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UBC Theses and Dissertations

Hydrodynamics of laser accelerated foils Josin, Gary M. 1982

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HYDRODYNAMICS OF LASER ACCELERATED FOILS by GARY M. JOSIN A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF SCIENCE Department of Ph y s i c s We accept t h i s major paper as conforming to the r e q u i r e d standard: THE UNIVERSITY OF BRITISH COLUMBIA • September,1982 © Gary M. J o s i n In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 (3/81) i i A B S T R A C T A r u b y l a s e r s y s t e m h a s b e e n c o n s t r u c t e d a n d c h a r a c t e r i z e d t o c h e c k t h e a p p l i c a b i l i t y o f a d i a g n o s t i c m e t h o d w h i c h e x t r a c t s a l l t h e h y d r o d y n a m i c p a r a m e t e r s w i t h o u t a n y k n o w l e d g e o f t h e m i c r o s c o p i c p h y s i c s . O u r d i a g n o s t i c m e t h o d i s n o t y e t e m p l o y a b l e s i n c e s t r o n g s h o c k w a v e s a r e n o t g e n e r a t e d w i t h t h e a v a i l a b l e l a s e r s y s t e m . H o w e v e r t h e e x p e r i m e n t a l r e s u l t s a g r e e w i t h a g e n e r a l h e a t w a v e m o d e l w h i c h i s b a s e d o n a u n i v e r s a l h e a t i n g c h a r a c t e r i s t i c . F u r t h e r m o r e t h e e x p e r i m e n t a l r e s u l t s a r e c o n s i s t e n t w i t h t h e w e l l d o c u m e n t e d M e d u s a h y d r o c o d e . I t i s o f i n t e r e s t t h a t f o r l a s e r p l a s m a s a u n i v e r s a l h e a t i n g c h a r a c t e r i s t i c e x i s t s f r o m w h i c h t h e e x h a u s t t e m p e r a t u r e f o r t h e l a s e r p l a s m a c a n b e p r e d i c t e d f r o m t h e l a s e r i n t e n s i t y a l o n e . i i i T A B L E O F C O N T E N T S A B S T R A C T 1 C H A P T E R I 2 I n t r o d u c t i o n 2 C H A P T E R I I 6 S h o c k W a v e D i a g n o s t i c s O n L a s e r F u s i o n T a r g e t s 7 A ) I n t r o d u c t i o n 7 B ) W e a k S h o c k W a v e s 11 C ) T h e E x p a n s i o n W a v e 14 D ) T h e S h o c k I n T h e T e s t G a s . . . 21 C H A P T E R I I I 24 E x p e r i m e n t a l A p p a r a t u s A n d P r o c e d u r e 24 A ) I n t r o d u c t i o n 24 B ) T h e R u b y L a s e r 24 C ) T h e P i n d i o d e A n d G e n t e c 25 D ) T h e T a r g e t C h a m b e r A n d T a r g e t H o l d e r 27 E ) T h e S t r e a k C a m e r a 30 F ) J i t t e r A n d T i m i n g O f T h e L a s e r S t r e a k C a m e r a . 33 H ) E x p e r i m e n t a l P r o c e d u r e A n d O p t i c a l S e t u p 34 C H A P T E R I V 40 T h e L a s e r P o w e r D e t e r m i n a t i o n A n d E x p e r i m e n t a l O b s e r v a t i o n s 4 0 A ) N e t P o w e r F l u x 40 B ) E x h a u s t V e l o c i t y 4 5 C ) P a r t i c l e V e l o c i t y 4 5 C H A P T E R V 49 A n A n a l y t i c a l M o d e l F o r A b l a t i v e P u s h e r s 52 i v CHAPTER VI 65 The Medusa Hydrocode 65 A) B r i e f D e s c r i p t i o n Of The Physics Of Medusa 65 B) The Time Levels In Medusa 69 C) User S p e c i f i c a t i o n s 70 CHAPTER VII 72 Comparison Of A n a l y t i c Model And Experiments With Medusa 72 A) Comparison 72 B) Future Work 74 REFERENCES 75 V L I S T O F F I G U R E S F i g u r e 1 -1 L a s e r T a r g e t 6 F i g u r e 11 — 1 S o l i d T a r g e t E x p o s e d T o L a s e r L i g h t W i t h T e s t G a s B e h i n d . P r e s s u r e D i s t r i b u t i o n W i t h A n d W i t h o u t P r e h e a t . 1 1 F i g u r e I I - 2 P a r t i c l e V e l o c i t y u 2 B e h i n d S h o c k W a v e A s A F u n c t i o n O f P r e h e a t P r e s s u r e P 15 l F i g u r e I I - 3 S p a c e T i m e D i a g r a m F o r S h o c k A n d E x p a n s i o n W a v e I n F o i l A n d T e s t G a s 16 F i g u r e I I - 4 P r e s s u r e , T e m p e r a t u r e , A n d V e l o c i t y P r o f i l e s A t D i f f e r e n t T i m e s A r e I d e n t i f i e d I n F i g . 3 17 F i g u r e I I - 5 E n t h a l p y C o e f f i c i e n t g 2 A n d N o r m a l i z e d P a r t i c l e V e l o c i t y u 2 A s F u n c t i o n O f T h e V e l o c i t y R a t i o u ^ c A i • • 1 9 F i g u r e I I - 6 C o e f f i c i e n t b A s F u n c t i o n O f V e l o c i t y R a t i o 20 F i g u r e 1 1 1 - 1 O s c i l l o s c o p e T r a c e O f T h e L a s e r P u l s e . H o r i z o n t a l D e f l e c t i o n 2 0 N s e c / d i v . V e r t i c a l D e f l e c t i o n 28 M W / d i v ' 26 F i g u r e I I I - 2 vi O v e r a l l E x p e r i m e n t a l L a y o u t .. 28 F i g u r e I I I - 3 T a r g e t H o l d e r 29 F i g u r e I I I - 4 S c h e m a t i c D i a g r a m Of M o d e l 1D Image C o n v e r t e r Camera Head 31 F i g u r e I I I - 5 O p t i c a l S e t u p F o r L a s e r - p a r a m e t e r F o i l E x p e r i m e n t s . 34 F i g u r e I I I - 6 I d e a l S p a c e - t i m e T r a v e l 37 F i g u r e 111-7 T i m i n g Sequence 38 F i g u r e IV-1 S e t u p F o r F o c a l L e n g t h D e t e r m i n a t i o n And B a c k r e f l e c t i o n D i a g n o s t i c 42 F i g u r e IV-2 R a y - t r a c e To D e t e r m i n e The F o c a l S p o t S i z e 43 F i g u r e IV-3 The H o l e Punched T h r o u g h F o i l By L a s e r 44 F i g u r e IV-4 S t r e a k P h o t o g r a p h Of L a s e r P u l s e B a c k l i g h t i n g A S t a t i o n a r y F o i l , 46". F i g u r e IV-5 S t r e a k P h o t o g r a p h Of P l a sma E x h a u s t V e l o c i t y 47 F i g u r e IV-6 S t r e a k P h o t o g r a p h Of A b l a t i v e l y A c c e l e r a t e d F o i l ... 49 F i g u r e IV-7 E l e c t r o n M i c r o g r a p h S i d e On View Of F o i l 50 v i i Figure IV-8 Electron Micrograph - Inner View Of F o i l 51 Figure V-1 Section Of Shell And Blowoff Plasma 54 Figure V-2 Parameters Of The Ablation Front As Function Of Net Absorbed Intensity W And Exhaust Enthalpy for A Flow With Rocket Type Momentum Balance. The Inverse Bremsstrahlung Relation Is Indicated As A Shaded Wide " l i n e " 62 Figure VI-1 F o i l Divided Into A Mesh Of 6 68 Figure VII-1 Medusa Simulation Up To Peak Compression .... 75 Figure VII-2 Ablation Temperature As A Function Of Laser Intensity And Experimental Values Of Ref. 27 .... 76 v i i i LIST OF TABLES T a b l e I 61 T a b l e I I 63 T a b l e I I I 73 i x A C K N O W L E D G E M E N T S I w o u l d l i k e t o t h a n k B o y e A h l b o r n f o r h i s e n t h u s i a s i u m 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 t h e s i s a n d m o r e i m p o r t a n t l y f o r g i v i n g me s o m e t h i n g m o r e t h a n a t i c k e t f o r t h e j o b m a r k e t . I w o u l d l i k e t o e x p r e s s my g r a t i t u d e f o r t h e v i s i t s t o t h e P l a s m a P h y s i c s d i v i s i o n o f N . R . C . O t t a w a . I w o u l d l i k e t o t h a n k A n d r e w N g f o r m a n y h e l p f u l d i s c u s s i o n s a n d f o r t h e u s e o f t h e t a r g e t c h a m b e r . I w o u l d a l s o l i k e t o t h a n k t w o o t h e r m e m b e r s o f t h e P l a s m a P h y s i c s g r o u p f o r t h e i r h e l p . H u b e r t H o u t m a n f o r h e l p i n g c o n s t r u c t t h e r u b y l a s e r a n d A l l a n C h e u c k f o r r e b u i l d i n g t h e s t r e a k u n i t a n d f o r t r o u b l e s h o o o t i n g m a n y e l e c t r o n i c p r o b l e m s . TO PATTI AND MICHAEL 2 CHAPTER I I n t r o d u c t i o n One of the aims of a modern t e c h n o l o g i c a l s o c i e t y i s to d e v e l o p an i n e x h a u s t i b l e source of a v a i l a b l e energy . A r e c e n t scheme i s to compress s o l i d deuter ium t r i t i u m to very h i g h d e n s i t i e s w i t h a l a s e r p r o i r to i g n i t i o n ( i . e . , l a s e r f u s i o n ) . The deuter ium t r i t i u m p e l l e t i s e n c l o s e d w i t h i n a h i g h e r d e n s i t y s p h e r i c a l s h e l l . T h i s outer s h e l l a c t s l i k e a p i s t o n or pusher when i t i s set in motion by the h i g h p r e s s u r e c r e a t e d by the a b s o r p t i o n of the l a s e r l i g h t and compresses the f u e l to thermonuclear c o n d i t i o n s . To study the hydrodynamics of the l i g h t - m a t t e r i n t e r a c t i o n p l a n a r t a r g e t s are u s u a l l y used for convenience s i n c e in s p h e r i c a l geometry the h i g h d e n s i t i e s make o p t i c a l measurements i m p r a c t i c a l ( F i g . 1 - 1 ) . When a t a r g e t i s exposed to a l a s e r p u l s e , a b s o r p t i o n of the l a s e r energy c r e a t e s a p r e s s u r e d i s t r i b u t i o n which can a c c e l e r a t e p a r t i c l e s to v e l o c i t i e s g r e a t e r than the l o c a l sound speed , thereby c r e a t i n g a shock wave which compresses t a r g e t m a t e r i a l . However, at the l a s e r i n t e n s i t i e s r e q u i r e d to compress the t a r g e t to the d e s i r e d d e n s i t y hot e l e c t r o n s are produced which p e n e t r a t e i n t o the t a r g e t and preheat the m a t e r i a l . The net e f f e c t i s tha t even a h i g h e r p r e s s u r e 3 would be necessary to reach the r e q u i r e d high d e n s i t y . T h e r e f o r e t a r g e t s must be designed to minimize the p r o d u c t i o n and t r a n s p o r t of hot e l e c t r o n s . The pressure e x e r t e d on a t a r g e t may be d e r i v e d from the measurement of the t r a n s i t time of shocks through the t a r g e t . We w i l l show that i f the p a r t i c l e v e l o c i t y behind the shock can be measured,it i s p o s s i b l e to e x t r a c t i n f o r m a t i o n about the d e n s i t y and t h e r e f o r e the equation of s t a t e or the r e l a t i o n s h i p between the pr e s s u r e and d e n s i t y . T h i s equation i s known approximately from t h e o r e t i c a l c a l c u l a t i o n s and t h e r e f o r e measurements which y i e l d the d e n s i t y as a f u n c t i o n of the pressure are of great importance f o r l a s e r f u s i o n s t u d i e s . In t h i s t h e s i s we propose to measure such high p r e s s u r e s and d e n s i t i e s by the measurement of shock waves which are produced when an in t e n s e l a s e r pulse i r r a d i a t e s a planar t a r g e t . The theory of t h i s method i s d e s c r i b e d i n Chapter II and i s based on the understanding of (weak) shocks and expansion waves propagating through s o l i d m a t e r i a l . During the development of t h i s theory we have n o t i c e d t h a t the p r e s s u r e s and d e n s i t i e s of the shock compressed matter can be found by the measurement of the propagation v e l o c i t y of the shock and the unloading v e l o c i t y of the shock compressed matter at the rear of the t a r g e t . Moreover the d i a g n o s t i c method has the advantage of e x t r a c t i n g the p r e s s u r e s and d e n s i t i e s without any knowledge of the m i c r o s c o p i c p h y s i c s . T h i s i n v e s t i g a t i o n a l s o shows 4 t h a t t h e r e s u l t s a r e n o t s i g n i f i c a n t l y c h a n g e d b y t h e p r e s e n c e o f a n y p r e h e a t i n g F o l l o w i n g t h e t h e o r e t i c a l d e v e l o p m e n t o f t h i s m e t h o d we t r y t o v e r i f y t h e d i a g n o s t i c m e t h o d u s i n g a t w o s t a g e r u b y l a s e r . T h i s l a s e r w a s s e l e c t e d f o r i t s a v a i l a b i l i t y . i n a d d i t i o n , t h e r e a r e n o t m a n y r e c e n t m e a s u r e m e n t s a t t h e i n t e r a c t i o n w a v e l e n g t h o f . 