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Experimental study of argon II line profiles in a pulsed arc plasma Neufeld, Carl Richard 1967

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The University of British Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of CARL RICHARD NEUFELD B . S c , Queen1s University, 1962 M o S c o , University of British Columbia, 196^ FRIDAY, JANUARY 27TH, 1967j AT 2:30 P. M. IN ROOM 3Q^> PHYSICS BUILDING COMMITTEE IN CHARGE Chairman: I„ M e l . Cowan A. J , Barnard F 0 L c Curzon Ao-V. Bree R. A c Nodwell A, M„ Crooker T* Ulrych External Examiner: H« Wulff Institut fur Plasmaphysik Garching bei Miinchen Germany Research Supervisor: A, J , Barnard AN EXPERIMENTAL STUDY OF A II LINE PROFILES IN A PULSED ARC PLASMA ABSTRACT Time-resolved spectrograph!c techniques were used to obtain the profiles of A II lines emitted from a laboratory plasma. For the dense, low-temperature plasma studied, most of the broadening of the observed lines results from interactions of the emitter with, free charges in the surrounding plasma« The plasma was created by discharging a previously^eharged lumped-^ parameter delay line through, a specially con-structed vessel containing an argoia^hydrogen mixture. By means of a rotatajag-mirror shutter^ light from the discharge was admitted to the spectrograph during a time interval when the intensity of the A II lines, was constant to within about 10$* This time interval was chosen after monitoring the time dependence of the intensity of several A II lines with a mono-chromator~photomultiplier combination. A calibration spectrum was also obtained with a seven-step neutral density wedge in order, to determine the response of the photographic emulsion. Of the twenty-four measureable A .11 lines.. . recorded, fourteen yielded profiles which could be treated by a Voigt analysis. In this way the profiles could, toe corrected f o r the effects of instrumental and floppier broadening. The electron number density was de= termined from the widths of the lines i n multiplet 6 of the A I I spectrum, previously measured by other workers. The re s u l t s indicate considerable disagreement with the o r i g i n a l theory of l i n e broadening as developed "by . Griem and h i s co-workers <, The half^widths of the l i n e s >reported here are up to hcQ times wider than predicted theoretically,, The l i n e shapes appear to be Voigt functions, rather- than the predicted Lorentzian p r o f i l e s „ The measure-• meats are i n good agreement with those of other workers,, where comparisons could 'be made*, Measurements of.some of the l i n e s reported here do not appear to have been pub-l i s h e d elsewhereo GRADUATE STUDIES Field of Study: Physics Elementary Quantum Mechanics Waves Electromagnetic Theory Plasma Physics Spectroscopy Advanced Plasma Physics Plasma Dynamics Related Studies; Applied Electronics Electronic Instrumentation Numerical Analysis I Wo Opechowski Jo Sc Savage G* Ma Volkoff Lo G„ de Sobrino A e M„ Crooker A e J„ Barnard F* Lo Curzon W„ A„ G„ Voss F 0 K0 Bowers Tc E„ Hull » AN EXPERIMENTAL STUDY OP ARGON I I LINE PROFILES IN A PULSED ARC P L A S M by CARL RICHARD NEUFELD B . S c , Queen's U n i v e r s i t y , 1962 M . S c , U n i v e r s i t y of B r i t i s h C olumbia, 1961L A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF • Ph.D. i n the Department of P h y s i c s We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA December, 1966 © Carl Richard Neufeld 1967 In, p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l able f o r reference and study, I f u r t h e r agree t h a t permission, f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of Physics^ The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date 26 January, 1967 i i ABSTRACT T i m e - r e s o l v e d s p e c t r o g r a p h i c t e c h n i q u e s were used t o o b t a i n the p r o f i l e s of A I I l i n e s e m i t t e d from a l a b o r -a t o r y plasma. F o r the dense, l o w - t e m p e r a t u r e plasma s t u d i e d , most o f the b r o a d e n i n g o f the observed l i n e s r e s u l t s f r om i n t e r a c t i o n s of t h e e m i t t e r w i t h f r e e charges i n the s u r r o u n d -i n g plasma. The plasma was c r e a t e d by d i s c h a r g i n g a p r e -v i o u s l y - c h a r g e d lumped-parameter d e l a y l i n e t h r o u g h a s p e c -i a l l y - c o n s t r u c t e d v e s s e l c o n t a i n i n g an argon-hydrogen mix-t u r e . By means of a r o t a t i n g - m i r r o r s h u t t e r , l i g h t f r o m the d i s c h a r g e was a d m i t t e d t o the s p e c t r o g r a p h d u r i n g a time i n t e r v a l when t h e i n t e n s i t y of the A I I l i n e s was c o n s t a n t t o w i t h i n about 10$. T h i s time i n t e r v a l was chosen a f t e r m o n i t o r i n g the time dependence o f the i n t e n s i t y of s e v e r a l A I I l i n e s w i t h a m o n o c h r o m a t o r - p h o t o m u l t i p l i e r c o m b i n a t i o n . A c a l i b r a t i o n spectrum was a l s o o b t a i n e d w i t h a se v e n - s t e p n e u t r a l d e n s i t y wedge i n o r d e r to determine the r e s p o n s e of the p h o t o g r a p h i c e m u l s i o n . Of the t w e n t y - f o u r measureable A I I l i n e s r e c o r d e d , f o u r t e e n y i e l d e d p r o f i l e s w h i c h c o u l d be t r e a t e d by a V o i g t a n a l y s i s . I n t h i s way t h e p r o f i l e s c o u l d be c o r r e c t e d f o r the e f f e c t s of i n s t r u m e n t a l and D o p p l e r b r o a d e n i n g . The e l e c t r o n number d e n s i t y was determined from the w i d t h s o f i i i t he l i n e s i n m u l t i p l e t 6 of t h e A I I spectrum, p r e v i o u s l y -measured by o t h e r w o r k e r s . The r e s u l t s i n d i c a t e c o n s i d e r a b l e disagreement w i t h t h e o r i g i n a l t h e o r y of l i n e b r o a d e n i n g as developed by Griem and h i s c o - w o r k e r s . The h a l f - w i d t h s of the l i n e s r e p o r t e d here are up to l i . O times w i d e r than p r e d i c t e d t h e -o r e t i c a l l y . The l i n e shapes appear t o be V o i g t f u n c t i o n s , r a t h e r t h a n the p r e d i c t e d L o r e n t z i a n p r o f i l e s . The measure-ments are i n good agreement w i t h t h o s e of o t h e r w o r k e r s , where comparisons c o u l d be made. Measurements of some of the l i n e s r e p o r t e d here do not appear t o have been p u b l i s h e d e l s e w h e r e . i v TABLE OP CONTENTS PAGE Abstract i i Table of Contents iv Index of Tables v i Index of Figures * * v i i Acknowledgements i x CHAPTER 1. Introduct ion 1 2. The Theory of Line Broadening 8 1. Introduction 8 2. The Stark Effect and Ionic Broadening 9 3. The Ef fec t of E l ec t ron ic C o l l i s i o n s 11 [j.. The Fold ing of Ionic and E l e c -tronic Ef fec ts 17 3. Experimental Work 20 1. Introduction 20 2. Plasma Generator 20 3. Opt i ca l Equipment and P r e l i m i n -ary Invest igat ion . . . . . . . . . . . . . . . . 25 Light Shutter and Tr igger ing A r -rangement 3° 5. A u x i l i a r y E l e c t r o n i c Equipment . . I4.O 6. P i n a l Experimental Arrangement . . I4.I 7. Experimental Procedure for De-termining the Instrument Function 1+2 V TABLE OF CONTENTS (c o n t ' d ) CHAPTER PAGE 8. G a t h e r i n g the P i n a l D a t a 1+6 l i . A n a l y s i s and R e s u l t s 1+8 1. I n t r o d u c t i o n 1+8 2. Data R e d u c t i o n 1+9 3. V o i g t A n a l y s i s of S p e c t r a l L i n e s 52 1+. The C a l c u l a t i o n of the I n s t r u -mental F u n c t i o n 60 5. O b t a i n i n g the A I I L i n e P r o f i l e s 61+ 6. The D e t e r m i n a t i o n of N and kT 66 e 1. The E x p e r i m e n t a l R e s u l t s ........ . 69 8. A D i s c u s s i o n of E r r o r s 71 5. C o n c l u s i o n 75 APPENDIX 1. The P h o t o g r a p h i c P r o c e s s 79 2. Thermal E q u i l i b r i u m and the C a l c u l a t i o n of S p e c t r o s c o p i c Temperature 81+ 3 . F o r b i d d e n L i n e s ., 88 l+. T a b l e of Standard V o i g t P r o f i l e s 92 5. I . B . M . Program used t o C a l c u l a t e L i n e P r o f i l e s 93 6. Readings of P l a t e P o s i t i o n and T r a n s m i s -s i o n Obtained by S c a n n i n g the S p e c t r o -g r a p h s P l a t e s . .... 91+ v i INDEX. OP TABLES NO. PAGE 1. A II l ines studied with the monochromator 26 2!. Manufacturer's data and experimental values for the density D of the H i l g e r step wedge 1+5 3. Determination of Voigt parameters^/h and h for A II 1+806 I l i n e 60 1+. Determination of instrumental funct ion i n the region around 1+300 2. 61+ 5 . Steps i n c a l c u l a t i n g the p r o f i l e of the A II l i n e at 1+806 2, correc t ing for i n s t r u -mental and Doppler broadening 66 6. P u l l half-widths for mult ip le t 6 of A I I 67 7. Re la t ive argon ion populations for kT = 2.0 ev. 68 8. P u l l half-widths of A II l ines 70 9. Standard Voigt P r o f i l e s 92 INDEX OP FIGURES NO. PAGE 1. Perturbat ion of energy leve ls of a 3 - l e v e l atom by the quadratic Stark ef fect 10 2. F u l l half-widths of l ines from mult ip lets 1, 6 and 10 of the A II spectrum as a funct ion of temperature • 18 3. Schematic of plasma generator 21 1|. Current pulse passing through plasma vessel . . . . . 22 5. Cross - sec t iona l view of e l e c t r o l y t i c t e r -minating r e s i s t o r . 23 6. Plasma vessel * 21+ 7. a) Current waveform 27 b) Luminosity of A II l i n e 27 8. Framing camera photographs of plasma discharge 29 9. Diagram of l i g h t shutter 31 10. Shape of l i g h t pulse entering spectrograph 32 11. Sequence of t r igger pulses and delayed pulses used i n the operation of the f r e -quency gate 3k-12. Block diagram of e l ec tron ic units , 35 13. Sequence of pulses used i n t r i g g e r i n g the discharge 36 Ik* Output of coincidence unit 37 15. F i n a l experimental arrangement 1+2 16. Sketch of plasma plate $1 17. Voigt f i t for A II 1+806 8 l i n e 57 18. Voigt f i t for A II 1+579 £ l i n e 59 v i i INDEX OP FIGURES ( c o n t ' d ) NO. PAGE 19. F u l l h a l f - w i d t h h of the i n s t r u m e n t a l f u n c t i o n p l o t t e d a g a i n s t w a v e l e n g t h 62 A l T y p i c a l b l a c k e n i n g (H and D) curve f o r p h o t o g r a p h i c e m u l s i o n 80 A2 Energy s t a t e s i n the absence of e x t e r n a l f i e l d s 88 A3 R e c i p r o c a l d i s p e r s i o n of the s p e c t r o g r a p h as a f u n c t i o n of w a v e l e n g t h 95 v i i i ACKNOWLEDGEMENTS I am indebted to Dr. A. J. Barnard for his stimu-l a t i n g supervision and invaluable aid. I wish to thank Mr. R. H. Nelson who, as a summer research assistant, constructed much of the apparatus. I am indebted to Mr. H. D. Campbell for his generous aid and co-operation i n the construction, maintenance, and operation of the apparatus. I would l i k e to thank the many graduate students and members of the physics department who have helped me through informal discussions. I am also g r a t e f u l to Dr. H. Wulff for his prompt and generous response to requests for aid in the experimental design. Thanks also to the various members of the techni-c a l s t a f f for the i r co-operation and valuable assistance. I am also g r a t e f u l for the considerable f i n a n c i a l support given me by the National Research Council and the Atomic Energy Commission of Canada. ix CHAPTER 1 I n t r o d u c t i o n I n t e r e s t i n the s u b j e c t of s p e c t r o s c o p y dates back at l e a s t t o the time of S i r I s a a c Newton. S p e c t r o s c o p i c s t u d i e s have y i e l d e d a s u r p r i s i n g amount of i n f o r m a t i o n about the n a t u r e of the u n i v e r s e . I t was by s p e c t r o s c o p i c means, f o r example, t h a t h e l i u m was d i s c o v e r e d i n the sun's atmos-phere b e f o r e b e i n g found on the e a r t h . The a n c i e n t o r i g i n s of s p e c t r o s c o p y have not dim-i n i s h e d the v i g o u r of contemporary i n t e r e s t i n the s u b j e c t . R a t h e r , s p e c t r o s c o p i c s t u d y i s t o - d a y b e i n g u n d e r t a k e n w i t h renewed e n t h u s i a s m . Much v a l u a b l e i n f o r m a t i o n about the p h y s i c a l w o r l d c o n t i n u e s t o be p r o v i d e d by s p e c t r o s c o p y , sometimes under c i r c u m s t a n c e s where no o t h e r method i s a v a i l -a b l e t o the e x p e r i m e n t a l i s t . " O p t i c a l astronomy and, more r e c e n t l y ; r a d i o a s t r o -nomy, have used s p e c t r o s c o p i c methods t o good advantage. I n f o r m a t i o n r e g a r d i n g the c o m p o s i t i o n s , t e m p e r a t u r e s , and v e l o c i t i e s of s t a r s can be o b t a i n e d by a s p e c t r a l a n a l y s i s o f the l i g h t e m i t t e d by them. R a d i o astronomy, i n a n a l y z i n g e l e c t r o m a g n e t i c r a d i a t i o n of l o n g e r w.avelength, can extend the o p t i c a l o b s e r v a t i o n s . The r e c e n t d i s c o v e r y o f q uasars by c o m bining the t e c h n i q u e s of o p t i c a l and r a d i o astronomy promis e s some v e r y i n t e r e s t i n g i n s i g h t s i n t o the nature of 1 2 the universe . An in teres t i n spectroscopy can be coupled with , or indeed stimulated by, an interes t i n plasma phys ics . The subject of plasma spectroscopy is both in teres t ing and r e -warding, and y ie lds information on two f ront i er s of phys ics . On the one hand, important plasma parameters such as the temperature and e lec tron number density can be measured ac-curate ly by spectroscopic means without perturbing the p l a s -ma. On the other hand, comparison of spectroscopic observa-t ions with the resu l t s of t h e o r e t i c a l ca l cu la t ions can revea l new ins ights into the study of atomic parameters. The branch of spectroscopy concerned with the study of the shape of spec tra l l ine s i s current ly a t t r a c t i n g con-s iderable a t t e n t i o n . Interest i n spectra l l i n e shapes was aroused before the turn of the century, when Michelson ( 1 8 9 5 ) published the f i r s t comprehensive paper on the subject . With the discovery of the Stark: and Zeeman e f f ec t s , and the devel -opment of quantum mechanics, a keen interes t i n the study of spec tra l l i n e shapes has developed. Strong l o c a l e l e c t r i c f i e l d s ex is t i n dense labor -atory plasmas because of the high concentration of charged p a r t i c l e s . These f i e l d s perturb the e l ec tron ic energy states of nearby atoms or ions , and th i s perturbat ion is re f lec ted i n the r a d i a t i o n they emit. The l i n e shapes are only weakly 3 i n f l u e n c e d by the D o p p l e r e f f e c t . A c l a s s i c paper on the i n f l u e n c e o f the S t a r k e f -f e c t on l i n e shapes was w r i t t e n by H o l t s m a r k (1919). I t i s the f i r s t attempt t o d e s c r i b e the p r o f i l e of a s p e c t r a l l i n e when the e m i t t i n g atom was s u b j e c t e d t o an e l e c t r i c f i e l d w h i c h v a r i e d s l o w l y i n t i m e . The o r i g i n a l t r e a t m e n t has been improved by many w o r k e r s , n o t a b l y Anderson (191+9) and Griem, K o l b and Shen (1959). Griem et a l (1959) c o n s i d e r i n d e t a i l the e f f e c t s of plasma e l e c t r o n s on the l i n e shape. E x t e n s i v e n u m e r i c a l c a l -c u l a t i o n s have been p u b l i s h e d on the b a s i s of t h i s t h e o r y . These r e s u l t s are summarized i n the book by Griem (1961+) p l+i+5 f f , w h i c h a l s o c o n t a i n s r e f e r e n c e s t o the o r i g i n a l p a p e r s . Some d i f f i c u l t i e s r e m a i n , however, i n the t r e a t m e n t by Griem (1961+) of r a d i a t i o n from i o n s . The use of s t r a i g h t -l i n e paths r a t h e r t h a n h y p e r b o l i c t r a j e c t o r i e s t o d e s c r i b e t h e "motions of plasma e l e c t r o n s w h i c h c o l l i d e w i t h the e m i t -t i n g i o n s seemed p a r t i c u l a r l y q u e s t i o n a b l e . E x p e r i m e n t a l s t u d i e s w i t h shock tubes by workers i n t h i s l a b o r a t o r y i n d i c a t e d t h a t the l i n e s from A I I i o n s might be c o n s i d e r a b l y w i d e r t h a n p r e d i c t e d by Griem (1961+). An ex-p e r i m e n t a l s t u d y of the shape of i o n i c s p e c t r a l . l i n e s was t h e r e f o r e u n d e r t a k e n . A plasma g e n e r a t o r was c o n s t r u c t e d i n wh i c h the plasma was c r e a t e d by d i s c h a r g i n g a p r e v i o u s l y -charged lumped delay l i n e through a spec ia l ly -cons tructed plasma ves se l . With the aid of a ro ta t ing -mirror shutter , spectra of the discharge were recorded on a photographic p l a t e , and the r e s u l t i n g l i n e p r o f i l e s were measured. While th i s experiment was i n progress, Ja lufka et a l (1966) and Popenoe and Shumaker (1965)) published the resu l t s of some measurements on A II l i n e s . The t h e o r e t i c a l estimates for the widths appeared to be i n error by factors ranging from about 2.6 to 10. A correc t ion to his e a r l i e r work was pub-l i shed by Griem (1966), g iv ing better agreement with exper i -mental r e s u l t s . This thes is describes the measurement of fourteen A II l i n e s . Measurements on three of these l ines have