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Impedance-mismatch experiments using laser-driven shocks Chiu, Gordon S. Y. 1988

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IMPEDANCE-MISMATCH EXPERIMENTS USING LASER-DRIVEN  SHOCKS  By Gordon S. Y . C h i u B . A . S c , T h e University of British C o l u m b i a , 1986  A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS  FOR T H E D E G R E E O F  M A S T E R OF A P P L I E D S C I E N C E  in T H E FACULTY OF G R A D U A T E STUDIES D E P A R T M E N T OF PHYSICS  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH COLUMBIA  September 1988  (c) Gordon S. Y . C h i u . 1988  In  presenting  degree  at  this  the  thesis in  University of  partial  fulfilment  of  of  department  this or  publication of  thesis for by  his  or  that the  her  representatives.  It  this thesis for financial gain shall not  Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  for  an advanced  Library shall make  it  agree that permission for extensive  scholarly purposes may be  permission.  DE-6G/81)  requirements  British Columbia, I agree  freely available for reference and study. I further copying  the  is  granted  by the  understood  that  head of copying  my or  be allowed without my written  Abstract  A series of impedance-mismatch experiments with aluminum-gold targets has been performed.  These experiments are used to probe the equation of state ( E O S ) of gold at  high pressure. B y measuring the shock breakout time from the target rear surface, the shock trajectory is determined and found to be i n good agreement with equation of state predictions.  In addition, temperatures derived from temporally resolved luminescence  measurements of the shocked target rear surface are compared with two different equation of state theoretical models. O u r results indicate that whereas the S E S A M E (from Los Alamos National Laboratory) E O S seems to overestimate the shock temperature, the equation of state of gold which incoporated both the solid and liquid phases gives much closer agreement with observations. The measurements of gold at a shock pressure of --6 M b a r and temperature of ~ 17500 K also represent the first study of gold under shock melting.  n  Table of  Contents  Abstract  ii  L i s t of T a b l e s  v  L i s t of F i g u r e s  vi  Acknowledgement  xi  1  2  Introduction  1  J.l  Introduction to H i g h Pressure Research  1  1.2  Thesis Objective  4  1.3  Thesis Outline  5  T h e o r y of L a s e r - d r i v e n S h o c k s 2.1  6  S h o c k G e n e r a t i o n by L a s e r - D r i v e n A b l a t i o n in S o l i d s  6  2.1.1  Laser Energy Deposition  6  2.1.2  Electron Thermal Conduction  8  2.1.3  Shock Wave Generation  9  2.2  T h e Hugoniot  10  2.3  T h e Impedance-Mismatch Technique  13  2.3.1  Pressure Enhancement.  18  2.3.2  R e d u c t i o n of R a d i a t i v e P r e h e a t  20  2.4  E q u a t i o n of S t a t e  23  2.4.1  23  S E S A M E E q u a t i o n of S t a t e  iii  2.4.2 2.5  3  4  26  Computer Simulations  31  2.5.1  S H Y L A C Code  32  2.5.2  H Y R A D Code  33  2.5.3  P T C Code  36  E x p e r i m e n t a l Facility, Diagnostics, and  Setup  38  3.1  Laser Facility  38  3.2  Irradiation Conditions  41  3.3  Experimental Arrangements  45  L u m i n e s c e n c e M e a s u r e m e n t s in S i n g l e and 4.1  4.2  5  N e w E O S C a l c u l a t i o n s for G o l d  Doubled-Layered Targets  49  Shock Velocity Study  49  4.1.1  Single Layer A l u m i n u m Foil  50  4.1.2  A l u m i n u m - G o l d Targets  57  Brightness Temperature Study with A l u m i n u m - G o l d Targets  '  69  4.2.1  Experimental Observations  71  4.2.2  Computer Simulations  77  Summary  98  5.1  Conclusions  98  5.2  Future Research  100  Bibliography  101  iv  L i s t of T a b l e s  4.1  c o m p a r a t i v e s t u d y of t h e effects of r a d i a t i o n t r a n s p o r t on free surface shock p a r a m e t e r s for a 19 pm A ] o n 13 pm A u t a r g e t  4.2  84  c o m p a r a t i v e s t u d y of t h e effects of o u r n e w g o l d E O S d a t a o n free surface shock p a r a m e t e r s for a 19 pm A l o n 13 pm Au t a r g e t , r a d i a t i o n t r a n s p o r t is i n c l u d e d  4.3  84  c o m p a r a t i v e s t u d y of t h e effects of o u r n e w g o l d E O S d a t a o n t h e s h o c k breakout times  t h e c o m p r e s s i o n r a t i o (p/po),  a n d t h e s h o c k t e m p e r a t u r e (T)  t h e shock pressure ( P ) ,  at b r e a k o u t for v a r i o u s A l - A u  R a d i a t i o n t r a n s p o r t is i n c l u d e d  targets. 85  v  L i s t of F i g u r e s  2.1  S c h e m a t i c d i a g r a m of a l a s e r - d r i v e n shock  7  2.2  A n i l l u s t r a t i o n of t h e s h o c k e d a n d u n s h o c k e d regions  2.3  T h e a l u m i n u m p r i n c i p a l H u g o n i o t i n t h e (a) P vs p p l a n e , a n d (b) T vs p  11  p l a n e , as g i v e n i n S E S A M E 2.4  14  T h e a l i m i n u m p r i n c i p a l H u g o n i o t i n t h e (a) Up vs Us p l a n e , a n d (b) Up vs P p l a n e . A l s o i n c l u d e d in (b) is t h e p r i n c i p a l H u g o n i o t of g o l d .  Data  are f r o m S E S A M E  15  2.5  S h o c k p r o p a g a t i o n a n d p a r a m e t e r s i n an i m p e d a n c e - m i s m a t c h e d target  .  2.6  T h e c a l c u l a t i o n of pressure i n the s a m p l e u s i n g t h e m i r r o r - r e f l e c t i o n m e t h o d .  17  T h e slope o l t h e straight, line i n v o l v e s t h e m e a s u r e m e n t of t h e shock vel o c i t y Us i n t h e s a m p l e 2.7  19  T h e mirror-reflection m e t h o d with the sample Hugoniot k n o w n , eliminati n g the n e e d t o m e a s u r e Us  2.8  21  T h e d e n s i t y - t e m p e r a t u r e regimes of t h e seven E O S m o d e l s of a l u m i n u m used in S E S A M E  2.9  25  T h e solid a n d l i q u i d Hugoniot. of g o l d as c a l c u l a t e d i n § 2 . 4 . 2 , t h a t i n S E S A M E is also i n c l u d e d ; also s h o w n is t h e m e l t i n g c u r v e  30  3.10  A s c h e m a t i c of t h e laser and d i a g n o s t i c s s y s t e m  39  3.11  A t y p i c a l laser p u l s e  40  3.12  A t i m e - i n t e g r a t e d laser i n t e n s i t y d i s t r i b u t i o n  42  3.13  E q u i v a l e n t s y m m e t r i c profile of t h e laser s p o t of F i g u r e 3.12  43  vi  3.14  A cross section of t h e laser s p o t i n F i g u r e 3.12 across (a) t h e x - c o o r d i n a t e a n d (b) t h e y - c o o r d i n a t e , each s p a n n i n g t h e c e n t r a l 5 pm of t h e s p o t  . .  3.15  T h e e x p e r i m e n t a l setup i n the luminscence study  4.16  S t r e a k r e c o r d s o f shock b r e a k o u t e m i s s i o n (left s t r e a k ) a n d f i d u c i a l s i g n a l  46  ( r i g h t s t r e a k ) i n (a) 38.4 pm a n d (b) 53 pm a l u m i n u m t a r g e t 4.17  51  T e m p o r a l h i s t o r y of t h e (a) shock b r e a k o u t a n d (b) f i d u c i a l s t r e a k i n a 38.4 pm  4.18  A l target  53  T h e c a l c u l a t e d abla.tion p r e s s u r e p u l s e f r o m H Y R A D (solid) and t h e G a u s sian p r e s s u r e p u l s e a s s u m e d i n S H Y L A C ( d a s h )  4.19  44  54  C a l c u l a t e d shock p a t h s by S H Y L A C ( d o t - d a s h ) , by H Y R A D w i t h o u t , rad i a t i o n t r a n s p o r t ( d a s h ) , a n d w i t h r a d i a t i o n t r a n s p o r t ( s o l i d ) ; also p l o t t e d are t h e e x p e r i m e n t a l results i n v a r i o u s a l u m i n u m t a r g e t s  4.20  4.21  56  S t r e a k r e c o r d of free surface l u m i n o u s e m i s s i o n (left s t r e a k ) a n d  fiducial  signal (right, s t r e a k ) of a 19 pm a l u m i n u m on 8.4 pm g o l d t a r g e t  . . . .  58  S h o c k p r e s s u r e profiles in A l - A u t a r g e t s w i t h t h e front a l u m i n u m t h i c k n e s s equal t o 5 p.m.  T h e i n i t i a l p r o f i l e c o r r e s p o n d s to a t i m e of 1.5 ns  before  the p r e s s u r e p u l s e p e a k , and subsequent, ones are 0.25 ns apart  60  4.22  S a m e as F i g u r e 4.21 b u t a l u m i n u m t h i c k n e s s is 11.5 pm  61  4.23  S a m e as F i g u r e 4.21 b u t a l u m i n u m t h i c k n e s s is 19 pm  62  4.24  S a m e as F i g u r e 4.21 b u t a l u m i n u m t h i c k n e s s is 50 pm  63  4.25  S h o c k i n d u c e d p r e s s u r e i n t h e free surface of gold as a f u n c t i o n of t h e a l u m i n u m thickness.  T h e v a r i o u s lines d e n o t e different g o l d  thicknesses:  2 pm ( s o l i d ) . 8.4 pm (clash), 13 pm ( d o t - d o t - d o t - c l a s h ) . 20 pm  (dot-dash).  A l s o s h o w n is t h e m a x i m i u m p r e s s u r e reached s o m e w h e r e i n a g o l d layer of i n f i n i t e t h i c k n e s s ( d o t )  65  vii  4.26  S h o c k pressure at t h e free surface of g o l d as a f u n c t i o n of t h i c k n e s s i n t h e g o l d layer for v a r i o u s front a l u m i n u m t h i c k n e s s e s :  11.5 fim  (dot-dot-  d a s h ) , 19 fim ( d o t - d a s h ) , 34 fi.m ( s o l i d ) , a n d 50 fim ( d a s h ) 4.27  68  S h o c k p a t h s as c a l c u l a t e d b y H Y R A D i n 19 fim A l a n d 13 fim A u t a r g e t using S E S A M E E O S (dot-dot-dash),  and using new gold E O S (dash); i n  26.5 fim A l a n d 13 fim A u target u s i n g S E S A M E E O S ( d o t - d a s h ) ,  and  u s i n g n e w g o l d E O S ( d o t ) . T h e shock p a t h i n 53 fim Al (solid) is i n c l u d e d . A l s o p l o t t e d are the e x p e r i m e n t a l p o i n t s for v a r i o u s A l - A u t a r g e t s a n d p u r e A l targets 4.28  70  T e m p o r a l l y r e s o l v e d a n d i n t e g r a t e d p l o t of t h e b a c k s i d e e m i s s i o n i n t e n s i t y of a 38.4 fim A l t a r g e t , w i t h t i m e zero b e i n g t h e peak of t h e laser p u l se.  72  4.29  S a m e as F i g u r e 4 . 2 8 e x c e p t target is 19 fim A l on 13 fim A u  73  4.30  S a m e as F i g u r e 4 . 2 8 e x c e p t target is 19 fim A l on 8.4 fim A u  74  4.31  S a m e as F i g u r e 4 . 2 8 e x c e p t target is 2 6 . 5 m i c r o n A l o n 8.4 fim A u  4.32  S a m e as F i g u r e 4.28exc.ept t a r g e t is 26.5 fim A l o n 13 fim A u  4.33  A s n a p s h o t of t h e h y d r o d y n a m i c profile i n a 19 fim A l on 13 fim A u t a r g e t  . . . .  75 76  at t = -1.26 ns. R a d i a t i o n t r a n s p o r t process is n e g l e c t e d , a n d b o t h A l a n d A u E O S d a t a are f r o m S E S A M E 4.34  !  79  S a m e as F i g u r e 4.33 e x c e p t r a d i a t i o n t r a n s p o r t process is i n c l u d e d . T h e a b s o r b e d X - r a y p o w e r is also p l o t t e d  80  4.35  S a m e as F i g u r e 4.33 e x c e p t t i m e is at t = 0.24 ns  82  4.36  S a m e as F i g u r e 4.35 b u t r a d i a t i o n t r a n s p o r t p r o c e s s is i n c l u d e d  83  4.37  Backside, e m i s s i o n f r o m a 19 fim A l on 13 ftm A u t a r g e t u s i n g ( d a s h ) a n d o u r new ( d o t - d o t - d o t - d a s h )  SESAME  g o l d E O S d a t a , as well as f r o m a  38.4 fim A l ( s o l i d ) t a r g e t , w i t h t i m e zero c o r r e s p o n d i n g to shock b r e a k o u t  viii  87  4.38  T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y of t h e p r e v i o u s F i g u r e 4.37: t h a t of a 19 pm A l o n 13 pm A u target u s i n g S E S A M E ( d o t ) a n d t h e new ( d a s h ) g o l d d a t a ; that, of a 38.4 pm A l t a r g e t ( d o t - d a s h )  4.39  T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y r a t i o for a 19  88 A l o n 13 pm A n t a r g e t  t o a 38.4 pm A l t a r g e t : (a) u s i n g S E S A M E ( d o t ) , a n d new g o l d ( d o t - d a s h ) E O S d a t a ; a n d ( b ) b e s t - f i t t e d t e m p e r a t u r e Tp c u r v e ( d o t - d o t - d a s h ) t o a n experimental curve (dot-dash) 4.40  Similar to F i g u r e 4.39(b):  -  89  an experimental time-integrated emission in-  t e n s i t y r a t i o is b e s t - f i t t e d w i t h a shock t e m p e r a t u r e Tp 4.41  S i m i l a r to F i g u r e 4 . 3 9 ( b ) :  90  an e x p e r i m e n t a l time-integrated emission in-  t e n s i t y r a t i o is b e s t - f i t t e d w i t h a shock t e m p e r a t u r e Tp 4.42  Similar to Figure 4.39(b):  91  an experimental time-integrated emission in-  t e n s i t y r a t i o is b e s t - f i t t e d w i t h a shock t e m p e r a t u r e Tp 4.43  T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y r a t i o for a 19 pm  . . . A l on 8.4 pm  92  Au  t a r g e t t o a 38.4 pm A l t a r g e t u s i n g S E S A M E ( d o t ) , a n d t h e new (1 o n g dot-dash) gold E O S data.  T h e experimental data (long dash, solid, long  d o t - d o t - c l o t - d a s h ) are i n d i v i d u a l l y b e s t - f i t t e d w i t h a shock  temperature  Tp ( s h o r t d o t - d o t - d o t - d a s h , s h o r t d a s h , short d o t - d a s h ) 4.44  93  T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y r a t i o for a 26.5 pm A l on 8.4 pm A u t a r g e t to a 38.4 pm A l t a r g e t u s i n g S E S A M E ( d o t ) , a n d t h e n e w ( d o t - d a s h ) g o l d E O S d a t a . T h e e x p e r i m e n t a l d a t a ( l o n g d a s h , solid) are i n d i v i d u a l l y b e s t - f i t t e d w i t h a s h o c k t e m p e r a t u r e Tp ( d o t - d o t - d o t - d a s h , short d a s h )  IX  .  94  4.45  T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y r a t i o for a 26.5 pm t a r g e t t o a 38.4 pm  A l o n 13 pm A u  A l t a r g e t u s i n g S E S A M E ( d o t ) , a n d t h e n e w ( dot-  dash) gold E O S data.  O n e e x p e r i m e n t a l d a t a ( l o n g dash) is  best-fitted  w i t h a shock t e m p e r a t u r e Tp (short d a s h ) w h i l e t h e o t h e r ( s o l i d ) coincides w i t h the calculated curve (dot-dash) 4.46  95  A p l o t of t h e H u g o n i o t of g o l d f r o m S E S A M E ( d o t - d a s h ) , t h e l i q u i d H u g o niot in our new calculations (dash) and the experimentally deduced points.  x  97  Acknowledgement  I w o u l d like to t h a n k m y supervisor, D r .  A n d r e w N g for his g u i d a n c e i n t h e present  p r o j e c t a n d for p r o v i d i n g a n e x c e l l e n t e x p e r i m e n t a l f a c i l i t y . M y i n d e b t e d n e s s  is to D r .  B . K . G o d w a l for his m a n y h e l p f u l s u g g e s t i o n s a n d assistance i n t h e o r e t i c a l c a l c u l a t i o n s i n t h i s thesis.  I a m e s p e c i a l l y g r a t e f u l to L u i z D a S i l v a , w h o has h e l p e d me g r e a t l y in  every p h a s e of t h e e x p e r i m e n t a l w o r k a n d t h e s i s p r e p a r a t i o n .  T o the other  members  a n d v i s i t o r s of t h e p l a s m a g r o u p , I say t h a n k y o u for p r o v i d i n g l i v e l y discussions  and  i n s i g h t f u l c o m m e n t s , w o r k r e l a t e d or o t h e r w i s e . T h i s work is s u p p o r t e d by t h e N a t u r a l Sciences a n d E n g i n e e r i n g R e s e a r c h C o u n c i l of Canada.  XI  Chapter 1  Introduction  1.1  I n t r o d u c t i o n to H i g h Pressure  Research  T h e g e n e r a t i o n of h i g h p r e s s u r e ( 1 0 b a t m o s p h e r e regime) i n m a t t e r n o t o n l y finds i m m e d i a t e a p p l i c a t i o n i n d r i v i n g i m p l o s i o n s i n i n e r t i a ! c o n f i n e m e n t f u s i o n [1, 2], w h e r e t h e t h e r m o n u c l e a r fuel m u s t b e b r o u g h t i n t o an e x t r e m e state of d e n s i t y a n d t e m p e r a t u r e ( b r o u g h t a b o u t b y h i g h p r e s s u r e c o m p r e s s i o n ) to i g n i t e a n d s u s t a i n t h e f u s i o n r e a c t i o n s , b u t also can be of f u n d a m e n t a l interest i n t h e s t u d y of equations of s t a t e ( E O S ) of m a t t e r at h i g h pressure[3], t h e d e t e r m i n a t i o n of s t r u c t u r a l p h a s e t r a n s i t i o n s i n crystals[4], a n d t h e i n v e s t i g a t i o n s of i n t e r m o l e c u l a r forces, e l e c t r o n i c , c h e m i c a l , a n d o p t i c a l p r o p e r t i e s of m a t e r i a l s u n d e r e x t r e m e c o n d i t i o n s [ 5 ] .  M a n y interesting physical phenomena  such  as s-d e l e c t r o n i c t r a n s f e r l e a d i n g to i n s u l a t o r - m e t a l l i c t r a n s i t i o n [ 6 , 7], or s h o c k m e l t i n g f r o m s o l i d to l i q u i d at h i g h pressure[8], h a v e r e m a i n e d m o s t l y u n e x p l o r e d a.nd n o t well u n d e r s t o o d (for e x a m p l e , S h a n e r i n reference [9] discusses the v a r i o u s difficulties b e s e t t i n g the measurements  i n high pressure m e l t i n g ) .  