6 9 u m w h i c h c o u l d c o m p l e m e n t t h e m e a s u r e m e n t s o f t h e o f t e n s t u d i e d . 5 0 3 u m a n d w a v e l e n g t h s . C h a p t e r I I I d e s c r i b e s t h e d e s i g n o f t h e l a s e r a n d t h e d i a g n o s t i c a p p a r a t u s a n d C h a p t e r I V g i v e s t h e e x p e r i m e n t a l r e s u l t s f o u n d w i t h t h e s t r e a k c a m e r a a n d o t h e r d i a g n o s t i c m e t h o d s . T h e p i c t u r e o f t h e l a s e r p l a s m a p r o c e s s e s t h a t c a n b e d r a w n f r o m t h i s d i a g n o s t i c m e t h o d r e v e a l s a r e l a t i v e l y w e a k p e r t u r b a t i o n e v e n a t o u r h i g h e s t l a s e r i n t e n s i t y , w h e r e s h o c k s i n t h e l a s e r t a r g e t s a r e o n l y m a r g i n a l l y e s t a b l i s h e d . F o r t h a t r e a s o n , t h e p r o p o s e d d i a g n o s t i c m e t h o d d e v e l o p e d i n C h a p t e r I I f o r s t r o n g s h o c k w a v e s i s n o t y e t e m p l o y a b l e . H o w e v e r we a r e a b l e t o v e r i f y t h e e x p e r i m e n t a l r e s u l t s i n a n o t h e r w a y b y t h e u s e o f a n a n a l y t i c a l h e a t w a v e m o d e l , t h a t a l l o w s u s t o p r e d i c t f o r i n s t a n c e t h e e x h a u s t v e l o c i t y w h e n e i t h e r t h e s h o c k v e l o c i t y o r t h e l a s e r i n t e n s i t y h a v e b e e n m e a s u r e d . T h i s m o d e l i s b a s e d o n u n i v e r s a l b r e m s s t r a h l u n g a b s o r p t i o n a n d we f i n d t h a t t h e m e a s u r e m e n t s a n d m o d e l a g r e e q u i t e w e l l . T h i s a b s o r p t i o n m e c h a n i s m i s r e p r e s e n t e d b y a h e a t i n g c u r v e w h i c h g i v e s t h e t e m p e r a t u r e o f t h e e x h a u s t p l a s m a w h i c h o n e c o u l d p u t o n t h e h e a t i n g 5 a n o t h e r p o i n t o n t h e T e m p e r a t u r e v s . I n t e n s i t y ( h e a t i n g c h a r a c t e r i s t i c ) c u r v e f o r l a s e r p l a s m a s . I t i s i n t e r e s t i n g t h a t a u n i v e r s a l h e a t i n g c u r v e e x i s t s f o r l a s e r p l a s m a s f r o m w h i c h t h e e x h a u s t t e m p e r a t u r e f o r t h e l a s e r p l a s m a c a n b e p r e d i c t e d f r o m t h e l a s e r i n t e n s i t y a l o n e . T h e e x p e r i m e n t a l r e s u l t s o f C h a p t e r I V a r e a l s o i n a g r e e m e n t w i t h d e t a i l e d n u m e r i c a l p r e d i c t i o n s o f t h e M e d u s a h y d r o c o d e w h i c h we d e s c r i b e i n C h a p t e r V I . A l l t h e s e r e s u l t s a r e s u m m a r i z e d i n C h a p t e r V I I , w h i c h a l s o g i v e s s o m e s u g g e s t i o n s f o r f u t u r e w o r k . 6 ABSORPTION REGION Figure 1 - 1 Laser Target 7 C h a p t e r I I S h o c k W a v e D i a g n o s t i c s o n L a s e r F u s i o n T a r g e t s  I n t r o d u c t i o n T h e d e p o s i t i o n o f a n i n t e n s e l a s e r p u l s e o n t o a s o l i d t a r g e t c a u s e s v i o l e n t m o t i o n i n t h e f o r w a r d a n d b a c k w a r d d i r e c t i o n s . T h i s i s k n o w n f r o m m a n y p u b l i s h e d s t r e a k p h o t o g r a p h s ( R e f . 1 - 4 ) . I n t h i s c h a p t e r we t r y t o e s t a b l i s h w h a t i n f o r m a t i o n we c a n e x t r a c t a b o u t t h i s p l a s m a f r o m a d e t a i l e d k i n e m a t i c a n a l y s i s o f s u c h s t r e a k p h o t o g r a p h s . O f t e n o n e c a n s e e s h o c k o r e x p a n s i o n w a v e s o n t h e s t r e a k p h o t o s a n d o n e r e a l i z e s t h a t a t h o r o u g h u n d e r s t a n d i n g o f s u c h h y d r o d y n a m i c p h e n o m e n a w i l l b e r e q u i r e d i n o r d e r t o c o m p r e h e n d t h e m o t i o n f u l l y . T h e s e s h o c k w a v e s o c c u r i f v e r y h i g h p r e s s u r e s a r e s u d d e n l y c r e a t e d i n a m e d i u m a n d t h e r e f o r e i t m u s t b e t h e l a s e r p u l s e t h a t i s r e s p o n s i b l e f o r t h e c r e a t i o n o f t h e s e h i g h p r e s s u r e s . S e v e r a l m e t h o d s h a v e b e e n p r o p o s e d t o m e a s u r e t h e a b l a t i o n p r e s s u r e . 1) O n e w a y i s t o u s e a s t a r g e t a b a l l i s t i c p e n d u l u m , a n d m e a s u r e t h e t o t a l m o m e n t u m ( r e f . 4). M V = A P t a W h e r e M = M a s s , V = f i n a l v e l o c i t y , A = A r e a o f l a s e r b e a m , t = d u r a t i o n o f l a s e r p u l s e . D i f f i c u l t i e s a r i s e i f t h e 8 l a s e r p u l s e i s v e r y i n t e n s e , and t h e t a r g e t c o n t i n u e s t o blow o f f p l a s m a a f t e r t h e p u l s e has been t u r n e d o f f . T h e r e f o r e t h i s method t e n d s t o [ o v e r e s t i m a t e t h e a b l a t i o n p r e s s u r e c r e a t e d by t h e l a s e r p u l s e . 2) C h a r g e c o l l e c t o r s have been u s e d f r e q u e n t l y t o measure and c o u n t t h e d e b r i s w h i c h i s r e l e a s e d f r o m t h e t a r g e t . T h e s e c h a r g e c o l l e c t o r s i g n a l s a r e r e c o r d e d a s f u n c t i o n o f t i m e , and by knowing t h e d i s t a n c e o f t h e c h a r g e c o l l e c t o r s f r o m t h e t a r g e t one c a n d e r i v e t h e v e l o c i t y f r o m t h e d e l a y t i m e o f t h e i o n s r e l e a s e d by t h e t a r g e t . I f t h e r e i s o n l y a s i n g l e p u l s e , a b l o w o f f v e l o c i t y c o u l d be d e t e r m i n e d as f u n c t i o n of d i r e c t i o n . From s u c h measurements t h e a b l a t i o n p r e s s u r e has been d e r i v e d . D i f f i c u l t i e s a r i s e i f t h e r e a r e more t h a n one peak on t h e c h a r g e c o l l e c t o r s i g n a l . A l s o t h i s method l a c k s t i m e and s p a c e r e s o l u t i o n and i t e s s e n t i a l l y m e a sures o n l y one q u a n t i t y , namely t h e v e l o c i t y o f ( u n i d e n t i f i e d ) p a r t i c l e s g e n e r a t e d somewhere i n t h e t a r g e t b l o w o f f p l a s m a r e g i o n . 3) A t h i r d method i n v o l v e d t h e d i r e c t o b s e r v a t i o n o f t h e s h ock f r o n t g e n e r a t e d i n t h e t a r g e t m a t e r i a l w i t h t i m e r e s o l v e d p h o t o g r a p h y . From t h e shock f r o n t v e l o c i t y t h e a b l a t i o n p r e s s u r e i s c a l c u l a t e d u s i n g s t a n d a r d s hock t h e o r y . C l e a r l y t h e r e s u l t s w i l l be wrong i f t h e r e i s any s i g n i f i c a n t p r e h e a t i n g , and f u r t h e r m o r e one w o u l d need t r a n s p a r e n t t a r g e t s f o r t h e o p t i c a l o b s e r v a t i o n s . 4) S p e c t r o s c o p i c measurements o f t e m p e r a t u r e _ a n d d e n s i t y i n t h e b l o w o f f r e g i o n c a n be c o m b i n e d t o o b t a i n t h e 9 a b l a t i o n p r e s s u r e . T h e s e m e a s u r e m e n t s a p p e a r t o b e t h e m o s t a c c u r a t e f o r t h e a b l a t i o n p r e s s u r e p r o v i d e d o n e c a n a s c e r t a i n t h a t n a n d T a r e i n d e e d m e a s u r e d a t t h e s a m e p l a c e a n d a t t h e s a m e t i m e . H o w e v e r t h e s e m e a s u r e m e n t s d o n o t r e v e a l t h e p a r a m e t e r s i n t h e r e g i o n a h e a d o f t h e a b l a t i o n f r o n t i t s e l f . 5 ) F i n a l l y t h e a b l a t i o n p r e s s u r e c a n b e i n f e r r e d f r o m m e a s u r e m e n t s o f t h e b u r n v e l o c i t y a n d o n e o t h e r p a r a m e t e r s u c h a s t h e e x h a u s t t e m p e r a t u r e b y u s i n g t h e c o n s e r v a t i o n e q u a t i o n s o f m a s s m o m e n t u m a n d e n e r g y a c r o s s t h e a b l a t i o n f r o n t . I n t h i s t h e s i s , we s h o w a n o t h e r m e t h o d o f e x t r a c t i n g t h e l a s e r p r o d u c e d f l u i d p a r a m e t e r s b y t h e m e a s u r e m e n t o f t h e u n l o a d i n g p r o c e s s a t t h e r e a r o f t h e t a r g e t f o i l s . T h i s d i a g n o s t i c m e t h o d h a s t h e a d v a n t a g e o f e x t r a c t i n g t h e f l u i d p a r a m e t e r s w i t h o u t a n y k n o w l e d g e o f t h e m i c r o s c o p i c p h y s i c s . M o r e o v e r t h e m o d e l s h o w s how t h e e n e r g e t i c e l e c t r o n s w h i c h c h a n g e t h e i n i t i a l s t a t e o f t h e t a r g e t a f f e c t t h e r e s u l t s . I n o r d e r t o u n d e r s t a n d t h e t e c h n i q u e c o n s i d e r a f o i l ( w i t h a t e s t g a s m o u n t e d b e h i n d i t ) w h i c h a s b e e n s t r u c k b y a n i n t e n s e l a s e r b e a m ( F i g . 2 - 3 ) . A s t h e i n t e n s e l a s e r p u l s e i r r a d i a t e s t h e t a r g e t , t h e l a s e r ' s e n e r g y i s a b s o r b e d i n a t h i n l a y e r n e a r t h e t a r g e t ' s s u r f a c e . T h e p l a s m a w h i c h i s p r o d u c e d o n t h e s u r f a c e o f t h e s o l i d t a r g e t r a p i d l y e x p a n d s a w a y f r o m t h e t a r g e t s u r f a c e . T o c o n s e r v e m o m e n t u m a s h o c k i s l a u n c h e d . T h i s s h o c k p a s s e s t h r o u g h t h e f o i l t o t h e r e a r s u r f a c e . A t t h a t i n s t a n t t h e t a r g e t m a t e r i a l h a s a n 10 i n c r e a s e d p r e s s u r e , d e n s i t y , t e m p e r a t u r e a n d a f o r w a r d p a r t i c l e m o t i o n u . T h e p h y s i c a l s i t u a t i o n i s s i m i l a r t o t h a t f o u n d i n a c o n v e n t i o n a l p r e s s u r e d r i v e r s h o c k t u b e , e x c e p t t h a t t h e p r e s s u r e d r i v e r g a s h a s t h e b u l k p a r t i c l e v e l o c i t y u I t i s w e l l k n o w n t h a t t h e k i n e m a t i c m o t i o n o f s u c h a p r e s s u r e d i s t r i b u t i o n i s e n t i r e l y g o v e r n e d b y t h e e x p a n s i o n w a v e r e l a t i o n s a n d t h e f a c t t h a t t h e p r e s s u r e a n d p a r t i c l e v e l o c i t y a r e c o n s t a n t a c r o s s t h e c o n t a c t s u r f a c e , a n d b y t h e j u m p c o n d i t i o n s a c r o s s t h e s h o c k i n t h e t e s t g a s . I f t h e s h o c k v e l o c i t y i n t h e f o i l a n d t e s t g a s a r e m e a s u r e d t h e n we h a v e t h e c a p a b i l i t y o f m e a s u r i n g t h e e q u a t i o n s o f s t a t e o f m a t e r i a l s s u b j e c t e d t o i n t e n s e l a s e r - g e n e r a t e d s h o c k w a v e s . A s p o i n t e d o u t e a r l i e r i n t h e i n t r o d u c t i o n , p r o b l e m s a r i s e i f t h e l a s e r l i g h t p r o d u c e s h o t e l e c t r o n s . T h e s e e l e c t r o n s p e n e t r a t e d e e p l y i n t o t h e t a r g e t a n d t h e a d j a c e n t t e s t g a s , a n d c a n c o n s e q u e n t l y c h a n g e t h e m a t e r i a l ' s i n i t i a l s t a t e b y p r e h e a t i n g . I f t h e s e e l e c t r o n s r a i s e t h e i n i t i a l t e m p e r a t u r e a n d p r e s s u r e a h e a d o f t h e s h o c k f r o n t t h e M a c h n u m b e r d e c r e a s e s a n d c o n s e q u e n t l y t h e s h o c k e d d e n s i t y a n d p a r t i c l e v e l o c i t y a l l b e c o m e f u n c t i o n s o f t h e M a c h n u m b e r ( F i g . I I - 1 ) . 