The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of JOHN CHARLES IRWIN B.A.Sc., • Un i v e r s i t y of B r i t i s h Columbia, 1958 MONDAY, SEPTEMBER 27, 1965 AT 2:00 P.M. IN ROOM 303, HENNINGS BUILDING (PHYSICS) COMMITTE IN CHARGE Chairman: B. N. Moyls A. J. Barnard R. D. Russell A. M. Crooker J. Williamson R. A. Nodwell L. Young External Examiner: W. Lochte-Holtgreven Univ e r s i t y of K i e l K i e l , Germany RELATIVE POPULATION DENSITIES AND TRANSITION PROBABILITIES IN A NEON GLOW DISCHARGE ABSTRACT An experimental technique has been developed for the i n v e s t i g a t i o n of departures from thermodynamic equilibrium conditions i n plasmas, The r e l a t i v e populations of the upper and lower le v e l s of a s p e c t r a l l i n e are measured by the rever s a l temperature method. The reversal temperatures themselves are determined by varying the r e l a t i v e exposure times of the background source and the plasma to be investigated. The r e l a t i v e population densities of the levels i n the 2p-*3s and 2p%p configurations of Nel have been measured. A neon glow discharge operated i n the current region 1mA to 100mA served as the plasma. The re s u l t s show that the excited gas i s d e f i n i t e l y not i n thermodynamic equilibrium. The r e l a t i v e i n t e n s i t i e s dfvthe emission li n e s between the 2p^3s and 2p^3p configurations of Nel were measured photometrically and corrected for s e l f -absorption. These i n t e n s i t i e s were then used i n conjunction with the r e l a t i v e population de n s i t i e s to determine r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s f o r the s p e c t r a l lines concerned. The r e s u l t s are accurate to approximately 10% to 15% and are compared to the values obtained previously by other workers. GRADUATE STUDIES F i e l d of Study: Plasma Physics Elementary Quantum.Mechanics Electromagnetic Theory Spectroscopy Plasma Physics Waves F. A. Kaempffer G.M. Volkoff A. M. Crooker L,. de Sobrino and F. L. Curzon R. W. Stewart Related Studies: Electron Dynamics D i f f e r e n t i a l Equations G. B, Walker C. A. Swanson PUBLICATIONS 1. A method of Determining the Reversal Temperatures i n an Excited Gas. R.A. Nodwell and J.C. Irwin. Canadian Journal of Physics 43, 1182 (1965) 2. A High Temperature Pulsed Light Source. R.A. Nodwell and J.C. Irwin. Reviews of S c i e n t i f i c Instruments, August, 1965 RELATIVE POPULATION DENSITIES AND TRANSITION PROBABILITIES IN A NEON GLOW DISCHARGE by JOHN CHARLES IRWIN B.A.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1958 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Ph. D. i n the Department of P h y s i c s We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1965 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 t h e r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r -m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s . . It. 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 The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT An experimental technique has been developed f o r the i n v e s t i g a t i o n of departures from thermodynamic e q u i l i b r i u m i n plasmas. The r e l a t i v e p o p u l a t i o n s of the upper and lower l e v e l s o f a s p e c t r a l l i n e are measured by the r e v e r s a l temperature method. The r e v e r s a l temperatures themselves are determined by v a r y i n g the r e l a t i v e exposure times of the background source and the plasma to be i n v e s t i g a t e d . The r e l a t i v e p o p u l a t i o n d e n s i t i e s of the l e v e l s i n the 2p^3s and 2p3>3p c o n f i g u r a t i o n s of Nel have been measured. A Neon glow d i s c h a r g e operated i n the c u r r e n t r e g i o n 1mA t o 100mA served as the plasma. The r e s u l t s show t h a t the e x c i t e d gas i s d e f i n i t e l y not i n thermal e q u i l i b r i u m . The r e l a t i v e i n t e n s i t i e s of the e m i s s i o n l i n e s between the 2p^3s and 2p^3p c o n f i g u r a t i o n s of N e l were measured p h o t o m e t r i c a l l y and c o r r e c t e d f o r s e l f -a b s o r p t i o n . These i n t e n s i t i e s were then used i n c o n j u n c t i o n w i t h the r e l a t i v e p o p u l a t i o n d e n s i t i e s to determine r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s f o r the s p e c t r a l l i n e s concerned. The r e s u l t s are accurate t o approximately 10% t o 1%% and are compared to the values obtained p r e v i o u s l y by other workers. i i i TABLE OP CONTENTS PAGE A b s t r a c t . . i i Table o f Contents . i i i Index o f Tables v Index o f F i g u r e s v i Acknowledgments v i i CHAPTER I . INTRODUCTION . 1 I I . THEORY 5 1. R e v e r s a l Temperatures. . . . . . . . . . . 5 2. R e l a t i v e E m i s s i o n Line I n t e n s i t i e s . . . . 10 I I I . EXPERIMENTAL APPARATUS 11+ 1. Background L i g h t Source lb, 2. O p t i c s 22 3. A b s o r p t i o n Tubes 21+ 1+. Photometric Equipment 26 5>. E l e c t r o n i c Equipment • . . . . . 28 IV. MEASUREMENT OF REVERSAL TEMPERATURES 30 1. Exp e r i m e n t a l Procedure 30 2. Exp e r i m e n t a l R e s u l t s 31+ 3. Departures from Thermodynamic E q u i l i b r i u m . 36 V. RELATIVE LINE INTENSITY MEASUREMENTS 1+1 1. S e l f - A b s o r p t i o n C o r r e c t i o n s 1+1 2. Measurement of the Doppler Half-Widths . . 1+3 i v TABLE OP CONTENTS (cont'd) CHAPTER PAGE V. (cont'd) 3. R e l a t i v e E m i s s i o n Line I n t e n s i t i e s . . . . l\.9 li. R e l a t i v e T r a n s i t i o n P r o b a b i l i t i e s . . . . . 52 V I . DISCUSSION AND CONCLUSIONS 55 1. R e v e r s a l Temperature Measurements 55 2. Neon T r a n s i t i o n P r o b a b i l i t i e s 57 3. Con c l u d i n g Remarks . . 62 APPENDIX I. BRIGHTNESS TEMPERATURES 63 I I . PHOTOGRAPHIC PHOTOMETRY 65 I I I . SELF ABSORPTION FACTOR S AND CURVE OF GROWTH. 67 IV. THE FABRYX-PEROT INTERFEROMETER. . . . . . . . 69 V. SPECTRAL LINE SHAPE . 73 V I . RECIPROCAL DISPERSION OF LITTROW AND EBERT SPECTROGRAPHS IN A/mm 7l\. BIBLIOGRAPHY 75 V INDEX OP TABLES NO. PAGE 1. Relative Population Densities (N U / N L xlO^) for Currents from 1mA to 100mA . . . . . . . . 35 2. Reversal Temperatures i n °K for Currents from 1mA to 100mA. . 37 3. Comparison of the Relative Population Densities Obtained Experimentally with Those Calculated from a Boltzmann D i s t r i b u t i o n . 38 3a. Relative Populations of the p-Levels at 1mA. . 39 lo.. Total Absorption WA and Wv , Doppler Half-Width4V D, and Self-Absorption Correction S. . 5. Apparatus Half-Width A A, Observed Half-Width A e, Doppler Half-Width ~VD, and Temperature T. I4.8 6. Measured and "True" Relative I n t e n s i t i e s . . . 5 l 7. Relative and Absolute Neon Tra n s i t i o n P r o b a b i l i t i e s , O s c i l l a t o r Strengths f , and Line Strengths S. . 5U-8. Comparison of the Neon T r a n s i t i o n P r o b a b i l i t i e s with Values Obtained by Doherty, P r i e d r i c h s , and Ladenburg 58 9. Line Strengths i n LS Coupling 6 l 10. Experimental Line Strengths . 6 l 11. S e l f Absorption Factor S and Product k 0 l S for k 0 l _v 1000 67 v i INDEX OP FIGURES NO. PAGE 1* Arrangement of Source and Plasma . * 6 2. Schematic Drawing of the Experimental Apparatus. 15 3« A G r o s s - S e c t i o n a l Drawing of the C y l i n d r i c a l C a p a c i t o r and Mounted Spark Gap 17 la.. The B r i g h t n e s s Temperature of the Background Source versus Wavelength at three V o l t a g e s . . . 21 5. A b s o r p t i o n Tubes • . 25 6. A P o r t i o n of a T y p i c a l P l a t e Showing a few Lines i n A b s o r p t i o n , E m i s s i o n , and near R e v e r s a l . . . 31 7. Example of P l o t f o r the D e t e r m i n a t i o n o f t p / t s at R e v e r s a l 33 8. P a r t i a l Term Diagram of N e l 1+0 9. The C h a r a c t e r i s t i c Curve 66 10. Curve of Growth f o r Pure Doppler Broadening... . 68 11. S p e c t r a l Line (I) and Apparatus ( II) P r o f i l e s . . 70 12. Curve f o r the D e t e r m i n a t i o n of the Doppler Half-Width 72 v i i ACKNOWLEDGMENTS I would l i k e t o thank Dr R. A. Nodwell f o r h i s guidance and a s s i s t a n c e to me i n t h i s work; thanks a l s o t o the other members of the plasma p h y s i c s group, f a c u l t y and students, f o r many h e l p f u l s u g g e s t i o n s . F i n a n c i a l a s s i s t a n c e i n the form of a N a t i o n a l Research C o u n c i l Studentship i s g r a t e f u l l y acknowledged. CHAPTER I INTRODUCTION T h i s t h e s i s d e s c r i b e s an experimental technique developed f o r the q u a n t i t a t i v e i n v e s t i g a t i o n o f thermo-dynamic e q u i l i b r i u m c o n d i t i o n s i n a plasma. The experiment e n t a i l s the o b s e r v a t i o n o f the a b s o r p t i o n spectrum of a s t r o n g l y e x c i t e d gas w i t h the subsequent d e t e r m i n a t i o n of the r e v e r s a l temperatures o f i n d i v i d u a l s p e c t r a l l i n e s and the measurement of the r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s of t r a n s i t i o n s between h i g h l y e x c i t e d energy l e v e l s . The r e l a t i v e p o p u l a t i o n d e n s i t i e s of the v a r i o u s energy l e v e l s can be found d i r e c t l y from the r e v e r s a l temperatures and compared w i t h those obtained from a Boltzmann d i s t r i b u t i o n . Garton and Rajaratnam (1957) have used a m o d i f i c a t i o n of the r e v e r s a l temperature method f o r the i n v e s t i g a t i o n o f some a r c plasmas. T h e i r method however, y i e l d s only an average or e f f e c t i v e temperature f o r the plasma and does not pro v i d e q u a n t i t a t i v e i n f o r m a t i o n c o n c e r n i n g the r e l a t i v e p o p u l a t i o n d e n s i t i e s of the energy l e v e l s when the plasma i s not i n thermodynamic e q u i l i b r i u m . The l i n e r e v e r s a l method has been w i d e l y used f o r the d e t e r m i n a t i o n o f temperatures i n flames, i n which c o n n e c t i o n the l i t e r a t u r e has been summarized by B r o i d a (1955), and Gaydon and Wolfhard (1953) • The procedure used i n these experiments c o n s i s t s of v a r y i n g the i n t e n s i t y o f a back--2 ground l i g h t source u n t i l i t equals that of a s p e c t r a l l i n e emitted by the flame, t h a t i s u n t i l r e v e r s a l of the s p e c t r a l l i n e i s o b t a i n e d . The e x t e n s i o n of t h i s method t o the hig h e r temperature r e g i o n s c h a r a c t e r i s i n g plasmas i n v o l v e s many problems, most, of which a r i s e from the requirement of a s u i t a b l e h i g h temperature l i g h t s o u rce. The l i g h t source chosen f o r t h i s experiment i s of the pulsed d i s -charge v a r i e t y and p r o v i d e s an e f f e c t i v e temperature of approximately 30000°K« I t was chosen f o r ease of o p e r a t i o n , high b r i g h t n e s s temperature, and the e x c e l l e n t continuous spectrum which i t a f f o r d e d . Lochte-Holtgreven (1958) and Vanyukov and Mak (1958) have summarized the v a r i o u s advant-ages and b r i g h t n e s s temperatures t o be expected from the d i f f e r e n t types o f high temperature l i g h t s o u r c e s . To avoid a l a b o r i o u s c a l i b r a t i o n of the l i g h t source and to enable us to compare two l i g h t sources whose i n t e n s -i t i e s d i f f e r by a l a r g e amount an experimental procedure w a s adopted which was more advantageous to our c o n d i t i o n s than t h a t used i n the flame temperature d e t e r m i n a t i o n s . In t h i s experiment r e v e r s a l i s obtained by v a r y i n g the r e l a t i v e exposure times o f the two s o u r c e s . Photographic photometry i s used throughout, a l l o w i n g s e v e r a l s p e c t r a l l i n e s to be analysed from a s i n g l e p l a t e . Under e q u i l i b -r ium c o n d i t i o n s each l i n e would have the same r e v e r s a l temperature and only one l i n e would have to be analysed to o b t a i n the temperature of the e x c i t e d gas. Under the -3-c o n d i t i o n s e x i s t i n g i n many di s c h a r g e s however, the r e v e r s a l temperatures of the v a r i o u s l i n e s are d i f f e r e n t and t h e i r d i f f e r e n c e s a l l o w a q u a n t i t a t i v e comparison w