UBC Theses and Dissertations

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UBC Theses and Dissertations

A study of the X-ray emission from the plasma focus 1975

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A STUDY OF THE X-RAY EMISSION FROM. THE PLASMA FOCUS by GRAHAM WHITELAW RANKIN B . S c . , The U n i v e r s i t y of B r i t i s h C o l u m b i a , .1372 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of PHYSICS 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 to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA D e c e m b e r , 1 9 7 5 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree l y ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t i on of th is thes is for f inanc ia l gain sha l l not be allowed without my writ ten pe rm i ss ion . Department of phvsics The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D a t e n p n . 1 f ABSTRACT The X - r a y e m i s s i o n from a plasma f o c u s has been s t u d i e d u s i n g t ime i n t e g r a t e d and s t r e a k p h o t o g r a p h y . The p lasma f o c u s , a s m a l l volume o f v e r y dense and hot p la sma was c r e a t e d i n a c o a x i a l p lasma gun d r i v e n by a f a s t c u r r e n t p u l s e o f p e r i o d T ~ 2 usee wh ich was p roduced by d i s c h a r g - i n g a condenso r bank o f V = 12-15 kV, and C = 84 y f . Measurements have shown t h a t a d i f f u s e X - r a y e m i t t i n g p lasma column i s formed i n the ' e a r l y ' p i n c h s t a g e , wh i ch ex tend s a few c e n t i m e t e r s i n the a x i a l d i r e c t i o n , has e x p a n s i o n v e l o c i t i e s o f between 2-6 x 1 0 7 cm/sec . and l a s t s f o r 30-60 n s e c . In the f o l l o w i n g 10-30 n s e c . X - r a y e m i s s i o n o c c u r s f rom s m a l l p lasma r e g i o n s wh ich have l i t t l e or no a x i a l v e l o c i t y . The d i s t a n c e between t h e s e " h o t " s p o t s a r e o f the o r d e r of h a l f a c e n t i m e t e r . These measurements and o b s e r v a t i o n s o f t h e X - r a y e m i t t i n g r e g i o n s a r e c o n s i s t e n t w i t h r e s u l t s o b t a i n e d by Peacock and Ma the r . By compar ing t h e i r r e s u l t s w i t h t h o s e of t h i s e x p e r i m e n t i t i s c o n c l u d e d t h a t the appea rance o f the i s o l a t e d X - r a y s ou r ce s i s a s s o c i a t e d w i t h t he m = 0 i n s t a b i l i t y . i i TABLE OF CONTENTS Page ABSTRACT i i L IST OF FIGURES v ACKNOWLEDGMENTS • . . v i Chap te r 1 INTRODUCTION 1 1 .1 The Plasma Focus 1 1.2 P r e v i o u s Work on the Plasma F o c u s . . . . 3 1.3 Un iquenes s o f the E x p e r i m e n t 4 2 APPARATUS 6 2.1 The Focus 6 2.2 The Spark Gap 9 2.3 X - r a y Imaging • • • ^ 2.4 T im i ng . . . . 15 3 OBSERVATIONS AND RESULTS 18 3.1 Image M a g n i f i c a t i o n 18 3.2 S p a c i a l R e s o l u t i o n 19 3.3 Temporal R e s o l u t i o n . . . 19 3.4 X - r a y Pho tog raph s 19 i i i Chap te r Page 4 DISCUSSION OF RESULTS 23 5 CONCLUSIONS 28 REFERENCES 29 i v LIST OF FIGURES F i gure Page 1 E x p e r i m e n t a l a r rangement 7 2 E l e c t r o d e a s semb ly 8 3 Spark gap e l e c t r o d e s 10 4 E l e c t r i c a l c i r c u i t o f t he plasma f o c u s . . . . . . 12 5 I l l u s t r a t i o n o f O p t i c a l a r rangement 13 6 P i n h o l e . . . . . 14 7 E l e c t r o - o p t i c a l X - r a y camera 16 8 T r i g g e r i n g a r rangement 17 9 X - r a y pho tog raph s and an o s c i l l o g r a m o f t he f o c u s i n g even t 21 10 S chemat i c f o r p roposed sequence o f e ven t s 27 v ACKNOWLEDGMENTS The i dea o f u s i n g s t r e a k photog raphy f o r a n a l y z - i n g t he dense p i n c h s t a ge o f t he plasma f o c u s i s t h a t o f Dr . J . Meyer . I would l i k e t o acknov/ledge the b u i l d i n g o f the plasma f o c u s a p p a r a t u s by J ack B u r n e t t . To Dough S i e b e r g and A l l e n Cheuck, I w i sh to 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 i r t e c h n i c a l a s s i s t a n c e . Many thank s to the members o f t he U.B.C. plasma p h y s i c s group f o r t h e i r h e l p f u l d i s c u s s i o n s . T h i s work was s u p p o r t e d by a g r a n t f rom t h e Atom Energy C o n t r o l Board of Canada. Chap te r 1 INTRODUCTION 1.1 The Plasma Focus The p la sma f o c u s i s a d e v i c e c o n s i s t i n g o f c o a x i a l e l e c t r o d e s i n s i d e a v e s s e l c o n t a i n i n g a m i x t u r e o f gases a t a p r e s s u r e of l e s s than s e v e r a l t o r r . The f o r m a t i o n o f t he dense p lasma f o c u s beyond the end o f t he c o a x i a l e l e c t r o d e geometry was f i r s t o b se r ved and s t u d i e d by the R u s s i a n , T . I . F l i p p o v a i n the 1 9 6 0 ' s . Over the y e a r s s t u d i e s o f t he plasma f o c u s have c o n c e n t r a t e d on the i n i t i a l e l e c t r i c a l breakdown between the e l e c t r o d e s , the dynamics o f the rundown o f the c u r r e n t s h e a t h , and t h e f i n a l dense f o c u s s t a ge o f t h e p lasma f o c u s , w i t h r e c e n t i n t e r e s t b e i n g on t he l a t t e r and more s p e c i f i c a l l y on t he neu t r on p r o d u c t i o n wh ich r e s u l t s i f a D 2 gas i s used i n the d i s c h a r g e v e s s e l . A h i gh v o l t a g e ( i n t h i s e x p t . 