11 C O N T A C T S U R F A C E L A S E R F i g u r e 11-1 S o l i d t a r g e t e x p o s e d t o l a s e r l i g h t w i t h t e s t gas b e h i n d . P r e s s u r e d i s t r i b u t i o n w i t h and w i t h o u t p r e h e a t . 12 I I - B W e a k S h o c k W a v e s T h e p h y s i c a l d e s c r i p t i o n g i v e n i n t h e p r e v i o u s s e c t i o n c a n b e d e s c r i b e d b y t h e c o n s e r v a t i o n e q u a t i o n s f o r m a s s , m o m e n t u m a n d e n e r g y . T h e s u b s c r i p t 1 r e f e r s t o q u a n t i t i e s a h e a d o f t h e d i s c o n t i n u i t y a n d 2 b e h i n d t h e d i s c o n t i n u i t y . P l V l = P 2 V 2 P i + P l V l = P 2 + P 2 V ^ 1 2 1 2 2 v l + h i = I v 2 + h 2 (1 ) ( 2 ) ( 3 ) w h e r e p i s t h e d e n s i t y , p t h e p r e s s u r e , a n d h i s t h e e n t h a l p y w h i c h i s r e l a t e d t o p a n d p b y t h e e q u a t i o n o f s t a t e . h = —2— E g ~ i P (4) t h r o u g h t h e e n t h a l p y c o e f f i c i e n t g ( r e f . 1 8 ) . T h e a b o v e j u m p e q u a t i o n s c a n b e s o l v e d i n g e n e r a l f o r m f o r t h e r a t i o s o f d e n s i t y a n d p r e s s u r e ( r e f . 1 9 ) . P o v. v r u 2 V i = 1 + P 2 — = 1 - F p i (5) ( 6 ) w h e r e F = g 2 - g iM i g 2 + l ^ 2 ( g 2 + l ) ( g 1 - g 2 ) M 1 g 1 I ( g 2 - D ( g 2 - g 1 M ^ ) 2 a n d 2 2 1 - 2 a i ^ i P l 13 I f the enthalpy c o e f f i c i e n t s q1 and g 2 ahead of and behind the shock are equal, the second term under the root of F vanishes, and major s i m p l i f i c a t i o n s r e s u l t . A l s o i f the Mach number M j i s l a r g e , F vanishes. In the absence of b e t t e r knowledge the assumption i s made t h a t : 9 2 = 9 j (7) An estimate of the e r r o r introduced by t h i s assumption i s made at the end of the c a l c u l a t i o n s . Compression r a t i o (5) and shock s t r e n g t h (6) can now be expressed f o r weak shocks as: ^ V j PI v 2 - u 2 g r l + j ^ ( 8 ) 2 p 2__ 2 ^ g 2 - l ^ o r 2oxv\ g - l P1 g 2 + l g 2 + l g 2 + l 1 g 2 + 1 and one can now give the sound v e l o c i t y : p 2 g 2 ( g 2 - l + l 2 , a 2 = g 2 : 1 2 ( 1 0 ) p2 <g,+u2 1 and the p a r t i c l e v e l o c i t y : 2 v L , i 1 x ( 1 1 ) u 2 = (1- ± 2, g7+l M i The- w e l l known strong shock r e l a t i o n s are found from (8) t o (11) by l e t t i n g M1 approach very l a r g e numbers. Fig u r e I I - 2 i n d i c a t e s how the p a r t i c l e v e l o c i t y u 2 depends on the 14 enthalpy c o e f f i c i e n t g 2 and the pressure r a t i o P 2 / p i w n i c n i s approximately equal t o Mx (see eq. 9). II-C The Expansion Wave Figure I I - 3 i l l u s t r a t e s i n a space-time diagram a shock propagating through a f o i l and t e s t gas. The v a r i o u s regions are i d e n t i f i e d by index numbers. Fig u r e 11-4 shows the p r o f i l e s of pressure and temperature and p a r t i c l e v e l o c i t y at time t 3 when the shock has j u s t reached the contact surface and at the time tk when the shock t r a v e l s through the low d e n s i t y t e s t gas. As shown i n the Figure f o r v e l o c i t y ^ t h e r e i s an increase i n the bulk v e l o c i t y u'=ul4-u2 of f o i l m a t e r i a l a f t e r expansion by the r a r e f a c t i o n wave. I t should a l s o be pointed out that the p a r t i c l e v e l o c i t y i s constant across the contact surface ( u 3 = u u ) . The standard r e l a t i o n f o r a r a r e f a c t i o n wave i s given b y : u 2 + a 2 = U | | + - 2 - a 3 ( 1 2 ) g 2 - i g 3 - i where u^, the p a r t i c l e v e l o c i t y i s d i r e c t l y r e l a t e d to the shock v e l o c i t y i n the t e s t gas. The sound speed a 2 can be r e l a t e d t o the i n i t i a l shock v e l o c i t y v x i n the t a r g e t f o i l by using r e l a t i o n (10). The standard r e l a t i o n P p ~ Y " c o n s t a n t holds i n the expansion process. I f one knew the a d i a b a t i c exponent Y , a 3 c o u l d be r e l a t e d to since i s an e x p l i c i t f u n c t i o n of v 4 . However Y and the l o c a l 1 5 16 C O N T A C T f 1 S U R F A C E y T T I M E F i g u r e I I - 3 Space time diagram f o r shock and expansion wave i n f o i l and t e s t gas. -17 F i g u r e I I - 4 Pressure, temperature, and v e l o c i t y p r o f i l e s at d i f f e r e n t times are i d e n t i f i e d i n F i g . 3. 18 enthalpy c o e f f i c i e n t g 3 are not known. Therefore, i f a t e s t gas w i t h a very low d e n s i t y i s mounted behind the t a r g e t f o i l , u 4 would a s y m p t o t i c a l l y approach the f r e e expansion v e l o c i t y as the d e n s i t y P approaches zero. With these c o n d i t i o n s the l a s t term can be neglected and equation (12) Assuming that u u 0 and v 2 can be measured equation (13) can be used to determine the enthalpy c o e f f i c i e n t g 2 . For convenience u 2 i s e l i m i n a t e d by the general shock r e l a t i o n (11) i n order that the r a t i o of the measured values u^Q and v 2 can be c a l c u l a t e d as a f u n c t i o n of g 2 and M 1. This i s i l l u s t r a t e d s c h e m a t i c a l l y i n Figure I I - 5 . I t should be noted that the Mach number has only a minor i n f l u e n c e on the r e s u l t s . I f the r a t i o u / V j i s known, even without the knowledge of the Mach number, the enthalpy c o e f f i c i e n t g 2 can be determined with l i t t l e u n c e r t a i n t y . A l s o shown i n Figure I I - 5 i s the p a r t i c l e v e l o c i t y u 2 as a f u n c t i o n of u /v and Mach number M,. This has been 4 0 1 1 d e r i v e d by the use of equation (11) t o e l i m i n a t e g 2 from equation (13). Again even i f the Mach number M2 i s not known and i f u l + 0/v 1 i s measured the p a r t i c l e v e l o c i t y can be obtained w i t h a t o l e r a b l e u n c e r t a i n t y . For convenience the p a r t i c l e v e l o c i t y u 2 i s w r i t t e n i n a n a l y t i c a l terms and p l o t t e d , as a f u n c t i o n of b ( g 2 , M 1 # u ^ / v j ) as defined by equation (13). Notice i n Figure 6 that b ( g 2 , Mj, u l t 0/v 1 ) i s l i n e a r i n u u 0/v, and can be expressed as: 19 •I • I i I • 1 ' L 0 1 ^ 3 4 F i g u r e I I - 5 Enthalpy c o e f f i c i e n t g 2 and normalized p a r t i c l e v e l o c i t y u ? as f u n c t i o n of the v e l o c i t y r a t i o u 4 0 /vy . 20 F i g u r e II-6 C o e f f i c i e n t b as f u n c t i o n of v e l o c i t y r a t i o , u = 0.1 u l n + 0.35 v. 2 h0 1 21 b = 0 . 9 U 4 0 - 0 . 3 5 (14) v l Hence by e n t e r i n g t h i s r e s u l t i n t o e q u a t i o n (13) we h a v e : u 2 = 0 ' 1 u „ 0 + ° - 3 5 v i ( 1 5 ) Now t h e d e n s i t y w i t h i n t h e s h o c k e d m a t e r i a l c a n be w r i t t e n a s : p i = P i P 2 = 0 . 6 5 - 0 . 1 u 4 0 ( 1 6 ) v i The p r e s s u r e i n t h e s h o c k e d f o i l may now be w r i t t e n a s : 2 P v 2 g -1 1 1 2 p 2 = — ^ - P i g 2 + i g 2 + i where t h e p r e h e a t t e r m may be n e g l e c t e d f o r Mach numbers e x c e e d i n g 2 . I n p r i n c i p l e , i f t h e e n t h a l p y c o e f f i c i e n t g was known, t h e Mach number and t h e r e f o r e t h e p r e h e a t p r e s s u r e P c o u l d be d e t e r m i n e d . However, f r o m a c a r e f u l i n s p e c t i o n o f F i g u r e I I - 5 , we f i n d t h a t t h e p r e h e a t p r e s s u r e , P 1 i s q u i t e i n a c c u r a t e s i n c e M* i s n o t a s e n s i t i v e p a r a m e t e r , I I - D The Shock i n t h e T e s t Gas At t h i s s t a g e we a r e a l r e a d y i n t h e p o s i t i o n t o d e t e r m i n e t h e f l u i d p a r a m e t e r s i f o n l y v x and u 4 0 a r e known; i t r e m a i n s t o be shown how u ^ g i t s e l f c a n be f o u n d . F o r t h i s r e a s o n we l o o k a t t h e d e t a i l s o f t h e p r o p a g a t i o n o f t h e s h o c k i n t h e t e s t g a s . A t h i g h e r t e s t gas d e n s i t i e s a w e l l d e v e l o p e d shock wave i s f o r m e d where t h e p a r t i c l e v e l o c i t y i s r e l a t e d t o t h e s h o c k v e l o c i t y v ^ by t h e s t a n d a r d 22 r e l a t i o n : I t may be p o s s i b l e to e x t r a c t the compression r a t i o P l+/p 0from streak photos, i f the contact surface at the r e f l e c t e d shock i s r e s o l v a b l e . In t h i s case from Figure D.-3 we have ll = ^° so that u^ can be w r i t t e n as: This r e l a t i o n i s v a l i d i r r e s p e c t i v e of any preheating of the t e s t gas. On the other hand i f such a measurement i s not p o s s i b l e one can s t i l l estimate that the shock should have a Mach number of at l e a s t M 4 = 4. I f the t e s t gas d e n s i t y i s low, the strong shock approximation i s reasonably accurate f o r the p a r t i c l e v e l o c i t y i n the t e s t gas. The strong shock r e l a t i o n i s given by: Moreover the c o n d i t i o n M4=4 i s found by assuming the t e s t gas i s preheated to the temperature T 2 obtained behind shock i n the f o i l . 23 T h i s c o n c l u d e s t h e k i n e m a t i c a n a l y s i s o f t h e h y d r o d y n a m i c f l o w . I n t h e n e x t f e w c h a p t e r s s u b s e q u e n t e x p e r i m e n t s a r e p r e s e n t e d w h i c h s h o w t h e a p p l i c a b i l i t y o f o u r m o d e l . 24 C H A P T E R I I I  E x p e r i m e n t a l A p p a r a t u s a n d P r o c e d u r e A ) I n t r o d u c t i o n A s y s t e m c o n s i s t i n g o f a 100MW r u b y l a s e r , a t a r g e t c h a m b e r , a t a r g e t h o l d e r , a n d a n o p t i c a l s e t u p h a s b e e n u s e d t o a t t e m p t t o e x p e r i m e n t a l l y v e r i f y t h e m o d e l o u t l i n e d i n t h e l a s t c h a p t e r . F i g u r e I I I - 2 s h o w s t h e o v e r a l l e x p e r i m e n t a l l a y o u t a n d F i g u r e I I I - 5 s h o w s t h e o p t i c a l s e t u p . B ) T h e R u b y L a s e r T h e r u b y l a s e r s e r v e s b o t h a s a s o u r c e o f h i g h i n t e n s i t y m o n o c h r o m a t i c l i g h t ( 4 0 n s e c h a l f w i d t h , 100MW p o w e r ) a n d f o r t h e s i d e o n b a c k l i g h t i n g i l l u m i n a t i o n o f f o i l t a r g e t s . T h e l a s e r s y s t e m i s s i m i l a r t o t h a t u s e d b y A l b a c h ( r e f . 7 ) a n d G o d f r e y ( r e f . 8 ) . F o r d e t a i l s o n t h e c o n s t r u c t i o n o f t h e s y s t e m r e f e r t o C h u r c h l a n d ( r e f . 