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Rayleigh scattering cross-sections of nitrogen and argon Wu, Michael W. H. 1972

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RAYLEIGH SCATTERING CROSS-SECTIONS OF NITROGEN AND ARGON by MICHAEL W. H. WU B.Sc. (Eng), University of Alberta 1970. A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIRMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of Physics We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF A p r i l , BRITISH 1972 COLUMBIA In present ing th i s thes is in pa r t i a l f u l f i lmen t o f the requirements for an advanced degree at the Un ivers i t y of B r i t i s h Columbia, I agree that the L?brary shal1 make it f r ee l y ava i l ab le for reference and study. I fu r ther agree that permission for extensive copying of th i s thes i s fo r s cho l a r l y purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i c a t i on o f th i s thes i s fo r f inanc ia l gain sha l l not be allowed without my wr i t ten permiss ion. Department of The Un ive rs i t y of B r i t i s h Columbia Vancouver 8, Canada Date Af/,f hf (]7*-- i i -ABSTRACT R a y l e i g h S c a t t e r i n g f r o m n e u t r a l n i t r o g e n a n d a r g o n a t room t e m p e r a t u r e has b e e n s t u d i e d u s i n g a 12 m e g a w a t t Q - s w i t c h e d p u l s e r u b y l a s e r . The s c a t t e r i n g a n g l e was c h o s e n t o be 90 d e g r e e s f r o m t h e i n c i d e n t beam. The r e l a t i v e d i f -f e r e n t i a l s c a t t e r i n g c r o s s - s e c t i o n a n d t h e p r e s s u r e d e p e n d -e n c e o f t h e s c a t t e r e d s i g n a l o f t h e s c a t t e r i n g m e d i a w e r e d e t e r m i n e d . M e a s u r e m e n t s o f t h e a b s o l u t e d i f f e r e n t i a l c r o s s -s e c t i o n o f n i t r o g e n a n d a r g o n w e r e a l s o o b t a i n e d . I f o u n d t h a t t h e r e s u l t s a g r e e v e r y s a t i s f a c t o r i l y w i t h t h e p r e d i c t i o n o f t h e t h e o r y w i t h i n e x p e r i m e n t a l e r r o r . TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF FIGURES V ACKNOWLEDGEMENTS v i i CHAPTER I - INTRODUCTION ' 1 CHAPTER I I - THEORY 3 A. General Theory of R a y l e i g h S c a t t e r i n g 3 B. P r e s s u r e Dependence o f Normalized S c a t t e r e d S i g n a l 9 C. A b s o l u t e C a l i b r a t i o n o f D i f f e r e n t i a l S c a t t e r i n g C r o s s - S e c t i o n s 11 CHAPTER I I I - APPARATUS 14 A. The Ruby La s e r 14 B. The La s e r M o n i t o r i n g Photodiode 17 C. The Gas Chamber 20 D. The D e t e c t i n g System 21 CHAPTER IV - PROCEDURES AND RESULTS 25 A. General Features o f the Ruby La s e r 25 B. Alignment of O p t i c a l System 26 C. O b s e r v a t i o n of the Dependence of Normalized S c a t t e r e d S i g n a l 27 - i v -Page D. Measurement of the R e l a t i v e D i f f e r e n t i a l S c a t t e r i n g C r o s s - S e c t i o n s . . . . 29 E. Measurement of the Absolute D i f f e r e n t i a l S c a t t e r i n g C r o s s - S e c t i o n s 32 F. E r r o r A n a l y s i s 47 CHAPTER V - DISCUSSION AND CONCLUSION 50 A. C o n c l u s i o n 50 B. D i s c u s s i o n 50 APPENDIX 52 BIBLIOGRAPHY 55 - v -INDEX OF FIGURES F i g u r e P a g e (1) The C o o r d i n a t e S y s t e m o f t h e P . a y l e i g h S c a t t e r i n g P r o b l e m 4 (2) I l l u s t r a t i o n o f t h e E x p e r i m e n t 15 (3) The L a s e r M o n i t o r i n g P h o t o d i o d e 18 (4) C i r c u i t D i a g r a m o f P h o t o d i o d e P o w e r S u p p l y . . . . 19 (5) P h o t o d i o d e C i r c u i t 19 (6) O s c i l l o s c o p e T r a c e o f L a s e r M o n i t o r i n g P h o t o -d i o d e P u l s e 20 (7) P o t e n t i a l D i s t r i b u t i o n o f t h e P h o t o m u l t i p l i e r Dynode C h a i n 2 3 (8) P r e s s u r e D e p e n d e n c e o f S c a t t e r e d S i g n a l o f N i t r o g e n a n d A r g o n 2 8 (9) I l l u s t r a t i o n o f S c a t t e r i n g V olume 34 (10) C a l i b r a t i o n o f L a s e r E n e r g y W i t h L a s e r M o n i t o r i n g P h o t o d i o d e P u l s e 37 o (11) I n s t r u m e n t P r o f i l e o f Neon L i n e 6929 .5 A 41 (12) C o m p a r i s o n o f I n s t r u m e n t P r o f i l e W i t h S c a t t e r i n g P r o f i l e o f A r g o n a t One A t m o s p h e r e . 42 - v i -F i g u r e Page (13) I l l u s t r a t i o n of S c a t t e r e d S i g n a l s With Focused and Unfocused D e t e c t i n g System 49 (14) P r e s s u r e Dependence of S c a t t e r e d S i g n a l o f Helium 53 - v i i -ACKNOWLEDGEMENT I m u s t s i n c e r e l y t h a n k D r . R. N o d w e l l f o r h i s g u i d a n c e a n d e n c o u r a g e m e n t t h r o u g h o u t t h e c o u r s e o f t h i s e x p e r i m e n t . Many t h a n k s a l s o go t o D r . R. M o r r i s a n d D r . H. B a l d i s f o r t h e i r m o s t h e l p f u l s u g g e s t i o n s d u r i n g t h i s w o r k . I w o u l d l i k e t o e x p r e s s my a p p r e c i a t i o n f o r t h e t e c h n i c a l a s s i s t a n c e o f M e s s e r s D. S i e b e r g a n d J . Z a n g a n e h t o g e t h e r w i t h t h e e n t i r e P h y s i c s m a c h i n e s h o p s t a f f . I am a l s o i n d e b t e d t o my w i f e P e g g y f o r h e r e n c o u r a g e -ment a n d h e r a s s i s t a n c e i n t h e p r e p a r a t i o n o f t h i s t h e s i s . T h i s w o r k i s s u p p o r t e d b y a g r a n t f r o m t h e A t o m i c E n e r g y C o n t r o l B o a r d o f C a n a d a . - 1 -CHAPTER I INTRODUCTION The m o t i v a t i o n o f t h i s e x p e r i m e n t h a s b e e n two f o l d . F i r s t l y ; t o c o n f i r m t h e a g r e e m e n t o f t h e m e a s u r e d a b s o l u t e d i f f e r e n t i a l s c a t t e r i n g c r o s s - s e c t i o n o f n e u t r a l n i t r o g e n a n d a r g o n w i t h t h e p r e d i c t i o n f r o m t h e t h e o r y . S e c o n d l y ; t o c a l i b r a t e t h e s c a t t e r e d n o i s e f r o m t h e n e u t r a l p a r t i c l e s o f a l a s e r - s c a t t e r i n g e x p e r i m e n t o f f a n i t r o g e n o r a r g o n p l a s m a . R a y l e i g h S c a t t e r i n g h a s b e e n p r e v i o u s l y d one by numer-ous g r o u p s o f S c i e n t i s t s ^ _ . I t was f i r s t r e p o r t e d i n 1965 by T.V. G e o r g e , L. G o l d s t e i n , L. S l a m a a n d M. Y o k o y a m a ^ j t h a t t h e a b s o l u t e d i f f e r e n t i a l s c a t t e r i n g c r o