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Measurement of spectral line profiles in dense plasmas James, Harry Gordon 1968

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MEASUREMENT OF SPECTRAL LINE PROFILES IN DENSE PLASMAS by HARRY GORDON JAMES B.Sc, Queen's University, 1963 M.Sc, University of B r i t i s h Columbia, 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the department of PHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1968 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o lumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n -t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department nf The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT The spectra emitted by a pulsed-arc discharge have been photographed with a medium resolution spectrograph to obtain Stark broadened l i n e images measurable for both width and s h i f t . Plasmas with densities near lO-^cm -^ a n c j temperatures of about 2.6 ev were produced by subjecting Argon - Nitrogen mixtures to a square current pulse. Light from the discharge was shuttered by a rota t i n g mirror system so that the plasma was photographed in an i n t e r v a l during the current pulse when the plasma had optimal conditions for measurement. A technique in which the spectral l i n e s from a standard source are photographed on the same plates as the plasma lines has been devised for c a l i b r a t i n g the measurement routine and for f a c i l i t a t i n g s h i f t measurements. Stark parameters were obtained by scanning the plates on a precision comparator. Nineteen A r i l l i n e s and six N i l l i n e s were studied. For Argon, the agreement with other experimental results i s s a t i s f a c t o r y but the theory i s inadequate. S i m i l a r l y , the N i l theory does not predict the values measured here. On the other hand, some of the q u a l i t a t i v e predictions by the Impact theory about the l i n e shape and about the common widths and s h i f t s of l i n e s i n the same multiplet have been confirmed. The experiment on the N i l l i n e s also reveals advantages of the present technique over other methods for obtaining Stark parameters. i i i TABLE OF CONTENTS Abstract Table of Contents L i s t of Tables L i s t of Figures Acknowledgement CHAPTER 1 - INTRODUCTION CHAPTER 2 - THEORY OF LINE BROADENING 6 A) Stark Broadening by Ions and Electrons 7 BJ Other Broadening and. S h i f t i n g E f f e c t s 15 CHAPTER 3 - THEORY OF THE MEASURING PROCESS 20 CHAPTER 4 - APPARATUS AND TECHNIQUE 25 A) Spectral Line Sources and Spectroscopic Equipment 25 i ) Energy Bank and Discharge Tube 25 i i ) The Standard Source 29 i i i ) The Spectrograph 33 iv) The Monochromator 35 v) The Light Shutter System 36 vi) C a l i b r a t i o n of the Step F i l t e r 43 Densities B) Plate Exposure Technique 45 i) Line I d e n t i f i c a t i o n and C a l i b r a t i o n 45 Page i i i i i v v i v i i 1 iv i i ) E s t a b l i s h i n g the Shutter Timing 46 i i i ) Exposing the Plate 47 iv) Plate Developement 51 C) Measurement of Plates on the Comparator 52 i ) The Comparator 52 i i ) Comparator Adjustment and Measuring 53 Technique D) Computation and Analysis 57 CHAPTER 5 - THE EXPERIMENT 60 A) The A r i l Lines 60 i ) The Conditions of Measurement 60 i i ) The Results 68 B) The N i l Lines 74 i ) The Conditions of Measurement 74 i i ) The Results 76 CHAPTER 6 - DISCUSSION 81 A) Estimate of Errors 81 i ) Systematic Errors 81 i i ) Random Errors 83 B) The' A r i l Measurements 85 C) The N i l Measurements 92 D) Conclusion 94 BIBLIOGRAPHY 97 LIST OF TABLES T i t l e Measured A r i l widths and s h i f t s , compared with current t h e o r e t i c a l and experimental data Measured N i l Stark parameters, compared with current t h e o r e t i c a l and experimental data. v i LIST OF FIGURES No. T i t l e Page 1 Layout of basic apparatus 26 2 Plasma discharge c i r c u i t 28 3 Plasma vessel 30 4 Electrodeless standard source 31 5 System for gathering and shuttering 37 plasma l i g h t 6 Logic c i r c u i t for shutter 41 7 Apparatus for step f i l t e r c a l i b r a t i o n 44 8 Portion of a plate with a l l necessary 48 images of one l i n e 9 T y p i c a l H-D curve 50 10 Reciprocal dispersion of spectrograph 62 11 Halfwidth of the apparatus p r o f i l e 63 12 H i s t o r i e s of pulsed arc current and a 65 l i n e i n t e n s i t y 13 Two parts of an A r i l plate 69 v i i ACKNOWLEDGEMENT The author wishes to sincerely thank Dr. A. J. Barnard for h i s i n s p i r a t i o n and supervision of the project. In the course of the work, the author has benefitted from discussions with many of the s t a f f and graduate school at U. B. C., and must express his indebtedness to the whole group. In p a r t i c u l a r , the help supplied by Mr. Hugh Campbell, whose f a m i l i a r i t y with the apparatus was e s s e n t i a l , and by Dr. Roy Nodwell, who c r i t i c i z e d the manuscript, i s hereby g r a t e f u l l y recognized. Thanks are due for the Atomic Energy Control Board of Canada and the National Research Council of Canada for f i n a n c i a l support of the laboratory i n which the experiment was conducted. F i n a l l y , the author expresses his thanks to his wife, E l s i e James, for her t o t a l and patient support of the Ph.D. project. -1-CHAPTER 1 - INTRODUCTION The theory of l i n e broadening has been developing quite s t e a d i l y over the l a s t 75 years. During t h i s period, r e a l ad-vances i n the comprehensiveness and the a p p l i c a b i l i t y of the theory have been made by such i l l u s t r i o u s workers as Lorentz, Michelson and Weisskopf. The study of spectral l i n e shapes has always been i n t e r e s t i n g because i t has been a useful area i n which new concepts of the character of the atom could be both t h e o r e t i c a l l y employed and then experimentally tested. The progress of the theory was d i r e c t l y dependent on the advent of the electro-magnetic theory, the quantum mechanical f o r -malism and, more recently, the ideas of plasma k i n e t i c s . Because l i n e broadening theory involves so much basic physics, i t provides a convenient basis for checking our con-cepts of the atom. But the inte r e s t in l i n e broadening i s not confined to the pure physics realm: once the physics i s under-stood, experimentalists may apply the theory to the f i e l d of plasma diagnostics. In fact considerable attention i s being given to the use of l i n e broadening as a plasma diagnostic since, as Margenau and Lewis(1959) say, the use of spectro-scopic equipment to analyse l i g h t emitted from a plasma seems to be the closest one can get to the i d e a l of the detached probe. Some plasmas are perturbed s i g n i f i c a n t l y by any kind of probe that i n t e r f e r e s with them phys i c a l l y , while others -2-l i k e c e l e s t i a l nebulae can only be understood through the ra d i a t i o n they emit. So, dependable l i n e broadening concepts are a d e f i n i t e boon to the observer who wishes to make re-l i a b l e measurements. Atoms i n a plasma so tenuous that they experience no i n -te r a c t i o n with th e i r neighbours emit unbroadened spectral l i n e s of a few milliAngstroms i n width. On the other hand, spectroscopic studies of a dense plasma depend on the fact that when some atoms are part of such a plasma - which d e f i n i t e l y i s a system of int e r a c t i n g p a r t i c l e s - the i r spec-trum becomes changed. Types of "changes" which may occur i n spectral l i n e structure are a l t e r a t i o n s i n the width of the l i n e , i n the wavelength position, i n the in t e n s i t y and i n the l i n e shape. These changes are dependent upon the state of the plasma, and may be used to determine densities and tempera-tures of the d i f f e r e n t constituent species. This thesis deals v/ith the broadening of atomic l i n e s of the A r i l and N i l spectra i n dense (electron densities near 10-^ cm~3) plasmas whose temperatures are a few electron-volts. The l i n e broadening process has been variously described as "pressure" broadening because the breadth of a l i n e shov/s a strong dependence on the density of the plasma, as "Stark" broadening because i t i s the e l e c t r i c f i e l d s of the perturbers that a f f e c t the atomic l e v e l s of the emitter, and as " c o l l i s -ional" broadening because ele c t r o n i c c o l l i s i o n s are the domin-ant broadening mechanism. A l l these names are v a l i d descrip--3-tions of some aspect of the problem. The theory of Griem, Baranger, Kolb and Oertel(1962) has been used by Griem(1964) to calculate widths and s h i f t s of A r i l l i n e s i n dense plasmas. Since these publications, the cal c u l a t i o n s have been refined by several workers - to be mentioned i n due course - but the o v e r a l l formalism remains unchanged. This theory i s e s p e c i a l l y useful i n regards to i t s a p p l i c a b i l i t y to nonequilibrium plasmas', i f the p a r t i c u l a r approach of Griem et a l . i s v a l i d , the shift-to-width r a t i o of a spectral l i n e can be used to determine the electron temp-ature( see eg. Burgess and Cooper,1965b). Although s h i f t and width both have l i n e a r dependences on perturber density, they have d i s s i m i l a r dependences on temperatureJ thus, s h i f t - t o -width should only depend on temperature. And so the great a t t r a c t i o n to s h i f t and width measurement i n the diagnosis of plasmas l i k e those studied here i s that L.T.E.(see eg. Cooper, 1966) i n the emitting species i s not required. Only the electrons need to have reached thermal equilibrium. The theory does not achieve great success i n i t s quanti-t a t i v e predictions of s h i f t and width of A r i l l i n e s . The widths even from the recent cal c u l a t i o n s (Cooper and Oertel, 1967) agree to no better than 20% with experiment i n a s i g n i f i c a n t number of the cases treated. For s h i f t s , there i s very l i t t l e experimental evidence with which the l a t e s t theory (Griem, 1964) can be compared. The present experimental work has been undertaken to f i n d some values of A r i l widths and s h i f t s , with -4-the hope that t h i s w i l l inspire attempts to improve the theory where d e f i c i e n t . The need for e s p e c i a l l y measuring the s h i f t s of l i n e s i n i o n i c spectra i s c l e a r l y revealed i n the existence of the "Plasma P o l a r i s a t i o n S h i f t " idea (see eg. Cooper, 1966). This i s an attempt at explaining blue s h i f t s of ion l i n e s ( eg. A r i l l i n e s ) that the above theory i s not able to predict. The c o l l i s i o n a l theory regards c o l l i s i o n s as d i s t i n c t events but does discuss the e f f e c t s of correlations among perturbing electrons. But t h i s afterthought c a l c u l a t i o n of plasma polar-i s a t i o n s h i f t assumes that the electrons produce a s t a t i c Debye potential around the emitter ion. This Debye theory y i e l d s s h i f t s of the same order of magnitude as the c o l l i s i o n a l theory, and i t i s not clear how, or i f , the tv/o e f f e c t s are to be added. Thus experimental evidence should be valuable when one has to decide between theories. The plasma source used i n t h i s experiment was a pulsed arc discharge, s i m i l a r to that described by Durand(1963). It was employed by Neufeld(1966) in the measurement of the pro-f i l e s of A r i l l i n e s . The present work extends and refines these measurements. F i r s t , observations were made at several a x i a l positions i n the discharge to show that the arc was uni-form so that s p a t i a l unfolding was not required. Secondly, a standard electrodeless l i g h t source was set up i n order to measure l i n e s h i f t s . T h i r d l y , measurements v/ere made in a Argon and Nitrogen mixture thereby keeping the Argon d i l u t e -5-enough to make s e l f absorption n e g l i g i b l e . F i n a l l y , some N i l l i n e s were also measured and compared with the r e s u l t s of Day(1965). Chapter 2 of t h i s thesis discusses q u a l i t a t i v e l y the various factors that cause spectral l i n e s emitted by a plasma to be d i f f e r e n t from those emitted by i s o l a t e d atoms. Such phenomena can be due either to perturbations of the energy l e v e l s of the i n d i v i d u a l emitters or to other e f f e c t s (eg. Doppler). F i r s t , a synopsis of the theory that predicts the Stark broadening of A r i l and N i l l i n e s i s given. Then comes a discussion of the other e f f e c t s which, i n p r i n c i p l e , can broaden a l i n e but which are shown to be unimportant i n our case. Chapter 3 describes the methods by which the observed l i n e p r o f i l e may be corrected, for the instrumental broadening to obtain the true p r o f i l e emitted by the plasma. In the next chapter, number 4, comes a description of the equipment and the experimental technique. The r e s u l t s for A r i l and N i l l i n e s are presented i n chapter 5. F i n a l l y , i n chapter 6, we summar-ize the work by c r i t i c i z i n g the technique and by discussing some in t e r e s t i n g physics that i s revealed by the measurements. CHAPTER 2 - THEORY OF LINE BROADENING Since the days of i t s infancy, the theory of l i n e broad-ening has t r a v e l l e d a great distance and? i n the course, has achieved d e f i n i t e progress. It has gone from the ideas of c l a s s i c a l o s c i l l a t o r s to those of quantum mechanical systems, from time averages to c o r r e l a t i o n functions, from "interupt-ion"to "impact" broadening, and so on. In i t s advance, i t has acquired a l i s t of recipes for d i f f e r e n t s i t u a t i o n s . Some of these recipes were e a s i l y obtained; other more recent ones required good insight into the quantum mechanical atom and therefore have taken some time to formulate. This thesis i s concerned with checking such a recent theory: that of pressure broadening of ion l i n e s i n cool, dense plasmas. Reviews of developements in t h i s f i e l d (Margenau and Lewis, 1959; Traving, 1960; Breene, 1961) are available. The state of the theory e s p e c i a l l y i n reference to plasma r a d i a t -ion i s well set out elsewhere (Baranger, 1958; Griem, 1964; Cooper, 1966). In the present chapter a q u a l i t a t i v e review i s given of the theory of l i n e broadening i n a cool, dense plasma as i t i s applied to the A r i l and N i l spectra. Our interest i s i n a plasma composed p r i n c i p a l l y of ions and electrons and we focus our attention on the e l e c t r o s t a t i c perturbation of an emitting ion by electrons and other ions i n i t s neighbourhood. For perspective, the account of Stark broadening w i l l be -7-followed by a review of other mechanisms that can perturb atomic energy l e v e l s . It w i l l be shown that these mechanisms, along with the Doppler e f f e c t and s e l f absorption, can be ignored in t h i s experiment. A) Stark Broadening by Ions and Electrons We begin with the work of Griem et al.