12-15 kV) f rom the c a p a c i t o r bank i s a p p l i e d between the i n n e r and o u t e r e l e c - t r o d e s o f t he d i s c h a r g e v e s s e l . T h i s p roduce s a breakdown i n t he r e g i o n a t the back o f the e l e c t r o d e s near a L u c i t e 1 2 i n s u l a t o r ( see F i g . 1 ) . C u r r e n t then f l o w s f rom the c e n t r e e l e c t r o d e back a l ong the i n s u l a t o r t o the back p l a t e p r o - d u c i n g a " w a t e r f a l l " f l o w ove r t he i n s u l a t o r s u r f a c e . S t u d i e s have shown [ 1 ] t h a t d u r i n g the e a r l y s t age s of c u r r e n t b u i l d - u p t h e r e i s a complex f i l a m e n t a r y l i g h t p a t t e r n p r o - duced a t the back p l a t e . The j , x B_, i n v e r s e p i n c h f o r c e Z 9 nex t d r i v e s t he c u r r e n t outward towards the o u t e r e l e c t r o d e . A t t h i s t ime the f i l a m e n t a r y p a t t e r n o f the c u r r e n t b l e n d s t o fo rm a u n i f o r m a x i s y m e t r i c d i s c h a r g e . Because i and B„ d e c r e a s e w i t h r a d i u s the f o r c e r o ( 5 r x B Q ) i s g r e a t e r n e a r e r the i n n e r e l e c t r o d e than a t the o u t e r e l e c t r o d e and so the c u r r e n t sheath has a c a n t . Pho tog raph s by Mather [ 2 ] have shown t h i s appea rance o f the s h e a t h . The c u r r e n t s hea th as i t moves down between t he coppe r e l e c t r o d e s a c c u m u l a t e s gas i n f r o n t o f i t . T h i s e f f e c t c a l l e d snowp lough ing has l e d to s e v e r a l models d e s c r i b i n g t he p h y s i c s o f t he c u r r e n t s hea th [ 3 ] . The maximum ave r a ge shea th v e l o c i t y i n the annu lu s has been r e c o r d e d to have an upper l i m i t o f 1.5 x 1 0 7 cm/sec [ 4 ] . When the c u r r e n t s hea th a r r i v e s a t the end o f the e l e c t r o d e s i t o v e r s h o o t s and e x p e r i e n c e s a f a s t ( 1 -4 x 1 0 7 cm/sec) [ 5 ] r a d i a l c o l l a p s e towards the a x i s as a r e s u l t o f t he s t r o n g r a d i a l p i n c h f o r c e , j x B Q . To max imize t h i s p i n c h f o r c e one chooses the gas m i x t u r e , and t he v o l t a g e such t h a t the peak o f the c u r r e n t p u l s e o c c u r s a t the t ime of 3 r a d i a l c o l l a p s e . In a d d i t i o n the peak of the c u r r e n t p u l s e i s d e t e r m i n e d by the i n d u c t a n c e of the v o l t a g e s u p p l y ne two r k . Any r e d u c t i o n i n t he i n d u c t a n c e , f o r e xamp le , by u s i n g s e v e r a l low i n d u c t a n c e c a b l e s to d e l i v e r the c u r r e n t f rom the c a p a c i t o r bank to the d i s c h a r g e v e s s e l w i l l r e s u l t i n a c h i e v i n g a g r e a t e r p i n c h f o r c e . The dense p lasma formed as a r e s u l t o f t h e p i n c h has been ob se r ved to have e l e c t r o n d e n s i t i e s o f o r d e r 1 0 1 9 c m " 3 and t e m p e r a t u r e of s e v e r a l keV. 1 .2 P r e v i o u s Work on the Plasma Focus Measurements o f d e n s i t i e s have been done by o b s e r v - i n g the shape o f the e m i s s i o n spec t rum arid the a b s o l u t e r a d i a t i o n f l u x i n t he s o f t X - r a y r e g i o n [8]. Shawdowgraphs and S c h l i e r e n pho tog raph s have been used to d e t e r m i n e the s p a c i a l and tempora l deve lopment o f the dense p lasma [ 1 2 ] , and i n t e r f e r o m e t r i c measurements have been used t o o b t a i n t he e l e c t r o n d e n s i t y [ 4 ] . The f i t t i n g o f d a t a t o both X - r a y e m i s s i o n and neu t r on y i e l d s (a s suming a t h e r m o n u c l e a r p l a sma) have g i v e n plasma d e n s i t i e s o f the o r d e r of 1 0 1 9 c m - 3 [ 4 ] . E l e c t r o n t e m p e r a t u r e s ( f o r d e u t e r i u m ) o f a p p r o x i m a t e l y .70 keV have been ob se r ved by l a s e r s c a t t e r i n g [ 7 ] . In a d d i t i o n , i t has been ob se r ved t h a t i n a d e u t e r i u m p lasma t he t o t a l n e u t r o n e m i s s i o n per d i s c h a r g e r e q u i r e s an i o n t e m p e r a t u r e o f s e v e r a l keV (as suming a t h e r m o n u c l e a r p lasma 4 [6]). The a s s umpt i on of t he rma l neu t r on p r o d u c t i o n i s not c l e a r l y v a l i d s i n c e t h e r e i s e v i d e n c e f o r a n o n t h e r m o n u c l e a r p r o d u c t i o n i n a d e u t e r i u m plasma f o c u s [9]. Due to the h i gh t e m p e r a t u r e s r eached i n t he plasma f o c u s most o f the r a d i a t i o n i s i n the X - r a y r e g i o n . These X - r a y s a re due to B r e m s s t r a h l u n g and l i n e r a d i a t i o n . T h i s t h e s i s devo te s i t s main i n t e r e s t to the i n v e s t i g a t i o n o f t he X - r a y e m i s s i o n f e a t u r e s o f the dense f o c u s s t a g e . The f o c u s a t U.B.C. does not p roduce neu t r on s and as such i s p r i m a r i l y an X - r a y e m i t t i n g p l a sma . 