s s - s e c t i o n o f g a s e s m e a s u r e d w e r e a p p r o x i m a t e l y t w i c e a s l a r g e as p r e d i c t e d by t h e c l a s s i c a l t h e o r y . L a t e r i n 196 8, t h i s e x p e r i m e n t was r e d o n e by R. R u d d e r a nd D. B a c h ^ , who r e p o r t e d t h a t t h e i r m e a s u r e d d i f f e r e n t i a l c r o s s - s e c t i o n s w e r e i n g o o d a g r e e m e n t w i t h t h e t h e o r y . R u d d e r a n d B a c h a l s o r e p o r t e d t h a t t h e l a s e r m o n i t o r i n g t e c h n i q u e u s e d i n G e o r g e ' s e x p e r i m e n t was n o t f e a s i b l e a n d t h e y h a d t o s e l e c t a d i f f e r e n t t e c h n i q u e i n t h i s p a r t w h i c h g a v e them v e r y g o o d r e s u l t s . - 2 I n t h i s e x p e r i m e n t , a g a i n a d i f f e r e n t l a s e r m o n i t o r i n g d e v i c e was u s e d w h i c h showed a s a t i s f a c t o r y o p e r a t i o n a l r e -s u l t . The d e t a i l d e s c r i p t i o n o f t h i s d e v i c e w i l l be shown i n C h a p t e r I I I - B . T h i s t h e s i s i s p r e s e n t e d i n f o u r m a j o r s e c t i o n s . The f i r s t s e c t i o n shows t h e g e n e r a l t h e o r y o f R a y l e i g h S c a t t e r i n g and t h e d e t e r m i n a t i o n o f t h e a b s o l u t e d i f f e r e n t i a l c r o s s -s e c t i o n o f g a s e s b y means o f a t u n g s t e n r i b b o n l a m p . S e c o n d s e c t i o n d e s c r i b e s i n much d e t a i l t h e a p p a r a t u s u s e d i n t h i s e x p e r i m e n t . T h i r d s e c t i o n shows t h e o p e r a t i o n , t h e m e a s u r e -ments o b t a i n e d a n d a c o m p a r i s o n o f t h e s e e x p e r i m e n t a l v a l u e s w i t h t h e t h e o r e t i c a l v a l u e s . C o n c l u s i o n a n d D i s c u s s i o n a r e p r e s e n t e d i n t h e l a s t s e c t i o n . - 3 -CHAPTER I I THEORY A. G e n e r a l t h e o r y o f R a y l e i g h S c a t t e r i n g i s b r i e f l y r e v i e w e d h e r e . C o n s i d e r a g a s m o l e c u l e l o c a t e d a t t h e o r i g i n o f a C a r t e s i a n C o o r d i n a t e S y s t e m . A m o n o c h r o m a t i c p l a n e wave ( l a s e r beam) p o l a r i z e d i n t h e z - d i r e c t i o n i s i n c i d e n t o n t o t h i s p a r t i c l e , a n d i t s e l e c t r i c f i e l d i s „ „ l W t A E = E e z — o Where z i s t h e u n i t v e c t o r p o i n t i n g t o w a r d s t h e z - d i r e c t i o n , (See F i g . 1) As t h e p a r t i c l e ( i d e a l g a s p a r t i c l e ) i s i s o t r o p i c , t h e i n d u c e d d i p o l e moment p e r m o l e c u l e i s „ l W t A p . = E „ a e z t-T o w h e r e a i s t h e p o l a r i z i b i l i t y o f t h e S c a t t e r i n g medium, ( S u b s c r i p t " j " i n d i c a t e s j m o l e c u l e ) FIGURE 1 THE COORDINATE SYSTEM OF THE RAYLEIGH SCATTERING PROBLEM I f an o b s e r v e r Q i s a t a d i s t a n c e r f r o m t h e o r i g i n a n d r » \ w h e r e A i s t h e w a v e l e n g t h o f t h e i n c i d e n t mono-c h r o m a t i c wave, t h e n t h e e l e c t r i c f i e l d a s s o c i a t e d v / i t h t h i s i n d u c e d d i p o l e moment i s _ E o ^ A A A i ( w t - k . r ) E = - r x ( r x z ) a e - s l w h e r e r i s t h e u n i t v e c t o r a l o n g r , and k i s t h e wave v e c t o r . L e t <J> be t h e a n g l e b e t w e e n r and z, t h e r e f o r e , r x ( r x z) = Sm<J> u - 5 -w h e r e u i s a u n i t v e c t o r p e r p e n d i c u l a r t o r . T h e r e f o r e , E . = -  E-°JlL a s i n O e 1 ^ ^ ' G ( 1 ) — s j v ; T h e r e f o r e , f l u x d e n s i t y r e c e i v e d b y O b s e r v e r Q due t o o n e m o l e c u r e i s I . = (E . . E . ) 3 • -3D -SD w h e r e E * i s t h e c o m p l e x c o n j u g a t e o f E T h e r e f o r e , r. 2 . 4 2 E k a I = _2 _ sin2<& I f t h e m o l e c u l e s do n o t i n t e r a c t , a n d i f t h e y a r e r a n d o m l y d i s t r i b u t e d i n s p a c e , t h e l i g h t s c a t t e r e d by a l a r g e number o f m o l e c u l e s i s e x p e c t e d t o be c o m p l e t e l y i n c o h e r e n t , a n d t h e t o t a l f l u x d e n s i t y r e c e i v e d a t Q i s t h e s u m m a t i o n o f I . o v e r a l l m o l e c u l e s i n s i d e t h e s c a t t e r i n g D v o l u m e . T h e r e f o r e , AJ 2 4 2 ^ N E k or 7 I = £ I . = _ o s i n 2 * D = l r - 6 -where N i s t h e t o t a l number o f m o l e c u l e s i n s i d e t h e S c a t t e r -i n g volume. I f t h e s c a t t e r i n g r a d i a t i o n i s measured o v e r an a r e a o f A s , t h e n t h e t o t a l f l u x measured w i l l be N E 2 k 4 a 2 „ P = As °- ^ S i n <J> As But --^  = Aft , the s o l i d a n g l e subtended by t h e d e t e c t i n g r system. T h e r e f o r e , P = N E 2 k 4 a2 Sin 24> Aft • ( 2 ) s o The i n t e n s i t y o f t h e i n c i d e n t p l a n e wave i s I o OC E q 2 — - ( 3) By d e f i n i t i o n , t h e d i f f e r e n t i a l c r o s s - s e c t i o n o f t h e s c a t t e r i n g medium p e r m o l e c u l e i s T o t a l s c a t t e r d r l u x o e r m o l e c u l e p e r . _ s o l i d a n g l e  d f i I n t e n s i t v o f i n c i d e n t p l a n e wave - 7 -N AP. (4) U E 2 k 4 a 2 S i n 2 * N A n T h e r e f o r e , d<r k 4 a2 S i n 2 * ( 5 ) By t h e C l a u s i u s - M o s s o t t i e q u a t i o n ( See S c h w a r t z ^ g j ) a = N w h e r e £ = p e r m i t t i v i t y o f s c a t t e r i n g medium 6a = x M v ( 1 + X e ) 60 p e r m i t t i v i t y o f f r e e s p a c e s u s c e p t i b i l i t y o f s c a t t e r i n g medium number o f p a r t i c l e s p e r u n i t v o l u m e B u t t h e r e f r a c t i v e i n d e x o f t h e s c a t t e r i n g medium, i n t h e o p t i c a l r e g i o n i s n = ( i f - 8 -T h e r e f o r e , a = n 2 - 1 rTTT A n d , da 9k 4 N. n - 1 n + 1 As t h e g a s s e s u s e d o b e y I d e a l Gas Law N v K T where T h e r e f o r e , p = p r e s s u r e o f g a s c h a m b e r K = B o l t z m a n n c o n s t a n t T = t e m p e r a t u r e o f g a s c h a m b e r = room t e m p e r a t u r e d a an 4 2 2 9k K T P n - 1 n 2 + 1 (6) F r o m t h i s e q u a t i o n , I c a n s e e t h a t f o r a c e r t a i n m o n o c h r o m a t i c i n c i d e n t wave a t a c e r t a i n t e m p e r a t u r e , t h e - 9 -s c a t t e r i n g c r o s s - s e c t i o n depends on the p r e s s u r e as w e l l as the index of r e f r a c t i o n o f the medium where the l a t t e r i s