ap-peared i n the open l i t e r a t u r e , these resu l t s being In good agreement with those reported here. For the remaining l ines presented here, no numerical ca lcu la t ions have appeared. Any t h e o r e t i c a l treatments of l ine broadening, such as the cor -r e c t i o n by Griem (1966) to his e a r l i e r work, should be con-s i s tent with the measurements reported here . This increased' amount of experimental data w i l l help to further the under-standing of atomic processes. The experimental technique used i n these i n v e s t i -gations i s bel ieved to be a useful contr ibut ion to the tech-nology. The photographic measurements were made during a time when condit ions in the plasma, as determined from the i n t e n s i t y of the A I I l i n e s , were f a i r l y steady. The e f f i -ciency of gathering data in th i s way is a vast improvement over that achieved with conventional photoe lectr ic methods. Extension and refinement of th is technique should encourage valuable invest igat ions that would otherwise be exceedingly l abor ious . Chapter 2 of th i s thesis i s devoted to a d iscuss ion of the theory of l i n e broadening which inspired the present experimental work. The book by G-riem (19611), Chapter 1+, contains a complete presentat ion of the theory, and a r e p e t i -t i o n here of the mathematical steps involved does not seem necessary. However, a d iscuss ion of the assumptions and ap-proximations involved i n the so lut ion of this problem is con-sidered to be appropriate . Wherever poss ib le , the discuss ion attempts to present the various assumptions i n p h y s i c a l , rather than mathematical, terms• Chapter 3 presents the experimental part of this i n v e s t i g a t i o n . The plasma generator is described, as wel l as the o p t i c a l equipment used, and the resu l t s of some of the pre l iminary invest igat ions are given. The ro ta t ing -mirror shutter , s p e c i a l l y made for th i s experiment, and the functions of the various e l ec tron ic units used in i t s operat ion, are described i n d e t a i l . The a u x i l i a r y e l ec tron ic equipment, f a i r l y - s t a n d a r d in th is type of research, is mentioned b r i e f -l y and the f i n a l experimental arrangement and condit ions are 6 descr ibed. The o p t i c a l instruments used in th is type of r e -search i n v a r i a b l y d i s t o r t the observed spectra l l i n e p r o f i l e s . To correct for th is instrumental broadening, the "instrument function" of the apparatus must be determined. The necessary experimental procedure is discussed in th i s chapter. Chapter ij. contains the data analys is and exper i -mental r e s u l t s . The information on the spectrographic plate must be converted into a form i n which i t can be r e a d i l y analyzed. The chapter begins with a descr ip t ion of th is data reduct ion . The A II l ine s on the spectrographic plate were subjected to a Voigt analys is (Voigt (1912)) i n order to com-pensate accurate ly for instrumental and Doppler broadening. The resul t s of the fourteen A II l ine s (out of a t o t a l of twenty-four) that could be treated in th i s way are g iven. The remaining l i n e s appeared to have wings too wide to be f i t t e d by Lorentz p r o f i l e s . To correct for instrumental broad-ening, the instrumental funct ion must f i r s t be calculated for a l l wave-lengths of i n t e r e s t . T h e o r e t i c a l l y - d e r i v e d expres-sions were used to ca lcu late the effect of Doppler broaden-i n g . The complete analys is is carr ied through i n d e t a i l for the A II l i n e at I4.806 2 from mult ip le t 6 (as catalogued by Moore (1959)). The plasma temperature, as determined from the fact that only A II ions emitted appreciable r a d i a t i o n , was 2 . 0 ev. The widths of the A II l ine s from mult ip le t 6 indicated 7 17 - 3 an e lectron number density of 3*23 x 1 0 cm. The widths of l ines from this mult ip le t have prev ious ly been measured by Ja lufka et a l ( 1 9 6 6 ) , who found them to he greater than pre-dicted by Griem (1961+) by a factor of 2 . 6 . The f i n a l h a l f -widths of the l ines reported here are greater than predicted by Griem (1961+) by factors of up to 1+.0. Chapter 5 presents some concluding remarks and suggestions for improving the experimental technique.' Sev-e r a l extensions and a l t ernat ive appl icat ions of the method are also mentioned. Several appendices have been included at the end of the t h e s i s . Reference is made to these appendices when the m a t e r i a l i n them becomes relevant to the matter being discussed. CHAPTER 2 The Theory of Line Broadening 1. Introduct ion This chapter presents a descr ip t ion of the approxi-mations and phys ica l assumptions in the theory of l i n e broad-ening* The discuss ion w i l l proceed without the use of math-ematics, since a l l of the mathematical operations appear in Chapter I4. of the book: by G-riem ( 1 9 6 L | . ) . The two plasma components, ions and e lec trons , each exert a c h a r a c t e r i s t i c influence on the shape of spec tra l l ine s emitted by dense laboratory plasmas. Because of the large di f ference in the thermal v e l o c i t y of ions and electrons,-t h e i r effects must be evaluated by separate methods. The ions move r e l a t i v e l y slowly and t h e i r ef fect can be calculated by means of the c u a s i - s t a t i c Stark e f f ec t . The e lec trons , on the other hand, move so r a p i d l y that t h e i r broadening ef-fects can be described In terms of impacts. C l a s s i c a l l y , the e f fect of e l ec tron ic c o l l i s i o n s is taken to be equivalent to an i n t e r r u p t i o n of the r a d i a t i o n of the emitter for a short period of t ime. When the emitter begins r a d i a t i n g again, i t w i l l have suffered a random change in phase. I f the emitter i s considered as a c l a s s i c a l harmonic o s c i l l a t o r , th i s i n t e r -act ion resu l t s i n the f a m i l i a r Lorentz, broadening of the monochromatic l i n e being emitted. The name sometimes as-signed to th i s mechanism is i n t e r r u p t i o n broadening. 8 9 To describe the broadening of both ions and e lec -trons the effects of the two mechanisms must be "folded." This i s accomplished by c a l c u l a t i n g the e lec tronic ef fect for a given value of the ion f i e l d and then averaging over a l l such f i e l d s . 2. The Stark Ef fec t and Ionic Broadening I f an atom exis ts i n a region i n which an e l e c t r i c f i e l d E is present, the o r b i t a l electrons w i l l experience a force eE due to the f i e l d . The ef fect of such a force on the various e l ec tron ic energy states must be evaluated with the aid of perturbat ion theory. The treatment i s quite standard and can be found, for example, in the book by Landau and L i f s h i t z (1965), Chapter V I . The resu l t s of the perturbat ion c a l c u l a t i o n for non-degenerate leve ls (non-hydrogenic atoms or ions) show that each energy l e v e l i s influenced by a l l of the others i n the atom, a s i t u a t i o n referred to as "mixing". For the p o t e n t i a l involved here, which is of the form eEz, (where z is the d i s -placement of the e l e c t r o n ) , there is no change i n the energy l eve l s when the c a l c u l a t i o n is carr i ed to f i r s t order . A second order c a l c u l a t i o n reveals a s l i g h t change in the en-ergies of the s ta t ionary s ta tes . Since the perturbat ion of the l eve l s is proport ional to the square of the absolute value of the f i e l d , the term "quadratic Stark effect" is usua l ly used to describe th is s i t u a t i o n . The behaviour of a 1 0 h y p o t h e t i c a l t h r e e - l e v e l atom e x h i b i t i n g the above e f f e c t i s shown i n F i g . 1 . 2 E X C I T E D S T A T E S G R O U N D S T A T E B F i g . 1 P e r t u r b a t i o n of energy l e v e l s of a 3 - l e v e l atom by the q u a d r a t i c S t a r k e f f e c t . The f i e l d v a r i e s from z e r o t o a maximum I n t h e r e g i o n AB. I t may be noted i n p a s s i n g t h a t a l i n e a r S t a r k e f f e c t i s e x h i b i t e d by hydrogen and h y d r o g e n - l i k e energy schemes. I n t h i s case the energy l e v e l s are degenerate i n the o r b i t a l quantum numbers. I n a plasma the e m i t t e r sees a t i m e - v a r y i n g e l e c -t r i c f i e l d i n d u c ed by the s l o w l y - m o v i n g plasma i o n s nearby. A l s o , e m i t t e r s i n d i f f e r e n t r e g i o n s of the same volume element w i l l see d i f f e r e n t v a l u e s o f the i o n f i e l d at any g i v e n i n -s t a n t . The observed s p e c t r a l l i n e i s the sum of c o n t r i b u t i o n s f r o m many e m i t t e r s . The e f f e c t of the s e p e r t u r b i n g i o n s i s c a l c u l a t e d 11 with the aid of the "quas i - s ta t ic approximation". This is e s s e n t i a l l y the method used by Holtsmark (1919) in which the f i e l d strengths corresponding to various ion ic configurations are c a l c u l a t e d . Averages over a l l configurations are taken and the p r o b a b i l i t y 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 at the emitter i s evaluated. Holtsmark used th i s d i s t r i b u t i o n of f i e l d s to ca lcu la te the p r o f i l e s of hydrogen l i n e s . Since the ions move r e l a t i v e l y slowly and s t a t i s t i c a l averages must be taken to ca lculate the l i n e p r o f i l e s , the q u a s i - s t a t i c approximation provides an adequate descr ip t ion of the effects of plasma Ions. An improvement to the f i e l d d i s t r i b u t i o n s of Holtsmark is due to Ecker (195>7), who considers c o r r e l a -t ions among the ions . In consequence, the various i on i c con-f igurat ions are weighted by addi t iona l p r o b a b i l i t i e s depend-ind on the strength of the repuls ive forces between the ions . Configurations in which a l l the ions are i n the same small volume element are then less probable than ones i n which the ions are d i s t r i b u t e d almost uniformly throughout the whole ava i lab le volume. The theory of Holtsmark assigned the same p r o b a b i l i t y to a l l i on ic conf igurat ions . 3. The Ef fec t of E l e c t r o n i c C o l l i s i o n s To describe the effect of c o l l i s i o n s between the emitter and plasma e lec trons , the "impact approximation" is made. The assumption here is that the electrons are moving 12 v e r y r a p i d l y and the e m i t t e r e x p e r i e n c e s the presence of p l a s -ma e l e c t r o n s as c o l l i s i o n s or impacts w i t h i n d i v i d u a l par-t i c l e s . The average i n t e r a c t i o n i s assumed t o be weak, but each c o l l i s i o n i s o f s h o r t d u r a t i o n and s e p a r a t e d i n time from o t h e r c o l l i s i o n s . T h i s assumption i s seen t o be the converse of the q u a s i - s t a t i c a p p r o x i m a t i o n as d e s c r i b e d above. The b r o a d e n i n g produced by t h e s e e l e c t r o n impacts can be e v a l u a t e d by c a l c u l a t i n g the a u t o - c o r r e l a t i o n f u n c t i o n . T h i s f u n c t i o n i s a measure of the d i s t r i b u t i o n of times be-tween c o l l i s i o n s , and of the phase change i n t r o d u c e d by each c o l l i s i o n . The quantum m e c h a n i c a l analogue of the c l a s s i c a l a u t o - c o r r e l a t i o n f u n c t i o n must be e v a l u a t e d , s i n c e the energy s t a t e s of the r a d i a t o r are q u a n t i z e d i n accordance w i t h atomic t h e o r y . The f o l l o w i n g p h y s i c a l p i c t u r e i l l u s t r a t e s the ap-p r o a c h t o the problem of e l e c t r o n c o l l i s i o n s . The e m i t t e r i s c o n s i d e r e d as a quantum m e c h a n i c a l system, whose H a m i l t o n i a n i n c l u d e s a terra due t o the i n s t a n t a n e o u s v a l u e of the i o n f i e l d . The e l e c t r o n s are c o n s i d e r e d as c l a s s i c a l p a r t i c l e s whose " c o l l i s i o n s " w i t h the e m i t t e r can be c h a r a c t e r i z e d by t h e i r v e l o c i t i e s and impact p a r a m e t e r s . The e f f e c t of a c o l -l i s i o n w i t h one e l e c t r o n h a v i n g a v e l o c i t y v^ and impact parameter p ^ i s c a l c u l a t e d . S i n c e o n l y the magnitudes of ^ and are i m p o r t a n t the d i r e c t i o n s are i g n o r e d . Next, a v e r -13 ages over the magnitudes of and v^ are t a k e n , assuming a M a x w e l l i a n v e l o c i t y d i s t r i b u t i o n f u n c t i o n a t a g i v e n temper-a t u r e f o r the plasma e l e c t r o n s . P r o c e e d i n g i n t h i s manner the a u t o - c o r r e l a t i o n f u n c t i o n f o r e l e c t r o n impacts can be c a l -c u l a t e d . I t i s p h y s i c a l l y obvious t h a t the above c a l c u l a -t i o n w i l l be temperature-dependent. The e l e c t r o n v e l o c i t i e s w i l l v a r y as the square r o o t of the temperature and a moder-ate t h e r m a l dependence might be e x p e c t e d . ( T h i s temperature dependence i s d i s t i n c t from t h a t due t o the D o p p l e r e f f e c t . ) T h i s t u r n s out t o be the c a s e , the l i n e p r o f i l e s b e i n g f a i r l y i n s e n s i t i v e t o changes i n t e m p e r a t u r e . The number of c o l l i -s i o n s between a s p e c i f i c e m i t t e r and t h e plasma e l e c t r o n s w i l l v a r y l i n e a r l y w i t h the e l e c t r o n number d e n s i t y , and the t h e o r y does p r e d i c t such a l i n e a r dependence. The p h y s i c a l model d e s c r i b e d above i s t r e a t e d m a t h e m a t i c a l l y by means of the s e m i - c l a s s i c a l a p p r o x i m a t i o n , so c a l l e d because the system of e m i t t e r - p l u s - p e r t u r b e r i s d e a l t w i t h by a c o m b i n a t i o n of quantum m e c h a n i c a l and c l a s -s i c a l methods. The e l e c t r o n t r e a t m e n t i s r e f e r r e d t o as the " c l a s s i c a l p a t h a p p r o x i m a t i o n " . T h i s a p p r o x i m a t i o n i n v o l v e s the a d d i t i o n a l assumption t h a t the e l e c t r o n t r a j e c t o r i e s are independent of the quantum m e c h a n i c a l s t a t e of the e m i t t e r . Such an assumption n e g l e c t s any back r e a c t i o n of the e m i t t e r Ik on the perturber . C l e a r l y this assumption is not quite con-s i s t e n t , since some back react ion must exis t i f the state of the emitter is changed by the c o l l i s i o n . Interact ions in which the state of the emitter is unchanged are not consid-ered as c o l l i s i o n s . Griem (1961+) states that the c l a s s i c a l path approximation is quite adequate when c a l c u l a t i n g l i n e p r o f i l e s , although the problem of perturber scat ter ing can-not be treated i n th is way. For the case of neutral emitters , then, the per-turber t r a j e c t o r i e s w i l l be s tra ight l i n e s . When the emitters are ions , the t r a j e c t o r i e s w i l l be hyperbolae, since there is then a net force on the perturber due to the ion ic ccharge,* -(It may be noted here that Griem's numerical ca lcu la t ions for A II l ine s were made using s t r a i g h t - l i n e t r a j e c t o r i e s , a l -though hyperbolae are p h y s i c a l l y more r e a l i s t i c . In the l a t e r paper by Griem (1966) hyperbol ic t r a j e c t o r i e s are used.) The use of the c l a s s i c a l path approximation sets a lower l i m i t on the impact paramet er , / 0 , for the c o l l i s i o n s . The de Brogl ie wavelength for the perturbing e lectron must a l -ways be small compared with {O, the distance of c losest ap-proach In the case of s t r a i g h t - l i n e paths. Hence, very close c o l l i s i o n s cannot be treated i n th i s s e m i - c l a s s i c a l p i c t u r e . i The actual cut -o f f at small values of f> i s based on consider-ations of the behaviour of the auto -corre la t ion funct ion for decreasing values of /O. The cu t -o f f is taken for values o fp 15 f o r w h i c h almost complete d e s t r u c t i o n of the c o r r e l a t i o n of the s t a t e s of the system b e f o r e and a f t e r the c o l l i s i o n o c c u r s . A s e p a r a t e e s t i m a t e i s made f o r s t r o n g c o l l i s i o n s . The r e s u l t i n g e s t i m a t e f o r the minimum v a l u e of p i s s t i l l much l a r g e r than the de B r o g l i e w a v e l e n g t h of the p e r t u r b i n g e l e c t r o n s and c o n s i s t e n c y w i t h the c l a s s i c a l p a t h approxima-t i o n i s a s s u r e d . A maximum impact parameter must a l s o be d e f i n e d , as the c a l c u l a t i o n o t h e r w i s e d i v e r g e s f o r l a r g e v a l u e s of p as w e l l as f o r s m a l l v a l u e s . The maximum v a l u e of p can be t a k e n as b e i n g r o u g h l y e q u a l t o the Debye r a d i u s f o r the p l a s -ma, as the- e f f e c t s of e l e c t r o n s w i t h l a r g e r impact p a r a -meters w i l l be s h i e l d e d by plasma e l e c t r o n s near the e m i t t e r . I t i s a l s o p o s s i b l e t h a t the e f f e c t of c o l l i s i o n s w i t h l a r g e Impact parameters w i l l be o v e r e s t i m a t e d by the impact approx-i m a t i o n . T h i s i s so because the c o l l i s i o n s may no l o n g e r be completed i n a s m a l l time i n t e r v a l , as r e q u i r e d by the impact a p p r o x i m a t i o n . Lewis (1961) g i v e s a c r i t e r i o n based on t h i s c o n s i d e r a t i o n t o determine the maximum impact parameter. The s m a l l e r of these two e s t i m a t e s f o r the maximum impact p a r a -meter i s used f o r each c a l c u l a t i o n of l i n e b r o a d e n i n g . Fo r the case of A I I l i n e s and l i n e s from the i o n s of l i g h t and medium elements g e n e r a l l y the n u m e r i c a l c a l c u l a -t i o n s are based on the v a l i d i t y of the " i s o l a t e d l i n e " approx-i m a t i o n t . The meaning of the term " i s o l a t e d l i n e " can be under-16 stood with the aid of P i g . 