the a b s o r p t i o n of a photon in a three-body c o l l i s i o n with an e l e c t r o n and an i o n . The presence of the ion i s r e q u i r e d to f u l f i l the c o n s e r v a t i o n laws of energy and momentum. Using the c ross s e c t i o n f o r t h i s c o l l i s i o n a ^ f ( S p i t z e r , 1 1962) we may c a l c u l a t e the a b s o r p t i o n c o e f f i c i e n t : K f f ( t ) = a f f n ( t ) n , ( t ) (1) v v e i 56 where f f a 3 e k T ( t ) h c m 3 / 2 v 3 e 9 f f v and where g .^ i s the Gaunt f a c t o r . The time dependence of the e l e c t r o n and ion number d e n s i t i e s , as we l l as e l e c t r o n temperature have been taken i n t o account . The number d e n s i t i e s of the e l e c t r o n s and ions w i l l vary du r i ng the time that the l a s e r i s p resen t because pa r t of the energy absorbed from trie l i g h t beam is used to produce f u r t h e r i o n i z a t i o n of the p lasma. Using equa-t i o n (1) we can c a l c u l a t e the energy absorbed per u n i t l eng th from the 1aser 1 igh t p u l s e : t f A E ) > f f f f A Z v J K V ( t ) L ( t ) dt o n e ( t ) n . ( t ) L ( t ) dt 5 7 = - 3.6-9 x 10 8 n e ( t ) n . ( t ) L ( t ) dt (10) v 3 [T e ( t ) 3 o where is the d u r a t i o n of the l a s e r pu lse with time dependent i n t e n s i t y L ( t ) , and A Z i s the l ength of plasma under the e f f e c t of the l a s e r l i g h t beam. If the plasma i s not homogeneous, the s p a t i a l dependence of n g and n.. shou ld a l s o be taken i n t o a c coun t . But s i n c e L ( t ) i s a l s o space dependent because of the f o c u s i n g lens and i s very l a r g e on ly in a r eg i on near the focus of the lens ( i n a r eg ion of the o rder of 1 mm), the inhomo-g e n i t y of the plasma can be n e g l e c t e d . IV-c Photo i o n i z a t i o n a b s o r p t i o n c o e f f i c i e n t . a photon a b s o r p t i o n , the e l e c t r o n a cqu i r e s an energy l a r g e r than i t s b i n d i n g energy and the e l e c t r o n escape f r e e . Th i s process i s c a l l e d p h o t o i o n i z a t i o n . S ince the energy of a photon of a ruby l a s e r i s on l y 1,78 eV and the i o n i z a t i o n p o t e n t i a l s are much l a r g e r ( e . g . 15.68 eV f o r Ar I and 27.62 eV f o r Ar II) on ly atoms or ions in an e x c i t e d s t a t e whose energy l a ys w i t h i n 1.78 eV from the i o n i z a t i o n p o t e n t i a l would become photo-i o n i z e d . Dur ing a bound-free t r a n s i t i o n as a r e s u l t of 58 Atoms at lower e x c i t a t e d s t a t e s can a l s o be p h o t o i o n i z e d wi th the s imu l taneous a b s o r p t i o n of two or more pho tons . However, the p r o b a b i l i t y P(n) of an atom abso rb ing s i m u l t a n e o u s l y n photons when in the f i e l d c o r r e s p o n d i n g to a photon f l u x d e n s i t y F i s P(n) ~ F n . The dependence on the photon f l u x i s very s h a r p , and f o r atoms in the ground s t a t e t h i s p r o b a b i 1 i t y i s very s m a l l . For Ar atoms in the ground s t a t e n=9, and the p r o b a b i l i t y f o r the a b s o r p t i o n of 9 photons from the ruby l a s e r i s (Gold and Bebb, 1965, Mor ton , 1967) : P(9) = 1.1 x T O " 3 3 F 9 -2 where F i s in GW cm . Only at ext remely l a rge photon f l u x e s would t h i s process have to be taken i n t o account and we can n e g l e c t i t in the p resen t d i s c u s s i o n . Let us then c o n s i d e r the process of p h o t o i o n i z a t i o n by a s i n g l e photon . In a complex atom in a s t r o n g l y e x c i t e d s t a t e , the " o p t i c a l " e l e c t r o n (or va l ence e l e c -t ron ) moves in a l