a , f u n c t i o n o f the former. B. P r e s s u r e Dependence of Normalized S c a t t e r e d S i g n a l s Next I w i l l d e r i v e the e q u a t i o n t h a t shows the p r e s s u r e dependence o f the n o r m a l i z e d s c a t t e r e d s i g n a l . Normal-i z e d s c a t t e r e d s i g n a l i s d e f i n e d as the s c a t t e r e d s i g n a l i n v o l t measured a c r o s s a 50 ohm l o a d r e s i s t o r from anode to ground of the p h o t o m u l t i p l i e r d i v i d e d by the peak v a l u e i n v o l t s o f the photodiode l a s e r p u l s e . T h e r e f o r e , P_ — = con s t a n t x ( N.S.) P o From eq u a t i o n (3) I know t h a t the i n t e n s i t y o f the i n c i d e n t beam i s T h e r e f o r e , the power of the i n c i d e n t beam i s - 10 -P = E 2 A_ o O TJ where A T i s t h e c r o s s - s e c t i o n o f t h e beam. From e q u a t i o n Li (4) I found t h a t dor p s an N An i Q T h e r e f o r e , P d a s _ N AQ I dQ o D i v i d i n g b o t h s i d e s by A, I g e t P P 3a A O M s _ __s _ f A * t N I A P d f l A o o = c o n s t a n t x n o r m a l i z e d s c a t t e r d s i g n a l , From I d e a l Gas Lav; P V N = K T T h e r e f o r e , - 11 -da AO V df) A T K T Li (7) For a c e r t a i n s c a t t e r i n g medium i n a f i x e d s c a t t e r i n g volume at c o n s t a n t temperature, the n o r m a l i z e d s c a t t e r e d s i g n a l i s a f u n c t i o n of P r e s s u r e of the gas chamber o n l y . C. A b s o l u t e C a l i b r a t i o n o f D i f f e r e n t i a l S c a t t e r i n g C r o s s - S e c t i o n A. To measure the a b s o l u t e d i f f e r e n t i a l c r o s s - s e c t i o n o f the gases, I need t o f i n d the s p e c t r a l response of the d e t e c t i n g system by u s i n g a tungsten r i b b o n lamp. F i r s t l y ; I have to c a l c u l a t e the f l u x d e n s i t y r a d i a t e d from the tungsten lamp which i s a grey body o f e m i s s i v i t y o f .432 a t o o 6943A and 2200 K. The i n t e n s i t y of a b l a c k body r a d i a t i o n (per u n i t s o l i d angle per u n i t wavelength) at a p a r t i c u l a r wavelength i s -1 (8) To f i n d the t o t a l i n t e n s i t y r a d i a t e to the s o l i d angle subtended by the d e t e c t i n g system over the whole 2hc W * 1 = he e * K t - 1 - 12 -i n s t r u m e n t p r o f i l e , I h a v e t o i n t e g r a t e I D _ ( X ) w i t h r e s p e c t t o t h e w a v e l e n g t h o v e r t h e i n s t r u m e n t p r o f i l e a n d m u l t i p l y i t by Aft t h e s o l i d a n g l e t h e d e t e c t i n g l e n s s u b t e n d s . As t h e e n t r a n c e s l i t a n d t h e e x i t s l i t o f t h e m o n o c h r o m a t o r i s i d e n t i c a l , t h e i n s t r u m e n t p r o f i l e i s o f t r i -a n g u l a r s h a p e (See F i g . 1 2 , C h a p t e r I V - E ) . T h e r e f o r e , y*IBB( A ) dX = i B 3 ( X ) AX w h e r e AX i s t h e i n s t r u m e n t w i d t h . T o t a l i n t e n s i t y r a d i a t e d f r o m t h e t u n g s t e n lamp t o t h e d e t e c t i n g s y s t e m i s I T ( X ) = e I B B ( X ) A X A Q w h e r e "e" i s t h e e r a i s s i v i t y o f t u n g s t e n . W i t h t h i s i n t e n s i t y , t h e p h o t o m u l t i p l i e r w o u l d g i v e c o r r e s p o n d -i n g s i g n a l i n t e r m s o f anode c u r r e n t i w h i c h I m e a s u r e d b y means o f a known l o a d r e s i s t o r a c r o s s t h e anode a n d g r o u n d . I n my c a s e a 10 K i l o - o h m r e s i s t o r was u s e d . T h i s i n f o r m a t i o n e n a b l e d me t o o b t a i n t h e s p e c t r a l r e s p o n s e o f t h e d e t e c t i n g s y s t e m . - 13 -S = A V A ) 1A * ( 9 ) e I B B ( X ) AX Aft M e a s u r e m e n t o f AX w i l l ' b e shown i n C h a p t e r I V - E . - 14 -CHAPTER I I I APPARATUS The apparatus used i n t h i s experiment can be d i v i d e d i n t o f o u r major p a r t s : the ruby l a s e r ; the l a s e r m o n i t o r i n g photodiode; the gas chamber and the l i g h t d e t e c t i n g system ( F i g . 2 ) . A. The Ruby L a s e r The ruby l a s e r used i s a TRG model 104A which has a Q-switching u n i t t h a t can produce a 70 nanosecond p u l s e of up to a maximum energy o f .8 j o u l e . The output o f the l a s e r i s r e p r o d u c i b l e to v/ith i n 10% over an extended p e r i o d o f continuous o p e r a t i o n at r e g u l a r i n t e r v a l o f one minute. The f r o n t m i r r o r i s a 30% r e f l e c t i n g s a p p h i r e r e s o n a t o r . The Q-sv/itching u n i t c o n s i s t s of a r o t a t i n g p r i s m which performs at a speed o f 30,000 r.p.m. The l a s e r beam v/ith diameter o f 1 cm. was focused by a l e n s of 13.6 cm. f o c a l l e n g t h so as to maximize the d e t e c t e d s c a t t e r e d s i g n a l and minimize the s t r a y l i g h t n o i s e from the gas chamber. F u r t h e r d i s c u s s i o n on t h i s matter w i l l be seen under " D e t e c t i n g System" i n the same Chapter. FIGURE 2 ILLUSTRATION OF THE EXPERIMENT - 16 -The l a s e r l i g h t dump i s a g l a s s c o n t a i n e r w i t h a B r e w s t e r w i n d o w c o n t a i n i n g a s t r o n g c o p p e r s u l p h a t e s o l u t i o n . T h i s g l a s s c o n t a i n e r i s p l a c e d i n a b l a c k b o x w i t h i t s B r e w s t e r window f a c i n g a s m a l l h o l e on t h e b o x b i g e n o u g h t o a l l o w t h e e n t r a n c e , o f t h e l a s e r beam. The a l i g n m e n t o f t h e l a s e r p l a y s t h e m o s t i m p o r t a n t r o l e i n t h e l a s e r o u t p u t p o w e r . To do t h i s , a g o o d t e l e s c o p e i s e s s e n t i a l . The t e l e s c o p e , w h i c h was b u i l t b y m y s e l f , h a s a s e t o f v e r y t h i n c r o s s - h a i r a t t h e common f o c a l p l a n e o f t h e o b j e c t i v e l e n s a n d t h e G a u s s e y e - p i e c e . The G a u s s e y e - p i e c e a l l o w s i l l u m i n a t i o n o f t h e c r o s s - h a i r u s i n g a d e s k l a m p . The t e l e s c o p e i s f i r s t a l i g n e d w i t h t h e b a c k m i r r o r o f t h e l a s e r ( w h i c h i s t h e r o t a t i n g p r i s m ) b y t h e m e t h o d o f p a r a l l e x o f t h e c r o s s - h a i r a n d i t s i m a g e r e f l e c t e d b a c k f r o m t h e p r i s m . Nov/ t h e t h r e e i n c h l o n g r u b y r o d i s i n s e r t e d i n t o t h e L a s e r h e a d . By a d j u s t i n g t h e p o s i t i o n o f t h e r o d , t h e f r o n t s u r f a c e r e f l e c t i o n o f t h e i l l u m i n a t e d c r o s s - h a i r i s a g a i n a l i g n e d w i t h t h e same m e t h o d . L a s t l y , t h e f r o n t m i r r o r o f t h e l a s e r i s p u t i n and i t i s a l s o a l i g n e d . T h i s m e t h o d o f a l i g n m e n t o f t h e TRG r u b y l a s e r h a s p r o v e n t o be m o s t s a t i s f a c t o r y a n d more e f f i c i e n t t h a n u s i n g a He-Ne g a s l a s e r . - 17 -B. The L a s e r M o n i t o r i n g P h o t o d i o d e T h i s d e v i c e (shown i n F i g . 