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Line profiles in a neon glow plasma Stansfield, Barry Lionel 1967

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i LINE PROFILES IN A NEON GLOW PLASMA by BARRY LIONEL STANSFIELD B . A . S c , U n i v e r s i t y of T o r o n t o , 1965 A T h e s i s Submitted i n P a r t i a l F u l f i l m e n t of The Requirements f o r the Degree of M.A. S c . i n the Department of P h y s i c s We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA JANUARY, 1967 In presenting this thesis in pa r t i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of IPHVS \ CS The University of Bri t i s h Columbia Vancouver 8, Canada ^ e MAECM 3Q; 13^ 7 i i A b s t r a c t A new experimental technique has been developed f o r the determination of absorption l i n e p r o f i l e s i n steady-state p l a s -mas. The method involves observing the t o t a l transmitted l i n e i n t e n s i t y of one component of the l o n g i t u d i n a l Zeeman patter n from a background source. The frequency s h i f t of t h i s l i n e i s determined from the known magnetic f i e l d and the Lande' g-factors i n v o l v e d . The l i g h t from the background source i s amplitude modulated by a chopping wheel, and the i n t e n s i t y of the t r a n s -mitted l i g h t i s measured w i t h a phase-sensitive d e t e c t o r . i i i TABLE OF CONTENTS A b s t r a c t Index of T a b l e s Index of F i g u r e s Acknowledgments CHAPTER I I n t r o d u c t i o n CHAPTER I I Theory (a) A b s o r p t i o n of R a d i a t i o n (b) A b s o r p t i o n of L i n e R a d i a t i o n (c) B r o a d e n i n g of S p e c t r a l L i n e s (d) E f f e c t s of Magnetic F i e l d CHAPTER I I I Experiment (a) Apparatus (b) E x p e r i m e n t a l P r o c e d u r e CHAPTER IV R e s u l t s CHAPTER V D i s c u s s i o n and C o n c l u s i o n s (a) Method (b) R e s u l t s (c) F u t u r e Work APPENDIX (a) D e t e r m i n a t i o n of L i n e P r o f i l e from T r a n s m i s s i o n (b) S e l f A b s o r p t i o n of S p e c t r a l L i n e s R e f e r e n c e s # . » . . « . . . . o . . . . . . . . . . . . . . . « • • • • • • • • • • • • • • • i v INDEX OF TABLES No. Page 1. I s o t o p e S h i f t s f o r L i n e s S t u d i e d 28 2# 3R©su.lts of S s s t P i t 0*«efto»oa«»o*«*« • • o o 0 0 o « » o e « 3^-INDEX OF FIGURES No. Page 1. P a r t i a l Term Diagram of Neon 21 2. E x p e r i m e n t a l Arrangement 2l\. 3 • -A."bs03r*p"fcxorjL T u."to G 0 o o « e » 0 O 0 « « o o e o o « « * « o « « « « « o « « o 0 » 2^ Ij.. R e s u l t s f o r 607i|. A3 l i n e 32 5>» R e s u l t s f o r 6266 A* l i n e . . . . o . . . . . . . . . » » » . . . . . » » 33 6. R e s u l t s f o r 6532 X l i n e o o . . . . . . . . . . . . . . . . . . . . . o 3U-7. E f f e c t of S e l f A b s o r p t i o n on L i n e Shapes .....<,. I4.7 V ACKNOWLEDGMENTS I w i s h to thank D r . R . A . Nodwel l f o r h i s guidance and con t i n u e d i n t e r e s t d u r i n g the course of t h i s work:. I am a l s o i n -debted to D r . F . ¥ . Dalby f o r the i n i t i a l idea and f o r many h e l p f u l s u g g e s t i o n s . Thanks a l s o to the other members of the plasma p h y s i c s group to D r . ¥ . Seka f o r many h e l p f u l d i s -c u s s i o n s , and to Mr.. ¥ . R a t z l a f f and Mr . J . Dooyeweerd f o r t h e i r f i n e work on the e l e c t r o n i c s . CHAPTER I I n t r o d u c t i o n H i s t o r i c a l l y , s p e c t r o s c o p i c methods have been used e x t e n -s i v e l y f o r the s t u d y of plasmas. T h i s broad a p p l i c a t i o n has a r i s e n because plasmas n a t u r a l l y are l i g h t e m i t t e r s , the wave-l e n g t h of l i g h t i s s h o r t so t h a t s p a t i a l r e s o l u t i o n i s good, and d a t a may be o b t a i n e d w i t h l i t t l e or no p e r t u r b a t i o n of the plasma. I n a s t r o p h y s i c a l plasmas, the o n l y t o o l a v a i l a b l e i s s p e c t r o s c o p y s i n c e the sources are f a r removed. U s u a l l y the s p e c t r o s c o p i s t l o o k s a t e i t h e r the l i n e i n t e n s i t i e s at v a r i o u s wavelengths or the i n d i v i d u a l l i n e shapes. I n the former c a s e , i 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 are known, r e l a t i v e abundances of e x c i t e d atoms and i o n s may be o b t a i n e d and e s t i m a t e s of temperature and degree of i o n i z a t i o n made. I n the l a t t e r case the shape of the l i n e depends on many f a c t o r s — f o r example, the t r a n s i t i o n p r o b a b i l i t y , the gas t e m p e r a t u r e , the p r e s s u r e , the d e n s i t y of charged p a r t i c l e s . I f the l i n e shape c o u l d be p r e c i s e l y determined and the c o n t r i b u t i o n s o f the v a r i o u s f a c -t o r s a s s e s s e d , many p h y s i c a l p r o p e r t i e s of the plasma c o u l d be d e t e r m i n e d . The p a r t i c u l a r i n t e r e s t i n d e t e r m i n i n g the l i n e shapes f o r a Neon glow plasma, as r e p o r t e d h e r e , was generated by p r e v i o u s e x periments i n t h i s l a b o r a t o r y (Robinson^- ; and I r w i n * " ) which determined o s c i l l a t o r s t r e n g t h s i n Neon by ab-s o r p t i o n methods. The a n a l y s i s of these experiments assumed a 1 2 Doppler-broadened l i n e , , and i t was deemed d e s i r a b l e t o check t h i s a ssumption e x p e r i m e n t a l l y and t o determine the magnitude of the d e p a r t u r e f rom D o p p l e r shape. The o b j e c t of the e x p e r i -ment r e p o r t e d here i s t o check the f e a s i b i l i t y of d e t e r m i n i n g t h i s d e p a r t u r e e x p e r i m e n t a l l y w i t h a n o v e l t e c h n i q u e . A l s o , i f a good t e c h n i q u e c o u l d be developed t o d e t e r -mine l i n e shapes, t h e n i t c o u l d be used t o stu d y the e f f e c t s of p r e s s u r e b r o a d e n i n g of s p e c t r a l l i n e s a t r e l a t i v e l y low p r e s -s u r e s . T h i s i s an ar e a where few r e s u l t s have been p u b l i s h e d , because of the d i f f i c u l t y i n d e t e r m i n i n g by p r e s e n t t e c h n i q u e s the shape of such narrow l i n e s a c c u r a t e l y . We use an i n t e n s i t y - m o d u l a t e d , f requency-modulated back-ground s o u r c e , and a p h a s e - s e n s i t i v e d e t e c t o r t o measure the t o t a l l i g h t i n t e n s i t y t r a n s m i t t e d t h r o u g h an a b s o r p t i o n t u b e . Prom a measure of t h i s l i n e i n t e n s i t y as a f u n c t i o n of f r e -quency s h i f t ( g i v e n by the Zeeman s p l i t t i n g ) , we determine the p e r c e n t t r a n s m i s s i o n as a f u n c t i o n of f r e q u e n c y . T h i s then a l l o w s us t o i n f e r ( f r o m a computer a p p r o x i m a t i o n ) the shapes of the a b s o r p t i o n l i n e s . I n the experiment r e p o r t e d h e r e , the l i n e w i d t h of the background source and a b s o r b e r were comparable. I t i s con-c e i v a b l e t h a t under such c o n d i t i o n s an a p p r o