1. In order to treat th is hypothet ica l atom by means of the i so la ted l ine theory, the l eve l s 2 and 3 must have an energy separation greater than kT, the mean thermal energy of the e l ec trons . The re su l t can be general ized to any atom by saying that the upper l e v e l i n -volved i n an o p t i c a l t r a n s i t i o n must be we l l separated from i t s nearest neighbour. The above approximation requires that the proba-b i l i t y of an e lectron i n an excited l e v e l moving to another l e v e l as the re su l t of a c o l l i s i o n i s n e g l i g i b l y s m a l l . Stated another way, broadening c o l l i s i o n s must be far more frequent than exc i t ing or de -exc i t ing c o l l i s i o n s . Since the average energy exchanged during a c o l l i s i o n is much less than kT/ for the c l a s s i c a l path approximation to h o l d , th is approx-imation does not normally e n t a i l a new assumption. The exception occurs i n the case of hydrogen. Here the l i n e a r Stark ef fect due to the ion f i e l d s p l i t s each l e v e l into a number of l e v e l s . These leve ls are too close to each other to be treated by the i so lated l ine theory. Before the advent of the general ized impact theory (Baranger (1958)* Kolb and Griem (1958)), no adequate way of c a l c u l a t i n g the e lec tron broadening for the case of hydrogen was poss ib le . A spec ia l treatment of hydrogen is given by Griem (I96I4.), p7h f f » in which the i so lated l i n e approximation is not made. 17 ij . . The F o l d i n g of I o n i c and E l e c t r o n i c E f f e c t s The s o l u t i o n of the l i n e b r o a d e n i n g problem p r o -ceeds by f i r s t c a l c u l a t i n g the a u t o - c o r r e l a t i o n f u n c t i o n f o r e l e c t r o n i m p a c t s , assuming a c e r t a i n v a l u e of the i o n i c f i e l d . N e x t , the e l e c t r o n i c e f f e c t i s " f o l d e d " i n t o the v a r i o u s p o s s i b l e i o n i c f i e l d s t r e n g t h v a l u e s t o a r r i v e at the f i n a l e s t i m a t e of the b r o a d e n i n g . The f o l d i n g of the e l e c t r o n i c and i o n i c e f f e c t s as d e s c r i b e d above assumes com-p l e t e independence of the motions of e l e c t r o n s and i o n s . Griem does not d i s c u s s the e r r o r i n t r o d u c e d by t h i s s i m p l i -f i c a t i o n o f the t h e o r y . The r e s u l t s of the c a l c u l a t i o n s of Griem (1961|) f o r s e v e r a l m u l t i p l e t s of i n t e r e s t i n the A I I spectrum are shown i n F i g . 2. The temperature dependence of the f u l l h a l f -w i d t h of l i n e s i n these m u l t i p l e t s i s shown f o r an assumed 17 e l e c t r o n number d e n s i t y of 3.0 x 10 ' cm J . The h a l f - w i d t h s c a l e s l i n e a r l y w i t h the e l e c t r o n number d e n s i t y . E l e c t r o n s are the dominant b r o a d e n i n g mechanism f o r l i n e s i n the A I I spectrum. The b r o a d e n i n g e f f e c t of the i o n s and e l e c t r o n s i s r e f e r r e d t o c o l l e c t i v e l y as " S t a r k b r o a d e n i n g " . W h i l e t h i s name i s c l e a r l y a p p r o p r i a t e when c o n s i d e r i n g p e r t u r b i n g i o n s , the meaning i s perhaps somewhat obscure when a p p l i e d t o p e r -t u r b i n g e l e c t r o n s . C l e a r l y , impact b r o a d e n i n g by the e l e c -t r o n s i s o n l y l o o s e l y a s s o c i a t e d w i t h the s t a t i c S t a r k e f f e c t . 18 P i g . 2 P u l l half-widths of l ines from mult ip lets 1, 6 and 10 of the A II spe ctrum as a funct ion of temperature. The broadening due to the Doppler e f fect is not inc luded . The assumed e lectron number density is 3 . 0 x 10 'cm"-'. 19 The o n l y f e a t u r e the two e f f e c t s have i n common i s the f a c t t h a t i n b o t h cases e l e c t r i c f i e l d s c o n s t i t u t e the i n t e r a c t i o n mechanism. F or t h i s r e a s o n the e l e c t r o n s are i n c l u d e d as con-t r i b u t o r s t o S t a r k b r o a d e n i n g , a l t h o u g h t h e i r e f f e c t f a l l s more n a t u r a l l y i n t o the g e n e r a l c a t e g o r y of p r e s s u r e b r o a d -e n i n g . I n summary, a l l o f the above d i s c u s s i o n may be c o n s i d e r e d as a d i c t i o n a r y of terms and concepts used i n the t h e o r e t i c a l t r e a t m e n t . The a u t h o r made no attempt a t im-p r o v i n g t h i s t h e o r y . CHAPTER 3 • E x p e r i m e n t a l Work 1. I n t r o d u c t i o n The plasma g e n e r a t o r i s s i m i l a r t o one used by Dur-and ( 1 9 6 3 ) . I n a d d i t i o n , v a r i o u s o p t i c a l i n s t r u m e n t s were used i n the c o u r s e of t h e s e i n v e s t i g a t i o n s . These i n s t r u -ments are d e s c r i b e d i n t h i s c h a p t e r , t o g e t h e r w i t h the p r e l i m -i n a r y r e s u l t s p r o v i d e d by t h e i r use. A d e t a i l e d d e s c r i p t i o n of the d e s i g n and adjustment of the o p t i c a l s h u t t e r i s g i v e n . T h e t a u x i l i a r y e l e c t r o n i c equipment i s b r i e f l y mentioned, and the f i n a l e x p e r i m e n t a l arrangement d e s c r i b e d . To c o r r e c t f o r the d i s t o r t i o n of s p e c t r a l l i n e shapes i n t r o d u c e d by the op-t i c a l a p p a r a t u s , the " i n s t r u m e n t f u n c t i o n " ' of the equipment must be known. The e x p e r i m e n t a l procedure f o r o b t a i n i n g t h i s f u n c t i o n i s o u t l i n e d . The c h a p t e r ends by g i v i n g the c o n d i -t i o n s under w h i c h the f i n a l d a t a were o b t a i n e d . 2. Plasma G e n e r a t o r The plasma was produced by d i s c h a r g i n g a p r e v i o u s l y -charged lumped-parameter d e l a y l i n e , c o n s i s t i n g of s i x t e e n 5/if. c a p a c i t o r s and s i x t e e n i n d u c t o r s , t h r o u g h a s p e c i a l d i s -charge v e s s e l . A d i s c u s s i o n of the t h e o r y of d e l a y l i n e s i s g i v e n i n the book by M i l l m a n and Taub (1956), p 286 f f . The g e n e r a t o r i s shown s c h e m a t i c a l l y i n P i g . 3. 20 21 U U L U L 1 6 | S R P i g . 3 Schematic of plasma generator S = spark gap switch R = terminat ing r e s i s t o r T = plasma vessel The dotted box encloses the delay l i n e . The delay l i n e , previous ly charged by a 0-20 kV power supply (not shown here) , was discharged through a spark gap switch. This switoh consisted of two brass e l ec -trodes mounted in a c y l i n d r i c a l container of brass and l u c i t e . D i f f erent f i r i n g voltages could be accommodated by adjust ing the spacing of the e lec trodes . A tungsten t r igger pin was i n -serted through a hole i n one of the electrodes and the switch was closed by applying a high-voltage pulse from a Theophanls t r i g g e r uni t (Theophanls (I960)) between th i s p in and the e l ec trode . The current then passed through a terminating r e s i s t o r in series with the plasma vesse l . This r e s i s t o r was designed to have a value of about 0.5 ohms to match the char-22 a c t e r i s t i c impedance of the bank. The r e s u l t i n g c u r r e n t waveform was a s t e p of about 90^asec. d u r a t i o n w i t h the am-p l i t u d e r e m a i n i n g c o n s t a n t t o w i t h i n about 5 $ . A. s k e t c h of t h e c u r r e n t waveform, measured by m o n i t o r i n g the v o l t a g e w i t h a h i g h - v o l t a g e probe at a p o i n t between the s w i t c h and the r e s i s t o r , i s shown i n P i g . 1+. < TIME fyisec.) P i g . 1+ C u r r e n t p u l s e p a s s i n g t h r o u g h plasma v e s s e l . I n o r d e r t o a c h i e v e the d e s i r e d shape f o r the c u r -r e n t waveform i t was n e c e s s a r y t o c o r r e c t f o r r e s i s t i v e l o s s e s i n the d e l a y l i n e components. T h i s was a c c o m p l i s h e d by a d j u s t -i n g t h e - v a l u e s of the i n d u c t a n c e s , t h o s e near the output end of the l i n e b e i n g s l i g h t l y l a r g e r than those a t the o t h e r end. The t e r m i n a t i n g r e s i s t o r was s p e c i a l l y c o n s t r u c t e d t o c a r r y the l a r g e c u r r e n t s i n v o l v e d (about lq. k A ) . F i g . 5 g i v e s a diagram of the c o n s t r u c t i o n , i n w h i c h a s o l u t i o n of Cross-sectional view of electrolytic terminating resistor. 50 cm. - C O P P E R - E L E C T R O D E S 0" RING SEAL copper s u l p h a t e a c t s as the r e s i s t i v e element. The plasma v e s s e l , shown i n P i g . 6, was made of g l a s s t u b i n g and had aluminum e l e c t r o d e s f a s t e n e d at each end w i t h epoxy. The end windows, f i t t e d t o the s h o r t s e c -2.5 Gm. 1.2 cm. ' j l« 71 - 2 2 cm. -* P i g . 6 Plasma V e s s e l t i o n s o f g l a s s t u b i n g i n the c e n t r e s of the e l e c t r o d e s w i t h D e k h o t i n s k y wax, f a c i l i t a t e d end-on o b s e r v a t i o n of the p l a s -ma, i f d e s i r e d . The v e s s e l was mounted t o p e r m i t b o t h end-on and s l d e - o n o b s e r v a t i o n . Some ca r e was t a k e n i n the c o n s t r u c t i o n of the tube t o a v o i d g e t t i n g any epoxy near the i n n e r s u r f a c e s of the 25 aluminum e lec trodes . It was hoped that this precaution would el iminate Impurity l ines in the plasma spectrum a r i s i n g from vaporized epoxy. The plasma vessel was connected to a vacuum pump and gas metering system. A1 chamber was also f i t t e d to allow mixing gases from two separate supply bot t les and using th i s mixture i n the plasma v e s s e l . The ent ire vacuum system could be pumped down to a base pressure of about 20^ Hg., with no noticeable pressure r i s e within about t h i r t y seconds of t u r n -ing of f the pump. 3. O p t i c a l Equipment and Prel iminary Invest igat ion The plasma r a d i a t i o n was f i r s t studied with a H i l -ger E l prism spectrograph with quartz o p t i c a l system. The r e c i p r o c a l d i spers ion of th is instrument varied from about 10 fi/ram. at 3100 £ to about 25 S/mra. at 6500 S. The f / - number of th is spectrograph was about 30. A t ime-integrated spec-trum of the plasma r a d i a t i o n was thus obtained, using a bank voltage of 12 kV and an i n i t i a l pressure of about 10 mm. Hg of pure argon i n the plasma vesse l . Ten exposures produced a measurable p l a t e . Analys is of the plate revealed the presence of about 60 A II l i n e s . One A III l i n e (3795 ft) appeared, and no A I l i n e s could be found. Very few impurity l ines were present,-the only strong l ine s coming from S i I I . In p a r t i c u l a r , the 26 hydrogen l i n e H^ a t 6563 &, a common plasma i m p u r i t y l i n e , was a b s e n t . The predominance o f A1- I I r a d i a t i o n i n d i c a t e d the s u i t a b i l i t y of the plasma as a source f o r ' t h e e x p e r i m e n t a l measurement of A I I l i n e w i d t h s . I t was i m p o r t a n t t o d e t e r -mine the time-dependence of the A I I r a d i a t i o n as w e l l , i n or d e r t o f i n d the optimum s e t t i n g of the l i g h t s h u t t e r des-c r i b e d l a t e r i n t h i s c h a p t e r . A c c o r d i n g l y , a J a r r e l l - A s h ,5>m. g r a t i n g monochrom-a t o r f i t t e d w i t h a p h o t o m u l t i p l l e r was used t o f o l l o w the time development of v a r i o u s A. I I s p e c t r a l l i n e s . The r e c i p -r o c a l d i s p e r s i o n of the monochromator was about 16 S/mm. i n f i r s t o r d e r , the i n s t r u m e n t h a v i n g an f / - number of about 10. A. l i s t of the A. I I l i n e s s t u d i e d w i t h the monochro-mator i s g i v e n i n T a b l e 1. P i g . 7 shows the t y p i c a l time T a b l e 1 Av I I l i n e s s t u d i e d w i t h the monochromator WAVELENGTH MULTIPLET (8) (Moore, 1959) 1+31+8 7 i+011i 2: 3968 2 391+1+ 2 3911+ 2 3891 2 10+26 7 27 v a r i a t i o n of the A I I l i n e s s t u d i e d , t o g e t h e r w i t h the c u r -r e n t wave form. The s h o t - t o - s h o t v a r i a t i o n i n the l i n e i n -t e n s i t i e s was l e s s than 10%» A l l the l i n e s s t u d i e d e x h i b i t e d the i l l u s t r a t e d b e h a v i o u r . 6- 15 30 90 TIME (ji sec.) F i g . 7 a) C u r r e n t waveform b) L u m i n o s i t y of A I I l i n e The time between 1$ and 30yusec. d u r i n g w h i c h the A. I I l i n e i n t e n s i t y v a r i e d by l e s s t h a n 10$ was chosen as a s u i t a b l e i n t e r v a l i n which t o make s p e c t r o s c o p i c measurements. / The f i n a l s p e c t r o s c o p i c measurements were made u s i n g a H i l g e r E7i|2 p r i s m s p e c t r o g r a p h w i t h g l a s s o p t i c a l system. T h i s i n s t r u m e n t had a r e c i p r o c a l d i s p e r s i o n of about 5 8/mm. at 1+000 8 and about 22 8/mm. a t 6500 8, and an f / - number of about 22. The p l a t e s were a n a l y z e d on a Grant 10" p l a t e 28 r e a d e r , c apable of r e a d i n g t o one m i c r o n , f i t t e d w i t h a Datex encoder and CDS-1 r e a d o u t t o an IBM 526 c a r d punch. The p l a t e t r a n s m i s s i o n was read as a f u n c t i o n of p l a t e p o s i t i o n , b o t h measurements b e i n g punched d i r e c t l y onto IBM punch cardls. A computer program was w r i t t e n t o p r o c e s s the d a t a o b t a i n e d I n t h i s manner. H i g h speed photographs of the plasma were taken w i t h a B a r r and S t r o u d f r a m i n g camera. T h i s camera can take a t o -t a l of 60 c o n s e c u t i v e exposures d u r i n g each r u n . The time i n t e r v a l c o v e r e d by the exposures v a r i e d between 15 and 1+0 jusec, and the plasma was observed f o r the f i r s t 80 ^ a s e c . a f t e r i n i t i a t i o n of the d i s c h a r g e . The camera was s e t up t o take s i d e - o n photographs of the plasma v e s s e l d u r i n g the d i s c h a r g e . The photographs r e v e a l e d a h e l i c a l type of i n s t a b i l i t y at v e r y low i n i t i a l p r e s s u r e s (about lOOyxHg). At t h e s e p r e s s u r e s the plasma was c o n s t r i c t e d t o a t h i n column which moved about i n s i d e the v e s s e l . At the f i n a l o p e r a t i n g p r e s s u r e s of about 10 mm. Hg, however, no s t r u c t u r e c o u l d be d e t e c t e d i n the plasma occupy-i n g the r e g i o n of i n t e r e s t near the middle of the c o n s t r i c t e d p o r t i o n of the v e s s e l . The v e s s e l appeared u n i f o r m l y i l l u m -i n a t e d over i t s e n t i r e d i a m e t e r , and no c o n s t r i c t i o n s were v i s i b l e i n the plasma. The f r a m i n g camera photographs shown i n P i g . 8 i l l u s t r a t e the r e s u l t s . 29 a) b) F i g . 8 Framing camera photographs of plasma d i s c h a r g e . Time sequence z igzags, i n c r e a s i n g from top t o bottom. a) ' I n i t i a l p r e s s u r e = 100 Hg argon. Time between frames = ,3 / x s e c , s t a r t i n g about l 8 / x s e c . a f t e r i n i t i a t i o n o f the d i s c h a r g e . b) I n i t i a l p r e s s u r e = 10 ram. Hg argon. Time between frames = 1.0//sec., s t a r t i n g about 2 0 / z s e c . a f t e r I n i t i a t i o n of the d i s c h a r g e . 3 0 The camera s t u d i e s c o n f i r m e d the s u i t a b i l i t y of the plasma f o r the planned e x p e r i m e n t . I f the plasma had shown s i g n s of i n s t a b i l i t i e s or c o n s t r i c t i o n s a t the p r e s s u r e s of i n t e r e s t , the s p e c t r o g r a p h i c r e s u l t s would have been j e o p a r -d i z e d . The i l l u m i n a t i o n of the s p e c t r o g r a p h s l i t by a t h i n , moving f i l a m e n t o f plasma would have been u n s a t i s f a c t o r y . i|o L i g h t S h u t t e r and T r i g g e r i n g Arrangement A s h u t t e r was d e s i g n e d t o a l l o w plasma l i g h t t o e n t e r the s p e c t r o g r a p h d u r i n g a s e l e c t e d time i n t e r v a l . The s h u t t e r was t o open at a time t a f t e r i n i t i a t i o n of t h e d i s -d charge and t o remain open f o r a time T. B o t h X and TT^  were chosen on the b a s i s of the t i m e - r e s o l v e d s p e c t r o g r a p h i c s t u d i e s d e s c r i b e d i n s e c t i o n 3 of t h i s c h a p t e r . A diagram o f the s h u t t e r i s shown i n F i g . 