(1962) i n which they attack the problem of broadening i n the Hel spectrum. This work makes a s i g n i f i c a n t step beyond the e a r l i e r theory of Hydrogenic emitters. Inasmuch as the A r i l and N i l spectra have well separated fine structure l i k e that of Hel, the work of Griem and others provides a good base from which to dev-elope the A r i l and N i l theories. The following paragraphs attempt to state the important ideas that characterize the theory of i s o l a t e d line.broadening. The basic i n t e r a c t i o n between the emitting ion and the perturbing ions and electrons i s the Stark i n t e r a c t i o n V = d^ .E^  , where d[ i s the dipole moment of the emitter and E_ the e l e c t r i c f i e l d of the perturber. In the l i m i t i n g case where we consider only ionic perturbers, i t i s permissible to en-visage a nearly s t a t i c f i e l d because ion-ion c o l l i s i o n times are much longer tham a l l other times of i n t e r e s t . At the other extreme, for el e c t r o n i c perturbations one thinks of the emitter experiencing many c o l l i s i o n s while completing an emission, and one adopts the "Impact" approximation. In - 8 -general, both e f f e c t s occur i n the spectra studied here. The present discussion delays the problem of combining the two e f f e c t s u n t i l the end. Considering a cert a i n t r a n s i t i o n , i t can be shown (see eg. Griem, 1964) that the spectrum ( v i z . the l i n e p r o f i l e ) has for i t s Fourier Transform the autocorrelation function of the l i g h t amplitude. If one writes the formula for the power spec-trum of the emitter-plus-perturber system and then takes the Fourier Transform, the problem becomes one of finding the matrix elements of the dipole operator between unperturbed states, and the time-evolution operators of the system. The character of the former i s well known from the stationary theory of atomic theory (eg. Condon and Shortley, 1935) ; c a l c u l a t i n g them i s a f a i r l y standard procedure and we take them as known. It i s the framing and manipulation of the l a t t e r that constitute the major d i f f i c u l t y i n the l i n e broad-ening c a l c u l a t i o n . In order to obtain solutions, i t i s neces-sary to make cer t a i n approximations. Foremost are the " C l a s s i c a l Path Approximation" which allows writing the sep-arated Schrodinger equation for the emitter ion, the "Impact Approximation" which says that c o l l i s i o n s are fast and d i s t i n c t , ( for use with ele c t r o n i c c o l l i s i o n s ) and the "Quasi-Static Approximation" which says that c o l l i s i o n s are slow (for use i n i o n i c c o l l i s i o n s ) . In the C l a s s i c a l Path Approximation the time-evolution operator i s calculated by assuming that the perturbers act - 9 -as c l a s s i c a l p a r t i c l e s following hyperbolic t r a j e c t o r i e s . The time-dependent Schrodinger equation of the emitter-perturber system i s assumed to have solutions of the form \Ct) !P("t) , where *\ ("t) involves only the emitter coordinates and '^ ("t) involves only the perturber coordinates. Thus, the Hamiltonian of the perturber contains only i t s k i n e t i c energy and the Coulombic a t t r a c t i o n to the stationary emitting ion. It i s found that *\("t) s a t i s f i e s a Schrodinger equation whose Hamiltonian i s that of the unperturbed ion plus the average, J f *(t) V fit) E x p e r t , of the int e r a c t i o n potential V over the perturber wavefunctions . At thi s point the c a l c u l a t i o n of the autocorrelation function already requires two d i f f e r e n t sums or averages. F i r s t , there i s a summing of dipole and time-evolution operators matrix elements between states of the emitter. Second, the sum over the states of the perturber becomes a s t a t i s t i c a l average over the perturber's impact parameters and v e l o c i t i e s . The range of v a l i d i t y of the C l a s s i c a l Path Approximation for c o l l i d i n g p a r t i c l e s may be determined by examining the conditions necessary for creating the i l l u s i o n of a c l a s s i c a l p a r t i c l e passing the emitter. The de Broglie wavelength of the c o l l i d i n g electron or ion must be much smaller than the im-portant impact parameters. We have already mentioned that the perturbation i s caused by the d_.E int e r a c t i o n which i s a long range force; thus since the distant c o l l i s i o n s are the major contributors to the perturbation, most c o l l i s i o n s can be -10-described using the C l a s s i c a l Path Approximation. Another re-quirement for t h i s approximation i s that the c o l l i d i n g ion or electron must r e l i n q u i s h n e g l i g i b l e energy during a c o l l i s i o n . That i s , we require that c o l l i d e r ' s energy be much greater than the energy spread corresponding to the separation of the upper l e v e l from the nearest i n t e r a c t i n g l e v e l . It i s now expedient to recognize the two mathematical l i m i t s that correspond to ion: and electron broadening. In a l l cases, the autocorrelation of the emitter goes to zero for large times: the narrower the l i n e , the longer the time required by the autocorrelation to go to zero. If the inverse l i n e width (width i n frequency units) i s small compared with the time to complete a c o l l i s i o n , as with the low v e l o c i t y ions, we may make the "Quasi-Static" assumption that during an emission a l l i o n i c perturbers are at fixed postions. We obtain f i r s t a Stark pattern of l i n e s with natural widths and then perform an average over a l l possible perturber configur-ations. This averaging i s done afte r separately c a l c u l a t i n g the d i s t r i b u t i o n of the ion e l e c t r i c field, i n some plasma ki n -e t i c model. The fine structure of the A r + and N + emitters i s well spaced so that one expects the above i o n i c f i e l d to s p l i t f i n e l y the components of a multiplet i n the usual quadratic Stark fashion (see eg. Condon and Shortley, 1935). Our ion-broadened l i n e has an asymmetric p r o f i l e whose Stark para-meters cannot be a n a l y t i c a l l y predicted i n general but whose width and s h i f t are heavily dependent on perturber density. -11-I f , as for ele c t r o n i c c o l l i s i o n s , i t takes the auto-c o r r e l a t i o n function many c o l l i s i o n times to d i f f e r appreciably from i t s unperturbed value, then the "Impact Approximation" can be made. When the suitable approximations are made i n find i n g the time-evolution operators involved, the r e s u l t i n g l i n e i s s h i f t e d and given a Lorentzian shape. Since i t takes many s t a t i s t i c a l l y independent c o l l i s i o n s to disturb the emitter s i g n i f i c a n t l y , i t i s only the average e f f e c t of c o l l i s i o n s that matters. One thinks of the l i g h t as being emitted by an i s o l a t e d ion whose Hamiltonian contains H e , where H e i s a time- average contribution given by the net re s u l t s of electron c o l l i s i o n s during an emission. The requirements of the "Impact Approximation" are imposed i n solving an Interaction Picture equation for the time-evolution operators. For the equation to be solvable, there has to be a time i n t e r v a l A S such that the d i s t r i b u t i o n of electrons around the radiator i s s t a t i s t i c a l l y independent of the d i s t r i b u t i o n at a time A S e a r l i e r . In other words, th i s time must be much greater than the electron c o r r e l a t i o n time (Jp--*- i where cjp i s the plasma frequency. On the other hand, the mean int e r a c t i o n between emitter and perturber during this i n t e r v a l of time ' As must be small. Ph y s i c a l l y , As must be shorter than the time between strong c o l l i s i o n s which i s of the order of the inverse l i n e width. These Impact requirements can be stated a l t e r n a t i v e l y as: the l i n e width in frequency units must be much smaller than the -12-plasma frequency and the approximation w i l l be v a l i d for those parts of the l i n e p r o f i l e whose frequency separations from the l i n e centre are small compared with the inverse c o l l i s i o n rate. When the Interaction Picture equation has been solved, the autocorrelation requires knowing only matrix elements of the zero-order Hamiltonian and of the perturbation operator (which i s now time-independent) between unperturbed states of the emitter. In f i n d i n g the perturbation operator, one averages over perturber v e l o c i t i e s and impact parameters. The range of integration of the impact parameter between "c u t - o f f s " i s a matter of importance (Cooper, 1966). The lower l i m i t i s set by the fact the only c o l l i s i o n s to be treated by t h i s theory are the weak onesJ c o l l i s i o n s ocurring inside t h i s minimum impact parameter are estimated separately with a strong c o l l i s i o n theory (Griem, 1964). The upper l i m i t i s usually about one Debye length. Further s i m p l i f i c a t i o n may be possible for the N and A r + emitters i n the cases where there i s n e g l i g i b l e perturb-ation expected in the lower levels of the l i n e s (Baranger, 1962). One then considers the time evolution of only the upper states involved in the t r a n s i t i o n of i n t e r e s t . It sometimes happens that i n t e r a c t i n g i o n i c l e v e l s are quite close together for high p r i n c i p a l quantum number. In such a case, i n e l a s t i c c o l l i s i o n s can occur e a s i l y and i t turns out (Griem,et a l . , 1962) that one should consider poss-i b l e c o r relations among perturbing : electrons. Griem and others -13-(1962) show that the c r i t e r i o n for deciding on the importance of c o r r e l a t i o n s i s whether the s p l i t t i n g between in t e r a c t i n g l e v e l s i s of the order of the plasma frequency. When i t i s , one has to go to a Hydrogenic theory i n which the emitter le v e l s with t h i s s p l i t t i n g are degenerate i n o r b i t a l quantum number . However the theory that w i l l be checked i n thi s work assumes that the A r + and N + upper l e v e l s are indeed i s o l a t e d , i e . , the s p l i t t i n g between opposite parity l e v e l s i s much greater than the spread corresponding to the plasma frequency, and so we get " i s o l a t e d " l i n e s . The C l a s s i c a l Path assumption makes certa i n requirements in the treatment of the atomic system. Since electrons involved in de-exciting c o l l i s i o n s (from the upper l e v e l to the lower level) gain energies equivalent to the plasma temperature, the C l a s s i c a l Path assumption requires that the weak, broadening, i n e l a s t i c c o l l i s i o n s be much more frequent than the de-exciting c o l l i s i o n s . This i s with the additional proviso that the separation between strongly i n t e r a c t i n g l e v e l s be much less than the average electron energy. Thus, the present treatment i s v a l i d only when the e l e c t r o s t a t i c s p l i t t i n g l i e s between certa i n upper and lower l i m i t s . As already mentioned, i t i s found that when an isola t e d upper l e v e l i s Impact broadened, a Lorentzian l i n e shape re-s u l t s : the width of the l i n e p r o f i l e i s given by the imaginary part of the matrix element of the time-averaged perturbation Hamiltonian in the state corresponding to the upper l e v e l , and -14-the s h i f t of the l i n e peak with respect to the position of the unperturbed l i n e i s given by the r e a l part of the same matrix element. It i s obviously important to have the correct quantum mechanical description of the unperturbed emitter states. Use of an incorrect coupling scheme, for instance, w i l l lead to wrong widths and s h i f t s i f a l l i n t e r a c t i n g states are not considered c a r e f u l l y . Here, the LS coupling scheme i s employed. The various j - l e v e l s of a given term w i l l be perturbed ident-i c a l l y and thus a l l the li n e s i n a corresponding multiplet w i l l have the same width and s h i f t . Use of LS wavefunctions i n t h i s c a l c u l a t i o n w i l l r e s t r i c t the application of the theory to the lower numbered multiplets of A r i l and N i l . Both A r + (Minnhagen, 1963) and N + (Eriksson, 1958; Day, 1965) have higher l e v e l s described under other coupling schemes. The e l e c t r o n i c and ioni c perturber e f f e c t s are "folded" together using the following recipe: f i n d the Stark s p l i t t i n g due to the ion f i e l d for the natural l i n e , calculate the ele c t r o n i c broadening of the above Stark components, convolute the electron-broadened spectrum with the prob a b i l i t y d i s t r i b -ution of the ioni c f i e l d . In a wide range of Argon or Nitrogen plasma conditions, including Ours, the electron impacts are the dominant broaden-ing mechanism whereas ions produce ^ 10% of the broadening (Griem, 1964). The asymmetry in l i n e p r o f i l e s expected from the ionic broadening w i l l be d i f f i c u l t to observe. -15-Griem(1964) gives tables of the half halfwidth w, the shift-to-width r a t i o d/w, and the "Quasi-Static Ion Broadening Parameter"a (a measure of the amount of ion broadening to be expected) for the lower numbered multiplets i n the A r i l and N i l spectra (multiplet numbering i n the notation of Moore, 1959). These are given as functions of temperature and at an electron density of 1 0 ^ cnf^, with the understanding that at a given temperature a oc ( n e ) 4 , wccn e, and dccn e , where n e i s the electron number density. Subsequent experimental work on A r i l widths has indicated appreciable discrepancies between th e o r e t i c a l and measured values. Later calculations have been undertaken (Griem, 1966; Roberts, 1966; Cooper and Oertel,1967} but the r e s u l t s are not as extensive as Griem 1s(1964) i n that widths only are given, and these for a few temperatures. Throughout t h i s thesis we refer to the whole halfwidth,that i s , the f u l l width at half maximum, as h, and the half halfwidth as w. Thus w = .5h . B) Other Broadening and S h i f t i n g E f f e c t s In order to complete th i s discussion on l i n e broadening, we mention other e f f e c t s and discuss why they are i n s i g n i f i c a n t i n the plasmas studied i n t h i s work. i ) Resonance Broadening (Griem, 1964) ':' Two l i k e atomic systems, one i n an excited state and the other in the ground state, can -16-be coupled together through the inte r a c t i o n of the i r dipbles and t h i s leads to the exchange of energy between the two. This constitutes broadening due to the rad i a t i n g system being damp-ed by the partner i n the in t e r a c t i o n . In the case of N + and A r + ions, t h e i r Coulombic i n t e r a c t i o n i s much stronger than the dipole-dipole i n t e r a c t i o n . i i ) van der Waals Broadening(Griem, 1964): This occurs when two d i s s i m i l a r emitting systems engage i n dipole-dipole i n t e r -action. Again, the Coulombic force keeps the A r + or N + ions far enough apart that this e f f e c t i s n e g l i g i b l e . Day(1965) shows how to mathematically estimate the order of magnitude of van der Waals broadening for plasmas l i k e the ones studied here. i i i ) Natural Broadening(Heitler, 1954): This i s the lower l i m i t on the breadth of a spectral l i n e , for even i f a l l external influences are removed from an emitting ion, i t s own r a d i a t -ion f i e l d w i l l react with i t . The theory predicts a damping out of the emitting system with a damping constant proportional to the sum of the spontaneous t r a n s i t i o n p r o b a b i l i t i e s of a l l the l i n e s o r i g i n a t i n g at either the upper or lower states of the t r a n s i t i o n in question. For the spectroscopic equipment used i n the present experiment, the natural width of a l l l i n e s i s extremely small and completely n e g l i g i b l e iv) Doppler Broadening and Shifting(Griem, 1964): The Doppler -17-e f f e c t i n spectral l i n e s arises because of the s h i f t i n the frequency of the l i g h t owing to the motion of the emitter with respect to the observer. With the ion i c emitters moving at random v e l o c i t i e s , the observed l i n e has a shape determined by the v e l o c i t y d i s t r i b u t i o n of the emitters. The amount of Doppler broadening i s proportional to the square root of the plasma temperature. In our plasma source, the temperature i s s u f f i c i e n t l y low that the ef f e c t i s n e g l i g i b l e ; neither i s there s u f f i c i e n t gross plasma motion to produce s i g n i f i c a n t Doppler shift(Neufeld, 1966). v) Self Absorption(Cooper, 1966): A photon emitted from the centre of a f i n i t e plasma either can be absorbed before es-caping or i t can escape. If the p r o b a b i l i t y of escape i s high, the plasma i s said to be " o p t i c a l l y t h i n " , and conversely i f the p r o b a b i l i t y i s low, i t i s said to be'bptically thick". When a plasma i s o p t i c a l l y thick, photons emitted with a f r e -quency near that of the l i n e centre can become imprisoned whereas those i n the t a i l s can escape. This leads to a f l a t t e n -ing of the l i n e p r o f i l e . Thus, when a " f u l l width - half maximum" c r i t e r i o n i s used to gauge l i n e width, the l i n e gets a greater width than i t would in the o p t i c a l l y thin plasma. It can be shown that the o p t i c a l depths of the l i n e centres i n the plasma studied here may be large(Burgess and Cooper, 1965a). Thus care w i l l have to be taken to arrange conditions so that even for the strongest l i n e s s e l f absorption i s not important. -18-The e f f e c t of s e l f absorption on l i n e p r o f i l e s i s as follows: i n an absorbing, homogeneous, L.T.E. plasma whose dimension along the l i n e of sight i s JU , the r a t i o of the intensity, l(oj), of a l i n e whose absorption c o e f f i c i e n t i s K(k>) to that emitted i n the o p t i c a l l y thin case,£(oj)l , i s 1 - exp f-k(co)i ) 1 - exp (-Tj(u))) (2.1) Here the o p t i c a l depth X ( ^ ) may be found by assuming that emission and absorption are as i n a black body cavity. Then(Griem, 1964) l ( c o ) = 2 T T 2 r o c f m n m ( 2 . 