p r i a t e i n v o l u t i o n of the cur v e would g i v e the shape of b o t h the e m i t t e r and absorb-e r . Some attempt has been made at t h i s and i t i s shown t h a t the 3 method i s indeed f e a s i b l e . I t i s obvious, though, that a bet-t e r r e s u l t would obtain i f the l i n e width of the emitter were s i g n i f i c a n t l y l e s s than that of the absorber. I t was not w i t h -i n the scope of the present work to pursue t h i s p o s s i b i l i t y . CHAPTER I I Theory (a) A b s o r p t i o n of R a d i a t i o n We c o n s i d e r a p a r a l l e l beam of l i g h t of i n t e n s i t y ly i n the frequency range y to v+d v> i n c i d e n t on a medium composed of atoms capable of absorb ing the l i g h t . We suppose there are N-[_ atoms per c c . i n the lower s t a t e of which X N-j_ are capable of absorb ing i n the frequency range y*to v/+dV , and atoms i n an e x c i t e d s ta te of which £ N2 are capable of e m i t t i n g i n t h i s f requency range . As the beam t r a v e r s e s a l a y e r of atoms of t h i c k n e s s dx , -then i n t e n s i t y at f requency V w i l l change b y : - d d v / j V ) = XN .dx h V B, 0 ly* - I N , dx h V B o n IV-JN, dx hv* A 2 1 Y 1 12 fiC 2 21 w 2 i p f t I f we have a b a i l a b l e a means f o r d i s t i n g u i s h i n g between the beam r a d i a t i o n and the spontaneous emiss ion from the ab-s o r b i n g medium, we can neglec t the l a s t term i n the e q u a t i o n , g i v i n g u s : -d(Iv>JV) = N n dxh B 1 ? I v - j " NodxhVB l y HTTT IfTT The B ' s are the E i n s t e i n c o e f f i c i e n t s , such that B ^ I y i s the p r o b a b i l i t y (per atom) per second that the atom i n s ta te 1 w i l l absorb a quantum h V and end up i n s t a t e 2 when ex-posed to r a d i a t i o n of i n t e n s i t y l y i n the f requency range V to k V'+dy^. i V / i i - T T i s the i n t e n s i t y of 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 the B's are d e f i n e d . Hence we have: - 1 d l y J V = h ^ ( B . J N . - B 9- J* N 9) fydT Iprr 1 2 1 2 1 2 Comparing t h i s t o the d e f i n i t i o n of the a b s o r p t i o n c o -e f f i c i e n t a t the f r e q u e n c y V : d I V = - I V k v » dx we have the c o n n e c t i n g r e l a t i o n : k v cfV= h y ( B 1 2 c f N 1 - B 2 1 J , N 2 ) . I f we c o n s i d e r the l i m i t as c/v'-^0, and i n t e g r a t e , we have : / k y d W = / YiV ( B 1 2 d N x - B 2 1 dN 2) l i n e l i n e = hVo ( B 1 2 N X - B 2 1 N 2 ) , i r n where i s the number d e n s i t y of the lower s t a t e and L T 2 the upper. 6 The E i n s t e i n c o e f f i c i e n t s are r e l a t e d by: A A 2 1 _ 2 h V ^ Jl ^12 ~~ S 2 h i <* J i , B 1 2 S2 where the g's r e p r e s e n t the d e g e n e r a c i e s of the s t a t e s 1 and 2, I t i s customary t o d e f i n e the l i f e t i m e f o r the t r a n s i t i o n f r o m s t a t e 2 t o s t a t e 1 a s : T = i A'21 U s i n g t h e s e r e l a t i o n s we have: l i n e ^ i T ( ^ i i T h i s r e l a t i o n i s t r u e f o r any a b s o r p t i o n l i n e shape, and hence i s independent of the b r o a d e n i n g mechanism. I n terms of the o s c i l l a t o r s t r e n g t h f o r the t r a n s i t i o n we have o f N P g-, V d V = N 1 f 1 2 T £ _ 1- % f — L rmc y 1 6 2 l i n e I n most cases the p o p u l a t i o n of the upper l e v e l i s much s m a l l e r t h a n t h a t of the lo w e r l e v e l , and i n t h i s a p p r o x i -7 n a t i o n : f ky 6-V= 0.0214. f 1 2 N 1 l i n e (b) Absorption of Line R a d i a t i o n Prom s e c t i o n (a) we have: d l ^ = -ly ky , dx where ky i s the absorption c o e f f i c i e n t at frequency ^ • S o l v i n g t h i s g i v e s : I y O f ) = I V ( o ) e - * V ^ , where ly {%) is the i n t e n s i t y i n the frequency i n t e r v a l V" to y + d V a f t e r t r a v e r s i n g a path of leng t h / cm., and ly (o) i s the i n c i d e n t i n t e n s i t y i n the same frequency range. I f the d e t e c t i n g instrument gives a reading p r o p o r t i o n a l to the t o t a l ( i n t e g r a t e d ) l i n e i n t e n s i t y , as i n a monochro-mater-photoraultiplier arrangement say, then the recorded r e s -ponse i s p r o p o r t i o n a l t o : I ( / ) = f i y ( o ) e " k V " ^ d V . l i n e The percent transm i s s i o n i s then given by: = l i n e I ^ j o ) e ' k ^ d V . IW(o) d v l i n e 8 Note t h a t l y - (o) and k y1 are f u n c t i o n s of the f r e q u e n c y V, and t h a t I y ( o ) and k y/ may be of d i f f e r e n t shape and need not be c e n t e r e d on the same f r e q u e n c y : I n t h i s experiment the i n c i d e n t l i g h t i s d e r i v e d from one component of the l o n g i t u d i n a l Zeeman p a t t e r n , and hence the s p a c i n g ^ V ' i s determined by the Zeeman s p l i t t i n g . I f we c o n s i d e r the f r e q u e n c y measured from the c e n t r e of the l i n e s , we have: k s/ = k (w) and l y (o) = I (w- Av> ), where w = V - Vo. T h i s g i v e s us for the t r a n s m i s s i o n : T (Z» V ) l i n e I (w- A v 1 ) e ~ k ( w ) ^ dw l i n e 9 which i s a convolution i n t e g r a l of complicated f u n c t i o n s . (c) Broadening of S p e c t r a l Lines ( i ) N a t u r a l Line Broadening An atom emits r a d i a t i o n when an atomic e l e c t r o n makes a t r a n s i t i o n from an upper energy s t a t e to a lower s t a t e . From Quantum Theory we know that the atomic st a t e s w i t h f i n i t e l i f e t i m e s do not have a p r e c i s e l y defined energy, but encompass a range of energies: A E = > & t where Z^t i s the l i f e t i m e of the s t a t e . A quantum mechanical treatment of the process of emission of r a d i a t i o n shows ( 1 0 ) the i n t e n s i t y d i s t r i b t u i o n w i t h i n a l i n e to be: ( f r ? 2 T T ) i 2 1 5 E 0 - E, ? 1 where V 2 I = t h ° e B o n r f r e q u e n c y ^ — - f o r the t r a n s i t i o n between the states 1 and 2 , and -A E- E, h~ We see that ^ -| = r e l a t i o n above* 1 2 T f ^ t 1 from the u n c e r t a i n t y 10 IT the atom i s in' s t a t e 1, then l/& i s ( a p p r o x i -m a t e l y ) the number of spontaneous t r a n s i t i o n s w h i c h can o c c u r per second. I f k i s a lower s t a t e c a p a b l e of c o m b i n a t i o n w i t h s t a t e 1, t h e n the number o f t r a n s i t i o n s 1-—>k i s : : 8 T T 2 e 2 \/ 2 f ~~3 v l k I k mc where V* l k = Bohr f r e q u e n c y •^lk = o s c i l l a t o r s t r e n g t h f o r the t r a n s i t i o n . 