O n the other h a n d , e x p e r i m e n t a l results  are c r i t i c a l l y n e e d e d to resolve d i v e r g i n g p r e d i c t i o n s a m o n g c o n t e n d i n g E O S  theories  as w e l l as to e x t e n d a n d t o e s t a b l i s h t h e ra.nge of a p p l i c a b i l i t y of e x i s t i n g c a l c u l a t i o n a l t e c h n i q u e s . H e n c e h i g h p r e s s u r e s t u d y c a n be seen t o be of i m m e n s e i m p o r t a n c e i n b o t h applied and theoretical studies. T h e basic p r i n c i p l e for o b t a i n i n g h i g h pressure i n various d y n a m i c . methods[10], i n  1  Chapter  1.  Introduction  2  c o n t r a s t to t h e s t a t i c t e c h n i q u e s ( s u c h as t h e d i a m o n d a n v i l c e l l j l l ] ) , i n v o l v e s t h e i n t r o d u c t i o n of a r a p i d i m p u l s e (shock wave) t h r o u g h : 1. t h e d e n o n a t i o n of e x p l o s i v e s y s t e m s , e i t h e r c h e m i c a l [ 1 2 , 13, 14, 15] or n u c l e a r [ l 6 , 17], 2. h y p e r v e l o c i t y i m p a c t u s i n g a h i g h - s p e e d p r o j e c t i l e f r o m a s i n g l e or two-stage l i g h t gas gun[18], 3. t h e e n e r g y d e p o s i t i o n by a n i n t e n s e i o n b e a m [ l 9 ] , 4. t h e a b s o r p t i o n of an intense p u l s e of r a d i a t i o n p r o v i d e d by a h i g h - p o w e r laser[20]. G e n e r a l l y s p e a k i n g , t h e m a i n a d v a n t a g e of d y n a m i c , over s t a t i c t e c h n i q u e s is t h a t h i g h e r p r e s s u r e can be a t t a i n e d .  T h i s is b e c a u s e t h e pressure a c h i e v e d i n d i a m o n d a n v i l cells  w i l l be u l t i m a t e l y r e s t r i c t e d by t h e plastic, d e f o r m a t i o n l i m i t of d i a m o n d s . H o w e v e r , for d y n a m i c p r e s s u r e studies u n i q u e a n d fast d i a g n o s t i c s (e.g.  sub-nanosecond resolution  i n la.ser-driven e x p e r i m e n t s ) m u s t also be d e v e l o p e d . In a d d i t i o n , d y n a m i c m e t h o d s are u s u a l l y m u c h m o r e c o s t l y in b o t h c a p i t a l a n d o p e r a t i o n a s p e c t s . A b r i e f d i s c u s s i o n o n the m e r i t s a n d short c o m i n g s of t h e v a r i o u s d y n a m i c m e t h o d s is i n o r d e r here. T h e use of c h e m i c a l e x p l o s i v e s has b e e n o n e of t h e earliest m e t h o d s i n h i g h p r e s s u r e g e n e r a t i o n [ 1 2 , 13], b u t t h e a t t a i n a b l e pressures h a v e b e e n l i m i t e d to ~ 1 0 M b a r (1 M b a r = 1 0 6 a t m o s p h e r e s ) i n metals[15]. U n d e r g r o u n d n u c l e a r e x p l o s i o n s [ 3 , 16, 17] offer t h e p o s s i b i l i t y to achieve r e c o r d - s e t t i n g pressures ( r e a d i l y e x c e e d i n g 100 M b a r , a n d r e c e n t l y , pressures of >4000 M b a r i n a l u m i n u m [ 2 l ] have been r e p o r t e d ) w i t h g o o d a c c u r a c y ( < 5 % ) , a l t h o u g h t h i s m e t h o d is v a s t l y e x p e n s i v e a n d o b v i o u s l y i n a c c e s s i b l e t o m a n y researchers. O n t h e other h a n d , the two-stage light-gas guns[22] have p r o d u c e d t h e m o s t p r e c i s e m e a s u r e m e n t s (< 1% a c c u r a c y i n p r e s s u r e [ l 8 ] ) , b u t t h e pressure a t t a i n e d is s o m e w h a t l i m i t e d ( u p to ~ 5 M b a r [ 3 ] ) . W h i l e h e a v y i o n b e a m s are p r o j e c t e d to be c a p a b l e  Chapter  1.  Introduction  3  of p r o d u c i n g d y n a m i c pressure of over 100 M b a r [ 2 3 ] , yet n o p r a c t i c a l d e m o n s t r a t i o n has been p e r f o r m e d . L a s t l y , l a s e r - d r i v e n s h o c k waves have b e e n s h o w n t o b e e m i n e n t l y able t o s p a n pressures i n t h e " i n t e r m e d i a t e " r e g i o n (tens to h u n d r e d s of M b a r s [ 2 4 , 25]) p r e v i o u s l y inaccessible by the more conventional means, thus b r i d g i n g the gap between the low p r e s s s u r e r e g i o n a p p r o p r i a t e t o gas g u n s / c h e m i c a l e x p l o s i v e s a n d t h e h i g h pressure r e g i o n c h a r a c t e r i s t i c of n u c l e a r e x p l o s i o n s . F u r t h e r m o r e , b e c a u s e of its h i g h r e p e t i t i o n r a t e a n d r e l a t i v e ease of o p e r a t i o n , laser has b e c o m e t h e sole m e a n s of g e n e r a t i n g pressures i n t h e intermediate region in laboratory-scaled experiments, a l t h o u g h the uncertainties in the m e a s u r e m e n t s c a n be s i g n i f i c a n t ( >  10%).  A s we w i l l be u s i n g the la.ser o p t i o n i n the w o r k of the p r e s e n t t h e s i s , we w i l l e l a b o r a t e f u r t h e r o n t h e v e r s a t i l i t y of t h e use of l a s e r - d r i v e n shock waves. A g r e a t m a j o r i t y of researches i n the p a s t decades have b e e n d i r e c t e d t o w a r d s u n d e r s t a n d i n g the m a n y a s p e c t s in l a s e r - m a t t e r i n t e r a c t i o n s such as laser a b s o r p t i o n efficiency, m a s s a b l a t i o n r a t e , target p r e h e a t m e c h a n i s m s , or t h e r m a l t r a n s p o r t p r o p e r t i e s , a n d hence a r r i v i n g at the o p t i m a l c o n d i t i o n s for l a s e r - d r i v e n fusion[26, 27, 28, 29]. N e v e r t h e l e s s i t is s o o n r e c o g n i z e d t h a t t h e a b i l i t y of l a s e r - d r i v e n s h o c k waves to g e n e r a t e h i g h pressures is also i d e a l for e q u a t i o n of s t a t e s t u d i e s of m a t e r i a l s at e x t r e m e c o n d i t i o n s of p r e s s u r e a n d d e n s i t y [ 2 4 , 30]. In add i t i o n , e l e c t r i c a l p r o p e r t i e s such as t h e p o t e n t i a l difference b e t w e e n surfaces of d e f o r m e d d i e l e c t r i c s caused by t h e m o t i o n of a. s h o c k wave (this is c a l l e d shock p o l a r i z a t i o n [ 3 l ] ) , or the e l e c t r o n i c c o n d u c t i v i t y i n dense p l a s m a [ 3 2 ] , have also been s t u d i e d u s i n g l a s e r - d r i v e n shock waves. M o r e recent e x p e r i m e n t s of interest i n c o n d e n s e d m a t t e r p h y s i c s a n d a t o m i c p h y s i c s , a l l u s i n g l a s e r - d r i v e n shocks to a,chieve t h e d e s i r e d materia.] s t a t e , i n c l u d e t h e m e a s u r e m e n t s of l a t t i c e c o m p r e s s i o n s a,nd stresses i n s i h c o n j 3 3 ] , t h e t e m p o r a l e v o l u t i o n of t h e K - a b s o r p t i o n edge i n shock c o m p r e s s e d p o t a s s i u m c h l o r i d e [ 3 4 ] , or t h e s h o r t range ion c o r r e l a t i o n effects i n a l u m i n u m p l a s m a [ 3 5 ] . F i n a l l y we w i l l c o n c l u d e t h e i n t r o d u c t o r y section b y d i s c u s s i n g t h e p h e n o m e n o n of  Chapter  1.  Introduction  4  shock m e l t i n g , as it represents one of t h e p r i n c i p a l areas of s t u d i e s i n t h i s thesis.  Shock  wave p r o p a g a t i o n i n a m a t e r i a l leads t o the c o m p r e s s i o n a n d h e a t i n g of t h e m a t e r i a l a b o v e s o l i d d e n s i t y a n d a m b i e n t t e m p e r a t u r e , a n d s o m e t i m e s t h i s h e a t i n g is sufficient to cause t h e m a t e r i a l to m e l t . K o r m e r et al.[36] have suggested t h e m e a s u r e m e n t of s h o c k t e m p e r a t u r e to detect t h e onset of m e l t i n g a n d t o resolve different p r e d i c t i o n s f o r w a r d e d b y s o l i d a n d l i q u i d states E O S t h e o r i e s .  F o r e x a m p l e , t h e o b s e r v a t i o n s of shock m e l t -  i n g a l o n g t h e H u g o n i o t i n m a t e r i a l s h a v e been p r e v i o u s l y r e p o r t e d . T h e earliest studies of K o r m e r [ 3 6 ] m e a s u r e d t h e b r i g h t n e s s t e m p e r a t u r e of t h e s h o c k front a n d d e t e r m i n e d t h e h i g h - p r e s s u r e m e l t i n g c u r v e i n a n u m b e r of t r a n s p a r e n t a l k a l i halides ( N a C l , K B r , L i F , etc.).  T h e L i v e r m o r e [ 3 7 ] a n d L o s A l a m o s group[38]- have c a l c u l a t e d the m e l t i n g  b e h a v i o r o n t h e H u g o n i o t of a n u m b e r of a l k a l i m e t a l s as w e l l as a l u m i n u m , a n d have e x p e r i m e n t a l l y d e t e r m i n e d t h e shock m e l t i n g r a n g e i n a l u m i n u m t h r o u g h s o u n d speed measurements.  T h e recent i n v e s t i g a t i o n s of R a d o u s k y et.al.[39] also use shock t e m p e r -  a t u r e m e a s u r e m e n t s to d e t e r m i n e t h e onset of m e l t i n g i n C'sl. I n p a r t i c u l a r , they f o u n d t h a t t h e i r da.ta were s u f f i c i e n t l y s e n s i t i v e detect  a n i n a d e q u a c y i n the s o l i d H u g o n i o t  c a l c u l a t i o n , a n d have s h o w n t h e v a l i d i t y of u s i n g a. l i q u i d t h e o r y i n the m e l t i n g r e g i m e . H e n c e , t h e a c q u i s a t i o n of e x p e r i m e n t a l da.ta is c r u c i a l i n h e l p i n g t o differentiate b e t w e e n the p r e d i c t i o n s of different t h e o r i e s .  1.2  Thesis Objective T h e p r i n c i p a l a i m of t h i s thesis is t o u t i l i z e i n t e n s e laser pulses to generate s t r o n g  shock waves for e q u a t i o n of s t a t e i n v e s t i g a t i o n s i n h i g h - Z m a t e r i a l s . A s a n e x a m p l e , we  Cha.pt.er  1.  Introduction  5  w i l l focus o n t h e b e h a v i o r of g o l d at h i g h p r e s s u r e a n d s p e c i f i c a l l y , t h e process of shock m e l t i n g . F r o m t i m e - r e s o l v e d m e a s u r e m e n t s of s h o c k - i n d u c e d l u m i n o u s e m i s s i o n s , we w i l l d e t e r m i n e t h e t e m p e r a t u r e of g o l d at ~ 6 M b a r , a b o v e i t s p r e d i c t e d m e l t i n g t r a n s i t i o n at —2 M b a r . T h e result w i l l b e u s e d to assess e x i s t i n g e q u a t i o n of s t a t e m o d e l s a n d t o p r o v i d e a n e x p e r i m e n t a l basis for n e w m o d e l s . ' A s e c o n d b u t s t r o n g l y r e l a t e d o b j e c t i v e is t o e m p l o y t h e i m p e d a n c e - m i s m a t c h t e c h n i q u e f ] 2, 14, 15, 22] in t h e s t u d y of h i g h - Z m a t e r i a l s u s i n g l a s e r - d r i v e n shock waves. T h e i m p e d a n c e - m i s m a t c h t e c h n i q u e involves t h e p r o d u c t i o n of a s h o c k wave i n a l o w Z (low d e n s i t y a n d l o w a c o u s t i c i m p e d a n c e ) m a t e r i a l , w h i c h then p r o p a g a t e s i n t o t h e h i g h - Z ( h i g h d e n s i t y a n d h i g h a c o u s t i c i m p e d a n c e ) m a t e r i a l of i n t e r e s t .  In t h i s s t u d y ,  g o l d a n d a l u m i n u m h a v e been chosen as t h e h i g h - Z a n d l o w - Z m a t e r i a l s We  will demonstrate  respectively.  t h e a d v a n t a g e s of t h i s t e c h n i q u e , n a m e l y , p r e s s u r e e n h a n c e m e n t  a n d r e d u c t i o n of r a d i a t i v e p r e h e a t . W e w i l l e x a m i n e t h e p r o p e r design of an i m p e d a n c e m i s m a t c h e d target a n d i d e n t i f y t h e c r i t i c a l c r i t e r i o n for o p t i m a l p r e s s u r e g e n e r a t i o n i n t h e h i g h - Z m a t e r i a l of i n t e r e s t .  1.3  Thesis Outline T h i s thesis is o r g a n i z e d as f o l l o w s : C h a p t e r 2 gives a r e v i e w of t h e t h e o r y o n shock  waves a n d t h e t e c h n i q u e of shock p r o d u c t i o n by i m p e d a n c e m i s m a t c h .  C h a p t e r 3 de-  scribes the e x p e r i m e n t a l facility, diagnostics, and the experimental setup.  T h e experi-  m e n t a l r e s u l t s a n d c o m p a r i s o n w i t h c o m p u t e r s i m u l a t i o n s w i l l be p r e s e n t e d i n c h a p t e r 4. F i n a l l y , t h e m a j o r c o n c l u s i o n s are s u m m a r i z e d i n c h a p t e r 5.  Chapter 2  T h e o r y of L a s e r - d r i v e n S h o c k s  2.1  Shock G e n e r a t i o n by L a s e r - D r i v e n A b l a t i o n in Solids T h e process for g e n e r a t i n g l a s e r - d r i v e n s h o c k s has been e x a m i n e d i n d e t a i l s i n ref-  erences  [l] a n d [2].  H e r e we s h a l l briefly r e v i e w t h e t h r e e p r i n c i p a l p h y s i c s processes  involved: 1. laser energy a b s o r p t i o n i n a laser-heated  target,  2. e l e c t r o n t h e r m a l c o n d u c t i o n w h i c h carries t h e heat flux f r o m t h e a b s o r p t i o n r e g i o n i n t o the target i n t e r i o r , effecting a b l a t i o n , a n d 3. shock wave g e n e r a t i o n by t h e o u t w a r d e x p a n s i o n of t h e a b l a t e d m a t e r i a l .  2.1.1  Laser Energy Deposition  F i g u r e 2.1 shows a s c h e m a t i c d i a g r a m of a l a s e r - i r r a d i a t e d s o l i d t a r g e t , w h e r e t h e o u t e r layer of t h e target is h e a t e d b y an energy a b s o r p t i o n m e c h a n i s m k n o w n as  brem,sstTahlung[AO],  or free-free a b s o r p t i o n .  inverse  T h i s p r o c e s s c a n be v i s u a l i z e d a.s e l e c t r o n s  o s c i l l a t i n g i n the e l e c t r i c field of t h e i n c i d e n t laser l i g h t a n d t h e r e b y a b s o r b i n g t h e energy of t h e p h o t o n . T h e e l e c t r o n s s u b s e q u e n t l y t r a n s f e r t h e i r energies t o t h e rest of t h e target (i.e. i o n s ) v i a e l e c t r o n - i o n c o l l i s i o n s . In t h i s m a n n e r , p a r t i c l e s i n t h e target a b s o r b the laser e n e r g y and b e c o m e h e a t e d , i o n i z e d a n d e x p a n d i n t o the v a c u u m , f o r m i n g a low d e n s i t y blow-off p l a s m a , c a l l e d t h e corona.  F o r s h o r t w a v e l e n g t h (<1 / i i n ) laser r a d i a t i o n  6  Chapter  2.  Theory  of Laser-driven  Shocks  F i g u r e 2.1: S c h e m a t i c d i a g r a m of a l a s e r - d r i v e n s h o c k  Chapter  2.  Theory  oi Laser-driven  Shocks  8  t h i s p r o c e s s is t h e d o m i n a n t a b s o r p t i o n m e c h a n i s m .  T h e laser energy c a n be a b s o r b e d  u p t o t h e c r i t i c a l d e n s i t y surface w h e r e t h e e l e c t r o n o s c i l l a t i o n f r e q u e n c y  equals t h e  f r e q u e n c y of t h e laser r a d i a t i o n a n d the laser l i g h t is reflected. A c c o r d i n g l y , the c r i t i c a l d e n s i t y nCTli  is defined by  ncrir  =  u  L £° e-  m  [MKS  units]  (2.1)  w h e r e u.^ is the laser f r e q u e n c y , m a n d e are t h e e l e c t r o n mass a n d c h a r g e respectively, a n d e 0 is t h e p e r m i t t i v i t y of space.  S i n c e t h e p l a s m a d e n s i t y scale l e n g t h  (^=(^ff)-1i  w h e r e n is the e l e c t r o n d e n s i t y ) i n the c o r o n a is i n v a r i a b l y m u c h l a r g e r t h a n t h e laser w a v e l e n g t h [ 4 0 ] , a n d since, t h e e l e c t r o n - i o n energy t r a n s f e r r i n g process b e c o m e s m o r e a n d m o r e efficient as e l e c t r o n d e n s i t y increases ( t h e e l e c t r o n - i o n c o l l i s i o n a l f r e q u e n c y scales a p p r o x i m a t e l y l i n e a r l y w i t h e l e c t r o n density[40]),  therefore e s s e n t i a l l y a l l of the laser  e n e r g y is a b s o r b e d i n t h e c o r o n a before" it reaches the c r i t i c a l surface.  Consequently, the  c o r o n a l p l a s m a is v e r y hot (~- 1 k e V ) [ 4 1 ] .  2.1.2  Electron Thermal Conduction  T h e la.ser energy a b s o r b e d on the surface of the t a r g e t is t r a n s p o r t e d i n w a r d due to large t e m p e r a t u r e g r a d i e n t b e t w e e n t h e h o i c o r o n a and t h e c o l d i n t e r i o r of the target. T h e d e p o s i t i o n of t h i s intense h e a t flux in t h e so-called conduction  or ablation  zone  (see  F i g u r e 2.1 ) causes the t a r g e t m a t e r i a l to be a b l a t e d (i.e., v a p o r i z e d f r o m the solid) w h i c h t h e n e x p a n d s r a p i d l y o u t w a r d i n t o the c o r o n a . T h e heat c o n d u c t i o n is m a i n l y c a r r i e d out b y t h e e l e c t r o n s , first s t u d i e d by S p i t z e r a n d H a r m [ 4 2 ] . T h e y a s s u m e d e l e c t r o n t h e r m a l c o n d u c t i o n to follow t h e c l a s s i c a l F o u r i e r heat l a w ,  (2.2)  Chapter  2.  