9 ) . A b r i e f o p e r a t i o n a l d e s c r i p t i o n o f t h e o p t i c a l l y p u m p e d r u b y s y s t e m , a l s o d e s c r i b e d b y H i l k o ( r e f . 1 0 ) , i s g i v e n i n t h e n e x t p a r a g r a p h . F o u r X e n o n g a s f l a s h l a m p s s u r r o u n d a r u b y r o d a l l e n c l o s e d i n a p o l i s h e d m u l t i - e l l i p t i c a l r e f l e c t o r . T h e f l a s h l a m p s a r e u s e d t o c r e a t e a p o p u l a t i o n i n v e r s i o n i n t h e 25 chromium i m p u r i t y i o n s o f t h e r u b y c r y s t a l . A 40ns, 100 MW l a s e r p u l s e i s p r o d u c e d by Q - s w i t c h i n g . The Q - s w i t c h o r o p t i c a l s h u t t e r i s a P o c k e l s c e l l i n c o m b i n a t i o n w i t h a c a l c i t e p o l a r i z e r . The ru b y r o d i s pumped w i t h f l a s h l a m p s and a p o p u l a t i o n i n v e r s i o n b u i l d s up. The P o c k e l s c e l l i s a b i r i f r e n g e n t KDP c r y s t a l . When t h e c r y s t a l h as 8 8 0 0 V i a p p l i e d between two f a c e s , b i r i f r e n g e n c e i s i n d u c e d i n t h e c r y s t a l . When r a d i a t i o n p a s s e s t h r o u g h t h e c r y s t a l i t becomes c i r c u l a r l y p o l a r i z e d . Upon r e f l e c t i o n f r o m t h e back m i r r o r t h e r a d i a t i o n a g a i n p a s s e s t h r o u g h t h e KDP c r y s t a l and becomes p l a n e p o l a r i z e d 90° t o t h e o r i g i n a l p o l a r i z a t i o n . T h i s r a d i a t i o n i s t h e n r e j e c t e d by t h e p o l a r i z e r . When t h e p o p u l a t i o n i n v e r s i o n w i t h i n t h e c r y s t a l i s a maximum t h e P o c k e l s c e l l i s s w i t c h e d o f f and t h e p l a n e of p o l a r i z a t i o n of t h e r a d i a t i o n i s u n a f f e c t e d . T h i s a l l o w s a b u i l d u p o f l a s e r l i g h t w i t h i n t h e c a v i t y v i a f e e d b a c k w i t h i n t h e ru b y c r y s t a l . S i n c e t h e r e a r m i r r o r i s 50% r e f l e c t i n g t h e l i g h t l e a v e s t h e c a v i t y and i s a m p l i f i e d . C) The P i n d i o d e and G e n t e c To c h a r a c t e r i z e t h e t e m p o r a l shape and m o n i t o r t h e r e l a t i v e l a s e r power o u t p u t f r o m s h o t t o s h o t a H e w l e t t P a c k a r d 5082-4200 p i n d i o d e d e t e c t s t h e l a s e r l i g h t w h i c h r e f l e c t s f r o m t h e t a r g e t chamber window. An o s c i l l o s c o p e t r a c e r e c o r d s t h e l i g h t s i g n s . A t y p i c a l p u l s e i s shown i n F i g u r e 111-1 . T h i s s i g n a l shows t h a t t h e l a s e r s y s t e m p r o d u c e s a 40ns 26 F i g u r e III-1 O s c i l l o s c o p e t r a c e of the l a s e r p u l s e H o r i z o n t a l d e f l e c t i o n 20nsec/div. v e r t i c a l d e f l e c t i o n 28 MW/div. 27 f u l l w i d t h h a l f maximum (FWHM) l a s e r p u l s e . The o u t p u t e n e r g y o f t h e s y s t e m was d e t e c t e d w i t h an e n e r g y m e t e r . The l a s e r s y s t e m i s c a p a b l e o f p r o d u c i n g 15J of e n e r g y . However i t was d i s c o v e r e d t h a t t o m a i n t a i n t h e o p t i c a l components w i t h o u t damage, t h e s y s t e m was o p e r a t e d t o a maximum l e v e l o f o n l y 4 . 0 J . The l a s e r s y s t e m had e x c e l l e n t r e l i a b i l i t y i f t h e r u b y r o d s were a l l o w e d t o c o o l f r o m s h o t t o s h o t . T y p i c a l l y t h e t i m e t a k e n between s h o t s was f i f t e e n m i n u t e s . D) The T a r g e t Chamber and T a r g e t H o l d e r The t a r g e t chamber, as shown i n F i g u r e I I I - 2 , was c o n s t r u c t e d t o e n s u r e t h a t breakdown would n o t o c c u r i n t h e gas w h i c h s u r r o u n d s t h e s o l i d t a r g e t . At t h e power i n t e n s i t i e s u s e d i n t h e s e e x p e r i m e n t s , a h i g h p r e s s u r e gas wo u l d be v e r y s t r o n g l y i o n i z e d and t h e r e s u l t a n t p l a s m a would a b s o r b t h e l a s e r l i g h t b e f o r e i t r e a c h e d t h e t a r g e t . The vacuum chamber was e v a c u a t e d t o 300 m i l l i t o r r t o m a i n t a i n a u n i f o r m b a c k g r o u n d p r e s s u r e . T h i s p r e s s u r e m a i n t a i n s t h e same i n i t i a l c o n d i t i o n s f o r t h e e x p a n s i o n o f t h e f o i l t a r g e t . I n s i d e t h e t a r g e t chamber i s a t a r g e t h o l d e r . The t a r g e t h o l d e r must s a t i s f y s e v e r a l c o n d i t i o n s ( F i g u r e I I I - 2 ) and t h e d i f f i c u l t y i n d e s i g n i n g an a p p r o p r i a t e h o l d e r i s f i r s t l y t h a t one wants t o l o a d a s e t o f t a r g e t s f o r s e v e r a l s h o t s s i n c e r e p l a c i n g a t a r g e t between s h o t s i s t i m e c o n s u m i n g , and s e c o n d l y t h e t a r g e t s must r e m a i n i n t h e same 28 STREAK C A M E R A F i g u r e I I I - 2 O v e r a l l Experimental Layout 29 F i g u r e 111-3 Target Holder 30 f o c a l plane to ensure the same f l u x on t a r g e t . T h i r d l y the holder had t o be designed to a l l o w the imaging of the back surface and the si d e of the f o i l s i m u l t a neously. F o u r t h l y , two of these tar g e t h o l d e r s used together w i l l a l l o w f o r double f o i l experiments. As shown s c h e m a t i c a l l y the f i n a l design s a t i s f i e s a l l the above c r i t e r i a . F o i l t a r g e t s 50cm lon g , 50cm wide and 37.5 microns t h i c k were wound on s p r i n g loaded spools (Figure I I I - 3 ) . F i g u r e I I I - 3 shows how the long s t r i p s of f o i l a llow f o r m u l t i p l e shots. By t u r n i n g the spools the f o i l winds from one spool to the other, p l a c i n g an unpunctured part of the f o i l i n the aim of the main beam. The spools are s p r i n g loaded t o keep a constant t e n s i o n on the f o i l s t r i p so that i t remains, i n the same f o c a l plane. E) The Streak Camera A TRW streak camera ( r e f . 11) which makes space-time p l o t s has been used to observe the plasma. The general operation i s best i l l u s t r a t e d w i t h the a i d of Figure I I I - 4 . When l i g h t i s imaged by the o b j e c t i v e l e n s onto the photocathode of the image converter tube e l e c t r o n s are emitted from a p h o t o s e n s i t i v e m a t e r i a l w i t h i n the tube. The number of e l e c t r o n s emitted from a p o i n t on the m a t e r i a l i s p r o p o r t i o n a l to the number of photons at that p o s i t i o n . These e l e c t r o n s are a c c e l e r a t e d by a r a d i a l e l e c t r i c f i e l d (I5kv) a p p l i e d between the anode and the cathode. These e l e c t r o n s are swept v e r t i c a l l y by a ramp v o l t a g e a p p l i e d t o d e f l e c t i o n p l a t e s . The r a t e at which the e l e c t r o n s are swept 31 Deflection Plates Photoanode F i g u r e 111-4 Schematic diagram of Model ID Image Converter Camera Head 32 is d i r e c t l y proportional to the slope of the ramp. When the electrons s t r i k e the photocathode, an i n t e n s i f i e d image i s created on the anode and thi s image i s relayed by the lens on the right into the fi l m plane and thereby a space-time image i s traced. A 10Kv voltage i s applied to the .grating g r i d to allow electrons to flow only when the grid i s properly pulsed. The exposure time was set at 200ns duration. The streak times used in t h i s study were set at 200ns and 100ns. Streaks shorter than 100ns were impractical since the ramp voltages were not synchronized in time. This i s a consequence of the impedance mismatch of the defle c t i o n plate c i r c u i t r y . Several attempts were made to match the impedance of the ramps but synchronization was limi t e d to approximately 50ns. The s p a t i a l resolution of the photoanode which i s 10 lines/mm or 100 microns fixed the temporal resolution ( i . e . , s l i t width). Since there i s a 4:1 reduction of the object size at the f i l m plane, the s l i t width was set at 400um for maximum s p a t i a l resolution ( i . e . , I00um). To f i r s t order the temporal resolution i s the time i t takes the s l i t to move i t s own width. The streak length i s 5cm and therefore the writing rate i s : d 5 cm 7 v = — = = 2.5 x 10 cm/sec t 20 ns Therefore the temporal resolution i s given by: d _ ioo cm v ~ T ~ c l n 7 / = .4 nsec v 2.5 x 10 cm/sec 33 One very bad feature of the available camera i s the property that the width of the image depends on the intensity of the l i g h t . If the intensity changes the width of the inte n s i t y changes too. When the in t e n s i t y of the backlighting beam was adjusted to ensure uniform streaks, streak duration was only 5ns, making a v e l o c i t y measurement impossible. Therefore the intensity of the backlighting beam had to be c a r e f u l l y adjusted in intensity to ensure as uniform a streak as possible. This pinching could be an ion focusing e f f e c t due to gas leakage in the tube ( i . e . , an old tube). F) J i t t e r and Timing of the Laser Streak Camera A l l Q-switched lasers have j i t t e r . To measure the ruby laser j i t t e r several streaks were made of the laser pulse with the camera. Since the j i t t e r of the laser system i s a random process the root-mean square of the a r r i v a l time of the laser pulse has been taken. The laser j i t t e r was found to be 40ns which corresponds to the FWHM of the laser pulse. It should be pointed out that t h i s can be considered j i t t e r in the camera and not the laser system since the experimental event i s synchronized in time ( i . e . , with respect to the backlighting beam and the main pulse). Since streak durations are 200ns in duration each shot in theory should record an event. (Refer to F i g . III-7 ). 34 Figure III-5 Optical setup experiments for laser-parameter f o i l 35 H) E x p e r i m e n t a l P r o c e d u r e and O p t i c a l Setup In o r d e r t o check the v a l i d i t y of the model p r e s e n t e d i n Chapter I I , the TRW s t r e a k camera ( r e f . 