1 = 8 T T 2e 2 X ~ ~ V 2 l k f l k mc3 2 f flTT2 2 \ ^ V l l c l k and so AE- , = 0 'V 2 i L mc J k Hence i f we c o n s i d e r the b r o a d e n i n g of b o t h l e v e l s 1 and 2, we have: {? v V • •£ vV*> I n a l l cases c o n s i d e r e d here the n a t u r a l h a l f w i d t h i s much s m a l l e r t h a n the w i d t h a s s o c i a t e d w i t h any o t h e r b r o a d -e n i n g mechanism, and hence n a t u r a l b r o a d e n i n g can be c o n s i d e r e d as a n e g l i g i b l e e f f e c t . ( i i ) D o p p l e r B r o a d e n i n g I f we assume t h a t e v e r y atom a t r e s t emits monochro-matic r a d i a t i o n of f r e q u e n c y V 0 » we f i n d t h a t the l i g h t from 11 any p r a c t i c a l s ource i s broadened because o f the t h e r m a l motion of the emitters i n the s o u r c e . S i m i l a r l y , the a b s o r p t i o n l i n e is broadened because of the t h e r m a l motion of the a b s o r b e r s . I f we c o n s i d e r a beam of p a r a l l e l l i g h t t r a v e l l i n g i n the p o s i t i v e x d i r e c t i o n , atoms moving w i t h a speed v_ i n t h i s d i r e c t i o n w i l l absorb l i g h t from the beam of f r e q u e n c y V* = V* 0 (1 + V x / c ) . I f we assume t h e r m a l e q u i l i b r i u m , we know t h a t the number of p a r t i c l e s dn w i t h v e l o c i t y component i n the range Vx t o Vx + dx i s : where m i s t h e atomic weight of t h e a b s o r b e r s , and T i s the ab-s o l u t e t e m p e r a t u r e . S i n c e the v e l o c i t y component i s r e l a t e d t o the f r e -quency absorbed by: vx = _° / ^ * ^ ( v - v J we can s e e t h a t the a b s o r p t i o n c o e f f i c i e n t must be of the form: k m 2"kT V 2 o cm -1 12 which is a Gaussian function of The half-width of the Doppler-broadened lines i s given by: ^ = 2 (In 2 ) * f2J£T \ 1 y 0 2 rac This gives for the half width: 2 - j -1 sec 4V d = 0 . 7 1 x 1 0 " 6 / T v 0 7 M A c where ^T^d is the half width in terms of wavelength, for a "line" of wavelength A o . For the plasmas used in this experiment the main broadening mechanism is the Doppler effect. If we assume that the absorption coefficient is completely determined by the Doppler profile, we have: ky dW = k c / e / | d v ^ line Y / Ko ^ 2 2 But from section (a) we have: ky d V = 0.021]. f 1 2 Ni , line 13 independent of any b r o a d e n i n g mechanism. -1 k 0 = 0.0225 I12 i N l cm = 0.75 x 10 -12 cm ( i i i ) P r e s s u r e B r o a d e n i n g I t i s found t h a t the s p e c t r a l l i n e s e m i t t e d by a gas at h i g h p r e s s u r e are broader than (and sometimes s h i f t e d w i t h r e s p e c t t o ) those l i n e s e m i t t e d by the same gas at lower p r e s -s u r e . T h i s b r o a d e n i n g o c c u r s because the e m i t t i n g atom i s p e r -t u r b e d by i t s n e i g h b o u r s . Because t h i s problem i s a v e r y d i f -f i c u l t one t h e o r e t i c a l l y , the t h e o r i e s of p r e s s u r e b r o a d e n i n g have developed a t each extreme of a p p r o x i m a t i o n . These two extremes g i v e r i s e t o the impact ( o r i n t e r r u p t i o n ) b r o a d e n i n g and s t a t i s t i c a l b r o a d e n i n g t h e o r i e s . I n the impact t h e o r y , the mean time between " c o l l i s i o n s " i s much g r e a t e r t h a n the. d u r a -t i o n of the c o l l i s i o n , and o n l y b i n a r y c o l l i s i o n s are c o n s i d e r -ed. T h i s t h e o r y can be seen t o have some v a l i d i t y i n the case of a r a r i f i e d g a s , and f o r the plasmas s t u d i e d i n t h i s e x p e r i -ment the impact t h e o r y c o u l d be expected t o be a f a i r l y good a p p r o x i m a t i o n . I n the s t a t i s t i c a l t h e o r y , the e m i t t i n g atom i s c o n s i d e r e d t o be i n a c o n s t a n t s t a t e of p e r t u r b a t i o n , the atom and i t s n e i g h b o r s f o r m i n g a q u a s i s t a t i c aggregate (a Ik p s e u d o - m o l e c u l e ) . T h i s t h e o r y i s capable of g i v i n g a b e t t e r a p p r o x i m a t i o n i n the case of dense g a s e s , or l i q u i d s . a f a i r l y good a p p r o x i m a t i o n i n the case of the low d e n s i t y , w e a k l y i o n i z e d plasmas used i n t h i s e x p e r i m e n t , we w i l l con-s i d e r f u r t h e r t h i s v i e w p o i n t , f o l l o w i n g the s i m p l e approach of L o r e n t z / ^  ^ : I f we c o n s i d e r an atom t o emit an i n f i n i t e l y l o n g w a v e - t r a i n i n the absence of c o l l i s i o n s , we may l o o k upon the impacts w i t h o t h e r p a r t i c l e s as g i v i n g r i s e t o i n t e r r u p t i o n s of t h i s w a v e - t r a i n , w i t h t h e phase ch a n g i n g randomly d u r i n g the c o l l i s i o n . We assume t h a t the c o l l i s i o n time i s much s m a l l e r t h a n the mean f l i g h t time T". The p r o b a b i l i t y d e n s i t y of a f l i g h t time t i s g i v e n by; D u r i n g the time i n t e r v a l 0 t o t , the wave i s s i n u s -o i d a l and so we have: S i n c e the impact t h e o r y can be expected t o p r o v i d e f ( t ) = -i - t / T e W0t o e 15 The i n t e n s i t y i s g i v e n by: oo It E 0 e -11 e J t and hence the h a l f w i d t h i s g i v e n by: , _ 2 -1 The mean f l i g h t time can be found from the r e l e -vant c r o s s s e c t i o n : _ 1 s e c , pT~ TT J>2 v n~~ where ^ i s the e f f e c t i v e " r a d i u s " o f the atom, v i s the average v e l o c i t y , n i s the p a r t i c l e d e n s i t y . T" = / 7 T m k T 1 __ sec • • J k P cr 2 where P i s the p r e s s u r e i n dynes/cm , m i s the atomic mass i n grams, 2 i s the c o l l i s i o n c r o s s - s e c t i o n . 16 s TC ITYN \<T xio P or where P i s t h e p r e s s u r e i n mm Hg. I n terms of w a v e l e n g t h : A A P •= \7.\ X P X l o crA . We s h o u l d note t h a t t h e " o p t i c a l c r o s s - s e c t i o n " can be s i g n i f i c a n t l y l a r g e r than t h e " ' k i n e t i c c r o s s - s e c t i o n " w h i c h appears i n e q u a t i o n s o f d i f f u s i o n e t c . More i n v o l v e d d e r i v a t i o n s v ; g i v e r i s e to an expres-s i o n : f o r the i n t e n s i t y d i s t r i b u t i o n i n a l i n e w hich i s broadened and s h i f t e d by c o l l i s i o n s . The f r e q u e n c y s h i f t ( ^/2-rr) i s of the o r d e r of l / l O t o 1/2 of the h a l f - w i d t h (ol/-^)t de-(£) p e n d i n g on the l i n e v - " . ( i v ) S t a r k B r o a d e n i n g S i n c e t h e r e are charged p a r t i c l e s p r e s e n t i n the glow d i s h c a r g e plasma we might expect some b r o a d e n i n g e f f e c t s due t o t h e c o l l i s i o n s o f the e m i t t i n g (or a b s o r b i n g ) atoms w i t h 17 charged p e r t u r b e r s . Since the current through the tubes i s small (5ma and 2ma), and the pressure i s low (iOmra and 2mm), 11 the charge d e n s i t y i s also small and should not exceed 10 p a r t i c l e s per cubic centimete^?