Theory  oi Laser-driven  Shocks  9  w h e r e K is t h e S p i t z e r t h e r m a l c o n d u c t i v i t y w h i c h is of t h e form[43] e  q  K e = 1.955 • 1 C T 9  0 . 0 9 5 ( £ + 0.24) T J -— „ >-A 1+0.24Z ZlnA h  2  K  2.3  1  w h e r e Z is t h e m a t e r i a l a t o m i c n u m b e r , Te is t h e e l e c t r o n t e m p e r a t u r e , a n d In A is t h e C o u l o m b l o g a r i t h m . A s a r e s u l t , t h e specific h e a t flux w i l l be  He  = - - V • KeVTe p  (2.4)  w h e r e p is t h e density. It has been o b s e r v e d t h a t at h i g h e n o u g h i n t e n s i t y ( > 1 0 1 4 W / c n r ) the S p i t z e r - H a r m t r a n s p o r t m o d e l b r e a k s d o w n [ 2 7 , 44, 45], so t h a t the a c t u a l heat c o n d u c t i o n is m u c h less t h a n p r e d i c t e d . ( T h i s is b e c a u s e for large t e m p e r a t u r e g r a d i e n t , e q u a t i o n (2.3) an excessively l a r g e heat  flux.)  predicts  T h i s decrease i n h e a t flux is c a l l e d e l e c t r o n t h e r m a l  flux  i n h i b i t i o n , a n d o n e u s u a l l y remedies  it a r t i f i c a l l y i n s i m u l a t i o n s by a s s i g n i n g a " f l u x -  l i m i t e r , ; / , so t h a t the a c t u a l flux Ha  = / • H£ is no m o r e t h a n a f r a c t i o n of t h e S p i t z e r  flux.  F u r t h e r m o r e , at h i g h i n t e n s i t i e s e n e r g e t i c electrons c a l l e d s u p r a t h e r m a l  electrons[2S,  46] w i t h energies m u c h g r e a t e r t h a n t h e t h e r m a l e l e c t r o n s of t h e  corona, are p r o d u c e d . transport  T h e s e s u p r a t h e r m a l electrons represent  t h e t a r g e t (i.e.  plasma  a n o t h e r m e a n s of energy  i n a d d i t i o n to the diffusive h e a t flow d i s c u s s e d above.  l o n g m e a n free p a t h s a n d w i l l '"preheat"  or hot  T h e s e electrons  heat u p the t a r g e t before  have the  shock a r r i v e s ) . T h e s e t w o aspects w i l l be f u r t h e r addressed i n § 2 . 5 . 2 a n d it w i l l be s h o w n t h a t t h e y are n e g l i g i b l e i n o u r e x p e r i m e n t s i n § 4 . 1 . 1 . A .  2.1.3  Shock W a v e G e n e r a t i o n  T h e o u t w a r d e x p a n s i o n of t h e a b l a t e d m a t e r i a l f r o m t h e a b l a t i o n front gives rise to a large o u t w a r d m o m e n t u m  flux.  B y m o m e n t u m c o n s e r v a t i o n , t h i s p r o d u c e s a large a b l a -  t i o n pressure w h i c h drives a shock wave i n t o t h e i n t e r i o r of t h e s o l i d t a r g e t ( F i g u r e 2.1).  Chapter  2.  Theory  of Laser-driven  Shocks  10  So l o n g as t h e a b l a t i o n pressure increases ( d u e to t h e i n c r e a s i n g laser i n t e n s i t y , for e x a m ple, i n t h e r i s i n g edge of a G a u s s i a n p u l s e ) , s h o c k waves o f i n c r e a s i n g a m p l i t u d e s w i l l be l a u n c h e d i n t o t h e t a r g e t . N o w t h e first l a u n c h e d s h o c k wave t r a v e l s at s l i g h t l y e x c e e d i n g t h e speed of s o u n d , a n d b e i n g a c o m p r e s s i o n a l d i s t u r b a n c e , w i l l c o m p r e s s t h e solid a l i t t l e . T h e s e c o n d s t r o n g e r shock wave w i l l therefore t r a v e l n e a r t h e c o r r e s p o n d i n g s o u n d speed of t h e c o m p r e s s e d r e g i o n , w h i c h is greater t h a n t h a t i n a n u n d i s t u r b e d m e d i u m , w i l l r e c o m p r e s s t h e target s t i l l f u r t h e r . ( T h e s o u n d speed c = yjdP/dp  and  (P,p  p r e s s u r e a n d d e n s i t y ) e q u a l s , i n the case of a n i d e a l a d i a b a t i c gas for e x a m p l e , w h e r e 7 is t h e r a t i o of specific heat. H e n c e c — c0(p/po) J~°' 5 s i t y a n d c o r r e s p o n d i n g s o u n d speed) oc / i  7 - 0 5  is t h e  ^JfP/p,  {po- Co is s o m e reference den-  = p 1 - 1 ' for a m o n a t o m i c gas.)  Evidently,  t h e l a t t e r w a v e s , p r o p a g a t i n g at h i g h e r speeds, w i l l t e n d to c a t c h u p w i t h t h e p r e c e e d i n g ones.  T h i s leads t o a " s t e e p e n i n g " of t h e wave f r o n t , o r t h e c o a l e s c e n c e of a sequence  of m u l t i p l e s h o c k waves i n t o a single s t e a d y shock f r o n t . T h e c o m p r e s s i v e effects of t h e i n d i v i d u a l s h o c k waves also a c c u m u l a t e , a n d t h i s shock f r o n t is c h a r a c t e r i z e d b y a s h a r p discontinuity in pressure, density, and t e m p e r a t u r e between the shocked and unshocked regions.  2.2  The  Hugoniot  C o n s i d e r a p l a n a r , steady  s t a t e s t r o n g shock wave a n d f u r t h e r a s s u m e t h a t  the  m e d i u m a h e a d of t h e shock is at rest whereas t h e s t a t e b e h i n d t h e s h o c k is u n i f o r m l y c o m p r e s s e d as i l l u s t r a t e d i n F i g u r e 2.2.  T h e n , c o n s e r v a t i o n of m a s s , m o m e n t u m , a n d  e n e r g y across t h e s h o c k f r o n t i n t h e l a b o r a t o r y f r a m e leads t o t h e R a n k i n e - H u g o n i o t  Chapter  2.  Theory  of Laser-driven  F i g u r e 2.2:  Shocks  A n i l l u s t r a t i o n o f t h e shocked a n d u n s h o c k e d regions  11  Chapter  2.  Theory  of Laser-driven  Shocks  12  e q u a t i o n s (see e.g.[47, 48]):  PoUs = pi{Us Pi-P0 E1-E0  =  =  ~  (2.5)  Up)  (2.6)  PoUsUp  (2.7)  l/2(P1+P0)(l/p0-l/pi)  w h e r e p, P , a n d P are t h e d e n s i t y , pressure a n d i n t e r n a l e n e r g y r e s p e c t i v e l y . T h e subs c r i p t s 0 a n d 1 denote t h e u n s h o c k e d a n d s h o c k e d r e g i o n s , w h i l e Us a n d Up are t h e s h o c k wave 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 i n t h e c o m p r e s s e d r e g i o n . In t h e l i m i t i n g case w h e n P j ^  P 0 . e q u a t i o n (2.6) reduces to  Pi =  (2.8)  PoUsUp  w h i c h is a s t r a i g h t line on t h e P vs Up p l a n e w i t h slope PoUs-  T h i s c o n d i t i o n is easily  satisfied w h e n P i is of t h e o r d e r of M b a r w h i l e PQ is at a t m o s p h e r i c pressure i n o u r experiment. G i v e n an i n i t i a l c o n d i t i o n (e.g. po, P o , and Pi, o r s o m e o t h e r shock p a r a m e t e r describi n g t h e s t r e n g t h of the s h o c k w a v e ) , t h e r e are five u n k n o w n p a r a m e t e r s ( p 3 , Eo, E\, Us,  Up)  a n d t h r e e e q u a t i o n s ( E q s . (2.5) to (2.7)). T h e r e f o r e t w o q u a n t i t i e s need to be m e a s u r e d e x p e r i m e n t a l l y i n order t o specify c o m p l e t e l y t h e t h e r m o d y n a m i c a l s t a t e i n the s h o c k e d region.  F o r e x a m p l e , t h e f r e q u e n t l y m e a s u r e d q u a n t i t i e s i n a h y p e r v e l o c i t y i m p a c t ex-  p e r i m e n t are t h e shock speed a n d p a r t i c l e speed.  In l a s e r - d r i v e n s h o c k  the. shock speed a n d t e m p e r a t u r e have been measured[49]. t i o n of s t a t e ( s u c h as E = E(p.P))  experiments,  A l t e r n a t i v e l y , if t h e equa-  of t h e m a t e r i a l is k n o w n or can be c a l c u l a t e d , t h e n  one c a n c a l c u l a t e all t h e u n k n o w n q u a n t i t i e s .  A n y h o w , a set o f five s h o c k  parameters  (pi, Pi, Ei, U$, Up) c o r r e s p o n d s to a f i n a l state of a s h o c k - c o m p r e s s e d m a t e r i a ] , a n d t h e l o c u s of t h e final states t h a t c a n be r e a c h e d by e m p l o y i n g shock waves of different s t r e n g t h f r o m t h e s a m e i n i t i a l s t a t e , p l o t t e d u s i n g any t w o of t h e five shock p a r a m e t e r s , is k n o w n  Chapter  2.  Theory  of Laser-driven  Shocks  13  as t h e shock a d i a b a t or t h e Hugoniot  c u r v e . T h a t p a r t i c u l a r c u r v e for w h i c h t h e m a t e r i a l  is i n i t i a l l y at s t a n d a r d  ( O K ) a n d p r e s s u r e (1 b a r ) is c a l l e d t h e p r i n c i p a l  temperature  Hugoniot. T h e p r i n c i p a l H u g o n i o t s of a l u m i n u m u s i n g v a r i o u s shock p a r a m e t e r s are i n F i g u r e s 2.3 a n d 2.4.  presented  W e n o t e t h e essentially l i n e a r r e l a t i o n s h i p b e t w e e n U$ a n d  f/p[47, 48]. F o r a l u m i n u m , i t is[50]  Us  = 0.58 + \.22UP  w h e r e b o t h Us a n d Up are g i v e n i n 1 0 6 c m / s .  (2.9)  I n F i g u r e 2.4(b) t h e p r i n c i p a l H u g o n i o t  of g o l d is also i n c l u d e d as a c o m p a r i s o n to t h a t of a l u m i n u m . T h e s e d a t a are a l l t a k e n f r o m t h e S E S A M E l i b r a r y ( d e t a i l s are p r e s e n t e d b e l o w i n § 2 . 4 . 1 ) .  2.3  The Impedance-Mismatch  Technique  T h e i m p e d a n c e - m i s m a t c h t e c h n i q u e has been v a r i o u s l y c a l l e d t h e r e f l e c t i o n m e t h o d , the deceleration  m e t h o d [ l 5 ] , or a n o n - s y m m e t r i c i m p a c t  W e s h a l l r e s t r i c t our d i s c u s s i o n s wave s t u d i e s ,  i n gas  of this t e c h n i q u e as i t applies  gun  experiments[22].  to l a s e r - d r i v e n  a l t h o u g h i t is o b v i o u s l y not l i m i t e d t o laser applic.ation[3, 15, 17].  impedance-mismatch  t e c h n i q u e refers t o t h e p r o p a g a t i o n  shock The  of a shock w a v e t h r o u g h  t a r g e t b o u n d together b y t w o (or m o r e ) layers of m a t e r i a l s of d i f l e r i n g shock  a  impedances.  In g e n e r a l , t h e q u a n t i t y pv r e p r e s e n t s t h e characteristic, i m p e d a n c e of a m a t e r i a l , w h e r e  p is t h e d e n s i t y of t h e m a t e r i a l a n d v t h e p r o p a g a t i o n v e l o c i t y of t h e d i s t o r t i o n a l wave through the material.  F o r e x a m p l e , if one replaces v by t h e s o u n d speed c, t h e n pc is  k n o w n as t h e acoustic i m p e d a n c e , a n d if one replaces v b y Us,  the resultant  quantity  Density in g/cm**3  tOOOOOn  (b)  ^  c  10000  y  £  "i_5 0 ) Q_ E  1000-)  /  /  /  /  /  100-  Density in g/cm**3  F i g u r e 2 . 3 : T h e a l u m i n u m p r i n c i p a l H u g o n i o t i n t h e (a) P vs p p l a n e , a n d ( b ) T vs p p l a n e , as g i v e n i n S E S A M E .  Chapter  2.  Theory  of Laser-driven  Shocks  15  2.5-1  (a) o  C *O O  1.5  o  1  $  -¥ o o  5  0.5  — I —  0.2  —r  -  0.4  0.6  — I —  0.8  1  -r— 1.2  1.4  Particle Velocity in 10**6 cm/s  —I  1.6  10  (b)  L. o  3  V<  4  0_  Legend +  Aluminum  X Gold 0.6  —i— 0.8  —i  1  1— 1.2  Particle Velocity in 10**6 cm/s  —i— 1.4  1.6  F i g u r e 2.4: T h e a l i m i n u m p r i n c i p a l H u g o n i o t i n t h e (a) Up vs Us p l a n e , a n d (b) Up vs P p l a n e . A l s o i n c l u d e d i n (b) is t h e p r i n c i p a l H u g o n i o t of g o l d . D a t a are f r o m S E S A M E .  Chapter  pUs  2.  Theory  of Laser-driven  Shocks  is k n o w n as t h e shock im.peda.nce.  16  A s m e n t i o n e d i n § 2 . 2 , it is g e n e r a l l y necessary t o  m e a s u r e t w o i n d e p e n d e n t s h o c k v a r i a b l e s i n o r d e r to d e t e r m i n e t h e H u g o n i o t s t a t e of t h e s h o c k e d m e d i u m . O n t h e o t h e r h a n d , for t h e i m p e d a n c e - m i s m a t c h t e c h n i q u e i n v o l v i n g t w o different m a t e r i a l s , t h e H u g o n i o t of one m a t e r i a l (the s a m p l e ) c a n be d e t e r m i n e d f r o m measurements is k n o w n .  of o n l y o n e s h o c k p a r a m e t e r if t h e e q u a t i o n o f s t a t e of t h e o t h e r m a t e r i a l  T h e l a t t e r t h e n serves as a refernence s t a n d a r d .  In t h e c o n t e x t of e q u a t i o n  of s t a t e s t u d i e s , a single H u g o n i o t is by i t s e l f insufficient t o describe t h e c o m p l e t e E O S of a m a t e r i a l ; n e v e r t h e l e s s , it serves as a g o o d v a l i d a t i n g m e c h a n i s m for t h e o r e t i c a l E O S e j a c u l a t i o n s a n d also as a useful e m p i r i c a l r e l a t i o n at h i g h pressure. In a n i m p e d a n c e - m i s m a t c h e x p e r i m e n t , t h e laser g e n e r a t e d shock o f t e n , t h o u g h not n e c e s s a r i l y , first passes t h r o u g h t h e s t a n d a r d m a t e r i a l a n d t h e n i n t o t h e a d j a c e n t s a m p l e of interest, as i l l u s t r a t e d i n F i g u r e 2.5. b a n c e s (see e.g.  In close a n a l o g y t o o t h e r c o m p r e s s i o n a l d i s t u r -  [51]), t h e s h o c k i m p e d a n c e c a n be used t o d e t e r m i n e t h e b e h a v i o r of a  s h o c k p r e s s u r e p u l s e at t h e i n t e r f a c e w h e r e t h e two m a t e r i a l s are j o i n e d t o g e t h e r .  For  t h e l a s e r - d r i v e n shock wave p r o p a . g a t i n g t h r o u g h the s t a n d a r d i n t o t h e s a m p l e , w h e n i t rea,ches t h e i n t e r f a c e , it w i l l s i m u l t a n e o u s l y g e n e r a t e a b a c k w a r d - m o v i n g , reflected wave i n t o t h e s t a n d a r d as well as a f o r w a r d - m o v i n g , t r a n s m i t t e d wave i n t o the s a m p l e .  One  c a n t h e n d e d u c e t h e s h o c k p r o p e r t y of t h e s a m p l e m a t e r i a l as f o l l o w s . A s s u m i n g a g a i n t h e p r o p a g a t i o n of a. p l a n a r a n d s t e a d y shock f r o n t , t h e r e are a t o t a l of ten u n k n o w n s  (p, P, E, Up, a n d Us for each of t h e two m a t e r i a l s ) . A p p l y i n g t h e m a t c h i n g c o n d i t i o n s of 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 at t h e interface of the t w o m a t e r i a l s reduces t h e n u m b e r oi u n k n o w n s to eight,  i n a d d i t i o n , there are t h r e e c o n s e r v a t i o n e q u a t i o n s ( E q s .  t o (2.7)) g o v e r n i n g each of t h e s h o c k e d states i n the s t a n d a r d a n d the s a m p l e ,  (2.5)  plus(the  E O S for t h e s t a n d a r d m a t e r i a l , g i v i n g a t o t a l of seven e q u a t i o n s . T h e r e f o r e one needs to m e a s u r e o n l y one p a r a m e t e r , u s u a l l y a shock v e l o c i t y i n e i t h e r one of t h e t w o m a t e r i a l s , i n o r d e r t o c o m p l e t e l y specify t h e final s h o c k - c o m p r e s s e d  t h e r m o d y n a m i c states of b o t h  Chapter  2.  Theory  of Laser-driven  Shocks  A  17  Interface Material 1: Standard Pi,  Pi,  E  Materia] 2: Sample Pi,  l  P2,  E  2  Interface Matching Conditions:  PQ  + Pi = P  2  Upi = Up  2  F i g u r e 2.5: S h o c k p r o p a g a t i o n a n d p a r a m e t e r s i n a n i m p e d a n c e - m i s m a t c h e d  target  Chapter  2.  Theory  of Laser-driven  Shocks  18  materials.  2.3.1  Pressure  Enhancement  A s m e n t i o n e d before, a reflected w a v e a n d a t r a n s m i t t e d w a v e are g e n e r a t e d at t h e i n t e r f a c e of t h e t a r g e t . W h e t h e r t h e reflected a n d t r a n s m i t t e d waves are e i t h e r a rarefact i o n or s e c o n d shock d e p e n d s u p o n t h e r e l a t i v e shock i m p e d a n c e s of t h e two m a t e r i a l s . S p e c i f i c a l l y , i f P0 is t h e a m p l i t u d e of t h e i n c o m i n g p r e s s u r e p u l s e , a n d Pi a n d P2  those  of the reflected a n d t r a n s m i t t e d pulses (refer to F i g u r e 2.5) r e s p e c t i v e l y , then[52]  =  P, = " where the subscripts  ( ^ - ; ^ ) .  (pUsh  +  P  o  (  2  .  1  0  )  (2.11)  .p (pUs)i  1,2 d e n o t e t h e regions i n front a n d b a c k of t h e interface.  Tn a n y  case, t h e r e s u l t a n t 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 m u s t be c o n t i n u o u s across the i n t e r f a c e . It can be seen t h a t p r e s s u r e e n h a n c e m e n t  i n the sample  can be a c h i e v e d by  i n g a s t a n d a r d w h i c h has a lower shock i m p e d a n c e t h a n t h a t of t h e s a m p l e (so  2(pUs)2  is g r e a t e r t h a n {pUs)?  -f (pUs)i  i n e q u a t i o n (2.11).)  usthat  T h e t r a n s m i t t e d shock  p r e s s u r e can therefore be g r e a t l y i n c r e a s e d u s i n g t h i s t e c h n i q u e .  T h e v a l i d i t y of s u c h  p r e s s u r e e n h a n c e m e n t was first, d e m o n s t r a t e d i n l a s e r - d r i v e n s h o c k s b y Vesser et al.[30] w i t h a l u m i n u m - g o l d t a r g e t s u s i n g 1.06 pm laser i r r a d i a t i o n . S u b s e q u e n t  studies i n c l u d e  those of H o l m e s et. a,l.[53] for a l u m i n u m - c o p p e r t a r g e t s i r r a d i a t e d w i t h 1.06 pm laser l i g h t a n d C o t t e t et al.