2 ) where L (^ - ) ) i s the normalized l i n e shape i n inverse frequency units and a l l the other symbols have their usual s i g n i f i c a n c e . From equation ( 2.1), i t i s seen that the true unabsorbed l i n e shape i n £ (co) i s changed by a correction factor (the extreme r i g h t side) that i s a function of frequency. To est-imate the e f f e c t of absorption on halfwidths, one may assume for Impact broadening the emission and absorption l i n e s have Lorentzian shapes with the same halfwidth. One then finds from W of an absorbed l i n e to i t s true halfwidth i s equation (2.1) that the r a t i o of the observed halfwidth w ^ { 1 + ex2p (-To) } - 1 (2.3) T i s the o p t i c a l depth at l i n e centre. The r a t i o i s an increasing function of T„ : W 0 J 1 -19-i t r i s e s to 1.10 at X 0 = 0--40 . Thus, i f s e l f absorption i s c tolerable only when —— ^ 110% , one must be sure to have the Vv o p t i c a l depth less than 0.40 for the centre of every l i n e mea-sured. Ideally, i n the event of absorption, one might correct halfwidths using formula (2.3). In the present experiment, however, uncertainties i n the o s c i l l a t o r strengths f ~ m h , i n the population densities of the lower states f l ^ , and i n the l i n e shapes would tend to produce large systematic errors i n the measured halfwidths. The best approach i s to make n m as low as possible while maintaining the electron density, and therefore the true halfwidth, constant. -20-CHAPTER 3 - THEORY OF THE MEASURING PROCESS The preceding chapter was a description of the i n t r i n s i c character of the spectral l i n e s emitted by a plasma. No mention was made of what e f f e c t the measuring technique can have on a l i n e p r o f i l e i n a l t e r i n g i t from i t s true shape into some observed shape. The present chapter w i l l give the general rules for removing (more te c h n i c a l l y : deconvolving ) the instrumental e f f e c t s from the observed l i n e p r o f i l e to get the true p r o f i l e . If a spectral l i n e emitted by a plasma has an in t e n s i t y p r o f i l e Srr(^) , and i f t h i s l i g h t goes through a measuring process whose normalised response function i s SA(w) a n d becomes S (°^) , then we can say in a l l generality that /CD S A ( u . - 6 J ) S E ( « ) ( 3 - 1 J where f " SA(*)dx = 1 •CO S i s c a l l e d the convolution of 3 A a n d S E (see eg. Wiese, 1965]. This convolution i s v a l i d when the functions being "folded" are s t a t i s t i c a l l y independent. There i s no reason to expect any of the functions of intere s t here to vi o l a t e t h i s . In many experimental si t u a t i o n s , the problem of decon-volving SA from S i s not e a s i l y solved. However, l e t us mention two cases i n which the unfolding can be done. F i r s t suppose that we had an apparatus with i n f i n i t e resolving power -21-and an. i n f i n i t e range of output linear with respect to .the input s i g n a l . Then we could close the chapter forthwith be-cause the observed l i n e shape would exactly duplicate the true shape. In reference to equation (3.1), t h i s would mean re-placing S A °y a delta function and i d e n t i f y i n g S and. S £ • Such cannot be done i n thi s experiment, however. Signals put through our spectroscopic equipment c l e a r l y suffer d i s t o r t i o n . Our basis for saying that S A i s not a delta function i s that, when a very sharp spectral l i n e i s sent through our apparatus, i t i s broadened. Herein we come to the second of the two casesj mathematically, /CO S A(C0 0 -Oj) £(co) doo . (3.2) P h y s i c a l l y t h i s equation implies that i f we send monochrom-a t i c l i g h t , whose spectrum i s represented by S(co), through the system we obtain the instrumental function 3^ • This determination of 5^ i s "the f i r s t step i n our actual proced-ure. The second step i s the placing of the now known S A i n equation (3.1) and then the unfolding of S A from the known 3 , where 3 i s i n e observed l i n e p r o f i l e when plasma l i g h t goes through the system. SA i t s e l f can be the convolution of two or more ef f e c t s . In our case these include the broadening by the spectrograph i t s e l f , by the optics of the projection sys-tem i n the comparator that scanned the plates, and by non--22-l i n e a r i t i e s i n the microdensitometer electronics associated with the comparator. The expected combined broadening would be d i f f i c u l t to calculate with s u f f i c i e n t precision (see Unsold, 1938). A much better approach, alluded to e a r l i e r , i s to send a very sharp spectral l i n e through the whole sys-tem and empirically determine S A . The l a t t e r technique i s used i n the present work. The unfolding process i s greatly s i m p l i f i e d i f 3 a n d S A are recognizable as ce r t a i n a n a l y t i c a l functions called. Voigt p r o f i l e s . Equation (3.1) i s the d e f i n i t i o n of the Voigt p r o f i l e when 5 A i s a Gaussian p r o f i l e and S £ i s a Lorentzian, or vice versa. Further, as shown i n van de Hulst and Reesinck(1947) , S i s a Voigt p r o f i l e when 5 A and Sr; are also Voigt p r o f i l e s . The advantage of using Voigt analysis i s that a n a l y t i c a l solutions of the deconvolution integrals can be obtained: tables of the entire range of possible Voigt p r o f i l e s exist(van de Hulst and Reesinck, 1947). In the gen-e r a l case, when either 5 or 5 A a r e n o ^ Voigt p r o f i l e s , one must return to equation (3.1) either to devise a new analyt-i c a l deconvolution or an approximate numerical solution. According to the theory outlined in Chapter 2, one ex-pects the plasma l i n e p r o f i l e 5 E t o D e mainly Lorentzian, electrons being the dominant broadeners. But for the i n s t r u -mental function SA > a s already shown, a l l one does i s determine S/^  a s detailed i n paragraph 4 of thi s chapter, hopefully to f i n d that i t has a Voigt shape to a good -23-approximation. To demonstrate the basic properties of the Voigt functions one uses Fourier Transforms, The F.T. of equation ( 3 . 1 ) reads: S(t) = S E(t)S A(t) (3.3) So i f Srrf0) i s a Gaussian, S EH-C Ee xp(-^) ; S(t) = C;exp(-4i2J (3.4, and i f S^ C6 )^ * s a Lorentzian, S A H Z Trfe^Y ; S A(t) = C'A e x p ( - A t ) . (3.5) With (3.4) and (3.5) i n ( 3 . 3 ) , one has S(t) = A exp(-^t - . ^ i - j . ( 3 . 6 ) It follows i n the case where S E( C 0) a n c * S A( t 0) a r e Voigt pro-f i l e s that they both have transforms of the form in ( 3 . 6 ) , namely 2. 2 S A ( t ) . = D ^ p { - f i ' t - ^ ) (3.7) S E (t) = E e x p ( - / e r t - 4 i ) <3-8) so that now S("t) w i l l be the transform of a Voigt p r o f i l e whose Gaussian halfwidth i s and whose Lorentzian halfwidth i s Z3! = A / + X ' ( 3 . 1 0 ) -24-Deconvolution of our apparatus p r o f i l e S A(co) from our observed p r o f i l e S(co) i s accomplished by the following simple procedure. Using the tables of van de Hulst and Reesinck(1947) we f i n d the best Voigt f i t s for the two p r o f i l e s . Then /3, and /32 characterize the observed p r o f i l e 5(w) while p[ and pz characterize the apparatus p r o f i l e S A(cu) . The operations im-p l i e d i n equations (3.9) and (3.10) are then performed to ob-ta i n fi and p2 characterizing the true p r o f i l e From the tables, one can f i n d the width of the p r o f i l e whose " it parameters are j3x and /92 . -25-CHAPTER 4 - APPARATUS AND TECHNIQUE In t h i s chapter the reader w i l l f i n d a description of a l l the apparatus that was used in exposing, c a l i b r a t i n g and measuring the spectrographic plates for width and s h i f t of lines.,The chapter also deals with measurement procedure i n -volving the Grant precision comparator and the subsequent computer processing of data. . Figure 1 shows the layout of the equipment used in obtain-ing spectrographic plates from which the width, and s h i f t of plasma l i n e s were obtained. The s p e c i f i c a t i o n s of each unit i n Figure 1 are found in sections i ) to v) of part A). Section vi) gives the method for finding the densities of the neutral density step f i l t e r that i s needed for the i n t e n s i t y c a l i b r a t i o n of the plates. Part B) d e t a i l s the technique of s e t t i n g up the equipment and. exposing the plates. Following t h i s , parts C) and D) respectively outline the remaining steps of the measurement on the comparator and describe how the data are reduced. A) Spectral Line Sources and Spectroscopic Equipment i ) Energy Bank and Discharge Tube: It has been shown (Durand, 1963) that when an open-ended delay l i n e , or the approxima-tion to i t known as the lumped-parameter delay l i n e , i s -26-PLASMA DISCHARGE VESSEL T c. c. STANDARD D SOURCE SS P HILGER E742 SPECTROGRAPH TO OSCILLOSCOPE PHOTOMULTIPLIER JACO 82-010 MONOCHROMATOR FIGURE 1 LAYOUT OF BASIC APPARATUS -27-charged up and then s h o r t - c i r c u i t e d through i t s c h a r a c t e r i s t i c impedance, the current flowing out i s a square pulse. The height and duration of the pulse depend on the charging v o l t -age and on the values of the inductances and capacitances co n s t i t u t i n g the delay l i n e . A lumped-parameter delay l i n e , symbolized in Figure 2 by what i s inside the broken l i n e , was constructed with the view that i f a steady current could be made to flow for an appreciable time through a plasma, one might obtain a good approximation to a homogeneous, e q u i l i -brium plasma, that i s , a plasma i n which the temperature and the densities are well defined The p r a c t i c a l bank c i r c u i t was constructed of 5|if capacitors (CDE type NG 201) and 5uh inductances. Each i n -ductance was a four turn c o i l of about 10 cm diameter, made by winding 1/4 inch copper tubing on a l u c i t e form. The con-ventional open a i r spark gap switch S had two brass electrodes contained in a c y l i n d r i c a l housing of brass and l u c i t e . An insulated f i r i n g pin sat i n the ground side of the gap so that when a fa s t , high voltage pulse from a Theophanis(1960) trigger c i r c u i t was put onto i t , the main discharge was i n i t -iated. When the discharge current flowed through the plasma vessel T, the l a t t e r had a resistance of the order of m i l l i -ohms, whereas the delay l i n e c h a r a c t e r i s t i c impedance was about 0.5 ohms. Therefore, a s p e c i a l l y constructed r e s i s t o r R, of 0.5 ohms and able to carry kiloamps of current, was placed THEOPHANIS TRIGGER UNIT li Co '16 J16 J FIGURE 2 PLASMA DISCHARGE CIRCUIT HIGH VOLTAGE PROBE i to co-" R ( f i v w w ^ — I y T A -29-i n the c i r c u i t as shown. The r e s i s t o r (see Neufeld, 1966) had two copper surfaces of about 50cm by 10 cm immersed i n a 10% solutio n of copper sulphate i n d i s t i l l e d water. These e l e c t r -odes were separated by 10 cm. The plasma vessel, shown in Figure 3, was sim i l a r to the one employed by Durand(1963). E s s e n t i a l l y , i t was a piece of glass tubing with f l a r e d ends into which annular Aluminum electrodes had been sealed. The windows on the outside ends of the glass tubing in the centre of the electrodes f a c i l i t -ated, end-on observations of the discharge. End-on observations were not made i n t h i s work, but the annular shape of the elec-trodes was e s s e n t i a l to the production of the arc. This vessel was connected to a vacuum system v i a a tube running from a hole i n the ground-side electrode. In the vacuum system, the pressure was measured by an aneroid gauge for the range 1 to 20 t o r r , or by a P i r a n i gauge for the 1 to 100 mtorr range. i i ) The Standard Source: An electrodeless discharge source of l i n e radiation(Minnhagen, 1964) was b u i l t in order to provide the unshifted, very narrow li n e s required for the determination of the instrumental broadening function, as mentioned in chap-ter 3, and also to give the unshifted position of the plasma l i n e s under study. Figure 4 schematically shows the vacuum system and e l e c t r i c c i r c u i t arrangements. The gas for study was bled into the discharge tube D by a needle valve and removed by a d i f f u s i o n pump through the Nitrogen cold trap. During operation, the gas was flushed FIGURE 3 PLASMA VESSEL FROM GAS BOTTLE TO DIFFUSION PUMP EDWARDS NEEDLE VALVE ELECTRODELESS DISCHARGE COIL D PIRANI GAUGE HEAD NITROGEN COLD TRAP AIR GAP H.V. CAPACITORS C """ NICHROME RESISTOR R QUARTZ COLLAR TRANSFORMER QUARTZ END PLATE 6 2 2 0 V, A.C. FIGURE 4 ELECTRODELESS STANDARD SOURCE -32-continuously through the system, i t s pressure being measured at the P i r a n i gauge head. On the ri g h t side of Figure 4 i s shown the e l e c t r i c c i r c u i t r y which produced high frequency currents through the c o i l at D. Currents of about 20 amps flowed i n the primary side of the transformer T, whose turns r a t i o was of the order of 1000 : 1. This primary current was limited by the 12 ohm r e s i s t o r R' which was made of appropriate lengths of 12 gauge Nichrome wire. The high voltage from the secondary charged two radar capacitors C (CDE type 52). Whenever the capacitors had a high enough voltage, the gap G broke down and underdamped o s c i l l a t i o n s occured in the discharge c o i l at D. The voltages at D were high enough to cause break down across the tube and thereby puncture the tube walls. To prevent t h i s , a quartz c o l l a r separated the tube from the c o i l . The gap G had a i r forced across i t i n order to insure that i t turned on and shut off cleanly for each r f burst. In order to allow d i f f e r e n t excitations i n the tube, that i s , to thus make possible a range of temperatures of the source, the gap distance was ad-justable. Also the gas temperature could be varied to some extent by changing the pressure: the spectra of higher i o n i z -ed species would appear as the pressure was lowered. The radio frequency (~7MHz) r e s u l t i n g i n the discharge was determined by the t o t a l capacitance C/2 (~ 0.0012ji.f) and by the inductance of the c o i l D. The l a t t e r was an eight-turn c o i l with a diameter of 5 cm and a length of 25 cm. -33-However, there was no requirement for tuning the o s c i l l a t i n g c i r c u i t - a wide range of c i r c u i t components could produce an electrodeless discharge. The main requirement was that the rate of change of current i n the c o i l be great enough to give the spectrum of in t e r e s t . i i i ) The Spectrograph: The photographic plates were a l l exposed i n a Hilger E742 large glass prism spectrograph. This instrument had a Littrow mounted prism and a collimating lens of diameter = 7.5 cm and f o c a l length = 170 cm. Reciprocal dispersions for t y p i c a l wavelengths studied here (4100A to 5500A) lay in the range 5 to 14 A/mm, and the resolving power was about 10*. The normal s l i t width of 20\i was always used for exposing l i n e s to be scanned ; when the step f i l t e r pattern was to be exposed, the s l i t was opened up to 90fi. The length of the s l i t exposed, on the other hand, was varied from 2 to 18 mm. A s l i d i n g cover on the Hilger F1386 s l i t produced the various lengths. A 2 mm length centred on the o p t i c a l axis, and therefore on the s l i t centre, could be arranged as could two s i m i l a r lengths s t a r t i n g from 1 mm on each side of the o p t i c a l axis. In addition to these set apertures, a crescent-shaped opening could produce a l l lengths from 5 mm to 18 mm centred at the o p t i c a l axis. Kodak IF plates were used throughout the work. The use of I plates was dictated by the need for a f a i r l y fast emul-sion so that many plasma f i r i n g s need not be taken even for -34-the weaker li n e s being considered. One aimed for as few shots per plate as possible i n order to minimize the e f f e c t s of d r i f t in plasma conditions from shot to shot. The spectral range of 4100A to 5500A was best studied using the F sensi- . t i v i t y , although 10 plates could just as well have" been used in the blue end of the range. Two devices were b u i l t to replace the plate holder and so f u l f i l s p e c i a l requirements in the setting up of the equip-ment. F i r s t , there was an adapter constructed v/hich allowed an IP 28 photomultiplier assembly to be mounted i n place of the plate. With th i s apparatus one could monitor the l i g h t coming to the plate area of the spectrograph and thus check the synchronization of the r o t a t i n g mirror shutter, as des-cribed i n part B). The photomultiplier had the usual cathode follower c i r c u i t to match i t s output impedance to the input impedance of the cable carrying the s i g n a l to an o s c i l l o -scope. Second, an incandescent lamp holder was also constructed, to replace the plate holder. This lamp shone l i g h t from the plate region back through the optics, and was used i n t h i s way to ali g n the whole o p t i c a l system from the plasma d i s -charge tube to the plate holder. A very important attachment for the spectrograph was the neutral density step f i l t e r , Hilger number F1273. This com-prised a quartz window onto which had been evaporated a 2 mm by 12 mm Rhodium neutral density f i l t e r of six steps, each step 2 mm long. The quartz plate was mounted in a barrel -35-which, in turn, could be fastened r i g h t in front of the spectrograph s l i t , with the length of the pattern l y i n g along the length of the s l i t . The purpose of the f i l t e r was to attenuate to six d i f f e r e n t known degrees the i n t e n s i t y of a uniform l i g h t beam f a l l i n g on the s l i t , so that "the experi-menter could obtain an i n t e n s i t y versus density curve ( i e . , the "H and D" r e l a t i o n ) for the emulsion being exposed. The c a l i b r a t i o n of the i n t e n s i t y factors i s described i n section vi) of t h i s part of the chapter, while that of the actual use of the f i l t e r comes i n part B). iv) The Monochromator: Figure 1 shows that the l i g h t from the discharge can be deflected from the spectrograph Z by the proper mirror at M3 causing i t rather to go to the mono-chromator entrance s l i t X. This JACO 0.5 metre instrument, number 82-010, was an Ebert mount type with adjustable en-trance and exit s l i t s . The monochromator was operated in f i r s t order where, for a lOu. entrance s l i t , the instrumental h a l f -width was about 0 . 