^ . To obtain an order of magnitude r e s u l t f o r "Stark half-width"' we can use the formula (®) f o r p e r t u r b a t i o n by e l e c t r o n s (since t h i s w i l l be the l a r g e s t i o n i c e f f e c t ) : x-jhere o*> = 3 f o r the Neon l i n e s s t u d i e d . This gives 2.85 x 10~6 N s e c ' 1 f o r an e l e c t r o n temperature of about 2 e v . This i s a completely n e g l i g i b l e e f f e c t f o r t h i s experiment: 10 11 12 10 *17 10 ' .38 x 10-5 a. .38 x io~^ £ 3.8i 18 (v) R e s u l t L i n e P r o f i l e i f more than one b r o a d l n g  mechanism i s p r e s e n t I f we c o n s i d e r a l i n e t o be broadened by d i f f e r e n t mechanisms D o p p l e r , n a t u r a l , p r e s s u r e and S t a r k broadening — we can, i n a f i r s t a p p r o x i m a t i o n , c o n s i d e r each of t h e mechanisms t o a c t i n d e p e n d e n t l y . I n t h i s a p p r o x i m a t i o n we can c o n s i d e r each s m a l l element of the L o r e n t z p r o f i l e t o be D o p p l e r broadened, o r v i c e v e r s a . T h i s r e s u l t s i n an e x p r e s -s i o n f o r the a b s o r p t i o n c o e f f i c i e n t : the mechanisms. T h i s r e s u l t a n t e x p r e s s i o n i s c a l l e d a V o i g t p r o f i l e , and t h e r e has been e x t e n s i v e n u m e r i c a l work done on computing these p r o f i l e s as a f u n c t i o n of the where the z^Vs are the h a l f - w i d t h s a s s o c i a t e d i v i t h each of parameter A V o T h i s I w i l l c a l l the " V o i g t a parameter." 1 9 ( v i ) B roadening due to S e l f - A b s o r p t i o n F o r completeness sake, I s h o u l d i n c l u d e s e l f -a b s o r p t i o n as a b r o a d e n i n g mechanism. A l t h o u g h i n some cases the s t u d y of absorbed l i n e s can g i v e u s e f u l and i m p o r t a n t i n -f o r m a t i o n about the m a t e r i a l l o c a t e d between t h e s o u r c e and the d e t e c t o r , i n t h i s e x p e r i m e n t s e l f - a b s o r p t i o n i n t h e background source i s an unwanted (because i t i s e s s e n t i a l l y unknown) b r o a d -e n i n g mechanism. I t s h o u l d be noted t h a t a l l s o u r c e s produce e m i s s i o n l i n e s w h i c h a r e s e l f - a b s o r b e d t o a g r e a t e r or l e s s e r degree, and t h i s can cause d i s c r e p a n c i e s i n the measurement of the t o t a l i n t e n s i t y o f s p e c t r a l l i n e s and t h e i r shapes. The i n h e r e n t d i f f i c u l t y due t o s e l f - a b s o r p t i o n i n t h i s e x periment l i e s i n the f a c t t h a t the t r a n s m i s s i o n p r o -f i l e depends on the shape of t h e background e m i s s i o n l i n e . T h i s shape i s determined by t h e mechanisms o u t l i n e d p r e v i o u s l y , and a l s o by s e l f - a b s o r p t i o n . Whereas the o t h e r causes are known w i t h some a c c u r a c y , t h e f a c t we are v i e w i n g an inhomogen-dous plasma s i d e - o n makes the a n a l y s i s o f the e f f e c t of s e l f -a b s o r p t i o n v e r y d i f f i c u l t t o a c c o u n t . F o r a homogeneous w i t h " ' l i n e of s i g h t depth" ^ , we f i n d t h a t the i n t e n s i t y p r o f i l e i s g i v e n by": oC 1 - e " See Appendix 20 (d) E f f e c t s of the Magnetic F i e l d ( i ) Zeeman E f f e c t i n Neon I n t h i s experiment the aim i s t o determine the ab-s o r p t i o n l i n e p r o f i l e from a measurement of the t r a n s m i s s i o n as a f u n c t i o n o f t h e f r e q u e n c y s h i f t . I t has been f o u n d , how-e v e r , t h a t the shape of t h e background l i n e has a marked e f f e c t on t h e t r a n s m i s s i o n . To a i d i n s i m p l i f y i n g the a n a l y s i s , t h e n , we have been l e d t o s t u d y i n g those l i n e s w h i c h e x h i b i t t h e normal t r i p l e t p a t t e r n . F o r t u n a t e l y , the Zeeman e f f e c t i n Neon has been s t u d i e d c a r e f u l l y , and e x c e l l e n t d a t a e x i s t ^ 1 ^ t o f a c i l i t a t e our s e a r c h . Most of the 3P - 3'S l i n e s i n the Neon s p e c t r u m e x h i b i t a complex Zeeman s t r u c t u r e , but t h e r e are a few w h i c h have the t r i p l e t p a t t e r n -- t h e 5852, 6O7I4., 6163, 6 2 6 6 and 6 5 3 2 l i n e s . t ( i i ) Accompanying E f f e c t s The magnetic f i e l d , i f i t i s not homogeneous a c r o s s the e m i t t i n g volume, w i l l g i v e r i s e t o Zeeman components of s l i g h t l y d i f f e r e n t f r e q u e n c y s h i f t s from d i f f e r e n t p a r t s of the s o u r c e . T h i s w i l l r e s u l t i n a b r o a d e r e m i s s i o n l i n e , w h ich i s a s y m m e t r i c a l w i t h r e s p e c t t o the peak: see R ZZ 21 F i g u r e 1 — P a r t i a l Term Diagram of Neon Showing Zeeman T r i p l e t L i n e s LS n o t a t i o n Paschen n o t a t i o n ' S o 3 R P , Pz, Ps P* Ps P 7 PS o vD vD v5 cv2 10 v0 4 ID Off LP Y Y v " no S 4 v9 to 22 T h i s a s y m m e t r i c a l b r o a d e n i n g w i l l i n c r e a s e w i t h f i e l d s t r e n g t h and hence the background l i n e w i d t h w i l l be g r e a t e r when we are making measurements i n the wings of t h e l i n e . The magnetic f i e l d w i l l cause the charged p a r t i c l e s t o g r y a t e around the f i e l d l i n e s . S i n c e the f i e l d l i n e s are p e r p e n d i c u l a r t o the tube t h i s may d r i v e the p a r t i c l e s i n t o the w a l l s i f the Larmour r a d i u s i s g r e a t e r than the tube r a d i u s . T h i s w i l l r e s u l t i n an i n c r e a s e i n the tube r e s i s t a n c e s i n c e we must a p p l y a l a r g e r v o l t a g e t o make up f o r thes e l o s s e s t o the w a l l s . I t i s found t h a t f o r the f i e l d s used i n t h i s experiment t h a t the e l e c t r o n Larmour r a d i u s i s much l e s s than the tube r a d i u s . T h i s means t h a t t h e e l e c t r o n s w i l l be " c o n t a i n e d " by the f i e l d , and w i l l t r a v e l f a r t h e r i n the d i s c h a r g e b e f o r e b e i n g l o s t . They w i l l , t h e n , be able t o make more c o l l i s i o n s and so i n c r e a s e the number of e x c i t e d atoms. CHAPTER I I I Experiment (a) A pparatus ( i ) Background Source The background l i g h t s ource c o n s i s t s o f a Neon G e i s s l e r t u b e , p l a c e d between the p o l e f a c e s of an e l e c t r o -magnet. The source was observed t h r o u g h a s m a l l h o l e i n one of the p o l e p i e c e s . T h i s ensures t h a t we a r e o n l y u s i n g the c i r c u l a r l y - p o l a r i z e d components which d e r i v e from the l o n g -t u d i n a l Zeeman e f f e c t . The s m a l l h o l e i s about 2mm. i n diam-e t e r , t h e same as the c a p i l l a r y i n the G e i s s l e r t u b e . The v a r i a t i o n i n magnetic f i e l d o v e r such a d i s t a n c e i s q u i t e s m a l l , h a v i n g been measured by means of a H a l l e f f e c t probe t o be of the o r d e r o f 5 gauss or l e s s a t the h i g h e s t c u r r e n t used where the f i e l d was about I4. k i l o g a u s s . The t e m p o r a l v a r i a t i o n of the f i e l d i s a l s o q u i t e s m a l l and so we f e e l s a f e i n n e g l e c t i n g the e f f e c t of f i e l d inhomogeneity as a b r o a d e n i n g mechanism. The p r e s s u r e of the gas i n the G e i s s l e r tube was about 10 mm Hg, and a t t h i s p r e s s u r e we f i n d t h a t the L o r e n t z c o n t r i b u t i o n (which d e r i v e s f rom p r e s s u r e b r o a d e n i n g ) t o have a s i g n i f i c a n t e f f e c t on the shape o f the e m i s s i o n l i n e , and hence of the t r a n s m i s s i o n c u r v e . The t e m p e r a t u r e of the gas i n the c a p i l l a r y was 23 Figure Z — Experimental A r r a n