[25] for 0.26 pin laser r a d i a t i o n o n a l u m i n u m - g o l d t a r g e t s . T h e a m o u n t of p r e s s u r e enhancement, can b e e a s i l y c a l c u l a t e d f r o m t h e H u g o n i o t of t h e s t a n d a r d by u t i l i z i n g the m i r r o r - r e f l e c t i o n m e t h o d , a n d is g r a p h i c a l l y i l l u s t r a t e d i n F i g u r e 2.6. T h e i n c o m i n g shock first p r o d u c e s a n i n t e r m e d i a t e s t a t e at t h e p o i n t (Up0,  Po)  Chapter  2.  Theory  of Laser-driven  Shocks  19  Principal Hugoniot of the Standard  Intermediate State of Standard  Reflected Hugoniot of the Standard  u  p  F i g u r e 2.6: T h e c a l c u l a t i o n of pressure i n t h e s a m p l e u s i n g t h e m i r r o r - r e f l e c t i o n m e t h o d . T h e slope of t h e s t r a i g h t l i n e i n v o l v e s t h e m e a s u r e m e n t of t h e s h o c k v e l o c i t y Us i n t h e sample.  Chapter  2. . Theory  in the standard.  of Laser-driven  Shocks  20  T h e reflected shock t h e n takes the s t a n d a r d f r o m t h e n e w i n i t i a l state  (UPO,PQ) t o a f i n a l s t a t e o n the reflected H u g o n i o t .  T h i s reflected H u g o n i o t can be  c o n s t r u c t e d on t h e p r e s s u r e - p a r t i c l e v e l o c i t y p l a n e f r o m a m i r r o r r e f l e c t i o n of t h e p r i n c i p a l H u g o n i o t of t h e s t a n d a r d a b o u t a v e r t i c a l line t h r o u g h t h e p o i n t ( Up 0 , P 0 ) [ 2 5 , 48], T h e p o i n t of i n t e r s e c t i o n of t h e reflected H u g o n i o t of t h e s t a n d a r d a n d t h e s t r a i g h t line w i t h slope polls  ( w h e r e pQ is t h e i n i t i a l d e n s i t y of t h e s a m p l e as g o v e r n e d b y e q u a t i o n (2.8))  a s s u m i n g t h a t U$ is m e a s u r e d for t h e s a m p l e , c o n s t i t u t e s t h e state r e a c h e d i n t h e sample. T h e m e t h o d so d e s c r i b e d is a n a p p r o x i m a t e one since the reflected shock i n t h e s t a n d a r d o r i g i n a t e s f r o m t h e p o i n t {Upo,Po)  r a t h e r t h a n f r o m n o r m a l c o n d i t i o n s . S u c h re-shocked  states are m o r e i s e n t r o p i c t h a n the states a t t a i n e d i n a single s h o c k [ 3 , 48, 54]. H o w e v e r , t h e difference is n e g l i g i b l y s m a l l for l o w values of P0 ( < several M b a r [ 1 7 ] ) . O f course, t h e m e t h o d b e c o m e s e x a c t if one takes t h e reflected H u g o n i o t t o b e t h a t w h i c h originates f r o m t h e i n t e r m e d i a t e p o i n t ( Up0, P0) b u t this i n v o l v e s the k n o w l e d g e of a n o t h e r H u g o n i o t curve. A l t e r n a t i v e l y , one can assume k n o w l e d g e of t h e p r i n c i p a l H u g o n i o t of t h e m a t e r i a l a n d uses t h e e x p e r i m e n t for v e r i f i c a t i o n .  U n d e r such a s s u m p t i o n ,  sample  the  final  s t a t e a c h i e v e d i n t h e s a m p l e is g i v e n b y t h e i n t e r s e c t i o n of t h e reflected H u g o n i o t of t h e s t a n d a r d a n d t h e p r i n c i p a l H u g o n i o t of the s a m p l e as i n d i c a t e d i n F i g u r e 2.7. i n t e r s e c t i o n p o i n t t h e n gives the p r e s s u r e Pf a n d p a r t i c l e v e l o c i t y Upj w h i c h can b e u s e d t o c o r r e l a t e w i t h e x p e r i m e n t s .  The  i n t h e sample,  F o r e x a m p l e , t h e shock speed i n t h e  s a m p l e can be c a l c u l a t e d u s i n g a r e l a t i o n s i m i l a r to E q . (2.9), a n d c a n b e c o m p a r e d w i t h measurements.  2.3.2  Reduction of Radiative Preheat  T h e i m p e d a n c e - m i s m a t c h m e t h o d is d o u b l y a t t r a c t i v e i n E O S studies of h i g h - Z m a t e r i a l s since it reduces t h e u n d e s i r a b l e effect of r a d i a t i v e p r e h e a t i n g a h e a d of the shock  Chapter  2.  Theory  of Laser-driven  P  / /  \ / Pi  •  Shocks  21  Principal Hugoniot o f the Sample  \t  Final State of Sample  '  \  1  / >^  /  Principal Hugoniot o f the Standard  Reflected Hugoniot o f the Standard  F i g u r e 2.7: T h e m i r r o r - r e f l e c t i o n m e t h o d w i t h t h e s a m p l e H u g o n i o t k n o w n , e l i m i n a t i n g t h e need t o m e a s u r e Us-  Chapter  front[55].  2.  Theory  of Laser-driven  Shocks  A s is w e l l d e m o n s t r a t e d [ 2 9 ,  22  56, 57, 58], t h e c o n v e r s i o n f r o m laser l i g h t to  X - r a d i a t i o n arises due to t h e v a r i o u s e l e c t r o n i c d e - e x c i t a t i o n a n d r e c o m b i n a t i o n i n a part i a l l y i o n i z e d p l a s m a . T h e r a d i a t i o n m a y b e due t o free-free ( b r e m s s t r a h l u n g ) , or b o u n d - b o u n d emissions[59].  free-bound  T h e first t w o processes l e a d to c o n t i n u u m r a d i a t i o n w h i l e  t h e last process t o l i n e r a d i a t i o n .  In g e n e r a l , f r e e - b o u n d a n d b o u n d - b o u n d r a d i a t i o n  d o m i n a t e over free-free r a d i a t i o n .  T h a t t h e c o r o n a a n d c o n d u c t i o n zone are n o t i n a  f u l l y i o n i z e d state is e s p e c i a l l y t r u e as t h e a t o m i c n u m b e r of t h e t a r g e t increases a n d these regions b e c o m e a s t r o n g source of X - r a y . T h e energetic, c o m p o n e n t s of these X - r a y s ( t h o s e w h o s e energies exceed ~ 1 k e V ) , w i t h c o r r e s p o n d i n g l o n g m e a n free, p a t h s , w i l l pass u n i m p e d e d t h r o u g h t h e c o r o n a a n d a b l a t i o n zone w h i c h are o p t i c a l l y t h i n (i.e.  transpar-  ent t o t h i s r a d i a t i o n ) a n d d e p o s i t t h e i r energy i n t h e m a t e r i a l a h e a d of t h e shock front. S u c h p r e h e a t of t h e u n s h o c k e d region of t h e target m a y affect t h e shock process a n d obscure the study of shock-induced phenomena.  T h i s d i f f i c u l t y c a n be c i r c u m v e n t e d i n  an i m p e d a n c e - m i s m a t c h e d t a r g e t w h e r e t h e shock is p r o d u c e d by l a s e r - d r i v e n a b l a t i o n i n t h e l o w - Z materia] before it p r o p a g a t e s i n t o the h i g h - Z m a t e r i a l of i n t e r e s t . T h e laser is t h e n incident, on a l o w - Z m a t e r i a l a n d the r e s u l t i n g p l a s m a is m o r e l i k e l y to be f u l l y ioni z e d , h e n c e r e d u c i n g t h e g e n e r a t i o n of X - r a y . M o r e o v e r , it takes a lower laser irradia.nce to a c h i e v e a given shock p r e s s u r e i n t h e h i g h - Z m a t e r i a l in an  impeda,nce-mismatched  target, t h a n t h a t is r e q u i r e d b y d i r e c t l y p r o d u c i n g t h e shock i n the h i g h - Z m a t e r i a l , since t h e i m p e d a n c e m i s m a t c h t e c h n i q u e y i e l d s t h e benefit of p r e s s u r e e n h a n c e m e n t  at t h e  i n t e r f a c e . A lower laser i n t e n s i t y can f u r t h e r d i m i n i s h t h e p r o d u c t i o n of h a r m f u l X - r a y s .  Chapter  2.4  2.  Theory  of Laser-driven  Shocks  23  E q u a t i o n of S t a t e An  e q u a t i o n of s t a t e ( E O S ) is a r e l a t i o n g o v e r n i n g t h e t h e r m o d y n a m i c a l p r o p e r t i e s  (pressure, temperature,  d e n s i t y , etc.)  of a s u b s t a n c e i n e q u i l i b r i u m . Its i m p o r t a n c e is  f u n d a m e n t a l since it p r o v i d e s t h e i n f o r m a t i o n i n p r e d i c t i n g s u c h d i v e r s e p h e n o m e n a  as  p h a s e t r a n s i t i o n s or m a t e r i a l responses (such as c o m p r e s i b i l i t y or t h e r m a l c o n d u c t i v i t y ) under various e x t e r n a l conditions.  G o o d r e v i e w a r t i c l e s of t h e E O S at h i g h p r e s s u r e  c a n be f o u n d i n references [47] a n d [48]. p r o c e d u r e s used i n t w o different E O S  2.4.1  H e r e we w i l l b r i e f l y d e s c r i b e t h e c a l c u l a t i o n a l  models.  S E S A M E E q u a t i o n of S t a t e  T h e S E S A M E E O S l i b r a r y f r o m t h e L o s A l a m o s N a t i o n a l L a b o r a t o r y [ 5 0 ] is an ext e n s i v e c o m p i l a t i o n of E O S p r o p e r t i e s (specific i n t e r n a l energy, p r e s s u r e , average charge state.) a n d o t h e r a t o m i c d a t a (such as t h e r m a l a n d e l e c t r i c a l c o n d u c t i v i t y , o p a c i t y ) of m a n y different m a t e r i a l s over a w i d e r a n g e of d e n s i t y a n d t e m p e r a t u r e .  It has  been  w i d e l y used to p r o v i d e E O S da.ta for s i m u l a t i o n s i n m a n y l a s e r - d r i v e n s h o c k studies (see, e.g.  [25, 60, 61]). W e w i l l d e s c r i b e s o m e of t h e t h e o r e t i c a l m e t h o d s i n S E S A M E as t h e y  a p p l y to g o l d a n d a l u m i n u m . T h e S E S A M E c a l c u l a t i o n s of t h e t o t a l i n t e r n a l energy E of g o l d are p a r t i t i o n e d i n t o three  c.omponents[62],  E=EC  + Ej + Ee  (2.12)  w h e r e t h e t h r e e t e r m s d e s c r i b e the c o l d ( O K ) c r y s t a l l i n e s o l i d (i.e. t h e t h e r m o d y n a m i c states of t h e s o l i d is on t h e zero degree i s o t h e r m ) , t h e i o n i c t h e r m a l v i b r a t i o n , a n d t h e e l e c t r o n i c t h e r m a l c o n t r i b u t i o n r e s p e c t i v e l y . T h e c o l d c u r v e c a l c u l a t i o n s are based on a n e m p i r i c a l m o d i f i e d M o r s e p o t e n t i a l m o d e l [ 6 3 ] , w h o s e p r e s s u r e t e r m is of t h e f o r m  P = a 7 7 ( r / e ^ " - e h* v) 2/3  (2.13)  Chapter  2.  Theory  "where ?/ = pjp0,  of Laser-driven  24  Shocks  v = 1 — 7 / / , ba — 3 -j- bT — 3 . B , B o is the b u l k m o d u l u s at O K , a n d a, 6 -1  3  0  r  are t w o p a r a m e t e r s t o b e fitted by m a t c h i n g o n to the c o l d c u r v e i n t h e T F D ( T h o m a s F e r m i - D i r a c ) model[64] at h i g h pressures.  T h e t h e r m a l i o n i c E O S m o d e l is b a s e d on  an i n t e r p o l a t i o n between the low temperature  (<1  e V ) D e b y e model[65] a n d the h i g h  t e m p e r a t u r e (>1 e V ) C o w a n model[65]. L a s t l y , t h e e l e c t r o n i c c o n t r i b u t i o n is also based o n the T F D m o d e l . T h e S E S A M E E O S c a l c u l a t i o n s for a l u m i n u m also a c c o u n t for its m e l t i n g t r a n s i t i o n at h i g h p r e s s u r e . In f a c t , seven different t h e o r e t i c a l m o d e l s are used to c o m p l e t e the E O S over a w i d e r a n g e of d e n s i t y a n d t e m p e r a t u r e . F i g u r e 2.8 shows t h e d e n s i t y - t e m p e r a t u r e regions w h e r e each m o d e l is a p p l i e d a n d e x p e c t e d to be v a l i d . T h e seven regions are t h e n j o i n e d s m o o t h l y by i n t e r p o l a t i o n m e t h o d s ( s h a d e d areas i n F i g u r e 2.8). T h e i n d i v i d u a l m o d e l s e m p l o y e d i n t h e v a r i o u s regions are: 1. A C T E X [ 6 6 ] for a s t r o n g l y c o u p l e d p l a s m a ( i n w h i c h t h e p o t e n t i a l energy o f the p l a s m a is m u c h l a r g e r t h a n its k i n e t i c e n e r g y ) . It is b a s e d on a m a n y - b o d y p e r t u r bation expansion. 2. F o r t h e low d e n s i t y low t e m p e r a t u r e case, Y o u n g ' s soft sphere m o d e l for metals[67] is u s e d .  T h i s is a s e m i - e m p i r i c a l m o d e l w h e r e free p a r a m e t e r s are a d j u s t e d  to  reproduce experimental isobaric data. 3. S a n a ' s i o n i z a t i o n model[6S]  is used i n t h e low d e n s i t y i n t e r m e d i a t e  temperature  region. 4. G R A Y [ 6 9 ] is a s e m i - e m p i r i c a l m o d e l t o t r e a t t h e r e g i o n b e t w e e n l i q u i d to t w o - f o l d s o l i d d e n s i t y at t e m p e r a t u n r e s  under 1 e V . T h e solid E O S utilizes the Dugale-  M a c D o n a l d form[70] of t h e G r i i n e i s e n t h e o r y . T h e m e l t i n g t r a n s i t i o n is e s t i m a t e d a c c o r d i n g to t h e L i n d e m a n n law[71], a n d e x p e r i m e n t a l d a t a a l o n g t h e H u g o n i o t  Chapter  2.  Theory  of Laser-driven  Shocks  25  F i g u r e 2.8: T h e d e n s i t y - t e m p e r a t u r e regimes of t h e seven E O S m o d e l s of a l u m i n u m used in  SESAME  Chapter  2.  Theory  of Laser-driven  Shocks  26  are a n a l y t i c a l l y f i t t e d . W e e m p h a s i z e t h a t i t is i n t h i s r e g i o n w h e r e t h e m e l t i n g of a l u m i n u m is t a k e n i n t o c o n s i d e r a t i o n . 5. T h e zero-degree i s o t h e r m at h i g h density is c o m p u t e d b y the self-consistent  aug-  m e n t e d p l a n e wave ( A P W ) m e t h o d [ 7 2 ] , 6. T F N U C [ 7 3 , 75] is u s e d i n t h e n o n - z e r o t e m p e r a t u r e s  a n d h i g h d e n s i t y case.  It  a d d s t o t h e c o l d s o l i d p a r t ( r e g i o n 5) an e l e c t r o n i c t h e r m a l c o n t r i b u t i o n u s i n g t h e T h o m a s - F e r m i - K i r z h n i t s t h e o r y [73, 74] a n d a n i o n i c t h e r m a l c o n t r i b u t i o n u s i n g a G r i i n e i s e n - l i k e t h e o r y at l o w t e m p e r a t u r e s [ 7 5 ] a n d a o n e - c o m p o n e n t p l a s m a t h e o r y at h i g h t e m p e r a t u r e s [7.5]. 7. T h e E O S for t h e r e m a i n i n g dense, p a r t i a l l y - i o n i z e d l i q u i d is c a l c u l a t e d b y a v a r i a t i o n a l l i q u i d m e t a l p e r t u r b a t i o n t h e o r y of Ross[76].  2.4.2  N e w E O S C a l c u l a t i o n s for G o l d  N e x t we discuss o u r n e w c a l c u l a t i o n s of t h e g o l d E O S . T h i s work is p e r f o r m e d by D r . B . K . G o d w a l (on leave f r o m t h e B h a b h a A t o m i c R e s e a r c h C e n t e r , I n d i a ) . T h e new E O S m o d e l is d e v e l o p e d f r o m b o t h s o l i d a n d l i q u i d s t a t e theories. T h e s o l i d p h a s e H u g o n i o t is s i m i l a r l y c o m p u t e d a c c o r d i n g to t h e model[62] i n w h i c h t h e t o t a l i n t e r n a l energy E is g i v e n b y eq. (2.12) a n d t h e t o t a l p r e s s u r e P of t h e m a t e r i a l at a g i v e n v o l u m e V  and  t e m p e r a t u r e T is  P = - P , + -yEi/V + i EJV  (2.14)  e  w i t h t h e 7's b e i n g t h e G r i i n e i s e n p a r a m e t e r s .  F o r the' e v a l u a t i o n s of E  c  and P c on the  c o l d c u r v e (OK i s o t h e r m ) as a f u n c t i o n of V , a first p r i n c i p l e energy b a n d m e t h o d , n a m e l y , the l i n e a r i z e d - m u f f m - t i n - o r b i t a l ( L M T O ) m e t h o d [ 7 7 ] , is used. a self-consistent  c a l c u l a t i o n c a p a b l e o f e v a l u a t i n g t h e g r o u n d state p r o p e r t i e s ,  structure T h i s is namely,  Chapter  2.  Theory  of Laser-driven  Shocks  27  t h e e n e r g y eigenvalue a n d w a v e f u n c t i o n of a n o r d e r e d c r y s t a l l i n e m e t a l (a m a n y b o d y s y s t e m ) b y s o l v i n g t h e effective o n e - e l e c t r o n S c h r o d i n g e r e q u a t i o n . In c o m p a r i s o n w i t h t h e m o r e s o p h i s t i c a t e d e l e c t r o n b a n d m e t h o d s u c h as t h e self-consistent a u g m e n t e d p l a n e w a v e ( A P W ) m e t h o d , t h e L M T O m e t h o d is at least a h u n d r e d t i m e s faster w i t h l i t t l e loss of a c c u r a c y . It is therefore a d o p t e d here to c a l c u l a t e t h e zero-degree i s o t h e r m . T h e L M T O m e t h o d is f o r m u l a t e d w i t h i n t h e f r a m e w o r k of t h e H o h e n b e r g - K o h n S h a m ( H K S ) l o c a l d e n s i t y f o r m a l i s m [ 7 8 ] , w h i c h p r o v i d e s t h e t h e o r e t i c a l basis for u s i n g a. v a r i a t i o n a l a p p r o a c h t o e v a l u a t e the g r o u n d s t a t e e n e r g y i n t h e c o n t e x t of a density f u n c t i o n a l theory. T h e m u f f i n - t i n o r b i t a l s ( w h i c h are s p e c i a l i z e d f o r m s of t h e basis wavef u n c t i o n s ) are c o n s t r u c t e d u s i n g t h e v o n B a r t h - H e d i n e x c h a n g e c o r r e l a t i o n potential[79] w i t h t h e g r o u n d s t a t e of g o l d a s s u m e d t o b e i n a fee (face center c u b i c ) s t r u c t u r e a n d 5 d 1 0 6 s 1 e l e c t r o n i c c o n f i g u r a t i o n . T h e energy a n d p r e s s u r e c o n t r i b u t i o n s f r o m i n d i v i d u a l a n g u l a r m o m e n t u m states u p to 1 = 3 (i.e. s,p,d,f s t a t e s ) i n t h e f r o z e n - c o r e a p p r o x i m a t i o n (i.e. a s t a t i c l a t t i c e w i t h i m m o b i l e a t o m s ) are i n c l u d e d . T h e c o m p u t a t i o n s also i n c l u d e c o r r e c t i o n s due t o t h e i n t e r c e l l u l a r C o u l o m b i n t e r a c t i o n b a s e d o n t h e m o d e l of G l o t z e l a n d M c M . a h a n [ 8 0 ] as w e l l as c o r r e c t i o n s d u e to l a t t i c e v i b r a t i o n s (i.e. core is n o t frozen b u t c a n b e c o m e a valence b a n d state) u s i n g a p r o c e d u r e by S i k k a a n d G o d w a l [ 8 l ] . S e c o n d l y , we have used t h e c l a s s i c a l D u l o n g a n d P e t i t law for t h e l a t t i c e t h e r m a l energy : E-t = 3fcgT per a t o m , w h e r e kp is B o l t z m a n n ' s c o n s t a n t . p r e s s u r e is ~yEJV.  