2 A ; the r e c i p r o c a l dispersion for wavelengths considered was 16A/mm. The l i g h t output from the monochromator was measured by an RCA IP 28 photomultiplier equipped with a cathode follower c i r c u i t for impedance match. Signals were taken vi a a 50 ohm cable to a multi trace oscilloscope for display, and could be used to check the temporal developement of a l i n e i n t e n s i t y during an arc discharge. In the case where two l i n e inten-s i t i e s were being compared, one had to use an exit s l i t -36-wide enough to allow the whole l i n e p r o f i l e to f a l l on the photomultiplier ( because the data thus obtained was to be used i n a theory that demands integrated l i n e i n t e n s i t i e s , not peak values). For t y p i c a l plasma l i n e halfwidths, an exit s l i t width of 200(1 was required. v) The Light Shutter System: We include i n t h i s discussion of the l i g h t shutter a l l the' o p t i c a l elements between the d i s -charge and the s l i t of the spectrograph. In addition, i t w i l l be necessary to describe here the function of the various e l e c t r o n i c units which provided or v e r i f i e d synchronization of events during a discharge. Rotating mirrors are widely used. In t h i s experiment, the purpose of the system was to i n i t i a t e the f i r i n g of the discharge, commence the plate exposure Tp seconds after the discharge and continue to expose for r seconds. Here, both Tp and T were required to be of the order of tens of microseconds. Mechanically these requirements could be stated as: the rotating mirror had to s t a r t sweeping an image of the i n t e r e s t i n g part of the discharge across the spectrograph s l i t Tp seconds after the discharge started and to f i n i s h t h i s sweep at ( Tp + T) seconds after the i n i t i a t i o n . Figure 5 i s a plan view of a l l the devices in the shutter system. The l i g h t from the plasma t r a v e l l e d i n a horizontal plane defined by the axis of the discharge tube and the cen-tre of the spectrograph s l i t S£. The basic o p t i c a l units were M2 M3 P INCANDESCENT BULB DIODE FOR LOGIC CIRCUIT DIODE FOR MONITORING SYNCHRONIZATION GLASS DEVIATOR LENS SYSTEM LENS STATIONARY MIRROR ROTATING MIRROR REMOVABLE MIRRORS DOVE PRISM SLIT SPECTROGRAPH ENTRANCE SLIT PLASMA DISCHARGE VESSEL FIGURE 5 SYSTEM FOR GATHERING AND SHUTTERING PLASMA LIGHT -38-lens system L^, s l i t S]_, lens L2 and s l i t Disregarding a l l the other elements i n the set-up, one can say that the function of the f i r s t three just mentioned was to gather l i g h t from a small volume of plasma at T and focus i t at Sg. Lenses L-^ took the plasma l i g h t and focussed i t on was ad-justable i n width and thus limited the smallest dimension of the plasma volume sampled, namely, the dimension p a r a l l e l to the tube radius. L2 then focussed the image of S-^  onto S 2 , Whereas the optics determined the width of the pattern swept across S2, the length of the pattern exposed was simply limited by the s l i d i n g aperture immediately i n front of S 0 which has already been discussed . The dimensions of the plasma volume sampled were small compared with those of the discharge : the sampled height was 0.5 mm, the width 2 mm, and the length equal to the distance on the o p t i c a l axis through the discharge column. One of the experimental aims was to see i f there were any s p a t i a l inhomogenieties i n the plasma and to correct the l i n e p r o f i l e s accordingly i f such existed. It was desirable that the image of formed by the lenses L^ at the plasma be horizontal so as to keep the r a d i a l dimension of the volume sampled as small as possible. This was accomplished by means of a Dove prism which rotated the image of S-^  by 90°. (It was judged that t h i s would be a l o t easier than setting the discharge tube v e r t i c a l ) . G was a glass plate hinged on an axis p a r a l l e l to that of the tube and i t acted as a beam -39-deviator. The light was deviated by simple refraction in the platej the plate's variable inclination meant that plasma volumes at different distances from the tube axis could be focussed at S^. /The rotating mirror was the centre of the shutter system. Distances to Mi to Mg, and Mg to S 2 were determined from the speed at which the plasma image had to sweep across S 2 , by the range of speeds available in the electric motor driving M2 , and by the available space. was a 5 cm square front-silvered mirror; M2 was similar a^d was driven by a 10,000 rpm Bodine motor, type NSE-13. The broken lines at Mg show the positions of various mirrors inserted at times to direct other light beams to the spectrograph or to direct plasma light to the monochromator. In Figure 5 we show other items required for synchronization. Light from the tungsten lamp B was reflected off a lower part of rotating mirror Mg and registered at photodiode D^ . This lamp-diode combination created a voltage signal t e l l i n g the logic circuitry that the mirror Mg was in position, The lower part of Mg was used so that this light v/hen reflected would pass below Sg and Dg at the time when Mg was sending i t in their direction. Dg was placed directly in the plasma light path but below the portion that entered the spectrograph. Dg monitored, the arrival of the plasma light during a plate exposure run. Figure 5 is not to scale; the specifications of the f i n a l -40-set-up were: Distance T to L 1 20 cm h1 to S S-, to M 45 cm 3 0 cm M± to L 2 11 cm to M 2 . 10 cm »» M 2 to S Width of s l i t S 27 cm 1 mm 20 j i The l i n i n g up of the whole o p t i c a l system has already been referred to; incandescent l i g h t was shone into the back of the spectrograph and then through the shutter ensemble with the ro t a t i n g mirror clamped so that the l i g h t reached the tube. Thus the "inverse" image at the tube showed the cross-section to be sampled, and the d i f f e r e n t components, such as the deviator G, could be adjusted so that radiation was c o l l e c t -ed from the desired r a d i a l position on the discharge. The c i r c u i t r y employed to switch on the discharge i s shown in Figure 6 . Neufeld(1966) describes i n ample d e t a i l the sequence of events during a discharge and only a condensed account need be given here. A pulse of a few vol t s was created by sweeping the l i g h t from the trigger lamp across the photo-diode D-^ . This pulse v/as inverted, and shaped by a Schmidt trigger; i t then triggered a Tektronix units 162 and 163 com-bination that put out a pulse of 5 volts delayed with respect to the shaped pulse by a timer^. . These two pulses were summed in a coincidence unit that produced a 25 vo l t pulse when the PULSE SHAPER AND INVERTER TEKTRONIX TYPE 162 WAVEFORM GENERATOR TEKTRONIX TYPE 163 PULSE GENERATOR -3-THEOPHANIS TRIGGER UNIT TO SPARK GAP SWITCH FIGURE 6 LOGIC C I R C U I T FOR SHUTTER -42-two input signals arrived together. Thus, when M2 had been accelerated to a frequency o f ( r ^ ) ^ , the coincidence c i r c u i t put out a 25 v o l t pulse which caused the single shot unit (a bistable multivibrator) to trigger the delay unit. This unit had a continuous range of delays from 1 [isec . to 1000 \isec. After the set delay, the unit emitted a sharp, po s i t i v e , 25 v o l t pulse that triggered the Theophanis c i r c u i t which then i n i t i a t e d the pulsed-arc discharge. The time T.J- was set in advance knowing the following: the mirror would be sweeping an image of S-^  past S 2 for T seconds. The given values of j and the distances S-^ -M-^ -Mg and M2-S2 determined the frequency of rotation of M2 at which the bank had to f i r e . Also, the delay unit had to be adjusted to provide the correct (the time between bank discharge and the s t a r t of the exposure). Let us suppose that the rotating mirror had just reached f i r i n g frequency. Then, when the tungsten bulb image h i t D-^ , the coincidence c i r c u i t put out a command to f i r e . At f i r i n g frequency, the time between the creation of t h i s coincidence pulse and when the plasma l i g h t started to sweep across S 2 was, say, j . Then the delay unit would be set to give a delay of (Tg-Tp). At T, after the f i r s t exposure, the image of S n was again x x being swept past S2. However, the plasma l i f e - t i m e was much smaller than r t , and therefore no "double exposure" problems arose. D2 shown in Figure 5 was a very small photodiode whose -43-junction was placed r i g h t in front of Sg and just below the aperture that admitted plasma l i g h t . It sampled the l i g h t pattern as i t passed the s l i t and so was useful, along with the photomultiplier unit on the spectrograph back, for estab-l i s h i n g and monitoring the synchronization. Neither output was used in the synchronizing l o g i c ; they were displayed d i r e c t l y on an oscilloscope. v i ) C a l i b r a t i o n of the Step F i l t e r Densities: In section i i i ) a neutral density step f i l t e r was referred to as part of the basic equipment of the spectrograph. Figure 7^shows the appar-atus employed to ar r i v e at the "known" densities of each step of the f i l t e r . One used the standard technique of f i r s t estab-l i s h i n g the l i n e a r i t y of the photomultiplier-recorder system and then measuring the r e l a t i v e transmissions of the steps. L i n e a r i t y was proven by p l o t t i n g the recorder output versus D , assuming that the s l i t - ribbon lamp configuration was a point source, and without the f i l t e r in position as shown. In both the l i n e a r i t y check and the transmission measurement , the l i g h t chopper - photodiode - phase sensitive detector combination .was employed i n the usual way to reduce the photomultiplier noise at the output. With 200 \i s l i t s i n the monochromator, the r e l a t i v e transmissions of the six steps were obtained at 200A i n t e r v a l s over the spectral range of 4000A to 5600A. JACO 82-010 MONOCHROMATOR NEUTRAL DENSITY \ STEP •-FILTER E.M.I. 9558 B PHOTOMULTIPLIER D LIGHT CHOPPER DIODE SLIT G.E. OSCILLOGRAPH TUNGSTEN RIBBON LAMP PHASE SENSITIVE DETECTOR CHART RECORDER FIGURE 7 APPARATUS FOR STEP FILTER CALIBRATION -45-B) Plate Exposure Technique In t h i s part, we outline how the equipment described i n part AJ was used to obtain photographic plates on which width and s h i f t of spectral l i n e s could be measured. Included here are the study of time-resolved i n t e n s i t i e s of t y p i c a l l i n e s , the method of f i r i n g the delay-line bank for plasma l i n e photography, the superposition of standard l i n e s from the electrodeless source and f i n a l l y , the development. This part follows the sequence of operations of a t y p i c a l experiment. i ) Line I d e n t i f i c a t i o n and C a l i b r a t i o n : The gas to be studied was bled through the standard source, Figure 4, and the appro-priate mirror was placed at M g in Figure 1 to r e f l e c t l i g h t from the standard source into the spectrograph. Photographs of the standard source were then taken with a 2 mm by 20 u. s l i t . M g was changed to r e f l e c t l i g h t from the iron arc I into the spectrograph whose aperture allowed the iron arc spectrum to straddle the electrodeless spectrum as recorded on the plate. For. the iron arc photograph, one used the two 2 mm by 20 u. s l i t s centred at 3 mm from the o p t i c a l axis on both sides of the standard spectrum. The above plate could be used to i d e n t i f y the l i n e s that the electrodeless discharge was producing. The conditions of ex c i t a t i o n and the length of exposure were varied and the photographic process repeated u n t i l s a t i s f a c t o r y plates of -46-the desired spectrum ( A r i l or N i l ) were obtained. Next, a choice was made as to which range of the spectrum for study was the most i n t e r e s t i n g and yet could be photograhed on one plate. This wavelength range was selected to contain measurable l i n e s from a vari e t y of multiplets and with a var-i e t y i n s h i f t and width. With this spectral range and a 2 mm by 20 \i entrance s l i t , one photographed the electrodeless discharge of the gas of in t e r e s t . Then, another portion of the same plate was exposed to the same source through the step f i l t e r and using an 18 mm by 90 p. s l i t . This plate was used to c a l i b r a t e the spectrograph for the re c i p r o c a l dispersion and the instrumental broadening function. i i ) E s t a b l i s h i n g the Shutter Timing: The intensity-versus-time graphs for a few of the li n e s chosen for s h i f t and width measurement were obtained. Referring to Figure 1, M was clamped to r e f l e c t the image of S-^  v i a the appropriate mirror Mg to the monochromator s l i t X. The whole system was li n e d up by shining laser l i g h t back through the system to the tube. Next, with the IP 28 photomultiplier on the monochromator, the plasma tube was discharged by manual triggering of the Theophanis unit. On a dual beam oscilloscope, both the dis-; charge current form and the photomultiplier output were d i s -played versus time. The times 7"D and r were e a s i l y read from these oscillographs (Typical oscillographs and the c r i t e r i a for chosing r n and r are given i n the next chapter). -47-i i i ) Exposing the Plate: Having adjusted the c i r c u i t r y to give the correct delays and exposure, one checked the timing by f i r i n g the bank and monitoring the discharge current wave-form, the output of D , and the voltage from the photomulti-p l i e r on the back of the spectrograph. The delay unit time was changed u n t i l the photomultiplier pulse occurred at the correct time with respect to the s t a r t of the discharge. Furthermore, the l a t e r a l position of Dg could be adjusted mechanically u n t i l the pulse from i t during a bank f i r i n g coincided with the pulse from the photomultiplier. Thus, although the photo-m u l t i p l i e r for the spectrograph back was not i n operation dur-ing a plate exposure run, the diode D Q could v e r i f y synchron-i z a t i o n on a l l plasma discharges. The exposure routine w i l l now be described with reference to Figure 8, In t h i s Figure are shown a l l the necessary images of one s p e c t r a l l i n e . The long dimensions of the images are the same as those of the s l i t s producing them because our spectrograph had a magnification of 1. The plasma was d i s -charged using the shutter synchronization for as many times as were required to obtain c o r r e c t l y exposed plasma l i n e images, a 2 mm by 20 (j. s l i t being used. The r e s u l t i n g broad, s h i f t e d l i n e image i s shown as the plasma l i n e i n position B. Then the plate was exposed to the standard source with the two o f f -centre 2mm by 20 IL s l i t s . Resulting standard l i n e s are shown straddling the plasma l i n e i n positions A and C. Next, the spectral range s e t t i n g of the spectrograph was changed - for -48-STANDARD \ REF. B PLASMA REF. STANDARD t REF. 2 MM 2 MM 2 MM x —o NEUTRAL DENSITY STEP FILTER PATTERN fl 1 MM * -FIGURE 8 PORTION OF A PLATE WITH ALL NECESSARY IMAGES OF ONE LINE -49-some plates i t was raised, for some, lowered - by about 10A and the s l i t dimensions changed to 6 mm by 20 JJ. , centred on the o p t i c a l axis. The plate was exposed to the standard source for the same length of time as the "straddling" spectrum; thus the 6 mm long reference l i n e was produced (in Figure 8 the s p e c t r a l range was lowered). F i n a l l y , the plate was lowered with respect to the spectrograph to expose a new part of i t , and the standard source again photographed, t h i s time with the step f i l t e r covering a 18 mm by 90 y. s l i t . The exposure time again was that given the straddling spectrum and the re-s u l t i n g step pattern image was centred at 15 mm below B on the plate. In p r a c t i c e , one could put two A-B-C patterns, corres-ponding to two d i f f e r e n t positions for viewing the discharge, on the same plate along with one step f i l t e r pattern. The second A-B-C pattern was placed on a d i f f e r e n t v e r t i c a l pos-i t i o n of the plate. In Figure 8 i t would be placed above the A-B-C pattern shown. Whether the spectrograph's spectral range was raised or lowered for the reference l i n e depended on the r e l a t i v e density of other l i n e s near the one to be studied. For instance, the s h i f t to lower range in Figure 8 would be recommended i f there were a greater density of l i n e s on the blue side of the l i n e than on the red side In the exposing of a plate as j u s t described, care had to be exercised to