i t h a Boltzmann d i s t r i b u t i o n . The methods used f o r the r e d u c t i o n of the data are d e s c r i b e d i n d e t a i l i n the f i r s t s e c t i o n of Chapter I I • The r e l a t i v e p o p u l a t i o n d e n s i t i e s obtained from the above measurements can be used i n c o n j u n c t i o n w i t h r e l a t i v e e m i s s i o n l i n e i n t e n s i t y measurements to deduce r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s , u s i n g E i n s t e i n ' s formula f o r the e m i s s i o n i n t e n s i t y of a s p e c t r a l l i n e . The measured i n t e n s -i t i e s must be c o r r e c t e d f o r s e l f a b s o r p t i o n however, i n the event that the e m i t t i n g l a y e r i s not o p t i c a l l y t h i n . T o t a l a b s o r p t i o n measurements p r o v i d e an estimate of the o p t i c a l t h i c k n e s s of the e m i t t i n g l a y e r and are used t o determine c o r r e c t i o n f a c t o r s f o r the measured em i s s i o n i n t e n s i t i e s . T h i s procedure i s f u l l y d e s c r i b e d i n the second s e c t i o n of Chapter I I . The experimental arrangement i s d e s c r i b e d i n d e t a i l i n Chapter I I I and the v a r i o u s components d i s c u s s e d i n d i v -i d u a l l y . The h i g h temperature l i g h t source p r o v i d e s a main p u l s e of r a d i a t i o n approximately 2r^sec l o n g , which i s i s o l a t e d by a Kerr C e l l s h u t t e r . The K e r r C e l l i s a l s o used to c o n t r o l the r e l a t i v e exposure times of the two l i g h t sources and e l e c t r o n i c c i r c u i t r y i s p r o v i d e d f o r s y n c h r o n i s a t i o n and c o u n t i n g o f the s h u t t e r openings. The r e l a t i v e population densities and reversal temp-eratures obtained from measurements performed on a Neon Glow discharge are l i s t e d i n Chapter IV. The measurements were made on the t r a n s i t i o n s a r i s i n g between the 2p^3s and 2p%P configurations of Nel. The results show that the discharge i s far from thermodynamic equilibrium and are i n q u a l i t a t i v e agreement with those of Ladenburg (1933)« The methods used for the r e l a t i v e i n t e n s i t y measurements and their corrections are described i n Chapter V. The r e s u l t i n g corrected i n t e n s i t i e s and t r a n s i t i o n p r o b a b i l i t i e s are tabulated and the t r a n s i t i o n p r o b a b i l i t i e s are compared to those obtained by Ladenburg (1933), Doherty (1961), and Priedrichs (1961+) . A q u a l i t a t i v e discussion of the deviations from thermodynamic equilibrium found i n the glow discharge i s given i n the f i r s t section of the f i n a l chapter. The second section of t h i s chapter considers the accuracy of the values obtained for the t r a n s i t i o n p r o b a b i l i t i e s and the advantages and disadvantages of the general experimental technique. Suggestions for further work are presented at the end of each section of the chapter. CHAPTER 11 THEORY 2-1 REVERSAL TEMPERATURES Consider t h a t the l i g h t from a source g i v i n g a continuous spectrum i s passed through an e x c i t e d gas whose atoms are e m i t t i n g s p e c t r a l l i n e s . I t i s assumed tempor-a r i l y t h a t the e x c i t e d gas ( h e r e a f t e r r e f e r r e d t o as the plasma) i s i n thermodynamic e q u i l i b r i u m and that a temper-a t u r e can-be d e f i n e d at each wavelength f o r the r a d i a t i o n emitted by the background source ( h e r e a f t e r r e f e r r e d t o as the s o u r c e ) . The r e s u l t i n g spectrum w i l l show the s p e c t r a l l i n e s i n a b s o r p t i o n or em i s s i o n depending on the r e l a t i v e temperatures o f the two sources o f l i g h t . I f the two sources have equal temperatures" the s p e c t r a l l i n e s w i l l not appear, as much l i g h t having been added t o the continuous spectrum as was absorbed. Thus i f we were t o c o n t i n u o u s l y i n c r e a s e the temperature of the source, from a value l e s s t h an that o f the plasma, the s p e c t r a l l i n e s would f i r s t ap-pear i n e m i s s i o n , then disappear and f i n a l l y they would appear as a b s o r p t i o n l i n e s i n the continuous background. The s p e c t r a l l i n e s are thus s a i d t o " r e v e r s e " and the source temperature at which they r e v e r s e i s d e f i n e d as the r e v e r s a l temperature. I f the e x c i t e d gas i s not i n thermodynamic e q u i l i b r i u m i t can no longer be c h a r a c t e r i s e d by a s i n g l e temperature. To develop q u a n t i t a t i v e r e l a t i o n s f o r t h i s case we w i l l t r e a t each s p e c t r a l l i n e i n d i v i d u a l l y * Consider a column -6-of e x c i t e d gas o r i e n t a t e d i n the x - d i r e c t i o n ( f i g u r e 1 ) • Source F i g u r e 1 - Arrangement of Source and Plasma Suppose there are N L atoms/cm 3 i n the lower l e v e l L of which tjN L are capable of a b s o r b i n g the frequency range between v and V + dv and J M atoms/cm? i n the upper s t a t e u o f which iN-^ are capable of e m i t t i n g over the same f r e -quency range. Let the s p e c i f i c i n t e n s i t y of a p a r a l l e l beam of l i g h t t r a v e l l i n g i n the x - d i r e c t i o n be I v ( x ) and suppose t h a t i t encompasses the frequency range V, V-t-dv/. The change i n i n t e n s i t y i n p a s s i n g through the l a y e r dx w i l l be ( M i t c h e l l and Zemansky 1961) ( i ) where A U L , B M L and B L^ are the E i n s t e i n t r a n s i t i o n probab-i l i t i e s f o r spontaneous e m i s s i o n , s t i m u l a t e d e m i s s i o n and a b s o r p t i o n r e s p e c t i v e l y . I v(x)/L^TT i s the i n t e n s i t y of the e q u i v a l e n t i s o t r o p i c r a d i a t i o n f o r which B V L and B L 1 J l are d e f i n e d • A. — H -"' t *— dx — — — 1 _ . X »• / -7-Now and i f one d e f i n e s the l i n e a b s o r p t i o n c o e f f i c i e n t e q u a t i o n (1) reduces to \ °VL/ (SNL &LH _ /) I f one now makes use of E i n s t e i n ' s r e l a t i o n s between the t r a n s i t i o n p r o b a b i l i t i e s _ r-\uL ~ c z D l l L where g u , g-^  are the s t a t i s t i c a l weights of the l e v e l s u, L = & fu<fML _ t - X,fr>). (ia) The r e v e r s a l temperature T R i s d e f i n e d by f <*p(rrj - ' 3 ) and the e f f e c t i v e e m i s s i o n i n t e n s i t y of a s p e c t r a l l i n e by -8-Upon substituting equations (3) and (I4.) into (la) we arrive at the f a m i l i a r equation of radi a t i v e transfer: I f the i n t e n s i t y of the source i s By(S), that i s IM = BJS) -3 / where S i s the brightness temperature of the source, and i f N u = / c^ N^ ctV and = J &NLdv are constant over the length -V//7C3 -'line of the tube, equation (5>) can be integrated over the length of the tube and yiel d s for the resultant energy incident on the spectrograph per unit time i n the frequency i n t e r v a l dv I f S = Tj-, t h i s reduces to the energy due to the source alone, B v(S ) c i V , and the spectral l i n e does not appear. This s i t u a t i o n corresponds to the occurence of r e v e r s a l . S i m i l a r i l y i f B V(S) = 0, s i g n i f y i n g the absence of an external source, the energy a r r i v i n g at the spectrograph per unit time from the plasma alone w i l l be where the factor ( 1 - exp represents the amount of s e l f absorption. - 9 -In t h i s experiment the reversal temperature i s obtained by varying the r e l a t i v e exposure times of the two sources. If the plasma and background source are exposed together for a time t a and the plasma alone i s exposed for an addit-i o n a l time tp - t a the t o t a l energy incident on the spectrographs plate w i l l be £> = CBv(S)exp(-K{)i«^ + C B&)0 - e*pt-&l))tF dv where C i s a constant depending on the geometry used. I f this energy i s subtracted from and normalised to that due to' the continuous source alone and i f the r e s u l t i s integrated over the l i n e we obtain T he integrals \A^= T ( i - e x p ( - - U ) j ^ ( 6 ) me are the t o t a l absorption as defined by Ladenburg and Reiche (1913). The i n t e g r a l on the l e f t i s of course the area under the r e s u l t i n g emission or absorption l i n e , normalised to the continuum i n t e n s i t y . Thus we have i n f i n a l form -10-I f the r a t i o t A A i s v a r i e d u n t i l the i n t e g r a l on the l e f t v a n i s h e s , t h a t i s u n t i l r e v e r s a l i s obtained, B ^ T J J ) i s determined by e q u a t i o n (7)« The r e v e r s a l temperature and the r e l a t i v e p o p u l a t i o n d e n s i t y N u/N L may then be found from the d e f i n i t i o n s (3) and .(ij.) . 2-2 RELATIVE EMISSION LINE INTENSITIES A c c o r d i n g t o the E i n s t e i n t h e o r y of r a d i a t i o n - t h e power emitted per s t e r a d i a n by the process of spontaneous e m i s s i o n i s p r o p o r t i o n a l t o where 1 i s the t h i c k n e s s of the e m i t t i n g l a y e r and V 0 i s the frequency at the centre of the l i n e . T h i s i n t e n s i t y w i l l be observed o n l y when th e r e i s no r e a b s o r p t i o n of the emitted photons however, t h a t i s only when the e m i t t i n g l a y e r i s o p t i c a l l y t h i n . As we have seen i n the f i r s t s e c t i o n the s p e c t r a l l i n e i n t e n s i t y emitted by an o p t i c a l l y t h i c k l a y e r can be r e p r e s e n t e d by Thus we must evaluate the t o t a l a b s o r p t i o n (equation (6)) i f we wish t o compare t h i s i n t e n s i t y t o t h a t emitted by an o p t i c a l l y t h i n l a y e r . Ladenburg and Levy (1930) ' have shown that i n d i s c h a r g e s i d e n t i c a l t o t h a t used i n t h i s experiment the shape o f the a b s o r p t i o n c o e f f i c i e n t i s i s determined almost e n t i r e l y by the Doppler e f f e c t . As I l -l s w e l l known the a b s o r p t i o n c o e f f i c i e n t can In t h i s case be r e p r e s e n t e d by ( M i t c h e l l and Zemansky 1961) i = **r-(^&tf (10) where i f we n e g l e c t s t i m u l a t e d e m i s s i o n N° A\>Q¥ -rr ,mc I^ULM i s the a b s o r p t i o n c o e f f i c i e n t at the centre of the l i n e i s the Doppler h a l f w i d t h of the l i n e . I f (10) i s s u b s t i t -u t e d i n t o (9) the i n t e g r a l can be evaluated by f i r s t expanding the e x p o n e n t i a l i n a s e r i e s ( f o r k 0 l < 3 ) and then i n t e g r a t i n g term by term, the r e s u l t i s W, = [(' - **pt-*>ty*= ^ A/du S-i (11) where (Ladenburg and Levy 1930) C _ / 7 _ l < J + ( K j f . .) ~> ' (..' z'.Yz ^ 3/V3 / F o r k 0 l > 3 j S must be evaluated by i n t e g r a t i n g (9) n u m e r i c a l l y . I f the w e l l known r e l a t i o n between the o s c i l l a t o r s t r e n g t h and the t r a n s i t i o n p r o b a b i l i t y A*L~ cfc " " ^ c T t i U ( 1 2 ) i s s u b s t i t u t e d i n t o e q u a t i o n ( l l ) the r e s u l t i s -12-\r-e,pl-Kj))dv, &£uKA*SJt ,13, yh/>e T I f stimulated emission i s neglected and equation (9) f i n a l l y reduces to W [NM AML n 4)5 Comparing. (14):, and;i^f) we see that the observed i n t e n s i t y must be divided by the factor S to obtain the i n t e n s i t y equivalent to that emitted by an o p t i c a l l y t h i n l a y e r . We s h a l l hereafter r e f e r to the l a t t e r as the true i n t e n s i t y . The formulae for the t o t a l absorption w i l l also be summarized at t h i s p o i n t . In the oase of an o p t i c a l l y t h i n emitting layer (kQ.1^1, S = 1 ) we have from (11) Wv = ZgNLfL*X (15) and for an emitting layer with intermediate o p t i c a l thickness ( l ~ k o 1 ^ 1 0 0 0 ) where S must be evaluated i n the manner described above, that i s by numerical integration when k 0 l > 3 • -13-The c o r r e c t i o n f a c t o r S t o be used w i t h the observed e m i s s i o n i n t e n s i t i e s i s determined i n the f o l l o w i n g manner: I f b o t h s i d e s of equation (16) are m u l t i p l i e d by the f a c t o r >$*2j>7fA\/[> a n d t l l e d e f i n i t i o n o f k Q i s used we can w r i t e (17) Thus i f the Doppler h a l f w i d t h of the s p e c t r a l l i n e Is measured w i t h a Pabry-Perot i n t e r f e r o m e t e r and the t o t a l a b s o r p t