9? A l i g h t beam i s swept over the s p e c t r o g r a p h s l i t by means of a r o t a t -i n g m i r r o r w h i c h i s a l s o used t o t r i g g e r the d i s c h a r g e . A d e t a i l e d d e s c r i p t i o n of the s h u t t e r w i l l be given^_ L i g h t from the plasma s t r i k e s the a d j u s t a b l e s l i t A- and a p o r t i o n of the beam c o n t i n u e s t o the f r o n t - s u r f a c e d m i r r o r B ? A f t e r r e f l e c t i o n the l i g h t passes t h r o u g h the l e n s C and th e n s t r i k e s the r o t a t i n g f r o n t - s u r f a c e d m i r r o r . When the m i r r o r has t u r n e d t o the c o r r e c t p o s i t i o n , the l i g h t i s r e f l e c t e d i n t o the s p e c t r o g r a p h . The l e n s C i s a d j u s t e d t o fo c u s p a r a l l e l l i g h t onto the s l i t of t h e s p e c t r o g r a p h . 31 PH0TOD10DB P i g . 9 Diagram of l i g h t s h u t t e r T h i s o p t i c a l arrangement i s s i m p l e r than an a l t e r -n a t i v e arrangement w h i c h c o u l d a l s o have been used, The s e c -ond arrangement r e q u i r e s a n o ther l e n s between the s l i t A and the plasma v e s s e l , t h e r e b y f o c u s s i n g the plasma l i g h t onto t h i s s l i t . The p l a c i n g of the e x t r a l e n s poses a problem, however, because of somewhat l i m i t e d space and the scheme i s g e n e r a l l y more complex. The s i m p l e r arrangement used conven-i e n t l y gave the d e s i r e d v a l u e of T w h i l e s a m p l i n g the l i g h t from a r e g i o n w i t h i n about 1.5 mm. of the a x i s of the d i s -charge v e s s e l . The l i g h t p u l s e e n t e r i n g the s p e c t r o g r a p h , as observed e x p e r i m e n t a l l y , was a l s o s a t i s f a c t o r y . The observed p u l s e was not a f l a t - t o p p e d s t e p w i t h 32 s h a r p l y - r i s i n g edges, as would r e s u l t i f the a l t e r n a t i v e o p t i c a l system were used (see F i g - 1 0 b ) ) . R a t h e r , the p u l s e appeared as a smooth curve w i t h a r i s e time of about $jusec,, as shown i n Fig.lOa). a) T I M E (ftsec) —* F i g . 10 Shape of l i g h t p u l s e e n t e r i n g s p e c t r o g r a p h a) w i t h the a c t u a l o p t i c a l arrangement b) w i t h the a l t e r n a t i v e a p p a r a t u s i n c o r -p o r a t i n g an e x t r a l e n s . The arrangement shown i n F i g . 9 was c o n s i d e r e d adequate f o r the purpose a t hand. The m i r r o r was d r i v e n at 10,000 r.p.m. by a Bodine a.c. e l e c t r i c motor. The m i r r o r , mounted on b a l l b e a r i n g s , was about [|. cm. s q u a r e . A r h e o s t a t c o n t r o l p e r m i t t e d v a r i a -t i o n o f the motor speed from z e r o t o a maximum of about 17,000 3 3 r.p.m. The complete s h u t t e r was mounted on the o p t i c a l bench of the s p e c t r o g r a p h . The bank d i s c h a r g e was i n i t i a t e d by a t r i g g e r p u l s e c o n t r o l l e d by the s h u t t e r . T h i s p u l s e was c r e a t e d by u s i n g the r o t a t i n g m i r r o r t o sweep the l i g h t from the t r i g g e r lamp a c r o s s the p h o t o d i o d e , as shown i n F i g . 9. A t r i g g e r p u l s e o c c u r s once d u r i n g each r e v o l u t i o n of the m i r r o r . The o c c u r r e n c e of a t r i g g e r p u l s e i s determined by the p o s i t i o n of the m i r r o r , w h i l e the i n t e r v a l between p u l s e s i s a measure of the m i r r o r speed. S i n c e the d i s c h a r g e must be i n i t i a t e d when the m i r r o r i s r o t a t i n g at a g i v e n speed, the t r i g g e r i n g system must con-t a i n a gate which i s opened when the time i n t e r v a l between p u l s e s r e a c h e s a r e q u i r e d v a l u e , say t ' . As the m i r r o r speed i s i n c r e a s e d from z e r o , the i n t e r v a l between p u l s e s d e c r e a s e s , f i n a l l y r e a c h i n g a v a l u e t ' . I f the m i r r o r speed c o n t i n u e s t o i n c r e a s e , the i n t e r v a l between p u l s e s becomes s m a l l e r than t ' . The g a t i n g can be v i s u a l i z e d i n the f o l l o w i n g way. Each t r i g g e r p u l s e i s d e l a y e d by a g i v e n amount^ t ^ , as shown i n F i g . 11. By f e e d i n g b o t h the t r i g g e r p u l s e s and the d e l a y e d p u l s e s i n t o an "and" gate ( c o i n c i d e n c e u n i t ) , an ou t p u t p u l s e i s f i r s t o b t a i n e d when the time i n t e r v a l between- p u l s e s reaches t ^ . The d e s i r e d o p e r a t i o n i s a c h i e v e d by s e t t i n g t^ = t ' . 3h T R I G G E R P U L S E S D E L A Y E D P U L S E S P i g . 11 Sequence of t r i g g e r p u l s e s and d e l a y e d p u l s e s used i n the o p e r a t i o n of the f r e -quency gate Thus an o u t p u t from the c o i n c i d e n c e u n i t i s f i r s t o b t a i n e d when the m i r r o r has reached the c o r r e c t speed and i s i n the c o r r e c t p o s i t i o n . The t r i g g e r i n g system, shown i n P i g . 12, i n c l u d e s a p u l s e i n v e r t e r and s h a p e r , which i n v e r t s and improves the r i s e time of the p u l s e from the p h o t o d i o d e . The delayed p u l s e i s c r e a t e d by a T e k t r o n i x type 162 waveform g e n e r a t o r and Type 163 p u l s e g e n e r a t o r . These u n i t s enable a d u t y c y c l e of 1 t o be a c h i e v e d . The undelayed p u l s e and the de-l a y e d p u l s e emerging from the p u l s e g e n e r a t o r are then f e d I n t o the c o i n c i d e n c e u n i t , a b i s t a b l e m u l t i v i b r a t o r w i t h manual r e s e t , and a d e l a y u n i t . P H O T O D I O D E P U L S E S H A P E R A N D I N V E R T E R T E K T R O N I X T Y P E 162 W A V E F O R M G E N E R A T O R T E K T R O N I X T Y P E 163 P U L S E G E N E R A T O R • C O I N C I D E N C E U N I T B I S T A B L E M U L T I V I B R A T O R 1 D E L A Y T H E O P H A N I S T R I G G E R U N I T T O U N I T S W I T C H Fig. 12: Block diagram of e l e c t r o n i c units. The dotted box encloses the frequency gate. 36 A diagram of the v a r i o u s p u l s e s which occur i n the o p e r a t i o n of the f r e q u e n c y g a t e i s g i v e n i n P i g . 13» i • T -f A) a) F i g . 13 Sequence of p u l s e s used i n t r i g g e r i n g the d i s c h a r g e a) P u l s e from photodiode b) Same p u l s e a f t e r i n v e r s i o n and shaping. c) Output of waveform g e n e r a t o r , t r i g g e r e d by p u l s e f rom b) d) Output of p u l s e g e n e r a t o r . The p u l s e i s i n i t i a t e d when the s a w - t o o t h . v o l t a g e r e a c h e s a s e t v a l u e . T i s the time i n t e r v a l between p u l s e s . The p u l s e s from b) and d) are f e d i n t o the c o i n c i -dence c i r c u i t w h i c h sends out a v e r y s m a l l p u l s e (about 5 v o l t s ) when e i t h e r p u l s e appears s e p a r a t e l y at one of the two i n p u t p o i n t s . When b o t h p u l s e s appear s i m u l t a n e o u s l y , a 25 37 v o l t p u l s e r e s u l t s . P i g . 11+ shows the c o i n c i d e n c e u n i t out-put i n the two c a s e s . a) 5* - n 25 1 b) 5 ' •as* P i g . 11+ Output of c o i n c i d e n c e u n i t &} - when p u l s e s a r r i v e a t s e p a r a t e t i m e s b) when p u l s e b) j u s t o v e r l a p s w i t h p u l s e d) c) when p u l s e b) o c c u r s d u r i n g the mi d d l e p a r t of p u l s e d) The o u t p u t of the c o i n c i d e n c e u n i t i n P i g . 11+ i s f e d i n t o the b i s t a b l e m u l t i v i b r a t o r . T h i s u n i t f u n c t i o n s as a s i n g l e shot d e v i c e . When man u a l l y r e s e t , the u n i t i s read y t o a c c e p t p u l s e s above the d i s c r i m i n a t i o n l e v e l , w h i c h i s s e t at a v a l u e g r e a t e r than 5 v o l t s . The a r r i v a l of the 25 v o l t p u l s e s e t s the u n i t i n t o the o t h e r s t a b l e o p e r a t i n g p o s i t i o n , w i t h the s i m u l t a n e o u s p r o d u c t i o n of a p o s i t i v e p u l s e of about 20 v o l t s w h i c h t r i g g e r s a d e l a y u n i t . The d e l a y of t h i s u n i t can be v a r i e d f r om about 3/usec. t o about 75 ^asec. w i t h a j i t t e r of l e s s than 1%. The output p u l s e from the d e l a y u n i t 38 f i r e s the Theophanls t r i g g e r u n i t . The o p e r a t i o n of t h i s t r i g g e r system can be v i s -u a l i z e d i f one c o n s i d e r s i t s b e h a v i o u r as the m i r r o r speed i s v a r i e d f rom z e r o t o a speed j u s t g r e a t e r than 10,000 r.p.m. F i g . 13 a p p l i e s , w i t h the time i n t e r v a l , T, between the p u l s e s i n a) g r e a t e r than 6 msec. S i m i l a r l y , p o i n t s i n t h e same phase i n s e c t i o n s b) t o d) are a l s o more t h a n 6 msec, a p a r t . The p u l s e s coming out of the c o i n c i d e n c e u n i t w i l l be g i v e n by F i g . I i i a ) . As the m i r r o r speed i n c r e a s e s , the p u l s e s i n F i g . 13 and F i g . II4. a) crowd c l o s e r t o g e t h e r . A t 10,000 r.p.m., the i n t e r v a l T i n F i g . 13 i s 6-msec. Then the t r a i l i n g p o r t i o n of the p u l s e i n F i g . 13 d) j u s t c o i n -c i d e s w i t h the next p u l s e i n F i g . 13 b ) . Now the output of the c o i n c i d e n c e u n i t i s g i v e n by F i g . 11+ b ) . As the m i r r o r speed i n c r e a s e s , the p u l s e i n F i g . 13 b) "moves f o r w a r d " a l o n g t h e p u l s e i n F i g . 13 d) and the output of the c o i n c i -dence u n i t i s g i v e n by F i g . II4. c ) . When F i g . II4. b) a p p l i e s , the m u l t i v i b r a t o r s w i t c h e s t o i t s o t h e r s t a b l e o p e r a t i n g p o s i t i o n and sends out a p u l s e t o the d e l a y u n i t . The d e l a y u n i t s e t t i n g Is chosen so t h a t the bank d i s c h a r g e i s i n i t i a t e d a t a time b e f o r e the m i r -r o r i s i n p o s i t i o n t o b e g i n a d m i t t i n g l i g h t i n t o the s p e c t r o -g r a p h . Subsequent p u l s e s i n t o the m u l t i v i b r a t o r do not r e s u l t i n any more p u l s e s b e i n g sent t o the d e l a y u n i t u n t i l the m u l t i v i b r a t o r i s man u a l l y r e s e t . T h i s " s i n g l e s h o t " f e a t u r e 39 was used t o i n c r e a s e the l i f e of the Theophanis t r i g g e r u n i t , w h ich would o t h e r w i s e r e c e i v e f i r i n g p u l s e s at a p p r o x i m a t e l y 6 m s e c . i n t e r v a l s as l o n g as the m i r r o r speed was 10,000 r.p.m. or g r e a t e r . I t w i l l be noted t h a t the s h u t t e r i s open a g a i n at a time m s e c , as the m i r r o r has t h e n t u r n e d t h r o u g h one complete r e v o l u t i o n . No c o m p l i c a t i o n s a r i s e from t h i s f e a t u r e , as a l l l i g h t from the plasma has d i e d axvay by the end of a time of the o r d e r of T^+100 jusec. W i t h a s h u t t e r of t h i s d e s i g n , i t Is d i f f i c u l t t o a v o i d sweeping the l i g h t beam from the t r i g g e r i n g lamp a c r o s s the s p e c t r o g r a p h s l i t . To m i n i m i z e the p o s s i b i l i t y of t h e r e -by f o g g i n g the s p e c t r o g r a p h i c p l a t e , t h i s beam was d i r e c t e d t o be as f a r below the p l a n e of the plasma l i g h t beam as the s i z e of the r o t a t i n g m i r r o r would p e r m i t . I n t h i s c o n f i g u r a -t i o n some l i g h t from the edges of the beam was observed t o f a l l on the s l i t f a c e . However, the i n t e n s i t y o f t h i s l i g h t was low and no d e t e c t a b l e f o g g i n g of the p l a t e s was o b s e r v e d . The sequence of o p e r a t i o n s i n u s i n g the s h u t t e r i s as f o l l o w s . The s i n g l e shot u n i t i s s e t m a n u a l l y and the m i r r o r speed i s i n c r e a s e d g r a d u a l l y from z e r o . When the c o r -r e c t speed i s r e a c h e d , the t r i g g e r p u l s e produced f i r e s the bank and the m i r r o r speed i s a g a i n reduced t o z e r o . T h i s s e -quence i s r e p e a t e d t o g i v e the d e s i r e d number of exposures on the s p e c t r o g r a p h i c p l a t e . 5. A u x i l i a r y E l e c t r o n i c Equipment An R.C.A. IP 28 p h o t o m u l t l p l i e r was used i n con-j u n c t i o n w i t h the J a r r e l l - A s h monochromator. The output of the p h o t o m u l t l p l i e r was f e d i n t o a cathode f o l l o w e r of s t a n d -ard d e s i g n . The i n p u t impedance of the cathode f o l l o w e r i s h i g h ( s e v e r a l kfi) and the output impedance chosen t o be about 50.fl. T h i s v a l u e f o r the output impedance i s near the c h a r a c -t e r i s t i c impedance of the c o a x i a l c a b l e (about 1+7 )^ used t o c a r r y the s i g n a l t o the o s c i l l o s c o p e . The r i s e time of the p u l s e i s improved and r e f l e c t i o n s from the o s c i l l o s c o p e are damped o u t . A s h i e l d e d c o a x i a l c a b l e c a r r i e d the s i g n a l t o the p r e a m p l i f i e r of a T e k t r o n i x Type 551 d u a l beam o s c i l l o s -cope f i t t e d w i t h a Dumont t r a c e - r e c o r d i n g camera. A 12 kV 1000:1 probe was a l s o used t o monitor the bank c u r r e n t wave-form by c o n n e c t i n g I t a c r o s s the t e r m i n a t i n g r e s i s t o r . An a d a p t e r was c o n s t r u c t e d t o r e p l a c e the p l a t e h o l d e r of the H i l g e r s p e c t r o g r a p h . I n t h i s way a IP28 pho-t o r a u l t i p l i e r mounted on the a d a p t e r c o u l d be used t o mo n i t o r the l i g h t p u l s e e n t e r i n g the s p e c t r o g r a p h . A d e f i n i t e check on the a c c u r a c y of the t i m i n g and the g e n e r a l shape of the l i g h t p u l s e e n t e r i n g the i n s t r u m e n t c o u l d thus be made. A l s o , the r e l i a b i l i t y of the o p t i c a l s h u t t e r , as w e l l as the r e p r o -d u c i b i l i t y o f the t r i g g e r i n g and breakdown of the main d i s -charge c i r c u i t c o u l d be det e r m i n e d . Photographs of the os-c i l l o s c o p e t r a c e s showed no d e t e c t a b l e j i t t e r ( i . e . l e s s t h a n about l ^ s e c ) i n the q u a n t i t i e s T and 7 ^ , i n d i c a t i n g s a t i s f a c t o r y o p e r a t i o n of the o p t i c a l s h u t t e r and plasma gen-e r a t o r . 6. F i n a l E x p e r i m e n t a l Arrangement I t was d e c i d e d t o view the plasma v e s s e l " s i d e - o n " , i n o r d e r t o reduce s e l f - a b s o r p t i o n of t h e plasma r a d i a t i o n , w i t h an o b s e r v a t i o i m p o i n t at about the middle of the c o n s t r i c ed p o r t i o n of the t u b e . S i n c e the a x i s of the plasma v e s s e l was h o r i z o n t a l , whereas the s p e c t r o g r a p h s l i t was v e r t i c a l , a Dove p r i s m , or image r o t a t o r , was i n s t a l l e d between the s h u t -t e r and the v e s s e l . I n t h i s way the image of the s l i t on the w a l l o f the plasma v e s s e l was r o t a t e d t h r o u g h 90°. A l l p o r t i o n s of the s p e c t r o g r a p h s l i t were th e n i l l u m i n a t e d by l i g h t o r i g i n a t i n g I n the r e g i o n a l o n g the a x i s of the plasma v e s s e l . The r e s u l t i n g i l l u m i n a t i o n was u n i f o r m a l o n g the l e n g t h of the s l i t , a c o n d i t i o n t h a t was n e c e s s a r y i n o r d e r t o c a l i b r a t e the response of the s p e c t r o g r a p h i c p l a t e . A d e s c r i p t i o n of the c a l i b r a t i o n t e c h n i q u e i s g i v e n i n S e c t i o n 7 of t h i s c h a p t e r (see a l s o Appendix 1). A diagram of the f i n a l arrangement of the apparatus i s g i v e n I n F i g . 15« J+2 S P E C T R O G R A P H P L A S M A V E S S E L F i g . 