12) has been u t i l i z e d t o r e c o r d d i f f e r e n t l a s e r plasma e v e n t s . F i g u r e 111-3 shows the parameters which may p o s s i b l y be measured. The two parameters which must be measured t o v a l i d a t e the model a r e u^g and v1. However a l l p arameters a r e of i n t e r e s t and F i g u r e 11-3 shows a l l t h e s e p a r a m e t e r s . F i g u r e 111-5 shows the o p t i c a l s e t u p . The l e n s L 1 w i t h f number of 2.5 and f o c a l l e n g t h of 10cm f o c u s s e s the beam onto the t a r g e t . A beam s p l i t t e r has been i n s e r t e d i n t o the beam p a t h b e h i n d the o s c i l l a t o r c a v i t y a t 45° t o the main beam. T h i s s p l i t o f f beam, c a l l e d t h e b a c k l i g h t i n g beam, i s s p a t i a l l y f i l t e r e d (not shown i n F i g u r e I I I - 5 ) by a p i n h o l e and then by . r e f l e c t i o n from two m i r r o r s p a s s e s t h e t a r g e t 90° t o the main beam. A f/2.5 l e n s forms an i n t e r m e d i a t e image onto t h e camera s l i t . T h i s 20X m a g n i f i e d image i s then imaged by the s t r e a k camera o p t i c s ( F i g u r e I I I - 4 ) . T h i s s e t u p a l l o w s f o r 4 d i f f e r e n t t y p e s of s t r e a k photos t o be taken."The f i r s t t y p e of s t r e a k photo i s o b t a i n e d by b l o c k i n g o f f the main beam. T h i s produces a s t r e a k of the b a c k l i g h t i n g p u l s e of a s t a t i o n a r y f o i l ( F i g u r e I V - 5 ) . For t h e second type of s t r e a k photo b o t h the main and b a c k l i g h t i n g p u l s e a r e p r e s e n t so t h a t a shadowgram of a l a s e r produced plasma i s produced ( F i g u r e I V - 6 ) . These shadowgrams depend on the bending of the ruby l i g h t and r e c o r d the time h i s t o r y of the event when the main beam i s 36 focussed and f i r e d on t a r g e t . A 6943 Angstrom f i l t e r was placed i n f r o n t of the streak camera's o b j e c t i v e lens to allow only the ruby l i g h t to enter the camera. For the t h i r d type of streak photographs, the b e a m s p l i t t e r , the b a c k l i g h t i n g beam and the ruby f i l t e r were removed. So that one obtains records of the plasma expansion, example F i g . IV-5. There i s however a chance that some of the s c a t t e r e d l i g h t from the main beam can reach the camera. To d i f f e r e n t i a t e between t h i s s c a t t e r e d l a s e r l i g h t and the plasma l i g h t a f o u r t h mode of operation was used. In t h i s case the b a c k l i g h t i n g beam was turned o f f and the 6943 Angstrom i n t e r f e r e n c e f i l t e r was i n s e r t e d , so that only the s c a t t e r e d ruby l i g h t c ould be recorded. This . a l lows a comparison of streak photos wi t h and without the f i l t e r so that the plasma l i g h t can be d i s c r i m i n a t e d a g a i n s t the ruby l i g h t . In order to measure the a b l a t i o n v e l o c i t y v_ a s o l i d piece of aluminum was i r r a d i a t e d . By knowing the burn depth and the pulse length an upper l i m i t to the a b l a t i o n v e l o c i t y can be c a l c u l a t e d . However, we found that the v e l o c i t y v a i s i n v a l i d since the t a r g e t m a t e r i a l i s i o n i z e d and i t continues to emit plasma m a t e r i a l a f t e r the l a s e r p u l s e ] i s o f f . To monitor the amount of i n c i d e n t l a s e r energy which r e f l e c t s from the t a r g e t surface a beam s p l i t t e r vas placed i n f r o n t of the focu s s i n g o p t i c s . F i g u r e IV-1 shows how the b a c k r e f l e c t e d l i g h t has been monitored with a g e n t e c - o s c i l l o s c o p e combination. F i g u r e I I I - 6 I d e a l space-time t r a v e l Camera Shutter Open F i g u r e I I1 -7 T i m i n g Sequence 39 F i g u r e I I I - 6 shows an i d e a l side-on streak photo of an expanded plasma with a b a c k l i g h t i n g pulse ( h o r i z o n t a l dotted l i n e s ) . The s o l i d l i n e l a b e l l e d v b i n d i c a t e s the leading edge of the exhaust plasma. By measuring the slope one can f i n d the exhaust v e l o c i t y , v b . The shock wave passing through the f o i l cannot be observed d i r e c t l y but one can see plasma emerging on the rear of the t a r g e t a f t e r the breakthrough at time A t , so t h a t the approximate path of the shock may be sketched (broken l i n e ) and the v e l o c i t y v } obtained from the slope. The slope u 4 0 of the plasma f r o n t on the rear of the t a r g e t g i v e s the unloading v e l o c i t y of the a c c e l e r a t e d f o i l m a t e r i a l . F i g u r e I I I - 7 shows the t i m i n g sequence f o r the a r r i v a l time of the main pulse and b a c k l i g h t i n g pulse w i t h respect to the opening of the camera s h u t t e r . 40 C H A P T E R I V T h e L a s e r P o w e r D e t e r m i n a t i o n a n d E x p e r i m e n t a l O b s e r v a t i o n s T h i s c h a p t e r p r e s e n t s t h e l a s e r p o w e r d e t e r m i n a t i o n a n d t h e e x p e r i m e n t a l r e s u l t s o b t a i n e d w i t h t h e m e t h o d s w h i c h w e r e o u t l i n e d i n t h e l a s t c h a p t e r . A s s t a t e d i n t h e i n t r o d u c t i o n t h e m a i n m o t i v a t i o n f o r t h i s s t u d y h a s b e e n t o e x t r a c t a l l t h e l a s e r p r o d u c e d f l u i d p a r a m e t e r s w i t h o u t a n y k n o w l e d g e o f t h e m i c r o s c o p i c p h y s i c s f r o m t h e m e a s u r e m e n t o f t h e s h o c k t r a n s i t t i m e t h r o u g h t h e f o i l a n d b y t h e m e a s u r e m e n t o f t h e v e l o c i t y o f t h e s h o c k c o m p r e s s e d m a t e r i a l u n l o a d i n g i n t o a t e s t g a s . I t s h o u l d b e p o i n t e d o u t t h a t t h e i n h e r e n t d i f f i c u l t y i n t h e s e e x p e r i m e n t s a r e t h e e x t r e m e l y s m a l l d i s t a n c e a n d t i m e s c a l e s . T h e f o c a l s p o t s i z e i s 100 m i c r o n s w h i l e t h e p h y s i c a l e v e n t s a r e o c c u r r i n g o n t i m e s c a l e s o f 1 0 " 9 s e c o n d s . T h e q u a n t i t i e s w h i c h h a v e b e e n m e a s u r e d a r e t h e n e t a b s o r b e d p o w e r W , t h e e x h a u s t v e l o c i t y a n d t h e p a r t i c l e v e l o c i t y o f t h e a c c e l e r a t e d f o i l m a t e r i a l . A ) N e t P o w e r F l u x T h e o u t p u t b e a m o f t h e r u b y l a s e r s y s t e m w a s f o c u s s e d w i t h a 1 0 c m f o c a l l e n g t h l e n s o n t o t h e s u r f a c e o f s o l i d a l u m i n u m t a r g e t s . T h e n e t a b s o r b e d i n t e n s i t y i s c a l c u l a t e d b y t h e m e a s u r e m e n t o f t h e a b s o r b e d e n e r g y , t h e FWHM p u l s e 41 w i d t h , beam d i v e r g e n c e and t h e f o c a l l e n g t h of t h e l e n s . The f o c a l l e n g t h of t h e l e n s was measured by s h i n i n g a He -Ne l a s e r beam t h r o u g h a p l a n o - c o n v e x l e n s a d i s t a n c e x f rom t h e c e n t r e . The d e v i a t i o n d of t h e l i g h t r a y s was t h e n measured a d i s t a n c e s f rom t h e l e n s . F i g u r e I V - 2 shows t h e e x p e r i m e n t a l a r r a n g e m e n t and f rom t h e geometry t h e f o c a l l e n g t h f i s g i v e n b y : S e v e r a l measurements were t a k e n and the r o o t mean s q u a r e c a l c u l a t e d . The f o c a l l e n g t h f e q u a l s 10 cm ± . 1 c m . T h i s r e s u l t a g r e e s w i t h t h e m a n u f a c t u r e r ' s s p e c i f i c a t i o n . The beam d i v e r g e n c e i s found by t a k i n g a near and f a r f i e l d burn p a t t e r n . By knowing t h e d i s t a n c e between t h e two burn p a t t e r n s and t h e i n c r e a s e i n a r e a of t h e burn p a t t e r n t h e beam d i v e r g e n c e was f o u n d t o be a m i l l i r a d i a n . F i g u r e I V - 2 shows f o c a l s p o t s i z e as a f u n c t i o n of the f o c a l l e n g t h f and t h e beam d i v e r g e n c e a . From the g e o m e t r y , t h e f o c a l s p o t s i z e i s c a l c u l a t e d t o b e : As p r e s e n t e d i n C h a p t e r I I I t h e ruby l a s e r o u t p u t e n e r g y i s 4 . 0 J , however , not a l l of t h e i n c i d e n t e n e r g y on t a r g e t i s a b s o r b e d . F i g u r e I V - 1 shows how t h e b a c k r e f l e c t e d l i g h t has been m o n i t o r e d . These measurements show t h a t of t h e 4 . 0 J i n c i d e n t on t a r g e t 50% of t h e e n e r g y i s a b s o r b e d , w h i l e t h e o t h e r 50% i s r e f l e c t e d and t r a n s m i t t e d . f = X S f s = f a =(10 cm)(10~ 3)= 100 um 42 F i g u r e IV-1 Setup f o r f o c a l l e n g t h d e t e r m i n a t i o n and b a c k r e f l e c t i o n d i a g n o s t i c . Beam I i s used to determine the t r a n s m i t t e d i n t e n s i t y and Beam II i s used to determine the r e f l e c t e d i n t e n s i t y . F i g u r e IV - 2 Ray-trace to determine the f o c a l spot s i z e Figure IV-3 The hole punched through f o i l by laser 45 Therefore the net in t e n s i t y on the target i s : W = nJL = (.50) (4.0 ± 10%)  • t * r 2 ( 4 0 x l 0 ~ 9 ) ( n 112 x 10~" ± 10%) 2 2 W = 5 .0 x 10 1 1 _W_ ± 30% 2 cm where r i s the focal spot radius. Figure IV-3.shows an electron micrograph of a hole in aluminum produced by the ruby system. Notice the agreement of the focal spot size with the above c a l c u l a t i o n . B) Exhaust Velocity A second quantity which was measured and i s of interest i s the expansion v e l o c i t y of the f o i l material. This v e l o c i t y can be attained from the streak photos recorded with the TRW streak unit. Figure IV-4 shows a t.ypical streak of a stationary f o i l before the removal of the backlighting beam, p e l l i c l e beam s p l i t t e r , and the 6943 Angstrom interference f i l t e r . The average expansion v e l o c i t y calculated by taking the slope of several streak photographs i s 9 x I0 6cm/sec.± 10%. Figure IV-4 shows a t y p i c a l streak from the photos which were analyzed. These streak photos are reproduceable from shot to shot. -dotted area shows the streak of the backlighting pulse 46 a F i g u r e IV-4 Streak photograph of l a s e r p u l s e b a c k l i g h t i n g a s t a t i o n a r y f o i l hatched area shows s c a t t e r e d ruby l i g h t slope of the dotted l i n e i n d i c a t e s l e a d i n g edge of the exhaust v e l o c i t y 47 a Figure I V - 5 Streak photograph of plasma exhaust v e l o c i t y (see page 47a) 48 C ) P a r t i c l e V e l o c i t y F i g u r e I V - 6 s h o w s a p h o t o g r a p h o f t h e s p a c e - t i m e h i s t o r y o f a n a b l a t i v e l y a c c e l e r a t e d f o i l . T h i s s t r e a k p h o t o g r a p h h a s b e e n t a k e n b y t h e i n s e r t i o n o f a b e a m s p l i t t e r i n t o t h e o s c i l l a t o r c a v i t y a s p r e v i o u s l y d i s c u s s e d i n t h e l a s t c h a p t e r . T h e p h o t o s a r e r e p r o d u c e a b l e f r o m s h o t t o s h o t a n d f r o m s e v e r a l p h o t o g r a p h s a n a v e r a g e v a l u e f o r t h e p a r t i c l e v e l o c i t y h a s b e e n f o u n d t o b e 2 . 