1.3 Un iquenes s o f the E xpe r imen t What i s un ique about t h i s e x p e r i m e n t pe r f o rmed a t the U.B.C. plasma p h y s i c s l a b i s t h a t i t i s t he f i r s t e x p e r i - ment t o t a k e s t r e a k pho tog raph s o f t he X - r a y e m i s s i o n s d u r i n g the f o c u s s t a ge of the p i n c h . O the r e x p e r i m e n t s wh i ch have i n v e s t i g a t e d the X - r a y e m i s s i o n f e a t u r e s o f the f o c u s have i n c l u d e d the r e c o r d i n g of X - r a y e m i s s i o n s by t he use o f X - r a y p i n h o l e cameras w i t h v a r i o u s a b s o r b e r s to o b t a i n t ime i n t e - g r a t e d pho tog raph s and thus i n f o r m a t i o n about the e n e r g i e s o f the X - r a y s e m i t t e d , i n a d d i t i o n to c o r r e l a t i o n o f f r a m i n g p i c t u r e s ( i n the v i s i b l e r e g i o n ) w i t h X - r a y m o n i t o r e d p u l s e s . Most o f t he t h e o r e t i c a l work done on the plasma f o c u s so f a r has been to e x p l a i n the o b s e r v a t i o n s o f the n e u t r o n f l u x t h a t o r i g i n a t e s f rom a d e u t r i u m f o c u s . To' 5 e x p l a i n the a n i s o t r o p i c d i s t r i b u t i o n of n e u t r o n f l u x e s and neu t r on energy s p e c t r a v a r i o u s models have been p r o p o s e d , as f o r example the beam t a r g e t m o d e l , and o t h e r mode l s , wh ich assume the rma l and t h e r m o n u c l e a r p r o c e s s e s o c c u r r i n g w i t h i n the f o c u s . O b s e r v a t i o n s and p o s s i b l e mechanisms o f X - r a y e m i s s i o n f e a t u r e s have been s t u d i e d by such no ted e x p e r i m e n - t a l i s t s i n t h i s f i e l d as Peacock and Mather and to a l e s s e r e x t e n t B o s t i c k . T h e i r o b s e r v a t i o n s and p roposed mechanisms i n c o n j u n c t i o n w i t h what has been ob se r ved a t t he U.B.C. plasma f o c u s i s d i s c u s s e d and summarized i n the c o n c l u s i o n o f t h i s t h e s i s . In summary i t was the aim of t h i s e x p e r i m e n t t o measure v e l o c i t i e s and l i f e t i m e s o f the X - r a y e m i t t i n g p lasma and to compare the X - r a y t ime i n t e g r a t e d pho tog raph s w i t h t ho se o b t a i n e d by o t h e r e x p e r i m e n t a l i s t s , and t o f i t and compare the r e s u l t s o b t a i n e d w i t h e x i s t i n g models so t h a t a p o s s i b l e mechanism f o r X - r a y p r o d u c t i o n c o u l d be f o r m u l a t e d . The e x p e r i m e n t was a s u c c e s s i n t h a t t h e s p a c i a l and tempora l f e a t u r e s of the X - r a y s u s i n g n s e c . s t r e a k , and t ime i n t e g r a t e d photog raphy were r e c o r d e d and a n a l y z e d . As a r e s u l t a p o s s i b l e mechanism f o r X - r a y p r o d u c t i o n c o u l d be f o r m u l a t e d . C h a p t e r 2 APPARATUS 2 .1 The F o c u s Th e e x p e r i m e n t a l a r r a n g e m e n t i s shown i n F i g . 1. The p l a s m a f o c u s i n v e s t i g a t e d i n t h i s e x p e r i m e n t c o n s i s t s b a s i c a l l y o f two c o a x i a l c y l i n d r i c a l c o p p e r e l e c t r o d e s o f a p p r o x i m a t e l y 25 cm i n l e n g t h . The i n n e r e l e c t r o d e c y l i n d e r o f p o s i t i v e p o l a r i t y has an o u t e r d i a m e t e r o f 5 cm a n d an i n n e r d i a m e t e r o f 2.5 cm. The c a t h o d e i s a p e r f o r a t e d c o p p e r c y l i n d e r o f 10 cm d i a m e t e r . T h e o u t e r c y l i n d e r i s s o l d e r e d o n t o a b r a s s d i s k w i t h a c o n c e n t r i c h o l e o f 6 cm" d i a m e t e r . T h e h o l e a l l o w s t h e c o a x i a l a s s e m b l y c o n s i s t i n g o f t h e a n o d e , and a c y l i n d r i c a l P y r e x i n s u l a t o r (5 cm i n n e r d i a m e t e r a n d 5 cm l e n g t h ) , w h i c h i s f i t t e d o v e r t h e a n o d e , t o be m o u n t e d i n s i d e t h e o u t e r c y l i n d e r ( s e e F i g . 2 ) . T h e g l a s s s l e e v e a n d a p l e x i g l a s s d i s k p r e v e n t p r e m a t u r e e l e c t r i c a l b r e a k d o w n b e t w e e n t h e o p p o s i t e p o l a r i t y e l e c t r o d e s . In a d d i t i o n t h e g l a s s s l e e v e a l l o w s t h e i n i t i a l f o r m a t i o n o f an i n v e r s e p i n c h f o l l o w i n g b r e a k d o w n t o o c c u r b e t w e e n t h e a n o d e a t t h e s l e e v e end a n d t h e i n s i d e o f t h e c o p p e r c a t h o d e c y l i n d e r . 