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An experimental investigation of the stark broadened profiles of He II 3203 and He II 4686 Bernard, John Edward 1978

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AN EXPERIMENTAL INVESTIGATION OF THE STARK BROADENED PROFILES OF He II 3203 AND He II 4686 by JOHN EDWARD BERNARD B . Sc-,;,'Iin iv'er s i t y of V i c t o r i a , 1977 THESIS SUBMITTED IN PARTIAL FULFILLMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Physics) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September* 1979 (§)' John Edward Bernard, 1979 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e 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 Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V6T 1W5 n. t. 0U>, MM0) DE-6 BP 75-51 1 E ABSTRACT Experimental p r o f i l e s of the He II l i n e s at 3203 A and 4686 X have been obtained from a w e l l diagnosed helium plasma. The plasma was produced i n a low power z-pinch discharge contained i n a v e s s e l of 15 cm diameter and 60 cm l e n g t h . Uniform plasma columns were l o c a t e d and s t u d i e d by means of two moveable quartz l i m i t e r tubes. The e f f e c t of the tubes on the measured e l e c t r o n temperature and d e n s i t y due to c o o l i n g and evaporated i m p u r i t i e s was measured and the tubes were p o s i t i o n e d so as to s e l e c t a uniform plasma column f o r study. E l e c t r o n temperatures were determined from the i n t e n s i t y r a t i o of the l i n e s He II 4686 and He I 5876 using a theory that considered f i n i t e escape p r o b a b i l i t i e s f o r the Lyman a resonance photons. E l e c t r o n j d e n s i t i e s were determined from the width of the He I 5876 l i n e . C o r r e c t i o n s were a p p l i e d f o r ion broadening due to doubly charged ion p e r t u r b e r s . An e l e c t r o n temperature of 4.0±0.4 eV and an e l e c t r o n d e n s i t y of . (6 . 1 ±0.6) xl 0 2 3m"^;.wlere determined f o r the a x i a l plasma o c c u r r i n g soon a f t e r the pinch phase. The experimental p r o f i l e of He II 4686 as measured by a spectrometer-o p t i c a l multichannel a n a l y z e r arrangement was compared to t h e o r e t i c a l p r o f i l e s r e s u l t i n g from a treatment of the e l e c t r o n broadening c o l l i s i o n s as s i n g l e eventfimpacts (Kepple (1972)) and from a treatment of the e l e c t r o n broadening which consider-jjS-'i the time development i n the i i c o l l i s i o n process ( u n i f i e d c l a s s i c a l - p a t h theory) (Greene (1976)). The experimental p r o f i l e was found to l i e midway between the t h e o r e t i c a l p r o f i l e s . Agreement between the experimental and u n i f i e d c l a s s i c a l - p a t h p r o f i 1 e i n the near l i n e wings was good. Agreement between experimental and e l e c t r o n impact r e s u l t s f o r He II 3203 was not good with a 60% disagreement i n l i n e widths. The He II l i n e had a double peak with the peak at s h o r t e r wavelengths being 9% higher than the other peak. : This i s s i m i l a r to the behavior observed i n the Balmer l i n e , H R, i n the atomic hydrogen spectrum. i i i TABLE OF CONTENTS ABSTRACT . i i TABLE OF CONTENTS < i v LIST OF TABLES . v i LIST OF FIGURES . . v i i ACKNOWLEDGEMENTS . . . . i x CHAPTER I INTRODUCTION 1 CHAPTER II SPECTRAL LINE BROADENING THEORY 4 CHAPTER III EXPERIMENTAL APPARATUS 18 111-1 The z-pinch discharge 18 111-2 The discharge c i r c u i t 19 111 -3 O p t i c a l system f o r l i n e p r o f i l e observations.23 III-4 Synchronizing the d i a g n o s t i c equipment to the discharge 27 I I I - 5 Measurement of temperatures 29 CHAPTER IV DENSITY MEASUREMENTS 35 IV- 1 Stark broadening of i s o l a t e d l i n e s 35 IV-2 Experimental d e t a i l s 37 IV-3 I n t e r a c t i o n s of the tubes with the plasma ...39 IV-4 L o n g i t u d i n a l u n i f o r m i t y of the plasma column..43 IV-5 Radial u n i f o r m i t y 43 IV-6 Time dependence of the plasma ....47 i v CHAPTER V TEMPERATURE MEASUREMENTS 50 V - l Theory 50 V-2 Experimental d e t a i l s ....57 V-3 I n t e r a c t i o n of the tubes with the plasma 58 V-4 U n i f o r m i t y of the plasma column 62 V-5 Temperature time dependence and r e p r o d u c i b i l i t y of the pinch 65 V- 6 Temperature estimate from l i n e to t, continuum r a t i o s 68 CHAPTER VI DATA ANALYSIS 70 VI- 1 C a l i b r a t i o n f o r i n t e n s i t y response 71 VI-2 C a l i b r a t i o n of the wavelength s c a l e 73 VI- 3 C a l c u l a t i o n of the c o r r e c t e d l i n e p r o f i l e s ..74 CHAPTER. VII LINE PROFILES OF He II 3203 AND He II 4686..79 VII- 1 Plasma c o n d i t i o n s 80 VII-2 P r o f i l e s of the s p e c t r a l l i n e s He II 3203 and He II 4686 83 VII-3 Comparison of the experimental and t h e o r e t i c a l l i n e p r o f i l e s 87 CHAPTER VIII CONCLUSIONS .91 BIBLIOGRAPHY 96 APPENDIX £ 97 APPENDIX 2 THE OMA GATING CIRCUIT. 98 APPENDIX 3 THE COMPUTER PROGRAMS 102 v LIST OF TABLES Table I I I - l v i LIST OF FIGURES II-1 T h e o r e t i c a l p r o f i l e s f o r He II 4686 f o r v a r i o u s e l e c t r o n d e n s i t i e s 12 II-2 T h e o r e t i c a l p r o f i l e s of He II 4686 f o r v a r i o u s e l e c t r o n temperatures 13 II-3 T h e o r e t i c a l p r o f i l e s of He II 3203 f o r v a r i o u s e l e c t r o n d e n s i t i e s 14 I I - 4 T h e o r e t i c a l p r o f i l e s of He II 3203 f o r va r i o u s e l e c t r o n temperatures 15 111 -1 The l i m i t e r tube mounts 20 111 - 2 The discharge c i r c u i t 21 I I I - 3 The discharge cu r r e n t measuring c i r c u i t and the discharge c u r r e n t waveform 24 111-4 Experimental arrangement f o r measuring l i n e p r o f i l e s 25 111 - 5 T r i g g e r i n g and timing c i r c u i t 28 I I I - 6 Experimental arrangement f o r measuring temperatures 30 IV- 1 Complete p r o f i l e of He I 5876 ..40 IV-2 E f f e c t of the l i m i t i n g tubes on the d e n s i t y r ^ * . . . .. 42 IV- 3 L o n g i t u d i n a l u n i f o r m i t y of the a x i a l e l e c t r o n dens i t y 44 V- l 11+6 86/^ 5876 a s a f u n c t i o n of e l e c t r o n temperature... 55 V-2 Photomultip 1 i e r t r a c e s of Ii+686 a n < * 1 5876 57 V-3 E f f e c t of the l i m i t e r tubes on the temperature. ...59 V-4 Iit6 86 a n c * 1 5876 a s a f u n c t i o n of tube s e p a r a t i o n . .61 V-5 The suspected e f f e c t s of the l i m i t e r tubes on the observed plasma 63 V-6 U n i f o r m i t y of the a x i a l e l e c t r o n temperature 64 V-7 Time h i s t o r y o f the e l e c t r o n temperature 66 v i i VI-1 S e n s i t i v i t y of the OMA i n the r e g i o n of 48,00 A. ..72 VI-2 P r o f i l e s of He II 4686 before and a f t e r smoothing and c o r r e c t i o n procedures 76 VI- 3 Complete p r o f i l e of He II 4686 1....78 VII- 1 Measured p r o f i l e of He II 4686 84 VII-2 Measured p r o f i l e of He II 3203. ....85 VII-3 Experimental and t h e o r e t i c a l p r o f i l e s of He II 4686 88 VII-4 Experimental and t h e o r e t i c a l p r o f i l e s of He He II 3203 89 Al-1 The r e s i s t i v e d i v i d e r s f o r the p h o t o m u l t i p l i e r dynode chains 97 A2-1 The OMA g a t i n g c i r c u i t 99 A2-2 The OMA g a t i n g pulse 101 v i i i ACKNOWLEDGEMENTS I would l i k e to thank Dr. F.L. Curzon f o r suggesting t h i s p r o j e c t and f o r the s u p e r v i s i o n I r e c e i v e d . His suggestions i n both the experimental and t h e o r e t i c a l aspects of the work were most h e l p f u l . I would also l i k e to thank Dr. A.J. Barnard f o r h i s a s s i s t a n c e i n the data a n a l y s i s and i n the computation of the t h e o r e t i c a l p r o f i l e s . A. Cheuck's a s s i s t a n c e with the e l e c t r o n i c s and the d i a g n o s t i c equipment was very b e n i f i c i a l . His w i l l i n g n e s s to provide prompt a t t e n t i o n i n r e p a i r i n g or a d j u s t i n g equipment was most a p p r e c i a t e d . G. Auchinleuck -was of great a s s i s t a n c e i n c o l l e c t i n g the i n i t i a l data. F i n a l l y , I would l i k e to thank T. Knop f o r machining the e l e c t r o d e s and E. Williams f o r the p r e p a r a t i o n of the quartz tubes. i x 1 CHAPTER I . INTRODUCTION There i s c o n s i d e r a b l e i n t e r e s t i n the l i n e p r o f i l e s of s p e c t r a l l i n e s o r i g i n a t i n g from s i n g l y i o n i z e d helium. In many plasmas c o n t a i n i n g s u b s t a n t i a l amounts of helium, the He II l i n e s are prominent i n the emitted s p e c t r a . S t e l l a r sources as well as p o s s i b l e f u s i o n devices are expected to c o n t a i n s u b s t a n t i a l amounts of helium i n the s i n g l y i o n i z e d s t a t e and He II l i n e s with well known l i n e shapes can serve as s e n s i t i v e d e n s i t y and temperature probes. In the v i s i b l e and near u l t r a v i o l e t regions the most prominent He II l i n e s are o f t e n He II 3203 ( 5-3 ) and He II 4686 ( 4-3 ). Accurate knowledge of the shapes of thesevtwo l i n e s i s t h e r e f o r e important i n the d e t e r m i n a t i o n of plasma c o n d i t i o n s . The broadening mechanisms i n v o l v e d i n helium II l i n e s are very s i m i l a r to those f o r n e u t r a l hydrogen. The s t a t e s i n both s p e c i e s are degenerate i n the o r b i t a l quantum number and t h i s leads to strong l i n e a r Stark e f f e c t s i n the broadening of the emitted l i n e s . These e f f e c t s , which cause a s p l i t t i n g of the degenerate l e v e l s , are caused by the almost s t a t i c e l e c t r i c f i e l d s present at the p e r t u r b e r s due to the slow moving ions that are present i n the surrounding plasma. A knowledge of the ion f i e l d d i s t r i b u t i o n can lead to accurate i o n broadened l i n e shapes. The broadening due to e l e c t r o n s , which has 2 the e f f e c t of mixing the i o n s h i f t e d and broadened components, however, i s not easy to c a l c u l a t e . Various approximations have been made i n order to s i m p l i f y the c a l c u l a t i o n s but e r r o r s are o f t e n i n t r o d u c e d i n the f i n a l p r o f i l e s . Therefore experimental measurements of the l i n e p r o f i l e s are of paramount importance i n determining d e f i c i e n c i e s i n the t h e o r i e s . The purpose of t h i s i n v e s t i g a t i o n was to measure the p r o f i l e s of the He II l i n e s at 3203 A and 4686 A i n a w e l l diagnosed plasma and to compare the experimental r e s u l t s to t h e o r e t i c a l p r o f i l e s obtained from d i f f e r e n t treatments of the e l e c t r o n broadening. The t h e o r e t i c a l treatments, one which t r e a t s the e l e c t r o n broadening c o l l i s i o n s as s i n g l e event impacts, and the other which con s i d e r s the time development i n the c o l l i s i o n p r o c e s s , lead to s i g n i f i c a n t d i f f e r e n c e s i n the broadening of the lower l e v e l s of the t r a n s i t i o n s of i n t e r e s t . Since i n t e r f e r e n c e between the upper and lower l e v e l s can lead to a narrowing of the l i n e , the two treatments of the lower l e v e l s lead to d i f f e r e n c e s i n the p r e d i c t e d l i n e shapes. The broadening of the lower l e v e l s i s expected to be a g r e a t e r e f f e c t i n the p r o f i l e of He II 4686 than i n the p r o f i l e of He II 3203. Therefore,a study of both these l i n e s i s important i n understanding the nature of the d e f i c i e n c i e s i n the t h e o r i e s . T h i s r e p o r t i s d i v i d e d i n t o e i g h t c hapters. Chapter ' : •• ' ' v:' '- .) y •"-3 II c ontains an o u t l i n e of the general theory of pressure broadening as well as of the approximations made i n p r e d i c t i n g l i n e shapes. D i f f e r e n c e s i n the two approaches to the e l e c t r o n broadening are mentioned and t h e o r e t i c a l p r o f i l e s are compared. Chapter I I I i s concerned with the c o n s t r u c t i o n of the z-pinch used i n the s t u d i e s and the nature of; the d i a g n o s t i c equipment. The p e r t i n e n t theory and r e s u l t s f o r the d e n s i t y measurements are presented i n Chapter IV. R e s u l t s of s t u d i e s of the u n i f o r m i t y and time development of the a x i a l plasma and of the i n t e r a c t i o n of the tubes with the plasma are r e p o r t e d . The theory behind\the temperature measurements i s examined i n Chapter V which a l s o i n c l u d e s an a n a l y s i s of how well the experimental plasma s a t i s f i e d the requirements of the theory. The e f f e c t of the tubes on the e l e c t r o n temperature as well as the u n i f o r m i t y and time development of the a x i a l plasma are a l s o d i s c u s s e d . The a n a l y s i s of the experimental p r o f i l e s obtained with an o p t i c a l m ultichannel a n a l y z e r appears in. Chapter VI. The c a l i b r a t i o n techniques and computer a n a l y s i s of the measured p r o f i l e s are also presented i n Chapter VI. An account of the plasma c o n d i t i o n s i n the experimental plasma i s given i n Chapter VII together with a comparison of the experimental and t h e o r e t i c a l p r o f i l e s of He II 3203 and He II 4686. Conclusions concerning the experimental p r o f i l e s and reasons f o r the observed d i s c r e p a n c i e s i n the (.results are presented i n Chapter V I I I . 4 CHAPTER II SPECTRAL LINE BROADENING THEORY To help understand the theory of l i n e broadening, a r a d i a t i n g atom may be thought of as a c l a s s i c a l o s c i l l a t o r e m i t t i n g r a d i a t i o n at a c a r r i e r frequency, w0 . The i n t e n s i t y of the emitted r a d i a t i o n decays e x p o n e n t i a l l y with a time constant, T, which i s r e l a t e d to the l i f e t i m e of the e x c i t e d s t a t e . A spectrograph e s s e n t i a l l y F o u r i e r transforms the emitted r a d i a t i o n and so the r e s u l t i n g spectrum f o r a s i n g l e atom at r e s t with r e s p e c t to the observer i s a L o r e n t z i a n with centre frequency, u 0 , and width p r o p o r t i o n a l to T - 1 . This form of broadening which i s due to the f i n i t e l i f e t i m e s or the s t a t e s i n v o l v e d i n the t r a n s i t i o n i s c a l l e d n a t u r a l broadening. I f the r a d i a t i n g atom i s moving the c a r r i e r frequency i s Doppler s h i f t e d . For an ensemble of atoms that are moving with d i f f e r e n t v e l o c i t i e s with respect to the observer, the Doppler s h i f t e d p r o f i l e s superimpose l e a d i n g to a Doppler broadened s p e c t r a l l i n e . In t h i s i n v e s t i g a t i o n the e f f e c t s of both n a t u r a l and i)opp l e r broadening were not s i g n i f i c a n t and can be ignored. S p e c t r a l l i n e s emitted by atoms or. ions i n a plasma may al s o be broadened as a r e s u l t of i n t e r a c t i o n s between the emitters and the ions and e l e c t r o n s present i n tlie plasma. I n t e r a c t i o n s with the ions cause the c a r r i e r 5 frequency, U Q , of a given atom to be a l t e r e d due to the Stark e f f e c t which s p l i t s and s h i f t s the energy l e v e l s of the e m i t t e r . I f the p o s i t i o n o f the ions changes slowly during the l i f e t i m e of the em i t t e r the r e s u l t i n g l i n e p r o f i l e i s an ensemble average over a l l p o s s i b l e c o n f i g u r a t i o n s of ions around the e m i t t e r , weighted according to the p r o b a b i l i t i e s of the occurrence of the c o n f i g u r a t i o n s . T h i s i s e s s e n t i a l l y the quasi-static-, approximation f o r ion broadening. I n t e r a c t i o n s with e l e c t r o n s can lead to f u r t h e r broadening. The e l e c t r o n s move q u i c k l y and i n t e r a c t ; with the em i t t e r f o r a few c y c l e s of the c a r r i e r frequency. The