4 7 x I 0 5 c m / s e c . ± 10%. T h i s g i v e s u s a s h o c k v e l o c i t y w h i c h c o r r e s p o n d s t o t h e s p e e d o f s o u n d i n a l u m i n u m . F i g u r e I V - 7 a n d F i g u r e I V - 8 s h o w s c a n n i n g e l e c t r o n m i c r o g r a p h p h o t o s o f a n i r r a d i a t e d t a r g e t . N o t i c e t h e l i p o f F i g u r e I V - 7 . T h e s e p h o t o s s h o w e v i d e n c e t h a t a f o r c e h a s b e e n c r e a t e d b y t h e a b s o r p t i o n o f l a s e r e n e r g y . I n o r d e r t o e x t r a c t a l l t h e f l u i d p a r a m e t e r s f r o m t h e e x p e r i m e n t a l r e s u l t s g i v e n i n t h i s c h a p t e r , a n a d d i t i o n a l s e t o f e q u a t i o n s m u s t b e a d d e d t o t h e s h o c k r e l a t i o n s i n t r o d u c e d i n C h a p t e r I I . -slope of the dashed l i n e indicates the f o i l v e l o c i t y F i g u r e IV-6 Streak photograph of a b l a t i v e l y a c c e l e r a t e d f o i l 49b 9 laser -superposition of the three from pages 46a,47a,and49a streak photographs F i g u r e IV-7 E l e c t r o n micrograph s i d e on view of f o i l F i g u r e IV-8 E l e c t r o n micrograph - inner view of f o i l 52 C H A P T E R V A n A n a l y t i c a l M o d e l f o r A b l a t i v e P u s h e r s I n t h i s c h a p t e r a n a n a l y t i c a l m o d e l f o r a s u b s o n i c h e a t w a v e w h i c h i s p r e c e d e d b y a s h o c k w a v e i s d e v e l o p e d f r o m a m o r e g e n e r a l h e a t w a v e m o d e l w h i c h c o n s i d e r s a l l p o s s i b l e p h y s i c a l m o d e s ( r e f . 1 4 ) . T h e m o d e f o r l a s e r - s o l i d t a r g e t i n t e r a c t i o n s h a s b e e n c l a s s i f i e d b y t h e p h y s i c s o f t h e s i t u a t i o n a s f o l l o w s . T h e t a r g e t i s a n a b l a t i v e p u s h e r s i n c e t h e e l e c t r o n m e a n f r e e p a t h a n d t h e a b s o r p t i o n l e n g t h a r e s m a l l i n c o m p a r i s o n t o t h e t a r g e t t h i c k n e s s . T h e s o l i d t a r g e t m a t e r i a l i s i r r a d i a t e d b y t h e l a s e r p u l s e f r o m t h e . l e f t a s s h o w n i n F i g u r e V - 1 . I n i t i a l l y t h e l a s e r h e a t s t h e s u r f a c e o f t h e m a t e r i a l t o w i t h i n a f e w w a v e l e n g t h s . T h e r e g i o n w h i c h i s h e a t e d a c t s a s a h e a t w a v e w h e r e t h e e x p a n s i o n w a v e d e n s i t y i s l o w e r o n t h e h o t s i d e t h a n o n t h e c o o l s i d e a n d t h e r e f o r e i s c l a s s i f i e d a s a s u b s o n i c h e a t w a v e . F u r t h e r m o r e , a s h o c k m a y p r o p o g a t e i n t o t h e t a r g e t a h e a d o f t h e h e a t f r o n t . F i g u r e V - 1 s h o w s a s e c t i o n o f t h e t a r g e t w h e n t h e l a s e r i n t e n s i t y i s a t p e a k p o w e r . T h e m o d e l c o n s i d e r s t h e f l u i d p a r a m e t e r s i n w h i c h t h e l o c a l p o w e r i n p u t I i s a c o n s t a n t . T h e a b l a t i o n p r o c e s s i s c o n s i d e r e d a t t h e i n s t a n t o f p e a k c o m p r e s s i o n a n d a c o m p a r i s o n i s m a d e w i t h t h e r e s u l t s o f t h e M e d u s a h y d r o c o d e . T h e h y d r o c o d e i s d e s c r i b e d i n t h e n e x t c h a p t e r . N o t a l l o f t h e l a s e r p o w e r I i s t r a n s f e r r e d t o t h e a b l a t i o n f r o n t b u t o n l y a s p e c i f i e d f r a c t i o n W = n I . I n t h i s 53 model i t i s assumed that the l a s e r t a r g e t a b s o r p t i o n occurs by the mechanism of inverse bremsstrahlung. This means that the e l e c t r o n s absorb energy from the e l e c t r i c f i e l d and c o l l i s i o n a l l y t r a n s f e r t h e i r energy t o the ions throughout the whole corona up t o the a b l a t i o n f r o n t . The a b l a t i o n f r o n t i s desc r i b e d by the heat wave r e l a t i o n s f o r a d i s c o n t i n u i t y by the equations of con s e r v a t i o n df mass, momentum and energy. In the a b l a t i o n f r o n t ' s frame of reference the r e l a t i o n s are w r i t t e n as: P a V a = P b v b ( D P a + P a v a = P b + P b v b (2) \ < + *a {4Jl I V b + h b where the s u b s c r i p t a r e f e r s t o q u a n t i t i e s ahead of the a b l a t i o n f r o n t and b r e f e r s to the q u a n t i t i e s behind the a b l a t i o n f r o n t and p i s the d e n s i t y , p the pressure,v the v e l o c i t y of the a b l a t i o n f r o n t , v^ the v e l o c i t y of the plasma plume. In a d d i t i o n , h i s the enthalpy which contains the thermodynamics of the m a t e r i a l i n the numerical value of the enthalpy c o e f f i c i e n t g. Along w i t h the above equations the shock conservation equations ( 1 ) , ( 2 ) , and (3) i n Chapter I I are r e w r i t t e n here f o r convenience: p l V l = P 2 V 2 1 1 2 2 (5) F i g u r e V -1 S e c t i o n of s h e l l and blowoff plasma 55 P i + p l v l = p 2 + P 2 v 2 ( 6 ) 2 V i + h i = 2 V 2 + h 2 (7) h 2 = g 2 P 2 g , - i P (8) a n d a r e d e s c r i b e d a s i n C h a p t e r I I . A s s u m i n g t h e W i s g i v e n , t h e n u m b e r o f u n k n o w n s i n b o t h s e t s o f e q u a t i o n s i s t w e l v e : v a ' v b ' v i ' v 2 ' V V V P a ' h a ' P b ' p b ' h b ' b u t t h e r e a r e o n l y 10 e q u a t i o n s , s o t h a t o n e n e e d s t o k n o w t w o m o r e r e l a t i o n s t o s o l v e t h i s s e t a n d p r e d i c t t h e p l a s m a p a r a m e t e r s . I n a d d i t i o n t o t h e a b o v e s e t o f e q u a t i o n s t h e s i m p l i f i e d r o c k e t e q u a t i o n u , v , P, = u (p v - p v ) (9) ODD a i i a a c a n b e u s e d , s o t h a t o n l y o n e a d d i t i o n a l r e l a t i o n i s m i s s i n g . I t i s t h e r e f o r e p o s s i b l e t o e x p r e s s a l l t h e u n k n o w n s a s a f u n c t i o n o f j u s t o n e p a r a m e t e r . H e r e t h e q u a n t i t y h ^ i s c h o s e n a s t h e i n d e p e n d e n t p a r a m e t e r . B y m a n i p u l a t i o n o f t h e c o n s e r v a t i o n e q u a t i o n s t h e r a t i o s o f t h e p r e s s u r e s , d e n s i t i e s a n d v e l o c i t i e s a c r o s s t h e h e a t w a v e b e c o m e : 56 P a - V b - 1 + 1 P p b V a 93M a a P P — = 1 - F ( 1 1 ) a where 2 and G = 2(gB-M)(ga-gb)gX (gb-i)(gb-gX>2 which vanishes i f either M >> 1 . M, « 1 , or g =g, . a D 3 a 3 b A useful l i n e a r approximation for slow subsonic waves i s that the heat input: (g -1) (g,-M2) 2 P v h „ a Jb a a a a 2 9 a M l ( ^ - D and then by linear expansions (ref. 21) one fi n d s : V_ D, [a_ ^b- 1 I  w r1 9h 1 p a v a  h a (12) 57 1 - M a  I p a v a h a W ^ J p a W 1 * ^ P a v a h a W ^ J (13) h a p a v a h a P b <14> f o r a subsonic heat wave preceded by a shock the f o l l o w i n g transformations h o l d : ua = v l " v 2 (15) u a = v b - v a (16) where u i s defined p o s i t i v e away from the heat wave (Figure IV-1). For shock waves W=0 and by manipulation: 2 p i v i 2g 2 M 2 P, = = = P, v. u 0 2 g 2 + l (g 2+l) 1 1 2 (19) p2 9 2 + 1 p j g 2 - l + 2g 2 (20) 9 2 M a U 2 = V l ~ V 2 (21) h _ 2g 2 2 _ g 2 2 2 " ( g 2 + l ) 2 V l = 2 U 2 (22) The enthalpy i s connected t o t h i s set of equations by the equation of s t a t e and then there are enough equations to ob t a i n the unknowns i n terms of W, p j , h f a . Table I , column (a) shows the r e s u l t . Often i t i s more convenient to d i s p l a y these r e s u l t s i n graphic form. T h i s can be done by p l o t t i n g 58 e v e r y p a r a m e t e r a s a f u n c t i o n o f h a n d W ( F i g . V - 2 ) . Now t h a t the ge n e r a l r e l a t i o n s f o r heat waves have been i n t r o d u c e d the r e s u l t s can now be a p p l i e d t o the lase r - p l a s m a i n t e r a c t i o n i f one a d d i t i o n a l r e l a t i o n i s given, Here we i n t r o d u c e the h e a t i n g c h a r a c t e r i s t i c h = ff w ( l j ) f o r i n v e r s e bremsstrahlung a b s o r p t i o n . A s m e n t i o n e d p r e v i o u s l y , t h e a b s o r b e d f r a c t i o n o f t h e t o t a l i n c i d e n t l a s e r i n t e n s i t y I i s : W = n i ( 2 3 ) T h e q u a n t i t y o f e n e r g y w h i c h i s a b s o r b e d p e r c m 3 p e r s e c . i s I / ^ i j - , . T h e l e n g t h ^ b i s t h e a b s o r p t i o n l e n g t h f o r i n v e r s e b r e m s s t r a h l u n g a n d i s g i v e n b y t h e s t a n d a r d r e l a t i o n : 2 A I Z A = 5 . 8 3 x 1 0 " 3 7 r n K 2 ( c m ) { 2 4 ) 1 £ > T 3 2 eb A b w h e r e A i s w a v e l e n g t h i n m i c r o n s , I i s t h e l a s e r i n t e n s i t y i n w a t t s p e r c m 2 , n e b i s t h e n u m b e r o f p a r t i c l e s p e r c m 3 a n d T ^ i s t h e t e m p e r a t u r e i n t h e p l a s m a p l u m e . I f we m u l t i p l y b y t h e l e n g t h o f t h e c o r o n a L , t h e t o t a l a b s o r p t i o n p e r c m 2 b e c o m e s : Q = I L , ( 2 5 ) A . , i b A t p e a k c o m p r e s s i o n w h i c h i s a s s u m e d t o b e i n s t e a d y s t a t e , t h e p o w e r d e n s i t y Q , a b s o r b e d p e r c m 2 m u s t b e u s e d u p i n t h e a b l a t i o n p r o c e s s a n d t h e r e f o r e i t c a n b e s e t e q u a l t o t h e n e t p o w e r d e n s i t y W . T h e n e t h e a t i n p u t W r e g u l a t e s t h e 59 t e m p e r a t u r e and d e n s i t y i n t h e c o r o n a w h i c h i n t u r n d e t e r m i n e s t h e a b s o r p t i o n by i n v e r s e b r e m s s t r a h l u n g a b s o r p t i o n . T h i s a b s o r p t i o n model i s c a l l e d s e l f - r e g u l a t e d i n v e r s e b r e m s s t r a h l u n g and t h e r e f o r e t h e a b l a t i o n and a b s o r p t i o n a r e c o u p l e d t h r o u g h t h e d e n s i t y w h i c h i s g i v e n by: p z n e b = - P - (2 6) m. 1 where P^ i s t h e d e n s i t y b e h i n d o f t h e a b l a t i o n f r o n t Z, i s t h e a t o m i c number and nu i s t h e mass o f an i o n . S u b s t i t u t i n g f o r P F A from T a b l e I , column (6) i n t o e q u a t i o n ( 3 ) , t h e e x h a u s t d e n s i t y becomes: p, z w D n , = = — eb m i / Z m. ^92_1j1//2 h b 3 / 2 ( 2 7 ) I f t h e a s s u m p t i o n i s made t h a t T =T^ t h e n t h e e n t h a l p y becomes: Z + 1 h*> = "mT k ^ (28) l As s t a t e d p r e v i o u s l y t h e t r a n s f e r r e d power W i s a f r a c t i o n o f t h e t o t a l i n c i d e n t i n t e n s i t y I a t peak c o m p r e s s i o n . T h e r e f o r e we f i n d t h a t : I L 3 — = n l (29) i b S u b s t i t u t i n g e q u a t i o n s 22, 24, and 27 i n t o 25 one f i n d s : T b ( e v ) = 1.2 x 1 0 - 3 ( L Z ) 2 / 7 n 2 / 9 ( x i ) ^ ( 3 0 ) 60 w h e r e L i s i n m i c r o n s , Z t h e a t o m i c n u m b e r , A i s i n m i c r o n s , a n d I i s i n w a t t s p e r c m 2 . T h e r e f o r e t h e h e a t i n g c h a r a c t e r i s t i c f o r i n v e r s e - b r e m s s t r a h l u n g a b s o r p t i o n i s f o u n d f r o m e q u a t i o n 2 8 : h b = 1.5 x i o ' n 2 / 9 ( L Z ) 2 / 7 ( I A ) " 7 9 ( 3 D I t m a y b e d i s p l a y e d a s a l i n e i n t h e r e s p o n s e p l a n e , a s s h o w n i n F i g . V - 2 . T h e p a r a m e t e r s L , Z a n d n a r e r a i s e d t o s m a l l p o w e r s a n d t h e r e f o r e h a v e l i t t l e e f f e c t o n t h e h e a t i n g c h a r a c t e r i s t i c a n d h e n c e t h e r e s u l t s . S e t t i n g Z = 1 0 a n d L = 5 0 urn a n d h , = 1.5 x 10 9 n 2 / 9 ( I A ) " / 9 D I f L i s v a r i e d b y a f a c t o r o f 1 0 , t h e n u m e r i c a l c o n s t a n t f o r t h e e n t h a l p y c h a n g e s o n l y b y a f a c t o r o f 1 . 7 ( r e f . 