3) c o n s i s t s o f a p i e c e o f p l a n e g l a s s p l a c e d a t B r e w s t e r a n g l e t o t h e i n c i d e n t beam. I t r e f l e c t s i a b o u t 4% o f t h e beam t o w a r d s a p i e c e o f g r o u n d g l a s s a n d a n e u t r a l d e n s i t y f i l t e r o f 1% t r a n s m i s s i o n b e f o r e t h e l i g h t h i t s t h e p h o t o d i o d e . T h i s p h o t o d i o d e i s a H e w l e t t P a c k a r d p a r t number 5082 - 4 2 2 0 . I t i s b i a s e d by a 100 v o l t r e g u l a t e d p o w e r s u p p l y whose c i r c u i t d i a g r a m i s shown i n F i g . 4. The d i o d e i s o p e r a t e d w i t h t h e 100 v o l t p o w e r s u p p l y , . O l p f c e r a m i c c a p a c i t o r i n p a r a l l e l and a 50 ohm t e r m i n a t o r ( F i g . 5 ) . I t w i l l g i v e a l i n e a r s i g n a l o f up t o 3 v o l t s a c r o s s t h e 50 ohm t e r m i n a t o r w h i c h m a t c h e s t h e i m p e d a n c e o f t h e t r a n s m i t t i n g c a b l e and h a s a r i s e t i m e o f l e s s t h a n one n a n o s e c o n d . T h i s m o n i t o r i n g d e v i c e i s c a l i b r a t e d a g a i n s t t h e e n e r g y m e a s u r e d by a TRG m o d e l 101 b a l l i s t i c t h e r m o p i l e w h i c h i s c o n n e c t e d t o a TRG m o d e l 102 e n e r g y m e t e r o f p a r t 183 - 1 5 . As t h e p h o t o d i o d e p u l s e shows a v e r y c o n s i s t e n t G a u s s i a n l i n e s h a p e p r o f i l e ( F i g . 6 ) , t h e p o w e r o u t p u t o f t h e l a s e r w i l l be t h e e n e r g y m e a s u r e d by t h e e n e r g y m e t e r d i v i d e d by t h e h a l f w i d t h o f t h e l a s e r p u l s e . To m e a s u r e t h e p u l s e w i d t h t o a b e t t e r a c c u r a c y , a f a s t T e k t r o n i x 454 O s c i l l o s c o p e w i t h r i s e t i m e o f 2.4 n a n o s e c o n d s i s u s e d . G R O U N D G L A S S F I L T E R N E U T R A L D E N S I T Y F I L T E R --7 P H O T O D I O D E T O ' T O P O W E R S C O P E S U P P L Y FIGURE 3 THE LASER MONITORING PHOTODIODE G L A S S P L A T E F R O M L A S E R ' A D J U S T M E N T S C R E W O P T I C A L S A D D L E - 19 -A / J 1 1 0 v o o 1 N 4 0 0 5 125v 125v 3 7 5 0 Q 4 0 M f 1N4005 0 B 2 1 0 0 K + \00\t FIGURE 4 C I R C U I T DIAGRAM OF PHOTODIODE POWER SUPPLY P h o t o d i o d e To O s c i l l o s c o p e FIGURE 5 PHOTODIODE C I R C U I T - 20 -FIGURE 6 OSCILLOSCOPE TRACE OF LASER MONITORING PHOTODIODE PULSE C. The Gas Chamber The g a s chamber i s o f f o u r i n c h e s i n d i a m e t e r a n d f i v e i n c h e s i n h e i g h t . The f o u r 3 r e v ; s t e r w i n d o w s p r o t r u d e a b o u t t h r e e i n c h e s f r o m t h e m a i n c a v i t y a n d a r e 90 d e g r e e s f r o m e a c h o t h e r . The c h a m b e r i s b u i l t a i r t i g h t s u c h t h a t t h e g a s e s c a n be f i l l e d a t c o n t r o l l a b l e p r e s s u r e . The t o p o f t h e c h a m b e r i s c o n n e c t e d t o a m e r c u r y p r e s s u r e g a u g e w h i c h r e a d s f r o m vacuum t o two a t m o s p h e r e . U n d e r n e a t h t h e chamber a r e two o u t l e t s : one o f w h i c h i s c o n n e c t e d t o a vacuum pump a n d t h e o t h e r t o t h e c o m p r e s s e d g a s t a n k s o f t h e v a r i o u s t y p e s o f g a s e s . T h i s c h a m b e r , whose t o p c a n b e r e m o v e d , s i t s o n a f o u r - w a y a d j u s t a b l e b a s e . T h i s c o n t r i b u t e s t o much e a s i e r o p t i c a l a l i g n m e n t . D e t a i l d i s c u s s i o n o n t h i s p a r t w i l l b e shown i n C h a p t e r I V - B . The f o c u s i n g l e n s o f t h e l a s e r and t h e d e t e c t i n g l e n s - 21 -s i t s i n f r o n t o f two ad j a c e n t windows o f the chamber. The remaining two windows are o c c u p i e d by the two l i g h t dumps which w i l l h e l p cut the s t r a y l i g h t n o i s e at the d e t e c t i n g system. D. The D e t e c t i n g System T h i s system c o n s i s t s of two l e n s e s , one c o n s t a n t d e v i a t i o n prism, one 45 degree prism, a monochromator, a p h o t o m u l t i p l i e r and an o s c i l l o s c o p e . The two l e n s e s are used t o c o l l i m a t e the s c a t t e r e d s i g n a l to the entrance s l i t o f the monochromator, or I may say the image o f the entrance s l i t o f the monochromator i s focused onto the s c a t t t e r i n g volume which i s s i t u a t e d i n the middle o f the gas chamber. The c o n s t a n t d e v i a t i o n p r i s m i s used t o i s o l a t e the o r d e r s of the monochromator, and i t i s a l s o used t o g e t h e r w i t h the 45 degree pr i s m t o r o t a t e the c o l l i m a t e d beam by 90 degrees. (This r o t a t i o n of the beam i s o n l y f o r the con-venience o f the o p t i c a l arrangement). To minimize the s t r a y l i g h t n o i s e from the e n v i r o n -ment, i t i s be s t to c o n f i n e the s i z e o f the entrance s l i t o f the monochromator to a minimum v/ithout l o s i n g much o f the - 22 -s c a t t e r e d s i g n a l , i n o r d e r t o be a b l e t o do an a b s o l u t e c a l i b r a t i o n o f t h e s p e c t r a l r e s p o n s e o f t h e d e t e c t i n g s y s t e m u s i n g a t u n g s t e n l a m p , t h e h e i g h t o f t h e m o n o c h r o m a t o r s l i t i s l i m i t e d t o l e s s t h a n t h e w i d t h o f t h e t u n g s t e n r i b b o n . T a k i n g i n t o c o n s i d e r a t i o n o f a l l t h e s e f a c t o r s , i t was d e t e r m i n e d t h a t t h e d i m e n s i o n o f t h e s l i t t o be a s q u a r e p i n h o l e o f d i m e n s i o n .57 nun. x .57 mm. The g r a t i n g m o n o c h r o m a t o r was b u i l t i n o u r l a b o r a t o r y (H.W. Van A n d e l ^ j ) . I t i s u s e d i n f o u r t h o r d e r w i t h a o l i n e a r d i s p e r s i o n o f 4.5A p e r m i l l i m e t e r a n d a t h e o r e t i c a l r e s o l v i n g p o w e r o f 3 0 0 , 0 0 0 . The e f f e c t i v e a p e r t u r e i s l i m i t e d b y t h e g r a t i n g a n d i s s u c h t h a t t h e f - n u m b e r i s a b o u t 6. The p h o t o m u l t i p l i e r u s e d t o c o n v e r t l i g h t s i g n a l i n t o an e l e c t r i c a l s i g n a l was a RCA t y p e 7 2 6 5 . I t i s a f o u r t e e n s t a g e t u b e w i t h an S-20 s p e c t r a l r e s p o n s e w h i c h h a s a o q u a n t u m e f f i c i e n c y o f 3% a t 6943A. The p h o t o t u b e i s b i a s e d w i t h a t o t a l a node t o c a t h o d e v o l t a g e o f 1500 v o l t s . The anode t o g r o u n d l o a d r e s i s t o r i s 50 ohms w h i c h m a t c h e s t h e i m p e d a n c e o f t h e t r a n s m i t t i n g c a b l e . The p o t e n t i a l d i s t r i b u t i o n a c r o s s t h e d y n o d e c h a i n i s i l l u s t r a t e d i n F i g . 