i n t e r a c t i o n s e s s e n t i a l l y r e s u l t i n random i n t e r r u p t i o n s i n the phase of the c a r r i e r s i g n a l . The FoCirier transform of a c a r r i e r wave with i t s phase i n t e r r u p t e d at random times leads to a L o r e n t z i a n spectrum with a width p r o p o r t i o n a l to the c o l l i s i o n frequency. T h i s method of t r e a t i n g ' the e l e c t r o n i n t e r a c t i o n s i s c a l l e d the impact,approximation. If both i on and e l e c t r o n broadening are important the t h e o r e t i c a l p r o f i l e i s obtained by c o n v o l u t i n g the two p r o f i l e s . In a proper quantum mechanical treatment the r e s u l t i n g l i n e p r o f i l e ( i n t e n s i t y of emitted r a d i a t i o n as a f u n c t i o n of fr e q u e n c y ) , n e g l e c t i n g the e f f e c t s of s e l f - a b s o r p t i o n and r e e m i s s i o n , i s given by: 6 1(0)) = (2-1) 3ire o c a,$ where N_ i s the number d e n s i t y of the r a d i a t o r s , CO i s the frequency at the l i n e c e n t r e , a> and B> are the i n i t i a l and f i n a l s t a t e s , cf i s the d i p o l e moment of the r a d i a t o r , and P Q i s the p r o b a b i l i t y that a given r a d i a t o r i s i n s t a t e |ct>. Since co i s approximately constant over the l i n e width, the f a c t o r o u t s i d e the sum i s considered to be a constant. Line broadening then a r i s e s from the i n t e r a c t i o n between the d i p o l e moment of the r a d i a t o r and the e l e c t r i c f i e l d s of the p e r t u r b e r s as a r e s u l t of c o l l i s i o n s . From the p r o p e r t i e s of the F o u r i e r transform, the time i n t e r v a l necessary f o r determining a frequency s e p a r a t i o n Aco i s At = l/Aco. For determining a l i n e p r o f i l e , t h i s time of i n t e r e s t corresponds to the h a l f width of the l i n e and i s t y p i c a l l y equal to the time between c o l l i s i o n s . The r a d i a t o r i s u s u a l l y c o n s i d e r e d to be perturbed only f o r the d u r a t i o n of the c o l l i s i o n which i s approximately given by x=p/v where p i s the d i s t a n c e of c l o s e s t approach (impact parameter) and v i s a t y p i c a l p e r t u r b e r v e l o c i t y . Since the ions are much more massive than the e l e c t r o n s , ion v e l o c i t i e s are much smaller than e l e c t r o n v e l o c i t i e s . T herefore two cases must be c o n s i d e r e d . For ions the 7 d u r a t i o n of the c o l l i s i o n s , t , i s u s u a l l y much gr e a t e r than the time of i n t e r e s t , At, and so the motion of the ions can be ignored during the c o l l i s i o n s . On the other hand, the d u r a t i o n of c o l l i s i o n s i n v o l v i n g e l e c t r o n s i s u s u a l l y much s h o r t e r than the time of i n t e r e s t . Therefore c o l l i s i o n s i n v o l v i n g ions are t r e a t e d by the quasi r-s-t'atic approximation while c o l l i s i o n s i n v o l v i n g e l e c t r o n s are t r e a t e d by the impact approximation. A quantum mechanical p e r t u r b a t i o n method i s used; i n both cases. In order to s i m p l i f y matters, the c l a s s i c a l path approximation i s o f t e n used. This means that the p e r t u r b e r s are assumed to t r a v e l along c l a s s i c a l paths that are independent of the s t a t e of the e m i t t e r . Charged p e r t u r b e r s t h e r e f o r e t r a v e l along s t r a i g h t l i n e s near n e u t r a l e m i t t e r s and h y p e r b o l i c paths near charged e m i t t e r s . T h i s assumption i s a good approximation as long as the impact parameters are much l a r g e r than the de B r o g l i e wavelengths of the pe r t u r b e r s and the change i n the momentum of the p e r t u r b e r s i s small compared to t h e i r momentum. It i s a l s o assumed that the p e r t u r b e r and the r a d i a t o r are weakly coupled so that t h e i r i n i t i a l s t a t e s are independent of each other. This c o n d i t i o n i s s a t i s f i e d i f the mean i n t e r a c t i o n energy i s much smal l e r than kT ( i e . i f broadening c o l l i s i o n s are much more frequent than e x c i t i n g and d e e x c i t i n g c o l l i s i o n s ) and i s a good approximation f o r a frequency s e p a r a t i o n , Aur^'such that IjAto <<kT. 8 For the quasi-static case, the e l e c t r i c f i e l d as seen by the emitter i s constant during the time of in t e r e s t . The f i n a l p r o f i l e in this case is obtained by calculating -> the energy s h i f t s in the emitter l e v e l s , AE (e) and AE.(e), a p and the i n t e n s i t i e s , | <a|3|$>|2pq, due to the e l e c t r i c f i e l d , e, and then weighting these s h i f t s according to the s t a t i s t i c a l d i s t r i b u t i o n of e l e c t r i c f i e l d s as seen by the emitters. The resul t i n g p r o f i l e is given by: ^—^ r « / AE (£)-AE Q(e)\ ^ '- 2 ^ / , < a | * | e > | 2 8 + —H (2-2) where W(e) i s the pro b a b i l i t y d i s t r i b u t i o n of the e l e c t r i c f i e l d . Line p r o f i l e s due to electron c o l l i s i o n s are calculated by averaging over a l l potentials produced by perturbers passing by with various impact parameters, v e l o c i t i e s , and times of closest approach. The c o l l i s i o n s are treated as occurring separately in time. This i s generally true for the strong c o l l i s i o n s but the long distance c o l l i s i o n s can never truly be separated in time. However, since the average interaction i s weak, to f i r s t order even the distant c o l l i s i o n s can be treated separately. The res u l t i n g p r o f i l e in the impact approximation i s given by: i ^ + fl.r i c H a - v I . (u>) = i-Re^J d o 6<<ael I icu- — — - ab a, a' (2-3) 9 where ct . are the d i p o l e matrix elements between substates oS OjO 1,... and 8,6',... of two groups of l e v e l s , a and b, H and H, are the e m i t t e r Hamiltonians which act a b , o n l y ; on the> substates | o>_ and | $> ' e;tCi • r e s p e c t i v e l y , and i s an operator that contains time and i n t e r a c t i o n p o t e n t i a l i n f o r m a t i o n . The problem i s to evaluate $ ab« Times are considered that are long compared to the d u r a t i o n of the c o l l i s i o n s . Each c o l l i s i o n i s then t r e a t e d as a separate event with no time development. ®&\> i s commonly evaluated in> terms of S-matrices d e s c r i b i n g the s c a t t e r i n g of the p e r t u r b i n g e l e c t r o n on upper and lower l e v e l s . C u t o f f s are i n t r o d u c e d f o r l a r g e and small impact parameters. The lar g e impact parameter c u t o f f i s of the order of the Debye length and so corresponds to the d i s t a n c e at which sc r e e n i n g of the p e r t u r b e r i s important. The small impact parameter c u t o f f i s i n t roduced because of a breakdown i n the s c a t t e r i n g matrices f o r strong c o l l i s i o n s . The e f f e c t on the l i n e p r o f i l e from c o l l i s i o n s with impact parameters l e s s than t h i s c u t o f f i s o f t e n small and these c o l l i s i o n s are t r e a t e d s e p a r a t e l y . The o v e r a l l l i n e p r o f i l e i s then c a l c u l a t e d by n e g l e c t i n g the motion of the ions and adding the s t a t i c ion p e r t u r b a t i o n to the unperturbed emitter Hamiltonians H a and H^ i n 2-3. The e l e c t r o n impact approximation i s then used to f i n d the l i n e shape f o r these new values of 10 H and H. and the f i n a l l i n e p r o f i l e i s found by averaging over the d i s t r i b u t i o n of i o n f i e l d s . I (to), * \f& W(e) _ f i [ H (t)-H (?)] - l - 1 - K R e 2 J ^ a B < < a 3 l [ i w *abj l a ' 6 , > > d a . e ' 3,V (2-4) where i t has been assumed that 4 ^ i s independent of I E . T h i s expression i s v a l i d i f the u n c e r t a i n t y i n t r o d u c e d by n e g l e c t i n g the i o n motion i s small compared to the e l e c t r o n impact h a l f width or the d i s t a n c e from l i n e c e n t r e , whichever i s l a r g e r . For i s o l a t e d l i n e s such as He I 5876 the matrix elements of ( H a ( e ) - H b ( e ) ] / n give the p o s i t i o n of l i n e s t h a t are s l i g h t l y s h i f t e d by the q u a d r a t i c Stark e f f e c t . The f i e l d dependence can o f t e n be i g n o r e d , however, s i n c e the energy s p l i t t i n g due to the ion f i e l d i s much l e s s than the energy u n c e r t a i n t y i n an e l e c t r o n broadening c o l l i s i o n . T h e r e f o r e the ion broadening r e s u l t s i n o n l y a small c o r r e c t i o n to the e l e c t r o n broadened p r o f i l e and the f i n a l p r o f i l e i s approximately L o r e n t z i a n i n shape. For l i n e s from hydrogen and i o n i z e d helium where the l e v e l s are degenerate with r e s p e c t to the o r b i t a l quantum numbers, s p l i t t i n g of the l e v e l s due to ion broadening i s important. The i o n s p l i t t i n g i n t h i s case i s by the l i n e a r Stark e f f e c t ( i e . the s h i f t i s p r o p o r t i o n a l to the f i e l d ) . 11 E l e c t r o n impact broadening then mixes the s p l i t l e v e l s . Kepple (1972) has used a c l a s s i c a l path impact theory that accounts f o r p e r t u r b a t i o n s of both upper and lower l e v e l s of the r a d i a t i n g ion i n order to c a l c u l a t e t h e o r e t i c a l p r o f i l e s of s e v e r a l He II l i n e s . P e r t u r b a t i o n s due to s i n g l y charged ions are t r e a t e d by the q u a s i - f s t a t i c l i n e a r S t a r k - e f f e c t approximation. F i n i t e d u r a t i o n of c o l l i s i o n s and screening of the e l e c t r o n f i e l d s are allowed f o r by c a l c u l a t i n g the v e l o c i t y dependence of the maximum impact parameter c u t o f f . The approximate e f f e c t of i n e l a s t i c c o l l i s i o n s -Gi.e. those c o l l i s i o n s that r e s u l t i n a change i n the p r i n c i p a l quantum number of the r a d i a t i n g ion) i s c a l c u l a t e d u s i n g semi-empirical Gaunt-f a c t o r s . Terms up to the quadrupole term i n the i n t e r a c t i o n p o t e n t i a l m u l t i p o l e expansion are considered i n a second order expansion. Resultant p r o f i l e s of the He II l i n e s at 3203 & and 4686 A are given i n Figures H - l to II-4. f o r v a r i o u s values of d e n s i t y and temperature. — P r o f i l e s of He II 4686 have a l s o been c a l c u l a t e d by Greene (1976) who has used the u n i f i e d c l a s s i c a l path theory to t r e a t . t h e e l e c t r o n c o l l i s i o n s . Ion c o l l i s i o n s are s t i l l t r e a t e d q u a s i - s t a t i c a l l y . The u n i f i e d c l a s s i c a l path theory u n i f i e s aspects of impact, one e l e c t r o n , and r e l a x a t i o n t h e o r i e s to produce a theory that can be used from the l i n e centre to the f a r l i n e wings. The c u t o f f s f o r l a r g e and small impact parameters i n t r o d u c e d i n the g u r e 11 -1 : T h e o r e t i c a l p r o f i l e s o f He I I 4 6 8 6 f o r v a r i o u s e l e c t r o n ' d e r f s i t i . e s . F i g u r e I I - 2 : T h e o r e t i c a l p r o f i l e s o f He I I 4 6 8 6 f o r v a r i o u s e l e c t r o n t e m p e r a t u r e s . 1.25-1 H e H 3 2 0 3 ( f r o m Kepp le ) 6 X 1 0 " " T = 4 0 0 0 0 K 2 4 I X 1 0 i r 6 0 8 0 . W A V E L E N G T H (A) Figure II-3: Theoretical p r o f i l e s of He II 3203 for various electron densities W A V E L E N G T H (A) F i g u r e 11-4 : T h e o r e t i c a l p r o f i 1 e s o f He I I 3 2 0 3 f o r v a r i o u s e l e c t r o n t e m p e r a t u r e s . 16 impact theory are avoided. R e l a x a t i o n theory i s used to reproduce the r e s u l t s of the strong c o l l i s i o n c u t o f f but i s v a l i d everywhere besides the l i n e wings. C o l l i s i o n s , i n the u n i f i e d theory, are t r e a t e d i n a time ordered manner ( i e . changes i n the d i r e c t i o n • and--~strengjfch o f . the e l e c t r i c f i e l d of the e l e c t r o n as i t moves by the r a d i a t o r are considered) as opposed to the n o n s t r u c t e r e d c o l l i s i o n s of the impact model. It i s assumed that no two strong c o l l i s i o n s occur simultaneously and that the e f f e c t of c o l l i s i o n s are a d d i t i v e . The r e s u l t a n t p r o f i l e s f o r He II 4686 are given i n Figures 11-1 and 11-2 . I n e l a s t i c c o l l i s i o n s were ignored i n c a l c u l a t i n g these p r o f i l e s and S-matrices were c a l c u l a t e d to a l l orders i n the d i p o l e i n t e r a c t i o n . From the p r o f i l e s c a l c u l a t e d by Kepple and Greene i t i s apparent that whereas the l i n e p r o f i l e depends s t r o n g l y on the e l e c t r o n d e n s i t y , the e f f e c t of the temperature on the p r o f i l e i s s m a l l . The p r o f i l e s p r e d i c t e d by Greene are s i g n i f i c a n t l y narrower than those p r e d i c t e d by Kepple. Greene s t a t e s that the primary cause ) 0f t h i s d i s c r e p a n c y i s i n d i f f e r e n t ways of t r e a t i n g the broadening of the lower l e v e l s . Kepple t r e a t s the matrix elements of the e l e c t r o n coordinate ve c t o r f o r the lower l e v e l as being r e a l i n c a l c u l a t i n g $ ak whereas Greene r e t a i n s t h e i r complex form. Since the broadening of the upper l e v e l s i n c r e a s e s with p r i n c i p a l quantum number, the e f f e c t of the d i f f e r e n t treatments of the broadening of the lower levels on the theoretical li n e p r o f i l e s should be less for He II 3203 than i t i s for He II 4686. 18 CHAPTER III EXPERIMENTAL APPARATUS 111-1 The z-pinch discharge The plasma which was s t u d i e d i n t h i s i n v e s t i g a t i o n was produced i n a small z-pinch discharge s i m i l a r to the one used e a r l i e r i n t h i s lab by Medley (1970). The discharge was formed by passing a high current between two e l e c t r o d e s at opposite ends of a g l a s s tube of 15 cm i n t e r n a l diameter. The c u r r e n t flowed i n i t i a l l y along the inner wall of the c y l i n d e r and was c o n s t r i c t e d to the ax i s by the r a d i a l Lorentz f o r c e , forming the s o - c a l l e d " p i n c h " . The c u r r e n t was d r i v e n by energy s t o r e d i n a c a p a c i t o r bank. Plasma c o n d i t i o n s could be v a r i e d by a l t e r i n g the charging v o l t a g e of the c a p a c i t o r s or by changing the f i l l i n g p r essure of the discharge v e s s e l . The plasma produced i n t h i s study had q u i t e high e l e c t r o n d e n s i t i e s ( = 1 024* m~3) but low temperatures (<4 eV). Plasma parameters have been found to vary c o n s i d e r a b l y with l o c a t i o n i n s i d e the pinch (Preston (1974)). Therefore o b s e r v a t i o n s of s p e c t r a l l i n e s from extended regions of plasma are o f t e n a f f e c t e d by the non-uniformity of the plasma and must be c o r r e c t e d by some form of A b e l - u n f o l d i n g . In order to avoid the problems of u n f o l d i n g the observed l i n e p r o f i l e s , the z-pinch used i n t h i s study was c o n s t r u c t e d so as to allow uniform regions of the plasma to be observed. 