1 4 ) . T h e r e f o r e t h e e r r o r i s a b o u t 3 . T h i s i s i l l u s t r a t e d b y t h e " s h a d e d w i d e " l i n e i n F i g u r e I V - 3 . T a b l e I I , c o l u m n ( b ) s h o w s a f t e r s u b s t i t u t i o n f o r h ^ t h e r e s u l t s f o r a b l a t i v e f l o w . F i g u r e V - 2 s h o w s t h e p a r a m e t e r s o f a b l a t i v e a c c e l e r a t i o n a s a f u n c t i o n o f n e t a b s o r b e d p o w e r W a n d t h e e x h a u s t e n t h a l p y h b . I t i s p o s s i b l e t o c a l c u l a t e t h e k i n e t i c e n e r g y g e n e r a t e d p e r u n i t t i m e i n t h e a b l a t i v e a c c e l e r a t i o n p r o c e s s a n d e x p r e s s i t a s a f u n c t i o n o f t h e a b s o r b e d p o w e r W. A m o s t i m p o r t a n t a n d i n t e r e s t i n g r e s u l t i s f o u n d w h i c h s h o w s t h a t 61 Free flow (a) 1-D heat wave, cgs units, g b = 5/3 (b) h b= 1.5 x l o V ^ U D ^ t e r g / g ) I (watt/cm2); Mum);P(g/cm3) Ablation pressure P a " P b 0.63 -2— h b h 1.6 x i o "1 0 i , ^ 1*9 > " 2 / 9 (Mbar) Shocked particle velocity u 2 0.69 (W/P)'/2 11 x f H p"H (cm/sec) Burn velocity vfl 0.25 W P. hb 1.7 x 1 0 "3 I ^ n 7 / 9 » " ^ p"1 (cm/sec) Mass ablation m w/hb 7 x 10 n '9 j * ) x /9 (g/cm Sec) Shock energy conversion n p u /W =0.44 imi^L 1.8 x 1 o" * n l/3 I !/6 jf !/3 p'h Exhaust density W/(0.63 h^2 + 0.25 W/Pj ) »2.7 x lo" ?n 2 /3 x_2/3 (g/cm3) Blow off velocity v^ 0.63 h b ^ +W/4P, h b •2.4 x l o " n'/9 I 2 / 9 » 2 / 9 (cm/sec) Blow off Mach number l/g b*^ "0.8 = 0.8 Absolute exhaust velocity u b 0.6 3h. ^  -0.7 (W/P, ) ^ h ' ^ " vb Table I 62 J F i g u r e V - 2 P a r a m e t e r s o f t h e a b l a t i o n f r o n t a s f u n c t i o n o f n e t a b s o r b e d i n t e n s i t y W a n d e x h a u s t e n t h a l p y f o r a f l o w w i t h r o c k e t t y p e m o m e n t u m b a l a n c e . T h e i n v e r s e b r e m s s t r a h l u n g r e l a t i o n i s i n d i c a t e d a s a s h a d e d w i d e " l i n e " . 63 t h e m e c h a n i c a l power p u can be d e t e r m i n e d f o r t h e a b l a t i v e mode. _ mechanical power absorbed heat = 40% f o r g a=5/3. The amount o f l a s e r e n e r g y a b s o r b e d by t h e t a r g e t i s 50%. From t h e above c a l c u l a t i o n s 40% o f t h e n e t a b s o r b e d e n e r g y went i n t o m e c h a n i c a l power w h i l e 60% went i n t o t h e h e a t i n g of t h e p l a s m a . T a b l e I I summarizes t h e s e r e s u l t s i n e n e r g y u n i t s . T a b l e I I T o t a l E n e r g y 4.0 J Net a b s o r b e d 2.0 J M e c h a n i c a l Power .80J Plasma H e a t i n g 1 .20J In C h a p t e r IV we d e s c r i b e d t h e measurement o f t h e n e t a b s o r b e d l a s e r e n e r g y and from t h e s e measurement a p o i n t i s l o c a t e d i n t h e r e s p o n s e p l a n e . I t i s i m m e d i a t e l y seen t h a t t h e p o i n t f a l l s w e l l w i t h i n t h e i n v e r s e b r e m s s t r a h l u n g 64 h e a t i n g c h a r a c t e r i s t i c . F u r t h e r m o r e , t h i s p o i n t a l l o w s t h e p r e d i c t i o n o f t h e " s h o c k " v e l o c i t i e s o f 3 . 3 x 1 0 s c m / s e c . T h i s p r e d i c t e d v a l u e a g r e e s w e l l w i t h t h e m e a s u r e m e n t s o f C h a p t e r I V . I n c o n c l u s i o n , we f i n d t h a t t h e m o d e l w h i c h a s s u m e s i n v e r s e b r e m s s t r a h l u n g a b s o r p t i o n a g r e e s w e l l w i t h t h e e x p e r i m e n t a l f i n d i n g s a n d i n d e e d d e m o n s t r a t e s t h e e x i s t e n c e o f a u n i v e r s a l h e a t i n g c h a r a c t e r i s t i c . I t i s i n t e r e s t i n g t o c o m p a r e t h e s e m e a s u r e m e n t s a n d s t e p w a v e m o d e l c a l c u l a t i o n s w i t h d e t a i l e d p r e d i c t i o n s o f a h y d r o c o d e . A v a i l a b l e i n t h i s l a b o r a t o r y i s t h e M e d u s a c o d e , a n d t h e n e x t c h a p t e r e x p l a i n s how i t o p e r a t e s . 65 C H A P T E R V I  T h e M e d u s a H y d r o c o d e A ) B r i e f D e s c r i p t i o n o f t h e P h y s i c s o f M e d u s a T h e M e d u s a h y d r o c o d e w a s d e v e l o p e d b y C h r i s t i a n s e n e t a l . ( r e f . 1 3 ) a t t h e R u t h e r f o r d L a b o r a t o r y , E n g l a n d . A v e r s i o n o f t h e M e d u s a h y d r o c o d e h a s b e e n i n s t a l l e d o n c o m p u t e r b y R . G . E v a n s ( r e f . 2 1 ) . T h e c o d e d e s c r i b e s t h e m o t i o n o f a f l u i d s l a b w h i c h i s g r a d u a l l y s e t i n m o t i o n w h e n a l a s e r p u l s e w i t h a g i v e n w a v e l e n g t h , b e a m w i d t h , a n d p o w e r i s a p p l i e d o n t o s o l i d t a r g e t s . I n i t i a l l y t h e a s s u m p t i o n i s m a d e t h a t t h e s o l i d t a r g e t i s f u l l y i o n i z e d . T h i s i s n o t a n u n r e a l i s t i c a p p r o x i m a t i o n ( r e f . 2 4 ) s i n c e t h e e n e r g y r e q u i r e d t o i o n i z e a n a t o m i s s m a l l c o m p a r e d t o t h e e n e r g y n e e d e d t o h e a t i t t o s o m e m i l l i o n s o f d e g r e e s K e l v i n . I n M e d u s a c a l c u l a t i o n s t h e i n i t i a l s t a g e s o f p l a s m a p r o d u c t i o n f r o m a s o l i d t a r g e t a r e i g n o r e d a n d a f u l l y i o n i z e d p l a s m a i s a s s u m e d t o e x i s t w i t h i o n a n d e l e c t r o n d e n s i t i e s e q u a l t o t h e s o l i d a t o m d e n s i t y . I n t h e s e e x p e r i m e n t s t h i s d e n s i t y c o r r e s p o n d s t o s o l i d a l u m i n u m . T h i s m e a n s t h a t i n i t i a l l y t h e t a r g e t i s n o t b o u n d t o g e t h e r b u t e x p a n d s d u e t o t h e 1 e V i n i t i a l t e m p e r a t u r e a n d p r e s s u r e a n d f o r m s a c o r o n a . T h e l a s e r l i g h t c a n n o t p e n e t r a t e i n t o t h e e x p a n d i n g c o r o n a b e y o n d c r i t i c a l d e n s i t y w h e r e t h e p l a s m a f r e q u e n c y i s e q u a l t o t h e l a s e r f r e q u e n c y . A t t h e c r i t i c a l d e n s i t y t h e 66 absor p t i o n i s assumed to occur v i a inverse bremsstrahlung ( r e f . 1). This means that the l a s e r l i g h t decreases e x p o n e n t i a l l y as i t penetrates i n t o the expanding plasma, causing the e l e c t r o n s to o s c i l l a t e i n the e l e c t r i c f i e l d and c o l l i s i o n a l l y t r a n s f e r t h e i r energy to the i o n s . This gives the r a t e of absorption of the l a s e r l i g h t . The exchange of energy between e l e c t r o n s and ions i s p r o p o r t i o n a l to the e l e c t r o n d e n s i t y and temperature, charge number and the d i f f e r e n c e between the ion and e l e c t r o n temperatures ( r e f . 25). Of course not a l l of the energy i s t r a n s f e r r e d by c o l l i s i o n s to ions and other e l e c t r o n s . Some energy i s r e - r a d i a t e d by a process which i s termed bremsstrahlung. The mechanism of energy l o s s i s that a f r e e e l e c t r o n a b r u p t l y reduces i t s v e l o c i t y i n the presence of an ion f i e l d and the r e s u l t i n g energy appears as a photon. As w i t h inverse bremsstrahlung the rat e cf energy l o s s i s p r o p o r t i o n a l to the e l e c t r o n d e n s i t y , temperature and charge number of the i o n . The energy t r a n s p o r t mechanism between the c r i t i c a l s urface and a b l a t i o n f r o n t i s a complicated phenomena ( r e f . 26). At 1 0 1 2 W/cm2 the heat conduction term i n the Medusa code i s taken from S p i t z e r ( r e f . 26). The important po i n t i s that the energy i s c a r r i e d i n t o the plasma and a b l a t e s the s u r f a c e , c r e a t i n g a rocket l i k e t h r u s t which a c c e l e r a t e s the t a r g e t s I f the energy trans p o r t e d to the surface i s l a r g e enough, a shock wave develops which f u r t h e r 67 c o m p r e s s e s and a c c e l e r a t e s t h e f o i l m a t e r i a l . The r a t e o f a b s o r p t i o n , t h e r a t e o f e n e r g y l o s s t o r a d i a t i o n e t c . , t h e h e a t c o n d u c t i o n and s h o c k h e a t i n g a r e s o u r c e and s i n k t e r m s f o r t h e c o n s e r v a t i o n o f e n e r g y . T h e s e s o u r c e and s i n k t e r m s i n t h e e n e r g y e q u a t i o n c o n s t i t u t e t h e c o n s e r v a t i o n o f e n e r g y . From t h e c o n s e r v a t i o n o f e n e r g y a n u m e r i c a l t e c h n i q u e i s u t i l i z e d w h i c h e x t r a c t s T e and Tj_. Once T e and T^ have been e x t r a c t e d by an i t e r a t i v e p r o c e d u r e t h e c o r r e s p o n d i n g p r e s s u r e s c a n be c a l c u l a t e d f r o m t h e p e r f e c t gas e q u a t i o n s o f s t a t e . The N a v i e r S t o k e s e q u a t i o n ( r e f . 15) i s t h e n s o l v e d f o r t h e p l a s m a v e l o c i t y w h i c h d e f i n e s t h e m o t i o n . The Medusa co d e i s L a g r a n g i a n . T h i s means t h a t a p o i n t w i t h i n t h e p l a s m a moves w i t h t h e f l u i d . The f o i l i s d i v i d e d i n t o N c e l l s (mesh) a s i l l u s t r a t e d i n F i g u r e VI-1 f o r N=7. Note t h a t w i t h i n t h e mesh some q u a n t i t i e s a r e d e f i n e d a t c e l l c e n t r e s and o t h e r s a t b o u n d a r i e s . The t e c h n i q u e f o r a d v a n c i n g a p a r t i c u l a r mesh p o i n t i s b a s i c a l l y u n d e r s t o o d as f o l l o w s . The c o d e has f i v e t i m e l e v e l s . The o l d , c u r r e n t and n e x t t i m e l e v e l s a r e r e p r e s e n t e d by 1,3, and 5 r e s p e c t i v e l y . The l e v e l s w h i c h a r e i n between 1 and 3, a n d 3 a n d 5 a r e d e n o t e d by 2 a n d 4 r e s p e c t i v e l y . F o r example, l e t us c o n s i d e r t h e f o l l o w i n g q u a n t i t i e s A P1, AP3, AP5, AU2, AU4 where AP i s t h e p r e s s u r e d i f f e r e n t i a l and AU i s t h e v e l o c i t y d i f f e r e n t i a l . 68 cells V Mesh Point Co-ordinate *J* Left Hand Boundry 6 NJ 7 NJPI Co ordinates Rl R3 R5 Velocities U2 U6 Ion Temperature TI1.TI3 Electron Temperature TE1,TE3 Average Charge Z FZ1, FZ3 Average Mass No. NIEFF Electron Density NE Ion Density NI Pressure e^ « i £ s given here F i g u r e VI-1 F o i l d i v i d e d i n t o a mesh of 6 69 B y k n o w i n g t h e p r e s s u r e a t t h e o l d t i m e l e v e l A P 1 , t h e c u r r e n t t i m e l e v e l A P 3 i s c a l c u l a t e d b y s o l v i n g t h e e n e r g y c o n s e r v a t i o n e q u a t i o n a s d i s c u s s e d p r e v i o u s l y . S o m e A U 1 a n d A U 3 a r e k n o w n b y t a k i n g t h e i r a v e r a g e A U 2 i s c a l c u l a t e d w i t h m i n i m a l e r r o r . T h e n s i n c e A U 2 a n d A P 3 a r e k n o w n t h e c o d e e x t r a p o l a t e s t o c a l c u l a t e A U 4 u n t i l : A u 4 + A u 2 . _ = A u 3 T h e n A U 4 a d v a n c e s t h e p o s i t i o n c o o r d i n a t e R 3 t o t h e new p o s i t i o n R 5 s i n c e t h e t i m e A t b e t w e e n s u c c e s s i v e a d v a n c e s i s k n o w n . S e c t i o n B s u m m a r i z e s t h e p r o c e d u r e o r a d v a n c i n g a m e s h p o i n t i n a d o l o o p f l o w d i a g r a m . B ) T h e T i m e L e v e l s i n M e d u s a M e d u s a h a s 5 t i m e l e v e l s , e . g . : R 1 , R 3 , R 5 , U 2 , U 4 w h e r e R r e p r e s e n t s c o o r d i n a t e s a n d U - v e l o c i t i e s . 