g e meoi Elec+romagne+ O Absorption "Kibe Nicol Prism Chopping Wheel q u a r t e r -v^cwe p l a t e Monochromare r Phatomult\pl i e r Photo diode P h a s e -Sensi+ive Detec+or A^plr-Fier Recorder 2 5 measured by u s i n g a crude r e s i s t a n c e thermometer to be about 67°C ( i e 3 i | 0 0K) w i t h a current of 5 ma through the G e i s s l e r tube — the same c u r r e n t va lue as used throughout the e x p e r i -(7) ment. From t h e o r y ent of r a d i u s . , the temperature i s a constant independ-( i i ) A b s o r p t i o n tube The absorbing medium i s the p o s i t i v e column of a low pressure glow discharge i n Neon: Z O c m . cm. 3 mm dia. Anode D i a p K r a g no Ca+hode " C p E l e c t r o d e s - Aluminum c y l i n d e r s F i g u r e 3 -= A b s o r p t i o n tube The p r e s s u r e of the gas i n the tube was 2mm Hg, and the c u r r e n t used throughout the experiment was 2 m a . The diaphragms used at each end of the tube had a 3mm diameter hole centered on the a x i s of the t u b e . The den-s i t y of e x c i t e d s ta tes v a r i e s l i t t l e , w i t h i n t h i s r a d i a l d i s -tance ^ ) ( The tube was viewed through the anode t o cut down the abnormal end e f f e c t s as much as p o s s i b l e . 26 Under the c o n d i t i o n s of the exper iment , the ab-s o r p t i o n l i n e p r o f i l e i s mainly determined by Doppler broaden-i n g , w i t h a c h a r a c t e r i s t i c temperature of about 295° K . ( i i i ) O p t i c a l System The l i g h t from the background source i s d i r e c t e d by a condensing lens through a chopping w h e e l , through the absorp-t i o n t u b e , and i s then focused on the s l i t of a Bausch and Lomb monochromater. The entrance s l i t was kept j u s t s u f f i c i e n t -l y l a r g e to accept a l l the l i g h t from the s o u r c e , and the e x i t s l i t was made j u s t wide enough to a l l o w a l l of one l i n e to enter the p h o t o m u l t l p l i e r but to exclude a l l other l i n e s . The p h o t o m u l t l p l i e r was a P h i l i p s model 150 CVP, cooled by dry i c e to cut down on the thermal n o i s e . A\ quarter-wave p l a t e - N i c o l p r i s m combinat ion was used to convert the c i r c u l a r l y - p o l a r i z e d Zeeman components to plane p o l a r i z e d and then to s e l e c t one of these components. This combinat ion was p laced a f t e r the a b s o r p t i o n tube to cut down the amount of r a d i a t i o n from the a b s o r p t i o n tube which enters the monochromater, and was a l i g n e d to accept the r i g h t -c i r c u l a r l y p o l a r i z e d component. When the magnet was. run i n the normal current mode t h i s was the h i g h frequency component. ( i v ) E l e c t r o n i c D e t e c t i o n The ampli tude-modulated l i g h t beam f a l l i n g on the 27 p h o t o m u l t l p l i e r photocathode i s converted to a p u l s a t i n g e l e c -t r o n c u r r e n t . This c u r r e n t s i g n a l i s then a m p l i f i e d by a n a r -row band a m p l i f i e r , centred on the chopping frequency of , 9 9 0 c p s . This a m p l i f i e d s i g n a l and the re ference s i g n a l are fed i n t o a p h a s e - s e n s i t i v e d e t e c t o r , and the output of the PSD i s shown on a H e a t h k i t char t r e c o r d e r . (b) Exper imenta l Procedure The t r a n s m i t t e d l i n e i n t e n s i t y was measured w i t h the p h a s e - s e n s i t i v e d e t e c t o r as a f u n c t i o n of the a p p l i e d magnetic f i e l d . I f the i n t e n s i t y i s measured both w i t h and without an absorb ing medium we can determine the t r a n s m i s s i o n as a f u n c t i o n of the f requency s h i f t . The frequency s h i f t i s determined by n o t i n g the c u r r e n t through the e lec t romagnet , u s i n g a c a l i b r a -t i o n curve d e r i v e d from measurements w i t h a H a l l e f f e c t probe to o b t a i n the corresponding magnetic f i e l d s t r e n g t h , and then u s i n g the formulae r e l a t i n g Zeeman s p l i t t i n g to f i e l d as g i v e n by Back The r e s u l t i n g t r a n s m i s s i o n p r o f i l e must then be i n -t e r p r e t e d i n terms of the l i n e p r o f i l e s of the absorbing medium and the background s o u r c e . An attempt at i n t e r p r e t a t i o n was made by c a l c u l a t i n g n u m e r i c a l l y the t r a n s m i s s i o n p r o f i l e as a f u n c t i o n of the a b s o r p t i o n and emiss ion l i n e shapes, and t r y i n g to f i t the t h e o r e t i c a l p r o f i l e to the e x p e r i m e n t a l l y determined one. In c a l c u l a t i n g the t h e o r e t i c a l t r a n s m i s s i o n p r o f i l e , there 28 are s e v e r a l e f f e c t s which must be taken i n t o account since they have a s i g n i f i c a n t e f f e c t : 20 ( i ) The presence of two isotopes of Neon — Ne and 22 Ne being the main c o n t r i b u t o r s — i s important. Although 22 the l e s s abundant isotope (Ne ) produces only about l / l O as 20 much l i g h t as the Ne ; t h i s l i g h t i s absorbed much l e s s 22 s t r o n g l y . As a r e s u l t , there are s i t u a t i o n s when the Ne r a d i a t i o n i s the dominant c o n t r i b u t i o n to the measured i n t e n -s i t y . I t was found both exper i m e n t a l l y and t h e o r e t i c a l l y that the presence of the a d d i t i o n a l isotope causes the transmission p r o f i l e to be asymmetrical. To a c c u r a t e l y match the t h e o r e t i -c a l t ransmission curves t o the experimental curves, we must know the isotope s e p a r a t i o n . For t h i s parameter we used the McT) values quoted by Nagaoka and Mishima •"' : ( I i ) The e f f e c t of non-Doppler broadening mechanisms on the emission and absorption l i n e p r o f i l e s i s a l s o s i g n i f i c a n t . The main non-Doppler mechanism i s pressure-broadening, which Table 1 — Isotope S h i f t s 6071+ - . 0 2 0 6 6 1 6 3 - . 0 2 1 0 6 2 6 6 - . 0 2 : 1 2 6£3'2 - . 02I|.0 . 0 5 6 . 0 5 5 .051+ . 0 5 6 can give a Voigt parameter a as l a r g e as 0.2 i n the case of the G e i s s l e r tube. 2 9 ( i i i ) The l i g h t from the background source w i l l un-doubtedly s u f f e r from s e l f - a b s o r p t i o n , but q u a n t i t a t i v e l y the extent of t h i s e f f e c t may be d i f f i c u l t to take i n t o account . The computat ional d i f f i c u l t y i s due to the r a d i a l v a r i a t i o n i n the d e n s i t y of the emi t ters and t o . t h e c y l i n d r i c a l geom-e t r y viewed from the s i d e . Prom Chapter I I , s e c t i o n (b ) , we have the e x p r e s s i o n f o r the t r a n s m i s s i o n (as a f u n c t i o n of frequency) which we must t r y t o c a l c u l a t e : ( e d v \ — \}ne | I^to} dv , where line I y ( o ) i s 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 the background l i n e . S ince the background l i n e and the a b s o r p t i o n l i n e (g iven by K\>) are of comparable w i d t h s , we f i n d t h a t the t r a n s m i s s i o n curve i s a f f e c t e d by the shape of l y ' ( o ) . S ince t h i s shape can