15 P i n a l experimental arrangement 7. Experimental Procedure for Determing the Instrument Funct ion . A d iscuss ion of the main sources of instrument broadening, and of the technique for correc t ing for th is broadening, can be found i n Chapter l+. The instrument func-t i o n is best determined experimental ly , and i t is th is part of the procedure which v^ill be discussed here. Instrument broadening manifests i t s e l f i n the fo l lowing way. I f a monochromatic l i g h t beam enters an op-t i c a l instrument, the l i n e as seen by some viewing apparatus w i l l in general appear to be made up of l i g h t covering a f i n i t e range of frequencies.. As may seem obvious, an exper i -1+3 mental way to determine the instrument funct ion is to meas-ure the instrumental response to monochromatic r a d i a t i o n . Such a procedure was followed here. Since the instrument funct ion i n general depends on the s l i t width of the spectrograph, i t was necessary to choose a width x^hich would be kept constant throughout the i n v e s t i -gat ion . An experimental test was used to choose the f i n a l spectrograph s l i t width. A series of Ge i s s l er spectra were taken, using s l i t widths between about $jx. and i\.Ojm. and the plates were examined with a Zeiss plate reader. The Ge i s s l er l ines appeared to increase p r i m a r i l y i n i n t e n s i t y for i n -creasing s l i t widths below about 2Cyxand to increase mainly i n width as the s l i t was opened f u r t h e r . It may be noted in passing that the "normal s l i t width", given by the product of the f / - number of the spectrograph and the wavelength, is about 10yu. at I L^OO S. The s l i t width was chosen to be 20jU. The spectrum from an a r g o n - f i l l e d Ge i s s l er tube was taken at this s l i t s e t t i n g . The pos i t ion of the plate holder was then changed and another exposure of the same spectrum was taken. For the l a t t e r exposure the s l i t was opened to 90jU and a seven step neutral density wedge placed immediately before I t . The r e s u l t i n g c a l i b r a t i o n spectrum was used to determine the plate response curve for the kk emulsion ; at each of the spectra l l ines of in teres t ( s e e Appendix 1) . funct ion to be v a l i d , the actual width of the argon G-eissler l i n e must be considerably less than the observed width,, In other words, for the Ge i s s l er l i n e to be "monochromatic," a l -most a l l of i t s apparent width must be the re su l t of i n s t r u -mental broadening* The Ge i s s l er l i n e width is due p r i m a r i l y to two f a c t o r s , namely natural l i n e width and Doppler broad-ening, the l a t t e r being by far the more important of the two. The f u l l width at h a l f maximum due to the Doppler ef fect can be found from the r e l a t i o n (see for example Griem (1961+) p. 101),., width i s at l east a fac tor of 1 0 greater (as was the case) , th i s method of determining the instrumental funct ion is ade-quate. Most of the instrumental broadening is introduced by the spectrograph. However, there w i l l also be a contr ibu-t i o n from the plate reader used for obtaining the plate t rans -mission readings . This a d d i t i o n a l effect can be completely For th i s method of determining the instrumental Using the value A Q = 1+300 %, and i f k T = l/l+O e y , the width w i s found to be about .01 2. I f the apparent l i n e compensated for by using i d e n t i c a l s l i t sett ings on the plate reader when scanning both the Ge i s s l er and the plasma spec-trum. Such a procedure was adopted for the analysis described i n this t h e s i s . A H i l g e r P1273 step wedge, having s ix steps plus the c lear quartz area, was used throughout these i n v e s t i g a -t i o n s . The manufacturer's spec i f i ca t ions for the dens i t ies of the various portions of the wedge were checked exper i -mental ly . For th i s purpose the J a r r e l l - A s h monochromator was used with the wedge mounted in front of the entrance s l i t . The l i g h t from a G . E . "Sun Gun" was interrupted with a chop-ping wheel, and the output of the IP28 photomult ip l ler d i s -played on an o s c i l l o s c o p e . The wedge was ca l ibrated at 3500 £, 1+000 A5, and 5000 2. and agreed with the manufacturer's spec i f i ca t ions wi th in about 1 0 $ . The given spec i f i ca t ions were used in the analysis of the data . Table 2 shows a com-parison of given and measured values for the wedge, Table 2 Manufacturer's data and experimental values for the density D of the H i l g e r step wedge. given ^ experimental 3500 S 1+000 A* 5000 8 .222 .259 .252 .230 .1+28 4 3 7 .1+1+2 .616 .638 .611+ -571+ .801 .816 .790 .796 .991 1.088 1.01+1 .996 1.191+ 1.259 1.221+ 1.188 1+6 8. Gathering the Pinal Data The f i n a l experimental data w e r e obtained under the following conditions. The bank voltage was set at 11+ kV, with a mixture of argon and hydrogen in the proportions 1+:1 as the working gas. The i n i t i a l gas pressure was 10 mm. Hg. After every second shot the vacuum system was pumped down to about 1+0 jU, Hg and fresh gas admitted to the plasma vessel. It was o r i g i n a l l y hoped that the hydrogen l i n e H^ could be used to determine the electron number density. Such a mea.surem.ent cannot be made accurately, however, unless the r a d i a l d i s t r i b u t i o n s of temperature and p a r t i c l e densities i n the plasma are known. It is probable .ithat the maximum H^ ra d i a t i o n does not come from a region i n the plasma which gives the strongest A. II r a d i a t i o n . It was decided to include hydrogen i n the ambient gas to give a rough estimate (a lower bound) for the electron number density. Also, the p r o f i l e of the H^ l i n e i s preserved on the plate u n t i l an experiment determining the necessary r a d i a l gradients has been performed. At such time a more accurate estimate of the electron number density can be made. The spectrograph s l i t was set at 20yU,and s i x ex-posures were made on the spectrographic plate. The plate was then shifted to a new position in the holder and a c a l i b r a -t i o n spectrum was taken. The s l i t was opened to 90yUand the Hilger wedge was placed d i r e c t l y i n front of the spectrograph 1+7 s l i t . Three exposures were made for the c a l i b r a t i o n spec-trum. A l l of these exposures were made using the o p t i c a l shutter described i n Chapter 3* The synchronizat ion and timing of the shutter were checked before and af ter the plate exposure by means of the adapter-photomult ip l ier combination described i n sect ion 1 + of this chapter. A l s o , for each of the exposures, the cur-rent waveform was monitored on the o sc i l l o scope . This was done to ensure that no j i t t e r developed i n the breakdown of the switch or the plasma ves se l . The osc i l loscope was always tr iggered by a pulse synchronous with the t r igger pulse pro-duced by the Theophanls t r igger u n i t . Any j i t t e r while gath-er ing the f i n a l data was less than l a sec. CHAPTER 1+ Analysis and Results l.j Introduct ion The experimental observations were recorded on two spectrographic p la te s . One, hereafter referred to as the "Geiss ler p la te , , ; , contained the information from which the instrumental funct ion was obtained. The other, to be re ferred to as the "plasma plate" , y ie lded information about the A II l i n e p r o f i l e s . The Grant plate reader was used to obtain readings of plate transmission as a funct ion of plate p o s i t i o n for each s p e c t r a l l i n e of in teres t on the G e i s s l e r and plasma p l a t e s . The transmission readings of the corresponding step wedge patterns were also recorded. Appendix 6 tabulates th i s Information for the fourteen plasma l i n e s presented i n sect ion 7 of this chapter and for one of the G e i s s l e r l ines used to ca lcu la te the instrumental func t ion . Prom the c a l i b r a t i o n readings , a plot of p late transmission as a funct ion of the r e l a t i v e energy densi ty of l i g h t f a l l i n g on the emulsion was obtained* As an example, the complete analys is for the A II l i n e at 1+806 8 (mult iplet 6) w i l l be g iven . The aexperimental points must f i r s t be f i t t e d by a Voigt p r o f i l e . This p r o f i l e i s then corrected for instrumental broadening. In order to do t h i s , the resu l t s of the Ge i s s l er plate must be u t i l i z e d . 1+8 1+9 The r e s u l t i n g l i n e p r o f i l e must then be corrected for Dop-p ler broadening (always small i n th i s experiment). The plasma temperature and e lectron number density must be evaluated. The temperature is required for two reasons. F i r s t l y , t h e o r e t i c a l ca lcu la t ions are somewhat temperature dependent, and the temperature must be known In order to make a comparison. Secondly, an estimate of the temperature is required for the Doppler c o r r e c t i o n . The e lectron number density was ca lculated from the widths of the A II l ines from mult ip le t 6, prev ious ly measured by Jalufka et a l ( 1 9 6 6 ) . The plasma temperature was calculated from Saha's equation (See Appendix 2 ) , using the experimental fact that the plasma r a d i a t i o n arose pr im-a r i l y from s i n g l y - i o n i z e d argon. The measured p r o f i l e s of the fourteen A II l ines that could be treated by a Voigt analys is are given in th i s chapter. A l s o , a d iscuss ion of experimental error i s pre-sented. 2:. Data Reduction The spectrographic plates were scanned with the C-rant plate reader. This instrument measures the pos i t i on of the carr iage holding the plate and the o p t i c a l transmis-s ion of the p l a t e . The l a t t e r reading is obtained by measur-ing the response of a photomult lp l ier to a l i g h t beam which 50 has passed through the emulsion on the p l a t e . This response i s presented as a number between 000 and 999 which is punched onto an I . B . M . card , together with the plate p o s i t i o n . A reading of 999 corresponds to a l i g h t beam of maximum per-miss ible i n t e n s i t y , and a reading of 000 indicates the m i n i -mum output of the photomul t ip l l er . The instrument was adjust -ed to read 980 when scanning a port ion of the emulsion that had not been exposed to l i g h t , and to read 006 when an opaque card was inserted i n the l i g h t beam. These sett ings enabled a check to be made on the d r i f t of the instrument while the plates were being scanned. The adjustment of the instrument was repeated before and after scanning each spec tra l l i n e . The p r o f i l e s of s i x A I l ines at about 1 + 3 0 0 8 on the G e i s s l e r plate were recorded, as we l l as a l i n e at 5172 X. This l i n e could not be found i n the A I spectrum and was a t tr ibuted to Mg I . The plate transmission was recorded at in terva l s of $j[/,on the p l a t e , using a scanning s l i t height of 25 mm. and a width of 2jm, The transmissions of the cor -responding wedge patterns were obtained with a s l i t height of 1+ mm., determined by the phys i ca l dimensions of the wedge pa t t ern , and a width of LL yu. to allow scanning a larger area on the p l a t e . Each wedge pattern was scanned twice and aver-age values used i n obtaining the plate response curve. The scanning procedure used with the plasma plate was v i r t u a l l y the same as that just descr ibed. I t was neces-51 sary , however, to take precautions to allow for the pre-sence of continuum r a d i a t i o n near the A II l ines of i n t e r e s t . The procedure used to assess the importance of continuum i r a d i a t i o n in analyzing a given l i n e can be understood with the aid of P i g . 16. DIRECTION OF SCANNING FOR SPECTRAL " LINES LIGHT BEAM P i g . 16 Sketch of plasma plate A = Region of spec tra l l ines B = Region of unexposed emulsion C = Region of wedge pattern The spec tra l l ines of i n t e r e s t , as wel l as the background continuum, appear i n a s t r i p i n Region A on the p l a t e . The wedge patterns appear in Region C . Region B cor-responds to a port ion of the plate which was never exposed to l i g h t . Before scanning each spec tra l l i n e or wedge pattern the densitometer was adjusted to give a reading of 980 when scanning Region B and 006 when the photometer l i g h t beam was 52 interrupted by interpos ing a piece of cardboard. With th i s technique, a correc t ion could be made for the continuum r a d i a t i o n present . I f the densitometer reading remained at 980 when scanning a port ion of the Region A near the s p e c t r a l l i n e of i n t e r e s t , the background was assumed to be n e g l i g i b l e . The presence of continuum r a d i a t i o n was i n d i -cated by a decrease i n the densitometer reading when scanning the Region A. An estimate of the amount of continuum present (up to a maximum of 10% of the l i n e height) was made before proceeding with the Voigt a n a l y s i s . A computer program was wr i t ten to analyze the data obtained. This program, presented in Appendix 5» converted the plate transmission readings to energy density readings with the aid of the data from the c a l i b r a t i o n spectrum. An i n t e r p o l a t i o n procedure, i n which three adjacent experimental points were f i t t e d by a parabola , was used i n th is conversion. A d iscuss ion of the c a l i b r a t i o n technique may be found in Appendix 1. The program also carr ied out the f i r s t few steps i n the Voigt a n a l y s i s , which w i l l now be discussed. 3. Voigt Analys is of Spectra l Lines The Voigt analys is grea t ly s impl i f i e s the problem of correc t ing for instrumental d i s t o r t i o n of the observed spec-t r a l l i n e s . The discuss ion w i l l proceed by f i r s t o u t l i n i n g the theory of Voigt funct ions , after which t h e i r app l i ca t ion to 53 the data analysis w i l l he described i n d e t a i l . The resul t s of the G e i s s l e r plate w i l l be presented i n the course of th i s d i scuss ion . The apparent frequency d i s t r i b u t i o n of the l i g h t comprising a spectra l l i n e is a l tered by the various o p t i c a l instruments used i n spec tra l ana lys i s . This e f f ec t , r e s u l t -ing i n an observed l i n e p r o f i l e that is wider than the undis -torted l i n e , is known as instrumental broadening. Such broad-ening ar ises mainly from the f i n i t e apertures of the d i sper -s ive systems of a l l spectrographs, as wel l as o p t i c a l aberra-t i o n s , imperfect s l i t s , s l i t s of f i n i t e width, and incorrect focuss ing . Care in design and adjustment can minimize a l l defects but the f i r s t , which remains as an important l i m i t i n g factor i n determining the performance of spectrographs. Once the image of a spec tra l l ine has been produced on a photographic p l a t e , i t must be scanned by a micro-dens i -tometer or s i m i l a r device to obtain a l i n e p r o f i l e . This scanning procedure can introduce further d i s t o r t i o n , p a r t i c u -l a r l y i f the spec tra l l i n e exhibi ts appreciable curvature . Experimental correct ions can be made to compensate completely for the instrumental broadening. For an i n f i n i t e l y narrow spec tra l l i n e entering the spectrograph, the instrumental broadening resul t s i n an ob-served l i n e shape having a f i n i t e d i s t r i b u t i o n of frequencies . Sk Mathematical ly, the observed shape of any spec tra l l ine can be represented as a convolution i n t e g r a l / f x ) = J f'(x-y) f'fy) dy . . . ( i ) Here f"(y) i s the p r o f i l e of the l ine before entering the i n -strument. I f f (x) i s the observed l i n e shape, where x is the distance from the l i n e centre in terms of e i ther wavelength or frequency u n i t s , the true l i n e p r o f i l e f"(y) can be deter-mined provided the "instrumental function" f ' (x ) is known. The instrumental funct ion is the response of the instrument to monochromatic r a d i a t i o n . General so lut ions for E q . (1) involve laborious methods. The problem is great ly s impl i f i ed i f the observed l i n e and the instrumental funct ion may be f i t t e d e i ther both by Lorentz ian or both by Gaussian p r o f i l e s . Then the true l i n e shape appears re spec t ive ly as Lorentz ian or Gaussian as w e l l , and the fo l lowing simple re la t ions are v a l i d : h" = h-h' (Lorentzian) h " 2 = h 2 - h « 2 (Gaussian)} where h"' is the true ha l f -width h i s the observed ha l f -width h' i s the ha l f -width of the instrumental func t ion . Unfortunate ly , no s ingle funct ion of e i ther type 55 gives a good f i t both for the observed l i n e shape and the instrumental function. It has been found that these func-tions can generally be f i t t e d quite well by Voigt functions (Voigt (1912)), and this technique was adopted in analyzing the present experimental data. Voigt functions are defined as the convolution i n t e g r a l between a Lorentzian and a Gaus-sian function, and can be used to f i t p r o f i l e s l y i n g between these two functions. I f f(x.) and f' (x) are both taken as Voigt functions, then the true l i n e shape in Eq. (1) i s also a Voigt function. Voigt functions can be characterized by two para-meters,^^ and ^ » ^ n ^h.e manner described by Van de Hulst and Reesinck (191+7). Then the Voigt function for the observ-ed l i n e shape can be written M 1 _l ( C x - a V ^ f j where M i s constant. The parameters (S^ and ^ are the magni-tudes of the Lorentzian and Gaussian contributions, respect-i v e l y , to the Voigt convolution. Writing analagous Voigt functions for f'(x) and f"'(x), i t follows from the theory of Voigt functions that ySj- p[ . ...(2) and = - f k ...(3) 56 2 The q u a n t i t i e s ^ a n d a r e of primary importance i n the Voigt a n a l y s i s . These quant i t ies w i l l be evaluated from the experimental determination of two parameters h, the f u l l h a l f width of the funct ions , and / ^ / h . These two inde-pendent parameters can also be used to character ize the Voigt funct ions . Table 9 i n . Appendix 1+ can be used to convert from one p a i r of parameters to the other. The above Voigt analysis i s v a l i d whenever a l i n e is broadened by two independent sources, i . e . when f'(x.) and f"'(x) i n E q . (1)) are s t a t i s t i c a l l y independent. Thus, broad-ening due to the Doppler ef fect can also be ca lculated in th is manner, with one prov i so . I f the predominant cause of Stark broadening is due to e lec trons , and the motions of the e l e c -trons and ions are not s trongly c o r r e l a t e d , the procedure i s v a l i d . I f the Stark broadening is p r i m a r i l y due to ions , the two broadening mechanisms may not be independent and the Voigt analys is is i n v a l i d . A discuss ion of th is point is given by Griem (1961+), p . 101. For the A II spectrum, most of the broadening is due to e lectron c o l l i s i o n s (see Griem (1961+) p. 87), and the Doppler broadening may be treated using the Voigt a n a l y s i s . The analysis w i l l be i l l u s t r a t e d for the A II l i n e at 1+806 A*. A plot of th i s l i n e i s given i n F i g . 