19 T h i s was accomplished by means of two c o l l i n e a r quartz tubes that p r o j e c t e d i n t o the plasma through s l o t s i n the brass e l e c t r o d e s . The tubes were a l i g n e d p a r a l l e l to the a x i s of the discharge v e s s e l and could be moved along t h i s a x i s or r a d i a l l y by means of a vacuum t i g h t rack and p i n i o n system i n each e l e c t r o d e (see F i g u r e 111-1) . Each of the tube h o l d e r s a l s o provided f o r small v e r t i c a l and h o r i z o n t a l adjustments i n order to allow f o r accurate alignment of the tubes before the e l e c t r o d e s were evacuated. The tubes acted as l i m i t e r s so that only l i g h t o r i g i n a t i n g from plasma between the tubes was sampled. The tubes had an .inside diameter of 6!.mm and were p a i n t e d black on t h e t i n s i d e and capped by quartz windows to ensure that only l i g h t o r i g i n a t i n g from between the tubes was accepted. Due to the a x i a l symmetry of the p i n c h , plasma anywhere w i t h i n the pinch v e s s e l could be s e l e c t e d by the tubes f o r study. Uniform columns of plasma were found and s t u d i e d by v a r y i n g the s e p a r a t i o n between the tubes as well as t h e i r l o c a t i o n i n s i d e the v e s s e l . III-2 The discharge c i r c u i t Figure-III-2~;shows the general layout of the discharge c i r c u i t . The discharge was powered by d i s c h a r g i n g a 53 yF c a p a c i t o r bank charged to -12 kV through a t r i g g e r e d spark gap switch (B) i n s e r i e s with the pinch e l e c t r o d e s . Gap B was photon coupled to the t r i g g e r i n g c i r c u i t i n order to e l i m i n a t e ground loop c o u p l i n g between the low 21 PINCH H.V. SUPPLY 500M 5 3 . f: ^ MAIN GAP B , „ A ) B A N K TRIGGER PULSE GENERATOR 0.05 M F 42il 4 r TRIGGER GAP and U.V. SOURCE! IM F i g u r e 111 -2 : T h e d i s c h a r g e c i r c u i t 22 v o l t a g e t r i g g e r i n g and measuring c i r c u i t s and the high v o l t a g e , high c u r r e n t discharge c i r c u i t . T h i s photon co u p l i n g was accomplished through a t r i g g e r pulse generator which produced a spark at the main gap. A t h y r a t r o n u n i t was used to produce a small u l t r a - v i o l e t f l a s h which, through i o n i z a t i o n of the a i r between the e l e c t r o d e s of a t r i g g e r gap (A) l e d to the f i r i n g of the t r i g g e r pulse generator. It was necessary to use the t r i g g e r pulse generator s i n c e e l e c t r o d e e r o s i o n i n the main gap can lead to l a r g e changes (>1 kV) i n the breakdown p o t e n t i a l and the u.v. f l a s h c ould only break down a gap that was l e s s than 500 V below breakdown p o t e n t i a l . Since the t r i g g e r gap generator was low energy (0.05 yF, =12 kV), e l e c t r o d e damage at gap A was much smal l e r than at gap B and the u.v. f l a s h c ould be used r e l i a b l y to i n i t i a t e breakdown. In order to s t a b i l i z e the v o l t a g e across gap A, the t r i g g e r generator c a p a c i t o r was charged through a vol t a g e d i v i d e r across the main c a p a c i t o r bank. The c u r r e n t from the bank was c a r r i e d to the pinch e l e c t r o d e s through 10 cm wide f l a t copper l e a d s . The leads at the pinch were c o n s t r u c t e d c o a x i a l l y to lower the c i r c u i t inductance as w e l l as to screen out e l e c t r i c a l n o i s e . The lead to the ground e l e c t r o d e surrounding the discharge v e s s e l was made of brass gauze to allow side-on o b s e r v a t i o n s of the plasma. A Rogowski c o i l i n s e r t e d between the leads to the pinch was used to determine the change i n the discharge 23 c u r r e n t . The discharge current was measured by i n t e g r a t i n g the output of the Rogowski c o i l with a p a s s i v e RC i n t e g r a t o r with an RC time constant of 100 ys. T h i s arrangement as w e l l as a t y p i c a l c u r r e n t t r a c e i s shown i n .Figure 111-3. The c u r r e n t waveform was underdamped with a p e r i o d of 22 us. The pinch phase (the time at which the c u r r e n t s h e l l stops and much of the discharge c u r r e n t i s c o n f i n e d to the a x i s of the pinch) i s i n d i c a t e d by the dip i n the t r a c e . The Rogowski c o i l was c a l i b r a t e d by equating the t o t a l charge stor e d i n the c a p a c i t o r s to the i n t e g r a l of the f i r s t h a l f c y c l e of the current t r a c e . III-3 O p t i c a l system f o r l i n e p r o f i l e o b s e r v a t i o n s Line p r o f i l e s were measured by means of the arrangement shown i n F i g u r e I I I - 4 . L i g h t o r i g i n a t i n g between the t i p s of the viewing tubes was c o l l e c t e d by Lens 1, mounted on the end of the tube p r o j e c t i n g through the ground e l e c t r o d e and sent down t h i s tube to Lens 2 which focussed the l i g h t onto the entrance s l i t of the monochromator. The output s l i t of the monochromator was r e p l a c e d by an o p t i c a l m u l t i c h a n n e l analyzer or OMA. The OMA d e t e c t o r face i s d i v i d e d i n t o 500 i n d i v i d u a l p h o t o d e t e c t o r s , each with a width of 0.001". I t was t h e r e f o r e p o s s i b l e to observe anf e n t i r e l i n e p r o f i l e i n a s i n g l e shot. The p r o f i l e was s t o r e d i n d i g i t a l form by the OMA 1205A console and could be d i s p l a y e d on an o s c i l l o s c o p e or recorded on 2 4 5 ps/div PINCH CURRENT TRACE F i g u r e 111-3 : A) B) C i r c u i t f o r m e a s u r i n g the d i s c h a r g e c u r r e n t D i s c h a r g e c u r r e n t waveform 2 5 , : Quartz lenses : Front surface mirror S: Stop A L I G N M E N T L A S E R PjTO D I S C H A R G E C I R C U I T D I S C H A R G E V E S S E L ) } \ \ T O M A N O M E T E R M E T E R f S P E X I 8 0 0 M O N O C H R O M A T O R 1 2 0 5 D TO V A C U U M S Y S T E M T H E R M O C O U P L E V A C U U M G A U G E timii'iiiiiiii l II 11111II I I I P T ' I T O C O M P U T I N G C E N T R E COMP. C O N S O L E Figure III-4: Experimental arrangement for measuring 1ine p r o f i 1 es. 26 a chart r e c o r d e r . A l i n e to the u n i v e r s i t y computing centre was i n s t a l l e d i n order to permit the computer c a l i b r a t i o n and a n a l y s i s of data. Data s t o r e d i n the 1205A console was f i r s t read and s t o r e d i n the memory of a small minicomputer. T h i s data was l a t e r sent to the computing centre where i t was s t o r e d i n f i l e s . The a n a l y s i s of the data i s d e s c r i b e d i n Chapter VI. It was found that the s e n s i t i v i t y of the OMA was about an order of magnitude l e s s at u.v. wavelengths than i t was at v i s i b l e wavelengths. Thus, although p r o f i l e s of the helium l i n e s at 4686 A and 5876 A could be r e a d i l y observed, c o n s i d e r a b l e d i f f i c u l t y was encountered i n o b t a i n i n g the p r o f i l e of He II 3203. The pinch f i l l i n g p ressure and the l o c a t i o n of the tubes were d i c t a t e d by the requirement to make t h i s l i n e as b r i g h t as p o s s i b l e . The o p t i c s were also arranged to t r a n s f e r the maximum amount of l i g h t to the OMA d e t e c t o r . Lens 2 was chosen so that i t s e f f e c t i v e f-number was c l o s e to that of the c o l l i m a t i n g m i r r o r i n the monochromatbr. T h i s r e s u l t e d i n the use of a la r g e p a r t of the monochromatOr g r a t i n g and so optimized the r e s o l u t i o n of the instrument. Since the plasma l i g h t r e c e i v e d by a lens placed o u t s i d e the pinch v e s s e l would be c o l l e c t e d from only a very small s o l i d angle, Lens 1 (f. l . = 5 cm) was mounted on the end of the viewing tube to i n c r e a s e the accepted s o l i d angle. The use of t h i s lens r a t h e r than a plane quartz window 27 r e s u l t e d i n a l a r g e i n c r e a s e i n the amount of l i g h t r e a c h i n g the monochromatpr. 111-4 S y n c h r o n i z i n g the d i a g n o s t i c equipment to the discharge For the a x i a l plasma used i n t h i s i n v e s t i g a t i o n , plasma parameters were found to change on a time s c a l e of the order of 100 ns. To ensure that the plasma . c o n d i t i o n s changed l i t t l e during the p e r i o d of the o b s e r v a t i o n s , the OMA was gated by a 200 ns, negative going square p u l s e . Since the delay between the f i r i n g of the t h y r a t r o n u n i t and the s t a r t of the breakdown i n the p i n c h v e s s e l was about 6 ys, with a shot to shot j i t t e r of about 0.5 ys, the OMA gating pulse could not be synchronized to the discharge through the t h y r a t r o n u n i t . Instead, the OMA was synchronized d i r e c t l y to the d i s c h a r g e . T h i s was accomplished by the c i r c u i t shown i n F i g u r e 111-5. The o p e r a t i o n of the 1205A OMA console d i c t a t e d the a c t u a l time at which the pinch f i r e d . Charges accumulated on each of the 500 photodetectors during the time that the g a t i n g pulse was a p p l i e d to the 1205D d e t e c t o r head were read by the 1205A console. The photodetectors were read s e q u e n t i a l l y every 32.7 ms with a 384 ys dead-time between r e a d i n g s . The pinch was f i r e d and the d e t e c t o r head gated during t h i s dead time. T h i s was accomplished by g a t i n g u n i t #1. The simultaneous c l o s u r e of the 28 I205A OMA CONSOLE MANUAL SWITCH DEAD TIME PULSE GATING UNIT * | I205D DETECTOR HEAD THYRATRON UNIT _ U.V. LIGHT i ^ ^ S J SOURCE AT TRIGGER GAP ROGOWSKI CO I L RC 1NTEGRATOF TRIGGER UNIT J L DELAY IT OMA GATING PULSE OMA GATING UNIT J ~ L TRIG O CH I CH 2 TEK. 551 ~ i _ r MON PULSE »OV F i g u r e 111 -5 : T r i g g e r i n g a n d t i m i n g c i r c u i t l i n e p r o f i l e m e a s u r e m e n t s . f o r 29 manual f i r i n g switch and the r e c e p t i o n of the l e a d i n g edge of a dead-time pulse (from the DELINHD1 output of the OMA console) by g a t i n g u n i t #1 l e d to the f i r i n g of the t h y r a t r o n u n i t and the p i n c h . The r e s u l t i n g current waveform, as measured by the Rogowski c o i l and RC i n t e g r a t o r was then used to synchronize the g a t i n g of the d e t e c t o r head to the pinch d i s c h a r g e . This was accomplished through the t r i g g e r u n i t which sent a delayed pulse to the OMA ga t i n g u n i t when the discharge c u r r e n t reached a preset l e v e l . The current waveform and the OMA g a t i n g p u l s e were monitored on a two channel scope to determine the time at which g a t i n g o c c u r r e d . Shot to shot j i t t e r was l e s s than 50 ns. III-5 Measurement of temperatures Plasma temperatures were determined from the i n t e n s i t y r a t i o o f the l i n e s He II 4686 and He I 5876. The experimental arrangement i s shown i n Figure I I I - 6 . For these measurements two mono chromatqrs were used i n order to measure the i n t e n s i t i e s of both l i n e s i n a s i n g l e shot. M i r r o r 2T i n t h i s case, was a beam s p l i t t e r . The outputs of the p h o t o m u l t i p 1 i e r s were terminated with 880 ft at a two channel scope. The t h y r a t r o n u n i t was f i r e d manually f o r the temperature measurements. Timing was determined from the scope which was t r i g g e r e d e x t e r n a l l y by the cu r r e n t waveform (see F i g . I I I - 5 , lower h a l f ) . 30 ALIGNMENT LASER L j , , : Quart z lenses M • 50% beam s p l i t t e r M 3: Front s u r f a c e m i r r o r P j , P 2: Photo-m u l t i p l i e r s S : Stop TO DISCHARGE CIRCUIT I METER r I DISCHARGE V E S S E L TO MANOMETER TO (VACUUM SYSTEM THERMOCOUPLE VACUUM GAUGE \ M^ SPEX 1800 34m MONOCHROMATOR Pi I 1 SPEX 1700 3 4m MONOCHROMATOR gure I I I - 6 : Experimental arrangement f o r measuring temperatures. J 31 Alignment of the system was accomplished with the alignment l a s e r mounted on a 12* aluminum channel which served as an o p t i c a l bench. This channel could be moved h o r i z o n t a l l y , p e r p e n d i c u l a r to i t s length so as to keep the o p t i c s a l i g n e d when the tubes were moved r a d i a l l y . The vacuum system c o n s i s t e d of an o i l d i f f u s i o n and a roughing pump. P u r i t y grade helium was used as the f i l l i n g gas and the f i l l i n g pressure was monitored with a manometer and a thermocouple gauge. A l l important experimental parameters as w e l l as the s p e c i f i c a t i o n s of the experimental equipment are given i n Table III-^l",^ R esults of d e n s i t y and temperature measurements obtained using the apparatus d e s c r i b e d i n t h i s chapter are presented i n the f o l l o w i n g two chapters. 32 Table Discharge V e s s e l M a t e r i a l Dimensions E l e c t r o d e s e p a r a t i o n Vacuum System Mechanical pump D i f f u s i o n pump Thermocouple gauge Manometer F i l l i n g system va l v e s F i l l i n g gas Pumping speed Pump aperture Buse pressure Leak r a t e Discharge C i r c u i t High v o l t a g e supply C a p a c i t o r s E l e c t r o d e s 111 -1 pyr ex length=76 cm; o.d.=17 cm, i.d.=15 cm. 60 cm Welch Duo-Seal 1402, pumping speed=90 1/min at 100 u Hg CVC MC275-01, (4" o i l ) V a r i a n 801, 0-2 To r r 0-15 T o r r , contained d i b u t y l p h t h a l a t e (p=1.047 gm/cm~3) Saunders Edwards Speedivalve Edwards high vacuum i s o l a t i o n v a l v e 05961R helium ( p u r i t y grade) 99.995% pure =30 1/min at 0.3 Torr 1.5" at d i f f u s i o n pump <1 y Hg 7 u Hg/hour U n i v e r s a l V o l t r o n i c s BAL-22kV-35mA 5x10.3 uF, NRG 203 V i j " brass 33 Table III-1 (cont) Voltage measurement Inductance of c i r c u i t Conway micro-Ammeter and 25000 HVC M u l t i p l i e r type B 0.36 mH Opt i c s L, M2 Tubes 8 mm, f6.3, f.l.=5 cm (quartz) 1.5", f l . 7 , f.l.=6.3 cm (quartz) 1", f 4 , f . l . = 10 cm ( g l a s s ) =50% beam s p l i t t e r ( g l a s s ) length=70 cm, o.d.=8 mm i.d.=6 mm (quartz) D i a g n o s t i c Equipment Monoclvromators P h o t o m u l t i p l i e r s P l P2 Termination Risetimes SPEX 1800 3/ it m, f6.8 blazed at 7500 A, > d i s p e r s i o n 10 A/mm SPEX 1700 3 / 4 m, f6.8 biased at 1 ym , d i s p e r s i o n 10 A/mm RCA 031034-01 (-1600 V) P h i l i p s 150CVP (-1100 V) 880 n 0.1 Us O p t i c a l M u l t i c h a n n e l Analy i e r S u p p l i e r Mode 1 Detector R e s o l u t i o n Number of channels P r i n c e t o n A p p l i e d Re-search 1205A 1205D 39 channels/mm 500 O s c i l l o s c o p e P l u g - i n s T e k t r o n i x Type 551 Type 1A1 r i s e t i m e 10 ns Table I I I - l (cont.) Experimental Conditions Charging voltage F i l l i n g pressure Discharge period Time of pinch phase Time of observations Maximum current * e T -1-2 kV 300 mTorr 22 us 4 us after breakdown 0.75 us after pinch ph 71 kA (6.1±0.6)xio; 4.0±0.4 eV , 2 3 m - 3 35 CHAPTER IV DENSITY MEASUREMENTS In this chapter the theory of Stark broadening of isolated spectral lines i s presented. This theory serves as the basis for the density measurements presented later in the chapter. The techniques employed to determine the electron density are discussed and results are presented for the uniformity and time behavior of the axial plasma,;, as well as for the effect of the l i m i t e r tubes on the plasma. IV-1 Stark broadening of isolated lines Isolated lines (see Chapter II) are broadened primarily by electron impacts. Ion c o l l i s i o n s are much less r important and usually result in very small corrections to the impact p r o f i l e . The ion broadening i s usually quasi-s t a t i c for most laboratory plasmas and can generally be treated by assuming that only quadratic Stark broadening is important although in some cases the effects of quadrupole interactions or linear Stark broadening may become s i g n i f i c a n t . Generally the entire l i n e p r o f i l e can be found by convoluting the electron impact p r o f i l e s with the q u a s i - s t a t i c , quadratic Stark effect p r o f i l e s for the ion broadening. The p r o f i l e s depend on two dimensionless parameters: A (a function of the electron 36 d e n s i t y ) , which i s a measure of the r e l a t i v e importance of i on broadening, and R (a f u n c t i o n of the e l e c t r o n d e n s i t y and temperature), which i s a measure of Debye s h i e l d i n g ^and i o n - i o n c o r r e l a t i o n s . For values of A between 0.05 and 0.5 and f o r R<0.8,Griem (1974) has given the f o l l o w i n g e x p r e s s i o n f o r the h a l f width h a l f maximum (HWHM) of an i i s o T a t e d l i n e " t o t a l = w + 1.75A(l-0V75R)w (4-1) where w i s the e l e c t r o n impact HWHM (a f u n c t i o n of the e l e c t r o n d e n s i t y and temperature). Values of w, A, and R are given by Griem. C o r r e c t i o n s to 4-1 to account f o r m u l t i p l e i o n i z a t i o n had to be made before i t could be used to f i n d the e l e c t r o n d e n s i t y . The e f f e c t of i o n broadening i s o f t e n expressed i n terms of the normal f i e l d s t r e n g t h , F 0 , which f o r the case of a plasma c o n t a i n i n g only s i n g l y i o n i z e d i o n s , i s given by: F 0 = 2 ' 6 1 eN 2 / 3 (4-2) For a helium plasma c o n t a i n i n g both s i n g l y and doubly i o n i z e d i o n s , the normal f i e l d s t r e n g t h becomes: F 0 = Foi + F 0 2 = l^ f-J- [ e N ^ ^ e N ? / 3 ] (4-3) where N^and a r e t n e number d e n s i t i e s of s i n g l y and 37 doubly i o n i z e d ions r e s p e c t i v e l y . Since N g = Nj+2N 2, 4-3 can be r e w r i t t e n as: N / 3+2N / 3 2 / , fil 2/ F q = 2^61_ _ J 2 e N / 3 = 2^61_ / 3 ( 4 . 