6 Spark gap Glass Insulator 84/jf Inner Electrode Current sheath X-ray Film Holder c m Outer Electrode (Perforated) Evacuated Tube Image Converter F i g u r e 1. E x p e r i m e n t a l a r r a n g e m e n t . 8 Coax Cablo lead in F i g u r e 2 . E l e c t r o d e a s s e m b l y . 9 The e n t i r e e l e c t r o d e a s s e m b l y i s f i t t e d i n s i d e a P y r e x v e s s e l w h i c h i s e v a c u a t e d a n d f i l l e d w i t h a g a s m i x t u r e o f H y d r o g e n and A r g o n ( a p p r o x i m a t e l y 10% A r g o n by p r e s s u r e ) t o a p r e s s u r e o f b e t w e e n .5 t o .8 T o r r . T h e e l e c t r o d e a s s e m b l y i s h e l d i n p o s i t i o n i n t h e P y r e x v e s s e l by a b r a s s p l a t e . T h e b r a s s p l a t e ( o r c a b l e h e a d e r ) a l s o p r o v i d e s an e l e c t r i c a l c o n n e c t i o n b e t w e e n t h e c o a x i a l c a b l e s c o m i n g f r o m t h e c a p a c i t o r b ank t o t h e i n n e r a n d o u t e r c y l i n d e r i c a l c o p p e r e l e c t r o d e s ( l o c a t e d i n s i d e t h e P y r e x v e s s e l ) . The power r e q u i r e d t o p r o d u c e t h e c u r r e n t s h e a t h i s p r o v i d e d by a b ank o f s i x , 14 u f c a p a c i t o r s c h a r g e d t o a v o l t a g e b e t w e e n 12 a n d 15 kV. T h i s e n e r g y i s d e l i v e r e d by 30 c o a x i a l c a b l e s ( f i v e c a b l e s f o r e a c h c a p a c i t o r ) w h i c h a r e a l l c o n n e c t e d t o t h e c a b l e h e a d e r . 2.2 T h e S p a r k Gap E a c h c a p a c i t o r h a s a s p a r k g a p . A l l s p a r k g a p s a r e t r i g g e r e d a t t h e same t i m e by a p u l s e p r o d u c e d by f i r i n g a n a u x i l i a r y s p a r k g a p . I n s i d e t h e s p a r k c a n , w h i c h h o u s e s t h e s p a r k g a p , a r e f o u r e l e c t r o d e s . F i g . 3 d e p i c t s t h e f o u r e l e c t r o d e s . One e l e c t r o d e (#2 i n t h e d i a g r a m ) i s c o n - n e c t e d t o t h e h i g h v o l t a g e t e r m i n a l o f t h e c a p a c i t o r a n d a n o t h e r (#1) i s e l e c t r i c a l l y c o n n e c t e d ( v i a t h e c a b l e h e a d e r ) t o t h e i n n e r p o s i t i v e c y l i n d r i c a l e l e c t r o d e . 10 F i g u r e 3. S p a r k gap e l e c t r o d e s . 11 Two o t h e r e l e c t r o d e s (#3 a n d #4) a r e l o c a t e d b e t w e e n t h e a b o v e m e n t i o n e d e l e c t r o d e s . A h i g h v o l t a g e p u l s e ( p r o d u c e d by t h e a u x i l i a r y s p a r k g a p ) i s a p p l i e d b e t w e e n t h e o u t e r d i s k s h a p e d e l e c t r o d e (#3) a n d t h e f i n e p o i n t o f a t u n g s t e n w i r e ( e l e c t r o d e # 4 ) , so t h a t a s p a r k i s p r o d u c e d b e t w e e n them. T h i s s p a r k p r o d u c e s a U.V. f l a s h w h i c h i n t u r n i o n i z e s t h e a i r a n d c a u s e s a c u r r e n t t o s t a r t f l o w i n g b e t w e e n e l e c t r o d e s #1 a n d #2. T h e r e s u l t i n g p l a s m a s h o r t c i r c u i t s e l e c t r o d e s #1 and #2 a n d t h e r e b y d i s c h a r g e s t h e c a p a c i t o r . T h i s e l e c t r i c a l a r r a n g e m e n t o f t h e s p a r k gap e n s u r e s a f a s t a n d j i t t e r - f r e e b r e a k d o w n o f t h e c a p a c i t o r b a n k . T h i s i s i m p o r t a n t s i n c e s i m u l t a n e o u s a r r i v a l o f t h e v o l t a g e p u l s e s a t t h e c a b l e h e a d e r i s i m p o r t a n t f o r t h e f o r m a t i o n o f a g o o d f o c u s . See F i g . 4 f o r t h e d e t a i l e d e l e c t r i c a l l a y o u t . 2.3 X - r a y I m a g i n g T i m e i n t e g r a t e d and s t r e a k e d X - r a y p h o t o g r a p h s w e r e t a k e n s i m u l t a n e o u s l y o f t h e same p l a s m a f o c u s e v e n t . T h e i m a g i n g was a c c o m p l i s h e d by u s i n g a p i n h o l e X - r a y c a m e r a . L o c a t e d a t r i g h t a n g l e s t o t h e e l e c t r o d e a x i s ( a n d a p p r o x i m a t e l y 17 cm f r o m t h e f o c u s ) a r e p i n h o l e s o f .5 mm ( o n e on e a c h s i d e ) w i t h a 1 m i l Be f o i l window ( s e e F i g s . 5 a n d 6 ) . The p i n h o l e d i a m e t e r i s o f t h e o r d e r o f a t h o u s a n d F r e s n e l z o n e s w i d e . T h e X - r a y s p a s s i n g t h r o u g h t h e p i n h o l e s 10 KV 20M : Trig Pulse 5C22 500p H M — Z I00K« 500p 5 25M To Plasma Focus electrodes To other 14 uf capacitors 4 K W v 100 M ferrite core r±- 100 M Charging Unit F i g u r e 4. E l e c t r i c a l c i r c u i t o f t h e p l a s m a f o c u s . Polaroid camera Image intensifier Streak unit scintillator Plasma focus electrodes plasma Be foil pinhole X - r ay film streak direction F i g u r e 5. I l l u s t r a t i o n o f o p t i c a l a r r a n g e m e n t . 14 F i g u r e 6. P i n h o l e . 