17, together with the Voigt p r o f i l e used to approximate the l i n e . 57 P i g . 17 V o i g t f i t f o r A I I 1+806 A l i n e . Assumed background Sp • E x p e r i m e n t a l p o i n t s y y V o i g t p r o f i l e 1 _ _A 5SU_MED ~ ~ ~ " " B A C K G R O U N D " _ L _ 1 . • (— 1 1-- 2 -I 0 I 2 A~)\ ( A ) 5 8 P i g . 1 8 shows the Voigt p r o f i l e as determined for another A II l i n e at 1+579 %. (mult iplet 1 7 ) . The analys is begins by drawing a smooth curve (not shown i n P i g . 1 7 ) through the experimental po int s . Then the widths, b^, of the l i n e are measured at points corresponding to one-tenth, two-tenths, e t c . , up to eight-tenths of the maximum amplitude of the l i n e . The width at one-tenth of the height was usua l ly discarded as the accuracy of the exper i -mental points In t h i s region may be doubtful . The uncertainty arises from the d i f f i c u l t y of c a l i b r a t i n g the emulsion accur-ate ly for very small exposures, such as occur in the wings of the observed l i n e s . The value b / h , where h = b is next c a l c u l a t e d , i 5 where i takes values from 2 to 8 . Table 1 from Van de Hulst and Reesinck ( 1 9 1 + 7 ) (reproduced here i n Appendix 1+ as Table 9 ) is used to obtain the corresponding Voigt parameter / ^ / h . The average of the s i x values of / ^ / h is taken to give the best value of fi^/h for the l i n e . Table 3 i l l u s t r a t e s the r e -sul ts of th i s procedure for the l i n e considered here. Using the ca lculated values of h and / ^ / h , the q u a n t i t i e s ^ a n d ^ ^ are evaluated using Table 9 . These two parameters character ize the Voigt funct ion used to f i t the observed l i n e p r o f i l e . 59 Fig. 18 Voigt f i t for A II 2+579 X l i n e . Assumed background 0% • Experimental points /\Voigt f i t 1 —I 1-I 0 I 60 T a b l e 3 D e t e r m i n a t i o n o f V o i g t parameters Z9 /h and h f o r A I I 4.806 § l i n e . The background i i t a k e n as 5$. >i/h fVh Average ^ l / h h ( X ) 2 3 6 7 8 1.718 l»]+05 1.186 1.000 0.839 0*685 0.531 .283 .300 .275 .275 .275 .275 .280 1.630 The i n s t r u m e n t a l f u n c t i o n must now be c a l c u l a t e d f o r each s p e c t r a l l i n e a n a l y z e d . A d e s c r i p t i o n of t h i s op-e r a t i o n w i l l now be g i v e n . I4.. The C a l c u l a t i o n of The I n s t r u m e n t a l F u n c t i o n Some of the p h y s i c a l phenomena w h i c h c o n t r i b u t e t o i n s t r u m e n t a l b r o a d e n i n g w i l l be d i s c u s s e d b r i e f l y . The s t e p s i n the a n a l y s i s s h o u l d t h e n be e a s i e r t o f o l l o w . The i n s t r u m e n t f u n c t i o n depends on the r e s o l v i n g power and the d i s p e r s i o n o f the s p e c t r o g r a p h . The V o i g t parameters h and / ^ / h f o r the i n s t r u m e n t a l f u n c t i o n were de-te r m i n e d by a c o m b i n a t i o n of t h e o r e t i c a l and e x p e r i m e n t a l methods^ The r e s o l v i n g power o f the s p e c t r o g r a p h i s a f u n c -t i o n o f w a v e l e n g t h . C o n s e q u e n t l y , one might expect a d i f f e r -ent v a l u e of h, the apparent h a l f - w i d t h of a monochromatic 6 1 s p e c t r a l l i n e , depending on the wavelength region being con-s idered . P h y s i c a l l y , the i n t e n s i t y pattern of a monochro-matic l i n e on the spectrograph plate is a s ingle s l i t d i f -f r a c t i o n pattern determined in most cases by the aperture of the spectrograph prism (Sawyer (1963) p . 63). Since the an-gular p o s i t i o n of the f i r s t minimum i n the d i f f r a c t i o n pat -tern increases l i n e a r l y with wavelength, h would also be ex-pected to depend l i n e a r l y on the wavelength. On the basis of the measured value of h at 1+300 the value at 5172 2, obtained by l i n e a r ex trapo la t ion , was 59 microns. The meas-ured value at 5172 $ of 60 microns encouraged l i n e a r i n t e r -p o l a t i o n . In the foregoing discuss ion h is the actual h a l f -width of the image on the p la t e , as could be measured by a t r a v e l l i n g microscope, for example. The r e c i p r o c a l d i spers ion also varies with wave-length , being highest i n the blue region of the spectrum. The actual dependence of d ispers ion on wavelength must be de-termined experimental ly . According ly , the plate posi t ions of about f i f t y l ines of known wavelength i n the i r o n arc spec-trum were measured. From these measurements the r e c i p r o c a l d i spers ion of the spectrograph i n the region of Interest was c a l c u l a t e d . The instrumental ha l f -width h i n 8 can now be ca lcu lated from the value of h i n microns on the plate and the r e c i p r o c a l d i s p e r s i o n . A graph of the resu l t s is shown i n F i g . 19» Fig. 19: Full half-width h of the instrumental function plotted against wavelength. ro 4100 4200 4^00 4400 45(30 4600 4700 48*00 4900 WAVELENGTH (K) 63 The wavelength dependence of £ ] _ / h must also be determined. Van de Hulst and Reesinck (1914-7) give the f o l -lowing t h e o r e t i c a l expression for the Voigt parameter ^ for a prism spectrograph of minimum aperture S. fii y/z *• S The quant i ty h ( in X) has the fo l lowing wavelength dependence h = k > X where k is an experimental ly determined constant and x is the r e c i p r o c a l d i spers ion at the wavelength ^ • I f ^ | and £ ^ are the values of (3^ at the wave-lengths A ' and V , then from which Thus, having measured @^/h at the wavelength ^ ' , i t s value at can be found by mul t ip ly ing by the r a t i o of the d i spers ions . Such an extrapolat ion procedure was used to ca lcu la te f^^/h at 5>172 2 from the measured value at I4.3OO 8. The extrapolated value of ^ / h was 0 . 2 5 ; the measured value was 0,214.. Consequently, the i n t e r p o l a t i o n procedure as de-61+ f ined by E q . (1+) was used. The instrumental p r o f i l e for the region around 1+300 2. was found by averaging the measurements on s ix A I l i ne s l y i n g between 1+198 % and 1+333 8 as shown i n Table 1+. Table 1+ Determination of instrumental funct ion in the region around 1+300 5 M i 5 ) h ( S ) P l / h 1+198 .238 .371 1+200 .21+2 .316 1+259 •271+ .303 1+272 .276 .326 1+301 .'289 .366 1+333 • .296 • 377 Average Average .270 .31+3 5. Obtaining The A II Line P r o f i l e s . Having ca lculated the instrumental parameters h and (3 / h at 1+806 Table 9 i s used to evaluate £J and ^ \ The ef fect of instrumental broadening can now be subtracted from the observed p r o f i l e . To do th is the r e l a t i o n s Pi . . . ( 2 ) P'SL - - . (3) A •- fit-and ,2. 2 -a Pz ~ as presented i n sect ion 3 of th i s chapter are used, the un-primed var iables r e f e r r i n g to the spec tra l l i n e parameters • 65 (as obtained In sect ion 3) while the primed var iables repre -sent the instrumental parameters. The r e s u l t i n g double-primed var iables describe the spec tra l l i n e as corrected for instrumental broadening, i . e . the l i n e before i t entered the spectrograph. The s p e c t r a l l i n e i s broadened by the Doppler ef-fect as we l l as the Stark e f f e c t , and the Doppler broadening must be subtracted from the observed l i n e p r o f i l e to deter-mine the Stark broadening accurate ly . The Voigt unfolding technique as expressed by Eqs. (2) and (3.)» i s again app l i ed , using the Voigt parameters fit - ( 2 * % c 4 ^ to character ize the Doppler e f f e c t , as given by Van de Hulst and Reesinck (19)4.7). Table 5 shows the intermediate and f i n a l resu l t s i n analyzing the A II l i n e at J 4 8 O 6 8. It is evident that the Doppler e f fect contributes very l i t t l e to the l i n e broadening. For some of the l ines measured a change did occur i n the t h i r d decimal place,: but th i s f igure was dropped i n presenting the f i n a l r e su l t s since It was f e l t that the accuracy of the measurements and analys is 66 did not warrant the inc l u s i o n of four s i g n i f i c a n t f i g u r e s . Table 5 Steps i n ca l c u l a t i n g the p r o f i l e of the A II l i n e at 1+806 A, correcting for Instrumental and Doppler broadening. Line or function Pi Half-Width (8) 1+806 8 l i n e as .1+18 measured M l 1.630 Instrumental function at .111 .01+0 .1+61+ 1+806 X 1+806 % l i n e ..cor-rected for i n -.31+6 .378 1,1+21+ strumental broadening Doppler p r o f i l e at 2,0 ev: .000 .002 1+806 8 l i n e cor-rected for i n s t r u -mental and Doppler .314-6 .376 1.M.21+ broadening 6 . The Determination of N and kT. e The results of measuring three l i n e s from multiplet 6 of the A II spectrum were used to calculate the electron number density. Lines from this multiplet have previously been measured by Jal uf ka et a l ( 1 9 6 6 ) , who found them to be wider than predicted by Griem (1961+) by a factor of 2 . 6 . Table 6 shows the results of analyzing the lines from multiplet 6 of A I I , The mean value of the measured half-widths was used to calculate the electron number density. 67 Table 6 P u l l half-widths for mult ip le t 6 of A II H a l f - r r W l d t h ( £ ) Mean (&.) Nfe (cm: 3) 14806 1+81+8 i+736 1.1+2 1.11+ 1.07 1.21^15^ 3 . 2 3 x l 0 1 7 t l 5 ^ Following Ja lufka et a l (1966), Griem's widths for th i s mul t ip le t were scaled by a factor of 2.6 to obtain the above value for N . e As w i l l be seen from F i g . 2., Chapter 2, the h a l f -widths of the Stark-broadened l ine s exhibi t a moderate temp-erature dependence. An estimate of the plasma temperature must therefore be made i n order to determine N Q from the Stark broadening of spec tra l l i n e s . The temperature was i n i t i a l l y estimated to be 20,000°K. The widths of the A II l ine s from mul t ip le t 6 then gave a f i r s t approximation to N . This value of N was subst i tuted into the Saha i e equation (Eq. ( A l ) , Appendix 2) and an i t e r a t i v e technique used to determine kT. The value of kT g iv ing good agreement with the experimentally determined value of N Q and that c a l -culated by E q . (Al) was 2 .0 ev. Table 7 gives the percent-age of argon in the various stages of i o n i z a t i o n at th is temp-erature . The ca lculated value of N_ was based on a computed i n i t i a l number density of argon atoms and hydrogen molecules 68 17 -3 of 3»26 x 10 cm. » The ca l c u l a t i o n assumes that no p a r t i -cles have escaped to the cooler region of the plasma vessel. The time taken for pressure e q u i l i b r a t i o n , based on the v e l o c i t y of sound i n the gas, is about 30/Usec. In view of the lack of information about the actual temperature and pressure gradients i n the vessel, the above c a l c u l a t i o n i s reasonable. Table 7 Relative argon ion populations for kT = 2.0 ev. Ion I population N e calculated (cm - 3)' N e experimental (cm - 3) A I A II A III 1.0 98.1 0.9 3.26 x 1 0 1 7 ±15$ 3.23 x 1 0 1 7 ±15$ As can be seen from Table 7 one would expect to db-serve only A II l i n e s at this temperature and electron den-s i t y . A l l of the hydrogen i s , of course, sin g l y ionized. As can be seen from the foregoing discussion of temperature, one would not expect any appreciable radia-t i o n from the region i n the plasma which emits strong A II r a d i a t i o n . The maximum radiatio n comes instead from a region i n which the temperature and electron density are low-er. One can however get a lower l i m i t to the value of N Q from the l i n e p r o f i l e . Accurate determinations of N Q by this method require a s p a t i a l "unfolding" of the density and tem-69 perature gradients in the plasma, perhaps using a method known as Abel unfolding (HBrmann (1935))• The coarse e s t i -mate y ie lded by the analys is of the l i n e on the plasma 17 — 3 plate is N Q = 1.98 x 10 'cm. J and should be considered as a lower bound on the actual number dens i ty . 7. The Experimental Results The experimental resu l t s are summarized in Table 8. The value of r , the r a t i o of the measured width to that c a l -culated by Griem (1961i), is given for mul t ip le t 7» I t should be pointed out that a recent correc t ion by Griem (1966) gives t h e o r e t i c a l widths which agree more c lo se ly with various r e -ported experimental values, the agreement in most cases be-ing within a factor of 2:. This paper should be consulted for d e t a i l s . I t w i l l also be noted that the value of the Voigt parameter P-^/h for the tabulated l ines l i e s between .09 and • 3 1 « A pure Lorentz p r o f i l e has a value j ^ / h equal to 0.5>0. Some of the l ines have been compared with the r e -su l t s of other workers. These resu l t s are summarized in the paper by Griem (1966). The widths i n Table 8 correspond to N e = 3*23 x l O ^ c m . " 3 and the temperatures are those reported by the i n d i v i d u a l workers, ranging between kT = 0.95 ev. to kT = 2.7 ev. No attempt has been made to evaluate t h e s ® r e -ported results,,; or the ca lcu la t ions by Griem (1966), for the temperature found in th is experiment. 70 Table 8 P u l l half-widths of A -II l ines N e = 3.23 x 1 0 1 7 c m ~ 3 kT = 2 .0 ev. Mul 1 • | P u l l Half-Widths (&) Voigt t i - Griem Griem Other J Para-pletj A) E x p e r i - Mean (196i|) (1966) Workers X meter :. No. mental (±15*)- 20;000°K 6 6 6 4806* Mh,8 . ^ 736 r I.I4.2 1.1)4 1.07 1.21 .46 .83 — (2 .6) .242 .252 .310 7 7 7. ! J 4.266 4380 1.19 .84 .97 1.00 .25 .81 1 .01 kP .087 .21+3 .308 Ik 4726 1 .31 1.31 1 .05 1.33 .185 15. 15 15 ! ! 4760 45^ 40 4657 //? &m 1.10 1.08 1.13 .224-3 .185 .154 1 7 4079 1.12 1.12 .186 31 4590 1.09 1.09 1.-14 .91 .258 32 4277 1.58 1.58 .260 39 [+14.81 1 1.27 1.27 .285 — For references see Griem (1966). These f i g -ures not corrected for temperature dependence. t Measurements on these l ines reported In the open l i t e r a t u r e . 71 8. A Discuss ion of E r r o r s . The various sources of possible experimental error should be mentioned and a l so , i f poss ib le , an estimate made of the amount of error introduced by each of these sources. The plasma generator is assumed to provide a r e -producible plasma, with l i t t l e v a r i a t i o n from shot to shot. The current waveform, as monitored by a high-voltage probe for each shot on the plasma p la te , was reproducible to better then 5$» The i n t e n s i t y of the. A\ II spec tra l l i n e s showed a s i m i l a r r e p r o d u c i b i l i t y . The i n t e n s i t i e s of the A II l ines during the time the o p t i c a l shutter was open were constant to better than 10$, i n d i c a t i n g a plasma temperature (assuming l o c a l thermal equ i l ibr ium to exis t ) constant to less than this (about 1 to 5$). The e lectron number density could be expected to be constant to better than 10$. It was not pos-s i b l e to monitor the i n t e n s i t i e s of the A II l ines at the same time as the spectrographic measurements were made. ' The l ines were monitored p r i o r to taking the plasma p l a t e . The accuracy of the t iming of the t r i g g e r pulse Is also important. No detectable j i t t e r in any of the e l e c t r o -nic uni ts was observed, and the t o t a l j i t t e r was less than ly^sec . N e g l i g i b l e error was introduced from th i s source, as the i n t e n s i t i e s of the A II l ines did not change apprec i -ably i n a time i n t e r v a l of 1 or 2 JJ-sec. 72 In considering the r a d i a t i o n from extended sources, the problem of o p t i c a l thickness must be considered. The plasma is o p t i c a l l y t h i n to r a d i a t i o n of a cer ta in frequency i f th i s r a d i a t i o n can pass through the plasma with a n e g l i -g ib le chance of absorpt ion . Otherwise, the plasma is o p t i c -a l l y th ick for that frequency. In order for l i g h t from the centre of a plasma volume to escape, i t must traverse a f i n i t e thickness of the plasma. I f the plasma i s o p t i c a l l y t h i c k , the l i g h t may be absorbed and re-emitted several times before escaping. This process can d i s t o r t the l i n e shape, p a r t i c u l a r l y i f tempera-ture and densi ty gradients exis t i n the plasma. In p a r t i c -u l a r , a cooler region at the plasma boundary can r e s u l t i n a reduct ion i n the i n t e n s i t y of the centra l maximum of the l i n e . This condit ion would manifest i t s e l f as an apparent broadening of the l i n e . In order for absorption to occur, a large number of atoms i n the absorbing gas must be i n the lower state of a pa ir of o p t i c a l energy l eve l s whose energy separation cor -responds to the wavelength of i n t e r e s t . The p r o b a b i l i t y of absorption also depends d i r e c t l y on the length of the absorb-ing column. For most laboratory plasmas, the number of absorb-ing atoms i n the correct energy state i s very smal l . The only exception occurs i n the case of resonance r a d i a t i o n , for 73 which the lower l e v e l involved is the ground state of the atom or i o n . A l s o , the absorbing lengths for most plasmas are only a few centimeters* Griem (I96I4.), p . 