4 ) 4 7 r E ° ( N i + 2N 2) 7 3 6 4 i r e ° e f f 6 N 1 / 3 + 2 N 2 / 3 where Q = a/ i s the e f f e c t i v e ion charge, e f f (N 1 +2N 2) / 3 Since i o n broadening i n i s o l a t e d l i n e s occurs through the q u a d r a t i c Stark e f f e c t , the value of A i n 4-1 should 3 . / . be m u l t i p l i e d by Q e £ £ to account f o r m u l t i p l e i o n i z a t i o n . Q g £ £ was c a l c u l a t e d using the Saha-Boltzmann r e l a t i o n s assuming t o t a l l o c a l thermodynamic e q u i l i b r i u m and the r e s u l t was used i n determining the e l e c t r o n d e n s i t y . IV-2 Experimental d e t a i l s The study of Stark broadened p r o f i l e s of s p e c t r a l l i n e s has long been used as a method f o r the d e t e r m i n a t i o n of e l e c t r o n d e n s i t i e s . The accuracy of the method depends on the c e r t a i n t y i n the t h e o r e t i c a l p r o f i l e s as well as the accuracy of the experimental methods. Since the t h e o r e t i c a l p r o f i l e s of some i s o l a t e d l i n e s are known a c c u r a t e l y , an .isolated l i n e was chosen i n t h i s i n v e s t i g a t i o n to serve as the r e f e r e n c e f o r d e n s i t y measurements. r 121 Previous s t u d i e s 1 J of helium plasmas i n a s i m i l a r pinch have used the He I l i n e at 3889 A f o r t h i s purpose. It was found, however, that f o r the a x i a l plasma s t u d i e d i n t h i s i n v e s t i g a t i o n , the i n t e n s i t y of He I 3889 was too 38 small to permit accurate measurements of i t s p r o f i l e . A probable cause of t h i s low i n t e n s i t y was the OMA's poor s e n s i t i v i t y at s h o r t e r wavelengths. As a s u b s t i t u t e , the He I l i n e at 5876 A was emoloyed i n the d e n s i t y measurements. T h i s l i n e i s a m u l t i p l e t but i t s p r o f i l e i s a c c u r a t e l y p r e d i c t e d . It was found that the i n t e n s i t y of He II 3203 was s u f f i c i e n t f o r p r o f i l e measurements only along the a x i s of the p i n c h . Therefore a l l o b s e r v a t i o n s of plasma c o n d i t i o n s were made with the l i m i t e r tubes l o c a t e d along 1 the pinch a x i s . Preston (1974) had found that the best c o n d i t i o n s f o r s p e c t r o s c o p i c o b s e r v a t i o n s from the p o i n t of view of plasma u n i f o r m i t y occurred at a p o s i t i o n 2.7 cm from the a x i s , but i t was found impossible to observe He II 3203 at t h i s p o s i t i o n . T h i s was unfortunate s i n c e the a x i a l plasma i s not as uniform and v a r i e s more r a p i d l y with time than the plasma near the r e g i o n advocated by Preston. Line p r o f i l e s of He I 5876 were obtained f o r v a r i o u s t u b e . p o s i t i o n s and se p a r a t i o n s using the apparatus d e s c r i b e d i n the previous chapter. The OMA was operated i n gated mode and the time of o b s e r v a t i o n was kept f i x e d at 0.75 us a f t e r the pinch phase. The discharge v e s s e l was evacuated and r e f i l l e d to 0.3 T o r r before each shot. At l e a s t three shots were f i r e d without r e f i l l i n g before any : data were taken. The measured p r o f i l e s were smoothed 39 and then c o r r e c t e d f o r d i s t o r t i o n s i n d i s p e r s i o n and i n t e n s i t y . The system was c a l i b r a t e d f o r wavelength d i s t o r t i o n s as well as f o r the nonuniform response of the OMA by using standard sources (see Chapter V I ) . C o r r e c t i o n s to the measured p r o f i l e s were performed using the programs d e s c r i b e d i n Appendix 3. The continuum l e v e l was found by s e t t i n g the monochromator to wavelengths 50 A above and 50 A below the l i n e centre and o b t a i n i n g f a r wing p r o f i l e s . The wings were then matched to an average main p r o f i l e and the continuum l e v e l estimated. A complete p r o f i l e of He I 5876 i s shown i n Figure IV-1. FWHM's were measured f o r each of the f i n a l c o r r e c t e d p r o f i l e s and d e n s i t i e s determined from 4-1 and Griem's data. IV-3 I n t e r a c t i o n s of the tubes with the plasma It was expected that the i n t r o d u c t i o n of quartz tubes i n t o the pinch v e s s e l would p e r t u r b the plasma. The magnitude of the p e r t u r b a t i o n depends, among other t h i n g s , on the s c a l e s i z e of the plasma and the r a t e s of p a r t i c l e d i f f u s i o n . Since these parameters are expected to vary i n time and with p o s i t i o n i n s i d e the p i n c h , i t i s l i k e l y that the p e r t u r b a t i o n s due to the tubes are also v a r i a b l e . An experimental measurement of the e f f e c t of the tubes was t h e r e f o r e performed. The tubes were l o c a t e d along the a x i s of the pinch and t h e i r s e p a r a t i o n was v a r i e d keeping the midpoint between t h e i r t i p s c o i n c i d e n t He I 5 8 7 6 T e =4 .0±0 .4eV N e= ( 6 . 1 * 0 . 6 ) * I O ^ m ' - 2 ' o ' 6 1 „ . W A V E L E N G T H ( A ) F i g u r e 1 V - 1 : C o m p l e t e p r o f i l e o f He I 5 8 7 6 , 41 with the centre of the p i n c h . The r e s u l t s are shown i n Figure IV-2. Each p o i n t was obtained from the average of three shots. The e r r o r bars represent standard d e v i a t i o n s i n any measurement. The s c a t t e r i n the data does not permit any strong c o n c l u s i o n s to be drawn, but i t i s apparent from these r e s u l t s that the tubes d i d i n f l u e n c e the plasma column. For tube s e p a r a t i o n s of l e s s than 4 cm,^the measured e l e c t r o n d e n s i t y was about 20% l e s s than f o r tube s e p a r a t i o n s of g r e a t e r than 8 cm. It i s a l s o apparent that f o r tube s e p a r a t i o n s of l e s s than 4 cm, no d r a s t i c changes i n the measured e l e c t r o n d e n s i t y occurred with decreased s e p a r a t i o n . This behavior can probably be e x p l a i n e d by the simple model i n which each of the tubes p e r t u r b s the plasma such that there i s a r e g i o n of uniform, l e s s dense plasma p r o j e c t i n g at l e a s t 2 cm from the end of each tube. When the tubes are separated by more than 8 cm, regions of unperturbed denser plasma are observed and the r e s u l t a n t p r o f i l e i s a combination of that due to t h i s unperturbed plasma as well as that due to the plasma l o c a t e d near the tubes. For tube s e p a r a t i o n s of l e s s than 4 cm, the perturbed r e g ions o v e r l a p and a r e g i o n of uniform plasma i s seen between the tubes. Any a d d i t i o n a l end e f f e c t s are l i k e l y s m a l l e r than 0.5 cm. 9 8 + 7 + T 6 + 5 - + N e ( X I 0 2 3 m " 3 ) ^ — — i 1 1 1 — — ! • j + 16 6 8 10 T U B E S E P A R A T I O N ( c m ) 12 14 Figure IV-2 : Effect of the l i m i t i n g tubes on the electron density 43 IV-4 L o n g i t u d i n a l u n i f o r m i t y of the plasma column In the previous s e c t i o n i t was assumed that any changes i n the measured e l e c t r o n d e n s i t y were due to p e r t u r b a t i o n s by the tubes and not due to a c t u a l v a r i a t i o n s of the e l e c t r o n d e n s i t y with p o s i t i o n along the a x i s . The u n i f o r m i t y of the plasma column w i l l now be d i s c u s s e d . Since i t was found t h a t the plasma between the tubes was l i k e l y uniform f o r tube s e p a r a t i o n s of l e s s than 4 cm, the tubes were moved along the axis of the pinch with a constant s e p a r a t i o n of 4'4£m i n order to study the u n i f o r m i t y of the plasma column. The c e n t r a l 12 cm were st u d i e d i n t h i s way. The r e s u l t s are presented i n Figure IV-3. Again the p o i n t s r e p r e s e n t the average of three shots and the e r r o r bars are standard d e v i a t i o n s . It i s apparent from these r e s u l t s t h a t , w i t h i n the u n c e r t a i n t y of the measurements, the plasma column along the c e n t r a l 12 cm of the a x i s was uniform with r e s p e c t to e l e c t r o n d e n s i t y . T h i s c o n c l u s i o n , of course, assumes^ that the e f f e c t of the tubes on the plasma i s to decrease the e l e c t r o n d e n s i t y u n i f o r m l y . IV-5 Radial u n i f o r m i t y The u n i f o r m i t y of the a x i a l plasma i n the r a d i a l d i r e c t i o n i s a l s o of i n t e r e s t . According to Preston (1974), who s t u d i e d the pinch dynamics at a f i l l i n g p ressure of 4 T o r r , l a r g e r a d i a l d e n s i t y g r a d i e n t s are r p r e s e n t at 9 - 4 -8 - f 7 + 6 + 5 + N e ( X I 0 2 3 m - 3 ) + - 4 - H 2 C e n t r e 2 P O S I T I O N O F T U B E S ( c m ) ( t u b e s 4 c m a p a r t ) + 6 .Negat ive " E l e c t r o d e Figure IV-3: Longitudinal uniformity of the axial electron density. 6 G r o u n d E l e c t r o d e 45 the a x i s when the p r e c u r s o r shock reaches the a x i s . The a x i a l plasma was found to begin d i f f u s i n g about 1 ys a f t e r the pinch l e a d i n g to smaller r a d i a l d e n s i t y g r a d i e n t s i n the v i c i n i t y of ifche a x i s . Since the obs e r v a t i o n s i n t h i s i n v e s t i g a t i o n were c a r r i e d out i n 0.3 Torr helium, d i f f u s i o n r a t e s i would be expected to be f a s t e r than i n Preston's case and the plasma at 0.75 ys may be expected to be q u i t e uniform. Although no d i r e c t measurements were made of the plasma c h a r a c t e r i s t i c s o f f the a x i s , r e s u l t s f o r the u n i f o r m i t y of the plasma i n the r a d i a l d i r e c t i o n can be i n f e r r e d from i n t e r f e r m e t r i c measurements. An attempt was made to determine the e l e c t r o n d e n s i t y using a Fabry-Perot i n t e r f e r o m e t e r to measure the changing r e f r a c t i v e index of the v a r i a b l e d e n s i t y a x i a l plasma. The i n t e r f e r o m e t e r was s i m i l a r i n c o n s t r u c t i o n to that used by Preston (1974). The i n t e r f e r o m e t e r had a c o n c e n t r i c c a v i t y with the plasma l o c a t e d at the c e n t r e . The beam from the alignment l a s e r was used as the probing beam and the c a v i t y was formed between the output m i r r o r of the alignment l a s e r and a 50% d i e l e c t r i c m i r r o r . A monochromator was used to s e l e c t the lase,r wavelength from the broad band of plasma l i g h t coming from the pinch and a p h o t o m u l t i p l i e r was used to count the f r i n g e s . Fringes could be detected on a x i s only at times g r e a t e r than 4 ys a f t e r the pinch phase.' At e a r l i e r times no 46 f r i n g e s could be seen due to a d r a s t i c a t t e n u a t i o n of the probing beam. Medley (1968) a l s o observed t h i s e f f e c t f o r an argon a x i a l plasma at f i l l i n g p ressures of 0.1 and 1.0 T o r r . At higher f i l l i n g p r essures f r i n g e s could e a s i l y be detected on ax i s during the pinch phase and i ^ - -d e n s i t i e s s i m i l a r to those obtained by Preston were found. An attempt was al s o made to detect f r i n g e s with a Michelson i n t e r f e r o m e t e r i n which the i n t e n s i t y of the r e f e r e n c e beam could be adjusted to compensate f o r a moderate l o s s f of i n t e n s i t y i n the probing beam but almost complete l o s s of the beam d i d not allow u s e f u l r e s u l t s to be obt a i n e d . T h i s a t t e n u a t i o n was thought to be due to r e f r a c t i o n of the beam out of the c a v i t y by r a d i a l g r a d i e n t s i n the e l e c t r o n d e n s i t y but a c a l c u l a t i o n of the r e q u i r e d g r a d i e n t s y i e l d e d a r e s u l t ( 6 x l 0 2 l t m"3/cm) that was much l a r g e r than a n t i c i p a t e d . The d e s t r u c t i o n of wavefront coherence i n the probing beam, however, can r e s u l t from much smal l e r d e n s i t y g r a d i e n t s and can lead to the l o s s of i n t e r f e r e n c e and the a t t e n u a t i o n of the probing beam. A lower l i m i t of the d e n s i t y g r a d i e n t s r e q u i r e d to cause the l o s s o f wavefrortt coherence can be c a l c u l a t e d . I f a beam of r a d i u s , a, passes through a r e g i o n p o s s e s s i n g r a d i a l g r a d i e n t s i n r e f r a c t i v e index, s i g n i f i c a n t l o s s of phase i n f o r m a t i o n occurs i f the inner p a r t of the beam t r a v e l s one h a l f wavelength ffarther than the outer p a r t : 47 (n 0-n a)& = X/2 (4-5) where ii j i s the r e f r a c t i v e index at the beam a x i s , n i s u •.. ' a the r e f r a c t i v e index at r a d i u s , a, 5. i s the length of the plasma column, and X i s the wavelength of the probing beam. To f i r s t order 4-5 can be w r i t t e n as: Vna! = X/2 (4-6) S u b s t i t u t i n g the values a p p r o p r i a t e to t h i s study v(a=0.3 cm, 9. = 10 cm, and X=6328 A) we f ind Vn=l. Ix 10' 5 cm"{. For the He-Ne l a s e r l i n e at 6328 A the r e l a t i o n between the r e f r a c t i v e index and the e l e c t r o n d e n s i t y i s n=1-1.79xl0~ 2 8N . ' e Therefore the minumum gr a d i e n t i n e l e c t r o n d e n s i t y r e q u i r e d to cause complete l o s s of wave f r o n t coherence i s approximately 6 x l 0 2 2 m~3/cm. This g r a d i e n t should be compared to the e l e c t r o n d e n s i t i e s encountered i n t h i s study of 6 x i o 2 3 m~3. I f the a c t u a l g r a d i e n t s were of about the same s i z e as those p r e d i c t e d above, the plasma column observed i n the s p e c t r o s c o p i c s t u d i e s can be assumed to be almost uniform over i t s diameter. This ! i s e s p e c i a l l y true s i n c e the ob s e r v a t i o n s were made a f t e r the pinch phase and the plasma had s t a r t e d to d i f f u s e . IV-6 Time dependence of the plasma Tiirie v a r i a t i o n s i n the i n t e n s i t y of l i g h t emitted by; the plasma were found to occur on a time s c a l e of about 100 ns. Two peaks of i n t e n s i t y occurred f o r the 48 a x i a l plasma during the f i r s t h a l f c y c l e i n the discharge c u r r e n t . The time v a r i a t i o n s during the f i r s t peak were more r a p i d than those during the second peak and d i s t o r t i o n s i n the observed l i n e p r o f i l e s during the f i r s t peak i n d i c a t e d a very nonuniform plasma column. Therefore o b s e r v a t i o n s were performed on the plasma that occurred during the second i n t e n s i t y peak. The time of o b s e r v a t i o n was chosen to be near the time of peak i n t e n s i t y s i n c e changes i n the plasma parameters were expected to be small over the 200 ns o b s e r v a t i o n time. P r o f i l e s of He I 5876 were obtained f o r times of 100 ns before and a f t e r the time of i n t e r e s t i n order to determine the time v a r i a t i o n s i n the e l e c t r o n d e n s i t y . The tubes were l o c a t e d 2 cm towards the hot e l e c t r o d e and t h e i r s e p a r a t i o n was 4 cm. The r e s u l t s were: Time (us a f t e r pinch) Density ( x l O 2 3 m~ 3) 0.65 5.4±0.6 , 0.7 5 6,1±0.6 0.85 7.6±0.2 The d e n s i t y was t h e r e f o r e i n c r e a s i n g s l i g h t l y during the time of o b s e r v a t i o n and hence, the p r o f i l e s obtained f o r He I 5876 as well as the He II l i n e s at 3203 A and 4686 A were l i k e l y somewhat d i s t o r t e d . In t h i s chapter i t has been shown that the l i m i t e r tubes p e r t u r b the plasma by lowering the e l e c t r o n d e n s i t y 49 i n t h e i r v i c i n i t y . For tube s e p a r a t i o n s of l e s s than 4 cm a uniform plasma column can be observed along the c e n t r a l 12 cm of the a x i s . N o n u n i f o r m i t i e s i n the observed plasma a r i s e from d e n s i t y g r a d i e n t s i n the r a d i a l d i r e c t i o n as well as temporal changes. In the next chapter the r e s u l t s of s i m i l a r i n v e s t i g a t i o n s of the e l e c t r o n temperature are presented. 