15 t r a v e l down an e v a c u a t e d h o l l o w t u b e ( a p p r o x i m a t e l y 17 cm i n l e n g t h ) u n t i l t h e y h i t i n one c a s e X - r a y r e c o r d i n g f i l m o r i n t h e o t h e r a t h i n s c i n t i l l a t o r ( 1 . 5 mm) p r o d u c i n g an i m a g e i n v i s i b l e - l i g h t . T h i s i m a g e i s t i m e r e s o l v e d by a TRW Image C o n v e r t e r C a m e r a . Th e s t r e a k e d i m a g e i s t h e n p a s s e d t h r o u g h an i m a g e i n t e n s i f i e r (RCA 8 6 0 6 ) b e f o r e f i n a l l y b e i n g r e c o r d e d by a c a m e r a o n t o 10,000 A.S.A. p o l a r i o d f i l m ( F i g . 7 ) . 2.4 T i m i ng T h e t i m i n g r e q u i r e d t o t a k e th^e X - r a y s t r e a k p i c t u r e s was a c h i e v e d by p l a c i n g a l i g h t p i p e n e a r t h e end a n d a b o v e t h e o u t e r p e r f o r a t e d e l e c t r o d e . As t h e l u m i n o u s f r o n t o f t h e c u r r e n t s h e a t h p a s s e d down b e t w e e n t h e e l e c t r o d e s t h e l i g h t r a d i a t e d f r o m i t was p i c k e d up by t h e l i g h t p i p e ( s e e F i g . 8) a n d t h e n s e n t t o a p h o t o m u l t i p i i e r w h i c h i n t u r n t r i g g e r e d t h e d e l a y g e n e r a t o r w h i c h s e n t a p u l s e t o t h e i m a g e c o n v e r t e r t o s t r e a k i t . T h i s m e t h o d was n e c e s s i t a t e d by t h e i r r e p r o d u c e - a b i l i t y i n t h e d i s c h a r g e , b e c a u s e o f v a r i a t i o n i n t h e g a s p r e s s u r e , g a s c o m p o s i t i o n ( d u e t o e l e c t r o d e m a t e r i a l c o n t a m i - n a t i o n ) , a n d b ank v o l t a g e . T r i g g e r i n g on t h e d l / d t p u l s e w h i c h i s p i c k e d up by a R o g o w s k i c o i l a t t h e b a c k p l a t e was t r i e d b u t p r o v e d t o o u n r e l i a b l e . F i g u r e 7. E l e c t r o - o p t i c a l X - r a y c a m e r a . Power and Trig. Unit Light pipe Photo - multiplier Delay Unit V Rogowski Coil X-rays X-ray Film Holder T Plasma Focus e _/ Scintillator Image Converter J Image Intensifier F i g u r e 8. T r i g g e r i n g a r r a n g e m e n t . C h a p t e r 3 OBSERVATIONS AND RESULTS B e f o r e an i n t e r p r e t a t i o n o f t h e X - r a y p h o t o g r a p h s a r e made, m e a s u r e m e n t s o f t h e m a g n i f i c a t i o n , t h e s t r e a k s p e e d , e t c . , m u s t be d o n e . T h e f o l l o w i n g d e s c r i b e s how s u c h m e a s u r e - m e n t s w e r e c o n d u c t e d . 3.1 Image M a g n i f i c a t i o n The m a g n i f i c a t i o n o f t h e t i m e i n t e g r a t e d p i c t u r e s was o b t a i n e d by m e a s u r i n g t h e o b j e c t - i m a g e d i s t a n c e s f r o m t h e f o c u s t o t h e p i n h o l e a n d f r o m t h e p i n h o l e t o t h e X - r a y f i l m , a s s u m i n g t h a t t h e o b j e c t ( i . e . t h e f o c u s ) i s on t h e c e n t r e a x i s ( z ) d e f i n e d by t h e i n n e r e l e c t r o d e . F o r t h e s t r e a k s h o t t h e o b j e c t - i m a g e d i s t a n c e s were m e a s u r e d t o t h e s c i n t i l l a t o r . A t t h e s c i n t i l l a t o r ' s s u r f a c e two p a r a l l e l w h i t e t h r e a d s w e r e u s e d a s o b j e c t s i n a s e p a r a t e e x p e r i m e n t t o d e t e r m i n e t h e m a g n i f i c a t i o n b e t w e e n t h e s c i n t i l l a t o r a n d t h e f i l m by m e a s u r i n g t h e r e a l d i s t a n c e b e t w e e n t h e t h r e a d s a n d t h a t r e c o r d e d by t h e f i l m . 18 19 3 . 2 S p a c i a l R e s o l u t i o n T h e s p a c i a l r e s o l u t i o n i s l i m i t e d t o 1 mm and i s d e t e r m i n e d by t h e p i n h o l e d i a m e t e r a n d o p t i c a l g e o m e t r y . The s c i n t i l l a t o r t h i c k n e s s (.15 cm) t h o u g h a f f e c t i n g i m a g e f o r m a t i o n d o e s n o t a f f e c t t h e r e s o l u t i o n due t o t h e com- p a r a t i v e l y l a r g e d i s t a n c e (17 cm) b e t w e e n i t and t h e p i n h o l e . T h e t i m e d u r a t i o n o f t h e s t r e a k f r o m 50 t o 200 n s e c . was d e t e r m i n e d by t h e s e t t i n g o f t h e c o n t r o l s on t h e i m a g e c o n v e r t e r u n i t . The l e n g t h o f t h e s t r e a k on t h e f i l m was o b t a i n e d by t a k i n g two p i c t u r e s o f t h e two p a r a l l e l w h i t e t h r e a d s , one a t t h e b e g i n n i n g a n d one a t t h e m i d d l e o f t h e s t r e a k . T h i s c h a n g e i n d i s t a n c e a s r e c o r d e d by t h e p o l a r i o d f i l m , and t h e s t r e a k d u r a t i o n , d e t e r m i n e s t h e s t r e a k s p e e d . 3.3 T e m p o r a l R e s o l u t i o n T h e t e m p o r a l r e s o l u t i o n o f t h e s t r e a k p h o t o g r a p h s i s l i m i t e d by t h e d e c a y t i m e o f t h e p l a s t i c s c i n t i l l a t o r w h i c h i s a p p r o x i m a t e l y 2 n s e c . S i n c e t h e i m a g e i n t e n s i f i e r h a s a v e r y l o n g d e c a y t i m e ( o r a f t e r i m a g e ) i t had t o be p o s i t i o n e d a f t e r t h e s t r e a k u n i t o r i m a g e c o n v e r t e r i n o r d e r t h a t t h e t e m p o r a l r e s o l u t i o n was n o t s a c r i f i c e d . 