270, discusses the problem of o p t i c a l thickness and concludes that l abora -tory plasmas are almost always o p t i c a l l y t h i n , the only ex-ceptions invo lv ing resonance r a d i a t i o n . The l ines studied here are not resonance l ines of A I I , and the s ide-on obser-vat ion minimized the length of the absorbing plasma column. A c c o r d i n g l y , . n o correct ions for s e l f absorption were deemed necessary. The resu l t s of th i s inves t iga t ion can be influenced i n another way by s p a t i a l inhomogeneities i n the plasma. Even i f the plasma is o p t i c a l l y th in to the l ines of i n t e r e s t , the f i n a l observed l i n e shape may re su l t from r a d i a t i o n a r i s -ing from d i f f erent regions of the plasma. The p r o f i l e s of the various contr ibut ions r e f l e c t l o c a l condit ions i n the plasma, so the f i n a l observed l i n e shape is an average over a l l plasma volumes from which appreciable r a d i a t i o n comes. It has been assumed that the r a d i a t i o n as observed (coming roughly from l i g h t o r i g i n a t i n g along a diameter of the p l a s -ma vessel) arose p r i m a r i l y from regions In which kT and N Q were everywhere constant. The framing camera photographs encouraged th i s be l ie f , , although future experiments w i l l be done to determine more accurately the v a l i d i t y of th i s assump-t i o n and to correct for any ex i s t ing gradients . No accurate 7k numerical estimate of the error due to s p a t i a l gradients can present ly be made, although i t is bel ieved to be considerably less than 20$. The remaining major source of error i s in the photographic process . The c a l i b r a t i o n technique was chosen to minimize the important errors that can ar ise when determ-in ing l i g h t energy d e n s i t i e s . The densi t ies of the various steps of the step f i l t e r are accurate to about 10$ or be t t er . The theory predic ts that a l l l ines a r i s i n g from the same mult ip le t should have the same h a l f widths. As can be seen from Table 8, the half-widths of l ine s i n the same mul t ip le t agree to within about 1 5 $ . The errors In the aver-age value of the ha l f -width for a given mult ip le t (where averages could be taken) should be or l e s s . CHAPTER 5 Conclus ion Two important points a r i s i n g out of t h i s exper i -mental work should be emphasized. F i r s t l y , measurements of the p r o f i l e s of fourteen A II l ines have been made. Second-l y , the development of a promising experimental technique has begun. Further refinement of this technique promises i n -teres t ing r e s u l t s . The A II l ine s measured f a l l into two categories , those prev ious ly reported by other workers and those not pub-l i shed elsewhere. The agreement with the resu l t s of other workers is quite good, as seen from Table 8, Chapter 4 . These measurements general ly i l l u s t r a t e the inaccuracy of the treatment given by G-riem (1959) for the case of s i n g l y -ionized argon. Experimental evidence exists (see Griem (1966)) that the resu l t s for other l i g h t and medium ions are a lso in error by factors of from 2 to 10. In addi t ion to the ha l f -width measurements, a measure of the shape of the spec tra l l ines was also obtained.. As can be seen from Table 8, Chapter 4, the shapes of the l ines reported here appear to be Voigt p r o f i l e s , not pure Lorentz ian p r o f i l e s as predicted by the theory of Griem both i n i t s i n i t i a l and revised forms. Although the accuracy of the l i n e shape measurements may wel l be less than that of the ha l f -width measurements, i t does not appear that the theoret-75 76 l e a l predic t ions have been f u l f i l l e d . No obvious reason for th is disagreement has presented i t s e l f . The correc t ion given by Griem (1966) to his e a r l i e r theory gives better agreement with the half-widths as repor t -ed in recent ly published experimental papers (for references see Griem (1966)). The re f ined theory considers c o l l i s i o n -induced t rans i t i ons between upper and lower leve ls of the l i n e and Coulomb interact ions of the perturbers with the per -turbed ions . No numerical ca lcu la t ions are as yet ava i lab le for the new l ines reported here. Nonetheless, any theory of l i n e broadening must give good agreement with a l l experimental data, inc lud ing that presented for the f i r s t time i n this thes i s • The photographic technique used appears quite prom-i s i n g . A great advantage over conventional photoe lectr ic methods is r e a l i z e d , since the desired data can be gathered with only about 10 exposures. The same experiment, performed p h o t o e l e c t r i c a l l y , would have required about 200 separate f i r -ings of the plasma generator. Errors due to the de ter iora t ion of the apparatus with repeated f i r i n g s are thus great ly r e -duced by the photographic technique. The data analys is as described i n th is thes is i s also simpler and more e a s i l y handled by modern computer methods. In a d d i t i o n , th is method has the advantage of s i m p l i c i t y i n i t s concept and operat ion. The e f f i c i e n c y and convenience of gathering the spectroscopic 77 data i n th i s way makes the extension and refinement of the technique we l l worth whi le . Some possible further appl icat ions of the technique should be mentioned. A d d i t i o n a l study of the A II spectrum could e a s i l y be undertaken by using a quartz, o p t i c a l system i n the spectrograph. Analys is of the many A II l ine s in the region 3 0°0 - 1+000 2 would amplify the present experimental r e s u l t s • Another important project involves the accurate use of a l i n e such as for determining N . Once a map of the s p a t i a l gradients i n the plasma vessel i s constructed, an i n -dependent and r e l i a b l e value of N g can be found from the p r o f i l e . This experimental method can then be extended to l ines from other gases by mixing them with hydrogen. An experiment concerning the phenomenon of f o r b i d -den l ines also suggests i t s e l f . A b r i e f d iscuss ion of f o r -bidden l ine s i s given in Appendix 3. This experiment could provide another independent estimate of the e lectron number density i n the region where the A II r a d i a t i o n i s strongest . It would also be useful to invest igate the present-l y accepted l i n e a r dependence of the hal f -width of the spec-t r a l l ine s on N . No check of this r e l a t i o n s h i p was possible e i n th is experiment, and a l i n e a r dependence was assumed. This experimental technique, coupled with a su i table plasma source, 78 could be used for such a check. The l i n e broadening theory of Griem also predicts a s h i f t of the maximum of the spec tra l l i n e . An experimental check on these predict ions would be a valuable contr ibut ion to the body of observat ional data . Accurate measurements require the a v a i l a b i l i t y of a reference spectrum of sharp, unshifted l i n e s , such as are found in the spectrum of an e l -ectrodeless discharge. APPENDIX 1 The Photographic Process Much has been wri t ten about the photographic pro -cess, although a f u l l understanding of this complicated phenomenon does not seem to have been reached as yet . Only a few de ta i l s w i l l be given here, and a book such as that by Sawyer (1963) (Chap. 8) should be consulted i f a more ex-haustive treatment i s desired^ When l i g h t f a l l s upon a photographic emulsion, a chemical react ion invo lv ing the photosensit ive agent, such as s i l v e r bromide, i s begun. This photosensit ive agent i s suspended in a th in layer of transparent g e l a t i n deposited on a c e l l u l o i d or glass base. When this emulsion undergoes the chemical operations of developing and f i x i n g , an image r e s u l t s . The portions of the emulsion which were exposed to l i g h t are darkened to a degree which, except for very large exposures, varies with the exposure. The term "exposure" can be given a prec ise mean-i n g , and is usua l ly defined by E * It where E is the exposure I is the energy density per uni t time, i . e . i n -t e n s i t y , of the incident l i g h t (assumed constant) t is the time for which the emulsion is exposed The amount of blackening of the emulsion can be 79 V. 80 described by def in ing a quanti ty D, the dens i ty , by the r e -l a t i o n r / \ P - l o 3 l 0 ( i j l ) where I Q Is the energy densi ty of l i g h t transmitted through the unexposed port ion of the emulsion I Is the energy density of l i g h t from the same source transmitted through the exposed port ion of the emulsion. ' With these d e f i n i t i o n s , a curve such as the one in P i g . A l can be drawn. Such a curve is often cal led the H and D curve for the emulsion, named after Hurter and D r i f f i e l d , who f i r s t presented the information i n this way. This curve represents a c a l i b r a t i o n of the response of the emulsion when exposed to l i g h t . l o g 1 0 ( E = I T ; P i g . A l T y p i c a l blackening (H and D) curve for photographic emulsion 8 1 The shape of the H and D curve w i l l vary with the wavelength of the incident l i g h t , the developing and f i x i n g techniques, the condi t ion of the developer and f i x e r , and the age of the emulsion. There is also considerable v a r i a t i o n with the Various:rtypes of emulsion a v a i l a b l e , as wel l as some f l u c t u a t i o n with d i f ferent samples of the same emulsion* However, the curve w i l l always have the same general , non-l i n e a r character displayed in P i g . A l . Photographic emulsions are subject to two types of dev iat ion from the H and D curve. One of these, the i n t e r m i t -tency e f f ec t , concerns the response of the emulsion when ex-posed to d iscrete l i g h t pulses on one hand, and to one c o n t i n -uous longer pulse on the other. The second, the r e c i p r o c i t y e f f e c t , is concerned with the response of the emulsion to l i g h t of widely d i f f e r i n g i n t e n s i t i e s . I f an emulsion is i l luminated by n consecutive l i g h t pulses of i n t e n s i t y I 6 , each g iv ing an exposure of E Q / n , the emulsion blackening should be the same as that produced by one l i g h t pulse of in tens i ty I g iv ing an exposure of E Q . F a i l u r e of the emulsion to respond in th is way is termed i n -termittency f a i l u r e . Care must be taken to minimize th is ef-fect when c a l i b r a t i n g the response of the emulsion. The ex-perimental method adopted here, i n which the same l i g h t source used in conjunction with the same shutter y ie lded both the experimental spectrum and the c a l i b r a t i o n spectrum eliminated 82 error due to the interraittency e f f ec t . An emulsion i l luminated by a l i g h t pulse of i n t e n -s i t y I Q , g iv ing an exposure of E Q should produce the same ef-fect as a longer l i g h t pulse of i n t e n s i t y I 0 / n g iv ing the same exposure E Q . Deviations from this ru le are known as r e c i p r o c i t y f a i l u r e , and appear, for example, when a stand-ard source of much f a i n t e r i n t e n s i t y than the experimental source i s used to c a l i b r a t e the photographic emulsion. R e c i -p r o c i t y f a i l u r e was also minimized i n th is experiment by using the plasma l i g h t for c a l i b r a t i o n purposes. The only drawback to the chosen c a l i b r a t i o n method is the i m p o s s i b i l i t y of determining absolute i n t e n s i t i e s . » Since a knowledge of absolute i n t e n s i t i e s was not e s s e n t i a l to the experiment, and i n view of the many advantages offered by i t , the method described above was chosen. In studying the shape of spec tra l l ine s one must determine the energy density of the r a d i a t i o n as a funct ion of distance from the l i n e centre . When using photographic techniques, th i s requires a knowledge of the "plate response" (H and D curve) . C a l i b r a t i o n of the plate response can be accomplish-ed by reducing, in a known way, the energy density of the l i g h t composing the various parts of a photographic image. For this purpose, a neutral density wedge was employed, and the H and D 83 curve drawn for each wavelength of i n t e r e s t . APPENDIX 2 Thermal E q u i l i b r i u m and the Ca lcu la t ion of Spectroscopic Temperatures There is considerable doubt about the existence of thermal equ i l ibr ium i n many laboratory plasmas. Such plasmas normally ex is t for short periods of time and t h e i r parameters may change appreciably while observations are being made. An estimate of the times required to reach equ i l ibr ium conditions must be made. The plasma e l ec trons , possessing high v e l o c i t i e s , make frequent c o l l i s i o n s among themselves and r a p i d l y reach a Maxwellian v e l o c i t y d i s t r i b u t i o n . Calculat ions for the times involved have been made by Sp i tzer ( 1 9 5 6 ) , p 76 f f , aid are of the order of l O " - ^ seconds for the dense plasmas s tud ied . The time for ions to come to equ i l ibr ium among them-selves ( ion- ion re laxa t ion time) i s of the order of 1 0 " ^ sec-onds. The i on -e l ec t ron re laxat ion time is of the order of o 1 0 seconds. These times re fer to e l a s t i c c o l l i s i o n s ; the times for i n e l a s t i c c o l l i s i o n s are considerably longer . Because of the very short e l ec tron-e l ec tron r e l a x a -t ion time, i t is always meaningful to speak of an e l ec tron temperature. The ion excited states are i n contact with the e lec tron bath, and w i l l be populated by c o l l i s i o n s with free e l ec trons . For states above a c r i t i c a l quantum number (usual-l y about 2 or 3 ) > such c o l l i s i o n s dominate and the populations 85 w i l l vary according to the expected exponential law at the e lec tron temperature. Since the spec tra l temperature deter-mination involves a measurement of excited state populat ions , such an analysis y i e lds the e lectron temperature. In cases of thermal equ i l ibr ium, l o c a l or complete, the ion tempera-ture w i l l be the same. th i s experiment i n order to evaluate the contr ibut ion to the spec tra l l i n e width a r i s i n g from the Doppler e f f e c t . For th i s purpose the ion temperature was assumed to be i d e n t i c a l to the e lectron temperature, i . e . the existence of thermal e q u i l i -brium, at l east l o c a l l y In the plasma, was assumed. The ab-sence of thermal e q u i l i b r i u m , l o c a l or complete, would norm-a l l y r e s u l t i n an ion temperature lower than the e lectron temperature. The magnitude of the Doppler correc t ion was a l -ways s m a l l . The Spectroscopic Determination of Temperature In equ i l ibr ium at a temperature T , the number den-s i t y of I - t h stage ions of energy E m is given by A n estimate of the ion temperature was required for where: C i s a constant g^ is the degeneracy of the energy l e v e l E, kT is the k i n e t i c temperature 'm 86 Thus where: Z'^  i s the p a r t i t i o n funct ion for the i - t h stage ions N i(0)) i s the density of i - t h stage ions in the ground state ( E D = 0) go i s the s t a t i s t i c a l weight of these ions r - N i (0 ) Here we have a set ^ ~ —i— So W r i t i n g Saha's equation for the r a t i o of the num-bers of ions i n various stages of i o n i z a t i o n , we have, approx-imately , A/ U l Z1 _ / Z IT 7ne/rr~2^ A/1 Zirl " /Ve I J GXPt 7KT) ...