obtain measurable plates. In reference to - 50-th e H - D curve (see eg. Mees and James, 1966J as sketched i n F i g u r e 9 below, one knew that the f i l m b l a c k e n i n g ( i e . , the d e n s i t y ] f o r our p l a t e s d i d not depend l i n e a r l y on the time-i n t e g r a t e d i n t e n s i t y of the l i g h t i n c i d e n t on i t . In p a r t i c -u l a r , i t was p o s s i b l e to s a t u r a t e a l i n e image i f i t r e c e i v e d too great an exposure ( r e g i o n S i n F i g u r e 9). U s e f u l l i n e im-ages were those whose b l a c k e s t f i l t e r s t e p had a d e n s i t y w e l l below complete s a t u r a t i o n and whose l i n e peak s i m i l a r l y had a d e n s i t y on the s t r a i g h t e s t p a r t of the H-D curve. In F i g u r e 9, A to B i s the best range. O p t i m a l l y t h i s was tr u e f o r the plasma, standard and r e f e r e n c e l i n e s ; s i n c e no two l i n e s i n the study had e x a c t l y the same i n t e n s i t y and s i n c e the r a t i o s of l i n e i n t e n s i t i e s i n the plasma were d i f f e r e n t from t h e i r r a t i o s i n the standard source, a number of p l a t e s with d i f f e r -ent combinations of exposure times f o r the two sources were needed to get c o r r e c t l y exposed p l a t e s f o r a l l the l i n e s i n the group s t u d i e d . LOG(EXPOSURE) = LOG(It) -51-It was not obvious that one could use the i n t e n s i t y c a l i -bration curve produced from the electrodeless discharge l i g h t and apply i t to the plasma l i n e p r o f i l e because r e c i p r o c i t y or intermittency f a i l u r e might obtain(see Mees and James, 1966). However, i t was found after some t r i a l experimentation that i t was much quicker and more convenient to achieve a uniform il l u m i n a t i o n of the 18 mm long s l i t by the electrodeless source than by the plasma source. Therefore, i n order to j u s t -i f y t h i s use of the standard source, step f i l t e r patterns were photographed on the same plate using both sources. With simi-l a r densities on the two patterns, r e l a t i v e i n t e n s i t y - versus - microdensitometer transmission curves read on the precision comparator (description to follow) agreed to well within the t o t a l error i n the i n t e n s i t y c a l i b r a t i o n method. Having thus confirmed that there were no such photographic f a i l u r e s , one used the standard source for a l l step f i l t e r patterns without further check. iv) Plate Development: Development of the Kodak IF plates was done e s s e n t i a l l y as prescribed by the manual (Kodak,1962). In order to minimize adjacency e f f e c t s which occur e s p e c i a l l y i n the sharp, standard l i n e images , the plate emulsions were brushed continuously with a camel hair brush during develop-ment. In addition, a f t e r the regular two hour wash, the plates were rinsed in d i s t i l l e d water to remove residual d i r t . -52-C) Measurement of Plates on the Comparator i j The Comparator: The plates were scanned on a Grant Spectrum Line Measuring Comparator. In t h i s apparatus, the plate stage was driven past a microdensitometer that measured the trans-mission of a small area of the plate. The longitudinal p o s i t i o n of the stage could be measured d i f f e r e n t i a l l y to - 1 |x, while the transmission readings had a maximum range of 1 to 999 i n i n t e g r a l steps. The actual end-points of the transmission scale were set for each plate to assure use of most of the scale: 980 for the unexposed part of the plate and 10 for zero transmission, that i s , t o t a l blackening. Tomkins and Fred(1951) describe the o p t i c a l p r i n c i p l e s involved i n the comparator. E s s e n t i a l l y ^ for the transmission readings, a zoom lens system projected an image of a portion of the plate onto a s l i t i n front of a photomultiplier. The magnification of the image was variable between 5 and 20, while the s l i t dimensions were variable in length from 1 mm to 25 mm and i n width from 0.1 mm to 1.0 mm. Since l i n e s were scanned across the width, the instrumental breadth therefore had l i m i t s of 5 LL and 200 | i . The transmission reading and the stage position were con-tinuously monitored by a Datex CDS - 1 system. This unit, in turn, was connected to an IBM 526 card punch for which the Datex instrument d i g i t i z e d the transmission and position readings. At each position on the plate where one required a -53-reading, the datawere recorded by pushing a button. Tomkins and Fred(1951] show that a comparator can be equipped to indicate approximately what the l i n e p r o f i l e looks l i k e and which position on the p r o f i l e i s being viewed by the microdensitometer. In the Grant comparator, an image of the l i n e was swept back and for t h across a s l i t - photomultiplier combination i d e n t i c a l to the one that measured transmission. The instantaneous s i g n a l from th i s photomuliplier was displayed on an oscilloscope screen where the horizontal sweep was synchronized with the motion of the l i n e image. This image was exactly parfocal with that projected onto the transmission photomultiplier. When the image was centred on the transmission s l i t , the oscilloscope displayed two l i n e p r o f i l e s . These moved together as the l i n e centre approached the s l i t centre. If the l i n e was symmetrical, the two oscilloscope traces corrw p l e t e l y merged when the photomultiplier viewed the centre of the p r o f i l e ; only the peaks merged when an asymmetrical l i n e was centred. In either case, one could r e a d i l y determine which part of the l i n e p r o f i l e was being sampled by examining the oscilloscope display. i i ) Comparator Adjustment and Measuring Technique: Let us suppose that a l i n e l i k e that shown in the plate segment of Figure 8 was to be measured for s h i f t and width. One f i r s t had to choose the best settings of magnifying power and trans-mission s l i t dimensions . The magnification and s l i t width - 5 4 -had to be set so that a small width of the plate was viewed and yet so that the transmission would s t i l l be close to 100% for the clear part of the plate. It was best to scan the plate with as small an instrument broadening as possible be-cause the smaller that width i n comparison with the observed width, the more r e l i a b l e the deconvolution process. In fa c t , i t was found that with narrow s l i t s (less than 0.1 mm i n width) i t was impossible to get a suitably long range of transmission values. Thus the s e n s i t i v i t y of the transmission reading put a lower l i m i t on the s l i t width. After the magnification was set, the transmission s l i t ; length had to be adjusted to read as much of the l i n e length as possible without encountering appreciable curvature i n the image (see la t e r i n t h i s section). But one wanted a long s l i t i n order to average the transmission reading over as many emulsion grains as possible. Again one came to the requirement that there be enough l i g h t coming through the j s l i t to ensure good transmission s e n s i t i v i t y . So then, the three parameters were interdependent and some experimenting was done before the optimal settings were found for the spectrographic plates at hand. The procedure for measuring a plasma l i n e for i t s width and s h i f t i s now given with reference to Figure 8. The position of the plate with respect to the stage was adjusted so that the central part of the reference l i n e B was at right angles to the d i r e c t i o n of t r a v e l of the stage. When the transmission -55-s l i t dimensions and the magnification had been set, (these were 0.5 mm by 10 mm and 12 respectively for a l l the work done here) and when the microdensitometer head had been zeroed c o r r e c t l y , the transmissions of the steps of the neutral den-s i t y f i l t e r pattern were read. At t h i s point, the use of the reference l i n e becomes ob-vious. In one uninterrupted sweep the standard and reference l i n e s of position A were scanned. The drive was toward i n -creasing wavelengths to avoid backlash problems i n the stage mechanism. Likewise the pairs of images i n positions B and C were scanned together. The distance standard-to-reference i n position A could be checked against that i n position C to v e r i -fy that the plate had been c o r r e c t l y oriented on the stage and that there had been no d i s o r i e n t a t i o n of the reference l i n e with respect to the plasma and standard l i n e s at the time during exposure when the spectral range of the spectro-graph was changed. Having found that these two distances i n positions A and C agreed, one could subtract from th e i r aver-age the distance plasma-to-reference i n position B. This difference was the net plasma l i n e s h i f t . A l l the distances referred to i n the present discussion are between l i n e peaks. In t h i s routine, the transmission and stage position data recorded during the scanning of the plasma B l i n e constituted the data for the observed l i n e p r o f i l e . Usually, about 50 readings per plasma l i n e scan were recorded; there was a greater separation between adjacent readings on a wide plasma -56-l i n e than on a marrow one. The plasma l i n e was scanned far enough out into the wings to ascertain how much, i f any, correction would be required for continuum radia t i o n . Standard and reference l i n e s were always read with 5 u. i n t e r - ' vals. Curvature of l i n e images i s a well known phenomenon and r e a d i l y observed on the plates taken i n the Hilger E742 spec-trograph. Since one was interested i n scanning l i n e p r o f i l e s with a f i n i t e length of microdensitometer s l i t - which had to sample o f f - a x i s parts of the spectrograph s l i t image - one wanted to know the order of magnitude of curvature i n the spectrograph. Erfle(1924) treats the geometrical problem and finds a formula for the displacements of the extremities of a s l i t image. However, i n the present work, the curvature of images could be found s a t i s f a c t o r i l y by measuring the peak positions of small segments of a standard l i n e image. For example, with reference to Figure 8, t h i s was done by choosing a s l i t length small i n comparison with the 2 mm length of reference B and then using the oscilloscope display and the stage l a t e r a l feed to f i n d the central positions of the o f f -axis extremities i n positions A and C with respect to the position of the l i n e i n the middle of B. The curvature measured for l i n e s i n spectrum position B in Figure 8 was small and i t was possible to choose a s l i t length for which there was i n s i g n i f i c a n t e f f e c t on measured plasma l i n e p r o f i l e s . The method of finding s h i f t s in positions -57-A and C where curvature e f f e c t s may be s i g n i f i c a n t i s designed to remove such e f f e c t s from the measured quantities. This i s explained as follows: although the profiles of the standard l i n e i n position A and the reference l i n e i n position A, say, were both distorted and s h i f t e d by curvature, t h e i r distortions and curvatures were i d e n t i c a l . The distance between the i r peaks i n position A was the same as what would have been measured between the i r peaks i n position B i f we had exposed the standard l i n e there instead of the plasma l i n e . This rests on the facts that a-} one set the stage drive perpendicular to the centre of the l i n e s i n position B; hence, the microdensitometer s l i t sampled exactly the same portion of the standard and reference images i n position A, and b) standard and reference l i n e s had the same curvature because they were produced by the same wavelength of l i g h t . D) Computation and Analysis An IBM 7040 computer was used to change the l i n e scan transmission data into r e l a t i v e i n t e n s i t i e s , to calculate some widths on the smoothed p r o f i l e , and to f i n d the centre of the p r o f i l e . In what follows, we outline the basic methods used i n the program to evaluate the required numbers. -58-F i r s t , the program took the transmission data for the d i f f e r e n t steps of the neutral density f i l t e r and, with the known r e l a t i v e i n t e n s i t y c a l i b r a t i o n , i n eff e c t created i t s own H-D curve. Then the l i n e scan readings were translated into r e l a t i v e i n t e n s i t i e s by interpolation on thi s H-D plot. The whole p r o f i l e was smoothed out by applying second degree polynomial least squares f i t t i n g to consecutive groups of f i v e points. This part of the program was able to calculate the abscissa of the l i n e peak after i t had found the parabola best describing the f i v e points on the p r o f i l e closest to the peak. This value of l i n e centre was printed out i n the units i n which the abscissae (stage positions) had been read, namely in microns. After normalising the smoothed p r o f i l e to one at the peak, the computer calculated some widths of the p r o f i l e as follows: i t found the two sets of three consecutive points on both shoulders of the p r o f i l e which were closest to the 80% l e v e l , which we c a l l .8I Q . It then performed quadratic i n t e r -polation to determine the abscissa of this- .8I 0 ordinate, on both sides of the p r o f i l e . Subtraction of one abscissa from the other gave the .8I 0 width. The .7I Q, .6I 0 , -Ho widths were s i m i l a r l y found. A l l the widths were normalised to the .5I Q width, which i s the whole halfwidth, and the whole halfwidth and the six normalised widths were printed out, the former i n microns. The p a r t i c u l a r form i n which the widths of an observed -59-l i n e were printed out by the computer was chosen to f a c i l i t a t e the use of van de Hulst and Reesinck's(1947) tables from which the fB^ and characterizing the p r o f i l e ( see page 23) could be immediately found. This step was not done by the com-puter because some judgement was required to decide which j3x^^ best f i t t e d the calculated widths. Having found that there were s a t i s f a c t o r y Voigt f i t s for the plasma (observed) l i n e , and the standard (apparatus p r o f i l e ) l i n e , one performed the Voigt deconvolution for the width of the true p r o f i l e . The half halfwidth and the s h i f t of thi s l i n e were converted from microns to Angstroms using the dispersion curve.--60-CHAPTER 5 - THE EXPERIMENT A) The A r i l Lines i ) The Conditions of Measurement: The plasma that was used to create A r i l l i n e r a d i a t i o n was produced by discharging the delay-line bank, charged to 13 kV, through a Nitrogen-Argon mixture at an i n i t i a l pressure of 10 to r r . The f i n a l r e s u l t s were taken from plates that had been exposed to plasma rad-i a t i o n during a 15 |isec i n t e r v a l centred i n time at 20 jisec a f t e r the commencement of the bank current. Some i n i t i a l work was necessary to est a b l i s h the f e a s i -b i l i t y of spectroscopic studies with t h i s source and then to f i n d the conditions, j u s t stated, i n which data was best gathered. Neufeld(1966) took side-on pictures of the d i s -charge with a high speed Barr and Stroud framing camera. At some i n i t i a l pressures (^100 mtorr) the plasma was constricted to a thin filament that moved unstably about the vessel. At the chosen pressure of operation, 10 tor r , the vessel appeared uniformly illuminated over i t s diameter during the whole current pulse. The plasma s t a b i l i t y thus guaranteed a suitably stationary source of ra d i a t i o n . Spectra of the standard source were photographed for varying exposures and electrodeless discharge conditions. A gap of 19 mm i n the secondary c i r c u i t and an Argon pressure -61-of 20 mtorr i n the discharge tube led to a s a t i s f a c t o r y standard spectrum, i t being almost exclusively A r i l l i n e s . These were i d e n t i f i e d using Minnhagen's(1963) c l a s s i f i c a t i o n . With the i d e n t i f i c a t i o n complete, the l i n e scan data taken from the same plates were used to plot the dispersion curve and the instrument broadening function of the spectro-graph over the 4000A to 5600A range. The r e c i p r o c a l dispersion i s shown i n Figure 10, i n which the v e r t i c a l errors are - 0.1 A/mm . The apparatus broadening function was obtained as out-lined i n chapter 4. Approximately 70 l i n e scans were pro-cessed i n order to obtain the l i n e p r o f i l e as a function of wavelength. The shape of the instrument p r o f i l e was constant across the s p e c t r a l range. In terms of the normalised widths, i t was: Y .8I C .7I G .6I Q .5I 0 .4I Q . .3I 0 .2I Q X .544h .696h .846h l.OOOh 1.179h 1.375h 1.588h This constituted a good f i t to the Voigt function for which ^ / h = 0.225. Therefore, i n a l l the deconvolutions, one used the Voigt analysis with t h i s p a r t i c u l a r Voigt function rep-resenting the instrumental e f f e c t s . The instrumental whole halfwidth h i s shown i n Figure 11 as a function of wavelength. Here, the v e r t i c a l errors are about ± 3 \L . Next, the time-integrated spectrum of the plasma was photographed along with the standard source to allow the i d e n t i f i c a t i o n of the plasma l i n e s . The plasma did emit a few - 6 2 -FIGURE 10 RECIPROCAL DISPERSION OF THE SPECTROGRAPH 4000 4200 4400 4600 WAVELENGTH (A) 4800 5000 -63-. 