i o n i s obtained from the r e v e r s a l temperature measurements f o r the e m i t t i n g l a y e r concerned, the f a c t o r S k 0 l i s determined. S may then be obtained from the t a b l e s of Ladenburg and Levy (1930) where the values o f S and S k 0 l have been t a b u l a t e d f o r .10 < kol_-.1000 . T h e i r t a b l e i s reproduced i n Appendix 3* The t r u e i n t e n s i t i e s may then be used i n c o n j u n c t i o n w i t h the r e l a t i v e p o p u l a t i o n d e n s i t i e s determined by the r e v e r s a l temperature measurements to o b t a i n r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s f o r the l i n e s concerned. -ILL-CHAPTER I I I EXPERIMENTAL APPARATUS The experimental i n v e s t i g a t i o n of plasmas by the r e v e r s a l temperature method n e c e s s i t a t e s the use of a high temperature background l i g h t s o u r c e . To o b t a i n l i g h t sources w i t h b r i g h t n e s s temperatures, greater than 20000°K i t i s convenient t o use some form o f impulsive d i s c h a r g e . That i s the l i g h t source w i l l l a s t f o r o n l y a b r i e f time, u s u a l l y of the order of m i c r o s e c o n d s . i f modest energy s u p p l i e s are u s e d . T h i s b r i e f l i f e t i m e however, imposes a f u r t h e r requirement on the experimental apparatus i n t h a t a v e r y high speed s h u t t e r i s r e q u i r e d when the plasma t o be i n v e s t i g a t e d has a d i f f e r e n t l i f e t i m e than t h a t of the s o u r c e . Furthermore the f i r i n g o f the source and the open-i n g o f the s h u t t e r must be s y n c h r o n i s e d . T h i s chapter w i l l d e s c r i b e the p r o p e r t i e s o f the l i g h t source and a u x i l i a r y components used i n the experiment. The g e n e r a l arrangement of the apparatus i s i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 2. 3-1 BACKGROUND LIGHT SOURCE Alth o u g h the p r e s e n t experiment i s c a r r i e d out on a gas at f a i r l y low temperature (lpOO°K) the equipment i s designed i n such a manner t h a t i n v e s t i g a t i o n s of much highe r temperature plasmas are p o s s i b l e . B r i g h t n e s s -15-F i g u r e 2 - Schematic Drawing o f the Experimental Apparatus ffl< CO < o Q LU U X L U ER CH 1 Z H I D «j O Q O CO o 4 LU I— O 1 ^ O 3 o -16-temperatures of 30000°K have beenobtained from arcs l a s t i n g for a few seconds (Lochte-Holtgreven 193?8) but the power requirements are somewhat high and become excessive i f s t i l l higher temperatures are desired. One of the most promising methods for achieving high temperatures, while keeping construction d i f f i c u l t i e s and energy requirements to a minimum, i a by an impulsive discharge. Fischer (1957) claims to have obtained a temperature of 250000°K i n a spark discharge i n Helium at a pressure of 35 atmospheres. Although t h i s temperature i s open t o some doubt (Vanyukov and Mak 1958) and somewhat higher than that required i n this,experiment Fischer's source has provided the basic design for our l i g h t source. The l i g h t source consists of a spark gap mounted on a l«6juif , 20kV low inductance capacitor and i s I l l u s t r a t e d i n cross section i n Figure 3» The enclosure around the spark gap ensures safe and quiet operation and allows the gap to be operated i n gases other than a i r at pressures other than atmospheric. The ultimate temperature achieved i n such a discharge depends on the rate of power intake by the discharge chajanel which i n turn can be i increased by using a s u f f i c i e n t l y high voltage, low inductance and high gas pressure. Also, due to differences i n i o n i z a t i o n p o t e n t i a l s , l i g h t e r gases produce hotter discharges than the heavier gases(Van-yukov and Mak 1958) • -16-temperatures of 30000°K have been obtained from a r c s l a s t i n g f o r a few seconds (Lochte-Holtgreven 1958) but the power requirements are somewhat high and become ex c e s s i v e i f s t i l l higher temperatures are d e s i r e d . One of the most p r o m i s i n g methods f o r a c h i e v i n g high temperatures,, w h i l e keeping c o n s t r u c t i o n d i f f i c u l t i e s and energy requirements t o a minimum, i s by an impulsive d i s c h a r g e . F i s c h e r (1957) c l a i m s t o have obtained a temperature of 250000°K i n a spark d i s c h a r g e i n Helium at a p r e s s u r e of 35 atmospheres. Although t h i s temperature i s open t o some doubt (Vanyukov and Mak 1958) and somewhat h i g h e r than t h a t r e q u i r e d i n t h i s experiment F i s c h e r ' s source has p r o v i d e d the b a s i c d e s i g n f o r our l i g h t s o u r c e . The l i g h t source c o n s i s t s of a spark gap mounted on a 1.6ymf , 20kV low inductance c a p a c i t o r and i s i l l u s t r a t e d i n c r o s s s e c t i o n i n F i g u r e 3» The e n c l o s u r e around the spark gap ensures safe and q u i e t o p e r a t i o n and allows the gap t o be operated i n gases other than a i r at p r e s s u r e s other than atmospheric. The u l t i m a t e temperature achieved i n such a d i s c h a r g e depends on the r a t e of power intake by the d i s c h a r g e channel which i n t u r n can be i n c r e a s e d by u s i n g a s u f f i c i e n t l y h i g h v o l t a g e , low inductance and h i g h gas p r e s s u r e . A l s o , due t o t h e i r lower thermal and e l e c t r i c a l c o n d u c t i v i t i e s , l i g h t e r gases produce h o t t e r d i s c h a r g e s than the heavier gases(Van-yukov and Mak 1958) . •17-F i g u r e 3 - A C r o s s - s e c t i o n a l Drawing of the C y l i n d r i c a l C a p a c i t o r and Mounted Spark Gap - 1 8 -The gap i s t r i g g e r e d w i t h a h i g h v o l t a g e pulse from a Theophanis t r i g g e r u n i t (Theophanis I960). T h i s p u l s e c r e a t e s a spark between the tungsten t r i g g e r p i n and the upper e l e c t r o d e and i n i t i a t e s the breakdown o f the gap. For minimum j i t t e r the t r i g g e r i n g p u l s e should have the same p o l a r i t y as the upper e l e c t r o d e and the t r i g g e r p i n should be r e c e s s e d s l i g h t l y from the s u r f a c e o f the e l e c t r o d e (van der Laan and de Jong 1963)• The spark gap should a l s o be operated at a v o l t a g e very c l o s e t o the breakdown l i m i t . The r e s u l t i n g d i s c h a r g e i s o s c i l l a t o r y w i t h a p e r i o d of approximately 2yi|sec. The l i g h t output i s c ontained p r i m a r i l y i n a s i n g l e pulse emitted d u r i n g the f i r s t c y c l e of the d i s c h a r g e . The p u l s e i s i s o l a t e d by a K e r r C e l l w i t h an e f f e c t i v e exposure time of about a microsecond and the r e s u l t i n g r a d i a t i o n p r o v i d e s a c o n t i n -uous spectrum w i t h no o v e r l y i n g s p e c t r a l l i n e s . I f the K e r r C e l l i s not used the spectrum has a few o v e r l y i n g e m i s s i o n l i n e s t h a t are emitted d u r i n g the " t a i l " o f the d i s c h a r g e d Anderson 1932). These emission l i n e s make an a c c u r a t e d e t e r m i n a t i o n o f the b r i g h t n e s s temperature of the discharge very d i f f i c u l t . The K e r r C e l l was thus used throughout the experiment, d u r i n g temperature measurements as w e l l as f o r the i n v e s t i g a t i o n o f r e v e r s a l temperatures. The b r i g h t n e s s temperature of the source has been measured u s i n g standard photometric techniques (Appendix 1 and 2) i n the wavelength r e g i o n fj^OOA t o 7000A. A General -19-E l e c t r i c T-2I+. 86-P-50 standard lamp w i t h a tungsten r i b b o n f i l a m e n t was used as the i n t e n s i t y standard d u r i n g the temperature measurements. The standard lamp was a l s o used t o c a l i b r a t e a Hartmann and Braun f i l a m e n t o p t i c a l pyrometer. The pyrometer was then used t o measure the b r i g h t n e s s temperature (Appendix l ) o f a S y l v a n i a sun gun (3130°K) which served as a secondary standard. The photometric d e t e r m i n a t i o n was c a r r i e d out under c o n d i t i o n s i d e n t i c a l t o those to be used i n the r e v e r s a l temperature measurements. The l i g h t ' source t o be measured and the standard were interchanged i n the p o s i t i o n occupied by the l i g h t source i n F i g u r e 2, thus e n s u r i n g ^equivalent geometries f o r the two experiments. A l s o , a l l measurements were made u s i n g the K e r r C e l l s h u t t e r , thus a v o i d i n g e r r o r s caused by the i n t e r m i t t e n c y e f f e c t . The s l i t widths, exposure times and photometric procedure were the same as those used l a t e r In the experiment. The f i n a l temperature obtained was independent of wavelength in. the s p e c t r a l r e g i o n i n v e s t i g a t e d . Measure-ments were made at 200A* i n t e r v a l s and the f i n a l r e s u l t corresponded t o the average o f the val u e s obtained from seven s p e c t r o s c o p i c p l a t e s . The measured b r i g h t n e s s temperature of the source, when operated at 18kV, was 32,000°Ki85°K. The f i g u r e 85°K corresponds t o the stand-ard d e v i a t i o n of the measurements and i t i s f e l t t h a t i t does not g i v e a t r u e i n d i c a t i o n of the a c t u a l accuracy. -20-The s c a t t e r i n the measurements amounted t o approximately 25>00°K. T h i s f i g u r e probably r e p r e s e n t s a more r e a l i s t i c estimate of the e r r o r s i n v o l v e d , a l l o w i n g f o r s m a l l changes i n alignment and f i r i n g v o l t a g e d u r i n g o p e r a t i o n of the source• The peak b r i g h t n e s s temperature of the source was a l s o measured p h o t o e l e c t r l c a l l y . A J a r r e l l Ash 82010 monochromator and a P h i l l i p s l^OCVP p h o t o m u l t i p l i e r were used i n c o n j u n c t i o n w i t h the Kerr C e l l s h u t t e r f o r t h i s measurement. The S y l v a n i a sun gun a g a i n served as the standard and b o t h sources were i n s t a l l e d i n a c o n f i g u r -a t i o n s i m i l a r t o t h a t used i n the photometric measurements. N e u t r a l d e n s i t y f i l t e r s were used t o prevent s a t u r a t i o n and t o c o n t r o l the s e n s i t i v i t y o f the p h o t o m u l t i p l i e r . The p u l s e s from the p h o t o m u l t i p l i e r were d i s p l a y e d on a T e k t r o n i x d u a l beam o s c i l l i s c o p e and were photographed w i t h a P o l a r o i d camera (Dumont). The r e s u l t s obtained p h o t o e l e c t r l c a l l y f o r the s p e c t r a l r e g i o n IL^OOA t o "JOOOK are summarised i n F i g u r e LL. The r e l a t i o n s used i n the d e t e r m i n a t i o n o f the b r i g h t n e s s temperature are g i v e n i n Appendix 1. I t was expected that the temperature determined p h o t o e l e c t r l c a l l y would be q u i t e d i f f e r e n t from that obtained p h o t o m e t r i c a l l y because of the r e c i p r o c i t y e f f e c t a r i s i n g from the l a r g e d i f f e r e n c e s i n i n t e n s i t y between the standard lamp and the s o u r c e . R e c i p r o c i t y curves g i v e n i n Sawyer (1963) i n d i c a t e t h a t the -21-Pig u r e l\. - The B r i g h t n e s s Temperature of the Background Source versus Wavelength a t Three D i f f e r e n t V o l t a g e s . The p o i n t s are accurate t o + $% > 00 1 > 4 > i n <0. in in in » ro i*> o x ro m -22-o f f e c t w i l l be s m a l l w i t h the short exposure times (10~ f oto 10 ^seconds) used i n t h i s experiment. Our r e s u l t s show i n any case t h a t e r r o r s caused by the r e c i p r o c i t y e f f e c t are no g r e a t e r than those i n h e r e n t i n the photometric process (approximately U~>%) . The p h o t o e l e c t r i c r e s u l t s are accurate t o approximately lf>00°K and t h e i r agreement w i t h the photometric r e s u l t s are w e l l below t h i s f i g u r e . The b r i g h t n e s s temperature i s a g a i n constant throughout the s p e c t r a l r e g i o n i n v e s t i g a t e d although a s m a l l decrease might be i n d i c a t e d at the lower wavelength end of the s p e c t r a l i n t e r v a l . 