(/Al) where: N is the e lec tron number density me, i s the e l ec t ron ic mass V i is the i o n i z a t i o n energy of the i - t h stage ions (the energy required to remove the ( i + l ) - t h e l e c -t r o n . ) h i s Planck's constant The depression of the excited levels by the e l e c t r i c f i e l d s i n the plasma is here neglected, introducing an error of a few per cent i n the populations. To solve th is equation for the k ine t i c temperature 87 requires a knowledge of the e lectron density N e , and of the various ion populat ions . The argon II l ine s from mult ip le t 6 were used to determine N , These l ines have been measured by several workers, inc lud ing Jalufka et a l (1966), and Po-penoe and Shumaker (1965)« Their resu l t s show the widths of these l ines to be greater than predicted by Griem (1959) by a fac tor of about 2,6, The values of Griem were scaled by th is factor in computing N . The ion populations were estimated from the exper i -mental observation that l ine s from A II Ions were the only argon l ine s present . The expected temperature would be such that almost a l l the argon would be s ing ly i o n i z e d . The c a l -c u l a t i o n of kT proceeded by guessing an i n i t i a l value and c a l c u l a t i n g the ion populat ions , using N Q as determined above. The e lec tron density was then calculated from the Ion dens i -t i e s , and the c a l c u l a t i o n repeated for various values of kT u n t i l the ca lculated value of N agreed with observed value , and most of the argon was s i n g l y i on ized . APPENDIX 3 Forbidden Lines In the conclusion of this thesis a b r i e f reference was made to forbidden l i n e s . A descr ip t ion of the measurement of a forbidden l i n e i n a helium plasma spectrum is given by Sadjian et a l (1961). A b r i e f d iscuss ion of forbidden l ines and t h e i r app l i ca t ion to plasma physics w i l l now be g iven. The existence of a set of s e l ec t ion rules regarding o p t i c a l t rans i t i ons grea t ly reduces the number of spec tra l l ines emitted by an atom or i o n , These rules make the proba-b i l i t y of r a d i a t i v e (dipole)' e l ec tron ic t r a n s i t i o n s between c e r t a i n l eve l s v i r t u a l l y zero. F i g . A2 shows the s i t u a t i o n which is of in teres t here. Two c l o s e l y - l y i n g energy leve ls are involved , F i g . A2 Energy states i n the absence of external e l e c t r i c f i e l d s 88 89 with a small energy separat ion, d . Opt ica l t rans i t ions are allowed between the l eve l s 1 and 0, and forbidden between l eve l s 2 and 0. I f such an energy system is placed i n an e l e c t r i c f i e l d , "mixing" of the l eve l s w i l l occur (as described i n Chapter 2) and leve ls 1 and 2 w i l l be pushed s l i g h t l y apart . The mixing of the wavefunctions ¥ ° and resu l t s i n a change i n the dipole t r a n s i t i o n p r o b a b i l i t y between the leve ls 2 and 0 from zero to some f i n i t e Talue. This "forbidden l i n e " can be observed spec troscop ica l l y . A\ b r i e f summary of the re su l t s of the ca lcu la t ions presented by Sadjian et a l (1961) w i l l be g iven. The atomic system i s perturbed by a p o t e n t i a l V, and the perturbat ion theory shows that the new energies E^ and E2 of the upper l eve l s are given by Here V^^ is t n e matrix element of the perturbat ion between a n d f f . where I f I i s the i n t e n s i t y of the allowed l i n e i n the 9 0 absence of perturbat ions , then i n the presence of V T m «» +1 J Thus both the i n t e n s i t i e s and the wavelengths of the two l ines are functions of a . The parameter a is in turn depend-ent on the f i e l d strength at the atom, which can be re lated to the charged p a r t i c l e dens i ty . The two, l ines normally appear as a pa ir of over-lapping l i n e s , the forbidden component appearing i n the wing of the allowed one. A scanning procedure is requ ired , pre-ferab ly with a standard unshifted source of the allowed l i n e ava i lable as a reference when measuring the l i n e s h i f t s . The l ines are close enough i n wavelength to allow the use of the plate c a l i b r a t i o n method described i n th i s t h e s i s . Having analyzed these l i n e s , a measure of the l o c a l ion density w i l l r e s u l t . A pre l iminary survey of the A II energy spectrum has been made to determine whether or not i t contains su i table forbidden l i n e s . A forbidden l i n e might be expected about 2.2 8 away from an A II l i n e at l i l 3 1 8 (mult iplet 32). This region i s just out of range of the inves t iga t ion described i n this 9 1 t h e s i s , but the allowed l i n e was found during the pre l iminary i n v e s t i g a t i o n . The technique described i n th is thesis is w e l l suited to inves t iga t ing the phenomenon of forbidden l i n e s . Appendix 4 Table 9: Standard Voigt Profiles Parameters Ordinates in Terms of Central Ordinate p\j/h 3 1 /p 2 p 2 /h p^/h2 0.8 0.7 0.6 0 .5 0 .4 0 .3 0 . 2 0 . 1 0.05 0 .02 0.01 Widths in Terms of Half-width (b^h) 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 0.325 0.350 0.375 0.400 0.425 0.450 0.475 0.500 0.00 0.04 0.09 0.14 0.19 0.24 0.30 0.36 0.43 0.51 0.59 0.69 0.79 0.92 1.07 1.26 1.50 1.83 2.38 3.54 oO 0.60 0.59 0.57 0.55 0.54 0.52 0.50 0.48 0.46 0.44 0.42 0.40 0.38 0.35 0.33 0.30 0.27 0.23 0.19 0.13 0.00 0.36 0.34 0.32 0.31 0.29 0.27 0.25 0.23 0.21 0.20 0.18 0.16 0.14 0.12 0.11 0.09 0.07 0.05 0.04 0.02 0.00 1.06 1.08 1.11 1.13 1.16 1.18 1.20 1.23 1.25 1.28 1.30 1.33 1.35 1.38 1.40 1.43 1.45 1.48 1.51 1.54 1.57 0.57 0.56 0.56 0.56 0.56 0.56 0.55 0.55 0.55 0.54 N ) . 5 4 0.53 0.53 0.53 0.52 0.52 0.52 0.51 0.51 0.51 0.50 0.72 0.72 0.71 0.71 0.71 0.71 0.71 0.70 0.70 0.70 0.70 0.69 0.69 0.68 0.68 0.68 0.67 0.67 0.66 0.66 0.66 0.86 0.86 0.86 0.86 0.86 0.86 0.85 0.85 0.85 0.85 0.84 0.84 0.84 0.84 0.84 0.83 0.83 0.83 0.82 0.82 0.82 1.00 1.00 1.00 1. 1. 1, 1. 1. 1. 00 00 00 00 00 00 1.00 1.00 1.00 •1.00 1.00 1. 1. 1. 1. 1. 1. 1. 00 00 00 00 00 00 00 1.15 1.15 1.15 1.16 1.16 1.17 1.17 1.17 1.18 1. 1. 1. 1. 1. 18 18 19 19 19 1.20 1. 1. 1. 1. 1. 1. 20 21 21 22 22 22 32 33 33 33 34 34 35 36 37 1.38 1.39 1.40 1.41 1.42 1.44 1.45 1.47 1.48 1.50 1.52 1.53 1.52 1.53 1. 1. 1. 1. 1. 1. 54 56 57 59 60 62 1.64 1.66 1.68 1.71 1.74 1.77 1.81 1.85 1.88 1.92 1.96 1.98 2.00 1.82 1.84 1.87 1.90 1.94 1.98 2.02 2.06 2.10 2.15 2.19 2.24 2.29 2.34 2.40 2.46 2.54 2.64 2.74 2.87 3.00 2.08 2.12 2.19 2.25 2.34 2.42 2.54 2.64 2.-?S 2.87 2.98 3.12 3.26 3. 3. 3. 3. 4. 4. 39 54 70 85 00 13 4.25 4.36 2.38 2.49 2.63 2.79 3.00 3.24 3.52 3.80 4.14 4 .44 4 .73 5. 5. 5. 5. 6. 6. 03 32 57 83 07 30 6.55 6.76 6.92 7.00 2.58 2.82 3.13 3.56 4.08 4.58 5.05 5.50 5.96 6.40 6.78 7.15 7.52 7.86 8.21 8.55 8.86 9.18 9.50 9.77 9.95 APPENDIX 5 I.B .M. Computer Program U s e d to Calculate Line P r o f i l e s 93 $ FORT RAN DIMENSION RELINW(7),MDENW(8),DENW(7),DISMM(150)•RELIN(150) , 2WIDTHQ0) READ 900,RELINW PRINT 990» RELINW ' : 1 READ 901, NA,NZ,LAMDA PRINT 902»NA,NZ,LAMDA DO 3 N = 1,7 3 DENW(N) = 0 . DO 5 NCOUNT = 1,2 READ 904,MDENW 5 10 ' DENW(l) = FLOAT (MDENW( 1 )+MDENW (8 ) ) M.+DENW( 1 )/2. DO 5 N = 2,7 DENW(N) = DENW(N) + FLOAT(MDENW(N))/2. DO 10 N = 1,7 DENW(N) = A LOG(DEN W(N) ) N = 1 . C 15 INTENSITIES BY QUADRATIC INTERPOLATION READ 9 1 5 , MICRON,MDENL IF(MICRON.EQ.O) GO TO 35 DISMM(N) = FLOAT(MICRON)/106 6• DENL = MDENL DENL = ALOG(DENL) ': 18 25 NI = 3 IF(DENL.LT.DENW1NI)) GO TO 25 I F ( N I . E Q . 7 ) GO TO 15 • NI "=" Ni' +""l GO TO 18 D2 = ( RELINW ( NI ) -REL INW ( NI-1 ) ) / ( DENW ( N.I ) -DENW ( NI-1 ) ) D l = ( RELI NW ( NI-1 )-REL I NW( NI-2 ) ) / (DENW ( N I . - l )-DENW( NI-2 ) ) D21 = (D2-DD/(DENW(NI )-DENW(NI-2) ) R i y _ N L l REL^NWf NI-2 )_+( DENL-DENW( NI-2 ) )*D1_+ 2TDENL-DENW ( NI-2 ) T * ( DENL-DENW "(-N i - l . ) " j *D2l'"' " " ' REL I N ( N ) = E X P ( R E L I N L ) 30 N = N + l GO TO 15 35 NMAX = N - 1 C MAXIMUM INTENSITY RELINM = R E L I N ( 1 ) DO 38 N = 2,NMAX , I F ( R E L I N ( N ) . L T . R E L I N M ) GO TO 38 RELINM = RELIN(N) 38 NM = N CONTINUE N = NM - 1 D l = ( R E L I N ( N + l ) - R E L I N ( N ) ) / ( D I S M M ( N + l ) - D I S M M ( N ) ) D2 '= ( R E L I N ( N + 2 ) - R E L I N ( N + l ) ) / ( D I S M M ( N + 2 ) - D I S M M ( N + l ) ) D21 = (D2-D1)/(DISMM(N+2)-DISMM(N)) RELI MM = R E L I N ( N ) - ( D 1 - D 21*'(DISMM (N + l ) -DI SMM ( N ) ) ) * * 2 / 4 . / D 2 1 C NORMALISE INTENSITIES DO 45 N = 1» NMAX 45 RELIN(N) = RELIN!N)/RELINM PRINT 950» (DISMM(N).RELIN(N)»N = 1,NMAX) C WIDTHS FOR VOIGT F I T 52 READ 952>CONINT IF(CONINT.GT..2) GO TO 1 PRINT 9 54y_CONI_NI _ _ _ _ _ •_ DO 80 NVOIGT = 2,8 ' ~~ ~~" ~ ' ' R EL I N V= FLOAT(NVOIGT)/10.*(1.-CONINT) + CONINT I F ( R E L I N V . L T . R E L I N ( 1 ) ) GO TO 75  I F ( R E L I N V . L T . R E L I N ( N M A X ) ) GO TO 75 N = 2 NSL = 0 • __ _ 55 I F ( R E L I N V . L f . R E L I N ( ' N ) ) GO TO 60 N = N + l GO TO 55 ' •60 N = N - 1 IF(N.GT.NM) N = N - l D l = ( D I S M M ( N + l ) - D I S M M ( N ) ) / ( R E L I N ( N + l ) - R E L I N ( N ) ) D2" = '( DISftW(*ff+ 2~7- ITl SWTN+1 T,7"("RECl N CH+2 ) - R"E*C'l N T N + T ) ) " "*"~ "" D21 = ( D 2 - D 1 ) / ( R E L I N t N + 2 ) - R E L I M ( N ) ) P I S = DISMM(N) + ( R E L I N V - R E L I N ( N ) ) * ( D 1 + D 2 1 * ( R E L I N V - R E L I N ( N + l ) ) ) I F ( N S L . E Q . l ) GO TO 70 DISS = DIS N S L - 1 N '= NM 6 5 I F ( R E L I N V . G T . R E L I N t N ) ) GO TO 6 0 N = N + l GO T O 6 5 7 0 W I D T H ( N V O I G T ) = D I S - D I S S GO T O 8 0 " 7 5 W I D T H ( N V O I G T ) = 0 . 8 0 C O N T I N U E W I D T H 5 = . W I D T H ( 5 ) DO 8 5 N = 2 , 8 8 5 W I D T H ( N ) = W I D T H ( N ) / W I D T H 5 P R I N T 9 9 0 > ( W I D T H ( N ) , N = 2 , 8 ) P R I N T ' 9 9 5 » W I D T H 5 G O TO 5 2 9 0 0 F O R M A T ( 7 F 1 0 . 4 ) 9 0 1 F O R M A T ( 2 1 2 » 1 4 ) 9 0 2 F O R M A T ( 1H - » 1 0 X » 9 H A T . N O . = , I 2 » 1 0 X , 3 H Z = , I 2 > U 5 » 1 0 H A N G S T R O M S , / ) 9 0 4 ' F O R M A T ( 7 X » 1 3 ) 9 1 5 F O R M A T ( 1 6 , 1 4 ) 9 3 0 F O R M A T ( " lOX , 16 » F l 5 . 3) ' "' """"" ' 9 5 0 F O R M A T ( 1 0 X . 6 F 1 2 . 3 ) 9 5 2 F O R M A T ( F 1 0 . 4 ) 9 5 4 F O R M A T ( l H 0 , 1 0 X , 1 2 H C O N T . I N T . = , F 7 . 4 ) 9 9 0 F O R M A T ( 1 H 0 . 5 X » 7 F 1 2 . 3 ) 9 9 5 F O R M A T ( 1 H 0 , 1 OX , 1 7 H F U L L H A L F W I D T H = , F 7 . 4 » 2 H M M ) E N D " " " " " " " " *" " I 12 i i >i0 9 8 17 S 5 '4 3 APPENDIX 6 Readings of Plate Pos i t i on and Transmission Obtained by Scanning the Spectrographic Plates The wavelength of the spec tra l l i n e is given i n the f i r s t l i n e . The next four l ines give the plate p o s i t i o n and transmission readings for the step wedge. The plate p o s i t i o n (which can be ignored for the wedge readings) is a f i v e - d i g i t number g iv ing the plate pos i t i on i n microns. The transmission reading appears as a t h r e e - d i g i t number separ-ated by a s ingle space from the p o s i t i o n reading . Each wedge pattern i s scanned twice, and the reading corresponding to the unweakened l i g h t beam is recorded at the beginning and end of each run , g iv ing s ixteen wedge readings in a l l . The remaining pairs of numbers give the readings for the spec tra l l i n e s . The f i r s t page gives the readings obtained by scan-ning one of the l ines from the G-eissler p l a t e . This informa-t i o n was used in c a l c u l a t i n g the instrumental func t ion . The remaining pages give the readings for the fourteen A II l ines which could be treated by a Voigt a n a l y s i s . A graph of the r e c i p r o c a l d i spers ion of the spectrograph as a funct ion of wavelength is included af ter which'the'plate- readings are given for the remaining ten A II l i n e s which could not be f i t t e d by Voigt p r o f i l e s . 4272 32793 214 32896 843 3 2 7 8 4 215 32888 861 32828 383 3 2897 946 32852 393 3 2 8 8 5 954 3 2 8 4 9 598 3 2 8 7 4 938 3 2 8 4 2 6 1 0 3 2 8 8 7 9 5 4 3 2 8 7 9 759 3 2 8 8 0 182 3 2 8 4 7 774 3 2 8 9 9 187 32510 988 32530 997 3 2 5 5 0 99 3 3 2 5 7 0 988 32590 987 3 2 6 1 0 984 3 2 6 3 0 98 1 3 2 6 5 0 968 3 2 6 6 0 956 32665 942 3 2 6 7 0 9 2 2 3 2 6 7 5 880 32680 814 32685 723 3 2 6 9 0 6 2 3 3 2 6 9 5 519 3 2 7 0 0 425 3 2 7 0 5 . 355 3 2 7 1 0 .3 04. 3.271.5 284.. 32720 281 32 72 5 2 99 3 2 7 3 0 3 44 3 2 7 3 5 421 3 2 7 4 0 513 32745 619 3 2 7 5 1 726 3 2 7 5 6 811 32760 873 32765 913 3 2 7 7 0 93 7 3 2 7 7 5 952 32780 964 32785 975 3 2 7 9 0 9 8 5 3 2 7 9 6 993 32801 997 3 2 8 1 0 998 3 2 8 2 0 9 9 7 i 12 l i ho 9 0 >7 6 5 k 3 4 8 0 6 9 0 4 4 8 122 9 0 4 4 1 197 9 0 4 5 4 352 9 0 4 5 4 5 38 9 0 4 5 4 717 9 0 4 5 4 861 9 0 4 5 4 9 1 8 9 0 3 9 0 116 9 0 4 4 0 121 9 0 4 4 0 193 9 0 4 5 1 352 9 0 4 5 1 537 9 0 4 5 1 716 9 0 4 5 1 858 9 0 4 5 1 918 9 0 3 9 0 118 89991 969 9 0 0 5 1 965 9 0 1 0 0 9 6 5 9 0 1 5 0 960 9 0 2 0 0 966 9 0 2 5 0 966 9 0 3 0 1 948 9 0 3 2 0 937 9 0 3 4 0 926 9 0 3 6 1 913 9 0 3 7 0 9 0 7 9 0 3 8 0 901 9 0 3 9 0 889 9 0 4 0 0 875 9 0 4 1 0 856 . 9 0 4 2 0 833 9 0 4 3 0 807 9 0 4 4 0 780 9 0 4 5 1 7 4 4 9 0 4 6 0 7 05 9 0 4 7 0 660 ' 9048 0" " V i ' i 9 0490 561 " " " 9 0 5 0 ( f "511 9 0 5 1 1 459 9 0 5 2 0 413 9 0 5 3 0 375 9 0 5 4 0 333 9 0 5 5 0 303 9 0 5 6 0 273 9 0 5 7 0 251 9 0 5 8 0 231 9 0 5 9 0 219 9 0 6 0 0 210 9 0 6 1 0 206 9 0 6 2 1 2 06 9 0 6 3 0 211 9 0 6 4 0 221 9 0 6 4 9 236 9 0 6 6 0 258 9 0 6 7 0 287 9 0 6 8 0 316 9 0 6 9 0 3 5 5 ^ 9 0 7 0 0 400 9 0 7 1 0 445 ~~ " ' [ 9072 0' 49 5 9 0 7 3 0 5 4 9 ' 9 0 7 4 0 598 9 0 7 5 0 649 9 0 7 6 0 693 9 0 7 7 0 736 9 0 7 8 0 773 9 0 7 9 0 803 9 0 8 0 0 825 9 0 8 1 1 846 9 0 8 2 1 870 9 0 8 3 1 887 9 0 8 4 0 901 9 0 8 5 1 9 1 4 9 0 8 6 1 924 9 0 8 7 0 929 9 0 8 9 0 938 9 0 9 1 1 943. 9 0 9 3 0 946 9 0 9 5 0 953 9 0 9 8 0 961 9 1 0 0 0 9 6 3 9 1 0 2 0 966 9 1062 961 9 1 1 1 0 "965" 9 1 1 8 1 " 9 7 3" '912 20 955- " 9 1 2 6 0 961 4848 9 5 3 1 1 268 9 5 3 1 8 444 9 5 3 1 8 668 9 5 3 1 8 816 9 5 3 1 8 921 9 5 3 1 8 958 9 5 3 1 8 981 9 5 2 5 6 246 9 5 3 0 5 269 9 5 3 1 6 443 9 5 3 2 2 668 9 5 3 2 2 824 9 5 3 2 2 924 9 5 3 2 2 961 9 5 3 2 2 9 8 6 9 5 2 5 9 250 9 4 7 1 0 981 9 4 7 5 0 974 9 4 8 0 0 9 7 2 9.49 00 976 9 5 0 0 0 .974 9 5 1 0 0 981 9 5 2 0 0 972 9 5 2 9 9 961 9 5 3 2 0 937 95 3 3 0 927 9 5 3 4 0 9 1 3 9 5 3 5 0 895 9 5 3 6 1 873 9 5 3 7 0 847 9 5 3 8 0 8 1 4 9 5 3 9 0 776 9 5 4 0 0 731 9 5 4 1 0 684 9 5 4 2 0 6 3 2 9 5 4 3 0 588 9 5 4 4 1 544 9 5 4 5 0 511 9 5 4 5 9 4 8 3 " 9 5 4 7 0 . 466 9 5 4 8 0 461 9 5 4 9 0 467 9 5 5 0 0 4 8 6 9 5 5 1 0 519 9 5 5 2 1 563 9 5 5 3 1 611 9 5 5 4 1 ' 6 6 0 9 5 5 5 0 7 06 9 5 5 6 0 755 . 9 5 5 7 1 803 9 5 5 8 1 836 95 590 867 9 5 6 0 1 892 95611 906 9 5 6 2 1 92 3 9 5 6 3 1 934 9 5 6 5 1 943 9 5 6 7 0 948 9 5 6 9 1 9 5 2 ... 9 5 7 1 1 ...9 56 9 5 7 3 1 96 3'"" 9 5 7 5 0 966 " 9 5 7 7 0 9 6 6 9 5 7*9 1 965 9 5 8 1 0 965- 9 5 8 4 0 970 9 5 8 7 1 9 6 7 9 5 9 0 0 971 - — - - - . — i i >I0 9 8 7 4736 81938 143 81949 248 81949 426 81949 625 8 1949 809 81949 900 8 1 9 4 9 933 81889 138 81940 143 81948 248 8 1948 4 3 9 • 81948 626 8 1948 810 81948 899 81948 927 81887 131 81481 944 81501 953 81551 957 81601 948 81650 942 81701 934 . 81750 937 81770 933 81790 935 81810 935 8 1 8 3 0 93 3 818 5 0 928 81861 924 81870 920 81881 911 81890 903 81900 894 81910 884 8 1920 873 .• 81930 858 81940 8~44~ "8 1950" ' "B'Zl" "81960 791 8 1971 7 49"""" " 8 1981 705 81990 655 82000 -604 82010 550 82020 498 82030 443 82040 395 82051 351 82061 316 82071. 287 82080 267 82090 250 82100 242 82110 240 • 82120 241 82131 254 82140 271 .82 151 304 ' 8 2 1 6 0 340 82170 383 82180 ' 4 33""" 82 190 "4 8 4. 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A 5 § 2 0 _ ..886. 65880 "897 6 5 891 90 7 6 5 911 923 65930 927 65950 935 65970 945 65990 954 66010 963 66030 966 66050 967 66070 972 66090 973 66110 975 66130 972 66160 975 4876 98948 153 98948 261. 98948 474 98948 661 98948 938 98948 826 98948 913 98894 141 98938 152 98950 256 98950 477 98950 654 98950 826 98950 904 98950 938 98892 138 98525 972 98561 974 98601 971 98631 967 98661 967 9869.1 968 98720 963 '98750 958 98780 953 98800 958 98820 950 98840 938 98861 934 98880 .924 " 98890 914 98900 903 98910 893 98920 8 77 9.8 9 30 861 98940, 839 9 89 50 816 *" 989 6 0 788 "98970 7 58 9 898 0" 717 98990 674 99000 634 99010 587 . 99020 542 99030 495 99040 454 99050 417 99060 383 99070 358 99079 336 99090 320 99100 307 99110 302 99120 299 •• 9 913 0 301 99140 312 99150 330 ,9916 0 352 99170 384 9 9 18 0, 417._ '"" 9 9190" " "459 ' 992 0 0 "5 0 3 99210 5 4 9 " 99220 600 99230 644 99240 69 0 99251 729 99260 76? 99271 798 99280 819 99 2 90 841 99300 863 99310 879 99320 892 99330 901 99340 911 99350 917 9 9 3.6 0 922 99370 930 99380 9 35 99390 941 . 99401. 948 99420 950 99 440 9 48 . .. ,r_ " 99461" 948 99480 9 49 99501 951 99532 9 5 5~ 99562 958 99590 957 99621 955 •99651 963 6563 HYDROGEN .ALPHA,. LINE RECIPROCAL DISPERSION AT 6563 A = 23 A/MM 215774 192 215774 313 215774 547 215774 7 23 . 215774 826 215774 890 215774 915 215774 186 215774 195 215774 215774.. 552 215774 725 215774 831 215774 888 215774 915 215774 185 • 213095 968 213149 954 213200 961 213299 ' 9 5 0 213399 958 213501 962 213600 960 213800 970 214000 _9_5 3_ . . _ _,„214199^ 913 . . . 2142 50.. 9 85 . 214399 _9.59..... .. .„ _ _ 214599 954 214700 952 214800 94 5 214900 931 214999 940 215110 926 215200 917 215299 922 215399 907 215499 895 2 15599 878 215699 845 215750 823 215800 799. 215850 789 215900 772 215950 760 216000 744 216049 738 216110 734 216149 J 4 3 ,„.. .' 216 2.00 . 750 . . . 216249 .76 4. . . 2.16299„ __,7J35 r _.._..„ 216350 80 3 216400 817 216450 837 216500 * 855" 216550 870 216599 869 216650 876 216700 886 216750 900 216799 905 216 8 5 0 909 216950 9 13 217050 931 217149 926 217249 93 1 217349 936 217451 942 217550 951 . 217650 94 5 217750 947 . 217850 940 217952 949 218049, 94 5 . 218199 926 218399 942 218600 ""94 2" ' ' 21879 9 940 219001 932 •10 9 8 »7 6 5 h 3 BIBLIOGRAPHY Anderson, P. W. ( 19^9 ) , Phys. Rev. 76, 6I4.7. Baranger, M, (1958), Phys. Rev. I l l , 1+914.. Durand, J . (1963), Z'e i t schri f t fflr Naturforschung 18a, 2 8 l . Ecker , G . (1957), 2. fUr Physik 11+J3, 593. Griem, H . R . , Ko lb , A . C , and Shen, K. Y . (1959), Phys. Rev. 116, 1+. See also Naval Research Lab. Report No. 3I+F5, I960. Griem, H . R. (1961+), Plasma Spectroscopy, McGraw-Hi l l . Griem, H . R. (1966), Phys. Rev. L e t t . 17, 509. Holtsmark, J , (1919), Phys. Z e i t . 20, 162. Hermann, H . (1935), Z . Physik 97, 539. J a l u f k a , N . W., O e r t e l , G. K . , and O f e l t , G. S. (1966), Phys. Rev. L e t t . 16, 1073. Kolb , A . C , and Griem, H . R. (1958), Phys. Rev. I l l , 5X1+.. Landau, L . D , , and L i f s h i t z , E . M. (1965), Quantum Mechanics, A d d i s o n - ¥ e s l e y . Lewis, M. ( 1 961 ) , Phys. Rev. 121, 501. Michelson, . A . A . (1895), Astrophys. J . 2, 251. Millman, J . , and Taub, H . (1956), Pulse and D i g i t a l C i r c u i t s , McGraw-Hi l l . Moore, G . E . (1959), A M u l t i p l e t Table of As trophys ica l In ter -est , Nat ional Bureau of Standards, Technica l Note 36. Popenoe, C. H . and Shumaker, J . B . , J r . (1965), J . Res. N a t l . Bur. S t d . 69A, 1+95. S.adjian, H . , Wimmel, H . K . , and Margenau, H . (1962), J . Quant* Spectrosc . Radia t . Transfer 1., 1+6. Sawyer, R. A . (1963), Experimental Spectroscopy, Dover. S p i t z e r , L . , J r . (1956), Physics of F u l l y Ionized Gases, I n -terscience 3* 96 97 Theophanis, G. A . (I960), Rev. S c i . Ins t . 31, 1+27. Van de H u l s t , H . C. and Reesinck, J . J . M. (191+7), A s t r o -phys. J . 106, 121. V o i g t , W. (1912), Munch. Ber . 603. 

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