7. - 23 -1 100 K 22 K 68 K 68K 68 K 68 K 68 K 68 K 68 K 68K 68K 68K 82K 100 K 39 K 120 K D Y N O D E N U M B E R C athode F o c u s i n g Dynode 1 2 3 4 5 6 7 8 9 10 11 12 1 3 C e r a m i c 0 4=001/i 4=.001/I c-• A c c e l e r a t i n g E l e c t r o d e .005^4= 14 150 K =t= .005M r •Anode - A A A -47. 6 n .01M P a p e r p d=.005n -> ±=.005^ < 4=.025M =J= ,0 5 M F I G U R E 7 P O T E N T I A L D I S T R I B U T I O N OF T H E P H O T O M U L T I P L I E R DYNODE C H A I N - 24 -A T e k t r o n i x 551 dual beam o s c i l l o s c o p e together w i t h p l u g - i n u n i t s Type L and Type K was used. The photodiode l a s e r pulse i s shown on the lower t r a c e of the screen w i t h the Type K p l u g - i n u n i t and the p h o t o m u l t i p l i e r pulse on the upper t r a c e w i t h the Type L p l u g - i n u n i t . This o s c i l l o -scope together w i t h p l u g - i n Type L has a r i s e time of 16 nanoseconds while w i t h Type K has a r i s e time of only 14 nanoseconds. S i g n a l s were recorded on P o l a r o i d f i l m s of type 410 at a sweeping speed of 100 nanoseconds per d i v i s i o n . - 25 -CHAPTER I V PROCEDURE AMD RESULTS A. G e n e r a l F e a t u r e s o f t h e Ruby L a s e r The r u b y l a s e r c a n be o p e r a t e d i n two modes: n a m e l y t h e n o r m a l mode and t h e Q - s w i t c h i n g mode. The n o r m a l mode g i v e s maximum e n e r g y o f 1.5 j o u l e s , a n d t h e Q - s w i t c h i n g mode g i v e s a maximum e n e r g y o f .8 j o u l e . The Q - s w i t c h i n g l a s e r p u l s e h a l f - w i d t h was m e a s u r e d t o be 35 n a n o s e c o n d s w h i c h g i v e s a p e a k p o w e r o f 20 m e g a w a t t s . The l a s e r o u t p u t p o w e r v e r y much d e p e n d e d o n t h e a l i g n m e n t o f t h e l a s e r a n d t h e c o o l i n g s y s t e m o f t h e l a s e r h e a d . T h i s c o o l i n g s y s t e m c o n s i s t s o f a c a r r a d i a t o r w i t h c o l d w a t e r r u n n i n g t h r o u g h i t t o c o o l t h e a i r w h i c h i s b e i n g pumped by a s u c t i o n f a n t o t h e l a s e r h e a d . The s h o r t e s t d u r a t i o n b e t w e e n f i r i n g t h e l a s e r i s one m i n u t e w h i c h g i v e s an a v e r a g e power o u t p u t o f 12 m e g a w a t t s . I f t h e l a s e r was f i r e d a t f o u r m i n u t e i n t e r v a l s , t h e o u t p u t c a n r e a c h i t s p e a k power o f 20 m e g a w a t t s . B e c a u s e o f t h e t i m e c onsumed i n w a i t i n g f o r t h e l a s e r h e a d t o c o o l o f f , a s a c r a f i c e o n t h e l a s e r p o w e r v/as n e c e s s a r y . T h e r e f o r e , i t was f i r e d - 26 -e v e r y one mi n u t e . The Q - s v / i t c h i n g u n i t o f t h e l a s e r has a d e l a y t i m e a d j u s t m e n t w h i c h s y n c h r o n i z e s t h e pumping a c t i o n o f t h e f l a s h tube and t h e p o s i t i o n o f t h e r o t a t i n g p r i s m . T h i s a l s o c o n t r i b u t e s s l i g h t l y t o t h e l a s i n g power. B. A l i g n m e n t o f t h e O p t i c a l System The a l i g n m e n t o f t h e whole system was done by u s i n g a He-We gas l a s e r by s h i n i n g t h e beam t h r o u g h t h e e x i t s l i t o f t h e monochromator v / i t h a d i f f u s e r i m m e d i a t e l y i n f r o n t o f t h e s l i t . The l i g h t coming o u t from t h e e n t r a n c e s l i t , a f t e r g o i n g t h r o u g h t h e l e n s e s and t h e p r i s m s , was f o c u s e d onto the c e n t r e p o r t i o n o f t h e gas chamber where a p i e c e o f t r a n s p a r e n t f i l m i s p l a c e d t o mark t h e s c a t t e r i n g volume. (The removable t o p o f t h e gas chamber a l l o w s t h e placement o f t h i s f i l m ) . On t h e o t h e r hand, t h e l a s e r beam i s a l s o b e i n g f o c u s e d onto t h e same s c a t t e r i n g r e g i o n by a d j u s t i n g t h e f o c u s i n g l e n s . The n e x t s t e p i s t o s e a r c h f o r t h e s o u r c e o f s t r a y l i g h t . By t r i a l and e r r o r , numerous b u f f e r s were i n s t a l l e d - 27 -to cut down thi s l i g h t to i t s minimum. I t was found that the remaining stray l i g h t came from the inside wall of the gas chamber which had already been painted d u l l black. C. Observation of the Pressure Dependence of the Normalized Scattered Signal As shown i n Chapter II-B equation (7) P do- A f i V s — = P P d£2 A_ K T O L where P /P i s proportional to the normalized scattered s o • ' ^ s i g n a l . In a c e r t a i n set of fixed conditions of the scatter-da ing medium, that i s f o r constant , A f i , V , A and dfi T, the normalized scattered signal i s l i n e a r l y dependent on the pressure. To obtain t h i s l i n e a r r e l a t i o n , the normalized scattered signals were recorded at f i v e d i f f e r e n t pressures. F i g . 