3-2 OPTICS The l i g h t from the source i s c o l l i m a t e d by the l e n s L-^, passes through the column of e x c i t e d gas and Kerr c e l l , and i s then focussed on the s l i t o f the s p e c t r o g r a p h by the l e n s 1-2. S u i t a b l e diaphragms D and b a f f l e s B l i m i t the l i g h t p a t h t o the middle 1/8 i n c h o f the e x c i t e d gas column and reduce r e f l e c t i o n s and s c a t t e r i n g . Two spectrographs were used i n the course o f the experiment. The f i r s t was e s p e c i a l l y c o n s t r u c t e d i n t h i s l a b o r a t o r y t o p r o v i d e b o t h h i g h speed and h i g h r e s o l u t i o n . I t i n c o r p o r a t e d an f / l L , 9l+0mm f o c a l l e n g t h l e n s and a Bausch and Lomb 20£mm x l65mm plane g r a t i n g w i t h 610 l i n e s per mm. The components were assembled i n a standard L i t t r o w mount on a 12 i n c h s t e e l channel beam^ which i n t u r n was mounted on a movable s t e e l frame. The l i m i t i n g -23-a p e r t u r e i n the spectrograph was formed by the g r a t i n g j r e s u l t i n g i n an o v e r a l l speed o f approximately f/6.- The g r a t i n g i s b l a z e d at 1.6^ and the t h i r d order d i s p e r s i o n i s l+.7!?A/mm at 61+00A. A more complete d i s p e r s i o n t a b l e i s g i v e n i n Appendix 6. The r e s o l u t i o n of the spectrograph was t e s t e d u s i n g the chan n e l l e d spectrum from a Fabry-P e r o t i n t e r f e r o m e t e r w i t h a 5mm s p a c e r . The channelled spectrum i s produced by i l l u m i n a t i n g the i n t e r f e r o m e t e r w i t h a continuous spectrum l i g h t source (Born and Wolf I960) and c r o s s i n g the i n t e r f e r o m e t e r w i t h a s p e c t r o g r a p h . I f the r e s o l u t i o n o f the sp e c t r o g r a p h i s l a r g e enough t o r e s o l v e l i n e s separated by a wavelength i n t e r v a l e q u a l t o the i n t e r - o r d e r s e p a r a t i o n o f the spectr o g r a p h a s e r i e s of a l t e r n a t i n g l i g h t and dark v e r t i c a l p a r a b o l i c bands w i l l be seen r u n n i n g h o r i z o n t a l l y along the p l a t e . I f the r e s o l u t i o n o f the spe c t r o g r a p h i s l e s s than the i n t e r -order s e p a r a t i o n the u s u a l continuous spectrum w i l l be observed. U s i n g a 5mm spacer at 5000A p r o v i d e d a value of 20000 f o r the r e s o l u t i o n o f the above spectrograph, a&gain i n the t h i r d o r d e r . T h i s s p e c t r o g r a p h w i l l h e r e a f t e r be r e f e r r e d t o as the L i t t r o w . In order t o photograph the weaker a b s o r p t i o n l i n e s at c u r r e n t s below 10mA i n the di s c h a r g e tube i t was found t h a t a spect r o g r a p h w i t h a higher r e s o l v i n g power was r e q u i r e d . T h i s was s u p p l i e d through the kindness of Dr. P. W. Dalby and h i s students i n the form o f a 3»5m - 2 1 ^ f o c a l l e n g t h E b e r t mounted g r a t i n g s p e c t r o g r a p h . The g r a t i n g has 1200 lines/mm b l a z e d at 1.0^ . The r e s o l v i n g power has been measured by Dr. Dalby to be approximately 100,000 i n the second o r d e r . The d i s p e r s i o n f o r the f i r s t and second orders i s t a b u l a t e d i n Appendix 6 • T h i s s p e c t r o g r a p h w i l l be r e f e r r e d t o as the E b e r t throughout the remainder of t h i s t h e s i s . A Fabry-Perot i n t e r f e r o m e t e r was used t o measure the Doppler widths o f the s p e c t r a l l i n e s emitted by the plasma. The o p t i c a l f l a t s used i n the i n t e r f e r o m e t e r were obtained from the van Keuren Co. w i t h a s p e c i f i e d f l a t n e s s of 1/25 of a wavelength at 6350A. The r e f l e c t -i v i t y produced by the d i e l e c t r i c a l l y coated s u r f a c e s was .90 at 6500A. The uncoated face of each f l a t was p o l i s h e d a t an angle o f 30 minutes t o the coated s u r f a c e . The i n t e r f e r o m e t e r mounting and 1.25mm, $mm, 10mm, and 25mm i n v a r spacers were obtained from the machine shop o f the P h y s i c s department a t U. B. C. 3 - 3 ABSORPTION TUBES Two a b s o r p t i o n tubes were used i n the course o f the experiment. Both were c o n s t r u c t e d from 8mm i n s i d e diameter g l a s s t u b i n g , one 50 cm In l e n g t h and the other 20 cm i n l e n g t h . The 50 cm tube has o p t i c a l l y f l a t windows mounted at each end and the 20 cm tube has o p t i c a l l y f l a t windows b o t h at the ends and the s i d e s . A diagram of the tubes i s give n i n F i g u r e 5 • The e l e c t r o d e s are p a r t i a l l y hollowed -25-F i g u r e 5 - A b s o r p t i o n Tubes (a) The $0cm Tube L|.5cm 7 Aluminum C y l i n d e r s .8cm i.d Tungsten . t o Glass S e a l (b) The 20cm Tube 20cm T • 8cm 7. Side View End View -26-alurainura c y l i n d e r s mounted i n side tubes by a tungsten wire sealed i n t o the g l a s s . The glow di s c h a r g e was maintained by a r e g u l a t e d 600V constant c u r r e n t power sup p l y * T h i s v o l t a g e i s much l e s s than t h a t r e q u i r e d f o r breakdown however and the discharge had to be i n i t i a t e d w i t h a T e s l a c o i l . Ladenburg (1933) found t h a t i m p u r i t i e s , p a r t i c u l a r l y Hydrogen, destroyed the lower metastable l e v e l s o f the Neon atoms and thus made i t d i f f i c u l t t o o b t a i n observable e f f e c t s a t the l i n e s t e r m i n a t i n g on these l e v e l s . E x t r a care was t h e r e f o r e taken t o o b t a i n a h i g h degree o f p u r i t y i n the Neon d i s c h a r g e . The a b s o r p t i o n tubes were evacuated t o an u l t i m a t e p r e s s u r e of 10"9 Torr on an u l t r a - h i g h vacuum system b u i l t by van Andel (1963) • The the tubes were baked at IL00°C, f i l l e d w i t h r e s e a r c h grade Neon t o a pr e s s u r e o f 2 T o r r and sealed o f f . The . r e s u l t i n g Neon di s c h a r g e i s q u i t e pure and no t r a c e of the t H,^  l i n e , or any other i m p u r i t y l i n e , has been observed i n any o f the s p e c t r a taken d u r i n g t h i s work. 3-1+ PHOTOMETRIC EQUIPMENT Kodak IF and IIF s p e c t r o s c o p i c p l a t e s were used t o photograph s p e c t r a l l i n e s i n the wavelength r e g i o n 5800A to 6800A. Kodak IN p l a t e s -were used t o photograph the longer wavelengths. A l l p l a t e s were developed i n Kodak D-19 developer at room temperature f o r the times p r e s c r i b e d i n the Kodak manual on s p e c t r o s c o p i c p l a t e s . -2-7-The p l a t e s were c o n t i n u o u s l y a g i t a t e d d u r i n g development t o reduce adjacency e f f e c t s such as the Eberhard e f f e c t . A • Hiflger . stepped wedge was used f o r the p r o d u c t i o n o f the c a l i b r a t i o n s p e c t r a . I t provided" seven d i f f e r e n t d e n s i t y steps i n c l u d i n g the c l e a r p o r t i o n of the wedge. The d e n s i t i e s quoted f o r the d i f f e r e n t steps were checked on a mic r o d e n s i t o m e t e r . The n e u t r a l i t y o f the wedge was confirmed by means o f i n t e r f e r e n c e f i l t e r s . The wedge was i n v e s t i g a t e d on the microdensitometer at three d i f f e r e n t wavelengths s i t u a t e d i n the s p e c t r a l i n t e r v a l 5500A t o 7000A. A c a l i b r a t i o n spectrum was photographed f o r every p l a t e and a c h a r a c t e r i s t i c curve p l o t t e d f o r each l i n e . - A d e t a i l e d account of the photometric procedure i s g i v e n i n Appendix 2. A J a r r e l l Ash microdensitometer w i t h a l i m i t i n g r e s o l v i n g power o f !?0y4 served f o r the r e d u c t i o n o f the s p e c t r a . The s l i t h e i ght could be v a r i e d from .1cm to 2cm. Higher r e s o l u t i o n was r e q u i r e d however f o r the i n v e s t i g a t i o n o f some of the narrower l i n e s . F o r t h i s purpose a M o l l spectrometer was m o d i f i e d w i t h a 931A p h o t o m u l t i p l i e r tube and 1.1+kV power s u p p l y . The output o f the p h o t o m u l t i p l i e r was fed i n t o a He a t h k i t r e c o r d e r . The M o l l microdensitometer p r o v i d e d a r e s o l u t i o n o f approximately 10/m as v e r i f i e d w i t h an Abbe t e s t p l a t e . T h i s r e s o l u t i o n was adequate f o r the i n v e s t i g a t i o n o f the narrowest l i n e s photographed - approximately 3QJM . -28-3-5 ELECTRONIC EQUIPMENT A b l o c k diagram of the e l e c t r o n i c components i s g i v e n i n F i g u r e 2. The p r i n c i p a l f u n c t i o n o f the e l e c t r o n i c s i s t o p r o v i d e a method f o r t r i g g e r i n g the background source and opening the Kerr C e l l s h u t t e r i n the proper time sequence. T h i s i s accomplished by u s i n g two channels of a three channel delay u n i t . The Theophanis t r i g g e r u n i t i s t r i g g e r e d from one channel and the K e r r C e l l power supply from the o t h e r . The time, d i f f e r e n c e between the outputs o f the two channels i s c o n t i n u o u s l y v a r i a b l e from zero t o t e n thousand microseconds. S y n c h r o n i s a t i o n can be obtained w i t h a dual beam o s c i l l i s c o p e by o b s e r v i n g the v o l t a g e p u l s e across the Kerr C e l l on one beam and the p u l s e of l i g h t t r a n s m i t t e d by the Kerr c e l l on the o t h e r . A simple m u l t i v i b r a t o r o s c i l l a t o r i s i n c o r p o r a t e d which all o w s the K e r r c e l l t o be p u l s e d s e v e r a l times per second independently of the source. An e l e c t r o n i c counter Is p r o v i d e d t o r e c o r d the t o t a l number of openings of the s h u t t e r . The K e r r c e l l was manufactured by B a r r and Stroud and equipped w i t h h i g h q u a l i t y p o l a r o i d s . The quoted open t o c l o s e r a t i o of the s h u t t e r was 10 . T h i s f i g u r e w a s checked however u s i n g red l i g h t and r e v i s e d to 3 x 10^" f o r the c o n d i t i o n s used i n the present experiment. The f u l l open v o l t a g e of the Kerr c e l l i s l 6 k V and the maximum a v a i l a b l e aperture i s 2cm i n diameter. -29-The compur shutter i s inserted to prevent s i g n i f i c a n t leakage of l i g h t over the comparitively long periods of time when the shatter i s nominally closed. It i s also used to i n i t i a t e a f i r i n g sequence, by shorting a single t r a n s i s t o r switch which i n turn t r i g g e r s the delay u n i t . Throughout the experiment a l l exposures were made with the Kerr C e l l to minimize errors a r i s i n g from i n t e r -mlttency e f f e c t s * The a d d i t i v i t y of the Kerr C e l l openings was also checked on various plates, using both continuous and l i n e spectra* The errors involved i n a l l cases were less than 15%, a value inherent i n the photometric process. -30-CHAPTER IV MEASUREMENT OP REVERSAL TEMPERATURES i l r l EXPERIMENTAL PROCEDURE The procedure adopted for the determination of the reve r s a l temperatures i s outlined i n the following paragraphs. A series of exposures i s made on the same plate (for example see Figure 6 ) . The f i r s t exposure, where t p / t a = 1 i s simply the absorption spectrum of the Neon glow discharge. The second "step" consists of the same absorp-t i o n spectrum with an addit i o n a l exposure of the plasma alone superimposed onto i t . The third "step" has a s t i l l greater additional exposure of the plasma added to the absorption spectra. In general fiv e o r - s i x "steps" are photographed on the same plat e , with the f i n a l "step" showing a l l the l i n e s i n emission on the continuous back-ground. A c a l i b r a t i o n spectrum i s then photographed on the same plate using the step wedge and standard tungsten lamp or the Sylvania sun gun. A v i s u a l examination of the developed plate w i l l then indicate d i r e c t l y the approximate r a t i o of exposure times necessary for r e v e r s a l . However to obtain a more accurate estimate of t h i s r a t i o and to enable us to process as many li n e s as possible on a single plate a more refined -31-P i g u r e 6 - A p o r t i o n o f a T y p i c a l P l a t e S h o w i n g a P e w L i n e s i n A b s o r p t i o n , E m i s s i o n , a n d n e a r R e v e r s a l 6598 V -32-technique was