50 CHAPTER V TEMPERATURE MEASUREMENTS Experimental d e t a i l s of the temperature measurements as well as r e s u l t s of these s t u d i e s are presented i n t h i s chapter. These r e s u l t s as we l l as those of the preceeding chapter i l l u s t r a t e the plasma c o n d i t i o n s present along the discharge axis soon a f t e r the pinch phase. Before d e s c r i b i n g the experimental d e t a i l s , the theory r e l e v a n t to the temperature measurements i s f i r s t presented. V - l Theory For a plasma i n some form of thermal e q u i l i b r i u m ^ the r e l a t i v e p o p u l a t i o n s of atoms or ions i n two d i f f e r e n t e x c i t e d s t a t e s can be p r e d i c t e d t h e o r e t i c a l l y . Since the i n t e n s i t y r a t i o of two s p e c t r a l l i n e s depends, among other t h i n g s , on the r e l a t i v e p o p u l a t i o n s o f the upper l e v e l s of the l i n e s , i t i s p o s s i b l e to determine the temperature of a plasma by measuring the i n t e n s i t y r a t i o of two l i n e s . For l i n e s o r i g i n a t i n g from atoms or ions i n the same i o n i z a t i o n s t a t e t h i s method i s r a t h e r i n s e n s i t i v e due to the small s e p a r a t i o n i n energy between the upper l e v e l s of the two l i n e s . For l i n e s o r i g i n a t i n g from atoms or ions i n s u c c e s s i v e i o n i z a t i o n s t a t e s , the s e p a r a t i o n i n energy between the upper l e v e l s i s much l a r g e r due to the i o n i z a t i o n energy and the r a t i o o f the 51 l i n e i n t e n s i t i e s depends s e n s i t i v e l y on the temperature. In order f o r a temperature to be a s c r i b e d to a c e r t a i n l i n e i n t e n s i t y r a t i o , i t i s necessary that the plasma be i n a form of thermal e q u i l i b r i u m . A concept commonly used i n plasma spectroscopy i s that of l o c a l thermal equi1ibrium (LTE). When a plasma i s i n a s t a t e of LTE the p o p u l a t i o n d e n s i t i e s of the v a r i o u s quantum s t a t e s are i d e n t i c a l to those f o r a system i n complete thermal e q u i l i b r i u m which has the same temperature and mass d e n s i t y as the a c t u a l system. The temperature assigned to the system i s that of the species dominating the r e a c t i o n r a t e s which i n most cases i s the e l e c t r o n s . Therefore the plasma temperature i s o f t e n r e f e r r e d to as the e l e c t r o n temperature. When c o l l i s i o n a l processes with e l e c t r o n s from a Maxwellian d i s t r i b u t i o n dominate over other r e a c t i o n processes i t can be expected that LTE w i l l h o l d . Since c o l l i s i o n a l c r o s s e c t i o n s i n c r e a s e r a p i d l y with p r i n c i p a l quantum number while r a d i a t i v e decay r a t e s decrease, LTE w i l l hold only f o r those s t a t e s with t h e i r p r i n c i p a l quantum numbers above a c e r t a i n v a l u e . Systems f o r which t h i s a p p l i e s are s a i d to be i n a s t a t e of p a r t i a l LTE. Using the c r i t e r i o n that the c o l l i s i o n a l d e e x c i t a t i o n r a t e i s ten times the r a d i a t i v e d e e x c i t a t i o n r a t e , Griem (1964) has estimated the e l e c t r o n d e n s i t y r e q u i r e d f o r the p o p u l a t i o n of the l e v e l with p r i n c i p a l quantum number, n, to be w i t h i n 10% of i t s value c a l c u l a t e d 52 with Saha-Boltzmann f a c t o r s from the number d e n s i t i e s of atoms i n higher l e v e l s or higher s t a t e s of i o n i z a t i o n : 6 N > 2 x l 0 2 - -r~~ (kT ^' 1 m"3 ^"^ n 1 ' 2 6 where Z - l i s the charge on the ion and kT g i s the e l e c t r o n temperature i n e l e c t r o n V o l t s . For the l i n e s s t u d i e d i n t h i s i n v e s t i g a t i o n the r e q u i r e d e l e c t r o n d e n s i t i e s are: He I 5876 ( 3 d - 2 p ) N e > 3 . 5 x l 0 m 3 2 1 He II 4686 ( 4 f - 3 d ) N > 2 . 0 x l 0 m 3 These values were c a l c u l a t e d f o r T =4 .0 eV which i s the e temperature encountered i n t h i s study. Complete LTE r e q u i r e s a much l a r g e r d e n s i t y . For an o p t i c a l l y t hin' helium plasma at 4 eV the r e q u i r e d d e n s i t y i s about 2 5 1 . 5 x 1 0 m 3 . In order to estimate the plasma temperature i t must be p o s s i b l e to p r e d i c t the r a t i o of the d e n s i t i e s of the two upper l e v e l s of the two s p e c t r a l l i n e s . U n f o r t u n a t e l y , p a r t i a l LTE f o r the two upper l e v e l s i m p l i e s only that each of the upper l e v e l s i s i n e q u i l i b r i u m with a l l higher l e v e l s i n the same i o n i z a t i o n s t a t e s as well as the ground l e v e l s i n the next higher i o n i z a t i o n s t a t e s . I t does not imply, f o r i n s t a n c e , that the He II ground s t a t e i s i n e q u i l i b r i u m with the f o u r t h e x c i t e d s t a t e of the He II i o n . Therefore complete LTE i s u s u a l l y r e q u i r e d at l e a s t f o r the higher i o n i z a t i o n s t a t e . F o r t u n a t e l y , i f 53 the plasma i s o p t i c a l l y t h i c k towards the Lyman a resonance l i n e o f He I I , the e l e c t r o n d e n s i t y r e q u i r e d f o r complete LTE, can be reduced by an order of magnitude. T h i s occurs because the ab s o r p t i o n of resonance photons r e s u l t s i n an a d d i t i o n a l c o n t r i b u t i o n to the e x c i t a t i o n processes and so the e f f e c t i v e r a d i a t i v e p o p u l a t i o n r a t e of the ground s t a t e from the upper s t a t e of the resonance l i n e i s reduced. Mewe (1966) has c a l c u l a t e d the p r o b a b i l i t i e s t h a t a Lyman a photon w i l l escape from the plasma and has used these (Z) p r o b a b i l i t i e s to estimate the values of the f a c t o r s , b^ , which are d e f i n e d as the r a t i o between the a c t u a l d e n s i t y of a s t a t e with p r i n c i p a l quantum number, p, i n an ion of charge, Z - l , and the d e n s i t y p r e d i c t e d by the Saha-Boltzmann r e l a t i o n s . The r a t i o of the i n t e n s i t i e s of a H e l l l i n e , a, with an upper l e v e l p r i n c i p a l quantum number, p, and a He I l i n e , b, with an upper l e v e l p r i n c i p a l quantum number, q, i s then given by: —= -thrc - 7 T T exp ( I — - | 1 (5-2) ' b b<»> ( , £ / » » ) „ ^ q where g i s the s t a t i s t i c a l weight of the lower l e v e l , f the o s c i l l a t o r s t r e n g t h averaged over the f i n e s t r u c t u r e (31 (21 components, and X the wavelength. n ' n i *-s t n e r a t i o of the d e n s i t i e s of completely i o n i z e d ions to s i n g l y i o n i z e d ions i n the ground s t a t e and i s given by; n ( 3 ) 10 6 2 g ( 3 ) 1 12 mkT \ 3 / 2 / - P ( 2 ) ^  (  k T e Y / 2 f-*\l>\ 54 (5-3) r 2") where E v ;=52.5 i s the i o n i z a t i o n energy of the ground l c s t a t e of He I I . Combining 5-2 and 5-3 and i n s e r t i n g the r e l e v a n t values f o r the 1ines . s t u d i e d : He II 4686 p=4, g=18, f=0.842 He I 5876 p = 3, g=9, f=0.623 the i n t e n s i t y r a t i o of these l i n e s i s obtained: b4 < k V /-52.5\ I 1 + 6 8 6 n B k ^ 2 ^ f k T 1 3 ^ 2 . 3 . 2 x l 0 2 8 D 4 CkT e)  T „„ /o\ exp (5-4) 3 Figure V - l shows the r e s u l t s f o r the e l e c t r o n d e n s i t i e s 2 3 2 3 2<t 1.28x10 , 6.1x10 , and 1.28x10 m 3 a f t e r i n t e r p o l a t i n g the values of b^ 2^ , b ^ 1 ^ , and b^ 2^ given i n Mewe's t a b l e s . The v a l u e s of b^ 2^ and b^ 1^ are approximately u n i t y s i n c e p a r t i a l LTE holds f o r the upper l e v e l s . C o r r e c t i o n s , (2) however, must be a p p l i e d to b£ ' to account f o r the escape of Lyman a photons. E r r o r s i n the f i n a l r a t i o s are mainly (Z) due to e r r o r s i n the f a c t o r s , b^ . Mewe estimates the accuracy of the f i n a l temperatures to be about 10 to 15%. For high e l e c t r o n d e n s i t i e s (=1021* m"3) the u n c e r t a i n t y i n the f i n a l r e s u l t i s somewhat s m a l l e r . It should be noted that Mewe's r e s u l t s are f o r a steady, homogeneous helium plasma. While the plasma s t u d i e d i n t h i s i n v e s t i g a t i o n can probably be assumed to be f a i r l y 55 2.5 3.0 35 4.0 4.5 5.0 T e (eV) F i g u r e V - l : 11+6 86 / 1 5 876 a s a f u n c t i o n o f e l e c t r o n t e m p e r a t u r e ( f r o m M e w e ) . ( d r e f e r s t o t h e l e n g t h o f t h e p l a s m a c o l u m n ) I 56 homogeneous, i t can not be assumed to be steady. Changes i n the plasma c o n d i t i o n s o c c u r r e d with a time s c a l e of about 100 ns. It i s t h e r e f o r e important to c o n s i d e r whether or not the plasma s a t i s f i e d the c r i t e r i o n of the theory. The e q u i l i b r a t i o n time f o r p a r t i a l LTE above a s t a t e with p r i n c i p a l quantum number, n, i s e s s e n t i a l l y the i n v e r s e of the e x c i t a t i o n r a t e . T h i s time i s given by (Griem 1964) r , 4 . 5 xl 0 1 3Z 3 x 2 " 1 = — ( — — | exp( — 1 seconds (5-5) n HN / k T e y / * e x / 2 Z 2 E H \ \ Z 2 E H / e X P \ n 3 k T e / where E„ i s the i o n i z a t i o n p o t e n t i a l of hydrogen. For n the two l i n e s used i n t h i s study, T * = 9 . 6 x l u ~ 1 3 seconds (He II 4686) and T°=6.4X10' 1 3 seconds (He II 5876) f o r a temperature of 4.0 eV and a d e n s i t y of 6 . 1 x l 0 2 3 m~3. The plasma s t u d i e d was t h e r e f o r e always i n p a r t i a l LTE during the experiments. T o t a l LTE, however, was not always s a t i s f i e d . For a temperature of 4.0 eV and a d e n s i t y of 6 . 1 x l 0 2 3 m~3 i n a helium plasma, the e q u i l i b r a t i o n time f o r complete LTE i s approximately 0.5 ys. T h i s r e s u l t i s of the same order as the time s c a l e of the experimental plasma. Therefore complete LTE l i k e l y d i d not e x i s t at a l l times of experimental i n t e r e s t , but due to the l o g a r i t h m i c r e l a t i o n between the l i n e i n t e n s i t y r a t i o and the temperature, e r r o r s i n the temperature were l i k e l y s m a l l . 5 7 V-2 Experimental d e t a i l s Line i n t e n s i t i e s were measured using the equipment de p i c t e d i n Figure 111-6. Photographs of the i n t e n s i t y t r a c e s of the l i n e s He I 5876 and He II 4686, s i m i l a r to those shown i n Figure V-2, were taken and measured to determine the l i n e i n t e n s i t y r a t i o s . The monochromator-p h o t o m u l t i p l i e r arrangements were c a l i b r a t e d f o r s p e c t r a l I p s / d i v T Time of interest Figure V-2: T y p i c a l p h o t o m u l t i p l i e r t r a c e s Top: He II 4686 Bottom: He I 5876 and i n t e n s i t y responses. A movie lamp tungsten c o i l was used as a black body source to f i n d the s p e c t r a l response of the o p t i c a l system. C o r r e c t i o n s f o r the e m i s s i v i t y of tungsten were made using the data of deVos (1954). The 58 movie lamp was placed between the discharge v e s s e l and the stop, S, and the response of each of the p h o t o m u l t i p l i e r s was found f o r monochromator s e t t i n g s of 4686 A and 5876 A. The i n t e n s i t y response was found by s e t t i n g both monochromators at 5876 A and measuring the p h o t o m u l t i p l i e r outputs both with the movie lamp and with the a c t u a l pinch r a d i a t i o n as the l i g h t source. In t h i s way, the d i f f e r e n c e between the r e l a t i v e i n t e n s i t i e s r e a c h i n g the two monochromators i n the c a l i b r a t i o n and i n the a c t u a l experiment were accounted f o r . 2.9 mm wide e x i t s l i t s were used i n the measurement of t o t a l l i n e i n t e n s i t i e s . From experimental p r o f i l e s o f the two l i n e s , c o r r e c t i o n s were c a l c u l a t e d f o r the p a r t s o f the p r o f i l e s cut o f f by the s l i t s and f o r the u n d e r l y i n g c o n t i n u a . V-3 I n t e r a c t i o n of the tubes with the plasma As i n the case of the e l e c t r o n d e n s i t y measurements, i t was expected that the i n t r o d u c t i o n of quartz tubes i n t o the discharge v e s s e l would a f f e c t the e l e c t r o n temperature. The e f f e c t of the tubes on the measured e l e c t r o n temperature was t h e r e f o r e s t u d i e d . The tubes were l o c a t e d along the pinch a x i s and t h e i r s e p a r a t i o n v a r i e d keeping the midpoint between t h e i r t i p s c o i n c i d e n t with the centre of the discharge v e s s e l . The r e s u l t s are shown i n Figure V-3. Each p o i n t was obtained from the average of four shots and the er.r_o.r__bar.s__r_e.pr_e.sent_-Standard H — 1 1- 1 1 f -6 8 10 12 14 16 TUBE SEPARATION (cm) V-3: Effect of the limiter tubes on the electron temperature, 60 d e v i a t i o n s i n any measurement. As i n the case of the d e n s i t y measurements (see s e c t i o n IV-3), the e f f e c t of the tubes on the temperature i s to lower the temperature i n t h e i r v i c i n i t y . For tube s e p a r a t i o n s of l e s s than '4 cm the temperature was s i g n i f i c a n t l y lower than f o r tube s e p a r a t i o n s of g r e a t e r than 8 cm. the measured temperature was a l s o found to vary very l i t t l e with tube s e p a r a t i o n when the s e p a r a t i o n was decreased below 4 cm or i n c r e a s e d above 8 cm. In Figure IV-4 the raw, un c o r r e c t e d r e s u l t s f o r the i n t e n s i t i e s of the l i n e s He I 5876 and H e l l 4686 are presented. While these r e s u l t s a c t u a l l y give i n f o r m a t i o n only on the number d e n s i t i e s of r a d i a t o r s i n the two upper s t a t e s , they a l s o give a rough i n d i c a t i o n of the number d e n s i t i e s of helium atoms and s i n g l y i o n i z e d helium i o n s . The i n t e n s i t y of He II 4686 was found to i n c r e a s e l i n e a r l y with tube s e p a r a t i o n with a zero i n t e n s i t y i n t e r c e p t at about 6 mm. This i n d i c a t e s that the tubes probably d i d not a f f e c t the number d e n s i t y of He II ions except at d i s t a n c e s of l e s s than 3 mm from the tubes. The r e s u l t s f o r He I 5876, however, i n d i c a t e an i n f l u e n c e extending at l e a s t 2 cm from the end of each tube. For tube s e p a r a t i o n s of l e s s than 4 cm the c o n c e n t r a t i o n of helium atoms i s s i g n i f i c a n t l y g r e a t e r than f o r tube s e p a r a t i o n s of greater than 8 cm. The non-zero i n t e r c e p t again i n d i c a t e s end e f f e c t r'egions -where there i s an excess of helium_.atoms. The s i t u a t i o n . _ 1 0 0 4 -I N T E N S I T Y ( a r b . u n i t s ) 8 0 4 -6 0 4 -4 0 4 -204-O H e U 4 6 8 6 O H e l 5 8 7 6 6 8 10 12 T U B E S E P A R A T I O N ( c m ) F i g u r e V-4 : I n t e n s i t i e s o f He I 5876 and_He I I 4686 as a f u n c t i o n o f tube s e p a r a t i o n 62 suggested by these data i s d e p i c t e d i n Figure V-5. The f a c t that a d i f f e r e n c e was detected i n the d e n s i t y of helium