be a f f e c t e d by a l l the broadening mechanisms, we must t r y to take them i n t o account . A. programme was set up to c a l c u l a t e the i n t e g r a l s n u m e r i c a l l y , u s i n g Simpson's r u l e , a l l o w i n g f o r f u n c t i o n a l ex-p r e s s i o n a l s f o r Iy(o) and K / . For s m a l l V o i g t a parameters i t was found that a p e r f e c t l y good r e p r e s e n t a t i o n f o r a V o i g t f u n c t i o n i s a l i n e a r combinat ion of Gaussian and L o r e n t z i a n 30 f u n c t i o n s : V y ( a ) = a •» Ly>+ (1 - a) * Gy-, where Vy" i s a normalized (to peak = 1 ) V o i g t f u n c t i o n , Ly* a s i m i l a r l y normalized Lorentz f u n c t i o n and G y* a Gauss f u n c t i o n , where a l l have the same h a l f width. By t a k i n g i n t o account the v a r i a t i o n of h a l f width with a change i n a, i t i s i n gen e r a l a simple t a s k to c o n s t r u c t a good Voi g t f u n c t i o n f o r any s m a l l a. K y = K Q V y " ( a ) , where a i s the V o i g t parameter a p p r o p r i a t e to the absorbing medium, and —. where a i s the V o i g t parameter a p p r o p r i a t e t o the e m i t t i n g medium, Ko" i s the peak of the a b s o r p t i o n c o e f f i c i e n t f o r the e m i t t i n g medium, and Jf i s the e f f e c t i v e depth of the e m i t t i n g medium, x^hich corresponds to the diameter of the G e i s s l e r tube. In the numerical computation we used JH^~ = 0.2 cm, and = 10. T h i s was thought t o be a f a i r l y reasonable approximation, i n the l i g h t o f our l a c k o f knowledge. We a l s o assumed that t h e only non-Doppler broadening was that due t o pr e s s u r e , and that t h i s dependence i s - l i n e a r n: a = a -"- P. Under t h i s approximation a 2 we have —_ - — ; and so we attempted t o o b t a i n a best f i t by a 1 10 v a r y i n g K„ and a . We assume that Ky* i s a Voig t f u n c t i o n w i t h peak height K , and t h a t l y ( o ) i s a s e l f - a b s o r b e d V o i g t f u n c t i o n : CHAPTER IV R e s u l t s The main r e s u l t s were achieved en measurements of the 607i|., 6266 and 6532 $ l i n e s , a l l of which e x h i b i t the normal t r i p l e t p a t t e r n but w i t h 6O7I4 having an abnormally l a r g e s p l i t -t i n g . We a l s o made a few runs on the 5852 $ l i n e , but the ab-s o r p t i o n was so s m a l l that l i t t l e confidence was placed i n the r e s u l t s . A\ s e r i e s of graphs i s shown on the next few pages showing the experimental r e s u l t s f o r the three l i n e s along with the computed t r a n s m i s s i o n p r o f i l e s which best f i t the observed p r o f i l e s . Subject to the approximations o u t l i n e d i n the pre-ceding chapter, I found a best f i t f o r the f o l l o w i n g parameters: Table 2 - - R e s u l t s of best f i t KO KOdopp AV AVA 6O7I4. 0.2 O.2I4 0 . 2 6 CO3I4. 6 2 6 6 1.2 1.37 0.12 . 0 2 6 6532 0.7 0.8 0.12 .026 where K0 i s the peak h e i g h t of the V o i g t f u n c t i o n K y , KOdopp i s the c o r r e s p o n d i n g "pure Doppler h e i g h t , " AV i s the V o i g t parameter for the background source and AVA i s the V o i g t para-meter for the absorber. 31 Transmission (per cent) lOOf 90 + 80 + 7 0 + 6 0 f 50 + 40 T 3 0 + zo t 1 0 + o 32 Figure Ij. — Results f o r 6071+ fi l i n e — theory KO = .205^7=0.16 - 4 -4-- 4 - a W a v e l e n g t h shi4H G O ' ^ A ) Transmission lOOripe? cent) \ 90 - \ 8 0 70 f 6 0 f 50 4 0 + 30 + 2 0 f 10 t O 33 Figure 5 ~- Results f o r 6266 £ l i n e \ \ \ \ \ Theory KD = 1.2 Av = 0.12 \ Theory Pure Lorentz Theory Pure Doppler \ w \ \ \ \ \\ \ \ \ / / M I, I, / i / / / / \\ \5 \ 7 - 4 Wavelength s h i f t S ) Transmission (Per cent) 100 T 3k Figure 6 Results f o r 6532 1 l i n e -4 -E 0 , -2 o , Wavelength s h i f t (10 A.) 35 Since the 6266 2 and 6532 8 l i n e s have the same lower l e v e l , we can determine 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 from the r e l a t i o n : ( K O d o P P ) 1 _ ;\ ( K 0 d o p p ) 2 T\ 2 f r e l . . f r e l ~ (6266) 078 -= 1.78 Prom the r e s u l t s obtained by A. M. R o b i n s o n ^ ^ , we have f r e l = = ^ This agreement i s encouraging. Comparison Up u n t i l t h i s time the main work: on the pressure M -3 ) broadening of Neon s p e c t r a l l i n e s has been by Lang ^ . He found that most l i n e s i n the Neon spectrum showed a s i m i l a r broadening due to pressure except f o r the l i n e s which have the S 2 lower l e v e l . These l i n e s have a larg e " c o l l i s i o n diameter," most l i k e l y because of the strong o p t i c a l coupling of the S 2 l e v e l vjith the ground s t a t e , g i v i n g r i s e t o a l a r g e perturba-t i o n of the lower e l e c t r o n i c s t a t e ( S 2 l e v e l ) . The other op-t i c a l l y - c o u p l e d l e v e l , the Sj^ l e v e l , i s much l e s s s t r o n g l y 36 coupled", and so e x h i b i t s much le s s resonance broadening, while the other two l e v e l s (S3 and S^) are metastable and hence e x h i b i t no resonance e f f e c t s . The r e s u l t s quoted i n t h i s thes-i s f o r the Voigt a parameters are about twice as great as would be found by Lang f o r the same l i n e : Lang would have a = 0.065 f o r the 6532 l i n e , where-as I found a best f i t f o r a = 0.12. I should a l s o note that Connor and B i o n d i 1 ^ ) , on measuring the pressure broadening of the 5852 l i n e , found a broadening rate twice as great as that quoted by Lang. I should f u r t h e r note a decided discrepancy between my r e s u l t f o r the 607I4. l i n e and Lang's r e s u l t s . I found a best f i t f o r t h i s l i n e w i t h a = 0.16, whereas from Lang's r e s u l t s we should have a = 0 .033« I t appears from Lang's r e s u l t s that the l i n e s w i t h the S^ lower l e v e l do not broaden l i n e a r l y w i t h pressure. This e f f e c t could be the r e s u l t of some resonance broadening at lower pressures which becomes l e s s important w i t h i n c r e a s i n g pressures. This n o n - l i n e a r i t y could r e s u l t i n a l a r g e r value of a f o r the "Sj^ l i n e s " f or the low pressures we used. See (12) P 250 CHAPTER V Di s c u s s i o n and Conclusions ( a ) Method The method employed i n t h i s experiment would appear to provide a s u c c e s s f u l means of studying l i n e p r o f i l e s . I t was found p o s s i b l e to f i t a t h e o r e t i c a l computed transmission curve t o the experimental data, and from t h i s to i n f e r a p p r oxi-mate values f o r some of the shape-determining parameters of the l i n e . I t should be emphasized that t h i s procedure involved the approximation of various e f f e c t s : ( i ) the isotope s h i f t was assumed to be given by the r e s u l t s quoted by Nagaoka and Mishima^^^, and i t was f u r t h e r assumed that the amount of l i g h t from each isotope was propor-t i o n a l to i t s n a t u r a l abundance; ( i i ) the gross approximation of the e f f e c t of s e l f -absorption i n the background source, which can be a large e f-f e c t ; ( i i i ) the approximation of the