3 i s t h e " c u r r e n t " t i m e l e v e l 1 i s t h e " o l d " t i m e l e v e l 5 i s t h e n e x t t i m e l e v e l B a s i c a l l y M e d u s a l o o p s a s f o l l o w s : 70 Knowing (R1,R3) and t h e P, u and T a t l e v e l 1 s o l v e e n e r g y c o n s e r v a t i o n f o r t h e r m o d y n a m i c s a t l e v e l 1 by i t e r a t i o n , t h e n c a l c u l a t e p r e s s u r e a t l e v e l 3, P3 knowing U2 and P3 p e r f o r m f l u i d a c c e l e r a t i o n t o g i v e U4 u s e U4 t o a d v a n c e R3 t o R5 c o p y R3 t o R1, R5 t o R3, U4 t o U1, ( t h e r m o ) 3 t o ( t h e r m o ) 1 t h e n l a s e r l i g h t i s a b s o r b e d r e t u r n F o r d e t a i l s o f t h e e q u a t i o n s and n u m e r i c a l t e c h n i q u e s r e f e r t o C h r i s t i a n s e n e t a l . ( r e f . 13) and t h e c i t e d r e f e r e n c e s . C) U s e r S p e c i f i c a t i o n s To use Medusa, one must s p e c i f y v a r i o u s p a r a m e t e r s w h i c h s u i t e a p a r t i c u l a r e x p e r i m e n t . In s p e c i f y i n g t h e p h y s i c s f o r most o r d i n a r y r u n s t h e u s e r must i n p u t t h e l a s e r w a v e l e n g t h , power, p u l s e shape and d u r a t i o n . The p u l s e shape c a n be s p e c i f i e d e i t h e r a s t r i a n g u l a r o r G a u s s i a n . The t a r g e t m a t e r i a l , t h i c k n e s s , and t h e number o f mesh p o i n t s must a l s o be s e t b e f o r e a r u n . F o r a l l n o r m a l t e r m s and i f i t i s d e s i r e d t o s a v e on CPU t i m e t h e p e r f e c t g a s laws a r e r e a s o n a b l e i n r e t r o s p e c t . F o r summary and a c o m p l e t e l i s t o f v a r i a b l e p a r a m e t e r s w h i c h may be o f use i n h i g h i n t e n s i t y s i m u l a t i o n s , see R.G. E v a n s ( r e f . 2 1 ) . I t has been f o u n d t h a t some o f t h e a s s u m p t i o n s and a p p l i c a t i o n s o f t h e e x i s t i n g c o d e a r e r a t h e r u n c e r t a i n . The 71 e q u a t i o n o f s t a t e i s o n l y t h e o r e t i c a l l y i n f e r r e d a n d t h e s t a b i l i t y o f t h e c o m p r e s s i o n p r o c e s s i s n o t c o n s i d e r e d . F u r t h e r m o r e , t h e c o d e d o e s n o t t r e a t t h e a b s o r p t i o n r e g i o n o r t h e p h y s i c s o f t h e b a c k o f t h e t a r g e t i n f u l l d e t a i l . I n t h e n e x t c h a p t e r a c o m p a r i s o n i s m a d e b e t w e e n e x p e r i m e n t s a n d m o d e l w i t h t h e M e d u s a h y d r o c o d e . 72 C H A P T E R V I I C o m p a r i s o n o f A n a l y t i c M o d e l a n d E x p e r i m e n t s w i t h M e d u s a A ) C o m p a r i s o n T h i s c h a p t e r c o m p a r e s t h e e x p e r i m e n t a l a n d a n a l y t i c r e s u l t s w i t h t h e M e d u s a h y d r o c o d e s i m u l a t i o n s a t p e a k p o w e r . T h e p r o g r a m h a s b e e n r u n f o r a p l a n a r a l u m i n u m t a r g e t 3 7 . 5 u m t h i c k , d e n s i t y P = 2 . 5 g . / c m 3 a n d i o n i c c h a r g e Z = 1 3 . T h e p u l s e s h a p e , n e t p o w e r a b s o r b e d a n d w a v e l e n g t h a r e s p e c i f i e d a c c o r d i n g t o t h e r e s u l t s p r e s e n t e d i n C h a p t e r I V . F i g u r e V I I - 1 s h o w s t h e r e s u l t s f o r t h e s i m u l a t i o n u p t o p e a k c o m p r e s s i o n . We n o t i c e f r o m t h e s i m u l a t i o n t h a t f o r o u r l a s e r i n t e n s i t y M e d u s a d o e s n o t p r e d i c t a s t r o n g s h o c k w a v e s i n c e t h e v e l o c i t y i s c l o s e t o t h e s o u n d v e l o c i t y i n a l u m i n u m . T h e r e f o r e M e d u s a i m p l i e s t h a t o u r s h o c k w a v e d i a g n o s t i c i s n o t a p p l i c a b l e t o o u r e x i s t i n g l a s e r s y s t e m . H o w e v e r o n e c a n c h e c k i f t h e e x p e r i m e n t a l r e s u l t s a n d h e a t w a v e m o d e l a r e c o n s i s t e n t w i t h M e d u s a c a l c u l a t i o n s . A t t h e p r e s e n t l a s e r i n t e n s i t y , t h e t a r g e t i s a b l a t i v e l y a c c e l e r a t e d i n a f o r w a r d d i r e c t i o n l i k e a r o c k e t . F r o m t h e s i m u l a t i o n s o n e e x t r a c t s t h e p a r t i c l e v e l o c i t y ( u 2 = 2 . 8 5 x 1 0 s c m / s e c ) , t h e a b l a t i o n v e l o c i t y ( v =10" c m . / s e c ) , t h e e x h a u s t v e l o c i t y (v_ = 1 0 7 a J b c m / s e c . ) a n d t h e a b l a t i o n p r e s s u r e ( P = = .1 M b a r ) ( s e e F i g . V I I - 1 ) . S i n c e t h e a m o u n t o f n e t p o w e r a b s o r b e d h a s b e e n 73 m e a s u r e d a n d t h e h e a t i n g c h a r a c t e r i s t i c i s k n o w n a l l t h e l a s e r p a r a m e t e r s c a n b e d e t e r m i n e d f r o m t h e h e a t w a v e m o d e l f r o m t h e m e a s u r e m e n t o f t h e l a s e r i n t e n s i t y a l o n e . F i g u r e V - 2 s h o w s t h e r e s p o n s e p l a n e . T h e p o i n t i n t h e p l a n e s h o w s a l l t h e l a s e r p a r a m e t e r s i n v o l v e d i n t h e a b l a t i v e f l o w . A s a c h e c k t w o a d d i t i o n a l p a r a m e t e r s w e r e m e a s u r e d a s d i s c u s s e d i n C h a p t e r I I I . T h e e x h a u s t a n d p a r t i c l e v e l o c i t i e s w e r e m e a s u r e d w h i c h v e r i f i e s t h e h e a t w a v e m o d e l s i n c e i t a g r e e s w i t h t h e m o d e l c a l c u l a t i o n s a n d n u m e r i c a l s i m u l a t i o n s . T a b l e I I I s h o w s t h e v a l u e s o f t h e p a r a m e t e r s f r o m t h e e x p e r i m e n t s a n d m o d e l a s c o m p a r e d t o t h o s e p r e d i c t e d f r o m t h e M e d u s a n u m e r i c a l s i m u l a t i o n a t p e a k c o m p r e s s i o n . T h e r e s u l t s s u g g e s t v e r y g o o d a g r e e m e n t a t t h e p r e s e n t l a s e r i n t e n s i t y . T a b l e I I I E x p e r i m e n t s M o d e l M e d u s a w 1 . 9 x 1 0 ' ' W - c m / g 1 . 9 x 1 0 1 1 W - c m / g 1 . 9 x 1 0 1 ' W - c m / g v b 9 . 0 x 1 0 6 c m / s e c 8 . 3 x 1 0 6 c m / s e c 1 . O x 1 0 7 c m / s e c U 2 2 . 4 7 x 1 0 5 c m / s e c 2 . 3 x 1 0 5 c m / s e c 2 . 8 5 x 1 0 5 c m / s e c V a - 5 . 0 x 1 0 3 c m / s e c 7 3 . 5 x 1 0 c m / s e c P a — . 1 M b a r . 1 M b a r F i g u r e V I I - 2 s h o w s t h e a b l a t i o n t e m p e r a t u r e a s a f u n c t i o n o f 74 l a s e r i n t e n s i t y . T h e c i r c l e s r e p r e s e n t e x p e r i m e n t a l v a l u e s f r o m o t h e r l a b o r a t o r i e s ( r e f . 2 7 ) . T h e s q u a r e r e p r e s e n t s t h e e x h a u s t t e m p e r a t u r e f o r t h e e x i s t i n g l a s e r f a c i l i t y . T h e s e r e s u l t s v e r i f y a u n i v e r s a l h e a t i n g c h a r a c t e r i s t i c f o r l a s e r p r o d u c e d p l a s m a s f r o m w h i c h t h e e x h a u s t t e m p e r a t u r e c a n b e p r e d i c t e d f r o m t h e m e a s u r e m e n t o f t h e l a s e r i n t e n s i t y a l o n e . B ) F u t u r e W o r k I n o r d e r t o t e s t t h e v a l i d i t y o f t h e a n a l y t i c a l m o d e l d e v e l o p e d i n C h a p t e r I I , i t w o u l d b e o f g r e a t i n t e r e s t a n d o f v a l u e t o i r r a d i a t e l a s e r t a r g e t s w i t h a h i g h e r i n t e n s i t y . F r o m t h e r e s p o n s e p l a n e ( F i g . V - 2 ) s t r o n g s h o c k s s t a r t a t a l a s e r i n t e n s i t y o f I 0 1 f t W / c m 2 . A C 0 2 l a s e r s y s t e m c a p a b l e o f p r o d u c i n g s u c h h i g h i n t e n s i t i e s i s o p e r a t i o n a l a t U n i v e r s i t y o f B r i t i s h C o l u m b i a . 75 F i g u r e VII-1 Medusa s i m u l a t i o n up to peak compression F i g u r e VII-2 A b l a t i o n temperature as a f u n c t i o n of l a s e r i n t e n s i t y and experimental v a l u e s of -ref. 27 77 REFERENCES 1 L.D. V e s s o r and J . C . Solem, P h y s . Rev. L e t t . 4CJ, 1391 (1978) 2 R . J . T r a i n o r , J.W. S h a n e r , J.M. A u e r b a c h , and N.C. Holmes, P h y s . Rev. L e t t . 42, 1154 (1979) 3 L.R. V e s s o r , J . C . Solem, and A . J . L e i b e r , A p p l . P h y s . L e t t . 35,. 761 (1979) 4 B. A r a d , S. F l i e z e r , Y. G a z i t , H.M. L o e b e n s t e i n , A. Z i g l e r , H. Szmora, and S. Zweigenbaum, J . App. P h y s . 50, 6817 (1979) 5 M.H. Key, N a t u r e 28^, 715 (1980) 6 N.H. B u r n e t t , G. J o s i n , B. A h l b o r n , and R. E v a n s , A p p l . P h y s . L e t t . 38(4) F e b . 15, 1981. 7 A l b a c h , G. M.Sc. T h e s i s . U n i v e r s i t y o f B r i t i s h C o l u m b i a 1972 8 G o d f r e y , L.A. M.Sc. T h e s i s . U n i v e r s i t y o f B r i t i s h C o l u m b i a 1972 9 C h u r c h l a n d , M., M.Sc. T h e s i s . U n i v e r s i t y o f B r i t i s h C o l u m b i a 1969 10 H i l k o , B. M.Sc. T h e s i s . U n i v e r s i t y o f B r i t i s h C o l u m b i a 1978 11 TRW M o d e l ID Image C o n v e r t e r Camera, T e c h n i c a l M a n u a l . 12 B. A h l b o r n , G. J o s i n , A. Ng, and N.H. B u r n e t t , P a p e r #5R75, B u l l . Am. P h y s . S o c . 25 933 (1980) 13 J . P . C h r i s t i a n s e n e t a l . , Computer P h y s . Comm. 7 (1974) 278-287. 14 B. A h l b o r n , M. Keg, R u t h e r f o r d L a b r e p o r t RL-79-033 78 15 N.H. B u r n e t t , G. J o s i n , B. A h l b o r n and R. E v a n s t o be p u b l i s h e d ( 1 9 8 0 ) . 16 Samson, P h y s i c s i n Canada (CAP M e e t i n g , Quebec) 32, No. 3, 12 ( 1 9 7 6 ) . 17 B.H. R i p i n e t a l . ICP '80 t o p i c a l m e e t i n g on i n e r t i a l c o n f i n e m e n t f u s i o n , San D i e g o F e b . 26-28 (1980) p a p e r WB 3. 18 B. A h l b o r n , Can. J . P h y s i c s ( 1 9 7 5 ) , 53, 976. 19 B. A h l b o r n , IPP R e p o r t 111/12 G a r c h i n g ( 1 9 6 3 ) . 20 A s hby, C h r i s t i a n s e n , and R o b e r t s Computer P h y s i c s C o m m u n i c a t i o n s V o l . 7, No. 5, p. 271 ( 1 9 7 4 ) . 21 R.G. E v a n s , U.B.C. Lab R e p o r t Number 75 22 W.I. L i n t o r , A p p l . P h y s . L e t t . 3, 210 ( 1 9 6 3 ) . 23 W. D e m t r i o d e , and W. J a n t z , Plasma P h y s i c s , V o l . 12, pp. 691-705. 24 Hughes, P l a s m a s and L a s e r L i g h t , A l a n H i l g e r 25 D . J . Rose and M. C l a r k e , P l a s m a s and C o n t r o l l e d F u s i o n ( J o h n W i l e y , I n c . , 1961) 26 L. S p i t z e r , P h y s i c s of F u l l y I o n i z e d G a s e s , 2nd e d . ( I n t e r s c i e n c e Pub., 1961) 27 P.T. Rumsby, M. M i c h a e l i s , M. B u r g e s s (1975) O p t . Comm. _1_5, 242. 

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