8 shows the t h e o r e t i c a l points and the experimental points with error bars. Each experimental point i s an average of twelve recordings. The error bar i s the root mean square value of the deviation from the mean. The two plots show good agreement. The sign a l to noise r a t i o was calculated to be the of the order of 100. D. Measurement of Relative D i f f e r e n t i a l Scattering Cross-sections From equation (5) of Chapter I I - A , I found that 4 2 2 ^ . _ = Ic a Sin® d « where k i s the wave number = — ( X = 6943A , wavelength A of the ruby l a s e r ) ; a i s the p o l a r i z i b i l i t y of the sc a t t e r i n g medium; and <I> i s 90 degrees, the angle between the incident e l e c t r i c f i e l d and the axis of observation. By the Clausius - Mossotte equation € - 6C " € + So where, - 30 -( 1 + xe ) <60 p e r m i t t i v i t y of scattering medium pe r m i t t i v i t y of free space s u s c e p t i b i l i t y of scattering medium number of scattering p a r t i c l e s per unit volume P K T pressure of gas chamber temperature of gas chamber Boltzmann constant At room temperature and one atmosphere, substitute a l l the appropriate values i n the equation, I get 2 = 1.13 - 31 -I h a v e shown t h a t P s p V A f i d a P o K T d n = c o n s t a n t x ( M.S.) w h e r e ( N.S.) = n o r m a l i z e d s c a t t e r e d s i g n a l . T h e r e f o r e a t c o n s t a n t t e m p e r a t u r e a nd p r e s s u r e , a nd t h e same d e t e c t i n g s y s t e m , t h e n o r m a l i z e d s c a t t e r e d s i g n a l i s l i n e a r l y p r o p o r t i o n a l t o t h e d i f f e r e n t i a l c r o s s - s e c t i o n . T h e r e f o r e , F r om e x p e r i m e n t : ( N.S.) m e a s u r e d n o r m a l i z e d s c a t t e r e d s i a n a l -s t r a y l i g h t n o i s e ( i n a r b i t r a r y u n i t s ) F r om F i g . 8 - 32 -( N.S.)„ = (4.857 - .05) x 10~ 2 + 9.5? N 2 = 4.807 x 10" 2 + 9.5% ( N.S.K = (4.332 - .05) x 10~ 2 + 7.4% Ar T h e r e f o r e , 2 Ar 4.282 x 10~ 2 + 7.4% ( N * S , ) N „ 4.307 x 10~ 2 ( N.S.), 4.282 x 10~ 2 = 1.12 T h i s v a l u e shows good agreement wi t h theory's pre-d i c t i o n . E. Measurement o f the Absolute D i f f e r e n t i a l C r o s s -s e c t i o n o f N i t r o g e n and Argon Before the c r o s s - s e c t i o n can be o b t a i n e d a b s o l u t e l y I need the f o l l o w i n g parameters: ( i ) room temperature, ( i i ) the l o a d r e s i s t a n c e a c r o s s anode and ground o f the p h o t o m u l t i p l i e r , ( i i i ) the s i z e o f the entrance s l i t o f the monochromator, (iv) the s c a t t e r i n g volume and t o t a l - 33 -s c a t t e r e d f l u x , (v) t h e h a l f - w i d t h o f t h e l a s e r p u l s e , ( v i ) c a l i b r a t i o n o f t h e l a s e r power v e r s u s t h e p h o t o d i o d e p u l s e , ( v i i ) t h e i n s t r u m e n t p r o f i l e . ( i ) Room t e m p e r a t u r e : t h i s c a n be e a s i l y m e a s u r e d by a t h e r m o m e t e r . T = 296.3 K ( i i ) The l o a d r e s i s t a n c e a c r o s s a n o d e a n d g r o u n d o f t h e p h o t o m u l t i p l i e r i s R = 47.6 ohms. ( i i i ) The s i z e o f t h e e n t r a n c e s l i t o f t h e mono-c h r o m a t o r was m e a s u r e d b y a t r a v e l i n g m i c r o s c o p e . A = 2 .57 x .57 mm ( i v ) The s c a t t e r i n g v o l u m e and t h e t o t a l s c a t t e r e d f l u x . L e t t h e l a s e r beam be f o c u s e d t o t h e o r i g i n o f a C a r t e s i a n c o o r d i n a t e s y s t e m ( F i g . 9) . L e t " f ; ' b e t h e f o c a l l e n g t h o f t h e f o c u s i n g l e n s , " R " be t h e r a d i u s o f t h e l a s e r beam a n d "W" be t h e h e i g h t o f t h e e n t r a n c e s l i t o f t h e m o n o c h r o m a t o r ( t h e beam was r o t a t e d 90 d e g r e e s ) . F i r s t we t a k e a s m a l l s t r i p o f t h e s c a t t e r i n g v o l -ume o f t h i c k n e s s " d x" a n d d i s t a n c e " x " f r o m t h e o r i g i n ( as shown i n d i a g r a m ) . L e t " r " be i t s r a d i u s . y - 34 -< f V >- X FIGURE 9 ILLUSTRATION OF SCATTERING VOLUME ( Much E x a g g e r a t i o n ) I f s u r f a c e a r e a o f s t r i p = A s T h e r e f o r e , v o l u m e o f s t r i p dV = A d x c s A s t h e g a s e s u s e d o b e y I d e a l g a s l a v ; , t h e r e f o r e number o s c a t t e r i n g p a r t i c l e s i n t h i s s t r i p i s p dV o A d x dN = = K T K T From e q u a t i o n (4) o f C h a p t e r I I - A ( F o r t h e s t r i p ) d cr an 'dp dN Aft 1 I w h e r e dP = t o t a l f l u x r a d i a t e d f r o m t h e s t r i p m e a s u r e d s the' d e t e c t i n g s y t e m Therefore, da dp K T A s s dQ D A dx All P s o P P n A f i da d P = - d x S K T dtt Therefore the t o t a l f l u x measured over a l l the s c a t t e r i n g volume i s W 2 P P „ AO da P s = | —-2 — d x 1 K T da / -w 2 P P n An da W (10 ) K T dfi From t h i s equation I can see t h a t the s c a t t e r e d f l u x only depends on the s l i t width, not the s i z e o f the l a s e r beam provided the s l i t h eight i s not too gre a t . (v) H a l f width of photodiode l a s e r p u l s e . The monitoring l a s e r pulse was recorded w i t h a sweeping speed of 50 nanoseconds per d i v i s i o n using a f a s t T e k t r o n i x 454 o s c i l l o s c o p e which has a r i s e time of 2.4 nano-- 36 -seconds. The l a s e r p u l s e i s o f G a u s s i a n l i n e p r o f i l e . A t y p i c a l t r a c e i s shown i n F i g . 6 (Chapter I I I - B ) . The p u l s e showed v e r y good r e p r o d u c i b i l i t y when the l a s e r was f i r e d r e g u l a r l y e v e r y m i n u t e . T h e r e f o r e t h e peak v a l u e o f t h e p u l s e i s p r o p o r t i o n a l t o b o t h t h e l a s e r power and t h e l a s e r energy where t h e f o r m e r i s e q u a l t o t h e l a t t e r d i v i d e d by t h e h a l f - w i d t h o f the p u l s e . A v e r a g i n g o v e r t e n t r a c e s , t h e h a l f p u l s e w i d t h was d e t e r m i n e d t o be At = 35.75 nanoseconds. ( v i ) C a l i b r a t i o n o f the l a s e r power v e r s u s t h e p h o t o d i o d e p u l s e . As shown i n p a r t (v) t h a t t h e peak v a l u e o f t h e l a s e r p u l s e i s p r o p o r t i o n a l t o b o t h t h e l a s e r energy and t h e l a s e r power, t h e r e f o r e I c o u l d c a l i b r a t e the l i n e a r r e l a t i o n be-tween t h e l a s e r power and t h e peak p u l s e v a l u e . The forme r was measured by a TRG model 101 b a l l i s t i c t h e r m o p i l e w i t h t h e measured v a l u e s d i v i d e d by t h e h a l f l a s e r p u l s e w i d t h A t ; and t h e l a t t e r was r e c o r d e d by a T e k t r o n i x 551 o s c i l l o -scope. A p l o t o f t h e l a s e r energy v e r s u s t h e peak p u l s e v a l u e i s shown i n F i g . 10. T h e r e f o r e E = l i n e a r r e l a t i o n between t h e l a s e r power and t h e peak l a s e r p u l s e v a l u e \ 1 tO 2.0 3.0 Photodiode Pulse (Volts) FIGURE 10 CALIBRATION OF LASER ENERGY WITH LASER MONITORING PHOTODIODE PULSE - 3 8 -. 