3 - 40 W H Q M < a w o 30 20 H FIGURE 11 HALFWIDTH OF THE APPARATUS PROFILE 10 0 4000 4200 4400 - 4600 WAVELENGTH ( A ) 4800 5000 -64-impurity l i n e s , ; b u t A r i l and N i l l i n e s dominated, no matter which d i l u t i o n r a t i o of Nitrogen to Argon was used. Some A r i l l i n e s were not s u f f i c i e n t l y removed from a l l others to allow study of t h e i r widths and s h i f t s ; t h i s r e s t r i c t i o n was not serious since other l i n e s i n the same multiplet could be measured. It was evident from the i d e n t i f i c a t i o n that the spectro-graph with i t s glass optics would allow the in t e r e s t i n g range of 3750A to 5000A to be photographed on one 10 inch plate. Lines i n t h i s region were selected for study. These l i n e s were well spread out, represented a variety of multiplets, including the most intense ones(therefore the most commonly measured l i n e s ) , and had i n t e r e s t i n g d i v e r s i t i e s of s h i f t s , widths and i n t e n s i t i e s . Time-resolved studies were carr i e d out with the mono-chromator for the l i n e s : A r i l 4014, A r i l 4806, N i l 3995, and NIII 4097. Each intensity-versus-time graph had the same shape during the times of intere s t , when both an on-axis and an o f f - a x i s portion of the discharge were viewed. During a 15 [isec period that started about 13 jisec after the onset of the bank discharge, the l i n e i n t e n s i t i e s were maximal and varied by about 10%. Measurement of the N i l 3995 and NIII 4097 signals permitted an estimate of the plasma temperature. A r l l l 3795, a strong l i n e i n the spectrum of the twice ionized Argon atom, could not be detected above the background with the photomultiplier. -65-Th e intensity-versus-time r e l a t i o n for A r i l 4806 was measured at four d i f f e r e n t r a d i a l positions on the discharge column. The r e s u l t s are shown below along with the bank current waveform,. FIGURE 12 HISTORIES OF PULSED-ARC CURRENT AND A LINE INTENSITY RELATIVE INTENSITY RELATIVE INTENSITY RELATIVE INTENSITY RELATIVE INTENSITY CURRENT WAVEFORM INTENSITY OF A r i l 4806 ON AXIS OF DISCHARGE INTENSITY OF A r i l 4806 2 MM OFF AXIS OF DISCHARGE INTENSITY OF A r i l 4806 4 MM OFF.AXIS OF DISCHARGE INTENSITY OF A r i l 4806 MM OFF AXIS OF DISCHARGE 60 80 TIME (uSEC) -66-One wanted to expose the plates when the l i g h t output from the plasma was large and not changing much, i t being assumed that when a l i n e i n t e n s i t y was least changing was the most l i k e l y time to have thermal equilibrium. It was desirable that the l i n e i n t e n s i t i e s be as high as possible during the exposure i n order to minimize the number of plasma shots per plate. On the basis of these c r i t e r i a and the foregoing oscillograms, the times r and r D in the shutter synchronization were set so that the exposure time was the 15 jisec i n t e r v a l centred at 20 usee after the onset of the bank current. Considerable experimentation with the discharge conditions was required to obtain measurable plates of a l l the l i n e s for the four r a d i a l positions on the arc given i n Figure 12. A most important reason for t h i s experimentation was the elimin-ation of s e l f absorption of l i n e s . For this purpose, the Argon gas was d i l u t e d with Nitrogen i n order to lower the density of A r + ions and yet keep n e high enough to produce wide, Impact broadened l i n e s . It was found, for instance, that when pure Argon was discharged, A r i l 4348, A r i l 4806 and other strong l i n e s could have o p t i c a l depths between 1 and 10, when reasonable estimates were made for the density of A r + ions and for the temperature, and i n which Olsen's(1963) t r a n s i t i o n p r o b a b i l i t i e s were used. The amount of d i l u t i o n of Argon by Nitrogen was chosen to be j u s t high enough to avoid s e l f absorption, At the same time, the number of plasma shots per plate had to be as large - 6 7 -as was necessary to y i e l d u s e f u l l y exposed l i n e images. Excessively high d i l u t i o n was avoided because then the experi-menter would have to take more time i n procuring well exposed plates and would r e l y more heavily on the plasma reproducibility. To check that absorption was not occurring, one measured the widths and s h i f t s of several l i n e s with a representative range of i n t e n s i t i e s at a d i l u t i o n r a t i o just above or just below the proposed conditions of study. It was found that the s h i f t s remained the same for a l l d i l u t i o n r a t i o s and that therefore the electron density- was also constant. The agree-ment between the widths of a l i n e at two d i l u t i o n s was thus taken to indicate that there was no s e l f absorption of that l i n e . The stronger A r i l l i n e s 4348 and 4806 had to be exposed at p Q(N 2) p Q(Ar) as 10 : 1, where p Q i s the p a r t i a l pressure of the gas i n the tube prior to discharge. The majority of l i n e s were taken i n a 3 : 1 mixture, while the two weak l i n e s , A r i l 4132 and 4933, were observed in pure Argon. Between 5 and 10 shots per plate were required for a l l the l i n e s . On the most heavily exposed plates i t was d i f f i c u l t to see any blackening i n the plasma spectrum that could be a t t r i b u t e d to continuum radiation. That i s , the density between s u f f i c i e n t l y separated l i n e s , according to both the micro-densitometer and the human eye, was n e g l i g i b l y d i f f e r e n t from the emulsion background fog seen on the unexposed portion of the plate. Our plates were exposed and developed so that the l i n e s of i n t e r e s t had their .21 points above the background -68-fog - below t h i s , l i t t l e could be said about the l i n e shape. Since the photographic fog always masked any continuum black-ening on the plates, no correction was made for continuum i n the data reduction process. Figure 13 shows two i n t e r e s t i n g parts of an actual A r i l plate taken from a pure Argon discharge. These pictures show li n e s with a quite large range of i n t e n s i t i e s . Hence, the bright ones, l i k e 4806, may be s e l f absorbed and/or over-exposed and not measurable on t h i s plate. Nevertheless, one can see the r e l a t i v e widths of the standard and plasma l i n e s , the cleanness of the spectrum, some, plasma l i n e s with large s h i f t s and curvature (in the step f i l t e r pattern). The scale at the bottom i s that produced by the spectrograph during the photographing; i n order to show t h i s scale conveniently in our picture, the plate i s inverted compared with that i n Figure 8. i i ) The Results: The r e s u l t s of measuring 19 A r i l l i n e s are shown i n Table .1. Having found widths and s h i f t s at four r a d i a l positions on the discharge, one noted that none of the l i n e s exhibited a systematic dependence of w or d on the distance of the viewing position from the tube axis. The average values are shown i n t h i s table i n which the data are grouped accord-ing to the d i l u t i o n r a t i o for which the l i n e s were exposed. The half halfwidths of the l i n e s i n Multiplet 6 - which i s a favourite with theoreticians and experimentalists - were used, i n estimating the electron density of the plasmas. Griem's FIGURE 13 TWO PARTS OF AN A r i l PLATE TABLE I MEASURED A r i l WIDTHS AND SHIFTS COMPARED WITH CURRENT THEORETICAL AND EXPERIMENTAL DATA MULT. WAVE- HALF HALFWIDTH w . A SHIFT d. A SHIFT-TO-WIDTH RATIO NO. LENGTH, A THIS ROBERTS GRIEM(1966) THIS THIS GRIEM(1964) EXP. (1966) EXP. THEORY EXP. EXP. THEORY 6 4 806 0.49±.06 0 .501.07 0.31 -0.18r.04 -0.37 -0.07 7 4348 0.41*.04 0.29 -0.101.02 -0.27 + 1.01 n e = (2.4i. 4) x 10 l 7cm~ kT = (2. 61 .2) ev 6 4736 0.48±.05 0.30 -0.18*.04 -0.38 -0.07 6 4848 0.481.07 0.30 -0.22i.04 -0.46 -0.07 7 4267 0.391.05 0.391.06 0.28 -0.14±.03 -0.36 + 1.01 7 4331 0.451.04 0.28 -0.131.03 -0.29 + 1.01 7 43 80 0.461.05 0.28 -0.14±.04 -0.30 + 1.01 14 4727 0.53±.04 0.37 -0.19±.03 -0.36 14 4880 0.621.05 0.57±.06 0.37 -0.19±.04 -0.31 15 4658 0.541.04 -0.151.03 -0.28 15 4765 0.54±.04 -0.161.03 -0.30 17 4579 0.53*.05 -0.061.04 -0.11 31 45S0 0.551.06 -0.08l.04 -0.15 31 4610 0.54±.06 -0.l i t . 0 4 -0.20 32 4278 1.07±.08 +0.301.05 +0.26 39 4482 0.551.05 +0.051.04 +0.09 52 4104 1.27±.12 +1.031.08 +0.81 n e = (2.31.4) x 10 l 7cm" 3 , kT = (2. 6: h .2) ev 6 4933 0.401.05 0.25 -0.201.05 -0.50 -0.07 32 4132 1.261.12 +1.051.07 +0.83 n e = (1.9±.4) x 10 l 7cm" 3 , kT = (2. 61 .4 ) ev -71-(1964) t h e o r e t i c a l halfwidth was multiplied by a factor of 2.6 which Jalufka and others(1966) say i s required to secure agreement with experiment in t h i s multiplet. This corrected width was used to scale the observed widths to f i n d the value of n e. It was assumed in t h i s c a l c u l a t i o n that Griem's values of width exhibit the correct temperature dependence i n order to correct for the difference between Jalufka's temperature(i&ev and ours(Jalufka found w(Mult.6)=0.20A at n e=l.03xl0 1 7cm~ 3). The measurement of the i n t e n s i t y r a t i o of N i l 3995 and NIII 4097 has been alluded to already. The r e s u l t i n g value, along with the electron density and the o s c i l l a t o r strengths for these l i n e s given by Griem(1964) were substituted into the equilibrium r e l a t i o n s (see eg., James, 1965) to f i n d kT, the temperature connecting the population densities of the N + and N + + ions. This temperature had to be that guessed during the electron density estimate ( at a given density, the l i n e widths do have some temperature dependence ). If i t was not, the n e and kT calculations were i t e r a t e d u n t i l the i n t e n s i t y r a t i o observed, the width of the Multiplet 6 l i n e s , and kT were consistent. The electron density and the plasma temperature thus found are shown in Table I. The errors on the temperatures are produced by the uncertainties in a l l the parameters of the Sana equation that was solved for kT, namely, i n the theoret-i c a l l i n e strengths, i n the experimental i n t e n s i t y r a t i o and in the experimental electron density. The l i n e strengths are -72-probably good to - 25%, while the i n t e n s i t y r a t i o has s i g n i f -icant error from the high background i n the NIII 4097 in t e n s i t y measurement and from possible s e l f absorption e f f e c t s i n the N i l 3995 i n t e n s i t y measurement. The error i n n shown has e contributions from the t o t a l error assessed i n our experi-mental width determination - this w i l l be discussed l a t e r i n t h i s thesis - and from the uncertainty that Jalufka et a l . place on t h e i r s c a l i n g factor. It i s possible to write the equilibrium r e l a t i o n s showing the i n t e n s i t y r a t i o I(ArII 4014) : I(ArIII 3795) as a function of electron density and plasma temperature. Using the o s c i l l -ator strength for A r i l 4014 quoted by Griem(1964) and the LS coupling formula with Bates and Damgaard's(1950) r a d i a l matrix elements for the A r l l l 3795 o s c i l l a t o r strength, one found that the above r a t i o was 23:1 for the p^Ng) : P0(Ar) as 3:1 plasma. This i s consistent with the experimental r e s u l t s c i t e d i n the preceding section. During those measurements, a signal 1/23 of the size of the A r i l 4014 s i g n a l at the photomultiplier would be buried i n the background. Indeed, no A r l l l 3795 l i g h t registered at the photomultiplier. Table I shows the comparison with recent t h e o r e t i c a l . predictions and with the r e s u l t s of an experiment(Roberts, 1966) i n which the temperature was very close to ours. One might also c i t e other experimental evidences for the widths, l i k e that of Popenoe and Shumaker (1965), but they would not be as relevant because the temperatures there were significantly -73-lower than 2.6 ev. S i m i l a r l y , there i s other t h e o r e t i c a l work on widths (Roberts, 1966J Cooper and Oertel, 1967) containing refinements on Griem's(1966) c a l c u l a t i o n but predicting values l i t t l e d i f f e r e n t from Griem's. In Table I, Roberts' experiment-a l widths have been scaled down by a factor of 2.3/ 4.4 - or 2.4/4.4, as the case may be - to convert from his n g condition to ours. Likewise, the t h e o r e t i c a l estimates i n columns 5 and 8 are evaluated for the plasma conditions indicated. This work i s among the f i r s t to measure A r i l l i n e s h i f t s i n dense plasmas, so there i s l i t t l e else available for comparison in the s h i f t column except the work of Popenoe and Shumaker(1965) in which the width and s h i f t of A r i l 4806 seem to be well measured. They f i n d that w = 0.36A and d/w = -0.49 at n g = 1 7 - 3 2.4 x 10 cm and kT = 1.1 ev . Their low temperature makes comparison somewhat strained, but the order of magnitude of the r a t i o s of t h e i r numbers to the present ones i s that predicted by the Impact theory. It i s thus concluded that t h i s one instance of s h i f t measurement i n A r i l agrees with the author's r e s u l t . The only t h e o r e t i c a l c a l c u l a t i o n s of s h i f t available are those of Griem(1964) and these are contained e f f e c t i v e l y in column 8. For a l l three multiplets studied commonly by Griem, Roberts and the present author, the two experimentalists measure the same widths and these disagree with the t h e o r e t i c a l r e s u l t s . Also, the shift-to-width r a t i o s measured bear l i t t l e resemblance to the theory's predictions. However, the Impact -74-theory requirement that a l l lines from the same multiplet have the same width and s h i f t i s substantiated in the present work. For the t h e o r e t i c a l widths, the t o t a l uncertainty deriving both from the basic uncertainty in the c a l c u l a t i o n (containing, for instance, inaccurate wavefunctions) and from the stated errors i n the n e and kT values i s almost large enough to allow one to say that the theory does agree with experiment. No such argument i s possible in the case of the shift-to-width calculation": t h i s quantity depends only on the temperature and one finds, for instance in Multiplet 6, that the error i n the temperature maps into an error i n d/w of about ± 0.05 . B) The N i l Lines i ) The Conditions of Measurement: This part of the experiment on N i l ra d i a t i o n was undertaken to check the work of Day(1965), e s p e c i a l l y to see i f the present photographic technique was better than the usual monochromator-photomultiplier approach for measuring widths and s h i f t s . Day studied eight l i n e s , namely: N i l 3006, N i l 3838, N i l 4026, N i l 4530, N i l 4553, N i l 4614, N i l 5045, N i l 5495. Of these, 3006 was not considered i n the present work because the wavelength lay outside the spectral range of the ex i s t i n g apparatus. The electrodeless discharge was run with Nitrogen at a -75-pressure of 1 mtorr and a secondary c i r c u i t gap of 19 mm. Molecular bands were much i n evidence i n the r e s u l t i n g spectrum, produced mostly i n the N2 and N 2 systems. Nevertheless, the standard source,also c l e a r l y produced the six l i n e s of longest wavelength studied by Day. N i l 3838 was present but obscured by a molecular band. The atomic lines were i d e n t i f i e d under Eriksson's(1958) c l a s s i f i c a t i o n . It was found that a good plasma for studying the N i l li n e s was the same as that from which most of the A r i l data were obtained: a PC(N2) : PQ(Ar) as 3:1 mixture was discharged at a bank voltage of 13 kV and with a s t a r t i n g pressure of 10 t o r r . As i n part A), the plates were exposed to plasma l i g h t for a 15 usee i n t e r v a l s t a r t i n g at 13 usee after the i n i t i a t i o n of the discharge. Time-integrated photographs of the N 2~Ar plasma spectrum did not show N i l 3838 c l e a r l y . For th i s reason and also i n view of i t s obscurity i n the standard spectrum i t was removed from the l i s t of l i n e s to be studied. This l e f t the six lines of longest wavelength in Day's l i s t , and they were a l l exposed on one spectral range s e t t i n g of the spectrograph, 3950A to 5500A. Five l i n e s from Multiplets 1 and 2 of the NIII spectrum had already been i d e n t i f i e d i n the plasma spectrum. The use of one of the l i n e s i n Multiplet 2, NIII 4097, for the temp-eraure determination has been described in section i ) , part A) of t h i s chapter. The instrumental broadening function was taken to be - 7 6 -the same Voigt p r o f i l e as found for the spectral range used for the A r i l l i n e s . The r e c i p r o c a l dispersion curve, Figure 10, was extrapolated to give