atoms i n the perturbed and unperturbed regions while no v a r i a t i o n was found i n the d e n s i t y of He II ions i s e x p l a i n e d by the f a c t t h a t the number d e n s i t y of helium atoms i s much more temperature dependent than the number d e n s i t y of*He II i o n s . The v a r i a t i o n of the e l e c t r o n d e n s i t y with tube s e p a r a t i o n d i s c u s s e d i n Chapter IV i s t h e r e f o r e l i k e l y due to small changes i n the d e n s i t y of He II ions which could not be detected as w e l l as d i f f e r e n c e s i n temperature which a f f e c t e d the c o n c e n t r a t i o n s of helium atoms and He I I I i o n s . V-4 U n i f o r m i t y of the plasma column Measurements s i m i l a r to those f o r 'the e l e c t r o n d e n s i t y (see s e c t i o n IV-4) were performed to study the l o n g i t u d i n a l u n i f o r m i t y of the a x i a l plasma. The tubes were moved along the c e n t r a l 12 cm of the a x i s of the discharge v e s s e l with a s e p a r a t i o n of 4 cm maintained between t h e i r t i p s . The r e s u l t i n g e l e c t r o n temperature f o r v a r i o u s tube p o s i t i o n s i s given i n F i g u r e V-6. The measurements were again made f o r a time 0.75 iis a f t e r the pinch phase. The s c a t t e r i n the data i s l a r g e b u t , w i t h i n the u n c e r t a i n t y of the measurements, the e l e c t r o n temperature was uniform along the c e n t r a l 12 cm of the discharge v e s s e l . No measurements of- t h e electron-temperature L O C A L (<.5cm) END EFFECT REGIONS Figure. V-5 The suspected effects of the limiter tubes on the observed plasma. T e (eV) 4.2-t 4.1 4.0" 3.9* 3.8*- + 6 Negative Electrode 1 Centre + POSITION OF TUBES (cm) (tubes 4cm apart) 1 ! r -Ground ^ Electrode ' F i g u r e V - 6 : U n i f o r m i t y o f t h e a x i a l e l e c t r o n t e m p e r a t u r e 65 were performed f o r p o s i t i o n s o f f the a x i s . Preston (1974) had found that f o r a f i l l i n g pressure of 4 T o r r , no l a r g e r a d i a l g r a d i e n t s i n the e l e c t r o n temperature occurred even f o r p o s i t i o n s along the a x i s at the time of the p i n c h . The r a d i a l temperature g r a d i e n t s i n t h i s study were t h e r e f o r e l i k e l y s maller than the d e n s i t y g r a d i e n t s and so, due to the weak dependence of the He II l i n e p r o f i l e s on the •'_ ' e l e c t r o n temperature, any d i s t o r t i o n s i n the l i n e p r o f i l e s r e s u l t i n g from temperature inhomogeneities were l i k e l y s m a l l . V-5 Temperature time dependence and r e p r o d u c i b i l i t y of the pinch The time h i s t o r y of the e l e c t r o n temperature near the time of i n t e r e s t (0.75 us) was s t u d i e d to determine i f r a p i d changes i n temperature could a f f e c t the measured l i n e p r o f i l e s . L i g h t t r a c e s were obtained f o r the tubes separated by 4 cm and l o c a t e d 2 cm from the centre of the d ischarge v e s s e l towards the negative e l e c t r o d e . The r e s u l t s are presented i n Figure V-7. I t i s seen from these r e s u l t s that whereas the d e n s i t y was i n c r e a s i n g during the time of i n t e r e s t (see s e c t i o n IV-6), the temperature was almost constant. Therefore d i s t o r t i o n s i n the measured p r o f i l e s due to changes i n the temperature during the 200 ns gating p e r i o d were s m a l l . It was mentioned i n s e c t i o n V - l that the e q u i l i b r a t i o n time f o r 4.0 + T e (eV) 3.9+ 3 .8+ 3.7+ 3.6 + 3 .5+ <t) 3.4-0 0.1 f 4 + + + + 0.2 0.3 0.4 0.5 0.6 TIME AFTER PINCH PHASE (ys) 0.7 0.8 Figure V-7: Time history of the electron .temperature. ON 67 LTE at a d e n s i t y of 6.1*10 Z 3 m 3 and a temperature of 4 eV was about 0.5 us. Therefore the temperatures determined from l i n e i n t e n s i t y r a t i o s a p p l i e d to times e a r l i e r than those f o r which the measurements were made and r a p i d v a r i a t i o n s i n temperature could not be d e t e c t e d . However, t h i s e f f e c t probably was not important i n t h i s study s i n c e the temperature d i d not change by more than 0.5 eV during times that were of importance i n determining the temperature. It was found that i n the measurements of d e n s i t i e s and temperatures, shot to shot v a r i a t i o n s i n the pinch c h a r a c t e r i s t i c s c o n t r i b u t e d s i g n i f i c a n t l y to the u n c e r t a i n t i e s i n the measured plasma parameters. Shot to shot v a r i a t i o n s i n the d e n s i t y as determined from the FWHM of He I 5876 were of the order of 10% while those i n the temperature were approximately 3%. The experimental u n c e r t a i n t y i n the temperature arose mainly from shot to shot v a r i a t i o n s i n the i n t e n s i t y of He II 4686. These were of the order of 40% while the shot to shot v a r i a t i o n s i n the i n t e n s i t y of He I 5876 were about 10%. The r e p r o d u c i b i l i t y of the pinch was found to improve s i g n i f i c a n t l y when the pinch v e s s e l as well as the e l e c t r o d e s were cleaned. The poor r e p r o d u c i b i l i t y o f the d i r t y p i nch was probably due to d e p o s i t s on the v e s s e l w a l l s l e a d i n g to changeable i n i t i a l breakdown c o n d i t i o n s . Although the r e s u l t s were f a i r l y r e p r o d u c i b l e f o r any given set of measurements, the 6 8 day to day v a r i a t i o n s were q u i t e s i g n i f i c a n t . Both the temperature and the d e n s i t y changed c o n s i d e r a b l y from day to day as can be seen by comparing F i g u r e s IV-2 and IV-3 and F i g u r e s V-3 and V-6. The reason f o r these v a r i a t i o n s i s unknown although changes to the discharge c i r c u i t due to humidity and d e p o s i t s of f o r e i g n m a t e r i a l as a r e s u l t of the high c u r r e n t discharge are p o s s i b l e e x p l a n a t i o n s . V-6 Temperature estimate from l i n e to continuum r a t i o s It i s a l s o p o s s i b l e to determine the e l e c t r o n temperature from measurements of l i n e and continuum i n t e n s i t i e s . R e s u l t s of t h e o r e t i c a l c a l c u l a t i o n s f o r the r a t i o of the i n t e n s i t i e s of both He II 3203 and He II 4686 to the 100 X, wide continuum bands centred at each of these l i n e s are given by D e l c r o i x and Volonte (1973) f o r va r i o u s e l e c t r o n d e n s i t i e s and temperatures. In the c a l c u l a t i o n s , c o n t r i b u t i o n s to the continuum i n t e n s i t y from both n e u t r a l and s i n g l y i o n i z e d helium atoms were c o n s i d e r e d . The r e s u l t s do not r e q u i r e LTE to be a p p l i c a b l e but only p a r t i a l LTE down to the t h i r d p r i n c i p a l quantum l e v e l i n He I I . An average p r o f i l e of He II 4686 was obtained by combining s i x p r o f i l e s and the l i n e to continuum r a t i o measured by g r a p h i c a l l y i n t e g r a t i n g the areas under the l i n e and due to the continuum. The r e s u l t i n g temperature, using the data of D e l c r o i x and Volonte, was -3.7±0.1 eV which agrees well with the r e s u l t s obtained . 69 from l i n e i n t e n s i t y r a t i o s (4.0±0.4 eV) f o r the same tube p o s i t i o n and time. It has been shown i n t h i s chapter that the tubes perturbed the plasma so as to lower the e l e c t r o n temperature. The c e n t r a l 12 cm of the a x i a l plasma has been shown to be uniform and time v a r i a t i o n s i n the temperature have been shown to be s m a l l . Results from l i n e to continuum measurements agreed well with temperatures obtained from l i n e i n t e n s i t y r a t i o s . From the r e s u l t s of the measurements of the e f f e c t of the tubes on the plasma and of the u n i f o r m i t y of the a x i a l plasma, a tube s e p a r a t i o n of 4 cm and a p o s i t i o n 2 cm from the v e s s e l centre towards the negative e l e c t r o d e were chosen f o r the f i n a l measurements of the He II l i n e p r o f i l e s . At t h i s s e p a r a t i o n the perturbed plasma regions overlapped and the r e s u l t i n g plasma column was uniform except f o r small end e f f e c t r e g i o n s . In Chapter VII p r o f i l e s obtained f o r the He II l i n e s at 3203 A and 4686 A are presented f o l l o w i n g a d i s c u s s i o n i n Chapter VI of the data a n a l y s i s f o r the f i n a l p r o f i l e s . 70 CHAPTER VI DATA ANALYSIS An o p t i c a l m ultichannel analyzer or OMA was used i n t h i s i n v e s t i g a t i o n i n order to measure the l i n e p r o f i l e s of the helium l i n e s at 3203 4686 k, and 5876 A. Problems encountered i n the use of the OMA as w e l l as methods of c a l i b r a t i o n w i l l be d i s c u s s e d i n t h i s chapter. Since shot to shot v a r i a t i o n s i n the i n t e n s i t y of the s p e c t r a l l i n e s s t u d i e d were as great as 40%, accurate measurement of the l i n e p r o f i l e s was not p o s s i b l e by shot to shot methods. The OMA p e r m i t t e d the accurate measurement of e n t i r e l i n e p r o f i l e s i n a s i n g l e shot. Shot to shot v a r i a t i o n s i n the e l e c t r o n d e n s i t y which l e d to changes i n the l i n e p r o f i l e s could t h e r e f o r e be measured independently of changes i n the temperature which e f f e c t e d the l i n e i n t e n s i t i e s but had l i t t l e e f f e c t on the l i n e shapes. A -900 V square pulse of 200 ns d u r a t i o n was a p p l i e d to the OMA d e t e c t o r head at the time of i n t e r e s t i n the pinch discharge c y c l e to gate the d e t e c t o r head a m p l i f i e r stages. The c i r c u i t f o r producing t h i s g a t i n g pulse i s d i s c u s s e d i n Appendix 2. While i n r e a l time o p e r a t i o n , the response of the OMA was very smooth across a l l 500 channels and f o c u s s i n g of the image was good, c o n s i d e r a b l e worsening i n the s e n s i t i v i t y and f o c u s s i n g c h a r a c t e r i s t i c s occurred when the OMA was operated i n the gated mode. 7 1 T h e r e f o r e , s p e c i a l c a l i b r a t i o n of the monochromator-. OMA arrangement was r e q u i r e d . VI-1 C a l i b r a t i o n f o r i n t e n s i t y response While th£ i n t e n s i t y response of any one of the 500 photodetectors was l i n e a r to ±1% i n both r e a l time and gated modes, the s e n s i t i v i t y from channel to channel was not uniform i n gated mode. Therefore p r o f i l e s obtained i n gated mode were d i s t o r t e d and c o r r e c t i o n s f o r non-uniform response had to be a p p l i e d . The i n t e n s i t y response of the OMA i n gated mode was found by s e t t i n g the monochromator- to a r e g i o n i n the helium spectrum where only continuum r a d i a t i o n o c c u r r e d . The pinch was f i r e d as usual and the spectrum of the continuum r e g i o n obtained at the time of i n t e r e s t . Since the i n t e n s i t y of the continuum r a d i a t i o n was constant over small s p e c t r a l regions, any channel to channel d i f f e r e n c e s i n the measured i n t e n s i t y were due to instrument e f f e c t s . A t y p i c a l response curve i s shown i n Figure VI-1. T h i s curve was obtained f o r the 130 A wide s p e c t r a l band centred at 4800 A and has been smoothed to remove s t a t i s t i c a l f l u c t u a t i o n s i n the recorded i n t e n s i t i e s . A l l measured p r o f i l e s of the He II l i n e at 4686 A were d i v i d e d by t h i s curve to c o r r e c t f o r instrument d i s t o r t i o n s i n s e n s i t i v i t y . A s i m i l a r curve was obtained f o r the continuum r e g i o n centred at 6050 A and was use_d_ to 73 c o r r e c t the He I 5876 p r o f i l e s . Since the s p e c t r a l response of the OMA 1205D d e t e c t o r head changed r a p i d l y around 3200 A the response curve used to c o r r e c t He II 3203 p r o f i l e s could not be obtained from a neighboring continuum r e g i o n . Instead hydrogen was used as the f i l l i n g gas and the response curve obtained f o r the hydrogen continuum r e g i o n centred at 3200 A. VI-2 C a l i b r a t i o n of the wavelength s c a l e Defocussing by the e l e c t r o n i c s i n the OMA d e t e c t o r head i n the gated mode was found to lead to b l u r r i n g of the image as we l l as wavelength d i s t o r t i o n s . The r e a l time HWHM of the 6328 A He-Ne l a s e r l i n e , as measured by the monochrometer-OMA arrangement,was about 1.5 channels. The apparent broadening of t h i s very narrow l i n e was due to e l e c t r i c a l c r o s s t a l k between adjacent channels of the OMA. When the OMA was operated i n gated mode t h i s c r o s s t a l k was found to i n c r e a s e . The ga t i n g v o l t a g e was adjusted to give the best focus and a minimum HWHM of about 4 channels was achieved f o r a ga t i n g pulse of -900 V. Since the d i s p e r s i o n of the Spex 1800 monochrometer was about 10 A/mm i n f i r s t o r d e r , the instrument HWHM was about 1 A. Since t h i s instrument p r o f i l e was roughly Gaussian i n shape, the a c t u a l width of the helium l i n e s was approximately given by: 2 2 l / w=(w -w.) 1 2 (6-1) v m l 1 74 where w i s the measured l i n e width and w. i s the instrument m 1 width. For the l i n e widths measured i n t h i s study (HWHM<13 A) the c o n t r i b u t i o n due to instrument broadening was only about 0.1 A. T h i s r e s u l t was n e g l i g i b l e compared to the shot to shot f l u c t u a t i o n s (=10%) i n the measured p r o f i l e s . Wavelength d i s t o r t i o n s , h o w e v e r , were s i g n i f i c a n t . A channel dependent s h i f t i n the l i n e p r o f i l e s occurred when the OMA was operated i n gated mode. The 6328 A He-Ne l a s e r l i n e was observed i n both r e a l time and gated modes f o r v a r i o u s monochrometer wavelength s e t t i n g s i n the r e g i o n o f 6328 A and the s h i f t i n the gated image with r e s p e c t to the r e a l time image was measured as a f u n c t i o n of the r e a l time p o s i t i o n . The wavelength versus channel number s c a l e s f o r monochrometer s e t t i n g s of 3203 A, 4686 A,via-iicL.58.7.6 A were found i n r e a l time mode using i r o n arc and G e i s s l e r tube sources. From these measurements and the r e s u l t s of the s h i f t measurements, the"gated mode wavelength versus channel number.scales were determined. This two step procedure was necessary s i n c e the i r o n arc and G e i s s l e r tube s p e c t r a were too f a i n t to be observed d i r e c t l y i n gated mode. VI-3 C a l c u l a t i o n of the c o r r e c t e d l i n e p r o f i l e s The c o r r e c t e d l i n e p r o f i l e s were c a l c u l a t e d from the measured 1 i n e - p r o f i l e s , the i n t e n s i t y response curves, 75 and the wavelength'versus channel number s c a l e s using the computer programs d e s c r i b e d i n Appendix 3. The measured l i n e p r o f i l e s and i n t e n s i t y response curves were f i r s t smoothed to remove random channel to channel i n t e n s i t y f l u c t u a t i o n s . A smoothing r o u t i n e was employed which assigned the value of a weighted average of the i n t e n s i t i e s of s e v e r a l neighboring channels to each of the 500 channels. The amount of smoothing could be c o n t r o l l e d by changing the number of neighboring p o i n t s considered i n c a l c u l a t i n g the weighted average as well as by changing the number of i t e r a t i o n s of the procedure. The f i n a l c o r r e c t e d p r o f i l e s were c a l c u l a t e d by f i r s t d i v i d i n g the smoothed raw p r o f i l e s , channel by channel, by the i n t e n s i t y response curves and then by a p p l y i n g the channel number versus wavelength data to determine the wavelength s c a l e s . P r o f i l e s of He II 4686 before and a f t e r the smoothing and c o r r e c t i o n procedures are shown i n F i g u r e VI-2. Both p r o f i l e s were normalized so that t h e i r maximum i n t e n s i t i e s were 1. The r a p i d d r o p o f f i n i n t e n s i t y at larg e wavelengths i s due to the poor s e n s i t i v i t y of the f i r s t 100 OMA channels which could not be c o r r e c t e d f o r completely. Since a l l three l i n e s s t u d i e d i n t h i s i n v e s t i g a t i o n were broad, s e v e r a l shots at d i f f e r e n t monochrometer s e t t i n g s were r e q u i r e d to observe the e n t i r e p r o f i l e s . Shots were, fir.ed f o r monochrometer s e t t i n g s 50 A above 76 F i g u r e VI - 2 : P r o f i l e s o f He a f t e r (Bottom) p r o c e d u r e s . II 4686 b e f o r e (Top) and s m o o t h i n g and c o r r e c t i o n ; 77 and below l i n e centre to o b t a i n the wing p r o f i l e s . The wing i n t e n s i t i e s were adjusted to match the i n t e n s i t y of the l i n e centre p r o f i l e at s e l e c t e d p o i n t s and the three p r o f i l e s were j o i n e d to form a complete p r o f i l e . A complete p r o f i l e of He II 4686 i s shown i n F i g u r e VI-3. The wings were j o i n e d at p o i n t s 30 A below and 20 A above l i n e c e n t r e . Although t h i s procedure r e q u i r e d s e v e r a l shots to o b t a i n a complete l i n e p r o f i l e , the important c e n t r a l p a r t of the l i n e was obtained i n a s i n g l e shot. In the next chapter, f i n a l p r o f i l e s of He II 4686. and He II 3203 are presented and compared to t h e o r e t i c a l p r o f i l e s . F i g u r e V I - 3 : Complete p r o f i l e o f He II 4686 c o n s t r u c t e d from t h r e e ^ i n d e p e n d e n t p r o f i l e s . 