1 4 3 w a t t s D e r v o l t A t ( v i i ) S p e c t r a l R e s p o n s e o f t h e D e t e c t i n g S y s t e m To d e t e r m i n e t h e e x a c t t o t a l s c a t t e r e d f l u x r e c e i v e d a t t h e d e t e c t o r , a c a l i b r a t i o n o f t h e s p e c t r a l r e s p o n s e o f t h e d e t e c t i n g s y s t e m i s e s s e n t i a l . T h i s was done by p l a c i n g a t u n g s t e n r i b b o n lamp a t t h e c e n t r e o f t h e g a s chamber w i t h t h e t u n g s t e n f i l a m e n t s i t u a t e d e x a c t l y w h e r e t h e s c a t t e r i n g t o o k p l a c e . W i t h o u t a l t e r i n g any p a r t o f t h e d e t e c t i n g s y s t e m t h e l a m p was t u r n e d t o a c e r t a i n b r i g h t n e s s . I m e a s u r e d t h e t e m p e r a t u r e o f t h e lamp w i t h a p y r o m e t e r and t h e anode c u r r e n t o f t h e p h o t o m u l t i p l i e r r e s p o n d e d t o t h e f l u x o a t 6943A. To g e t a b e t t e r a c c u r a c y i n t h e l a t t e r m e a s u r e -ment, a F l u k e m o d e l 8100A d i g i t a l v o l t m e t e r was u s e d t o m e a s u r e t h e anode c u r r e n t a c r o s s a 10 k i l o - o h m r e s i s t o r . T e m p e r a t u r e o f lamp t = 2 2 0 0 ° K Anode c u r r e n t 3 0 . 9 _ 3 i . = ~ x 1 0 amp. A 1 0 x 1 0 = 3.09 x 10 6 amp. - 39 -From equation (9) Chapter II-C S = I T ( A ) e I B B B ( A ) AX Aft From eq u a t i o n (8) Chpater II-C At And 2hc he A k t - 1 -1 t = 2200 K A = 6943A X B B < X > = 6.00 x 10 10 j o u l e s m sec s t e r a d i a n o o e = e m i s s i v i t y o f Tungsten a t 2200 K and 6943A = .432 T h e r e f o r e , 3.09 x 10 -6 S = .432 x 6.00 x 1 0 1 0 A A A n 4-16 1.19 x 10 AA A n 2 - i - l m amp sec j o u l e ( v i i i ) The I n s t r u m e n t P r o f i l e To d e t e r m i n e t h e S p e c t r a l R e s p o n s e s p e c i f i c a l l y , I h a v e t o know A A , t h e i n s t r u m e n t w i d t h . ( L a t e r I w i l l show t h a t AH w i l l c a n c e l o u t when f i n d i n g t h e a b s o l u t e c r o s s -s e c t i o n ) . T h i s p a r t was done by u s i n g a Neon G e i s s l e r t u b e . A s b o t h o f t h e s l i t s o f t h e m o n o c h r o m a t o r h a d i d e n t i c a l w i d t h , t h e m e a s u r e m e n t s h a d shown a v e r y g ood t r i a n g u l a r s h a p e . A t y p i c a l i n s t r u m e n t p r o f i l e o f 6929.5A i s shown i n F i g . 1 1 . S e v e r a l l i n e s i n t h e r e d r e g i o n o f t h e n e o n o o o s p e c t r u m w e r e u s e d , n a m e l y 6929.5A , 7032A , 7174A and o 7245A. The a v e r a g e h a l f w i d t h o f t h e i n s t r u m e n t p r o f i l e was d e t e r m i n e d t o be A A = 4.22A A c o m p a r i s o n o f t h i s n o r m a l i z e d s c a t t e r i n g p r o f i l e was d o n e . They a p p e a r e d t o b i n s t r u m e n t p r o f i l e w i t h t h e o f a r g o n a t one a t m o s p h e r e e i n g o o d a g r e e m e n t ( F i g . 1 2 ) . W i t h t o c a l c u l a t e n i t r o g e n a nd t h e a b o v e p a r a m e t e r s a v a i l a b l e , t h e a b s o l u t e d i f f e r e n t i a l c r o s s a r g o n . I am now - s e c t i o n s a b l e o f - XV -- 43 -From e a u a t i o n (10) C h a p t e r I V - E , p P 0 Aft da P = — - W S K T d n T h e r e f o r e , da K T P S (11) dn w An p p o The t o t a l s c a t t e r e d f l u x o b s e r v e d a t t h e d e t e c t i n g s y s t e m i s s c a t t e r e d s i g n a l i n v o l t a r e a o f s l i t P = x s l o a d r e s i s t o r f r o m anode s p e c t r a l t o g r o u n d o f p h o t o m u l t i p l i e r r e s p o n s e ( S.S.) A x — R S The t o t a l i n p u t p o w e r o f t h e r u b y l a s e r P q = t h e p h o t o d i o d e l a s e r p u l s e p e a k v a l u e i n v o l t x l i n e a r r e l a t i o n o f l a s e r power v e r s u s l a s e r p u l s e = ( L.S.) x E - 44 -T h e r e f o r e , Pg ( S.S.) A P Q ( L . S . ) E S R B u t , S.S. = N o r m a l i z e d S c a t t e r e d s i g n a l ( d e f i n e d L . S . i n C h a p t e r I I - B ) ( N . S . ) S u b s t i t u t e t h i s i n t o e q u a t i o n ( 1 1 ) , I g e t da K T A = x ( N . S . ) (12) dO A f l p E R SW and s u b s t i t u t e f o r S, t h e s p e c t r a l r e s p o n s e d a K T A A A ( N . S . ) = _-, (• x dQ W E R 1.19 x 10 p K = B o l t z m a n n c o n s t a n t i n j o u l e s p e r d e g r e e K e l v i n T = T e m p e r a t u r e o f g a s c h a m b e r i n d e g r e e s K e l v i n W = H e i g h t o f m o n o c h r o m a t o r s l i t i n m e t e r 2 A = A r e a o f s l i t i n s q u a r e m e t e r = W - 45 -p = Pres s u r e of gas chamber i n newton per square meter E = L i n e a r r e l a t i o n between l a s e r power and l a s e r p u l s e i n watts per v o l t R = Load r e s i s t a n c e from anode t o ground of p h o t o m u l t i p l i e r i n ohms ( N.S.) = Normalized s c a t t e r e d s i g n a l ( u n i t l e s s ) S u b s t i t u t e the c o n s t a n t v a l u e s , I get da ( N.S.) = 4.32 x 10 D x m dO p At one atmosphere and room temperature ( N.S.) X T = 4.807 x 10~ 2 + 9.5% N 2 ( N . S . ) A r = 4.282 x 10" 2 + 7.4% -5 2 p = 1.007 x 10 newton m T h e r e f o r e , \ d n / N . 9 f i 4.807 x 10 ? 4.32 x 10 b x F — - 9.5% m 1.007 x 10 2.07 x 1 0 " 3 2 + 9.5% m 2 - 46 -~ , 4 . 2 8 2 x 1 0 2 . _ 2 , , - 2 6 + 7 . 4 % m = 4 . 3 4 x 10 x p— -1 . 0 0 7 x 1 03 Ar = 1.86 x 1 0 ~3 2 + 7 . 4 % m2 To compare these v a l u e s with the t h e o r e t i c a l v a l u e s , I can c a l c u l a t e from e q u a t i o n (5) Chapter I I - A d a , 4 2 k a d n k = Wave number 3 € - • € o a = = P l a r i z i b i l i t y o f N v £ + £ 0 s c a t t e r i n g medium N = number of s c a t t e r i n g p a r t i c l e s per u n i t volume a t one atmosphere and room temp-e r a t u r e a = 1 . 7 8 x 1 0 m N2 i co m-30 3 a, = 1.68 x 1 0 m Ar T h e r e f o r e , And / d a \ -3? 2 j = 1 . 3 7 x 1 0 m The t h e o r e t i c a l v a l u e s a n d t h e e x p e r i m e n t a l v a l u e s show a g r e e m e n t w e l l w i t h i n e x p e r i m e n t a l e r r o r . I a l s o a t t e m p t e d t o m e a s u r e t h e s c a t t e r i n g c r o s s -s e c t i o n o f H e l i u m . D e t a i l e d d i s c u s s i o n i s shown i n t h e A p p e n d i x . F. E r r o r A n a l y s i s F r o m t h e r e s u l t s I o b t a i n e d , I c a n s a y t h e e x p e r i m e n t a l v a l u e s a r e i n g o o d a g r e e m e n t w i t h t h e p r e d i c t i o n f r o m t h e t h e o r y . I t was u n f o r t u n a t e t h a t t h e s t a n d a r d d e v i a t i o n o f t h e v a l u e s o b t a i n e d w e re 9.5% f o r n i t r o g e n a nd 7 . 