T h e corresponding  F i n a l l y , t h e e l e c t r o n i c t h e r m a l energy is d e r i v e d u s i n g a free e l e c t r o n  gas m o d e l (see, e.g.  Ee  [47]):  cient a n d is equal to \>ir 2k 2BN  =  \(3T 2  w h e r e j3 is t h e e l e c t r o n i c specific heat coeffi-  (e f) w i t h N{ej)  b e i n g t h e d e n s i t y of states at t h e F e r m i  l e v e l . T h e G r i i n e i s e n p a r a m e t e r s used a b o v e are c a l c u l a t e d w i t h D u g a l e a n d M a c D o n a l d ' s e x p r e s s i o n [70],  V d 2(PcV 2' 3)/dV 2 7  (  V  )  =  ~  i d{PcVW)/dV  1 " 3  ( 2  -  1 5 )  Chapter  2.  Theory  of Laser-driven  w h e r e t h e c o l d p r e s s u r e P (V)  is o b t a i n e d f r o m p r e v i o u s r e s u l t s of t h e O K i s o t h e r m  C  calculations using the L M T O  28  Shocks  method.  O n t h e o t h e r h a n d , t h e l i q u i d p h a s e is m o d e l l e d b y t h e c o r r e c t e d r i g i d spheres ( O R I S ) m e t h o d [ 8 2 ] . T h i s is a first o r d e r p e r t u r b a t i o n m e t h o d for c a l c u l a t i n g t h e E O S of a  fluid  f r o m t h e zero-degree i s o t h e r m of t h e c o r r e s p o n d i n g s o l i d . L i k e m a n y o t h e r p e r t u r b a t i o n t h e o r i e s , t h e b a s i c reference s y s t e m in t h e O R I S m e t h o d is t h a t o f a h a r d sphere f l u i d ( a h a r d s p h e r e fluid is one w i t h " b r i c k - w a l l " p a i r p o t e n t i a l , i.e. t h e p o t e n t i a l U(r) i f r < <j0 and 0 o t h e r w i s e , w h e r e a0  = a0(p,T)  — +oo  is t h e h a r d s p h e r e d i a m e t e r ) whose p r o p -  erties are k n o w n . Y e t , t h e O R I S m e t h o d is d i s t i n g u i s h e d b y t h e fact t h a t i t s first order p e r t u r b a t i o n t e r m is a n average over t h e O K - i s o t h e r m r a t h e r t h a n t h e p a i r i n t e r a c t i o n pot e n t i a l , w h i c h is m o r e d i f f i c u l t to a s c e r t a i n . T h e r e f o r e , t h e c a l c u l a t i o n of t h e zero-degree i s o t h e r m u s i n g t h e L M T O m e t h o d i n t h e s o l i d p a r t c a n be e m p l o y e d c o n v e n i e n t l y i n t h e l i q u i d c o m p u t a t i o n . B r i e f l y s p e a k i n g , t h e m e t h o d e v a l u a t e s t h e H e l m h o l t z free energy F of t h e l i q u i d w i t h F = F0 + A'<<£>o  (2.16)  w h e r e F0 is t h e free e n e r g y of t h e h a r d sphere f l u i d , N t h e t o t a l n u m b e r of p a r t i c l e s , a n d  < <p > t h e p o t e n t i a l e n e r g y of a p a r t i c l e i n t h e field of its n e i g h b o r s , a v e r a g e d over a l l configurations.  T h e c a l c u l a t i o n s of t h e t h e r m o d y n a m i c p r o p e r t i e s t h e n p r o c e e d i n t w o  steps. F i r s t of a l l , t h e free energy a n d c o r r e s p o n d i n g pressure o f a h a r d s p h e r e fluid are g i v e n by[82] ( - £ - ) o = -31n(l - - ) + NkT rlc  E ^  A „ ( ^ f r)c  (2.17)  f  (2.18)  and ( w h e r e r\ = TTNO~Q/6V p a c k e d spheres.  ^  ^  I  f  -  ^  + E  ^  is t h e p a c k i n g f r a c t i o n a n d 7] c (=0.6452) t h a t f o r r a n d o m l y close-  T h e coefficients A ' are o b t a i n e d f r o m a v i r i a l e x p a n s i o n a n d are also K  Chapter  2.  Theory  of La.ser-driven  Shocks  29  g i v e n i n [82]. T h e s e c o n d step is t o c a l c u l a t e <</>>0, w h i c h is t h e average value of the p o t e n t i a l i n t h e h a r d sphere s y s t e m .  W e n o t e t h a t w i t h i n t h e C R I S m o d e l , each p a r t i c l e is l o c a t e d  i n a s p h e r i c a l cell of r a d i u s R f o r m e d b y its n e i g h b o r s . If one f u r t h e r assumes t h a t o n l y t h e c o n t r i b u t i o n s f r o m t h e nearest n e i g h b o r s are significant, t h e n < (f)>o is r e l a t e d t o the O K - i s o t h e r m energy £"c[82] v i a  < & >0=  It  f  m  3 J<? 3 J (7r,  E (NR 3/V2)g (R)R dR  (2.19)  2  c  s0  0  where R ,  t h e cutoff r a d i u s a n d g o{P),  m  s  t h e nearest n e i g h b o r c o n t r i b u t i o n to the r a d i a l  d i s t r i b u t i o n f u n c t i o n R D F of t h e h a r d sphere f l u i d ( R D F is a m e a s u r e of the n e i g h b o r s ' d i s t r i b u t i o n a n d is k n o w n ) are a l l f i t t e d a n a l y t i c a l l y in reference  [82].  The  resultant  i n t e r n a l e n e r g y a n d p r e s s u r e are a c c o r d i n g l y ,  E = F - T ( ^ )  (2.20)  and  8F  L a s t l y , t h e m e l t i n g c u r v e P m ( T m ) is c a l c u l a t e d by s t i p u l a t i n g t h a t m e l t i n g o c c u r s at pressures a n d t e m p e r a t u r e s G solid P  m  • Tm ) = Gij id(P ,T ). gu  m  m  w h e r e t h e t w o p h a s e s have e q u a l G i b b s free energies,  i.e.  R e s u l t s of t h i s new e q u a t i o n of s t a t e c a l c u l a t i o n are  p l o t t e d in F i g u r e 2.9, w i t h t h e c o r r e s p o n d i n g S E S A M E d a t a i n c l u d e d for c o m p a r i s o n . T h e c a l c u l a t e d s o l i d H u g o n i o t agrees well w i t h t h a t in S E S A M E - , b u t t h e new E O S pred i c t s t h a t m e l t i n g of g o l d w i l l b e g i n at ~ 1 . 3 T h e r e f o r e i t is e x p e c t e d temperature  M b a r a n d be c o m p l e t e d at —2.2 M b a r .  t h a t u n d e r a shock p r e s s u r e of over 2.2 M b a r , t h e pressure-  p a t h w i l l be a l o n g t h e l i q u i d H u g o n i o t as i l l u s t r a t e d i n F i g u r e 2.9.  Fur-  t h e r m o r e , i t can be seen t h a t for g o l d at h i g h p r e s s u r e , say 7 M b a r , t h e solid and l i q u i d  Chapter  2.  Theory  of Laser-driven  0  1  30  Shocks  2  3  4  5  6  7  Pressure (Mbar)  F i g u r e 2.9:  T h e s o l i d (solid l i n e ) a n d l i q u i d ( d a s h ) H u g o n i o t of g o l d as c a l c u l a t e d i n  § 2 . 4 . 2 , t h a t i n S E S A M E ( d o t - d a s h ) is also i n c l u d e d ; also s h o w n is t h e m e l t i n g c u r v e (dot-dot-dot-dash)  Chapter  2.  Theory  of Laser-driven  Shocks  31  p h a s e s are r e s p e c t i v e l y at a t e m p e r a t u r e of 25600 K (2.20 e V j a n d 22400 K (1.93 e V ) , a difference t h a t s h o u l d be d i s c e r n i b l e i n e x p e r i m e n t s .  2.5  Computer  Simulations  T h e g e n e r a l l y t i m e d e p e n d e n t n a t u r e of a l a s e r - d r i v e n shock wa.ve r e n d e r s t h e steady s t a t e a s s u m p t i o n of § 2 . 2 u n s o u n d . M o r e o v e r , t h e m a n y p h y s i c a l processes i n v o l v e d i n t h e i n t e r a c t i o n of a. laser a n d a p l a s m a , a n d the fact t h a t t h e g o v e r n i n g p a r t i a l differential equations  are c o u p l e d a n d n o n l i n e a r m a k e a n a l y t i c a l c a l c u l a t i o n s e x t r e m e l y r e s t r i c t i v e  a n d often u n r e a l i s t i c . C o m p u t e r s i m u l a t i o n s offer a v i a b l e a l t e r n a t i v e i n p r o v i d i n g theo r e t i c a l s u p p o r t for e x p e r i m e n t s .  T h r e e different codes, S H Y L A C , H Y R A D , a n d P U C  are used i n o u r studies. B o t h S H Y L A C and H Y R A D strive to model the hydrodyna.mic and t h e r m o d y n a m i c e v o l u t i o n s of a m a t e r i a l u n d e r shock c o n d i t i o n , t h o u g h t h e y differ by t h e i r l e v e l of sophist i c a t i o n . B r i e f l y , S H Y L A C is a p u r e l y f l u i d c o d e , w h i l e H Y R A D incoporat.es  laser-matter  i n t e r a c t i o n s . B o t h are o n e - d i m e n s i o n a l , L a g r a n g i a . n codes. ( A L a g r a n g i a n s y s t e m is one i n w h i c h t h e f l u i d elements or cells are a s s i g n e d c o o r d i n a t e s w h i c h do not v a r y w i t h t i m e . In a d i t i o n , each cell m o v e s w i t h its l o c a l f l u i d ( p a r t i c l e ) v e l o c i t y , so t h a t t h e mass in each cell is c o n s e r v e d .  F o r t h i s r e a s o n , a L a g r a n g i a n s y s t e m is s o m e t i m e s c a l l e d a c o m o v i n g  s y s t e m . ) E s s e n t i a l l y , t h e t w o codes i n t e g r a t e t h e three c o n s e r v a t i o n e q u a t i o n s of m a s s , m o m e n t u m , a n d t o t a l energy, as well as the r a d i a t i o n t r a n s p o r t e q u a t i o n (in H Y R A D o n l y ) , as t h e y a p p l y t o e i t h e r p a r t i c l e s (ions or e l e c t r o n s ) or r a d i a t i o n field i n our onedimensional planar geometry.  O n the o t h e r h a n d , t h e codes differ by t h e degree as to h o w  Chapter  2.  Theory  of Laser-driven  32  Shocks  these e q u a t i o n s axe s i m p l i f i e d a n d t h e v a r i o u s t e r m s i m p l e m e n t e d .  F o r instance, both  t r e a t t h e p l a s m a as a s i n g l e , i n v i s c i d a n d c o m p r e s s i b l e fluid of i n t e r p e n e t r a t i n g ions a n d e l e c t r o n s , b u t S H Y L A C is o n e - t e m p e r a t u r e (i.e. it assumes t h e s a m e t e m p e r a t u r e for the i o n s a n d e l e c t r o n s ) w h e r e a s H Y R A D , i n its m o r e c o m p l e t e d e s c r i p t i o n , assigns different temperatures  t o t h e i o n s a n d e l e c t r o n s i n v i e w of t h e finite e n e r g y e q u i p a r t i t i o n t i m e  b e t w e e n i o n s a n d electrons[83] d u e to t h e k n o w n d o m i n a n t , inverse b r e m s s t r a h l u n g abs o r p t i o n m e c h a n i s m w h e r e b y t h e laser e n e r g y is first d e p o s i t e d i n t h e e l e c t r o n s a n d later t r a n s f e r r e d to t h e ions (as d i s c u s s e d b r i e f l y i n § 2 . 1 . 1 ) . In g e n e r a l S H Y ' L A C is s i m p l e r a n d t h u s r e l a t i v e l y fast, w h i l e H Y R A D is m o r e c o m p l e x b u t m o r e c o m p l e t e i n its t r e a t m e n t of l a s e r - p l a s m a i n t e r a c t i o n . B o t h S H Y L A C  a n d H Y R A D w i l l be used i n c h a p t e r . 4 t o  s i m u l a t e t h e shock b e h a v i o r i n single a n d m u l t i - l a y e r e d t a r g e t s .  2.5.1  SHYLAC  Code  S H Y ' L A C is d e v e l o p e d b y C o t t e t a n d M a r t y [ 8 4 ] at U n i v e r s i t e de P o i t i e r s , F r a n c e . In S H Y L A C , t h e l a s e r - i n d u c e d a b l a t i o n pressure is s u b s t i t u t e d b y a n e q u i v a l e n t  pressure  p u l s e . T h i s is d o n e a c c o r d i n g to t h e e x p e r i m e n t a l s c a l i n g l a w b e t w e e n t h e laser i n t e n s i t y a n d t h e a b l a t i o n pressure[85]  Pabl  ~  1.4 ( y j ^ . )  [Mbar]  a 8  (2.22)  w h e r e §A ( i n W / c m 2 ) is t h e a b s o r b e d laser i r r a d i a n c e averaged over an area e q u a l to t h a t of t h e s h o c k b r e a k o u t r e g i o n , t h a t is, t h e a r e a of the s h o c k f r o n t . F u r t h e r m o r e , this c o d e i n c o p o r a t e s an a r t i f i c a l v i s c o s i t y , as w e l l as an a n a l y t i c a l ( M i e - G r i i n e i s e n ) e q u a t i o n of state.  A l t h o u g h t h e a s s u m p t i o n of an i n v i s i d  fluid  (i.e. no v i s c o u s stress) is u s u a l l y  v a l i d , i t has b e e n shown[86] t h a t t h e absence of v i s c o s i t y i n a h y d r o d y n a m i c t r e a t m e n t of s h o c k waves r e n d e r s t h e pressure a n d d e n s i t y d i s c o n t i n u o u s at t h e s h o c k f r o n t . T h i s u n p h y s i c a l s i t u a t i o n w i l l p r o d u c e s t r o n g o s c i l l a t i o n s in t h e d e n s i t y or p r e s s u r e profiles[87]  Chapter  2.  Theory  of Laser-driven  Shocks  33  (i.e. p a r t i c l e s t e n d i n g t o leave t h e i r cell) a n d thus be n u m e r i c a l l y u n s t a b l e . A f i c t i t i o u s t e r m - t h e a r t i f i c i a l viscosity[88] - is therefore used t o i n t r o d u c e e x p l i c i t l y some a m o u n t of d i s s i p a t i o n a r o u n d t h e shock front i n o r d e r t o " s m e a r o u t " t h e s h o c k f r o n t , t h e r e b y l i m i t i n g its m a x i m u m steepness. T h e M i e - G r i i n e i s e n E O S c a l c u l a t i o n , of t h e f o r m  P = ~E  (2.23)  ( w h e r e 7 is t h e G r i i n e i s e n p a r a m e t e r a n d V t h e specific v o l u m e ) has b e e n best fitted w i t h e x i s t i n g h i g h - p r e s s u r e H u g o n i o t d a t a to m a k e i t m o r e r e a l i s t i c . T h e s e  approximations  - t h e r e d u c t i o n of t h e c o m p l i c a t e d l a s e r - m a t t e r i n t e r a c t i o n s i n t o a pressure pulse, the a s s u m p t i o n t h a t t h e s t a t e of t h e m a t e r i a l b e h i n d t h e shock lies on t h e H u g o n i o t , together w i t h t h e neglect of r a d i a t i o n t r a n s p o r t - m a k e S H Y L A C a p u r e l y fluid c o d e a n d therefore m u c h faster a n d less c o s t l y to r u n .  2.5.2  HYRAD  Code  H Y ' R A D ( H Y d r o d y n a m i c - R A D i a t i o n c o d e ) is d e v e l o p e d at U B C . D e t a i l s of the code c a n be f o u n d i n t h e theses of Celliers[89] a n d D a Silva[90]. fied version of t h e h y d r o d y n a m i c c o d e M E D U S A [ 9 1 ] .  It is an e x t e n s i v e l y m o d i -  L i k e S H Y L A C , H Y R A D is one-  d i m e n s i o n a l , p l a n a r , a n d L a g r a n g i a n i n t r e a t m e n t . It m o d e l s t h e d y n a m i c s of laser-target i n t e r a c t i o n s a n d solves for t h e h y d r o d y n a m i c s , i o n i z a t i o n state, as w e l l as r a d i a t i o n transp o r t i n a self-consistent m a n n e r . T h e h y d r o d y n a m i c s is governed b y t h e u s u a l set of coup l e d d i f f e r e n t i a l e q u a t i o n s r e p r e s e n t i n g t h e c o n s e r v a t i o n of m a s s , m o m e n t u m , a n d energy of t h e ions a n d e l e c t r o n s i n o n e d i m e n s i o n :  Chapter  2.  Theory  of Laser-driven  Shocks  De,  - m = where  34  _ dV  p  - m  +  Q  '  ( 2  '  2 7 )  D j Dt = d j dt -f ud/dx is t h e L a g r a n g i a n t i m e d e r i v a t i v e , P = P + P t h e t o t a l t  %  t  p r e s s u r e , V — l/p t h e specific v o l u m e , e t h e specific i n t e r n a l energy, a n d Q t h e e n e r g y source t e r m d u e to v a r i o u s energy d e p o s i t i o n a n d d i s s i p a t i o n processes. F o r i n s t a n c e , t h e e l e c t r o n heat f l u x t e r m O  e  i n c l u d e s c o n t r i b u t i o n s f r o m S p i t z e r heat c o n d u c t i o n (see E q .  ( 2 . 4 ) ) , e l e c t r o n - i o n energy exchange (not present i n one t e m p e r a t u r e d e s c r i p t i o n ) , laser energy d e p o s i t i o n , a n d r a d i a t i v e energy i n p u t . E q u a t i o n s (2.24) t o (2.27) give t h e t e m p o r a l e v o l u t i o n of d e n s i t y , f l u i d v e l o c i t y , a n d i o n a n d e l e c t r o n t e m p e r a t u r e r e s p e c t i v e l y . T h e i o n i z a t i o n m o d e l is t h a t of t h e c o l l i s i o n a l - r a d i a t i v e e q u i l i b r i u m ( C R E ) type[92], w h i c h has been s h o w n to best d e s c r i b e l a s e r - p r o d u c e d p l a s m a [ 5 8 , 93], e s p e c i a l l y t h a t i n t h e c o r o n a . In t h i s m o d e l , t h e average i o n i z a t i o n a n d t h e a s s o c i a t e d r a d i a t i v e p o w e r are o b t a i n e d by s o l v i n g a s y s t e m of r a t e e q u a t i o n s of t h e f o r m  w h e r e A/,- is t h e p o p u l a t i o n d e n s i t y of s t a t e i , a n d  W  ZJ  t h e r a t e coefficients of v a r i o u s  m e c h a n i s m s w h i c h change t h e s y s t e m f r o m s t a t e j t o i a n d f r o m s t a t e i to j r e s p e c t i v e l y . H e n c e , t h e first t e r m i n E q .  (2.28) represents t h e p o p u l a t i o n of s t a t e i f r o m a l l o t h e r  states, a n d t h e second t e r m the d e p o p u l a t i o n of s t a t e i i n t o t h e o t h e r states. T h e v a r i o u s m e c h a n i s m s affecting s t a t e p o p u l a t i o n s i n c l u d e r a d i a t i v e or c o l l i s i o n a l i o n i z a t i o n , r e c o m bination, and excitation.  T h e c o m p l e x i t y of C R E lies i n t h e fact t h a t a large n u m b e r  of p a r t i c i p a t i n g energy states a n d t r a n s i t i o n s , a n d c o n s e q u e n t l y a large n u m b e r of r a t e e q u a t i o n s , n e e d to be c o n s i d e r e d self-consistently.  In t h e l i m i t of h i g h - t e m p e r a t u r e a n d  l o w - d e n s i t y , r a d i a t i v e processes are faster t h a n c o l l i s i o n a l ones a n d we w i l l recover t h e familiar c o r o n a l model[59]. O n the other h a n d , in the high-density l i m i t where collisional  Chapter  2.  Theory  of Laser-driven  Shocks  35  processes d o m i n a t e , t h e p l a s m a w i l l be i n L T E ( l o c a l t h e r m o d y n a m i c e q u i l i b r i u m ) [ 9 4 ] . T h e h y d r o d j r n a m i c s a n d i o n i z a t i o n m o d e l are c o u p l e d as f o l l o w s . T h e t e m p e r a t u r e  and  d e n s i t y p r o d u c e d b y t h e h y d r o d y n a m i c p a r t of t h e c a l c u l a t i o n are n e e d e d t o c o m p u t e t h e l e v e l p o p u l a t i o n s a n d e m i s s i o n of r a d i a t i o n (since t h e r a t e coefficients are d e n s i t y a n d temperature dependent). the O  e  T h e e m i s s i o n p o w e r t h e n enters as an e n e r g y source t e r m i n  t e r m of e q u a t i o n (2.27).  F i n a l l y , a m u l t i g r o u p a p p r o x i m a t i o n , w h i c h divides the r a d i a t i o n energy i n t o a d i s c r e t e set of f r e q u e n c y g r o u p , each w i t h its o w n g r o u p - a v e r a g e d  spectrum  opacity and  m e a n free p a t h , is used t o solve t h e r a d i a t i v e transfer e q u a t i o n ,  --^ c  dl„  at  + ~  ox  r  (2.29)  = S - I, V  X  w h e r e / is t h e r a d i a t i o n i n t e n s i t y , 5 t h e e m i s s i o n source t e r m , \ t h e o p a c i t y , a n d s u b s c r i p t v the g r o u p f r e q u e n c y . represents a b s o r p t i o n .  The S  v  t e r m r e p r e s e n t s r a d i a t i v e e m i s s i o n , a n d t h e \I , t e r m X  O f course, the w a y r a d i a t i o n is t r a n s p o r t e d is i n f l u e n c e d by t h e  t h e r o m o d y n a m i c s t a t e of the  fluid,  w h i c h is i n t u r n affected  by t h e r a d i a t i v e  energy  c o n t r i b u t i o n . T h e p r o c e s s of r a d i a t i o n t r a n s p o r t , can also be " s w i t c h e d off" i n H Y R A D . T h i s m a y be d o n e to assess the effect of r a d i a t i o n t r a n s p o r t . H Y R A D has been e x t e n s i v e l y tested i n t h e simula.tions of shock b e h a v i o r in b o t h a l u m i n u m [ 9 5 ] a n d fused silica[96]. H Y R A D n o r m a l l y i n c o r p o r a t e s t h e S E S A M E d a t a ( L T E c a l c u l a t i o n ) for its E O S . In a d d i t i o n , heat c o n d u c t i o n is g o v e r n e d b y S p i t z e r [ 4 2 j c o n d u c t i o n . T h e n u m e r i c a l s c h e m e is t h a t of t h e P P M ( p i e c e w i s e p a r a b o l i c m e t h o d ) type[97]. T h i s is a second o r d e r e x t e n s i o n of the G o d u n o v ' s m e t h o d [ 9 8 ] ,  b u t i m p r o v e s u p o n it by i n t r o d u c i n g t h e p a r a b o l a e  as  t h e basic, s p a t i a l i n t e r p o l a t i o n f u n c t i o n s , w h i c h a l l o w s for a steeper r e p r e s e n t a t i o n  of  discontinuities.  T h e P P M has been s h o w n to be t h e m o s t a c c u r a t e method[99]  in the  t r e a t m e n t of shock h y d r o d y n a m i c s . S t i l l , s o m e processes are n o t i n c l u d e d i n H Y R A D : s u p r a / t h e r m a l e l e c t r o n t r a n s p o r t , or  Chapter  2.  Theory  of Laser-driven  Shocks  36  n u m e r i c a l f l u x l i m i t e r . It c a n be seen (in c h a p t e r 3) t h a t o u r e x p e r i m e n t a l c o n d i t i o n s f a l l w i t h i n t h e ' c l a s s i c a l ' l a s e r - m a t t e r c o u p l i n g r e g i m e [20, 100] w h e r e IX  2  < 1014 p m 2 - W / c m 2  (7 is t h e i r r a d i a t i o n i n t e n s i t y a n d A t h e laser f r e q u e n c y ) a n d effects such as e l e c t r o n  flux  i n h i b i t i o n o r hot e l e c t r o n g e n e r a t i o n are n e g l i g i b l e . A l t h o u g h we are not s p e c i f i c a l l y s t u d y i n g r a d i a i o n i n t h i s t h e s i s , t h e effect of r a d i a t i o n is w o r t h m e n t i o n i n g . E n e r g y t r a n s p o r t b y r a d i a t i o n m a y p l a y a n i m p o r t a n t role p a r t i c u l a r l y i n e x p e r i m e n t s u s i n g a r e l a t i v e l y l o n g laser pulse[58, 101]. A x i a l r a d i a t i v e t r a n s p o r t can lead t o p r e h e a t i n g i n t h e t a r g e t as d i s c u s s e d i n § 2 . 3 . 2 , w h i l e l a t e r a l r a d i a t i o n transp o r t leads t o t h e r m a l losses, a n d w i l l t h u s m o d i f y t h e h y d r o d y n a m i c a n d t h e r m o d y n a m i c profile of t h e m a t e r i a l (see e.g.  [61, 102, 103, 104]). T h e r e f o r e it m a y affect o u r s t u d y of  t e m p e r a t u r e d u e to shock h e a t i n g a n d f u r t h e r d i s c u s s i o n s w i l l b e presented i n c h a p t e r 4.  2.5.3  PUC  Code  W e now d e s c r i b e P U C ( P l a s m a U n l o a d i n g C o d e ) , w h i c h is also d e v e l o p e d at U B C . It is a n i m p r o v e d ( i n t h e n u m e r i c a l s c h e m e ) v e r s i o n of t h e P E C ( P l a s m a E x p a n s i o n  Code)  d e s c r i b e d i n t h e thesis of P a r f e n i u k [ 8 5 ] . S i n c e a l l of t h e m e a s u r e m e n t s presented i n t h i s w o r k are m a d e at t h e back or free surface of a t a r g e t as the shock wave emerges f r o m t h i s surface, a specific code ( P U C ) is d e v e l o p e d i n o r d e r t o o b t a i n a n a c c u r a t e c a l c u l a t i o n w i t h h i g h s p a t i a l a n d t e m p o r a l r e s o l u t i o n of t h e p l a s m a profiles at t h e r e a r surface of the t a r g e t . In p a r t i c u l a r , P U C is used t o access t h e effect of shock u n l o a d i n g o n t h e free surface e m i s s i o n m e a s u r e m e n t s d u r i n g a n d s u b s e q u e n t to s h o c k b r e a k o u t .  T h e one-dimensional  h y d r o d y n a m i c c o d e P U C t r e a t s o n l y t h e h y d r o d y n a m i c s of a c o m p r e s s e d t a r g e t r a r e f y i n g i n t o t h e v a c u u m . T h e process of l a s e r - m a t t e r i n t e r a c t i o n s is n o t i n c l u d e d . T h e s i m u l a t i o n b e g i n s at t i m e t = surface.  0, w h i c h is d e f i n e d t o be t h e t i m e of shock b r e a k o u t  at t h e free  A t t = 0, t h e t a r g e t - v a c u u m i n t e r f a c e is a s s u m e d t o b e a d i s c o n t i n u i t y w i t h t h e  s h o c k e d s t a t e o f t h e target specified t o have t h e d e n s i t y a n d t e m p e r a t u r e  corresponding  Chapter  2.  Theory  of Laser-driven  Shocks  37  t o t h e s h o c k e d c o n d i t i o n as c a l c u l a t e d by, for e x a m p l e , H Y R A D . T h e r e f o r e , P U C c a n be r e g a r d e d as a " p o s t - p r o c e s s o r "  t o be used i n t a n d e m w i t h  HYRAD.  P U C is a L a g r a n g i a n , o n e t e m p e r a t u r e code a n d uses t h e s a m e P P M n u m e r i c a l scheme as i n H Y R A D . It also solves t h e h y d r o d y n a m i c e q u a t i o n s for m a s s , m o m e n t u m a n d t o t a l i n t e r n a l energy, a n d uses E O S d a t a f r o m either S E S A M E or t h e n e w e q u a t i o n of s t a t e of g o l d w h i c h i n c o p o r a t e s t h e m e l t i n g t r a n s i t i o n . F u r t h e r m o r e , the e m i t t e d r a d i a t i o n f r o m t h e u n l o a d i n g m a t e r i a l is a s s u m e d t o o r i g i n a t e l o c a l l y f r o m a b l a c k b o d y source, i.e., t h e e m i t t e d r a d i a t i o n is i n t h e r m o d y n a m i c e q u i l i b r i u m w i t h every region (hence l o c a l ) of t h e c o m p r e s s e d m a t t e r . H e n c e , t h e e m i s s i o n i n t e n s i t y Ix of w a v e l e n g t h A at t i m e t b y a p l a s m a l o c a t e d at p o s i t i o n x w i t h t e m p e r a t u r e T(x,t)  h(x,  2 t) = — Ab  fee2 exp[h.c/Xkl  is[l05]  1 [x,t)\  (2.30)  —1  W e h a v e t o a c c o u n t for t h e fact t h a t t h e p a t h t h r o u g h w h i c h the r a d i a t i o n must  traverse  on its w a y to t h e d e t e c t o r is not o p t i c a l l y t h i n (i.e. r a d i a t i o n does not pass u n i m p e d e d ) . T h e r a r e f y i n g p l a s m a w i l l a b s o r b its o w n r a d i a t i o n . T h e t o t a l l u m i n o s i t y l{  d e t e c t e d by  a. r e m o t e d e t e c t o r is t h u s  Ixi )= t  <r(x)p{x)h(x,t)exp[-  w h e r e cr(x) is t h e o p a c i t y a n d p(x)  j ° a(x')p{x )dx'} r  dx  (2.31)  t h e density a l o n g t h e d e t e c t o r line of sight. P U C w i l l  b e used i n t h e b r i g h t n e s s t e m p e r a t u r e s t u d y to s i m u l a t e t h e t i m e e v o l u t i o n of t h e rear surface e m i s s i o n i n t e n s i t y (see § 4 . 2 . 2 . B ) .  Chapter 3  E x p e r i m e n t a l Facility, Diagnostics, and Setup  3.1  Laser Facility A s c h e m a t i c d i a g r a m of t h e laser s y s t e m a l o n g w i t h t h e b e a m d i a g n o s t i c s is s h o w n i n  F i g u r e 3.10. T h e Q u a n t e l n e o d y m i u m - g l a s s laser s y s t e m i n c l u d e s a N d - Y A G ( n e o d y m i u m doped y t t r i u m a l u m i n u m garnet) oscillator, a N d - Y A G preamlifier, four Nd-glass amplifiers, a n d a s s o c i a t e d b e a m e x p a n d e r s a n d s t e e r i n g o p t i c s . T h e b e a m d i a m e t e r at t h e e x i t of t h e f i n a l a m p l i f i e r r o d is 45 m m . T h e laser o s c i l l a t o r is p a s s i v e l y Q - s w i t c h e d w i t h a d y e - c e l l a n d p r o d u c e s a single p u l s e at 1.064 p m i n t h e T E M 0 o m o d e . T h r e e s p a t i a l filters are also d i s t r i b u t e d w i t h i n t h e laser c h a i n . T h e y consist, essentially of t w o lenses a n d a p i n h o l e i n v a c u u m to p a r t i a l l y r e m o v e t h e h i g h e r s p a t i a l f r e q u e n c y i n t e n s i t y m o d u u l a t i o n s i n t h e la.ser pulse. F o r our present e x p e r i m e n t s , t h e laser b e a m is f r e q u e n c y - d o u b l e d to y i e l d 0.532 p m green l i g h t u s i n g a K D * P ( d e u t e r a t e d p o t a s s i u m d i h y d r o g e n p h o s p h a t e ) crystal.  T h e s y s t e m is o p e r a t e d to deliver u p to 7 j o u l e s at 0.532 p m , a n d t h e energy  can b e c o n t i n u o u s l y v a r i e d b y a d j u s t i n g , the a m p l i f i e r p u m p i n g l e v e l . T h e e n e r g y of t h e o u t p u t b e a m is m o n i t o r e d b y a, G e n t e c e n e r g y meter[106], w h i l e a fast (350 ps rise t i m e ) H a m a m a t . s u p h o t o d i o d e [ l 0 7 ] r e c o r d s t h e laser p u l s e s h a p e . A t y p i c a l 0.53 p m laser p u l s e as m e a s u r e d w i t h t h e p h o t o d i o d e is s h o w n i n F i g u r e 3.11. It is seen t h a t t h e pulse, s h a p e is a p p r o x i m a t e l y G a u s s i a n t e m p o r a l l y w i t h a full w i d t h h a l f m a x i m u m (FWHM) ns.  38  of 2.3  Chapter  3.  Experimental  Facility,  OSC = OSCILLATOR  PA = PRE-AMPLIFIER  A = AMPLIFIER  Diagnostics,  and  S  F  =  S  Setup  P  A  T  ]  A  L  39  F  ]  L  T  £  R  BE = B E A M E X P A N D E R  SHG = S E C O N D HARMONIC G E N E R A T O R  Figure 3.10: A schematic of the laser and diagnostics system  Chapter  3.  Experimental  Facility,  Diagnostics,  and  Setup  F i g u r e 3.11: A t y p i c a l laser p u l s e  40  Chapter  3.2  3.  Experimental  Facility,  Diagnostics,  and  Setup  41  Irradiation Conditions We  d e t e r m i n e t h e laser i n t e n s i t y d i s t r i b u t i o n on t a r g e t by i m a g i n g t h e laser f o c a l  s p o t o n t o a s t r e a k c a m e r a i n its focus (i.e. ultrafast  The  Hamamatsu  ( r e s o l u t i o n l i m i t of 10 ps) c a m e r a i n c l u d e s a t e m p o r a l d i s p e r s e r m o d e l C 9 7 9  a n d a t e m p o r a l a n a l y s e r C1440[108]. spectrum.  static, non-streak) mode.  T h e c a m e r a is s e n s i t i v e i n t h e o p t i c a l a n d n e a r - U V  T h e o v e r a l l m a g n i f i c a t i o n of t h e o p t i c a l s y s t e m is f o u n d b y p l a c i n g a g r i d of  k n o w n s p a c i n g s i n t h e t a r g e t p l a n e . T h e m a g n i f i c a t i o n is t h e n c a l c u l a t e d b y r e l a t i n g t h e s p a c i n g s of t h e i m a g e of t h e g r i d as d i s p l a y e d o n t h e v i d e o m o n i t o r of t h e s t r e a k c a m e r a t o t h a t of the. o b j e c t .  T h e laser is f i r e d at f u l l energy a n d a p p r o p r i a t e l y  by N D ( n e u t r a l d e n s i t y ) f i l t e r s pla.ced before t h e final f o c u s s i n g lens.  attentuated  T h e laser is also  f o c u s s e d at t h e t a r g e t p l a n e t o give t h e m o s t u n i f o r m i n t e n s i t y d i s t r i b u t i o n . F i g u r e 3.12 shows a n i n t e n s i t y d i s t r i b u t i o n of t h e laser f o c a l s p o t , t i m e i n t e g r a t e d over t h e e n t i r e laser pulse. T h e s p a t i a l r e s o l u t i o n i n this m e a s u r e m e n t  is ~ 2 . 5 p.m. It shows  t h e laser spot t o b e c o n f i n e d i n a. r e g i o n of a p p r o x i m a t e l y 80 by 100 p.m. A s s u m i n g t h i s laser s p o t to be a p p r o x i m a t e l y a z i m u t h a l l y s y m m e t r i c , t h e s a m e d i s t r i b u t i o n is p l o t t e d i n t o an e q u i v a l e n t a z i m u t h a l l y s y m m e t r i c i n t e n s i t y p r o f i l e i n F i g u r e 3.13. shows t h e cross-section of t h e laser spot o f F i g u r e 3.12 across t h e x- a n d s p a n n i n g the c e n t r a l 5 p m of t h e s p o t .  Figure  3.14  y-coordinates  T h e laser p r o f i l e is a p p r o x i m a t e l y  trapezoidal  s p a t i a l l y , and we c a l c u l a t e t h e i n t e n s i t y $ 5 b y c o r r e l a t i n g w i t h t h e shock b r e a k o u t region as f o l l o w s . F r o m § 4 . 1 . 1 . A i t w i l l be s h o w n t h a t t h e shock breakout, r e g i o n  corresponds  t o an a r e a of ~ 8 0 p m i n d i a m e t e r , a n d t h e laser i n t e n s i t y i n t h i s area, w i l l be c a l c u l a t e d . O n t h e o t h e r h a n d , i t is seen f r o m F i g u r e 3.13 t h a t 8 0 % of t h e laser energy is c o n t a i n e d w i t h i n a. r a d i u s R  &0  of ~ 4 2 p m .  T h e r e f o r e , t h e effective i n t e n s i t y $ 5 c o r r e s p o n d i n g to  t h e a r e a of shock b r e a k o u t is $ s = 0.80 _ ^ £ £ 1 _  (3.32)  Chapter  3.  Experimental  Facility,  Diagnostics,  and  X_Posit.ion  Setup  (Junri)  F i gure 3.12: A time-integrated laser intensity distribution  42  F i g u r e 3.13: E q u i v a l e n t s y m m e t r i c p r o f i l e of the laser s p o t of F i g u r e 3.12  Chapter  3.  Experimental  on 0  Facility,  1 20  Diagnostics,  1  40  and Setup  —  1 60  44  1 80  1 100  Y - C o o r d i n a t e ( urn )  F i g u r e 3.14:  A cross s e c t i o n of t h e laser spot i n F i g u r e 3.12 across (a) t h e x - c o o r d i n a t e  a n d ( b ) t h e y - c o o r d i n a t e , e a c h s p a n n i n g t h e c e n t r a l 5 um of t h e spot  Chapter  3.  w h e r e Eiaser  Experimental  Facility.  Diagnostics,  is t h e t o t a l laser energy, T\  ASER  and  Setup  45  the F W H M of t h e laser t e m p o r a l p r o f i l e , a n d  ^4-80 ( = TT-PCSO) t h e a r e a w h e r e 8 0 % of the laser e n e r g y is c o n t a i n e d . T h e laser i r r a d i a n c e c a l c u l a t e d u s i n g t h i s p r o c e d u r e has been successfully  used  as an i n p u t p a r a m e t e r  in  p r e v i o u s h y d r o c o d e s i m u l a t i o n s , w h e r e t h e a b l a t i o n p r e s s u r e a n d shock t r a j e c t o r y t h e r e b y p r e d i c t e d agree w e l l w i t h e x p e r i m e n t a l results (see  [49, 5 5 , 109]).  In our experiments,  t h e i n t e n s i t y d i s t r i b u t i o n is a p p r o x i m a t e l y G a u s s i a n i n t i m e , a n d u s i n g e q u a t i o n ( w i t h Eiaser  — 4 . 