adopted. The areas under each a b s o r p t i o n and e m i s s i o n l i n e were measured w i t h the microdensitometer f o r each value o f the exposure time r a t i o t p / t & . A p l o t of these areas versus the r a t i o t / t was then made f o r P a each s p e c t r a l l i n e ( see f o r example F i g u r e 7) • Prom e q u a t i o n (7) we see t h a t the r a t i o t / t r e q u i r e d f o r P r e v e r s a l corresponds t o the a b s c i s s a i n t e r c e p t of the above p l o t . At r e v e r s a l of course equation (7) reduces t o Si n c e E>v(S) i s known we can immediately determine the f a c t o r ^^^Q^/KTR) . a n d thus the r e l a t i v e p o p u l a t i o n d e n s i t y and r e v e r s a l temperature f o r the s p e c t r a l l i n e under i n v e s t i g a t i o n . S i m i l a r l y the t o t a l a b s o r p t i o n W>y i s g i v e n by the o r d i n a t e i n t e r c e p t on the p l o t of area versus exposure time r a t i o . The accuracy o f the value a r r i v e d at f o r the r e l a t i v e p o p u l a t i o n d e n s i t y and thus the r e v e r s a l temperature i s s t r o n g l y i n f l u e n c e d by the r e s o l u t i o n o f the equipment employed. Thus an attempt was made t o optimize the r e s o l u t i o n o f the s p e c t r o s c o p i c components. In t h i s experiment no n o t i c e a b l e improvement was gained by d e c r e a s i n g the s l i t w i d t h below 2%ju[ . T h i s was because of the l i m i t i n g r e s o l u t i o n of the Kodak IP s p e c t r o s c o p i c p l a t e s . When IIP p l a t e s were used the optimum s l i t w idth was reduced t o approximately • Although narrower s l i t s - 3 3 -F i g u r e 7 - Example of P l o t f o r the D e t e r m i n a t i o n o f t p / t Q at R e v e r s a l '3f Jhfle +1 0 -1 -2\ -5\ *J I, nO x l O ' ^ s e c " 1 i X= 6506A E b e r t Spectrograph Sun Gun as Source > -31*-were used on some occasions the average s l i t width employed d u r i n g the experiment was i n the range 20/4 t o 3 0 ^ . I4.-2 EXPERIMENTAL RESULTS The r e v e r s a l temperatures o f the s p e c t r a l l i n e s a r i s i n g from t r a n s i t i o n s between the 2p^3s and 2p-^3p c o n f i g u r a t i o n s o f Neon I have been determined f o r discharge c u r r e n t s between 1mA and 100mA. The s p e c t r a l l i n e s concerned are shown i n the p a r t i a l term diagram of N e l t h a t i s given i n F i g u r e 8 . The l e v e l s are l a b e l l e d u s i n g the Paschen scheme of n o t a t i o n . The values obtained f o r the r e l a t i v e p o p u l a t i o n d e n s i t i e s are given i n Table 1 f o r the v a r i o u s c u r r e n t s at which measurements were made. The corresponding r e v e r s a l temperatures are g i v e n i n Table 2 . The r e s u l t s l i s t e d i n the 1mA and 5mA columns were measured on the E b e r t s p e c t r o g r a p h u s i n g the 20cm a b s o r p t i o n tube. The measurements at c u r r e n t s above 10mA were performed on the L l t t r o w s p e c t r o g r a p h w i t h the 50cm tube. I n , a l l cases the r e s u l t s r e q u i r e d a d i s p e r s i o n c o r r e c t i o n because o f the v a r i a t i o n of the s p e c t r o g r a p h d i s p e r s i o n w i t h wavelength. The d i s p e r s i o n of the spectrographs i s t a b u l a t e d i n Appendix 6 . Because of the l a r g e v a r i a t i o n s In the r e v e r s a l temperatures a complete measurement of a l l the l i n e s r e q u i r e d three p l a t e s f o r each value of the c u r r e n t . -35-Table 1 - R e l a t i v e P o p u l a t i o n D e n s i t i e s . N U / N L x 10^. f o r C u r r e n t s from 1mA t o 100mA ' Term 1mA 5mA 15mA 25mA 1+OmA 60mA 8 OmA 100mA s 2 p 1 5852 100 11+0 150 1 166 190 200 230 270 35P2 5882 .521 8.1+1 12.0 33,0 ,1^.3 51.1 72 .3 90.1 s5Pl+ 591,5 .933 ll+.O 22.1+ 55.0 78.0 90.2 il+5 150 s5 p5 5975 .571 9.02 15.6 33.8 .1+8.7 81+. 1 115 11*5 6030 1+9.7 70.5 120 151+ 165 187 231+ 607b. 2.66 20.1+ 29.0 v 37.3 1+3.3 53.7 66.6 96.0 6096 13.3 100 125 153 205 272 320 376 s ^ p 6 6ll+3 2.02 20.5 1*1.6 61+.3 80.1+ 110 11+6 179 S 3 P 2 6163 3.89 36.7 96.5 165 211 315 361+ 1+52 S 5P7 6217 .609 9.1 15.1 1+1.8 51,.0 75.0 90.5 111+ s 3 p 5 6266 l*.5l 1+5.0 83.8 150 195 255 360 1*55 sb,P6 6301+ 25.0 120 131 1P7 230 272 315 369 s 5 p 8 6331+ 1.79 30.5 ,1+1 *0 56.9 80.0 95.5 110 135 6383 10.9 79.8 81+.0 92 .1 110 11+9 180 210 s 5 p 9 61+02 5.20 77.0 119 230 320 1+25 700 995 sbP8 6506 25.0 11+2 165 200 269 367 1+50 710 s 3 p 7 6532 3.90 1+5.0 86.7 178 255 390 1+55 5l*o s 2 p 2 6599 95.0 135 165 200 235 305 370 l*i*o s 2Ph. 6678 165 233 285 350 1+31 1*71+ 615 715 S2P5 6717 100 11+5 175 210 256 291+ 355 1+23 S2P6 6929 370 S 5 P 1 0 7 0 3 2 2.58 -36-A few l i n e s however could be processed on two of the three plates and an average value could be obtained. The r e s u l t s quoted for 1mA represent the average of three measurements for each l i n e but the values at higher currents are at the most the average of two measurements and i n some cases represent the r e s u l t of a single measurement. The measurements at 1mA were carried out both with the high' temperature sourcej and with the Sylvania sun gun as a background source . The exposure time r a t i o , and thus the r e l a t i v e population density, are determined to within approximately 30% by a single measurement with the Littrow spectrograph and to about lf>% with the Ebert spectrograph. Thus the res u l t s obtained for a current of 1mA should be accurate to less than 10% a f t e r averaging. The re s u l t s quoted for currents above 10mA however are only accurate to 30%, since they represent at most only two measurements on the Littrow spectrograph. The actual scattering i n the values obtained i n the case of repeated measurements was of the same order as the figures given above for the accuracy of the single measurements. b,-3 DEPARTURES PROM THERMODYNAMIC EQUILIBRIUM The absence of thermodynamic equilibrium i s graphically i l l u s t r a t e d by the photographs ( see Figure 6 ) i n that one can see the li n e s reversing quite i r r e g u l a r l y with respect to exposure time r a t i o s . This i n turn means -37-T a b l e 2 - R e v e r s a l Temperatures i n °K f r o m 1mA to 100mA MA) 1mA 5mA 15mA 25mA 1+OmA 6 0mA 8 0mA 100mA 5852 1+200 1+1+60 1+560 1+650 1+750 1+7 60 1+810 5000 5882 2100 2750 2860 3260 3380 3580 3660 3700 591+5 2090 2750 2880 3260 3380 3580 3660 3700 5975 2100 2730 2900 3260 3370 3600 3710 3820 6030 3130 3300 351+0 3660 3700 3790 3920 607I+ 21+90 3050 3380 31+60 3550 3690 3790 1+050 6096 2500 3100 3270 3370 3500 3666 371+0 381+0 611+3 2170 2790 2990 3180 3270 31+50 3550 3700 6163 2070 2590 2900 3100 3190 31+00 31+1+0 3600 6217 2020 2620 2800 3170 3290 31+60 3560 3690 6266 2090 2600 2800 301+0 3130 3280 31+20 3550 6301+ 2600 3150 3200 3300 31+70 3550 3620 3720 6331+ 2080 2800 2900 3030 3200 3250 331+0 31+20 6383 21+60 3160 3180 3220 331+0 31+70 3550 3720 61+02 2200 3000 3300 3500 3670 3880 1+200 1+1+50 6506 21+20 301+0 3150 3280 31+30 3620 371+0 1+000 6532 2080 2500 2700 2980 3100 3310 3370 31+70 6599 3130 3300 31+00 3520 3620 3730 3850 3960 6678 3130 3300 3380 3520 361+0 3710 3830 3970 6717 3130 3300 3380 3500 3620 3690 3800 3930 6929 3330 7032 2160 -38-that the e f f e c t i v e temperature which governs the r e l a t i v e populations of the upper and lower levels i s di f f e r e n t for each spectral l i n e . The deviations from thermodynamic equilibrium can be demonstrated q u a n t i t a t i v e l y by comparing the experimentally obtained r e l a t i v e populations of the various s-levels with those calculated from the Boltzmann r e l a t i o n . In t h i s c a l c u l a t i o n i t w i l l be assumed that electron-atom c o l l i s i o n s are the predominant mode of e x c i t a t i o n . The electron temperature 2:.0eV s h a l l therefore be used i n the exponential of the Boltzmann f a c t o r . This value was taken from the probe measurements of Seeliger and Hirchert (1931)5 and Kagan et a l (1963). These probe measurements were carried out on discharges similar to that used i n this experiment. The r e l a t i v e values obtained experimentally are calculated by using the r e s u l t s for l i n e s having common upper l e v e l s . Table 3 presents a summary of the comparison. As expected the values i n no way correspond to an equilibrium d i s t r i b u t i o n . Table 3 - Comparison of Relative Population Densities Obtained Experimentally with Those Calculated from a Boltzmann D i s t r i b u t i o n Measured Boltzmann Ratio 1mA 5mA 15mA 25mA 60mA 100mA leV. 2eV Ns2/Ns£(4) .0055 .016 .080 .15 .19 .21 .1+8 .53 .135 .200 .180 .20 .19 .20 .18 .19 Ns^/Ns5(fe) .075 .11+0 .20 .35 .1+0 .1+8 .57 .58 -39-The numbers i n b r a c k e t s a f t e r the r a t i o d e s i g n a t i o n denote the number o f p a i r s o f s p e c t r a l l i n e s t h a t were used i n the d e t e r m i n a t i o n o f the r e l a t i v e p o p u l a t i o n s . The s - l e v e l p o p u l a t i o n s are then checked i n t e r n a l l y f o r c o n s i s t a n c y . A s i m i l a r c a l c u l a t i o n was c a r r i e d out f o r the upper p - l e v e l s f o r the r e s u l t s obtained at 1mA. Table 3a summarizes the r e l a t i v e p o p u l a t i o n s of the p - l e v e l s at 1mA f o r f u t u r e use. Table 3a - R e l a t i v e P o p u l a t i o n s of the p - L e v e l s at 1mA P1/P9 .10 P2/P9 .10 P3/P9 .036 P l / P 9 .18 P5/P9 .10 P6/P9 .36 P7/P9 .12 P8/P9 .26 P10/P9 .60 -ILO-Figure 8 - P a r t i a l Term Diagram of Ne I . A l l wavelengths shown are i n Angstroms. Paschen Notation! B pt Ps ^ LS Notation s8 CO ^ ^ 3 oo oo oO to M <\j IM to in o N N!} rt 8 »0 to N O o NO NO N0 O N0 NO O NS 8 o NO Metastable NO I O to NS N Q N O tNJ If) N O NO VO N O \ JV1 to NO '4 NO CN-N Q O N | o N O rp'o to 00 Metastable N O tt Ground Level -1*1-CHAPTER V RELATIVE LINE INTENSITY MEASUREMENTS 5 - 1 SELF-ABSORPTION CORRECTIONS In most d i s c h a r g e s the r a d i a t i o n emitted by atoms i n the i n t e r i o r i s p a r t i a l l y absorbed by other atoms o f the same type which are s i t u a t e d between the e m i t t i n g atoms and the e x t e r i o r o f the d i s c h a r g e . The s p e c t r a l l i n e s emitted by the di s c h a r g e are s a i d to be i n f l u e n c e d by s e l f - a b s o r p t i o n i n t h i s case and t h e i r i n t e n s i t y i s no longer d i r e c t l y p r o p o r t i o n a l t o the atomic d e n s i t y and t r a n s i t i o n p r o b a b i l i t y f o r the t r a n s i t i o n concerned. I t was shown i n the second s e c t i o n o f Chapter 2 t h a t the observed l i n e i n t e n s i t y must be d i v i d e d by a f a c t o r S (Eq u a t i o n ll*) t o o b t a i n a value which i s d i r e c t l y p r o p o r t i o n a l t o the number d e n s i t y and t r a n s i t i o n p r o b a b i l i t y . In a d d i t i o n t o b e i n g a d i r e c t measure o f the amount of s e l f - a b s o r p t i o n the f a c t o r S a l s o governs the t o t a l a b s o r p t i o n to be expected by a l a y e r o f gas (E q u a t i o n 1 7 ) • Thus t o t a l a b s o r p t i o n measurements can be used t o determine c o r r e c t i o n f a c t o r s f o r the measured s p e c t r a l l i n e , i n t e n s i t i e s . The t o t a l a b s o r p t i o n i s d e f i n e d as -U2-and can be determined from the r e v e r s a l temperature measurements as d e s c r i b e d i n Chapter 3. The product k Q l S can t h e n be l o c a t e d i n Ladenburg and Levy's t a b l e and the a p p r o p r i a t e value o f S read o f f . Prom the t a b l e one sees however, t h a t as the s e l f - a b s o r p t i o n c o r r e c t i o n s become l a r g e r , t h a t i s as S becomes s m a l l e r , the product kQlS v a r i e s very slowly w i t h changes i n S. T h i s i s e q u i v a l e n t to s a y i n g t h a t the t o t a l a b s o r p t i o n i n c r e a s e s very s l o w l y w i t h l a r g e i n c r e a s e s i n d e n s i t y . T h i s f a c t i s demonstrated c l e a r l y by a p l o t of E q u a t i o n (17). The r e s u l t i n g curve i s commonly c a l l e d the curve of growth and i s reproduced i n Appendix 3 f o r the case o f pure Doppler b r o a d e n i n g . I t i s evident from the curve t h a t an accu r a t e d e t e r m i n a t i o n of the atomic d e n s i t y , and thus the f a c t o r S, i s very d i f f i