3.4 X - r a y P h o t o g r a p h s E n l a r g e m e n t s o f t h e r e c o r d e d X - r a y p i c t u r e s w e r e t a k e n s u c h t h a t t h e f i n a l e n l a r g e m e n t s o f t h e t i m e i n t e g r a t e d 20 a n d s t r e a k s h o t s h a v e t h e same m a g n i f i c a t i o n ( o r r a t i o o f i m a g e t o o b j e c t s i z e ) . T h e s e m e a s u r e m e n t s c o m b i n e d w i t h t h e p h o t o g r a p h s t a k e n h a v e g i v e n t h e f o l l o w i n g r e s u l t s and o b s e r v a t i o n s . Two s t r e a k p h o t o g r a p h s w i t h t h e i r c o r r e s p o n d i n g t i m e i n t e g r a t e d X - r a y p h o t o g r a p h s a r e shown i n F i g . 9. From p i c t u r e s a s t h e s e i t was d e t e r m i n e d t h a t a l o n g e m i t t i n g X - r a y r e g i o n o f p l a s m a , e x t e n d i n g o v e r d i s t a n c e s o f o r d e r o f c e n t i m e t e r s w i t h l i f e t i m e s o f 30-60 n s e c . i s p r o d u c e d w h i c h moves a x i a l l y t o w a r d s and away f r o m t h e a n o d e a t v e l o c i t i e s b e t w e e n 2 a n d 6 x 1 0 7 c m / s e c . T h i s X - r a y b u r s t i s f o l l o w e d 10-30 n s e c . l a t t e r by s m a l l i n t e n s e X - r a y e m i t t i n g r e g i o n s e x t e n d i n g o v e r d i s t a n c e s < .5 cm w i t h l i f e t i m e s o f 10-30 n s e c ( s e e F i g . 9 b , c ) . Some o f t h e s e X - r a y e m i t t i n g r e g i o n s e x h i b i t no n o t i c e a b l e a x i a l v e l o c i t y ( s e e F i g u r e 9 f ) . From s p a c i a l c o r r e l a t i o n w i t h t h e c o r r e s p o n d i n g t i m e i n t e g r a t e d p h o t o g r a p h s ( s e e F i g . 9 a , c ) t h e s e s o u r c e s show up as v e r y s m a l l d a r k d o t s on t h e X - r a y f i l m i n c o m p a r i s o n t o t h e s o f t e r a n d d i f f u s e b a c k - g r o u n d p r o d u c e d f r o m r a d i a t i o n e m i t t e d f r o m an e a r l i e r t i m e . T h e d l / d t s i g n a l was d i s p l a y e d on a s c o p e , t h e f o c u s b e i n g i n d i c a t e d by a s u d d e n d i p i n t h e d l / d t w a v e f o r m ( s e e o s c i l l o g r a m F i g u r e 9e - u p p e r t r a c e A ) . T h e s t r e a k d u r a t i o n was a l s o m o n i t o r e d a n d a p p e a r s a s a 'gap' i n t h e l o w e r t r a c e ( B ) , on t h e o s c i l l o g r a m . The r e a l t i m e o f b o t h t r a c e s c o i n c i d e w i t h i n 10 n s e c . o f e a c h o t h e r , e x t r e n o u s (Z = a x i a l d i s t a n c e f r o m t h e e l e c t r o d e s ) F i g u r e 9. X - r a y p h o t o g r a p h s and an o s c i l l o g r a m o f t h e f o c u s i n g e v e n t . 22 t i m e d e l a y i n t h e e l e c t r i c a l c a b l e s arid t h e e q u i p m e n t i s t a k e n i n t o a c c o u n t when c a l c u l a t i n g t h i s f i g u r e . The d i s c h a r g i n g o f t h e c a p a c i t o r s c r e a t e s c o n - s i d e r a b l e e l e c t r i c a l n o i s e . T h i s n o i s e was e l i m i n a t e d by t h e u s e o f f e r r i t e c o r e s on m o s t o f t h e e l e c t r i c a l c a b l e s , a n d by t h e u s e o f a l i g h t p i p e f o r d e t e c t i n g t h e p a s s a g e o f t h e c u r r e n t s h e a t h . To f u r t h e r m i n i m i z e e l e c t r i c a l i n t e r - f e r e n c e t h e t r i g g e r d e l a y u n i t , p h o t o m u l t i p i i e r , a n d s c o p e w e r e p l a c e d i n a s h i e l d e d room. The room has d o u b l e c o p p e r w a l l s and t h e e l e c t r i c a l power t o t h i s room was f i l t e r e d b e f o r e a n d a f t e r e n t e r i n g i t . C h a p t e r 4 DISCUSSION OF RESULTS The o b s e r v e d f e a t u r e s o f t h e f o c u s a g r e e w e l l w i t h t h e r e s u l t s o f o t h e r e x p e r i m e n t e r s who h a v e s t u d i e d t h e f o c u s . The t i m e i n t e g r a t e d p h o t o g r a p h s t a k e n a r e s i m i l a r t o t h o s e o b t a i n e d by M a t h e r [ 1 0 ] , P e a c o c k [ 1 1 ] , a n d B o s t i c k [ 1 3 ] . P e a c o c k [ 1 2 ] has o b s e r v e d t h a t t h e s u s t a i n m e n t t i m e o f t h e p i n c h e d p l a s m a i s n o t more t h a n 50 n s e c . a n d c o r r e s p o n d s d i r e c t l y t o t h e d u r a t i o n o f t h e i n i t i a l b u r s t o f t h e r m a l X - r a y s . He a l s o f o u n d t h a t t h e l o c a l b r e a k - u p o f t h e p i n c h i s o f t e n due t o m = 0 i n s t a b i l i t i e s , a n d t h a t t h e t i m e b e t w e e n f o r m a t i o n o f t h e d e n s e p i n c h a n d i t s b r e a k - u p i s n o t g r e a t e r t h a n 100 n s e c . T h e s e o b s e r v a t i o n