a rge o r b i t in the f i e l d produced by the nuc leus and by the remain ing e l e c t r o n s . I f the d imens ions of the system of charges forming the atomic 59 remainder are not very l a rge in comparison with the o r b i t of the o p t i c a l e l e c t r o n , then the whole system can be r ep re sen t ed as a po in t charge produc ing a Coulomb f i e l d . Then the problem i s s i m p l i f i e d by us ing r e s u l t s ob ta ined f o r hydrogen-1ike atoms and ex tend ing these r e s u l t s to more complex atoms. The a b s o r p t i o n c o r r e c t i o n f o r an hydrogen -l i k e atom i s ob ta ined from the r eve r se p r o c e s s , r a d i a -t i v e c a p t u r e , by the p r i n c i p l e of d e t a i l e d b a l a n c e . Once t ha t the c ross s e c t i o n a (p) of a b s o r p t i o n of a photon of f r equency v by an hydrogen-1ike atom in l e v e l p i s known, the a b s o r p t i o n c o e f f i c i e n t can be c a l c u l a t e d (see e . g . Z e l ' d o v i c h and R a i z e r , 1966) a f t e r i n t e g r a t i o n (or summation) over a l l the p o s s i b l e l e v e l s : bf 16 TT2 e 6 Z 2 k T n 3 /3~ h 4 c v 3 ' r hv' exp kT v. J exp kT -1 (3) where I i s the i o n i z a t i o n p o t e n t i a l , and n Q the t o t a l number d e n s i t y of the atoms. In o rder to o b t a i n equa-t i o n (3 ) , the Boltzmann d i s t r i b u t i o n among the p o p u l a t i o n of the atomic l e v e l s has been assumed to r e l a t e the p o p u l a t i o n s n(p) of the d i f f e r e n t l e v e l s to the number 60 d e n s i t y of atoms n . If the system is not in thermal equ i l i b r i um the Boltzman equat ion can be r ep l a ced by an i n -e q u a l i t y ( W i l s o n , 1962) under the assumptions tha t the plasma i s o p t i c a l l y t h i n and tha t the f r e e e l e c t r o n s have a Maxwel l i an energy d i s t r i b u t i o n . The Boltzmann equat ion i s then r e p l a c e d by the i n e q u a l i t y : n(p) 9 p n " U (T) e x p o o v ' E k T e W i i c r i c I I l o ( . t i e u u o u i I I . U I I I U ^ I u . c i i o i . u y o n e ut I M o . . • ~> o e the e l e c t r o n t empera tu re , and U Q ( T ) the p a r t i t i o n f u n c t i o n f o r the atom. I f the system i s not in thermal e q u i l i b r i u m , on l y an upper va lue of the energy absorbed would be ob -t a i n e d . Fu r the rmore , to take i n t o account the more complex s t r u c t u r e of non-hydrogenic atoms, the a b s o r t i o n c o e f f i c i e n t i s m u l t i p l i e d by the f a c t o r s Y / U . ( T ) and £ ( v , T ) which have been i n t r o d u c e d p r e v i o u s l y in s e c t i o n 111 -d in connec t i on with the continuum emiss ion from f ree-bound t r a n s i t i o n s . U . j ( T ) i s the equ i p a r t i t i on f unc t i on f o r the i o n s . We then o b t a i n f o r the emiss ion c o e f f i c i e n t the i n e q u a l i t y 61 16-rr2 e 6 k T ( t ) n ( t ) K b f ( t ) < £ 5 3 / 1 h 4 c v : exp k T e ( t ) exp hv -1 k T e ( t ) (4) Y where the time dependence of n Q and T g i s taken i n t o account 2 The f a c t o r Z have been se t equal to 1 s i n ce on ly c o n t r i b u -t i o n from the atoms have to be taken i n t o account.. The ions g i ve a c o n t r i b u t i o n two orders of magnitude s m a l l e r because of the l a r g e r i o n i z a t i o n p o t e n t i a l . The maximum energy absorbed by p h o t o i o n i z a t i o n per u n i t l eng th in the plasma is then g i ven by : AE AZ b f K b f ( t ) L ( t ) d t 16TT 2 e 6 k 3 V3 h 4 c v 3 U(T ( t ) ) £ ( v , T ( t ) ) exp kT ( t ) exp hv kT( t ) X T ( t ) n o ( t ) L ( t ) dt (5) 62 In t h i s e q u a t i o n , the t o t a l number of