l i n e s as Voigt func-t i o n s involves n e g l e c t i n g the e f f e c t s of f i e l d inhomogeneity i n broadening the background l i n e and n e g l e c t i n g any pressure s h i f t which accompanies the pressure broadening; ( i v ) the. e f f e c t i v e temperatures were estimated and so may not be very accurate, but i t was found that the t r a n s -mission curve i s not very s e n s i t i v e to a change i n the assumed 37 38 temperatures. (b) R e s u l t s In the face of these approximations i t can only be hoped th a t the r e s u l t s quoted i n t h i s t h e s i s give a f a i r ap-proximation of the relevant parameters — the c o l l i s i o n diam-e t e r s . But i t i s c e r t a i n l y obvious that we cannot i n v e s t i g a t e the e f f e c t s of pressure-broadening on the b a s i s of a measure-ment at one pressure. I f e e l i t i s d e f i n i t e l y worthwhile t o study t h i s more i n t e n s i v e l y , since the technique employed here provides a good method of studying the shape of narrow s p e c t r a l l i n e s , and there seem to be many i n t e r e s t i n g e f f e c t s In the pressure-broadening of Neon s p e c t r a l l i n e s . (c) Future Work The necessary sequal to t h i s f i r s t attempt i s t o change the experimental c o n d i t i o n s so to have the unknown parameters more under c o n t r o l . Since we would l i k e to study the e f f e c t s of pressure on the absorption l i n e , we must t r y to make the e f f e c t of the shape of the background l i n e s m a l l . This can be helped by mak-ing the emission l i n e narrow w i t h respect t o the absorption l i n e . The main attack towards making the emission l i n e narrow seems to be i n reducing the s e l f - a b s o r p t i o n i n the background source. This could be accomplished by using a lower pressure source w i t h a small depth of f i e l d , so that the opacity i s 39 s m a l l . This would a l s o tend to reduce the pressure broaden-ing and serve to make the emission l i n e more purely Doppler. As an a i d i n ' s i m p l i f y i n g the a n a l y s i s , we could use an i s o t o p -i c a l l y pure gas i n the background source so that we would have only one component i n the spectrum. We can a l s o t r y to make the absorption l i n e broader, e i t h e r by i n c r e a s i n g the Doppler width or i n c r e a s i n g the pressure. I f we want to study pressure-broadening i t would appear that the most l i k e l y candidate i s the $Q$2 £ l i n e since i t shows a l a r g e pressure broadening. APPENDIX (a) D etermination of L i n e P r o f i l e from T r a n s m i s s i o n The t r a n s m i s s i o n f u n c t i o n which one observes by such an experiment has been shown to be: "T(AV) = J ICuj -AVJG doO where K (to) d e s c r i b e s the a b s o r p t i o n l i n e p r o f i l e , and I ( w - ^ V ) the emission l i n e p r o f i l e . Our problem, being to determine K(w) from a knowledge of T ( A V ) , r e q u i r e s a knowledge of I ( w - A V ) s i n c e t h i s may be considered t o be the response func-t i o n of the apparatus on a measurement of the f u n c t i o n exp( - K(w)J?), For a ^ - f u n c t i o n response of the apparatus ( i . e . a p u r e l y monochromatic source) we f i n d : T ( A ^ ) = e~k^^%, and hence we can f i n d K(w) d i r e c t l y . But s i n c e the background l i n e has a f i n i t e width, i n f a c t comparable to the a b s o r p t i o n l i n e width, the a c t i o n of the response f u n c t i o n w i l l be to cause a d i s t o r t i o n of the measured f u n c t i o n . The response f u n c t i o n can be regarded as g i v i n g r i s e to a t r a n s f o r m a t i o n : ,.. > » T = T r ( e from xvhich i t would appear d e s i r a b l e to o b t a i n the i n v e r s e ( i . e . the d e c o n v o l u t i o n ) : ho $ J O B 7 9 2 6 6 B S T A N S F I E L D S T I M E 5 S F O R T R A N _ _ C T R A N S AS F C N OF L I N E P A R A M E T E R S C B A C K G R O U N D L I N E H A S SOME L O R E N T Z S H A P E C ' I N C L U D I N G S E L F A B S IN B A C K G R O U N D C I N C L U D I N G T H R E E ' I S O T O P E S OF NEON R E A L K O . L REAL. K O S A B > L G T \ :  KO= i . . 2 L = 2 0 . W 0 = - 8 . '  WN = 8 . E Q U I V A L E N C E ( W P R I M . D Z ) T E = 3 4 0 . . . . . . . . . . . _ _ T A = 2 9 5 . H = 0 . 2 N = 80 : . . C QA I S P U R E D O P P L E R WIDTH IN . 0 1 A N G S T R O M Q A = 0 . 0 9 9 5 * S Q R T ( T A ) • _ QEj^0.J )9 9 5 * S Q R T (JjE )„ •_ — C AV IS"" VO I GT " P A R A M E T ER •  - . A V = 0 . 0 DO 9 4 M = l > 2 ; • Y = 1 0 . X = 0 . 2 C D l IS I S O T O P E S H I F T I N _ ._0 1 A N G S J_R OM_ D I =2 - "12 A V A = X * A V * S Q R T ( T E / T A ) . K 0 S A B = K 0*Y  L G T = 0 . 1 P = 1 . - A V _ _ _ J R = 1 . - A V A _ _ "P l "=3 . '1415*9 26 5 ~ " " ~ ~ C DD I S W I D T H OF L I N E WHEN' I N C L U D E SOME L O R E N T Z DD = Q E * ( 1 « + . 6 3 5 * A V + . 1 5 * A V * * 2 •) . _ _ DL=DD • DDI = 0 . 9 5 4 * D ' D _ D L I = D D T _ _ ' ' " DDA=QA*( 1 . + . 6 3 5 * A V A + ~ 15*AVA'**2~) " . D L A= DDA D D A I = 0 . 9 5 4 * D D A D L A I = D D A I D D 2 1 = 0 . 9 7 7 * D D D L 2 1 = D D 2 1 D D A 2 1 = 0 . 9 7 7 * D D A DL A 2 1 = DDA 2 1 Z = 0 . D P E = Z * A V # Q E i D P A = Z * A V A * Q A C V O I G T L I N E I S REP BY L I N E A R COMB OF L O R E N T Z $, G A U S S I A N B ( W ) = E X P ( - ( 2 . * W * S Q R T ( A L O G ( 2 . ) > / D D ) * * 2 ) + 1 0 . 1 * E X P . ( - ( 2 . * ( W+DI ) * S Q R T ( A L O G ( 2 . ) ) / D D I ) #*2 ) + 2 0 . 0 0 3 * E X P ( - ( 2 . * ( W + D I / 2 . ) * S Q R T ( A L O G ( 2 . ) ) / D D 2 1 ) * # 2 ) C ( W ) = l . / < l . + ( 2 . * ( W - D P E ) / D L ) # * 2 ) + 0 . 1 / ( l . + < 2 . * ( W + D I - D P E ) / D L I ) # * 2 ) S A B ( W ) =P*.B ( W ) + A V * C ( W ) E ( W ) = 1 . - E X P ( - S A B ( W ) * K 0 S A B * L G T ) D ( W ) = E X P ( - ( 2 . * W * S Q R T ( A L O G ( 2 . ) ) / D D A ) * * 2 > 1 + 0 . 1 * E X P ( - ( 2 . * ( W + D I ) * S Q R T ( A L 0 G ( 2 . ) ) / D D A I ) ' * * 2 ) 2 + 0 . 0 0 3 * E X P ( - ( - 2 . * ( W + D I / 2 . ) *SQR T ( A L O G ( 2 • ) ) V D D A 2 1 ) * * 2 ) S ( W ) = 1 . / ( 1 . + ( 2 ..# ( W - D P A ) / D L A )**2 ) 1 + 0 . 1 / ( 1 . + ( 2 . * ( W + D I - D P A ) / D L A I ) * * 2 ) ' •'• F ( W ) =R*D ( W ) + A V A * S ( W ) G ( W ) = E X P ( - F ( W ) * K O * L ) A S U M 4 = 0 . A S U M 2 = 0 i K = l W = - 8 . „ . . . . 9 A S U M 4 = A S U M 4 + E ( W + H ) A S U M 2 = A S U M 2 + E(W + 2 . - » H ) R E A L NORM I F ( K - N + 3 ) 1 2 , 3 3 » 3 3 12 K = K + 2 W=W+2.*H GO . TO 9 N O R M = H / 3 . * ( 4 . * A S U M 4 + 2 . * A S U M 2 + E ( WO ) + 4 . * E ( W N - H ) +E ( WN > ") • . W P R I M = - 4 . DO 4 4 J = l > 2 1 S U M 4 = 0 . -S U M 2 = 0 . 1=1 W = - 8 . 1 7 S U M 4 = S U M 4 + E ( W+H ) #G ( W-WPR IM+'H ) S U M 2 = S U M 2 + E ( W + 2 . # H ) * G ( W - W P R I M + 2 . * H ) ' ! I F ( I - N + 3 ) 11 ' 3 2 » 32 11 1=1+2 W^ _W + 2 . J -H__ _ * G 0 T 0 ~ 7 " 32 T R A N S = H / 3 , 1 + 4 . » E ( WN-* C 4 . * S U M 4 + 2 . * S U M 2 + E (WO H ) ' » G ( WN-WPR I M - H )+E (WN)• * G ( W O - W P R I M ) •G ( W N - W P R I M ) ) . 6 1 . 