4 % f o r a r g o n . I s u s p e c t t h a t t h e e r r o r was m a i n l y due t o t h e i m p u r i t i e s i n t h e g a s e s . B e f o r e e a c h s a m p l i n g o f d a t a , t h e g a s chamber was f l u s h e d a t l e a s t s i x t i m e s w i t h t h e h i g h p u r i t y g a s ( p u r i t y o f 99.999%) t o a v o i d m i x t u r e o f i m p u r i t i e s . E v e n w i t h t h i s p r e c a u t i o n , i t was n o t p o s s i b l e t o g e t 1 0 0 % p u r e - 4 8 -gas. There v;as f u r t h e r i n d i c a t i o n showing the b i g d e v i a t i o n of s c a t t e r e d s i g n a l from gas w i t h i m p u r i t i e s . A g e n e r a l grade n i t r o g e n which has 9 9 . 9 % p u r i t y was used. The normal-i z e d s c a t t e r e d s i g n a l measured was at l e a s t f o u r times b i g g e r than expected. A l s o from e q u a t i o n (11) o f Chapter IV-E I have shown t h a t P Aft W P d a — = OC ( N.S.) P K T dfi o T h e r e f o r e , f o r any gas at a c e r t a i n temperature and p r e s s u r e , the s i z e o f the Normalized S c a t t e r e d s i g n a l w i l l i n c r e a s e w i t h the h e i g h t o f the monochromator entrance s l i t p r o v i d e d the l a s e r beam i s narrower than the width o f the s l i t . By f o c u s i n g down the l a s e r beam, I am able to c l o s e down the width o f the monochromator t o .57 mm. and t h i s h e l p e d enormously i n e l i m i n a t i n g the s t r a y l i g h t n o i s e . U n f o r t u n a t e -l y the h e i g h t o f the s l i t was l i m i t e d by the s i z e o f the tungsten ribbon lamp f i l a m e n t , t h e r e f o r e the s l i t was chosen to have both the h e i g h t and the width e q u a l . To i l l u s t r a t e t h i s p a r t , the d e t e c t i n g system was unfocused from the s c a t t e r i n g volume. A comparison of the s c a t t e r e d s i g n a l s o f both f o c u s i n g case and unf o c u s i n g case i s shown i n - 49 -F i g . 1 3 . The l o w e r t r a c e i s t h e m o n i t o r i n g l a s e r p u l s e and t h e u p p e r t r a c e i s t h e s c a t t e r e d s i g n a l . S o u r c e o f s t r a y l i g h t was f o u n d t o be c o m i n g f r o m i n s i d e t h e g a s c h a m b e r . T h i s was t e s t e d b y means o f b u f f e r s p l a c e d a t d i f f e r e n t r e g i o n s o f t h e s y s t e m . The i n s i d e w a l l o f t h e g a s c h a m b e r was p a i n t e d d u l l - b l a c k t o c u t down r e f l e c t -i o n f r o m t h e s u r f a c e . The d i a m e t e r o f t h i s c h amber was l i m i t e d by t h e f o c a l l e n g t h o f t h e l e n s e s a v a i l a b l e a t t h e t i m e i t was b u i l t . I b e l i e v e i f t h e chamber s i z e was b i g g e r , t h e s t r a y l i g h t n o i s e w o u l d be f u r t h e r d e c r e a s e d . FOCUSED UNFOCUSED FIGURE 13 ILLUSTRATION OF SCATTERED SIGNAL WITH FOCUSED AND UNFOCUSED DETECTING SYSTEM - 50 -CHAPTER V CONCLUSION AND DISCUSSION A. Conclusion The measurement of the absolute scattering cross-sections of argon and nitrogen have shown close agreement with the theory's p r e d i c t i o n within experimental error. The main objective of t h i s experiment was to c a l i b r -ate the scattered signal from neutral p a r t i c l e s i n a l a s e r -plasma i n t e r a c t i o n experiment using a nitrogen or argon plasma. The r e s u l t s also confirm the work done by Rudder and Bach. B. Discussion This technique could be applied to the measurement of scattering cross-sections of gas mixtures at constant pressure, and study the turbulence and perturbation of p a r t i c l e density of gas flow. - 51 -F o r f u r t h e r w o r k t o be clone i n R a y l e i g h S c a t t e r i n g , o n e s h o u l d c o n s i d e r u s i n g a CG^ l a s e r . T h e r e a r e numerous r e a s o n s t o c h o o s e t h e CG^ l a s e r , b u t t h e m o s t i m p o r t a n t r e a s o n i s i t s o p e r a t i n g power c a n r e a c h t h e g i g a w a t t r a n g e , and i t s r e p e t i t i o n r a t e c a n be much more f r e q u e n t t h a n t h e r u b y l a s e r . To f u r t h e r i m p r o v e t h e e x p e r i m e n t , one s h o u l d a l s o be c a u t i o u s w i t h t h e c h o i c e o f t h e t y p e o f p h o t o m u l t i -p l i e r . I n t h i s e x p e r i m e n t , a RCA 7265 p h o t o t u b e w i t h S-20 r e s p o n s e was u s e d . W i t h t h e new t u b e s now a v a i l a b l e i n t h e m a r k e t , one c o u l d e a s i l y c h o o s e a t u b e w i t h much b e t t e r s e n s i t i v i t y a n d q u a n t u m e f f i c i e n c y i n t h e r e d s p e c t r u m . - 52 -BIBLIOGRAPHY (1) T.V. George, L. G o l d s t e i n , L. Slama and M. Yokoyarna (1965), P h y s i c a l Review 137, A369. (2) T.V. George, L. G o l d s t e i n , L. Slama and M. Yokoyarna (1963), P h y s i c a l Review L e t t e r s 11 , 403. (3) R. Rudder and D. Bach (1963), J o u r n a l o f The O p t i c a l S o c i e t y of A m e r i c a 5_8 , 1260. (4) R. Watson and M. C l a r k (1965), P h v s i c a l Review L e t t e r s 14, 1057. (5) O. Theimer (1964), P h y s i c a l Review L e t t e r s 13, 622. (6) W. Schwarz ( 1 9 6 4 ) , I n t e r m e d i a t e E l e c t r o m a g n e t i c Theory, W i l e y . (7) H. H e l e n i u s Van A n d e l (1966), Ph.D. T h e s i s , U n i v e r s i t y o f E r i t i s h C o l u m b i a . - 53 -APPENDIX H e l i u m was a l s o u s e d as a s c a t t e r i n g medium, b u t i t s s c a t t e r i n g c r o s s - s e c t i o n i s o f a f a c t o r o f 70 t i m e s s m a l l e r t h a n t h o s e o f n i t r o g e n . T h e r e f o r e , t h e m e a s u r e d v a l u e s o f t h e c r o s s - s e c t i o n o f h e l i u m v/as n o t s a t i s f a c t o r y . R e g a r d -l e s s , t h e p r e s s u r e d e p e n d e n c e o f h e l i u m s c a t t e r e d s i g n a l showed f a i r l y g o o d a g r e e m e n t w i t h t h e t h e o r y ( F i g . 14). The t h e o r e t i c a l v a l u e o f a b s o l u t e d i f f e r e n t i a l s c a t t e r i n g c r o s s - s e c t i o n o f h e l i u m i s ( - ) -32 2 = .0291 x 10 m The m e a s u r e d v a l u e was (-) -32 2 = .036 x 10 m .036 - .0291 E r r o r P e r c e n t a g e = 100% .0291 - 55 -= 24% The s i g n a l to n o i s e r a t i o i n t h i s p a r t was a p p r o x i -mately equal to 1 i n comparison to 100 f o r argon and n i t r o g e n . 

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