atoms as a f u n c t i o n of time n ( t )-can be obta ined from the time dependent e l e c t r o n d e n s i t y n e ( t ) which have measured du r i ng the t ime that the l a s e r beam is p r e s e n t . If we n e g l e c t the d i f f u s i o n of atoms and ions from or i n t o the f o c a l r eg ion of the l a s e r beam du r i ng a time of the o rde r of the l a s e r p u l s e , we have n ( t ) + n . ( t ) = N T = cons tan t o i l or n 0 ( t ) = N T - n e ( t ) s i n c e " e V ^ ; ~ " j l M • -d Energy absorbed by the p lasma. We can now compare the c o n t r i b u t i o n s to the amount of energy absorbed by the p rocesses of i n v e r s e b remss t rah lung and p h o t o i o n i z a t i o n . Induced emiss ion reduces the e f f e c t i v e a b s o r p t i o n c o e f f i c i e n t ; to take t h i s i n t o a c coun t , the equa t ions (2) and (5) must be m u l t i p l i e d by 1 - exp(-hv>/kT) . The i n t e g r a t i o n of equa t ions (2) and (5) have been performed n u m e r i c a l l y us ing the time depend-ent e l e c t r o n d e n s i t y ob ta ined from the continuum e m i s s i o n . The e l e c t r o n temperature i s c o n s i d e r e d a cons tan t du r ing the l a s e r p u l s e . Because of the weak dependence on t h i s 63 paramet r, the assumpt ion does not a f f e c t a p p r e c i a b l y the r e s u l t s f o r the purpose of our d i s c u s s i o n . The va lue of ^ have been ob ta ined from S c h l u t e r (1968) and i s ^= 2.8 f o r a rgon . Y /U^ i s approx imate l y one. For a 0.9 j ou l es l a s e r pu lse and a l eng th of the f o c a l volume of 0.06 cm we ob ta in from equat ions (2) and (5) r e s p e c t i v e l y : A E f f = 0.24 1 0 " 3 j ou l e s (6) and A E f b = 0.17 1 0 " 5 j ou l es (7) «N ^ ~ , „ „ +. n o o < " r> o n r>./>/!<" „ r J . u _ i . _ ^ _ . . - ! . -K n u t , i C J C H I, u , u u » a n u > j . u u u t - T / o u I L u c l a i d | j u I b e e i i c I C) j( , Of the two mechanisms, p h o t o i o n i z a t i o n g i ves a n e g l i g i b l e c o n t r i b u t i o n to the t o t a l energy abso rbed . The power absorbed by the two mechanisms i s shown in F igu re 24 f o r a l a s e r pu lse of 0.9 j o u l e s . The time dependence of the t o t a l energy absorbed by the plasma i n s i d e the f o c a l volume i s p l o t t e d i n F i gu re 25. Note that most of the energy is absorbed du r i ng the second h a l f of the l a s e r pu lse s i n c e most of the a b s o r p t i o n i s done by the new e l e c t r o n s . The smal l c o n t r i b u t i o n due to p h o t o i o n i z a t i o n i s absorbed du r i ng the f i r s t h a l f of the l a s e r pu lse when the number d e n s i t y of Ar I atoms i s s t i l l h i g h . 64 0.24 j — ~r X 1 0 5 -60 -30 0 30 60 TIME ( nsec ) FIGURE 24 ' Power absorbed by the plasma by photo i o n i z a t i o n and by i n v e r s e b remss t rah lung from a 0.9 j o u l e s l a s e r pu l se . -65 0.30 X 10~ 3 0.24 0.18 0.12h R 0.06 0 -60 30 0 TIME ( nsec ) FIGURE 25 Energy absorbed by the ,p lasma from a 0.9 j o u l e s 1aser p u l s e . -66 Resu l t s (6) and (7) have been ob ta ined t ak i ng i n t o account the t r a n s i e n t e l e c t r o n d e n s i t y which has i n -c reased from i t s i n i t i a l va lue du r ing the time tha t the l a s e r pu l se was p r e s e n t . I f we c a l c u l a t e the energy absorbed from the l a s e r beam c o n s i d e r i n g on ly the e l e c t r o n d e n s i t y of p r e - i o n i z a t i o n and not t ak ing i n t o account the enhancement in the e l e c t r o n d e n s i t y dur ing the l a s e r p u l s e , we o b t a i n A E f f • = 0.97 x 1 0 " 6 j o u l e s , & E f b = 0.61 x 1 0 " 5 j o u l e s . I f we compare these r e s u l t s with the va lues ob ta ined be-f o r e , (6) and (7 ) , we f i n d tha t a l a rge f r a c t i o n of the energy absorbed i s accompl i shed by the new e l e c t r o n s . An es t ima te of the p e r t u r b a t i o n of the plasma based on ly on the e l e c t r o n d e n s i t y of p r e - i o n i z a t i o n would g ive o b v i o u s l y er roneous r e s u l t s . Let us c o n s i d e r now the i n c r e a s e in e l e c t r o n temperature in the h y p o t h e t i c a l s i t u a t i o n where the energy absorbed by the plasma remains on ly among the e l e c t r o n s . S ince the r e l a x a t i o n time f o r the e l e c t r o n s i s s h o r t e r than the d u r a t i o n of the l a s e r p u l s e , the energy absorbed from the l a s e r beam i s conver ted q u i c k l y i n t o random motion of the e l e c t r o n s which can then be c h a r a c t e r -i z e d by a temperature T If the energy absorbed by the 67 e l e c t r o n s i s not transferee! to the atoms and ions du r ing the time of the l a s e r p u l s e , the i n c r ease in e l e c t r o n temperature would then be g i ven by A ( k T ) = i A F . f f  m K V 3 n e A = 1.44 x 1 0 2 5  1 9 f f n i "A V 3 ( k T j ^ X ( l-exp(-hV>/kT e ) ) \ L ( t ) dt (8) where k T g i s in eV, L ( t ) i s in watts , and A i s the c ross s e c t i o n of the f o c a l spot of the l a s e r in the .p lasma in cm The es t imate of the e l e c t r o n temperature used in Chapter III s e c t i o n 111 -e, to o b t a i n the e l e c t r o n d e n s i t y from the measurements of the continuum emiss ion ,was c a l c u l a t e d us ing equa t ion (8 ) . Equa t ion (8) have been ob ta ined be fore by Kunze (1965) to es t ima te the upper l i m i t of the p e r t u r b a t i o n of a plasma in l a s e r s c a t t e r i n g expe r imen t s . In o rde r to assure tha t the absorbed energy i s s t i l l c on t a i ned on ly i n the e l e c t r o n s , Kunze makes the assumption tha t the equ i-p a r t i t i o n time between e l e c t r o n s and ions t . g (as g i ven by S p i t z e r ,1962) i s l a r g e r than the d u r a t i o n of the l a s e r pu l se t L < A l though the i n e q u a 1 i t y t L < t . i s v a l i d in the plasma j e t , the assumpt ion that the absorbed energy i s con-68 t a i ned on ly in the e l e c t r o n s because of t L < t . , i s not n e c e s a r i l y t r u e . Dur ing the time tha t the l a s e r pu lse i s p r e s e n t , i n e l a s t i c c o l l i s s i o n s can p lay an impor tant r o l e to reduce the temperature of the e l e c t r o n s and to i n c r e a s e the e l e c t r o n d e n s i t y , thus mod i f i ng the amount of energy absorbed from the l a s e r p u l s e . IV-e Non l i nea r e f f e c t s due to the l a s e r beam. In h igh i n t e n s i t y r a d i a t i o n f i e l d s the. i n ve r se b remss t rah lung a b s o r p t i o n c o e f f i c i e n t i s no l onger a cons tan t but i s . i n s t e a d a f u n c t i o n of. the r a d i a t i o n f i e l d . The n o n l i n e a r c r o s s - s e c t i o n have been c a l c u l a t e d by Rand (1964) and the r a t e of energy absorbed from the r a d i a t i o n f i e l d by a plasma have been s t u d i e d by A l b i n i and Rand (1965) . They show tha t n o n l i n e a r d e v i a t i o n s beg in to be impor tan t when the maximum k i n e t i c energy which a f r e e e l e c t r o n can ob t a i n in the r a d i a t i o n f i e l d equa ls or exceeds the energy of the photons . Then , i ndependen t l y of the i n i t i a l e l e c t r o n v e l o c i t y , the e l e c t r o n acqu i r e s s u f f i c i e n t energy such that i t may emit pho tons , mod i f y