the value required for N i l 5495; the instrumental halfwidth was obtained by treating the graph Figure 11 s i m i l a r l y . Then, the accuracy of the extrapolated values was checked by scanning some i d e n t i f i e d N i l l i n e s i n the 5495A region of the plate. The variety i n widths and i n t e n s i t i e s of the N i l lines of int e r e s t led to the requirement of between 3 and 10 plasma shots per plate and a complementary range of exposure times of the standard source. Since none of the optics i n the system was changed between the work described i n part A) of this chapter and that i n part B), the comparator measurement routine also required no adjustment. Again, there was no need to correct l i n e p r o f i l e s for underlying continuum radi a t i o n . A l l the N i l l i n e s i n t h i s experiment had Voigt p r o f i l e s , none showing s i g n i f i c a n t asymmetry. Among the deconvolved true p r o f i l e s there was a variety of shapes but, again, the Lorentzian shape dominated. i i ) The Results: The widths and s h i f t s of the six N i l l i n e s are shown in Table II. The values are the averages of readings taken from on-axis and from 3 mm o f f - a x i s of the discharge. Sampling only at two positions, instead of four as previously, was adopted aft e r i t was confirmed that, as with the A r i l l i n e s , the widths and s h i f t s i n N i l showed no dependence on which part of the discharge was photographed. In t h i s table, TABLE II MEASURED N i l STARK PARAMETERS COMPARED WITH CURRENT THEORETICAL AND EXPERIMENTAL DATA MULT. NO. WAVE-LENGTH , A HALF HALFWIDTH w, A THIS EXP. DAY (1965) EXP. BERG (1967) EXP. GRIEM (1966) THEORY SHIFT-TO-WIDTH RATIO d/w THIS EXP, DAY (1965) EXP. BERG (1967) EXP. GRIEM (1964) THEORY 4 5 29 40 58 59 5045 4614 5496 4026 4553 4530 0.631.07 0.581.05 0.691.17 2.901.45 2.661.28 2.671.70 0.191.03 0.171.03 0.221.03 1.581.25 0.551.15 1.841.18 2.3 1.6 0.46±.05 2.071.21 2.531.25 2.3 1.93 0.37 0.28 O. 58 2.53 0.94 3.22 2.3 1.6 +0.03 1.03 +0.211.04 -0.291.17 -0.03 1.09 -0.03 1.12 -0.051.13 2.6 +1.001.34 +1.101.37 +0.831.28 -0.091.32 -0.281.56 -0.161.20 1.6 0.0±.3 -0.3±.2 1.93 +0.84 +0.87 +0.67 -0.22 -0.58 -0.25 2.6 -78-the plasma conditions are those estimated for the A r i l measurements at the same d i l u t i o n r a t i o , and the errors i n d i c -ated on the r e s u l t s of t h i s experiment are the sum of random and systematic uncertainties as mentioned in part A) previous. Again, i n almost a l l of the cases, the random error i s s i g n i f i c a n t l y greater than the systematic. One could expect the strong l i n e s i n our discharge to suffe r s e l f absorption. Using the estimates of n g and kT already found for the A r i l l i n e s and assuming that for t h i s 3 : 1 mixture n e = |n(N +) = 7n(Ar +), where n(N +) i s the number density of N + ions and s i m i l a r l y for the Ar ions, then one could evaluate the o p t i c a l depth according to equation (2.2). This was done for the l i n e s i n M u l t i p l e t s 4, 5, 29, and 59 with Griem's(1964) o s c i l l a t o r strengths. The greatest reduction i n width according to equation (2.3) was that of the 5045A l i n e - 7%. A l l other l i n e s had 4% or less broadening due to s e l f absorption. This correct-ion was s i g n i f i c a n t l y less than the random error on the width and was not applied because the main interest in t h i s N i l work was to check shift-to-width r a t i o s . In comparison with the random uncertainties i n the values of w and d, the above s e l f absorption correction was completely n e g l i g i b l e . A review of the l i t e r a t u r e revealed no published o s c i l l a t o r strengths for the l i n e s i n Multiplets 40 and 58. However, the two l i n e s were observed to have i n t e n s i t i e s and -79-widths of the same order as the 4530A l i n e . Since t h i s l i n e was calc u l a t e d to have l i t t l e broadening by absorption, the former two were also assumed to be n e g l i g i b l y affected in t h i s way. Although the primary purpose of this work on N i l was to photographically v e r i f y Day's(1965) results,of s h i f t measurements, experimental and theore t i c a l r e s u l t s from other sources are also given i n Table II i n order to indicate over-a l l agreement. Since the publication of Day's r e s u l t s , Griem (1966) corrected the theory and pointed out that there was agreement between i t and Day's numbers only to within a factor of 2. Roberts(1966), and Cooper and Oertel(1967) also amended the N i l theory but found discrepancies comparing their pre-d i c t i o n s with the work of Day. Again, therefore, Griem's(1966) work has been taken as representative of the progress i n the f i e l d of width c a l c u l a t i o n . As opposed to the case of the A r i l widths, there i s no independent experimental data on N i l widths at the temperature of the plasma under study here. In Table II, the experimental values, and their errors, from Day(1965) and from Berg et al.(1967) have been scaled to correspond to the electron density found in the plasma of the present work. The most relevant experimental reports on N i l s h i f t s are those of -Day (1965) and Berg et al.(1967), while Griem's( 19 64) work i s the l a t e s t t h e o r e t i c a l e f f o r t for such l i n e s . In order to si m p l i f y comparison, only the shift-to-width r a t i o s are shown -80-i n Table II; one thus avoids any apparent disagreement between theory and experiment a r i s i n g from a poor n e c a l i b r a t i o n . The agreement among the r a t i o s of the N i l 4026, N i l 4530, and N i l 4553 l i n e s i s obviously s u p e r f i c i a l . These r a t i o s are evidently too small to be measured by any of the three techniques; for a l l experiments, the percentage error i n s h i f t , and therefore i n shift-to-width r a t i o , i s of the order of 100%. For the three narrow l i n e s N i l 4614, N i l 5045, and N i l 5496, the disagreement between the two sets of s h i f t -to-width r a t i o s i n columns 7 and 8 i s complete, even with l i b e r a l error estimates on both groups of r e s u l t s and allowing for the temperature dependence of d/w. Griem's(1964) c a l c u l -ations show d/w as a function of temperature. If one uses these data to estimate the amount of change i n d/w i n going from 1.6 ev to 2,6 ev, one expects nowhere near as much per-centage change i n the quantity as there i s between Day's and the present r e s u l t s . -81-CHAPTER 6 - DISCUSSION A) Estimate of Errors The errors i n the width and s h i f t values i n Tables I and II measured by the author contain both systematic and and random error. The tolerances shown were calculated by taking the square root of the sum of the systematic error squared plus the random error squared. For most data, the ran-dom error completely outweighed the systematic. We now review how these quantities were estimated. i ) Systematic Errors: It was possible to assess systematic error from the uncertainty in the step f i l t e r transmissions, from the inherent inaccuracy and i r r e p r o d u c i b i l i t y of the transmission readings from the microdensitometer, and from the plate position reading of the comparator stage. An estimate of the systematic error i n the step f i l t e r transmissions was obtained through consideration of the uncer-tain t y of the output signal of the c a l i b r a t i n g apparatus described on page 43. Here, the noise on the signal constituted an uncertainty much larger than a l l the others i n the tech-nique, and was therefore taken to be the t o t a l error. In the worst case studied, namely at a wavelength of 4000A, the transmissions were good to about 10% on account of the poor s e n s i t i v i t y of the EMI photomultiplier at t h i s wavelength. -82-However, throughout most of the spectral range of int e r e s t , the experimentally determined transmissions could be quoted to ±5%. The microdensitometer readings were found to be reproduc-i b l e to i l % . With errors thus established for both the Datex transmission readings and the step f i l t e r transmissions , one could then draw the extreme p o s s i b i l i t i e s that could arise for the "H-D" plo t . For any p a r t i c u l a r l i n e i t was then simple to determine gr a p h i c a l l y how much difference there was between an i n t e n s i t y p r o f i l e taken from one extreme curve and that taken from the other extreme. T y p i c a l l y , systematic errors on the normalised ordinates of p r o f i l e s were -4%. The comparator stage could be driven with an incremental precision of better than i l u. Thus, considering that a l l p r o f i l e s were of the order of 100 u wide, one needed to allow systematic errors only i n the v e r t i c a l d i r e c t i o n on a l i n e p r o f i l e , In turn, these produced uncertainties i n the widths of the standard l i n e s of O.OlA and of 0.02A in the plasma l i n e width. The l a t t e r figure includes an allowance of ± 0 . 0 l A for the uncertainty i n the width of the apparatus p r o f i l e that was deconvolved from the observed to y i e l d the true plasma p r o f i l e . In the t h i r d column of Table I the systematic error of i0.03A has been added to the random error to give the t o t a l error indicated. f- In addition, one expects the aforementioned systematic error i n the p r o f i l e ordinates to produce a spread in the -83-point on a l i n e p r o f i l e which the computer chooses as the l i n e centre. One could locate the standard l i n e peaks to no worse than to.005A and the plasma l i n e peaks to to.OlA. The systematic error i n the distance calculated between the standard and reference l i n e s was ^O.OlA while that between the plasma and reference l i n e s - O.OlA. Hence, the systematic error i n the difference between these two distances , v i z . i n the l i n e s h i f t , was taken as i o . 0 2 A . The uncertainty estimate i n column 6 of Table I contains t h i s estimate of A d . i i ) Random Errors: The spread that was found i n the values of w and d for the four d i f f e r e n t positions of discharge viewing was attributed to random errors i n the experiment. Sources of randomness i n the technique were the i r r e p r o d u c i b i l i t y of the plasma, j i t t e r i n the timing of an exposure, differences i n exposure that led to use of d i s s i m i l a r portions of the H-D r e l a t i o n , and the subjectiveness of the choice by the analyst as to which Voigt p r o f i l e was the best f i t to the observed widths. It would be very d i f f i c u l t to analyse the various c o n t r i -butions to random error. Here we consider the t o t a l random error in general terms. The t o t a l error i n the width i s pro-portional to the width; an approximate figure of l l O % i s evidently s u f f i c i e n t to describe the t o t a l accuracy. The proportionality i s reasonable because the gentler the slope of a l i n e p r o f i l e , the greater the spread in possible abscissae - 8 4 -that could be read for a given ordinate. S i m i l a r l y , random processes tended to "smear out" the peak of a l i n e such that the wider a l i n e , the more d i f f i c u l t i t was to decide where the centre lay. The whole technique was such that the absolute s h i f t error varied as the width but the percentage error i n s h i f t , as the shift-to-width r a t i o . Having looked at the values of d, Ad, w, A W , i n Table I, one can conclude that the present experimental method i s useful for measuring s h i f t s of l i n e s whose d/w i s not less than 0 . 1 0 . One became quite aware of the random errors while deconvolving the apparatus p r o f i l e from the observed p r o f i l e s . It was found that the four p r o f i l e s of a plasma l i n e taken from the four positions of the discharge column could have d i f f e r e n t Voigt parameters - some shapes might be close to a true Lorentzian while others would have more Gaussian character. Each l i n e scan was deconvolved according to i t s own apparent Voigt parameters. The average of the unfolded true halfwidths shown in the tables was taken after the complete Voigt analysis of each scan. Also, i t was found in a number of cases that the p r o f i l e was not t r u l y Voigt shaped, eg., the . 8 1 and . 51 widths taken together would characterize a d i f f e r e n t Voigt p r o f i l e than the . 7 1 and . 5 1 widths, say. In such cases, the analyst would average the Voigt parameters to choose a f i t ' intermediate between the extremes suggested by the d i f f e r e n t widths. This averaging introduced more randomness into the f i n a l numbers. - 8 5 -B) The A r i l Measurements The values of the widths in Table I from the present work agree s a t i s f a c t o r i l y with the r e s u l t s of Roberts(1966) and t h i s i s taken as an i n d i c a t i o n of the correctness of using Jalufka and others'(1966) widths to estimate the electron density. In connexion with the A r i l 4132 and A r i l 4933 measurements, i t i s i n t e r e s t i n g to note that Neufeld(1966) estimated the electron density of e s s e n t i a l l y the same plasma by scaling the width of the Ea l i n e . Using Griem's(1964) theory of Hydrogen l i n e broadening, he arrived at n g = 1.98 x 17 -3 10 cm . Neufeld had reservations about the exactness of the figure because of suspected density gradients i n the pulsed-arc. The present work asserts that, on account of the independ-ence of l i n e width on the position of discharge viewed, Abel unfolding i s not necessary for the p r o f i l e s and the H^ width i s a v a l i d check on the values presented here for the pure 17 —3 Argon discharge (here, n g was estimated to be 1.9 x 10 cm ). On the other hand, agreement in widths and s h i f t s of l i n e s from Multiplets 6, 7 or 14 between theory and experiment i s poor, considering either Griem's or other r e s u l t s l i k e those of Roberts(1966) or Cooper and Oertel(1967). These la t e r authors attempt t h e o r e t i c a l improvement i n several ways: allowing the upper l e v e l of inte r e s t to interact with many other l e v e l s , refinement of the estimate of the strong c o l l i s i o n e f f e c t s , i n c l u s i o n of higher order terms than dipole i n the expansion of the perturbation energy, - 8 6 -allowance for perturbation of the lower l e v e l for a t r a n s i t i o n . While i n one or two cases some such modification may bring the theory closer to r e a l i t y , i t appears that i n general i t lacks the comprehensiveness to make predictions for the A r i l widths to better than ^ 5 0 % Unfortunately, no s h i f t c a lculations accompany the aforementioned publications on width, so one cannot c r i t i c i z e the l a t e s t theory i n t h i s respect. Obviously, G r i e m ' s ( 1 9 6 4 ) theory i s inadequate. Interestingly, the "Plasma P o l a r i s a t i o n S h i f t " concept leads to numbers that, at best, are only the same order of magnitude as the observed ones. With the present work, the legitimacy of'using a time-average pote n t i a l to represent correlated shift-producing electrons becomes more suspect( see further the discussion by Cooper, 1 9 6 6 ) . While the formalism, for obscure reasons, f a i l s to come through with the correct numbers, some of the q u a l i t a t i v e predictions are corroborated. In about 6 0 % of a l l the l i n e deconvolutions, the true p r o f i l e r e s u l t i n g was very close to the Lorentzian l i m i t , and i n the remainder i t was closer to the Lorentzian than to the Gaussian. This does indicate that most probably Impact-broadened lines have Lorentzian shapes. The tendency of the plasma conditions and of the timing syn-chronization to be irreproducible, along with the speed of the Kodak IF emulsion , have meant that several l i n e p r o f i l e s with some range of c h a r a c t e r i s t i c s had to be superimposed on a plate for good exposures. Lineshapes thereby suffered -87-d i s t o r t i o n that was not r e a d i l y analyzable. The approach for determining l i n e shape i n t h i s experiment had to be to take a large number (~ 100) of l i n e scans, using only the central parts of p r o f i l e s . This, i n f a c t , leads to the guarded con-clusion above about the shape of the experimental p r o f i l e . This experiment anticipates a better one i n which the quantum e f f i c i e n c y of the l i n e p r o f i l e recorder i s high enough to require only one plasma discharge for adequate information. The e f f i c i e n c y of the spectroscopic device i s indeed the key to checking the l i n e shape: i n order to avoid s e l f absorption, i n e f f e c t one must keep the i n t e n s i t y of the l i g h t emitted by the plasma low. In addition to measuring a r e l a t i v e l y small photon flux , one w i l l want to record the p r o f i l e for as short a time as possible. In the present experi-ment, i t i s acknowledged that vduring the exposure, the i n t e n s i t i e s of the l i n e s change by 1 0 % and that therefore the plasma parameters are s i m i l a r l y transient. Resulting l i n e images, when f i v e records are taken, each an i