4 4 9 4 A T R A N W R I T E - F O R M WPRI M AV = AV -STOP END S = 1 0 0 . * T R A N S / N O R M , ( 6 » 6 1 ) A V > K O » D I »W P R I M » A T R A N S' TJ.2Fl_Qj.3jJ. F 10.._2J = W P R I M + 2 . * H + 1 . 0 i f S E N T R Y J The determination of t h i s i n v e r s e t r a n s f o r m i s no sm a l l t a s k , and i n the present experiment the response f u n c t i o n I(w- i s known so p o o r l y that i t was deemed d e s i r a b l e to i n v e s t i g a t e the e f f e c t of v a r i o u s parameters -- l i n e shapes, is o t o p e e f f e c t , s e l f - a b s o r p t i o n on the t r a n s m i s s i o n p r o f i l e . As a r e s u l t , we used a computer programme employing Simpson's r u l e of numerical i n t e g r a t i o n to c a l c u l a t e the t r a n s m i s s i o n T as a f u n c t i o n of s e v e r a l parameters. (b) S e l f A b s o r p t i o n of S p e c t r a l L i n e s When a beam of r a d i a t i o n t r a v e l s through a medium, i t ' s i n t e n s i t y w i l l be attenuated i f the m a t e r i a l i s capable of a b s o r v i n g the l i g h t . have: I f we j u s t consider the one-dimensional problem, we dx i , \ -,- i \ -k v*. (x)dx l y (x + dx:j = l y (xj e Y , where we c o n s i d e r the a b s o r p t i o n c o e f f i c i e n t to be a f u n c t i o n of p o s i t i o n . 42 T h i s g i v e s d x and hence: > ( fyCx") d x l v ( o ) e I f we c o n s i d e r t h e r a t i a t i o n f r o m a t h e r m a l plasma of t e m p e r a t u r e T, we must have f o r each volume element: > d x and hence the absorbed i n t e n s i t y i s IQ ky; dx. S i n c e t h i s volume element must a l s o be i n thermodyn-amic e q u i l i b r i u m , we must have the c o n t r i b t u i o n beam i n t e n s i t y f rom t h i s volume element: I D K y dx where I Q i s the b l a c k body i n t e n s i t y . k3 X. A- O I f t h i s volume element i s immersed i n the plasma at a d i s t a n c e x from t h e o b s e r v i n g edge, we have the c o n t r i b u t i o n t o the observed i n t e n s i t y f r om t h i s volume element: X - f M O 0 I 0 Mx") dx e I f we now i n c l u d e c o n t r i b u t i o n s from a l l such e l e -ments, we have: •x. a - ( M O d * ; f 0 have I n the case of a p e r f e c t l y homongeneous plasma, we -Kv> & Iv = Io I \ ~ e which approaches a b l a c k body i n t e n s i t y d i s t r i b u t i o n as J . - ? C20 . To c o n s i d e r the s p e c i f i c case of s e l f - a b s o r p t i o n i n t h i s experiment, we need only to be concerned with the s e l f -a b s o r p t i o n of the background l i g h t s i n c e f o r the a b s o r p t i o n tube there i s no such e f f e c t . Since the d e n s i t y of e x c i t e d atoms i s not uniform across the G e i s s l e r tube c a p i l l a r y , we need to con-s i d e r the case where the a b s o r p t i o n c o e f f i c i e n t depends on p o s i -t i o n . T h i s i s , however, a d i f f i c u l t numerical problem and so I w i l l o u t l i n e the two stages of approximation we c o n s i d e r e d : ( i ) Homogeneous Plasma In t h i s case, we saw that the i n t e n s i t y d i s t r i b u t i o n i s Riven by v - I 0 ( x- e f o r a plasma of depth X » In order t o show q u a n t i t a t i v e l y the e f f e c t on the l i n e p r o f i l e , we assumed a pure Doppler l i n e : w i t h a £±\>> $ corresponding to T = 3^0° K. The peak value K 0, was w r i t t e n as 1.2-»-Y where 1.2 r e p r e s e n t s the value of K Q f o r the (axis of the) a b s o r p t i o n tube as determined from the experi-ment ( f o r 6266 l i n e ) , and Y represents a m u l t i p l a t i o n f a c t o r to take i n t o account the higher d e n s i t y of e x c i t e d atoms i n the G e i s s l e r tube compared to the a b s o r p t i o n tube. The f u n c t i o n l y i s shoi^n g r a p h i c a l l y i n F i g . 7 with Y as a parameter and /f = 0.2 cm. ( i i ) Inhomogeneous Plasma i n Slab Geometry I f a plasma i s contained between two w a l l s , then we / -I Q \ f i n d the d e n s i t y of charged p a r t i c l e s to vary as : sin(J-£j2£-j where: and the d e n s i t y o of charged p a r t i c l e s i s assumed to be zero at the w a l l s . Thus, i f we observed the plasma through a hole i n one of the w a l l s , we would be l o o k i n g through a h i g h l y inhomogene-ous plasma. I f we again assume a pure Doppler l i n e , we can w r i t e : - 0.823 U J 2 , Kv = Kco S i n ( ^ ) e where K G 0 represents the peak of the absorption c o e f f i c i e n t at x = 4« In order to determine K . we must somehow r e l a t e K „ 2 C O ' C O to the K determined experimentally, which i s assumed to give a f a i r l y good approx. to the peak of the absorption c o - e f f i c i e n t on the axis of the absorption tube. The paper by Ecker and Z B l l e r (l) was taken as showing c o r r e c t dependence of the charge d e n s i t y as a f u n c t i o n of various parameters, and we assume that the e x c i t e d atom density i s d i r e c t l y p r o p o r t i o n a l to the charged p a r t i c l e d e n s i t y . Comparing the absorption tube and the Geiss-U-6 "Ier tube, and using data from ( 7 ) , we f i n d t h a t TV (abs.+ube) where Yl_ ( G e i s s l e r ) i s the d e n s i t y of e x c i t e d atoms on the axis of the G e i s s l e r tube and 71 (abs. tube) i s the a x i a l d e n s i t y f o r c the absorption tube. Since K q i s p r o p o r t i o n a l t o n , we have: K A O ( G e i s s l e r ) ^ ^ K A O (abs.tube) ' where the K a 0 's are the a x i a l absorption c o e f f i c i e n t peaks. I f we now assume K C O = K A 0 , we have Kco-»68-;:- K A O (abs.tube) and K ^ = 68* 1.2 s i n ( T * ) e ~ * 8 1 3 i f I consider the 6266 l i n e , say. This gives f o r the l i n e i n t e n s i t y d i s t r i b u t i o n : I v = Io I K^Cx^dx e ° , o w i t h K ^ ( x ) as above. This f u n c t i o n was c a l c u l a t e d n u m e r i c a l l y , and r e s u l t i s shown f o r d = 0 .2 cm. i n P i g . 7 ° IL8 REFERENCES (I) E. Back Ann. der Phys. 76, 317 (1921). (?) R. G. Breene J r . R.M.P. 29, 9i| (1957) (3) R. G. Breene J r . S h i f t and Shape of S p e c t r a l Lines Pergamon - London - 1961 (ij.) S. Chandrasekla<f R a d i a t i v e T r a n s f e r Dover - N.Y. - I960 (5) S. Ch'en and M. Takeo R.M.P. 29, 20 (1957) (6) T. Connor and M. B i o n d i P.R. 11;O, A778 (1965) (7) G. Ecker and 0. Z o l l e r P.F. 1, 1996 ( I 9 6 J 4 . ) ( 8 ) R. Fowler Handhuch der Physik V o l . XXII P. 209 (9) G. F r a n c i s Handbuch der Physix V o l . XXII P. 53 (10) W. H e i t l e r Quantum Theory of R a d i a t i o n Oxford Press - London - 1951+ (II) J . C. Irwin PhD t h e s i s ~ U.B.C. '(1965) (12) R. Ladenburg R.M.P. 5, 2l±3 (1933) (13) K. Lang Acta Phys. Aust. 376 (195D (II4.) A . , M i t c h e l l and M. Zemansky Resonance R a d i a t i o n and E x c i t e d Atoms C.U.P. - Cambridge - 1961 (15) H, Nagaoka and T. Mishima S c i . Pap. I.P.C.R.. 13, 293 (1930) 25, 223 (1934) (16) A„ M. Robinson PhD t h e s i s - U.B.C. (1966) (17) W. Thompson I n t r o d u c t i o n to Plasma P h y s i c s Addison Wesley - London (1961+) (18) A. Von Engel Ionized Gases Oxford U. Press - London - 1965 

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