ing the r a d i a t i o n f i e l d . In the presence of an a l t e r n a t i n g e l e c t r i c f i e l d of peak va lue E and f r e q u e n c y . v , an e l e c t r o n o s c i l l a t e s with peak v e l o c i t y 69 e E rn 2TTV e N o n l i n e a r e f f e c t s would become impor tant when e 2 E 2 \ m e < = r r - f — - h v • ( 8 ) 8TT vz m e In the r a d i a t i o n f i e l d E = /? E o 4TT W c irr • = 26.6 irr' V o l t , cm" where W i s the l a s e r power in watts and r i s the r ad ius in cm of the f o c a l volumn. Then , c o n d i t i o n (8) can be wri t t en as : W 8TT: hv 3 m hv 3 m = 0.112 -i r r 2 (26.6) 4 - 2 At l a s e r energy d e n s i t i e s < 10 GW cm n o n l i n e a r e f f e c t s due to the l a s e r beam can be n e g l e c t e d . In our p a r t i c u l a r case t h i s i s comp le te l y j u s t i f i e d . 70 Chapter V DISCUSSION AND CONCLUSIONS In the work presented in t h i s t h e s i s we have s t u d i e d the p e r t u r b a t i o n in the l i g h t emi t ted by a plasma when a l a s e r beam is focused i n t o i t . The enhancement of the e l e c t r o n d e n s i t y has been s a t i s f a c t o r i l y determined and a b e t t e r unde rs tand ing of the t r a n s i e n t plasma .has been o b t a i n e d . In t h i s f i n a l chapte r I would l i k e to d i s c u s s some f e a t u r e s of t h i s pe r tu rbed plasma and to c o n c 1 < • d <? the t h e s i s wi th sugges t i ons f o r f u t u r e work. Let us c o n s i d e r f i r s t the a b s o r p t i o n of energy by the p lasma. When the l a s e r l i g h t beam i s f i r e d i n to the plasma we know that a f r a c t i o n of i t s energy i s absorbed main ly by the mechanism of i n v e r s e b r emss t r ah lung . The energy absorbed w i l l i n c r e a s e the k i n e t i c energy of the e l e c t r o n s and s i n c e e l e c t r o n s q u i c k l y t h e r m a l i z e (-j n the o rde r of p i coseconds in our plasma) we may c o n s i d e r them to have a temperature T . The change in e l e c t r o n tempera -tu re w i l l upset the ba lance between p rocesses tha t depend on e l e c t r o n c o l l i s i o n s such as r e c o m b i n a t i o n , i o n i z a t i o n , e x c i t a t i o n , and d e - e x c i t a t i o n . The r a te of these p rocesses 71 would be m o d i f i e d in such a way to f a vo r i o n i z a t i o n and e x c i t a t i o n . The c o l l i s i o n a l i o n i z a t i o n w i l l i n c r e a s e the degree of i o n i z a t i o n , and the c o l l i s i o n a l e x c i t a t i o n w i l l i n c r e a s e the p o p u l a t i o n of the upper l e v e l s of the atoms, f a v o r i n g the i o n i z a t i o n by e l e c t r o n c o l l i s i o n s . New f r e e e l e c t r o n s are then produced dur ing the time that the l a s e r pu l se i s s t i l l p resent so they a l s o absorb photons in f r e e - f r e e c o l l i s i o n s and c o n t r i b u t e to the t o t a l amount of energy absorbed from the l a s e r beam. The i n c r e a s e ob ta ined in the e l e c t r o n d e n s i t y shows tha t we have ob ta ined at a time near the maximum of the l a s e r l i g h t p u l s e , an a lmost complete f i r s t i o n i z a t i o n on the pe r tu rbed p lasma. New e l e c t r o n s are be ing produced by p h o t o i o n i z a t i o n or by c o l l i s i o n a l i o n i z a t i o n , but in e i t h e r case the source f o r e l e c t r o n s are the remain ing Ar I atoms. Ar II ions are very u n l i k e l y to be f u r t h e r i o n i z e d due to t h e i r h ighe r i o n i z a t i o n p o t e n t i a l . The maximum e l e c t r o n . number d e n s i t y o b t a i n a b l e i s then the sum of the e l e c t r o n number d e n s i t y p lus the number d e n s i t y of Ar I p resen t in the plasma, p r i o r to the l a s e r p u l s e . At h igh p r e - i o n i z a t i o n s the number d e n s i t y of Ar I i s s m a l l e r and consequen t l y a s m a l l e r i n c r e a s e in the e l e c t r o n d e n s i t y i s o b t a i n e d . a s seen from the continuum r a d i a t i o n i n F i g u r e ! 