2 ± 0 . 4 J , rlaser  x 1013 W/cm2.  = 2 . 3 ± 0.2ns),  t h e i n c i d e n t i n t e n s i t y is therefore  3.3  = fa-  $s  2.6±0.7  T h e a b s o r p t i o n of 0 . 5 3 p m laser o n a l u m i n u m t a r g e t s has b e e n m e a s u r e d  i n p r e v i o u s s t u d i e s [ l l O , 1 1 1 ] . B a s e d o n those m e a s u r e m e n t s ,  $A  (3.32)  = - 2 . 3 ± 0 . 6 x 1 0 1 3 W / c m 2 , where fa  t h e a b s o r b e d i r r a d i a n c e is  is t h e a b s o r p t i o n f r a c t i o n ] ! 1 0 ] .  Experimental Arrangements F i g u r e 3 . 1 5 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  inside the target chamber and the  i m a g i n g o p t i c s for o b s e r v a t i o n of t h e taget rear surface.  T h i s s e t u p is used to r e c o r d t h e  l u m i n o u s r a d i a t i o n e m i t t e d f r o m t h e rear surface of t h e t a r g e t as t h e s h o c k wave emerges f r o m t h i s free surface.  T h e t a r g e t c h a m b e r is m a i n t a i n e d at a p r e s s u r e of a b o u t 6 0 m t o r r s .  I n the e x p e r i m e n t , p l a n a r targets o f a l u m i n u m foils or d o u b l e d - l a y e r e d a l u m i n u m - g o l d t a r g e t s are i r r a d i a t e d - w i t h 0 . 5 3 p m , 2 . 3 ns F W H M  laser pulses.  T h i s m a i n laser  pulse  is d i r e c t e d i n t o t h e c h a m b e r w i t h a series of t h r e e d i c h o r i c m i r r o r s , a n d is focussed o n t o t h e front a l u m i n u m s u r f a c e of the t a r g e t w i t h f / 6 . 7 o p t i c s at n o r m a l i n c i d e n c e . T h e rear surface of t h e target is i m a g e d o n t o t h e e n t r a n c e slit of t h e streak  camera  w i t h f/1.4 a c h r o m a t i c o p t i c s p l a c e d at target n o r m a l . T h e rear surface l u m i n o u s e m i s s i o n  apter  3.  Experimental  Facility.  Diagnostics,  and  Setup  F i g u r e 3.15: T h e e x p e r i m e n t a l s e t u p i n t h e l u m i n s c e n c e s t u d y  46  Chapter  3.  Experimental  Facility,  Diagnostics,  and  47  Setup  is o b s e r v e d t h r o u g h a l O O A - b a n d p a s s i n t e r f e r e n c e f i l t e r c e n t e r e d at A 0 = 4 3 0 0 A ( r e j e c t i o n r a t i o o u t s i d e t h e b a n d b e t w e e n 0 . 8 2 A 0 a n d 1.1 A 0 is 0.01%) p l a c e d at t h e streak c a m e r a entrance.  T h i s e l i m i n a t e s laser s t r a y l i g h t f r o m e n t e r i n g t h e c a m e r a .  The temporal  h i s t o r y of t h e s p a t i a l d i s t r i b u t i o n of t h e l u m i n o u s e m i s s i o n is r e c o r d e d b y the streak camera and then displayed on the video monitor. A s t h e r e is a t i m e j i t t e r of u p to 50 ps b e t w e e n t h e t i m e t h e s t r e a k c a m e r a is t r i g g e r e d b y a laser p u l s e d e r i v e d f r o m t h e m a i n b e a m t o t h e t i m e w h e n i t a c t u a l l y begins i t s " s t r e a k i n g " o p e r a t i o n , t h e t i m i n g of t h e free surface e m i s s i o n w i t h respect to the laser p u l s e can o n l y b e d e t e r m i n e d u s i n g a reference laser p u l s e or f i d u c i a l w h i c h is r e c o r d e d s i m u l t a n e o u s l y by t h e streak c a m e r a . S u c h a f i d u c i a l is d e r i v e d f r o m t h e m a i n laser b e a m as i n d i c a t e d i n F i g u r e 3.15. laser c h a i n (i.e.  T h e o p t i c a l p a t h l e n g t h of t h e f i d u c i a l f r o m t h e e x i t of t h e  after t h e K D * P c r y s t a l ) t o t h e e n t r a n c e of t h e streak c a m e r a is m a d e  n e a r l y e q u a l to t h a t of t h e m a i n laser b e a m g o i n g t h r o u g h t h e t a r g e t a n d t h e i m a g i n g o p t i c s at t h e t a r g e t rear side. H e n c e , t h e f i d u c i a l s i g n a l b e c o m e s a n " e f f e c t i v e " m a i n laser p u l s e a n d t h e t i m i n g of t h e l u m i n o u s e m i s s i o n f r o m the free surface of the target c a n b e c o r r e l a t e d u n a m b i g u o u s l y w i t h t h e i n c i d e n t laser p u l s e . O u r e x p e r i m e n t a l setup y i e l d s a fiducial  reference w h i c h leads t h e m a i n b e a m b y 3 7 5 + 7 5 ps. T h i s is t a k e n i n t o a c c o u n t  i n t h e a n a l y s i s o f shock v e l o c i t y d a t a . In a d d i t i o n , t h e  fiducial  also p r o v i d e s a m e a s u r e of t h e laser p u l s e s h a p e o n t h e  s t r e a k c a m e r a m o n i t o r . A l t h o u g h the s t r e a k camera, has a l o w e r d y n a m i c r a n g e ( < t h a n t h a t of t h e p h o t o d i o d e ( > 1 0 0 0 ) , t h e p u l s e s h a p e r e c o r d e d b y t h e streak  100)  camera  nevertheless r e a d i l y identifies t h e t i m e of p e a k laser i n t e n s i t y ^ w h i c h is n e e d e d as t h e t i m e reference ( t a k e n as t i m e z e r o here) for any s h o c k - r e l a t e d p h e n o m e n o n u n d e r s t u d y . D e p e n d i n g o n t h e t y p e of m e a s u r e m e n t s , the d u r a t i o n of t h e s t r e a k m a y b e set at 5.42 or 1.26 ns.  T h e slower streak m o d e (5.42 ns) is u s e d for s h o c k v e l o c i t y  measurements  w h e r e t h e e n t i r e fiducial p u l s e c a n be r e c o r d e d . I n t h e case of t e m p e r a t u r e m e a s u r e m e n t s ,  Chapter  3.  Experimental  i n w h i c h t h e laser  fiducial  Facility,  Diagnostics,  and  Setup  48  is n o t necessary, t h e faster s t r e a k s p e e d (1.26 ns) is chosen  i n s t e a d t o i m p r o v e t h e t e m p o r a l r e s o l u t i o n of t h e  measurement.  I n t h e e x p e r i m e n t , an a p p r o p r i a t e n u m b e r of n e u t r a l d e n s i t y filters are i n s e r t e d i n t o t h e o p t i c a l p a t h of t h e  fiducial  pulse.  T h i s helps to r e d u c e t h e l i g h t i n t e n s i t y t o an  a c c e p t a b l e l e v e l so as n o t to s a t u r a t e t h e s t r e a k c a m e r a t u b e , w h i c h c a n l e a d to p r e m a t u r e tube deterioration.  Chapter 4  Luminescence Measurements in Single and Doubled-Layered Targets  4.1  Shock Velocity Study A s a shock w a v e p r o p a g a t e s t h r o u g h t h e target t h e r e g i o n b e h i n d the s h o c k front is  h e a t e d . W h e n t h e shock front reaches t h e b a c k or free surface of t h e t a r g e t , t h e l u m i n o u s e m i s s i o n f r o m t h e h e a t e d m a t e r i a l c a n t o b e d e t e c t e d b y a streak c a m e r a . S i n c e t h e target is i n i t i a l l y c o l d (i.e. at r o o m t e m p e r a t u r e ) a n d o p a q u e , n o r a d i a t i o n w i l l be o b s e r v e d f r o m t h e s a m p l e u n t i l t h e t i m e of shock e m e r g e n c e . A c t u a l l y , the r a d i a t i o n w i l l b e c o m e v i s i b l e w h e n t h e s h o c k f r o n t is w i t h i n a d i s t a n c e of several o p t i c a l m e a n free p a t h s / f r o m t h e free surface.  F o r e x a m p l e , for r a d i a t i o n at 4 3 0 0 A ( 2 . 8 8 e V ) , t h e mass a b s o r p t i o n coefficient  ( o p a c i t y ) K of a l u m i n u m u n d e r n o r m a l c o n d i t i o n s is ~ 5 x l 0 4 c m 2 / g a n d the c o r r e s p o n d i n g m e a n free p a t h is / = ( p / v ) - 1 ~ 0 . 1 p.m. T h e r e f o r e , t h e t i m e of shock b r e a k o u t at t h e free surface is s i g n i f i e d b y a s u d d e n o c c u r e n c e o f l u m i n o u s e m i s s i o n . B y m e a s u r i n g t h e shock b r e a k o u t t i m e s i n t a r g e t s of different t h i c k n e s s e s , one c a n m a p out the shock t r a j e a t o r y f r o m w h i c h t h e s h o c k speed Us c a n be d e t e r m i n e d d . S u c h m e a s u r m e n t s can therefore be used as a d i a g n o s t i c s t o s t u d y t h e l a s e r - d r i v e n shock wave. A s d i s c u s s e d i n c h a p t e r 2, e q u a t i o n of s t a t e s t u d i e s u s i n g t h e i m p e d a n c e - m i s m a t c h t e c h n i q u e r e q u i r e s t h e e x p e r i m e n t a l d e t e r m i n a t i o n of the shock v e l o c i t y i n e i t h e r t h e s t a n d a r d m a t e r i a l , or t h a t i n t h e s a m p l e of i n t e r e s t . H o w e v e r , i n s h o c k - i n d u c e d l u m i n o u s e m i s s i o n m e a s u r e m e n t s w i t h i m p e d a n c e - m i s m a t c h e d t a r g e t s , one is r e s t r i c t e d t o m e a s u r e t h e s h o c k a r r i v a l t i m e s at t h e free surface of t h e s a m p l e o n l y . T h i s b y itself is n o t sufficient  49  Chapter  4.  Luminescence  Measurements  in Single  and Douhled-La.ye.red  Targets  50  t o y i e l d t h e s h o c k speed i n e i t h e r t h e s t a n d a r d or t h e s a m p l e , since i t represents t h e t o t a l 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 t w o m a t e r i a l s of t h e t a r g e t . O n t h e o t h e r h a n d , one c a n first  c h a r a c t e r i z e the s h o c k p r o d u c e d i n the s t a n d a r d . I n o u r e x p e r i m e n t s f l 12], a l u m i n u m ( Z = 13, p 0 = 2.7 g / c m 3 ) is chosen as t h e l o w -  i m p e d a n c e s t a n d a r d i n t h e a l u m i n u m - o n - g o l d t a r g e t s ( g o l d as t h e h i g h - i m p e d a n c e s a m ple, with Z =  79, p 0 =  19.3 g / c m 3 ) i n t h e i m p e d a n c e - m i s m a t c h s t u d y .  A l u m i n u m is  selected as o u r s t a n d a r d since its E O S d a t a are w e l l t a b u l a t e d , b o t h i n t e r m s of t h e o r e t i c a l c a l c u l a t i o n s [ 5 0 ] a n d e x p e r i m e n t a l measurements[49].  4.1.1  Single Layer A l u m i n u m Foil  4.1.1.A E x p e r i m e n t a l O b s e r v a t i o n s A l u m i n u m f o i l s [ l l 3 ] o f v a r i o u s t h i c k n e s s e s r a n g i n g f r o m 25 to 53 p m are used. l u m i n o u s emission associated  The  w i t h shock b r e a k o u t at t h e free surfaces of the t a r g e t s  are. r e c o r d e d b y the streak c a m e r a .  T h e overall m a g n i f i c a t i o n of t h e d i a g n o s t i c s y s t e m  ( i n c l u d i n g t h e i m a g i n g o p t i c s a n d t h e streak c a m e r a o p t i c s ) is m e a s u r e d by p l a c i n g a fine w i r e m e s h of k n o w n s p a c i n g at t h e target p l a n e , f o c u s s i n g it o n t o t h e streak c a m e r a , a n d n o t i n g t h e s p a c i n g of t h e m a g n i f i e d i m a g e d i s p l a y e d o n t h e c a m e r a m o n i t o r . W i t h a m a g n i f i c a t i o n of ~ 1 2 5 , t h e s p a t i a l r e s o l u t i o n a c h i e v e d is a p p r o x i m a t e l y 8 p m .  The  e n t r a n c e slit of t h e c a m e r a is set at 200 p m . T h i s p r o d u c e s a streak i m a g e w i t h g o o d s i g n a l - t o - n o i s e r a t i o of ~ 5 0 , however i t degrades t h e t i m e r e s o l u t i o n to —50 ps. T h i s far e x c e e d s ' t h e i d e a l streak c a m e r a r e s o l u t i o n of 10 ps. A s d i s c u s s e d i n c h a p t e r 3, the l u m i n o u s e m i s s i o n is o b s e r v e d t h r o u g h a 100 A b a n d pass filter c e n t e r e d at 4300 A . F i g u r e 4.16 shows s p a t i a l l y r e s o l v e d streak r e c o r d s of t h e e m i s s i o n f r o m t h e shock b r e a k o u t regions i n 38.4 a n d 53 p m a l u m i n u m t a r g e t s . A  fiducial  s i g n a l is also r e c o r d e d to a l l o w d e t e r m i n a t i o n of t h e shock b r e a k o u t t i m e w i t h respect t o  Chapter  4.  F i g u r e 4.16:  Luminescence  Measurements  in Single  and Doubled-Layered  S t r e a k r e c o r d s of s h o c k b r e a k o u t e m i s s i o n (left s t r e a k ) a n d  ( r i g h t s t r e a k ) i n (a) 38.4 p m a n d ( b ) 53 p m a l u m i n u m t a r g e t .  Targets  fiducial  51  signal  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  52  Targets  t h e m a i n laser p u l s e . T i m e zero c o r r e s p o n d s to t h e p e a k of t h e laser pulse. T h e shock is o b s e r v e d t o e m e r g e at t h e free surface i n a r e g i o n of ~ 8 0 ± 1 0 um d i a m e t e r . N o hot spots (regions of v e r y h i g h i n t e n s i t i e s ) are o b s e r v e d .  In t h e a n a l y s i s of t h e e m i s s i o n i n t e n s i t y ,  we c o n s i d e r t h e e m i s s i o n s p a t i a l l y i n t e g r a t e d over t h e c e n t r a l 45 um s p a n i n the shock b r e a k o u t r e g i o n w h i c h is w i d e e n o u g h t o y i e l d a s u f f i c i e n t l y g o o d s i g n a l to noise r a t i o , b u t n a r r o w e n o u g h to ensure a p p r o x i m a t e shock p l a n a r i t y . F i g u r e 4.17 shows t h e t e m p o r a l h i s t o r y of t h e s h o c k - i n d u c e d l u m i n o u s e m i s s i o n i n t e n s i t y a n d t h e f u d i c i a l for a 38.4  um  a l u m i n u m t a r g e t . T h e rise t i m e s ( b e t w e e n t h e 10% t o 90% i n t e n s i t y of t h e i n i t i a l p e a k ) of t h e e m i s s i o n for a l l t h e t a r g e t s are t y p i c a l l y 2 3 0 ± 7 0 ps.  T h e shock b r e a k o u t  times  i n 2 5 , 29.3, 38.4, a n d 53 um a l u m i n u m are f o u n d to b e r e s p e c t i v e l y 0 . 0 ± 0 . 1 , 0 . 3 0 ± 0 . 0 6 , 1 . 0 3 ± 0 . 0 5 , a n d 1 . 8 9 ± 0 . 1 1 ns after t h e t i m e of t h e laser p e a k .  N o t a r g e t preheat  is  o b s e r v e d as i n d i c a t e d b y t h e fast rise t i m e s in t h e e m i s s i o n i n t e n s i t y .  4.1.1.B Computer Simulations T o m o d e l t h e d y n a m i c s of t h e s h o c k , t h e p u r e l y h y d r o d y n a m i c code S H Y L A C is used first.  A l t h o u g h t h i s c o d e does n o t i n c o p o r a t e t h e l a s e r - m a t t e r i n t e r a c t i o n processes, it is  n e v e r t h e l e s s fast, a n d i n e x p e n s i v e . O u r p a r t i c u l a r s i m u l a t i o n s assume, a G a u s s i a n pressure p u l s e of 2.5 ns F W H M  w i t h a peak p r e s s u r e of 3.5 M b a r .  a b l a t i o n pressure g e n e r a t e d i r r a d i a n c e of $  A  b y o u r 0 . 5 3 / m i , 2.3 ns F W H M  T h i s is to a p p r o x i m a t e laser pulse at a n  the  absorbed  = 2.3 x 1 0 1 3 W / c m J a c c o r d i n g t o t h e p r e v i o u s l y o b t a i n e d e x p e r i m e n t a l  s c a l i n g la.w i n e q u a t i o n (2.22). T h i s a p p r o x i m a t i o n of t h e a b l a t i o n p r e s s u r e a p p e a r s to be r e a s o n a b l e as seen f r o m results of t h e m o r e e l a b o r a t e H Y R A D s i m u l a t i o n s w h i c h i n c l u d e t h e l a s e r - i n d u c e d a b l a t i o n p r o c e s s . A c o m p a r i s o n of t h e c a l c u l a t e d a b l a t i o n pressure f r o m H Y R A D a n d t h e G a u s s i a n p r e s s u r e pulse a s s u m e d i n S H Y L A C ' is s h o w n i n F i g u r e 4.18. T h e r i s i n g p o r t i o n s of t h e t w o pulses ( w h i c h d r i v e t h e s h o c k ) agree r e a s o n a b l y w e l l , b u t t h e a b l a t i o n p r e s s u r e p u l s e has a longer F W H M (2.9 ns) t h a n the a s s u m e d pressure p u l s e  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  F i g u r e 4.17: T e m p o r a l h i s t o r y of t h e (a) shock b r e a k o u t a n d ( b ) p m A l target  fiducial  Targets  53  streak i n a 38.4  Chapter  4.  Luminescence  Measurements  in Single  TIME  and Doubled-Layered  Targets  54  (ns)  F i g u r e 4.18: T h e c a l c u l a t e d a b l a t i o n p r e s s u r e p u l s e f r o m H Y R A D ( s o l i d ) a n d t h e G a u s sian p r e s s u r e p u l s e a s s u m e d i n S H Y L A C  (dash)  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-La.yered  Targets  55  u s e d i n S H Y L A C (2.5 n s ) . F i g u r e 4.19 shows t h e m e a s u r e d shock t r a n s i t t i m e as a f u n c t i o n of t a r g e t t h i c k n e s s for t h e g i v e n a b s o r b e d irra,diance as well as the c a l c u l a t e d s h o c k t r a j e c t o r y u s i n g S H Y L A C . T o test t h e a c c u r a c y of t h e S H Y L A C s i m u l a t i o n , we h a v e a l s o c a l c u l a t e d the s h o c k t r a j e c t o r y u s i n g H Y R A D . T w o different, cases are c o n s i d e r e d i n t h e H Y R A D s i m u l a t i o n s , o n e w h e r e t h e process of r a d i a t i o n t r a n s p o r t is t a k e n i n t o a c c o u n t , a n d t h e o t h e r w h e r e r a d i a t i o n t r a n s p o r t is n e g l e c t e d . ( I n this a n d s u b s e q u e n t s i m u l a t i o n s w h e r e t h e r a d i a t i o n t r a n s p o r t process is i n c l u d e d , t h e r a d i a t i o n is d i v i d e d i n t o 10 energy g r o u p s f r o m 0.3 to 10 k e V , as d e s c r i b e d i n t h e d i s c u s s i o n of m u l t i g r o u p a p p r o x i m a t i o n i n § 2 . 