s c o r r e s p o n d w e l l t o t h e m e a s u r e d l i f e t i m e s o f t h e h e a t e d ( X - r a y e m i t t i n g ) p l a s m a a s r e c o r d e d by s t r e a k p h o t o g r a p h y i n t h i s e x p e r i m e n t . P e a c o c k [ 1 4 ] has f u r t h e r o b s e r v e d t h a t t h e q u a s i - c y l i n d i r c a l c o m p r e s s i o n p r o d u c e s a ' f o u n t a i n ' o f a h o t a n d d e n s e p l a s m a w h i c h t r a v e l s a x i a l l y away f r o m t h e e l e c t r o d e s w i t h a v e l o c i t y o f a p p r o x i m a t e l y 1 0 7 c m / s e c , w h i c h a g r e e s 23 24 with the measured observed r a d i a l v e l o c i t i e s of 2-6 x 10 7 cm/sec. Bostick [13] observes that the duration of the X-ray emission from small i n d i v i d u a l intense sources i s only 10 to 30 nsec. This agrees with observations i n t h i s epxeriment. But he i n c o r r e c t l y assumes that these small intense sources are t r i g g e r e d i n sequence along the a x i a l r e g i o n . As i s seen from the streak photograph ' f in F i g . 4, t h i s i s c l e a r l y not always the case. B o s t i c k s t a t e s that 10 7 cm/sec. i s the order of magnitude of the v e l o c i t y of the plasma ejected from the a x i a l r e g i o n , which i s in agreement with the,values measured by Peacock and i n t h i s experiment. From a time sequence of shadowgraphs Peacock observes that the dense pinch breaks up due to a m = 0 i n s t a b i l i t y and that the time i n t e r v a l between formation of the dense pinch and onset of the i n s t a b i l i t y , the sustainment time, i s of the order of 10 nsec. He measures f u r t h e r , that the wavelength of the i n s t a b i l i t y , the d i s t a n c e between c o n s t r i c t i o n s , i s ' o f the order of h a l f a centimeter. From time resolved X-ray photographs of the plasma i n v e s t i g a t e d here (see F i g . 4) one measures time i n t e r v a l s between the appearance of the X-ray emission, spreading over the whole pinch channel, and the appearance of the i s o l a t e d p o i n t - l i k e X-ray sources to be of the order of 10 n s e c , which corresponds to Peacock's substainment time. The distance between the 25 i s o l a t e d X - r a y s o u r c e s i s on t h e a v e r a g e h a l f a c e n t i m e r w h i c h c o r r e s p o n d s t o t h e w a v e l e n g t h o f t h e m = 0 i n s t a b i l i t y a s o b s e r v e d by P e a c o c k . T h e s e c o r r e l a t i o n s s t r o n g l y s u g g e s t t h a t t h e a p p e a r a n c e o f t h e i s o l a t e d X - r a y s o u r c e s i s a s s o - c i a t e d w i t h t h e i n s t a b i l i t y . The f e a t u r e s o f t h e f o c u s o b s e r v e d h e r e a n d by P e a c o c k s u g g e s t t h a t t h e f o l l o w i n g s e q u e n c e s o f p h y s i c a l e v e n t s t a k e s p l a c e . T h e s e e v e n t s a r e d e s c r i b e i n f i v e s t a g e s . T h e f i r s t s t a g e i s t h e c o l l a p s e o f t h e c u r r e n t s h e a t h o f t h e e n d o f t h e e l e c t r o d e s , t h e B e f i e l d c o m p r e s s - i n g t h e g a s m i x u t r e r a p i d l y i n w a r d . The s e c o n d s t a g e s t a r t s by t h e p l a s m a b e i n g p i n c h e d , a n d a s a r e s u l t t h e p l a s m a o b t a i n s an a x i a l m o t i o n w i t h v e l o c i t i e s o f t h e o d e r o f 1 0 7 c m / s e c . I n t h e t h i r d s t a g e t h e p l a s m a c o o l s by e x p a n s i o n a n d by r a d i a t i v e l o s s e s . S t a g e f o u r s t a r t s when t h e i n s t a b i l - i t i e s , p a r t i c u l a r l y t h e m = 0 s a u s a g e i n s t a b i l i t y f o r m s , w i t h g r o w t h r a t e s o f t h e o r d e r o f 10 n s e c , a t i m e w h i c h i s c o n s i s t e n t w i t h t h e o b s e r v e d t i m e s b e t w e e n t h e d e c a y o f t h e d i f f u s e p l a s m a a n d t h e c r e a t i o n o f " h o t " s p o t s . As a r e s u l t t h e p l a s m a i s h e a t e d by l o c a l i z e d f i e l d s a n d X - r a y e m i s s i o n o c c u r s a g a i n . S i n c e t h e p i n c h f o r c e o r t h e m a g n e t i c B 0 f i e l d i s s y m m e t r i c and p e r p e n d i c u l a r t o t h e r e g i o n o f p i n c h - i n g , t h e p l a s m a e x p a n d s e q u a l l y away a n d t o w a r d s t h e e l e c t r o d e ( w i t h a p p r o x i m a t e l y t h e same a x i a l v e l c o i t y ) d u r i n g i t s v e r y s h o r t l i f e t i m e , a n d t h u s l o o k s l i k e an a b l o n g ' d o t ' on t h e 26 s t r e a k p h o t o g r a p h . In s t a g e f i v e t h e " h o t " s p o t i n s t a g e f o u r c o n t i n u e s t o e x p a n d w h i l e a t t h e same t i m e r a p i d l y c o o l i n g a n d e m i t t i n g l i t t l e o r no X - r a y s . T h i s s e q u e n c e w o u l d e x p l a i n t h e o b s e r v a t i o n s d u r i n g t h e f o r m a t i o n a n d b r e a k u p o f t h e d e n s e f o c u s s t a g e as o b s e r v e d i n t h i s a n d o t h e r e x p e r i m e n t s . The f o l l o w i n g ( F i g . 