c u l t when the t o t a l a b s o r p t i o n f a l l s on the almost h o r i z o n t a l p a r t of the curve. An attempt was t h e r e f o r e made t o keep the c o r r e c t i o n s as s m a l l as p o s s i b l e . The r e l a t i v e i n t e n s i t i e s , and of course the t o t a l a b s o r p t i o n or e q u i v a l e n t widths, were measured at the lowest c u r r e n t that c o u l d be maintained. Measure-ments were a l s o c a r r i e d out w i t h the 20cm a b s o r p t i o n tube I n s t a l l e d p e r p e n d i c u l a r t o the o p t i c a x i s o f the spectrograph, thus p r o v i d i n g a path l e n g t h equal to the diameter of the d i s c h a r g e . The f i r s t column of Table l * c o n t a i n s the r e s u l t s ; o f t o t a l a b s o r p t i o n measurements c a r r i e d out w i t h a 1mA c u r r e n t In the di s c h a r g e tube. Column 2 of the same t a b l e g i v e s the same r e s u l t s i n frequency u n i t s . These measurements were performed on the E b e r t s p e c t r o g r a p h u s i n g Kodak IN and IP s p e c t r o s c o p i c p l a t e s . The a b s o r p t i o n tube was mounted w i t h i t s l o n g i t u d i n a l a x i s p e r p e n d i c u l a r t o the o p t i c a x i s o f the spectrograph, t o o b t a i n the, s h o r t e s t p o s s i b l e a b s o r p t i o n p a t h l e n g t h . A blank space opposite the wavelength s i g n i f i e s t h a t the a b s o r p t i o n was so s m a l l that the e q u i v a l e n t width couldn't be measured. In t h i s case S must be g r e a t e r than .95 and i s taken t o be equal t o 1. As can be seen from Table l * the 32 l e v e l i s so lowly populated t h a t there i s no a b s o r p t i o n at any of the l i n e s (5852A, 6599A, 6678A, etc.) t e r m i n a t i n g on i t . S i m i l a r i l y the p o p u l a t i o n o f the s^ l e v e l i s smal l In comparison wi t h the metastable s-^  and S£ l e v e l s . The e q u i v a l e n t widths are accurate t o approximately 15% which i n t u r n l e a d s t o an e r r o r of approximately 5% i n the d e t e r m i n a t i o n of S, p r o v i d e d the value of S i s gr e a t e r than . 5 • 5 - 2 MEASUREMENT OF THE DOPPLER WIDTHS. The other parameter r e q u i r e d f o r the d e t e r m i n a t i o n of the s e l f - a b s o r p t i o n c o r r e c t i o n s i s the Doppler h a l f - w i d t h o f the emitted s p e c t r a l l i n e s . The h a l f width i s e s s e n t i a l l y a measure o f the temperature of the n e u t r a l -1+1+-Table 1+ - Total Absorption Wx and , Doppler Half-width^y^, and Self-Absorption Correction S. A blank row opposite the spectral l i n e desig-nation indicates that the t o t a l absorption at that l i n e was too small to measure and S i s therefore set equal to 1. ¥ A(A) W v(xl0" 8 S sec"') sec"') 5852 1.00 5882 .0029 2.52 7.00 .30 .86 59IL5 .001+7 3.98 6>90 .1+8 .78 5975 1.00 6030 1.00 60714. 1.00 6096 1.00 611+3 .0093 7.1+5 6.70 .93 .56 6163 .0021 1.67 6.65 .21 .90 6216 .0026 1.98 6.60 .25 ...89 6266 .0039 3.00 6.55 .38 .85 630LL 1.00 6331+ .0078 5.81+ 6.50 .75 ....66 6383 1.00 61+0-2 .0120 8.90 6.1+1 1.15 . 4 3 6506 1.59 1.0.0. 653? .0023 6.30 .21 .90 6599 1.00 6678 1.00 6717 1.00 6929 1.00 7032 .0086 5.26 5.85 .75 .66 717I+ 1.00 721+5 1.00 -1+5-gas atoms as can be seen from the e x p r e s s i o n f o r the h a l f w i d t h ; \FzRTl*>2. The temperature was determined by measuring the Doppler widths of s e v e r a l s p e c t r a l l i n e s w i t h a Fabry-Perot i n t e r f e r o m e t e r . The c o n s t r u c t i o n of the i n t e r f e r o m e t e r has been d e s c r i b e d i n the second s e c t i o n of Chapter 3» The experimental method of Burger and van C i t t e r t (1927) was employed f o r the measurement of the e m i s s i o n l i n e h a l f - w i d t h s . An i n t e n s i t y c a l i b r a t i o n of the p l a t e i s avoided i n t h i s method by p a s s i n g one h a l f of the f r i n g e p a t t e r n through a n e u t r a l d e n s i t y f i l t e r w i t h $0% t r a n s -m i s s i o n . The peak of one f r i n g e thus corresponds t o the h a l f I n t e n s i t y p o i n t of the f r i n g e t h a t has not passed through the f i l t e r . The h a l f width of the l i n e can then be measured at t h i s p o i n t d i r e c t l y from a micr©densitometer t r a c i n g of the f r i n g e p a t t e r n . T h i s measured or observed h a l f - w i d t h does not however equal the Doppler or true w i d t h , but must be s t i l l c o r r e c t e d f o r d i s t o r t i o n due t o the i n t e r f e r o m e t e r . T h i s problem has been i n v e s t i g a t e d by Minkowski and Bruck (1935) • They co n s i d e r e d the c o n v o l u t i o n of the i n t e r f e r o m e t r i e i n t e n s i t y d i s t r i b t i t i o n f o r monochromatic r a d i a t i o n and the Doppler s p e c t r a l l i n e shape. T h e i r a n a l y s i s i s summarized i n Appendix 1+. I t produces a graph which enables one t o determine the a c t u a l l i n e shape -b,6-when the apparatus half-width and the observed half-width are known. The apparatus function describes the intensity d i s t r i b u t i o n produced by the interferometer for the idea l i z e d case of p e r f e c t l y monochromatic l i g h t . The apparatus function half-width can be determined by i l l u m i n a t i n g the interferometer with the l i g h t due to a spectral l i n e that Is much narrower than the In t e r f e r -ometer can resolve. Thus i f the interferometer Is used with a very small spacer, In t h i s experiment 1 .25mm, and illuminated by the l i g h t from a Geissler tube for example, the r e s u l t i n g i n t e n s i t y d i s t r i b u t i o n i n the spectral line i s due e n t i r e l y to the interferometer. Burger and van C i t t e r t (1927) have shown that the apparatus half-width is inversely proportional to the spacing between the f l a t s and thus can be obtained for any spacing from the apparatus half-width measured with the 1.25mm spacer, simply by d i v i d i n g by the r a t i o of the spacings. This e s s e n t i a l l y assumes that defects i n the f l a t s have the same e f f e c t on the i n t e n s i t y d i s t r i b u t i o n f o r any spacing used i n the interferometer. The absorption tube was set up i n the same p o s i t i o n used i n the t o t a l absorption measurements and the spectral l i n e s passed through the interferometer equipped with a 25mm spacer. The fringe pattern was then focussed on the s l i t of-the Littrow spectrograph. The fringe pattern, which could be observed v i s u a l l y on the s l i t head, was -1+7-h a l f covered with a .3 neutral density f i l t e r . The interferometer was masked to r e s t r i c t the useable area of the f l a t s to a c i r c l e approximately 1cm i n diameter. Column 1 of Table 5 contains the apparatus h a l f -widths that were measured using the 1.25mm spacer. The photographs were taken with a 1mA current i n the 20cm absorption tube. Only those l i n e s showing n e g l i g i b l e self-absorption were investigated. Column 2 gives the corresponding apparatus half-width r ^ y for a 25mm spacer and Column 3 gives the observed half-width / l eobtained from the microdensitometer t r a c i n g of the photograph. Only the innermost fringes were used i n the reduction of the data i n order to obtain the highest dispersion p o s s i b l e . The height of the photometer s l i t was chosen s u f f i c i e n t l y small during photometrisation of the curved fringes to diminish nonalignment e r r o r s . To calculate the observed half-width i n Angstroms we used the formula Ae _ -where r ^ and are the r a d i i of two successive rings on the r e g i s t e r i n g paper, Ae i s the observed half-width i n A, r i s the radius of the measured r i n g , dr i s the measured half-width on the paper, and <£/0> i s the inter-order separation i n I. Column I I of Table 5 gives the true half-widths which i n t h i s experiment correspond to the Doppler -1*8-h a l f - w i d t h s and column 5 c o n t a i n s the temperatures c a l c u l a t e d by E q u a t i o n (18). The values thus obtained f o r the temperature e x h i b i t a s c a t t e r of about 10% about an average value o f 290°K. T h i s temperature has been used to c a l c u l a t e the h a l f - w i d t h s AVp which appear i n column 3 of Table 1*. Table 5 Apparatus H a l f - w i d t h A-^ , Observed H a l f - w i d t h A e , Ddppler H a l f - w i d t h 6X^, and C a l c u l a t e d Temperature T ACA) A A ( A ) Ail) A e ( A ) Mil) T ( ° K ) (1,25mm) (25mm) 6030 .0150 .0075 .0200 .0162 280 6096 .0160 .0080 .0220 .0170 305 6301+ .0160 .0080 .0210 .0161* 275 6598 .0180 .0090 .0230 .0175 282 6717 .2000 .0100 .0260 .0190 315 -1+9-5-3 RELATIVE EMISSION LINE INTENSITIES The r e l a t i v e i n t e n s i t i e s of the spectral l i n e s emitted by the discharge were measured photometrically at a current of 1mA. The discharge tube was mounted at r i g h t angles to the optic axis of the spectrograph and measurements were made with the tube 2m from the s l i t of the spectrograph i n one case and approximately lm i n the second case. In both cases the discharge tube was diaphragmed to allow only l i g h t from the middle portion of the discharge to f a l l on the s l i t . In the f i r s t case no lenses were used and each point on the s l i t should thus receive l i g h t from every available point i n the discharge. The discharge i s focussed on the s l i t i n the second case and the r e l a t i v e i n t e n s i t i e s were photometrised at three d i f f e r e n t points on the spectral l i n e . The measurements were performed on both the Ebert and the Littrow spectrographs. A s l i t , width of 1+OOyU was employed i n a l l cases. The s l i t image was thus much wider than the frequency i n t e r v a l covered by the i n d i v i d u a l spectral l i n e s , ensuring that the peak intensity of the image of the spectral l i n e corresponded to the integrated i n t e n s i t y of the line( Appendix 5)• Kodak IP, IIF, and IN plates were used to record the i n t e n s i t i e s of the l i n e s . The IIP emulsion provides a f a i r l y high contrast and thus enabled a more accurate determination of the r e l a t i v e i n t e n s i t i e s of spectral -50-l i n e s w i t h almost equal i n t e n s i t i e s . The IN p l a t e s enabled us t o photograph wavelengths g r e a t e r than 7000A. The i n t e n s i t y of each l i n e was measured r e l a t i v e t o the i n t e n s i t y of the continuum emitted by the S y l v a n i a sun gun. The i n t e n s i t y of the sun gun, c o r r e c t e d f o r v a r i a t -i o ns i n the d i s p e r s i o n of the spectrograph, thus served as the comparison s t a n d a r d . In a p p l y i n g the d i s p e r s i o n c o r r e c t i o n s i t was assumed t h a t the continuum i n t e n s i t y v a r i e d l i n e a r l y w i t h the d i s p e r s i o n . Thus i f I^/jTfc,) i s the r a t i o of the l i n e i n t e n s i t y t o the continuum i n t e n s i t y at the wavelength Tl, , and i f i f t ^ / ^ J i s the r a t i o at A a ? the r e l a t i v e i n t e n s i t i e s of the two l i n e s i s g i v e n by I, _ Jj&J&J 5 "~ Jfc) IM where I D ( ^ ) i s the continuum i n t e n s i t y c o r r e c t e d f o r d i s p e r s i o n . The r e s u l t s of the measurements are g i v e n i n the f i r s t column of Table 6. The values presented are the average of s e v e r a l measurements. The number of t r i a l s r e p r e s e n t e d by the average i s denoted by the number i n b r a c k e t s immediately f o l l o w i n g the value f o r the i n t e n s i t y . The f l u c t u a t i o n s t h at occured i n the values from v a r i o u s t r i a l s were i n g e n e r a l l e s s than 10$, but i n a few cases as h i g h as The accuracy of the average v a l u e s t h e r e f o r e should be approximately There were no systematic d e v i a t i o n s noted between the r e s u l t s -51-Table 6- Measured and "True" R e l a t i v e I n t e n s i t e s . The i n t e n s i t i e s were measured r e l a t i v e t o the l i n e 61*02A which was s e t equal t d 1.00 Term Imeas. s •'•true S2P1 5852 .1+90(5) 1.00 .1+90 35P2 5882 .063(9) .86 .073 s5pl* 591+5 .09l+(9) .78 . 