79 CHAPTER VII LINE PROFILES FOR He II 3203 AND He 11 4686 The p r o f i l e s of the He II l i n e s at 3203 A and 4686 A, measured f o r a well diagnosed plasma r e g i o n , are presented i n t h i s chapter. The experimental p r o f i l e s are compared to the t h e o r e t i c a l p r o f i l e s of Kepple (1972) and Greene (1976) . The measurements of the f i n a l l i n e p r o f i l e s were made along the axis of the discharge v e s s e l at a p o s i t i o n 2 cm from the centre of the v e s s e l towards the negative e l e c t r o d e . Observations were made 0.75 us a f t e r the midpoint i n the pinch phase. From the measurements of the e f f e c t of the tubes on the e l e c t r o n temperature and d e n s i t y , a tube s e p a r a t i o n of 4 cm was chosen f o r the f i n a l measurements. At t h i s s e p a r a t i o n the perturbed regions of plasma surrounding each tube overlapped, r e s u l t i n g i n the formation of a uniform plasma column between the t i p s of the tubes. Local end e f f e c t s , as i n d i c a t e d by the temperature measurements ( s e c t i o n V-3) were probably small and extended l e s s than 0.5 cm from the end of each tube. P r o f i l e s of He II 3203, He II 4686, and He I 5876 were obtained i n a s i n g l e s e r i e s of shots. A t o t a l o f nine p r o f i l e s of He II 3203 and s i x of both He II 4686 and He I 5876 were obtained. The l i n e under study was changed every three s t o t s to reduce the e f f e c t s A of systematic changes i n the pinch c h a r a c t e r i s t i c s . 80 Wing p r o f i l e s were a l s o obtained f o r each of the s t u d i e d 1ines. VII-1 Plasma c o n d i t i o n s The d i a g n o s t i c s d e s c r i b e d i n Chapters IV and V were used to determine the c o n d i t i o n s i n the plasma that was s t u d i e d to o b t a i n the l i n e p r o f i l e s . An e l e c t r o n temperature of 4.0±0.4 eV was determined from l i n e i n t e n s i t y r a t i o s f o r the l i n e s He II 4686 and He I 5876. The quoted u n c e r t a i n t y was due to u n c e r t a i n t i e s i n whether the upper l e v e l s of the two l i n e s were i n thermal e q u i l i b r i u m with the e l e c t r o n s . Experimental u n c e r t a i n t i e s were somewhat smaller (=0.1 eV). Six p r o f i l e s of He I 5876 were added together by a computer program i n order to average out shot to shot v a r i a t i o n s i n the l i n e shape. An e l e c t r o n d e n s i t y of (6.1±0.6)x10 2 3 m 3 was determined from the FWHM of the r e s u l t a n t / p r o f i 1 e . The experimental u n c e r t a i n t y was estimated from the s c a t t e r i n the widths of the s i x p r o f i l e s and represents the e r r o r i n any measurement. As was mentioned i n Chapter ?, the plasma s t u d i e d was not i n a s t a t e of complete thermal e q u i l i b r i u m . The plasma d e n s i t y was below the value at which LTE i s maintained by the predominance of c o l l i s i o n a l processes over other e x c i t a t i o n - d e e x c i t a t i o n p r o c e s s e s . The time s c a l e s i n v o l v e d i n the s t u d i e d plasma were a l s o too short f o r complete LTE to be achieved. The plasma, however, e a s i l y 81 s a t i s f i e d the c o n d i t i o n s f o r p a r t i a l LTE. Plasma d e n s i t i e s and time s c a l e s were s e v e r a l orders of magnitude above those r e q u i r e d f o r p a r t i a l LTE f o r each of the s p e c t r a l l i n e s s t u d i e d . The lack of t o t a l LTE would be expected to be a greater source of u n c e r t a i n t y i n the temperature measurements than i n the d e n s i t y measurements. Pressure broadening t h e o r i e s do not r e q u i r e complete LTE. A thermal e l e c t r o n d i s t r i b u t i o n i s assumed only i n c a l c u l a t i n g the e l e c t r o n impact broadening. This c o n d i t i o n was e a s i l y s a t i s f i e d i n t h i s i n v e s t i g a t i o n s i n c e the upper e x c i t e d s t a t e s i n the He II ions were i n p a r t i a l LTE. E r r o r s , however, may have occurred i n the c a l c u l a t i o n of the s t a t i c ion e l e c t r i c f i e l d d i s t r i b u t i o n s i n c e LTE was assumed i n c a l c u l a t i n g the e f f e c t i v e ion charge,(see s e c t i o n IV-1). The l i n e p r o f i l e s p r e d i c t e d by the l i n e broadening t h e o r i e s do not consid e r the e f f e c t s of s e l f - a b s o r p t i o n of the emitted r a d i a t i o n . T h e r e f o r e , before the experimental p r o f i l e s can be compared to the t h e o r e t i c a l p r o f i l e s , the e f f e c t s of s e I f - a b s o r p t i o n must be shown to be n e g l i g i b l e . The o p t i c a l depth T, i s given by: T = 8.853xl0" 25 N,, Lf A 2S(A) (VII-1) x J L U where N^ i s the number d e n s i t y of atoms i n the lower l e v e l of the t r a n s i t i o n of i n t e r e s t , L i s the length of the plasma column ( i n meters), 82 i s the a b s o r p t i o n o s c i l l a t o r s t r e n g t h , X i s the wavelength of the s p e c t r a l l i n e of i n t e r e s t ( i n A ) , and S(X) i s the l i n e shape, normalized to u n i t area. The e f f e c t s of s e l f a b s o r p t i o n can be ignored i f T i s much l e s s than one. Assuming LTE,the p o p u l a t i o n of the lower e x c i t e d s t a t e i s given by the Boltzmann Equation: N. = N — e x p ( ~ ) (VII-2) g 0 icT e where N i s the p o p u l a t i o n d e n s i t y of the ground s t a t e , g„ and g n a r e the s t a t i s t i c a l weights of the lower Jc - •<• u s t a t e and the ground s t a t e r e s p e c t i v e l y , and EQ^ i s the e x c i t a t i o n energy of the lower l e v e l above the ground s t a t e . C o n s i d e r i n g the worst case, which occurs at the l i n e centre where S(X)= / . where W, i s the EWHM of the ^ t r a n s i t i o n W A ' of i n t e r e s t , TC canape w r i t t e n as: f •, g E -x = 8.853X10" 2 5 LN - l u 1 e x p ( — ^ ) (VII-3) W g 0 kT I f , as an approximation, we assume that most of the He II ions were i n the ground s t a t e (N=6.1xl0 2 3 m 3 ) , the approximate o p t i c a l depth f o r the l i n e s of i n t e r e s t i n a 0.04 m plasma column were: 83 He II 3203 T = 1.2x10 * He II 4686 x = 1.8X10" 1* He I 5876 T = 3.3X10"1* Since the o p t i c a l depth f o r each of these l i n e s was much l e s s than one, s e l f a b s o r p t i o n of the l i n e r a d i a t i o n was not great enough to e f f e c t the measured l i n e shapes. VII-2 P r o f i l e s of the s p e c t r a l l i n e s He II 3203 • and He II 4686 Experimental p r o f i l e s of the He II l i n e s at 3203 A and 4686 A are presented i n Figures VII-1 and VII-2. The p r o f i l e s were smoothed and c o r r e c t e d f o r instrument d i s t o r t i o n s i n i n t e n s i t y and d i s p e r s i o n . The l i n e centre p r o f i l e f o r He II 3203 was obtained by adding together ei g h t p r o f i l e s while that f o r He II 4686 was obtained from the sum of s i x p r o f i l e s . Wing p r o f i l e s were obtained i n a s i n g l e shot and j o i n e d to the l i n e centre p r o f i l e s at the p o i n t s shown. The random noise i n ' t h e p r o f i l e of He II 3203 was much more evident than the noise i n the p r o f i l e of He II 4686 due to the much sm a l l e r measured i n t e n s i t y of the He II 3203 l i n e . The a d d i t i o n of s e v e r a l p r o f i l e s aided i n i n c r e a s i n g the s i g n a l to noise r a t i o as well as averaging out shot to shot changes i n the l i n e shapes. Lines due to contaminants were present on the wings of both He II 3203 and He II 4686. The two prominent F i g u r e V I I - 1 : M e a s u r e d p r o f i l e o f He I I 4 6 8 6 . 00 F i g u r e V I I ^ 2 : M e a s u r e d p r o f i l e o f He I I 3 2 0 3 . w 86 l i n e s on the short wavelength wing of He II 3203 were i d e n t i f i e d as S i IV 3166 and S i IV 3150. The other bumps i n the wings were due to random noise which was more evident i n the wings than i n the r e g i o n of the l i n e , centre s i n c e the wing p r o f i l e s were obtained from only one shot. The two l i n e s on the short wavelength wing of He II 4686 were i d e n t i f i e d as 0 II 4649 and 0 IT 4.64 2. The oxygen and s i l i c o n contaminants probably o r i g i n a t e d from m a t e r i a l burnt o f f the walls of the discharge v e s s e l and quartz tubes. F i r s t order theory p r e d i c t s that both He II 3203 and He II 4686 should be symmetric about the u n s h i f t e d l i n e c e n t r e . The experimental p r o f i l e s were symmetric w i t h i n experimental u n c e r t a i n t y except i n the r e g i o n of the double peak i n the He II 3203 p r o f i l e . The blue peak was approximately 9% more inte n s e that the red peak. The discrepancy was at f i r s t thought to be due to contamination l i n e s or poor i n t e n s i t y c a l i b r a t i o n but experiments i n d i c a t e d that the e f f e c t was r e a l . Checks were performed by a d j u s t i n g the monochromator wavelength s e t t i n g so that the He II 3203 l i n e centre was l o c a t e d at high channel numbers where the i n t e n s i t y response was uniform (see Figure VI-1) and a l s o by p o s i t i o n i n g the OMA d e t e c t o r head upside down so the apparent d i s p e r s i o n was r e v e r s e d . In both cases the blue peak was s t i l l found to be more inten s e than the red peak. 87 Previous s t u d i e s of a hydrogen plasma c a r r i e d out i n other i n v e s t i g a t i o n s ^ ' 1 5 ^ have r e v e a l e d an asymmetry between the two peaks of the l i n e which favored the blue peak. A study of the t h e o r i e s r e v e a l s s e v e r a l spots at which at which asymmetries may occur. By c o n s i d e r i n g the a)** dependence i n equation 2 - 1 , the Boltzmann d i s t r i b u t i o n among the substates of the i n i t i a l s t a t e , and the proper conversion between angular f r e q u e n c i e s and reduced wavelengths an asymmetry of about 8% i n favour of the blue wing i s introduced. However, these c o r r e c t i o n s only a f f e c t the f a r wings and have l i t t l e e f f e c t i n j t h e r e g i o n of the peaks. Asymmetries i n the ion broadening, however, may lead to d i f f e r e n c e s i n the peak i n t e n s i t i e s . These asymmetries a r i s e from higher order (quadrupole etc.) i n t e r a c t i o n s between the r a d i a t o r and the p e r t u r b i n g ions as well as from q u a d r a t i c Stark e f f e c t s . The .. d i f f e r e n c e s i n the i n t e n s i t y of the He II 3203 peaks may be due to these e f f e c t s . VII-3 Comparison of the experimental and t h e o r e t i c a l l i n e p r o f i l e s The experimental p r o f i l e s of He II 4686 and He.II 3203 are compared to the p r o f i l e s p r e d i c t e d by Kepple and Greene i n F i g u res VII-3 and VII-4. The experimental p r b f i l e s were obtained from those i n Figures V I I - 1 and VII-2 by s u b t r a c t i n g o f f the continuum l e v e l s and n o r m a l i z i n g the r e s u l t a n t p r o f i l e s to u n i t area. T h e i t h e o r e t i c a l p r o f i l e s He II 4 6 8 6 T e = 4 . 0 * 0 . 4 e V N e s ( 6 . l ± 0 . 6 ) x | 0 2 3 n f 3 G R E E N E E X P E R I M E N T A L K E P P L E i I -120 - 1 0 0 - 8 0 - 4 0 - 2 0 0 2 0 4 0 W A V E L E N G T H (A) - . - i r - n i I 100 120 Figure VII-3: The experimental and t h e o r e t i c a l p r o f i l e s of He II 4686. 00 00 Figure VII-4: The experimental and t h e o r e t i c a l p r o f i l e s of He II 3203. 00 to 90 were obtained by i n t e r p o l a t i n g p r o f i l e s (Griem (1974), Greene ( p r i v a t e communication)) and were c a l c u l a t e d f o r an e f f e c t i v e charge of 1.22e and a temperature and d e n s i t y of 4.0 eV and 6 . 1 x l 0 2 3 m"3 r e s p e c t i v e l y . Comparison of the experimental p r o f i l e f o r He II 4686 to the t h e o r e t i c a l p r o f i l e s i n d i c a t e s that the experimental r e s u l t s are somewhere between those of Kepple and those of Greene. T h e o r e t i c a l data f o r He II 3203 was only a v a i l a b l e from Kepple's treatment. Comparison of the t h e o r e t i c a l and experimental p r o f i l e s r e v e a l e d s i g n i f i c a n t d i f f e r e n c e s i n the regions of the l i n e centre and f a r l i n e wings. For both He II 3203 and He II 4686 comparison between experiment and theory i n the l i n e wings should be made f o r the s h o r t e r wavelength wing s i n c e the l a r g e r wavelength regions have been recorded i n the l e s s responsive channels of the OMA. In the f o l l o w i n g chapter, p o s s i b l e reasons f o r d i s c r e p a n c i e s between the t h e o r e t i c a l and experimental p r o f i l e s are d i s c u s s e d and c o n c l u s i o n s are presented concerning the plasma c o n d i t i o n s . 