10) i s a p i c t o r i a l summary o f t h e p r o p o s e d p r o c e s s . 27 Stage 1 Stage 2 Stage 3 X-rays Stage 4 Stage 5 Stage 1 : gas i s pinched by B & f i e l d Stage 2 : plasma i s pinched, X-ray emission occurs Stage 3 : plasma i s c o o l i n g by expansion and r a d i a t i v e l o s s e s Stage 4 : m=0 i n s t a b i l i t y forms, X-ray emission occurs Stage 5 : Plasma expanding and c o o l i n g F i g u r e 10. S c h e m a t i c f o r o f e v e n t s . p r o p o s e d s e q u e n c e C h a p t e r 5 CONCLUSIONS M e a s u r e m e n t s o f t h e X - r a y e m i s s i o n s f r o m t h e p l a s m a f o c u s by t i m e i n t e g r a t e d a n d s t r e a k p h o t o g r a p h y h a s y i e l d e d i n f o r m a t i o n a b o u t t h e v e l o c i t i e s , l i f e t i m e s a n d g r o w t h o f t h e X - r a y e m i t t i n g r e g i o n s . A d i f f u s e X - r a y e m i t t i n g p l a s m a , e x t e n d i n g s e v e r a l c e n t i m e t e r s i n t h e a x i a l d i r e c t i o n , h a v i n g v e l o c i t i e s o f 2-6 x 1 0 7 c m / s e c . and l i f e t i m e s o f 30-60 n s e c . has b e e n o b s e r v e d . T h i s i s f o l l o w e d 10-30 n s e c . l a t e r by s m a l l i n t e n s e X - r a y s o u r c e s w h i c h h a v e l i t t l e o r no a x i a l v e l o c i t y , a n d l i f e t i m e s o f t h e o r d e r o f 10 n s e c . The d i s t a n c e b e t w e e n t h e s e s h o r t - l i v e d s m a l l X - r a y e m i t t i n g r e g i o n s c o r r e l a t e d t o o b s e r v a t i o n s made by P e a c o c k s t r o n g l y s u g g e s t t h a t t h e s e X - r a y s o u r c e s a r e a s s o c i a t e d w i t h t h e m = 0 i n s t a b i l i t y . A p o s s i b l e model f o r e x p l a i n i n g t h e s e q u e n c e o f X - r a y e v e n t s h a s b e e n p r o p o s e d w h i c h i s c o n s i s t e n t w i t h t h e o b s e r v a t i o n s a n d m e a s u r e m e n t s o b t a i n e d by P e a c o c k and M a t h e r . 28 REFERENCES 1. M a t h e r , J . W . , and W i l l i a m s , A . H . , P h y s i c s o f F l u i d s , 9, 2081 ( 1 9 6 6 ) . 2. M a t h e r , J .W. , N u c l e o n i c s i n a e r o s p a c e - p r o c e e d i n g s o f t he 2nd i n t e r n a t i o n a l sympos ium, Co lumbus , O h i o , U.S .A. , 12-14 J u l y 1967 (New Y o r k : I n s t r u m e n t S o c i e t y o f A m e r i c a 1968 ) , pp. 290 -6 . 3. P e r t , 6 . J . , B r i t . J . App l . P h y s i c s , S e r . 2 V o l . 1, 1487 ( 1 9 6 8 ) . 4 . M a t h e r , J .W. , Plasma P h y s i c s and C o n t r o l 1ed N u c l e a r F u s i o n Re sea r ch V o l . I I , P r o c e e d i n g s o f a C o n f e r e n c e on Plasma P h y s i c s and C o n t r o l l e d N u c l e a r F u s i o n Re sea r ch h e l d by the I .A .E.A. a t Cu lham, 6-10 S e p t . , 1965, pp. 389 -403 . 5. T o e p f e r , A . J . , Smi th D.R., and B e c k e r , E .H . , P h y s i c s o f F l u i d s , V o l . 14, #1 (1971 ) . 6. P e a c o c k , N . J . , et al. 3 5 th European C o n f e r e n c e on C o n - t r o l l e d F u s i o n and Plasma P h y s i c s , G r e n o b l e , F r a n c e , V o l . I I , 2 1 - 25 , A u g . , 1972, p. 66. 7. Downing, J . N . , The P h y s i c s o f F l u i d s , V o l . 18, #8, 1975, pp. 991 -1001 . 8. Morgan, P .D. , et al. 3 3 rd European C o n f e r e n c e on C o n t r o l l e d F u s i o n and P lasma P h y s i c s , N o v o s i b i r s k , U.S .S .R. , 1-7 A u g . , 1968, p. 118. 9. B e r n s t e i n , M . J . , and H a i , F., P h y s i c s L e t t e r s , V o l . 31A #6, 317 ( 1 9 7 0 ) . 29 30 10. M a t h e r , J .W. , The P h y s i c s o f F l u i d s , V o l . 8, #2, 1965, pp. 366 -377. 11 . Long , J .W. , Peacock , N . J . , W i l c o c k , P.D. , T o p i c a l Con - f e r e n c e i n P u l s e d High D e n s i t y P l a s m a s , Los A l amos , New M e x i c o , U.S .A. , S e p t . 19 - 22 , 1967. 12. P e a c o c k , N . J . , Hobby, M.G. , Morgan, P .D. , 4 th European C o n f e r e n c e on P lasma P h y s i c s and C o n t r o l l e d N u c l e a r F u s i o n Re sea rch ( I n t e r n a t i o n a l A tom ic Energy Agency c n - 2 8 / D - 3 ) , M a d i s o n , W i s c o n s i n , U.S .A. , 17-23 June 1971, pp. 1-10.^ 13. B o s t i c k , W.H., N a r d i , V . , P r i o r , W . J . , and R o d r i q u e z - T r e l l e s , F., 5 th European C o n f e r e n c e on C o n t r o l l e d F u s i o n and Plasma P h y s i c s , G r e n o b l e , F r a n c e , V o l . I I 2 1 - 2 5 , A u g u s t , 1972, p. 70. 14. P e a c o c k , N . J . , Wi1 c o c k , P . D . , S p e e r , R . J . , Morgan, P .D. , 3rd European C o n f e r e n c e on Plasma P h y s i c s and C o n t r o l l e d N u c l e a r F u s i o n Re sea rch ( I . A . E . A . c n - 2 4 / G - 4 ) , N o v o s i b i r s k , U.S.S.R., 1-7 A u g u s t , 1968, pp. 1-22.

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