3 . 72 A f t e r the i n j e c t i o n of energy i n t o plasma from the l a s e r pu lse the s t rong g r a d i e n t in the e l e c t r o n den -s i t y d i s appea r s q u i c k l y and the peak e l e c t r o n d e n s i t y dec reases r a p i d l y . Nodwell and Van der Kamp (1968) have measured. . and compared the e l e c t r o n d e n s i t y p r o f i l e s in an argon plasma j e t s i m i l a r to o u r s , us ing s p e c t r o s c o p i c measure-ments and l a s e r s c a t t e r i n g . They found tha t the e l e c t r o n d e n s i t y ob ta ined from l a s e r s c a t t e r i n g were s y s t e m a t i c a l l y h ighe r than the one ob ta ined from the abso lu t e l i n e r a d i a -t i o n of Ar l i n e s . A l though the d i s c r e p a n c y was a t t r i b u t e d • to e r r o r s in the s p e c t r o s c o p i c method, the p e r t u r b a t i o n produced in the plasma cou ld e a s i l y have i n c r ea sed the e l e c t r o n d e n s i t y by 25% at the l a s e r power output tha t was used in the exper iment . The d e t e r m i n a t i o n s of the e l e c t r o n d e n s i t y from the Ar II l i n e widths shown in F igure 17 have been performed us ing t h e - l i n e s Ar II 4&06 A and Ar II 4880 A whose Stark c o e f f i c i e n t s have been measured by o thers (see f o r example R o b e r t s , 1968) and are wel l known. We have measured the l i n e width of s e ve r a l o ther Ar II l i n e s and we have found d i s c r e p a n c i e s in the va lues of the e l e c t r o n d e n s i t i e s so o b t a i n e d . S ince the c o n d i t i o n s : are i d e n t i c a l f o r a l l the l i n e s , t h i s would suggest tha t the d i s c r e p a n c i e s ob t a i ned 73 are due to d i s c r e p a n c i e s in the Stark c o e f f i c i e n t s . Th i s suggests tha t a d e t e r m i n a t i o n of S tark c o e f f i c i e n t s in a pe r tu rbed plasma s i m i l a r to tha t presented in t h i s work cou ld g i ve c o n s i s t e n t r e s u l t s . We are in a f a v o r a b l e s i t u a t i o n f o r a r e l i a b l e d e t e r m i n a t i o n of S tark c o e f f i c i e n t s because we measure the width of the l i n e s emi t ted on ly from the smal l r eg ion of the plasma where the p e r t u r b a t i o n i s made. In t h i s way we e l i m i n a t e the need of Abel u n f o l d i n g ac ross the e n t i r e plasma because the number d e n s i t y of e x c i t e d Ar II ions o u t s i d e t h i s pe r tu rbed r eg ion is very s m a l l . In o rder to perform an abso lu t e de t e rm ina t i on of S tark c o e f f i c i e n t s , the e l e c t r o n d e n s i t y cou ld be measured i ndependen t l y us ing the t r a n s i e n t cont inuum emiss ion as i t has been done in the p resen t work, or by measur ing the a b s o r p t i o n c o e f f i c i e n t of a CC>2 l a s e r beam. From the v a r i a t i o n of the t r a n s m i t t e d l a s e r beam, the e l e c t r o n d e n s i t y can be ob ta ined i f the e l e c t r o n temperature i s known a p p r o x i m a t e l y . Because of the l a r g e a b s o r p t i o n c o e f f i c i e n t at the 10.6um wavelength of t h i s l a s e r , a s e n s i t i v e d e t e r m i n a t i o n of the e l e c t r o n d e n s i t y cou ld be a c c o m p l i s h e d . In a per tu rbed plasma