n t e g r a l over a f i n i t e time and each a l i t t l e d i f f e r e n t in i t s timing, can only be expected to show some variety. A future experiment to record the l i n e p r o f i l e from a discharge l i k e the pulsed-arc requiring an exposure of only, say, 0.5 fisec during one shot should unequivocally e s t a b l i s h the l i n e shape. Current theory predicts that the asymmetry i n l i n e prof-i l e s due to io n i c broadening should be no greater than 1 0 % . The widths found i n t h i s experiment are quoted to t l 0 % , and , -88-i n f a c t , no . s i g n i f i c a n t asymmetry was observed. Except f o r the two l i n e s from a s p e c i a l multiplet,(number 32, to be mentioned s h o r t l y ) i t appears that the common width and s h i f t p r e d i c t i o n f o r a l l members of the same m u l t i p l e t i s s u b s t a n t -i a t e d . T h i s c h a r a c t e r i s t i c i s p r e d i c t e d f o r the dominant e l e c t r o n broadening, not the i o n i c broadening, and a l s o i s e x p e r i m e n t a l l y proven to 110% . Griem(1964) t a b u l a t e s Stark parameters o n l y up to M u l t i p l e t 10, thus i n d i c a t i n g , p o s s i b l y , that the remainder of t h a t spectrum c o u l d not be t r e a t e d with that theory. In our l i s t of l i n e s , there are some t r a n s i t i o n s which d e f i n i t e l y appear to v i o l a t e some of the c o n d i t i o n s g i v e n i n chapter 2, p a r t A ) . I t w i l l be u s e f u l to mention how these l i n e s are d i f f e r e n t , and how t h e i r data may be used to check e n l a r g e - " ments of the theory which c o n s i d e r e f f e c t s not accounted f o r e a r l i e r . M u l t i p l e t 32 i s i n t e r e s t i n g ' , i n our study, i t was r e p r e -sented by the t r a n s i t i o n s : 4132 ( 1 D ) 4 s 2 D 3 / 2 - ( 1 D ) 4 p 2 p J / 2 4278 ( 1 D ) 4 s 2 D 5 / 2 - ( 1 D ) 4 p 2 P ° / 2 The v a l u e s of s h i f t and width given f o r these l i n e s i n Table I are s i g n i f i c a n t l y d i f f e r e n t , as w e l l as being a p p r e c i a b l y l a r g e r than the same q u a n t i t i e s i n nearby-numbered m u l t i p l e t s , n o t a b l y number 31. A r i l 4278 r e p r e s e n t s a t r a n s i t i o n that cannot be t r e a t e d w i t h the I s o l a t e d L i n e assumption.because i t s upper l e v e l i s -89-122 cm away from an even parity l e v e l , ( D)3d D5/2 j l n the unperturbed energy l e v e l system (Minnhagen, 1963). The plasma frequency i n t h i s plasma corresponds to an energy separation of 132 cm ^; since this i s approximately the same as the separation between opposite parity l e v e l s , we may expect the e f f e c t of electron screening of the emitting ions to be important. Thus, a theory to treat the Hydrogenic degen-eracy between the level s ("4) H p^Pg/g and ("*TJ )3d^D5/ 2 i s required. Minnhagen(1947) states that the upper l e v e l of A r i l 4132 1 2 i s strongly repelled by the ( D)3d D3/2 l e v e l which i s only 13 cm * higher in energy. The half halfwidth of A r i l 4132 converted into energy units i s 8 cm while the s h i f t corresponds to minus 6 cm C It therefore appears that the above two in t e r a c t i n g states are overlapping. Standard Stark theory requires that when levels suffer perturbation of the order of their zero-order s p l i t t i n g , one must, i n general, use the l i n e a r theory. Although the approach to overlapping l i n e theory i s outlined by Griem et al.(1962), no such calculations exist for A r i l t r a n s i t i o n s . It i s suggested here that attempt-ing the c a l c u l a t i o n for this one unusual l i n e w i l l be worth-while because a) thi s i s a case where ioni c e f f ects may contribute s i g n i f i c a n t l y to the s h i f t and i s therefore a si t u a t i o n where the understanding of the r e l a t i v e importance of electron and ion processes can be tested, and b) the v a l i d i t y of using LS wave functions (or better ones) can -90-be examined for these mixed states. Neufeld(1966) alludes to the p o s s i b i l i t y of dipole-forbidden l i n e s appearing in the plasma spectrum; such a phenomenon i s another aspect of the same s i t u a t i o n of per-turbed l e v e l s . Mixing of the two preceding strongly i n t e r -1 2 acting le v e l s should cause a forbidden l i n e , ( D)4s D 3 / 2 1 2 ( D)3d D 3 / 2 , to appear at 4129.6A . This figure i s calculated assuming that the (*D )3d%>3/2 l e v e l i s perturbed p o s i t i v e l y — 1 1 2 o by 6.1 era , which i s the decrease i n energy of the ( D)4p Py state implied by the positive s h i f t of the A r i l 4132 l i n e , 1.05A. On the plates taken by the author for the greatest exposure there was a broad l i n e centred at 4128.5A which had no partner of l i k e i n t e n s i t y in the standard spectrum and yet whose i n t e n s i t y did increase with increasing percentage of . I • Argon gas i n the discharge mixture. No d e f i n i t e claims are made here, however, on the i d e n t i f i c a t i o n and measurement of th i s l i n e because of i t s weakness in the present spectra. Again, the advent of a more sensi t i v e p r o f i l e reading tech-nique should f a c i l i t a t e the evaluation of t h i s i n t e r e s t i n g p o s s i b i l i t y . The fact that the "forbidden l i n e " appears weak in the spectra of the present work i s no guarantee that the perturb-ation c a l c u l a t i o n of the Stark e f f e c t s , such as that of Sadjian et al(196'l) or Griem(1964), can be used for this t r a n s i t i o n . It i s estimated that the l i n e at 4128.5A may have 20% of the i n t e n s i t y of the A r i l 4132A l i n e . In t h i s case, -91-i t may be necessary to recalculate the wave functions of the i n t e r f e r i n g states using a strong f i e l d Hamiltonian. If our i d e n t i f i c a t i o n of the l i n e i s correct, then the fact that i t s centre p o s i t i o n i s s i g n i f i c a n t l y d i f f e r e n t from that calculated i n the previous paragraph may be an in d i c a t i o n of the need of a better approach than the perturbation treatment. At any rate, M u l t i p l e t 32 should be very useful as a test case for nonisolated or overlapping levels theory. A r i l 4104 vi o l a t e s the current theory's requirements i n 3 4 o another way: i t s lower l e v e l , ( P)4p D7/2 , does suffer appreciable perturbation. To wit, t h i s state i s the upper l e v e l for the strong l i n e A r i l 4348 in Multiplet 7. The use-fulness of measuring the A r i l 4104 t r a n s i t i o n i s assured because current theory(Cooper and Oertel, 1967) i s s t a r t i n g to take lower state p o l a r i z a b i l i t y into account. In th i s case, 3 4 o the amount of broadening of the ( P)4p l e v e l i s now f a i r l y well known experimentally - the chief l i m i t a t i o n on the accuracy of the figure for A r i l 4348 in Table I i s the ignor-ance of the broadening of the lower l e v e l of that l i n e which, Roberts(1966) says, i s not n e g l i g i b l e . With these data, the theoretician w i l l be able to v e r i f y that his c a l c u l a t i o n for A r i l 4104 c o r r e c t l y adds the broadening and s h i f t i n g of both le v e l s involved i n the t r a n s i t i o n . Figure 13 shows the large widths and s h i f t s of the li n e s i n M ultiplets 32 and 52. The very weak "forbidden" l i n e image i s at a scale reading of 10.53 . -92-C) The N i l Measurements Looking at Table II, one has to conclude that agreement between the d i f f e r e n t experimental r e s u l t s of width, and s h i f t measurement in N i l i s hardly outstanding. It does appear that something went wrong with Day's measurement of the three narrow li n e s NII5045, N i l 4614 and N i l 5496. The disagree-ment between Berg and others'(1967) re s u l t s for widths and the present ones i s small enough to be put down to temperature d i s s i m i l a r i t y . The d i s p a r i t y between those two sets of data and Day's cannot be thus explained. The error estimates given in a l l three experiments seem to be of reasonable s i z e , considering the techniques used, and t h i s argues against poor sampling. It should, be remarked that the widths of the f i r s t three l i n e s i n Table II stand i n the same r a t i o among themselves i n Day's work as i n the present and t h i s suggests that his electron density c a l i b r a t i o n , done by scaling the halfwidth of the Hel 3889 l i n e , may be in error. For instance, i n si m i l a r T-tube plasmas (eg. James, 1965), i t has been found that Hel 3889 i s not dependable for l i n e p r o f i l e measurements because of a f a i r l y bright impurity l i n e , CIII 3889, i n i t s blue wing. Day also voices d i s s a t i s f a c t i o n with the use of the Hel 3889 p r o f i l e as a density probe because the Stark parameters are not well known from experiment. On the other hand, the n e estimate i n the present work, which was done by -93-comparing measured A r i l widths with other experimental r e s u l t s , i s defended as r e a l i s t i c because the present widths check out with scaled widths from independent work on A r i l by Roberts(1966), who used a laser - interferometer technique for the n e determination, and from work on N i l by Berg et a l (1967), who estimated n g from the width of a Hel l i n e . The widths of the l a s t three l i n e s in Table II show agreement between Berg and others' work and the present. While l i t t l e can be said about the values i n columns 4 and 6 for a l l six t r a n s i t i o n s , Griem's(1966) t h e o r e t i c a l estimates in column 6 give l i t t l e assurance that the broadening processes are well understood when compared with the numbers in columns 3 and 5. For the l a s t three t r a n s i t i o n s i n the table, the experi-mental shift-to-width r a t i o s do a l l agree, even though the percentage error in these quantities i s very large. The d i f f e r e n t authors' work together puts l i m i t s on the r a t i o s which leads to the useful information that the shift-to-width value i s no larger than a comparatively small(~0.01) number. This i s i n contrast with the A r i l character where broad l i n e s also have big s h i f t s . Here too, the three sets of d/w values remind one that, no matter what the technique, the wider the l i n e the more d i f f i c u l t i t i s to decide where i t s centre i s , and thus the greater the uncertainty in the measured s h i f t . -94-Dj Conclusion Some l i n e s i n the A r i l and N i l spectra emitted by a dense plasma have been measured for width and s h i f t using a photographic technique. It has been found that the width r e s u l t s agree well with those from some other experiments, and that there remains at least a 20% discrepancy between these and t h e o r e t i c a l values. The work i s one of the f i r s t i n extensive A r i l s h i f t measurement and, as such, has l i t t l e a v a ilable for comparison i n other experiment. The A r i l and N i l s h i f t theories seem to be t o t a l l y inadequate. The width measuring technique i s s u f f i c i e n t l y accurate i n the l i g h t of the present quantitative theory. The next step i n researching Stark p r o f i l e s should involve a device to accurately measure the l i n e p r o f i l e and peremptorily establish i t s shape. In the current c a l c u l a t i o n s , the electron impacts give the Lorentzian shape to the centre of the l i n e p r o f i l e while the far wings characterize the io n i c broadening. But the demarcation between the extremities i s not sharp, and the question of how to calculate the i n t e n s i t y p r o f i l e for the intermediate frequencies should now be regarded by theoretic-ians as an important one. So then, an experimental determination of the precise form of I(u) which c o r r e c t l y contains even the f a r wings w i l l be a great boon in testing the understanding of the r e l a t i v e importances of the d i f f e r e n t perturbations. It i s possible that the N i l widths produced by Day(I965) - 9 5 -s u f f e r from a poor n e c a l i b r a t i o n . His shift-to-width r a t i o s , however, should have no such troubles since t h i s quantity ought to depend only on the plasma temperature. Certainly, on the plates measured by the present author, l i n e s with a d/w of the order of 1 stood out rather spectacularly - one needed merely to examine the plates by eye to appreciate them. None of the thre narrow N i l l i n e s i n the group studied were seen to thus d i s t i n g u i s h themselves. Herein we see the great convenience i n the technique of putting the standard and plasma spectra side by side on the same plate; our i d e n t i f i c -ation of the plasma l i n e was quickly determined from the i d e n t i f i c a t i o n of the standard l i n e beside i t . The approximate siz e of the d/w value to be expected was noted at the same time. Monochromator - photomultiplier systems do not normally allow of these safety features. Technologically, the measurement of s h i f t seems to have advanced to s a t i s f a c t o r y state with t h i s work, considering the state of the theory. One can determine s h i f t s even more e a s i l y than in the present method i f one does not need to read widths from the photographic records, because then time need not be spent i n making sure that the plasma i s o p t i c a l l y thin and that the photographic technique i s c o r r e c t l y used, as i n the measurement of l i n e p r o f i l e s . Thus, the comparatively easy method of using s h i f t s rather than widths for gauging electron density commends i t s e l f to the experimentalist. - 9 6 -In summary, the experiment has been successful i n quanti t a t i v e measurements. Hopefully, i t w i l l not be too long before theoreticians are inspired to improve at least the N i l and A r i l c a l c u l a t i o n s . It would be i n t e r e s t i n g to see the problems of Debye shielding(nonisolated line s ) and of overlapping and forbidden l i n e s i n these spectra attended to. The general understanding of three body physics, as required in the treatment of the above sit u a t i o n s , w i l l prosper, i t i s hoped, by the measurements submitted herewith. -97-BIBLIOGRAPHY Baranger, M. (1962), i n "Atomic and Molecular Processes" ( D. R. Bates, ed. ), 493 ( New York; Academic Press-). Bates, D. R., and Damgaard, A. (1950), P h i l . Trans. Roy. Soc. A242, 101. Berg, H. F., Ervens, W., and Furch, B. (1967), Z. Physik 206, 309. Breene, R. G. (1961), "The S h i f t and Shape of Spectral Lines" (New York; Pergamon Press). Burgess, D. D., and Cooper, J. (1965a), Proc. Phys. Soc. 85, 1261. Burgess, D. D., and Cooper, J. (1965b), J. S c i . Instr. £2, 829. Condon, E. U., and Shortley, G. H. (1935), "The Theory of Atomic Spectra" (London; Cambridge University Press). Cooper, J. (1966), Rep. Prog. Phys. 29, 35. Cooper, J., and Oertel, G. K. (1967), Phys. Rev. Letters 18, ' 985. Day, R. A., (1965), Ph.D. Thesis, University of Maryland. Durand, J. (1963), Z. Naturforsch. 18a, 281. E r f l e , H. (1924), i n "Grundzuge der Theorie der Optischen Instrumente" ( Czapski and Epstein, ed. ), 320 ( Leipzig; Barth ). Eriksson, K. B. S. (1958), Ark. Fys. 13_, 303. Griem, H. R. (1964), "Plasma Spectroscopy" ( New York; McGraw H i l l ). Griem, H. R. (1966), Phys. Rev. Letters 17, 509. Griem, H. R., Baranger, M., Kolb, A. C., and Oertel, G. (1962), Phys. Rev. 125, 177. H e i t l e r , W. (1954), "The Quantum Theory of Radiation" ( London; Oxford University Press ). -98-Jalufka, N. W., Oertel, G. K., a n d O f e l t , G. S. (1966), Phys. Rev. Letters 16, 1073. James, H. G. (1965), M.Sc. Thesis, University of B r i t i s h Columbia. Kodak (1962), "Kodak Plates and Films for Science and i Industry" Kodak publication P-9 ( Rochester; Eastman Kodak.)-. Margenau, H., and Lewis, M. (1959), Rev. Mod. Phys. 31, 569. Mees, C. E. K., and James, T. H. (1966), "The.Theory of the Photographic Process" ( New York; Macmillan ). Minnhagen, L. (1947), Ark. Mat. Ast. Fys. 35A, No.16 . Minnhagen, L. (1963), Ark. Fys. 25, 203. Minnhagen, L. (1964), J. Res. of N.B.S. 68C, 337. Moore, C. E. (1959), "A Multiplet Table of Astrophysical Interest" N.B.S. Tech. Note 36. Neufeld, C. R. (1966), Ph.D. Thesis, University of B r i t i s h Columbia. Olsen, H. N. (1963), J. Quant. Spectr. Rad. Transfer 3, 59. Popenoe, C. H., and Shumaker, J. B. j r . (1965), J. Res. of N.B.S. 69A, 495. Roberts, D. E. (1966), Phys. Letters 22, 417. Sadjian, H., Wimmel, H. K., and Margenau, H. (1962), J, Quant. Spectr. Rad. Transfer ]., 46. Theophanis., G. A. (1960), Rev. S c i . Instr. 33., 427. Tompkins, F. S., and Fred, M. (1951), J. Opt. Soc. Am. 41, 641. Traving, G. (1960), "Uber die Theorie der Druckverbreiterung von S p e k t r a l l i n i e n " ( Karlsruhe; G. Braun .) . Van de Hulst, H. C , and Reesinck, J. J. M. (1947), Astrophys. J. 106, 121. Unsold. A. (1938), "Physik der Sternatmospharen" ( B e r l i n ; Springer ). Wiese, W. L. (1965), i n "Plasma Diagnostic Techniques" ( Huddlestone and Leonard, ed. ), 265 (New York;Academic Press). 

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