1 2 0 S5P5 5975 .022(5) 1.00 .022 skp2 6030 .032(5) 1.00 .032 slip 3 607k .110(9) 1.00 .110 sl+pk 6096 .180(9) 1.00 .180 s5p6 6.11+3 .361(7) .56 .61+5 s3p2 6163 .083(9) .90 .092 s5p7 6217 .033(5) .89 .037 s3p5 6266 .135(9) .85 .159 skp6 630k .090(9) 1.00 .090 s5p8 6331+ .191(9) ..6.6. .281 sk P7 6383 .210(7) 1.00 .210 s5p9 6k02 1.00 (5) .1*3 3.10 skp8 6506 .kk (7) 1.00 .1+1+1 S3P7 6532 .063(7) .90 .070 s2p2 6599 .11+2(9) 1.00 .11+2 s2pk 6678 .2k2(9) 1.00 .21*2 s2p3 6717 .150(9) 1.00 .150 s2p6 6929 .391(7) 1.00 .391 s5pio 7032 .395(5) ,.66 .600 s2p9 7171+ .072(5) 1.00 .072 skplO 721+5 .200(5) 1 .00 .200 -52-obtained from the d i f f e r e n t spectrographs nor between the two s e t s of values obtained w i t h the d i f f e r e n t tube p o s i t i o n s . The h i g h e s t s c a t t e r i n the r e s u l t s was obtained however i n the comparison o f the r e s u l t s from the two s p e c t r o g r a p h s . The r e s u l t s o f the measurements d e s c r i b e d i n the f i r s t and second s e c t i o n s of t h i s Chapter can now be used t o c o r r e c t the above determined i n t e n s i t i e s f o r s e l f -a b s o r p t i o n . The value of S i s obtained from Table 5 and r e e n t e r e d i n Table 6 opposite the a p p r o p r i a t e s p e c t r a l l i n e . The measured i n t e n s i t y i s then d i v i d e d by S and the r e s u l t i s entered i n the t h i r d column of Table 6. We s h a l l c a l l the i n t e n s i t y thus obtained the true i n t e n s i t y and denote I t by Ijj.. The numbers entered i n the t h i r d column are thus p r o p o r t i o n a l t o the p o p u l a t i o n d e n s i t y of the upper l e v e l and the t r a n s i t i o n p r o b a b i l i t y of the t r a n s i t i o n concerned. 5-ll- RELATIVE TRANSITION PROBABILITIES The r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s are determined u s i n g the r e l a t i v e p o p u l a t i o n d e n s i t i e s from Table 1 and the c o r r e c t e d i n t e n s i t y r a t i o s o f Table 6 , by the r e l a t i o n The r e l a t i v e values thus obtained are l i s t e d i n column 1 o f Table 7 where the t r a n s i t i o n p r o b a b i l i t y f o r the O s p e c t r a l l i n e 61+02A has been s e t equal t o 100. -53-The l i f e t i m e of the p 2 l e v e l has been measured r e c e n t l y by Klose (1965) who obtained the value Tp£ - 16.3 nanoseconds The t r a n s i t i o n p r o b a b i l i t i e s are p l a c e d on an a b s o l u t e b a s i s by u s i n g t h i s l i f e t i m e and the r e l a t i o n 3 *i Since t r a n s i t i o n s t o the ground s t a t e from the 2p-^3p c o n f i g u r a t i o n are f o r b i d d e n the r e c i p r o c a l of the sum o f the t r a n s i t i o n p r o b a b i l i t i e s o f the l i n e s 5882A, 603OA, 6163A, and 6598A must equal 16.3x (10"^)sec. The a b s o l u t e v a l u e s thus obtained are l i s t e d i n column 2 of Table 7 • The c o r r e s p o n d i n g a b s o r p t i o n o s c i l l a t o r s t r e n g t h s are l i s t e d i n the t h i r d column and the l i n e s t r e n g t h s Sjas d e f i n e d by the r e l a t i o n (Condon and S h o r t l e y 1935) are l i s t e d i n the f o u r t h column f o r comparison purposes. -51*-Table 1 - R e l a t i v e and Absolute Neon T r a n s i t i o n P r o b a b i l i t i e s , O s c i l l a t o r Strengths f , and Line Strengths S. A'REL A^ggxlO sec f S 5852 120 7.3 .13 7.3 5882 21.5 1.3 .01+0 1+.2 591*5 20 .5 1.2 .063 6.7 5975 6.7 .1+1 .013 1.3 6030 9.6 .58 .031 •1.9 607I* 90.5 5.5 .100 6.05 6096 30 1.8 .150 10.1 611*3 52 3.15 .18 18 6163 28.5 1.7 .29 6.0 6216 11.5 .70 .021+ 2.5 6266 1*1 2.5 .1+1* 8.1+3 6301* 7.3 .1+1+ .039 2.7 6331+ 26 1.6 .095 10.1 6383 1*7 2.85 .17 11 61+02 100 6.05 .1*9 55 6506 1*2 2.55 .27 17 6532 23 1.1+ .27 5.8 6599 1+1 2.5 .16 11 6678 1*2 2.5 .28 18.I* 6717 1+2 2.5 .17 11.5 6929 32 1.95 .23 16 7032 38.5 2.32 .12 12.0 7171+ 5.6 .31+ .01+3 3.1 721+5 13.5 .82 .061+ 1+.6 - 5 5 -CHAPTER VI DISCUSSION AND CONCLUSIONS 6-1 REVERSAL TEMPERATURE MEASUREMENTS The measurements d e s c r i b e d i n Chapter 1+ have shown that the Neon glow discharge i s d e f i n i t e l y not i n thermal e q u i l i b r i u m at low c u r r e n t s . Ladenburg (1933), i n the course of h i s anomolous d i s p e r s i o n experiments on a Neon glow d i s c h a r g e , noted the departure of the lower s - l e v e l p o p u l a t i o n s from a Boltzmann d i s t r i b u t i o n and d i s c u s s e d i t i n some d e t a i l . He a t t r i b u t e d the absence of thermodynamic e q u i l i b r i u m t o the f a c t t h a t the e l e c t r o n d e n s i t y i s very low f o r c u r r e n t s i n the m l l l i a m p e r e range. Thus c o l l i s i o n s would not dominate the r a t e equations governing the d e p o p u l a t i o n of the non-metastable l e v e l s and e q u i l i b r i u m would not be expected:. Griem( 196ij.) f u r t h e r suggests t h a t i n the case of metastable s t a t e s c o l l i s i o n s c o u l d e a s i l y keep t h e i r p o p u l a t i o n s i n e q u i l i b r i u m w i t h nearby l e v e l s of s h o r t l i f e t i m e . The r e s u l t s o f Chapter l\. show t h a t the r a d i a t i v e s ^ - l e v e l , which Is s i t u a t e d very near the metastable s-j and s ^ - l e v e l s , has a p o p u l a t i o n c l o s e t o the v a l u e p r e d i c t e d from the Boltzmann r e l a t i o n . The r e l a t i v e p o p u l a t i o n of the h i g h e r S2-l©vel i s f a r from the e q u i l i b -r i u m value however, as i s p r e d i c t e d by Griem. The r e s u l t s obtained are t h e r e f o r e q u a l i t a t i v e l y p r e d i c t e d by the - I n -v a l i d i t y c r i t e r i a o u t l i n e d by Griem. The g r a d u a l t r e n d toward an e q u i l i b r i u m d i s t r i b u t i o n at higher c u r r e n t s i s a l s o p r e d i c t e d because of the g r e a t e r number of c o l l i s i o n s . Also, as the c u r r e n t i s i n c r e a s e d the e l e c t r o n temperature decreases while the e x c i t a t i o n temperatures i n c r e a s e . Thus one might expect t h a t at some higher c u r r e n t the two temperatures would c o i n c i d e and e q u i l i b r i u m would p r e v a i l . A q u a n t i t a t i v e p r e d i c t i o n of the r e s u l t s would r e q u i r e a knowledge of the c o l l i s i o n c r o s s - s e c t i o n s , t r a n s i t i o n p r o b a b i l i t i e s , e l e c t r o n temperature and d e n s i t y and other f a c t o r s . In a d d i t i o n , even i f a l l these parameters are known, a le n g t h y a n a l y s i s i s r e q u i r e d . For these reasons a c a l c u l a t i o n o f the r e l a t i v e p o p u l a t i o n d e n s i t i e s was not attempted i n t h i s t h e s i s . I t i s f e l t however t h a t the e x p e r i m e n t a l technique developed and demonstrated i n t h i s work p r o v i d e s an e x c e l l e n t d i a g n o s t i c method f o r the i n v e s t i g a t i o n of thermodynamic e q u i l i b r i u m c o n d i t i o n s i n plasmas. The apparatus i s designed such t h a t experiments c o u l d e a s i l y be performed w i t h much higher temperature plasmas l a s t i n g f o r much b r i e f e r times. The c o l l i s i o n and S t a r k broadening of the s p e c t r a l l i n e s emitted by higher temperature plasmas would a l s o decrease the s p e c t r o g r a p h s r e s o l u t i o n r e q u i r e d , thus f a c i l i t a t i n g the attainment of more accurate r e s u l t s . -57-6-2 NEON TRANSITION PROBABILITIES The t r a n s i t i o n p r o b a b i l i t i e s f o r the s p e c t r a l l i n e s between the 2p^3p and 2p^3s c o n f i g u r a t i o n s have been measured p r e v i o u s l y by Ladenburg (1933), Krebs (1936), Doherty (1961), and F r i e d r i c h s (1961+) . Ladenburg measured the r e l a t i v e o s c i l l a t o r s t r e n g t h s of the l i n e s t e r m i n a t i n g on the same lower l e v e l by the method of anomolous d i s p e r s i o n . He then combined the r e s u l t s of these experiments w i t h measurements of the r a t i o o f the i n t e n s i t i e s of l i n e s b e l o n g i n g t o the same upper, but d i f f e r e n t lower l e v e l s , t o o b t a i n the r e l a t i v e o s c i l l a t o r s t r e n g t h s f o r s p e c t r a l l i n e s having d i f f e r e n t lower l e v e l s . The r e s u l t s were p l a c e d on an absolute s c a l e by assuming that f = 0.5 f o r the l i n e 61+02A. Doherty obtained absolute t r a n s i t i o n p r o b a b i l i t i e s from absolute i n t e n s i t y measurements on a shock tube and P r i e d r i c h s performed s i m i l a r measurements on an a r c . The t r a n s i t i o n p r o b a b i l i t i e s measured i n t h i s experiment are compared to the r e s u l t s o f Ladenburg, Doherty, and P r i e d r i c h s i n Table 8. The agreement between the r e l a t i v e values obtained here and those of Doherty i s e x c e l l e n t w i t h the e x c e p t i o n of the two l i n e s 6LL02A and 6II4.3A. The e r r o r s i n v o l v e d i n the experiments of Ladenburg and P r i e d r i c h s are i n the range 20% t o 30$ as g i v e n by the aut h o r s . The r e l a t i v e agreement i s thus w i t h i n the experimental e r r o r present i n the two experiments. -58-Table 8 - Comparison of Neon T r a n s i t i o n P r o b a b i l i t i e s w i t h the Values Obtained by Doherty (1962), P r i e d r i c h s (1961+), and Ladenburg (1933) 1 AABS A D0H. AFR. ALAD. } 5852 7.31 3.51 6.0 12.8 5882 1.3 .69 .96 2.12 591+5 1.2 .61 .93 1.70 5975 .1+1 .25 .1+6 .9 6030 .58 .29 .1+7 1.2 6071+ 5.50 3.00 5.9 7.8 6096 1.8 .89 2.1+ 611+3 3.15 1.3L+ ' 3.25 6163 1.7 .78 1.5 2.L+L+ 6217 .70 .35 .77 1.1+6 6266 2.5 1.20 • 3.81+ 6301+ ••kk .27 .1+0 .93 6331+ 1.6 .81+ 2.07 6383 2.85 1.5 1+.17 61+02 6.05 2.8 5.78 6506 2.55 1.3 3.1+0 6532 1.1+ .70 2.11+ 6599 2.5 1.2 1+.32 6678 2.5 1.1 1+.10 6717 2.55 1.1 1+.17 6929 1.95 .80 3.56 7032 2.32 1.06 3.21+ 7171+ .31+ .15 .80 721+5 .82 .1+2 1.80 -59-With the e x c e p t i o n of the values f o r the l i n e s 61L02A and 6II4.3A the t r a n s i t i o n p r o b a b i l i t i e s obtained here should be a c c u r a t e to 10$ f o r those l i n e s not r e q u i r i n g a c o r r e c t i o n f o r s e l f - a b s o r p t i o n and t o l e s s than 15$ f o r a the remainder. The s e l f - a b s o r p t i o n a t the l i n e s 6Lu02A and 6lii3A i s somewhat higher however and the e r r o r s a s s o c i a t e d w i t h t h e i r values are estimated to l i e i n the range 20$ to 25$. T h i s would account f o r a p a r t of the d i s c r e p a n c y e x i s t i n g between our and Doherty's r e s u l t s f o r these two l i n e s . Doherty however, made no c o r r e c t i o n s f o r s e l f - a b s o r p t i o n and i t i s p o s s i b l e that h i s r e s u l t s f o r these s t r o n g l i n e s a r i s i n g from the metastable s c j - l e v e l are s l i g h t l y low. The agreement between absolute v a l u e s i s poor except i n the case of P r i e d r i c h s 1 r e s u l t s . However, as has been mentioned, Ladenburg's a b s o l u t e s c a l e i s based on an assumption f o r the o s c i l l a t o r s t r e n g t h of 6J4.O2X, and on the b a s i s of K l o s e ' s (1965) l i f e t i m e measurements Doherty's a b s o l u t e s c a l e would have t o be c o n s i d e r e d t o be i n e r r o r . I t i s f e l t t h a t K l o s e ' s measurements pr o v i d e a very a c c u r a t e b a s i s f o r an a b s o l u t e s c a l e . The r e l a t i v e v a l u e s measured i n t h i s experiment can a l s o be compared t o t h e o r e t i c a l p r e d i c t i o n s by means o f the J - f i l e sum r u l e . T h i s r u l e ( S h o r t l e y 1935) s t a t e s t h a t f o r any c o u p l i n g scheme i n which the jumping e l e c t r o n i s not e q u i v a l e n t to any other e l e c t r o n i n the i n i t i a l or -60-f i n a l c o n f i g u r a t i o n , the s t r e n g t h s of the J - f i l e s r e f e r r i n g t o the l e v e l s o f the i n i t i a l ( f i n a l ) c o n f i g u r -a t i o n s are p r o p o r t i o n a l to the values of 2J + 1 for those l e v e l s . In a t r a n s i t i o n a r r a y the set of l i n e s c o n n e c t i n g a s i n g l e g i v e n l e v e l o f one c o n f i g u r a t i o n w i t h a l l l e v e l s of the other c o n f i g u r a t i o n i s c a l l e d the J - f i l e r e f e r r i n g t o t h a t l e v e l . Thus i n Table 9 f o r example, the sums 'of each column and of each row ( the numbers i n b r a c k e t s ) should be p r o p o r t i o n a l t o the 2J + 1 value of the term d e s i g n a t i n g t h a t column or row ~and the sums should be independent o f c o u p l i n g . The values l i s t e d i n Table 9 are the l i n e s t r e n g t h s c a l c u l a t e d by u s i n g LS c o u p l i n g c o n d i t i o n s . In the Neon atom o f course the c o u p l i n g i s i n t e r m e d i a t e and thus the i n d i v i d u a l v a l u e s l i s t e d i n Table 9 cannot be compared to the experimental r e s u l t s . Table 10 c o n t a i n s the e x p e r i m e n t a l l y determined l i n e s t r e n g t h s a d j u s t e d so t h a t the sum of the Py column i s equal to the t h e o r e t i c a l sum f o r that column. The agreement between the sums i s q u i t e good and i s w i t h i n the e x p e r i m e n t a l e r r o r . The r e s u l t of column p i s another i n d i c a t i o n t h a t our e x p e r i m e n t a l value f o r 6k02A i s perhaps somewhat h i g h . The s t r e n g t h s of the s^ l i n e s however a p p e a r to b e lower than those p r e d i c t e d by the J - f i l e r u l e . The above comparisons v i n d i c a t e the f e a s i b i l i t y and p r a c t i c a l i t y of the e x p e r imental method. The r e s u l t s are b e l i e v e d t o p r o v i d e the most accurate values a v a i l a b l e f o r -61-Table 9 - Line Strengths i n L-S Coupling Term I s 3 P 1 3 » 1 3 * 1 V \ s Sum J P 2 1 2 . 