91 CHAPTER VIII CONCLUSIONS In Figures VII-3 and VII-4 experimental p r o f i l e s f o r He II 3203 and He II 4686 were compared to t h e o r e t i c a l p r o f i l e s p r e d i c t e d by an e l e c t r o n impact (Kepple (1972)) and a time e v o l u t i o n a r y treatment of the e l e c t r o n c o l l i s i o n s (Greene (1976)). The experimental r e s u l t s f o r He II 4686 were found to l i e between the two t h e o r e t i c a l p r o f i l e s . Greene's c a l c u l a t i o n s r e s u l t e d i n a p r o f i l e with a value f o r the FWHM 45% l e s s than the experimental r e s u l t whereas Kepple's c a l c u l a t i o n s r e s u l t e d i n a FWHM that was 40% greater than f o r the experimental p r o f i l e . E r r o r s i n the e s t i m a t i o n o f the e f f e c t o f strong e l e c t r o n c o l l i s i o n s on* the f a r l i n e wings were l i k e l y the major cause of the d i s c r e p a n c i e s between the experimental and t h e o r e t i c a l ; ' p r o f i l e s . Since the i n t e r f e r e n c e between the upper and lower l e v e l s of the He II 4686 t r a n s i t i o n can lead to a narrowing of the l i n e p r o f i l e , i t can be concluded that Greene has probably overestimated the broadening of the lower l e v e l s ,while Kepple's c a l c u l a t i o n s have l i k e l y underestimated the e f f e c t of the lower l e v e l s . Since the upper l e v e l of He II 3203 i s broadened much more than that of He II 4686 i t i s expected that the e f f e c t of lower l e v e l b r oadening'is of g r e a t e r importance i n determining the l i n e shape of He II 4686 than i n the 92 p r o f i l e of He II 3203. Therefore agreement between the t h e o r e t i c a l and experimental p r o f i l e s of He II 3203 i s expected to be b e t t e r than f o r the He II 4686 p r o f i l e . U n f o r t u n a t e l y data f o r He II 3203 was only a v a i l a b l e from Kepple's method and so comparison between the two t h e o r i e s was not p o s s i b l e . Comparison of Kepple's p r e d i c t e d l i n e shape with the experimental r e s u l t s f o r He II 3203 i n d i c a t e d l a r g e disagreements i n both 1 the shape and the width of the experimental and t h e o r e t i c a l p r o f i l e s . The d i f f e r e n c e i n the peak i n t e n s i t i e s , as mentioned i n the previous chapter, can probably be p a r t l y a t t r i b u t e d to higher m u l t i p o l e i n t e r a c t i o n s and q u a d r a t i c Stark e f f e c t s . However, the disagreements i n the l i n e width (the FWHM of the t h e o r e t i c a l p r o f i l e was l a r g e r by =60%) cannot be f u l l y accounted f o r . T h i s poor agreement between t h e o r e t i c a l and experimental r e s u l t s may i n d i c a t e that the He II 3203 and He II 4686 l i n e s o r i g i n a t e d from d i f f e r e n t plasma r e g i o n s . However, experimental measurements of the u n i f o r m i t y of the plasma column and of the i n t e r a c t i o n of the tubes with-the plasma^suggested' that the observed plasma column was uniform i n both temperature and d e n s i t y except i n very small end e f f e c t regions extending l e s s than 0.5 cm from the t i p s of the tubes. P o s s i b l e n o n u n i f o r m i t i e s i n the observed plasma column due to r a d i a l d e n s i t y g r a d i e n t s cannot be considered as an e x p l a n a t i o n f o r the observed d i s c r e p a n c i e s s i n c e 93 the upper l e v e l s of He II 3203 and He II 4686 d i f f e r e d i n energy by only 1.23 eV and so the l i n e s would be expected to o r i g i n a t e from the same plasma r e g i o n s . D i f f e r e n c e s between the experimental and t h e o r e t i c a l p r o f i l e s f o r both He II 3203 and He II 4686 may have occurred due to e r r o r s i n the determined e l e c t r o n d e n s i t y . A p o s s i b l e source of e r r o r may have occurred i n the c a l c u l a t i o n of the e f f e c t i v e ion charge. T o t a l LTE was used i n c a l c u l a t i n g the e f f e c t i v e charge but only p a r t i a l LTE e x i s t e d . I f the value of Q e £ f w a s underestimated then the e f f e c t of ion broadening on the p r o f i l e of He I 5876 would a l s o be underestimated and the determined d e n s i t i e s would be too l a r g e . The e f f e c t s of the underestimated e f f e c t i v e charge and the corresponding overestimated e l e c t r o n d e n s i t y on the c a l c u l a t e d t h e o r e t i c a l p r o f i l e s of He II 3203 and He II 4686, however, would tend to cancel s i n c e the t h e o r e t i c a l l i n e widths i n c r e a s e with'-both e f f e c t i v e charge and d e n s i t y . Therefore e r r o r s i n the c a l c u l a t e d t h e o r e t i c a l p r o f i l e s due to small u n c e r t a i n t i e s i n the value of the e f f e c t i v e charge would be s m a l l . It i s p o s s i b l e that the He I and He II l i n e s o r i g i n a t e d from d i f f e r e n t plasma r e g i o n s . Much of the He I 5876 emission may have o r i g i n a t e d from the small ( <Q. 5 cm) e n d ? e f f e c t regions i n which the plasma temperature and d e n s i t y was l e s s than i n surrounding regions (see 94 Figure V-5). I f t h i s o c c u r r e d , the e l e c t r o n d e n s i t y , c a l c u l a t e d from the FWHM of He I!5876, would be smaller than the d e n s i t y of the plasma from which the He II l i n e s o r i g i n a t e d . The t h e o r e t i c a l p r o f i l e s would then be expected to be narrower than the experimental p r o f i l e s but, at l e a s t f o r the case of Kepple's p r o f i l e s , the opposite was t r u e . C o n s i d e r i n g these arguments, i t seems l i k e l y that r e a l d i s c r e p a n c i e s e x i s t e d between the t h e o r e t i c a l and experimental p r o f i l e s and these d i s c r e p a n c i e s were p r i m a r i l y due to d e f i c i e n c i e s i n the t h e o r i e s . Concluding Remarks It has been shown i n t h i s study that the l i m i t e r tubes may be used to s e l e c t uniform plasma columns f o r o b s e r v a t i o n . Plasma c o n d i t i o n s along the axis of the discharge v e s s e l were found to be uniform although small r a d i a l d e n s i t y g r a d i e n t s l i k e l y o c c u r r e d . D i f f e r e n c e s between the t h e o r e t i c a l and experimental He II l i n e p r o f i l e s were shown to be mainly due to d e f i c i e n c i e s i n the t h e o r e t i c a l treatments. Improvements i n the plasma c o n d i t i o n s ( i e . smaller d e n s i t y and temperature g r a d i e n t s and longer time s c a l e s ) are p o s s i b l e i f o b s e r v a t i o n s are performed well o f f the discharge axis and with f i l l i n g p r essures g r e a t e r than 300 mTorr. Density determinations by means of a l a s e r i n t e r f e r o m e t e r should be p o s s i b l e f o r these plasmas and so e r r o r s due to the He I and He II 95 l i n e s o r i g i n a t i n g from d i f f e r e n t plasma regions could be avoided. Observations of He II 4686 could be made under these c o n d i t i o n s but improvements i n the o p t i c a l and d e t e c t i o n systems would be necessary i n order to study the He II 3203 p r o f i l e . 96 BIBLIOGRAPHY 1. A s c o l i - B a r t o l i , U., In Plasma P h y s i c s , .International Atomic Energy Agency, Vienna, 287 (1965). 2. Cooper, J . , Lectures i n T h e o r e t i c a l P h y s i c s , V o l . XIC, Gordon and Breach, New York, 241 (1969). 3. D e l c r o i x , A. and Volonte, S., J o u r n a l of Physics B: Atomic and Molecular Physics 6_, L4 (1973). 4. Greene, R.L., P h y s i c a l Review A 1_4, 1447 (1976). 5. Griem, H. , Z e i t s c h r i f t f i i r Physik, 137, 280 (1954). 6. Griem, H.R., Plasma Spectroscopy, McGraw-Hill Book Co . , New York, (1964). 7. Griem, H.R., S p e c t r a l Line Broadening by Plasmas, Academic Press, New York, (1974). 8. Kepple, P.C., P h y s i c a l Review A 6_, 1 (1972). 9. Medley, S.S., J o u r n a l of A p p l i e d Physics 4_1 , 142 (1970) 10. Medley, S.S., Ph.D. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, (1968). 11. Mewe, R., B r i t i s h J o u r n a l of A p p l i e d P h y sics 18, 107 (1967). 12. Preston, J.M., Ph.D. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, (1974). 13. U.S. Department of Commerce., N a t i o n a l Bureau of Standards, Atomic T r a n s i t i o n P r o b a b i l i t i e s V o l . 1, U.S. Department of Commerce, Washington, (1966). 14. deVos, J.C., Physica 2£, 690 (1954). 15. Wiese, W.L., K e l l e h e r , D.E., Paquette, D.R., P h y s i c a l Review A 6, H32 (1972) . K SI S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 v p v p v p v I ' V I / v L v I / v L s I 8 120 K 8 2 K 8 2 K 8 2 K 82 K 8 2 K 8 2 K 8 2 K S  82 K 1100 V K LOUF T O S i o 0 S C O P E <>R S 820X1 82 K 6 8 K I.OIuF 0. O. lj»F 0.02j4EL S l s* so 56 S7 S8 S 9 [V <D \D VT> <L> vj/ vj> <L / v I / v X S 2 S 3 S 4 S 5 vi/ vp q> vl  S  7 8\I D <L> vj/ 1.2 M 1.8 M 1.2 M 1.2 M 1.2 M I.2M 1.2 M 1.2M 1 6 0 0 V . 2 M .2 M T O ° S C O P E v I I > , 8 2 0 n 1.2 M Hr 001 yF O.OI^ F 0 0 1 j*fj_ > m O X F i g u r e A l - 1 : T h e r e s i s t i v e d i v i d e r s f o r t h e p h o t o m u l t i p l i e r d y n o d e c h a i n s . T o p : P h i l i p s 1 5 0 C V P Bottom": RCA C 3 1 0 3 4 - 0 1 98 APPENDIX 2 THE OMA. GATING CIRCUIT The f o c u s s i n g c h a r a c t e r i s t i c s of the OMA de t e c t o r head are h i g h l y s e n s i t i v e to the a p p l i e d g a t i n g v o l t a g e . To achieve sharp focus i t i s necessary that the gati n g pulse r i s e - t i m e s be short compared to the pulse d u r a t i o n . The schematic diagram of the c i r c u i t used to produce short d u r a t i o n high v o l t a g e OMA ga t i n g p u l s e s i s shown i n Figure A2-1. Two KN22 kry t r o n s were used to form the p u l s e . The pulse was i n i t i a t e d when k r y t r o n #1 was turned on by a t r i g g e r pulse a p p l i e d to i t s g r i d . This t r i g g e r pulse was produced by a delay u n i t connected to the input of the g a t i n g c i r c u i t . ' Charge store d i n c a p a c i t o r C i then flowed to the c a p a c i t i v e l y coupled OMA d e t e c t o r head through the output pulse t e r m i n a l and also charged c a p a c i t o r C 2 which was connected to the g r i d of the second k r y t r o n . When C 2 was s u f f i c i e n t l y charged krytron#2 was turned on and the output to the OMA was shorted to ground. The pulse d u r a t i o n could be adjusted (0.2 to 1.0 us) by changing the value of C 2 and Rj or by a l t e r i n g the supply v o l t a g e (provided by a Fluke 412B high v o l t a g e power s u p p l y ) . This c i r c u i t d i f f e r e d from previous k r y t r o n based gating c i r c u i t s i n that the k e e p - a l i v e c u r r e n t s were a p p l i e d to both k r y t r o n s at a l l times. Previous c i r c u i t s -1300 V 60 pF 1.4 M > 0.0l5j,F 47_i TRIG G — i 47f l r rx 330K> ____ | lOUTPUT _ PULSE V " £ I M MONITORe- IpF: 3.3 K F i g u r e A 2 - 1 : T h e OMA g a t i n g c i r c u i t . 100 were designed so that the keep a l i v e c u r r e n t was a p p l i e d to the second k r y t r o n only a f t e r the s t a r t of the pulse and so these c i r c u i t s were incapable of pulses of l e s s than 1 ps d u r a t i o n . A t y p i c a l output pulse i s shown i n Figure A2-2. The upper t r a c e was measured with a 10x probe connected d i r e c t l y to the output pulse t e r m i n a l while the lower t r a c e was measured across the monitor output. The OMA d e t e c t o r head was connected to the output pulse t e r m i n a l by a 30 cm l e n g t h of RG-59/U ca b l e . The use of longer cables r e s u l t e d i n r i n g i n g i n the p u l s e , probably due to mismatched impedences. The pulse r i s e -times were measured to be l e s s than 30 ns of which a s i g n i f i c a n t p a r t was probably due to the greater than 10 ns r i s e times of the T e k t r o n i x 1A1 scope p r e a m p l i f i e r s . 101 100 n s / d i v F i g u r e A 2 - 2 : T h e OMA g a t i n g p u l s e . (A) : O u t p u t t o OMA ( B ) : O u t p u t f r o m m o n i t o r 102 APPENDIX 3 THE COMPUTER PROGRAMS The computer programs used f o r smoothing the measured p r o f i l e s as well as f o r c o r r e c t i n g f o r instrument d i s t o r t i o n s i n d i s p e r s i o n and s e n s i t i v i t y are d e s c r i b e d i n t h i s appendix. A l l the programs were i n t e r a c t i v e so execution time changes could be made i n the smoothing e t c . Smoothing the data The data r e c e i v e d from the 1205A OMA console c o n s i s t e d of 500 signed f i v e d i g i t numbers r e p r e s e n t i n g the i n t e n s i t i e s measured by the 500 photodetectors* The f i r s t step i n the p r o c e s s i n g of the data was to apply smoothing r o u t i n e s which removed random channel to channel f l u c t u a t i o n s from the raw data. Two smoothing r o u t i n e s were employed. A s p l i n e f i t t i n g r o u t i n e was adapted to the data using the l i b r a r y subroutines SPLNFT a n d ; SPLN.- Standard-, d e v i a t i o n s i n the measured i n t e n s i t i e s could be s p e c i f i e d and smoothing was performed be f i t t i n g a t h i r d order curve to every two adjacent p o i n t s w i t h i n the l i m i t s of the s p e c i f i e d e r r o r bars. The neighboring curves were j o i n e d and f i r s t and second d e r i v a t i v e s matched at the j o i n i n g p o i n t s . In p r a c t i c e , the amount of smoothing was found to be very dependent on the chosen standard d e v i a t i o n s and the r o u t i n e ' s e r r a t i c behavior made i t s use 103 i m p r a c t i c a b l e . A simpler r o u t i n e was found to be s u i t a b l e f o r smoothing the experimental p r o f i l e s . T h i s r o u t i n e c a l c u l a t e d weighted averages of the i n t e n s i t i e s from s e v e r a l neighboring channels on both s i d e s of a given channel and then assigned the r e s u l t to the given channel. The number of channels considered i n the average (3 , 5 ,7 , . . . , 19) could be s p e c i f i e d and the weighting was done according to the formula, W=1-0.1(|N-X|), where W was the weight assigned to the i n t e n s i t y of channel X i n c a l c u l a t i n g the new average i n t e n s i t y at channel N. The procedure was c a r r i e d out f o r a l l 500 channels f o r which the average could be found. End channels ( i e . those f o r which the average could not be extended to i n c l u d e the same number of channels of both s i d e s of the given channel) were assigned the i n t e n s i t y of the nearest channel f o r which the procedure worked. A d d i t i o n a l smoothing could be achieved by i t e r a t i n g the procedure s e v e r a l times. The f i n a l smoothed p r o f i l e s were v i s u a l l y compared to unsmoothed p r o f i l e s to ensure that no important i n f o r m a t i o n was l o s t . In p r a c t i c e a 9 point smooth with 3 i t e r a t i o n s was s u f f i c i e n t except f o r the i n t e n s i t y response curves where 15 p o i n t smooths and 7 to 15 i t e r a t i o n s were used. I n t e n s i t y c a l i b r a t i o n and c o r r e c t i o n The measured p r o f i l e s were c o r r e c t e d f o r n o n u n i f o r m i t i e s i n the channel to channel s e n s i t i v i t y by f i r s t smoothing the i n t e n s i t y response curve obtained f o r a neighboring 104 continuum r e g i o n and then d i v i d i n g the measured p r o f i l e s , channel by channel, by the response curve. N o r m a l i z a t i o n of the maximum"' i n t e n s i t y to a value of one was performed by d i v i d i n g the i n t e n s i t y at a l l channels by the maximum i n t e n s i t y . Wavelength c a l i b r a t i o n and c o r r e c t i o n Values of the wavelengths and corresponding gated mode channel numbers, as determined from the wavelength s c a l e c a l i b r a t i o n measurements, were i n t e r p o l a t e d using the s p l i n e i n t e r p o l a t i o n subroutines SMOOTH and SMTH to f i n d the wavelengths corresponding to each of the 500 channels. The f i n a l smoothed and c o r r e c t e d p r o f i l e s were then p l o t t e d . Wing f i t t i n g The wing f i t t i n g program performed a l l of the above mentioned, smoothing and c o r r e c t i o n procedures f o r each of the wing p r o f i l e s as well as f o r the l i n e centre p r o f i l e -Each p r o f i l e was smoothed independently. D i s t o r t i o n s i n i n t e n s i t y were then removed by d i v i d i n g each of the p r o f i l e s , channel by channel, by one i n t e n s i t y response curve.; The wavelength s c a l e s were then c a l c u l a t e d u s ing the wavelength versus channel number data and a s p l i n e i n t e r p o l a t i o n procedure. The wavelength s c a l e s f o r the wing p r o f i l e s were determined by adding the s h i f t i n the monochromator wavelength s e t t i n g to the i n t e r p o l a t e d wavelengths. F i n a l l y , the wing p r o f i l e s were j o i n e d to 105 the l i n e centre p r o f i l e at s p e c i f i e d wavelengths by : I a d j u s t i n g the i n t e n s i t y of the e n t i r e wing p r o f i l e s so that the i n t e n s i t i e s at tthe matching p o i n t s on the wings were i d e n t i c a l to the i n t e n s i t i e s of the corresponding p o i n t s on the l i n e centre p r o f i l e . 

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