of s i m i l a r c o n d i t i o n s as presented in t h i s t h e s i s , by f o c u s i n g the l a s e r beam i n to the same f o c a l volumn of the ruby l a s e r , one would o b t a i n a t r a n s m i t i o n of 99% be fo re the 74 plasma has been pe r tu rbed and a t r a n s m i t i o n of on ly 6% at maximum of the p e r t u r b a t i o n . A smal l l a s e r u n i t cou ld be used f o r t h i s pu rpose , wi th an output power in accordance with the s e n s i t i v i t y of the d e t e c t o r employed. A mercury-doped germanium d e t e c t o r cou ld be s u i t a b l e f o r t h i s pur -pose . For any f u r t h e r work on per tu rbed p lasmas , the use of aC02 pu lsed l a s e r should be cons ide red i n s t ead of the ruby l a s e r employed in t h i s work to produce the pe r -t u r b a t i o n . The reason i s t w o f o l d . F i r s t l y , s i n ce the a b s o r p t i o n c o e f f i c i e n t of the plasma i s p r o p o r t i o n a l to A 3 , . a t the wavelength of 10.6 ym of the C0^ l a s e r , i t would be .3560 times l a r g e r than the co r r e spond ing a b s o r p -t i o n c o e f f i c i e n t f o r a ruby l a s e r . It w i l l then r e q u i r e on ly a 6KW l a s e r to produce a s i m i l a r p e r t u r b a t i o n as r e p o r t e d in t h i s work. S e cond l y , the r e p e t i t i o n r a t e o b t a i n a b l e in a CO2 l a s e r w i l l a l l ow to r eco rd a l o t of data in a very sho r t i n t e r v a l of time thus a s s u r i n g the same c o n d i t i o n s in the plasma and improv ing the s t a t i s t i c of the r e s u l t s . The p ropaga t ion of the p e r t u r b a t i o n in the plasma i s of i n t e r e s t s i n ce the k inemat i c of the expans ion cou ld p r e d i c t the energy absorbed by the p lasma. Fu r the r study on the expans ion shou ld be done. .The a p p l i c a b i l i t y of the Chapman-Jouguet de tona t i on theory and of the T a y l o r b l a s t 75 wave theory in a plasma should a l so be i n v e s t i g a t e d . In l a s e r produced plasmas these t h e o r i e s are v a l i d because the expans ion f r o n t moves i n t o a gas , whereas in our exper iment the p e r t u r b a t i o n f r o n t moves i n t o ah i o n i z e d medium. As a resume to the work presented in this" t h e s i s I w i l l mention b r i e f l y the major o r i g i n a l c o n t r i b u t i o n s tha t we have made in t h i s exper iment : 1 - The enhancement and s p a t i a l d i s t r i b u t i o n i n ' the e l e c t r o n d e n s i t y caused by a. focused l a s e r beam have been determined in the t r a n s i e n t 'plasma .• They have been ob ta ined from measurements of the abso lu t e i n t e n s i t y of the continuum emiss ion and a l so from the Stark broadening of Ar II l i n e s . It has been found tha t the plasma reaches an a lmost complete f i r s t i o n i z a t i o n , and tha t s t rong e l e c t r o n d e n s i t y g r a d i e n t s are set up i n s i d e the pe r tu rbed r eg ion of the .p lasma; 2 - The l i n e , shape of Ar II l i n e r a d i a t i o n have been determined in the presence of the l a s e r pu l se and s t rong assymmetr ies have been found in the. l i n e s . Based on the s p a t i a l d i s t r i b u t i o n of the e l e c t r o n d e n s i t y determined from measurements of the continuum e m i s s i o n , the observed assym-met r i es have been exp la ined ' , 76 3 - The p e r t u r b a t i o n of the plasma f o r d i f f e r e n t i n c i d e n t l a s e r power d e n s i t i e s and f o r d i f f e r e n t degrees of i o n i z a t i o n of the plasma have been determined in the p resen t work. 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