5 .833 16.7 37.5 1 2 . 5 70 (150) 10 7 .5 12.5 10 12.5 37.5 (90) 10 30 50 (90) 10 16 J ? 3.3 (30) Sum- (10) 1 (10) (30) (30) (30) (30) (50) (5o) (50) (70) Table 10 - Experimental Line Strengths Term p l p 3 P2 P5 V PlO p l + P6 p 8 P9 Sum s 5 si. s 2 s 3 V . 3 . 11 9 .2 v.s. 6.1+ 2.9 16 .1 9 .1 2.0 V . 3 . 17.5 13 3 ,8 17 v.s. 8.8 18 7 .0 v.s. v.s. 10 15 28 27 l+.l 21+ 15 26 1+.7 83 (165) (81) (101) ( 3 D Sum ( I D , (9 .2) (35) (32.5) (29 .6) (25) (53) (55) (1+6) (83) Table 10a- Key to Tables 9 and 10 P l P3 p 2 P5 p 7 PlO P6 p 8 p 9 s 5 5882 5975 6217 7032 591+5 611+3 6331+ 61+02 V % 51+00 6071+ 6030 6128 6383 721+5 6096 6301+ 6506 5852 6652 6599 6717 7021+ 8083 6678 6929 7171+ s 3 6163 6266 6532 71+39 -Ls b 0 3 p r o \ % \ 3 S i *2 s \ - 6 2 -the transition probabilities of the red yellow lines of Neon when our data i s used in conjunction with the lifetime measurement of Klose (1965), whiph i s corroborated by the results of Friedrichs (1965). 6-3 CONCLUDING REMARKS The application of the experimental technique developed in this work to the investigation of other plasmas such as those created by arcs, plasma Jets, and shock, tubes should provide much useful information. In many recent experiments the assumption of thermodynamic equilibrium has been necessary (see for example boherty 1962), The technique described in this thesis enables a quantitative investigation of equilibrium conditions among the excited states of the atoms and furthermore provides information about the atomic constants without the assumption of equilibrium. It i s hoped that this work w i l l provide a basis for many such future experiments. -63-APPENDIX 1 BRTGHT1ESS TEMPERATURES Prom Planck's Law the r a d i a t i o n i n t e n s i t y per u n i t wavelength emitted by a b l a c k body at a t r u e temperature T may be w r i t t e n where c 1 = 2 h c 2 = 1.1909(10" 1 2) watt cm 2 s t e r - 1 , = hc/k = 1.1+380 cm°K , and C i s a constant determined by the s o l i d angle subtended by the emitted l i g h t . I f tj(X,~r) i s the e m i s s i v i t y o f the standard lamp b e i n g used and Tft) Is the t r a n s m i s s i o n f a c t o r of the medium through which the l i g h t t r a v e l s the i n t e n s i t y f a l l i n g on the r e c e i v e r i s gi v e n by CBfcTlfrdU Cc, Ase(Pi)r)rO\)(e^Ccyxr) - / ) ' ^ d t The b r i g h t n e s s temperature of the l i g h t source i s d e f i n e d by where B(/\)S) i s the Planck f u n c t i o n at the wavelength A and the b r i g h t n e s s temperature S. In terms of the b r i g h t n e s s temperature the i n t e n s i t y f a l l i n g on the r e c -e i v e r may thus be r e p r e s e n t e d by -6 L L -For a f l a s h tube with a brightness temperature at the wavelength A the i n t e n s i t y a r r i v i n g at the detector i s CBfa Qd* dt* cc rs(e*p(cV*s) - iT'd*. I f the same geometry i s used for both sources and i f they are exposed for equal times the r a t i o of t h e i r i n t e n s i t i e s at the wavelength A is exp(cV*S) ' I This r a t i o must be mul t i p l i e d by the exposure time r a t i o i n the case of photometric investigations. Sfi can thus 8fa> Sf!) be determined d i r e c t l y i f ^ Is measured and the brightness temperature S of the standard source is known. -65-APPENDIX 2 PHOTOGRAPHIC PHOTOMETRY Photographic photometry i s the technique used t o r e l a t e the b l a c k e n i n g on a photographic emulsion t o the i n t e n s i t y o f l i g h t which caused the b l a c k e n i n g . T h i s b l a c k e n i n g i s c a l l e d the d e n s i t y D and i s de f i n e d i n terms o f the emulsion t r a n s m i s s i o n by D * l o g 1/T. The t r a n s m i s s i o n T i s measured w i t h a densitometer and the d e n s i t y found d i r e c t l y . The s p e c t r o g r a p h i c p l a t e may be c a l i b r a t e d by v a r y i n g the l i g h t f a l l i n g on I t In known s t e p s . The t o t a l amount o f l i g h t f a l l i n g on the f i l m i n each step Is d e f i n e d as the exposure E = I t , " ' ' ' ' where I i s the i n t e n s i t y o f l i g h t and t i s the exposure time. The emulsion d e n s i t y c o r r e s p o n d i n g t o each exposure step i s then measured and p l o t t e d versus the the l o g a r i t h m of the exposure. The zero on the exposure a x i s i s f i x e d a r b i t r a r i l y f o r the measurement, of r e l a t i v e i n t e n s i t i e s . The r e s u l t i n g p l o t i s known as the c h a r a c t -e r i s t i c curve and a " t y p i c a l example i s shown i n F i g u r e 9 The i n t e n s i t y o f an unknown l i g h t source i s obtained r e l a t i v e to t h a t of the c a l i b r a t i o n source by measuring i t s : d e n s i t y and u s i n g the c h a r a t e r i s t i c c u r v e . For the h i g h e s t accuracy measurements should be r e s t r i c t e d t o the almost l i n e a r p a r t of the curve. When one wishes t o compare i n t e n s i t i e s at two -66-d i f f e r e n t wavelengths either the spectral d i s t r i b u t i o n of the c a l i b r a t i n g l i g h t source must be known, or an additi o n a l spectrum of a l i g h t source of known frequency v a r i a t i o n must be taken on the same p l a t e . The r a t i o of the two i n t e n s i t i e s can then be obtained with the help of a c h a r a c t e r i s t i c curve plotted for each wavelength and the known in t e n s i t y r a t i o of the standard or* c a l i b r a t i n g source. Figure 9 - The Cha r a c t e r i s t i c Curve Log It The c h a r a c t e r i s t i c curve varies with development time^ -developer temperature, and wavelength. To reduce errors a c h a r a c t e r i s t i c curve should therefore be plotted for each wavelength and for each p l a t e . -67-APPENDIX 3 SELP-ABSORPTION k 0 l S k Q l S 0.10 0.96k 0.096k 0.15 0.91+8 0.1k2 0.20 0.933 0.187 0.25 0.917 0.229 0.30 0.902 0.270 0.35 0.887 0.311 o.I+o 0.872 0.3k8 0.1+5 0.859 O.387 0.50 0.81+1+ 0.1+21 o.55 0.831 Q.k57 0.60 O.818 0.1+91 0.65 0.806 0.52k 0.70 0.793 0.555 0.75 O.78O 0.585 0.80 O.768 0.620 o.85 0.757 0.61+0 0.90 0.71+5 0.675 0.95 0.73k 0.700 1.0 0.725 0.725 1.2 I.683 0.820 1.1+ 0.61+6 0.905 1.6 0.616 0.985 1.8 0.58k 1.050 2.0 0.556 1.112 2.2 0.532 1.170 2.1+ 0.507 1.218 2.6 O.I+87 1.267 2.8 0.1+68 1.311 3.0 0.ii50 1.350 FACTOR S AND CURVE OF GROWTH k 0 l S k 0 l S 3.2 0.1+32 1.385 3 4 0.kl7 U. .0 0.372 1.1+88 1+.1+ 0.31+7 1.530 5 0.316 1.580 6 0.27 1.65 7 0.21+ 1.72 8 0.22 1.77 9 0.20 1.82 10 0.18 1.86 12 0.16 1*92 Ut 0.1k 1.98 17 0.12 2.0k 20 0.10 2.09 25 0.08 2.15 30 0.073 2.20 35 0.061+ 2.2k 1+0 0.056 2.27 0.051 2.31 50 0.01+6 2.3k 60 0.039 2.38 70 0.031+ 2.1+2 80 0.030 2.1+6 90 0.027 2.1+9 100 0.025 2.52 200 Q.013 2.69 500 0.005 2.88 1000 0.003 3.02 K° ]J.-TT / V ^ V 2lVE 3/V3 Table 11 - S e l f - A b s o r p t i o n F a c t o r S Tabulated versus k Q l and the Product k Q l S (Ladenburg and Levy 1930) -69-APPENDIX It THE PABRY-PEROT INTERFEROMETER The g e n e r a l t h e o r y of the Pabry-Perot i n t e r f e r o m e t e r has been thoroughly d i s c u s s e d by Meissner (I9I4.1,19l|.2) . F o l l o w i n g h i s treatment we wish t o c o n s i d e r the i n t e n s i t y d i s t r i b u t i o n produced by the i n t e r f e r o m e t e r when i t i s i l l u m i n a t e d by a Doppler broadened s p e c t r a l l i n e . As i s w e l l known, the i n t e n s i t y d i s t r i b u t i o n prod-uced by the i n t e r f e r o m e t e r f o r monochromatic l i g h t i s A l where r i s the r e f l e c t i o n c o e f f i c i e n t of the p l a t e s and p i s the order number., I f we l e t p be the sum of an i n t e g e r and a s m a l l f r a c t i o n a l p a r t 2f of the next order A l reduces to In terms of the apparatus h a l f - w i d t h the apparatus f u n c t i o n can be w r i t t e n T = where <JV/' i s the f r e e s p e c t r a l range and X ^ ^V) i s the d i s t a n c e from the centre o f the f r i n g e . - 7 0 -The Doppler l i n e p r o f i l e w i t h the h a l f - w i d t h i s r e p r e s e n t e d by curve I i n F i g u r e 11 and the apparatus funct i o n Iff) by curve I I . A s m a l l i n t e r v a l between x and x + dx having an I n t e n s i t y p r o p o r t i o n a l t o produces at the frequency V , by the a c t i o n of the i n t e r f e r o m e t e r , an i n t e n s i t y p r o p o r t i o n a l t o d i - y£u Id) = fa) 4x I6J-V0- *=; F i g u r e 1 1 - S p e c t r a l Line (I) and Apparatus ( I I ) P r o f i l e s -71-The summation over a l l c o n t r i b u t i o n s g i v e s — OO T h i s i n t e g r a l has been evaluated by Minkowski and Bruck (1935) who summarized t h e i r r e s u l t s i n the form of a graph which i s reproduced i n F i g u r e 12. T h i s curve can to the Doppler h a l f - w i d t h A\>D i f the apparatus h a l f - w i d t h c a l c u l a t e d i f the r e f l e c t i o n c o e f f i c i e n t o f the p l a t e s i s known. The ex p e r i m e n t a l d e t e r m i n a t i o n d e s c r i b e d i n the second s e c t i o n of Chapter 5 a l s o takes i n t o account any s l i g h t i r r e g u l a r i t i e s I n the s u r f a c e of the p l a t e s however, and Is t h e r e f o r e the more a d v i s a b l e method f o r the d e t e r m i n a t i o n o f the apparatus h a l f - w i d t h . be used f o r the r e d u c t i o n of the measured h a l f w i d t h Ae Mv Is known. T h e o r e t i c a l l y the apparatus width can be -73-APPENDIX $ SPECTRAL LINE SHAPE The s p e c t r a l l i n e p r o f i l e observed on a ph o t o g r a h i c p l a t e a f t e r the l i g h t has passed through the spectrograph can be re p r e s e n t e d by too where^/l^l i s the observed i n t e n s i t y at the frequency V , _L(\J') i s the f u n c t i o n which d e s c r i b e s the a c t u a l l i n e p r o f i l e , and c a l l e d the apparatus f u n c t i o n of the s p e c t r o g r a p h . The c o n v o l u t i o n i n t e g r a l r e p r e s e n t s • the d i s t o r t i o n o f the a c t u a l l i n e shape by the apparatus. I f the s l i t o f the spectrograph i s very wide compared to the h a l f w i d t h of the s p e c t r a l l i n e the apparatus f u n c t -i o n can be re p r e s e n t e d by a r e c t a n g l e of dimension A which depends on the dimensions of the image of the s l i t , t h a t i s Thus I ' M ^ J- f rev')** and the peak i n t e n s i t y of the observed p r o f i l e i s equal t o the i n t e g r a t e d i n t e n s i t y o f the s p e c t r a l l i n e . -7k-A P P E N D I X 6 R E C I P R O C A L D I S P E R S I O N S OP L I T T R O W AND E B E R T S P E C T R O G R A P H S I N A /mm L I T T R O W (3rd Ord») 5852.1*9 5.13 5881.90 5.13 5910*.83 5.12 5975.53 5.07 6030.00 5 . 0 5 607i*.3k 5.01* 6096.16 5 .02 611*3.06 5 .00 6163.59 i*.98 6217.28 1*.95 6266.50 1*.93 6301*,79 1*.90 6331*.1*3 1*.86 6382.99 k . 8 k 6k02.25 k .76 6506.53 -k .7k 6532.89 ,1*.62 6598.95 l*.6k 6678.27 1*.55 6717.01*. 6929 7032 E B E R T E B E R T (1st Ord.) 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