5 . 2 ) F r o m t h e s i m u l a t i o n s , we n o t e t h a t t h e shock is a c c e l e r a t i n g (i.e. n o n - s t e a d y ) at e a r l y t i m e s . T h e s h o c k t h e n reaches a q u a s i - s t e a d y m a t e l y 20 p m i n t h e t a r g e t .  state w h e n i t has p r o p a g a t e d  t o a d e p t h of a p p r o x i -  T h e q u a s i - s t e a d y s h o c k speed is f o u n d t o be (1.5 ± 0.1) x  106 cm/s. T h e agreement  a m o n g t h e three c a l c u l a t e d s h o c k p a t h s a n d e x p e r i m e n t a l d a t a  are  e q u a l l y g o o d , a n d t h e r e is n o i n d i c a t i o n t h a t one s i m u l a t i o n is m o r e p r e f e r a b l e t o a n o t h e r . T h u s , t h e shock t r a n s i t t i m e m e a s u r e m e n t is n o t s e n s i t i v e e n o u g h to d i s c r i m i n a t e one m o d e l ( S H Y L A C ) against, a n o t h e r ( H Y R A D ) or to i d e n t i f y t h e s i g n i f i c a n c e of r a d i a t i o n t r a n s p o r t i n t h e s h o c k process.  It a p p e a r s t h a t S H Y L A C is a d e q u a t e in t h e p r e d i c t i o n of  s h o c k p a t h a n d v e l o c i t y . H o w e v e r , we s h a l l use H Y R A D i n c l u d i n g t h e r a d i a t i o n t r a n s p o r t p r o c e s s to s i m u l a t e o u r s u b s e q u e n t e x p e r i m e n t s , a.s i t has t h e m o s t c o m p l e t e t r e a t m e n t of t h e l a s e r - m a t t e r i n t e r a c t i o n s . It s h o u l d be n o t e d t h a t t h e shock pressure c a n a l s o be e s t i m a t e d by c o m p a r i n g t h e m e a s u r e d shock v e l o c i t y w i t h H u g o n i o t d a t a . F r o m t h e S E S A M E E O S l i b r a r y , the meas u r e d shock speed of (] .5 ± 0.1) x 10c"' c m / s c o r r e s p o n d s to a p r e s s u r e of 3.1 ± 0.5 M b a r . T h i s is i n agreement w i t h t h e pressure of 3.5 M b a r u s e d in S H Y L A C .  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  56  Time (ns)  F i g u r e 4.19: C a l c u l a t e d s h o c k p a t h s b y S H Y L A C ( d o t - d a s h ) , by H Y R A D w i t h o u t r a d i a t i o n t r a n s p o r t ( d a s h ) , a n d w i t h r a d i a t i o n t r a n s p o r t ( s o l i d ) ; also p l o t t e d are t h e e x p e r i m e n t a l results in various a l u m i n u m targets  Chapter  4.1.2  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  57  A l u m i n u m - G o l d Targets  4.1.2.A Experimental Observations T h e l a y e r e d t a r g e t s used m t h i s e x p e r i m e n t are m a n u f a c t u r e d c o m m e r c i a l l y b y v a p o r d e p o s i t i o n , i.e. e v a p o r a t i o n of g o l d o n t o a l u m i n u m s u b s t r a t e .  These targets include a  c o m b i n a t i o n of e i t h e r 19 or 26.5 p m of a l u m i n u m layers w i t h e i t h e r 8.4 or 13 p m of g o l d layers.  In o r d e r t o o b t a i n p r e s s u r e e n h a n c e m e n t , t h e t a r g e t s are i r r a d i a t e d on t h e  a l u m i n u m side. F o r these t a r g e t s , t h e s h o c k a r r i v a l t i m e s at t h e b a c k surfaces ( t h e free surfaces of t h e g o l d l a y e r ) are m e a s u r e d b y t h e s a m e t e c h n i q u e as d e s c r i b e d i n § 4 . 1 . 1 . A . F i g u r e 4.20 shows a s a m p l e streak r e c o r d of t h e s h o c k - i n d u c e d l u m i n o u s e m i s s i o n a n d t h e laser f i d u c i a l for a 19 p m a l u m i n u m on 8.4 p m g o l d t a r g e t . W e see s i m i l a r q u a l i t a t i v e b e h a v i o r s i n t h e b a c k s i d e l u m i n o u s e m i s s i o n as those i n p u r e a l u m i n u m t a r g e t s ; a g a i n , n o t a r g e t p r e h e a t or h o t s p o t s are o b s e r v e d . T h e shock b r e a k o u t t i m e s are 0.74 ns in 19 p m a l u m i n u m on 8.4 p m g o l d , 1.08 ns i n 19 p m a l u m i n u m on 13 p m g o l d , 1.10 ns i n 26.5 p m a l u m i n u m on 8.4 p m g o l d , a n d 1.89 ns i n 26.5 p m a l u m i n u m o n 13 p m g o l d .  The  u n c e r t a i n i t i e s in t h e m e a s u r e d b r e a k o u t t i m e s are ± 0 . 1 ns.  4.1.2.B C o m p u t e r Simulations T h e s i m u l a t i o n s are p e r f o r m e d i n t w o p a r t s . T h e first p a r t is t o e x a m i n e the v a r i o u s issues a n d criteria, g o v e r n i n g t h e design of an i m p e d a n c e - m i s m a t c h e d  target.  Since a  large n u m b e r of a l u m i n u m - g o l d t a r g e t s of different thicknesses need t o be c o n s i d e r e d , we h a v e selected t h e S H Y L A C code b e c a u s e it is speedy to r u n a n d c o n t a i n s the relevant p h y s i c s of shock p r o p a g a t i o n .  H Y R A D is used i n t h e s e c o n d p a r t of t h e s i m u l a t i o n s t o  p r o v i d e d e t a i l e d c a l c u l a t i o n s for t h e i n t e r p r e t a t i o n of e x p e r i m e n t a l d a t a for specific a n d a l i m i t e d n u m b e r of t a r g e t c o n f i g u r a t i o n s .  Chapter  4.  F i g u r e 4.20:  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  S t r e a k r e c o r d of free surface l u m i n o u s e m i s s i o n (left s t r e a k ) a n d  s i g n a l ( r i g h t s t r e a k ) of a 19 um a l u m i n u m on 8.4 um g o l d target  58  fiducial  Chapter  4.  Luminescence  4.1.2.B.i S H Y L A C  Measurements  in Single, and Doubled-Layered  s i m u l a t i o n s for T a r g e t O p t i m i z a t i o n  Targets  59  In S H Y L A C , the M i e -  G r i i n e i s e n e q u a t i o n of s t a t e m o d e l s for a l u m i n u m a n d g o l d are used a n d t h e shock press u r e is c o m p u t e d a c c o r d i n g l y .  A s b e f o r e , we h a v e a s s u m e d t h a t a G a u s s i a n  pressure  p u l s e of 2.5 ns ( F W H M ) a n d p e a k pressure of 3.5 M b a r is a p p l i e d o n t h e front surface of t h e a l u m i n u m l a y e r . In t h e s i m u l a t i o n s , t h e thicknesses of the g o l d layer are t a k e n to be t h i c k e n o u g h so t h a t t h e shocks d o not r e a c h t h e free surfaces d u r i n g the s i m u l a t i o n periods.  E q u i v a l e n t l y , t h e g o l d l a y e r t h i c k n e s s i n these s m u l a t i o n s c a n be t a k e n t o be  i n f i n i t y so t h a t n o free surface e x i s t s i n t h e t i m e d u r a t i o n of t h e ' s i m u l a t i o n s a n d n o free surface r a r e f a c t i o n s are p r o d u c e d .  T h e r e s u l t i n g pressure profiles at different t i m e s i n  a l u m i n u m - g o l d t a r g e t s for a l u m i n u m layers w i t h thicknesses r a n g i n g f r o m 5 um t o 50 um are p l o t t e d i n F i g u r e s 4.21 to 24.  O n e c a n c l e a r l y see t h e l e a d i n g edge of t h e s t r o n g  s h o c k w a v e , r e p r e s e n t e d b y t h e s h a r p increase i n pressure, a n d the " d y n a m i c " n a t u r e of t h e s h o c k as i t p r o p a g a t e s i n t o t h e t a r g e t . T h e pressure at t h e shock f r o n t represents t h e s h o c k b r e a k o u t pressure i f a free surface were at t h a t p o s i t i o n . F o r e x a m p l e , i n t h e case of a 19 um A l o n 13 um A u target ( F i g . 4.23), t h e free surface pressure at shock b r e a k o u t (i.e. w h e n t h e shock f r o n t reaches a target d i s t a n c e of 32 um)  would be approximately  7.3 M b a r . A n u m b e r of c o n c l u s i o n s c a n i m m e d i a t e l y b e d r a w n f r o m t h e  figures.  F i r s t of a l l ,  p r e s s u r e e n h a n c e m e n t c a n i n d e e d be a c h i e v e d at. the i n t e r f a c e w i t h a p p r o p r i a t e choices of t h e front a l u m i n u m t h i c k n e s s e s . S e c o n d l y , by n o m e a n s is t h e shock t r u l y steady. T h i s is d u e to t h e fact t h a t t h e d r i v i n g pressure p u l s e is t i m e - d e p e n d e n t . S h o c k b u i l d u p takes p l a c e d u r i n g t h e t i m e w h e n t h e pressure pulse is i n c r e a s i n g i n a m p l i t u d e . T h e f o r m a t i o n  oi a single s t r o n g shock front, has a l r e a d y been discussed i n § 2 . 1 . 3 . F u r t h e r m o r e , as t h e p r e s s u r e of the. d r i v i n g p u l s e d r o p s a n d e v e n t u a l l y ceases, a r a r e f a c t i o n o r u n l o a d i n g wave d e v e l o p s at t h e f r o n t surface of t h e t a r g e t .  T h i s p r o p a g a t e s i n t o t h e shocked m e d i u m  w i t h t h e v e l o c i t y of s o u n d i n t h e s h o c k e d r e g i o n , w h i c h is faster t h a n t h e shock speed.  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  60  F i g u r e 4 . 2 1 : S h o c k p r e s s u r e profiles i n A l - A u t a r g e t s w i t h t h e front a l u m i n u m t h i c k n e s s equal to 5 p m .  T h e i n i t i a l p r o f i l e c o r r e s p o n d s to a t i m e of 1.5 ns before t h e pressure  p u l s e p e a k , a n d s u b s e q u e n t ones are 0.25 ns a p a r t .  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-La.yereci  DISTANCE IN TARGET  Targets  ( pm)  F i g u r e 4.22: S a m e as F i g u r e 4.21 b u t a l u m i n u m t h i c k n e s s is 11.5 p m  61  pter  4.  Luminescence  Measurements  in Single  and Doubied-Layered  DISTANCE IN TARGET  Targets  ( jjm)  F i g u r e 4.23: S a m e as F i g u r e 4.21 b u t a l u m i n u m t h i c k n e s s is 19 p m  pter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  DISTANCE IN TARGET  Targets  (jjm)  F i g u r e 4.24: S a m e as F i g u r e 4.21 b u t a l u m i n u m t h i c k n e s s is 50 p m  Chapter  4.  Luminescence  Measurements  in Single  and Douhled-Layered  Targets  64  W h e n i t c a t c h e s u p w i t h t h e shock f r o n t , the p r e s s u r e at the sock front w i l l be r e d u c e d . T h i s is c a l l e d shock a t t e n t u a t i o n or d a m p i n g . ( F i g u r e 4 . 2 4 ) , t h e shock w i l l be a t t e n t u a t e d  T h u s i f t h e a l u m i n u m l a y e r is t o o t h i c k before i t reaches t h e interface; hence t h e  t r a n s m i t t e d p r e s s u r e i n t o t h e g o l d layer w i l l n o t b e as h i g h as it c a n be.  O n the other  h a n d , i f t h e a l u m i n u m l a y e r is t o o t h i n ( F i g u r e 4.21), an i n c o m p l e t e l y f o r m e d  shock  f r o n t w i l l i m p i n g e t o o e a r l y on the interface to benefit s i g n i f i c a n t l y f r o m t h e p r e s s u r e e n h a n c e m e n t b y shock r e f l e c t i o n . F u r t h e r m o r e , if t h e s h o c k waves reach t h e interface t o o s o o n , t h e b a c k w a r d - m o v i n g reflected wave, p r o p a g a t i n g back i n t o t h e a l u m i n u m l a y e r , w i l l therefore effect p r e m a t u r e shock a t t e n t u a t i o n i n t h e a l u m i n u m layer ( F i g u r e 4.22), a n d a g a i n o n e w i l l not h a v e d e r i v e d t h e m a x i m u m benefit f r o m i m p e d a n c e - m i s m a t c h i n g . A s for t h e g o l d layer, if i t is t o o t h i n , t h e n the t r a n s m i t t e d shock m a y not have b e e n c o m p l e t e l y f o r m e d (cf.  t h e process of shock s t e e p e n i n g i n g o l d i n figures 4.22 a n d  22)  w h e r e a s i f it is t o o t h i c k , s h o c k a t t e n t u a t i o n w i l l o c c u r before the shock reaches t h e free surface. F i g u r e 4.25 i l l u s t r a t e s t h e effects of the a l u m i n u m a n d g o l d thicknesses on t h e free s u r f a c e p r e s s u r e i n d u c e d i n g o l d . T h e s e effects are c o m p l i c a t e d , a n d t h e final free surface pressures c e r t a i n l y c a n n o t b e c a l c u l a t e d on t h e basis of e q u a t i o n (2.11) alone. ( N . B . In t h e case of an i d e a l s t e a d y s h o c k , t h e t r a n s m i t t e d shock pressure as g i v e n i n eq. (2.11) e q u a l s the. free surface p r e s s u r e i n gold.)  A l s o p l o t t e d in the  figure  is t h e m a x i m u m  p r e s s u r e JPsw w h i c h can b e i n d u c e d i n the gold l a y e r for t h e g i v e n i n i t i a l pressure p u l s e if t h e i n c i d e n t s h o c k . w e r e i d e a l , i.e. a steady shock of 3.5 M b a r . A s s t a t e d i n p r e v i o u s d i s c u s s i o n s , t h e s h o c k - i n d u c e d pressure, in t h e g o l d layer is i n f l u e n c e d by t h e t h i c k n e s s e s of b o t h t h e front a l u m i n u m layer a n d t h e rear g o l d layer. H e n c e p r e s s u r e o p t i m i z a t i o n , or a l t e r n a t i v e l y t h i c k n e s s o p t i m i z a t i o n , represents the o p t i m i z a t i o n b e t w e e n i n c o m p l e t e shock b u i l d u p i n t h i n t a r g e t s a n d shock a t t e n t u a t i o n i n t h i c k ones. P r e v i o u s studies u s i n g c o m p u t e r s i m u l a t i o n s i n c l u d e t h e w o r k of S a l z m a n n et al.[54]  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  65  8-1  Front Aluminum Thickness (pm)  F i g u r e 4.25:  S h o c k i n d u c e d pressure i n t h e free surface o f g o l d as a f u n c t i o n of t h e  a l u m i n u m thickness.  T h e v a r i o u s lines d e n o t e different g o l d t h i c k n e s s e s :  8.4 um ( d a s h ) , 13 urn ( d o t - d o t - d o t - d a s h ) , 20 um ( d o t - d a s h ) .  2 um  (solid),  A l s o s h o w n is t h e m a x i m i u m  p r e s s u r e reached s o m e w h e r e i n a g o l d layer of i n f i n i t e t h i c k n e s s  (dot)  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  66  o n C H 2 - a l u m i n u m t a r g e t s i r r a d i a t e d b y m o d i f i e d G a u s s i a n pulses of 1.06 um as w e l l as t h a t of K a u s i k a n d G o d w a l [ l l 4 ] w i t h C H 2 - p l a t i n u m t a r g e t s a n d 1.06 um laser pulses. In a d d i t i o n to aasessing pressure enhancement, they c o n c l u d e d that pressure m a x i m i z a t i o n at t h e i n t e r f a c e c a n b e a c h i e v e d by o p t i m i z i n g t h e t h i c k n e s s of t h e s t a n d a r d . H o w e v e r , as i t is n o t p o s s i b l e t o m e a s u r e d i r e c t l y t h e p r e s s u r e at t h e interface, we s h a l l i n s t e a d a d o p t a n o t h e r c r i t e r i o n . T a k i n g t h e o p t i m i z a t i o n c r i t e r i o n as one of m a x i m u m p r e s s u r e at t h e free surface of t h e g o l d layer a n d r e f e r r i n g t o F i g u r e 4.25, o n e c a n  see  t h a t for e v e r y g o l d layer t h i c k n e s s , t h e r e e x i s t s a c o r r e s p o n d i n g o p t i m a l t h i c k n e s s i n t h e a l u m i n u m l a y e r . F o r e x a m p l e , t h e o p t i m a l a l u m i n u m t h i c k n e s s for a 2 p m g o l d l a y e r is a b o u t 40 p m , w h i l e i n t h e case of a n 8.4 p m g o l d l a y e r , one w o u l d choose an a l u m i n u m layer of a b o u t 26 p m . N o t e t h a t t h e p e a k pressures a c h i e v e d at t h e free surfaces i n t h e a b o v e t w o cases are never as h i g h as ?sw-  T h i s is b e c a u s e t h e f r o n t a l u m i n u m layers are  a l r e a d y t h i c k e n o u g h to a l l o w shock a t t e n t u a t i o n t o o c c u r . S i m i l a r l y , if the g o l d l a y e r is 20 p m t h i c k , t h e n t h e o p t i m a l a l u m i n u m t h i c k n e s s is a r o u n d 23 p m .  Once again,  Psw  is not r e a c h e d at t h e free surface since, i n t h i s case, t h e rear g o l d layer is t o o t h i c k a n d shock d a m p i n g  dominates.  Is t h e b e s t o p t i m i z a t i o n t h e n a c h i e v e d w h e n t h e f o r m a t i o n of t h e s t r o n g shock o c c u r s at t h e i n s t a n t w h e n it reaches t h e interface?  If so, t h e best s o l u t i o n w o u l d seem to be  solely d e p e n d e n t on t h e f r o n t a l u m i n u m t h i c k n e s s , g i v e n a n i n i t i a l d r i v i n g p u l s e . w o u l d be t h e case if one were to d e r i v e t h e m a x i m u m i n t e r f a c e p r e s s u r e [ l l 4 ] , satisfied  (i.e.  P$w  This a n d is  is r e a c h e d ) w h e n t h e a l u m i n u m t h i c k n e s s a p p r o x i m a t e l y equals to  19 p m as seen i n F i g u r e 4.23.  H o w e v e r , f r o m F i g u r e 4.25, i t is clear that s e t t i n g  a l u m i n u m t h i c k n e s s to be 19 p m is n o g u a r a n t e e t h a t t h e o p t i m a l pressure Psw  the  would  be i n d u c e d at t h e free surface of t h e g o l d l a y e r . T h i s is b e c a u s e t h e g o l d layer also p l a y s a. s i g n i f i c a n t r o l e i n d e t e r m i n i n g t h e f i n a l p r e s s u r e a t t a i n e d at its free surface.  This point  is best i l l u s t r a t e d i n F i g u r e 4.26, w h e r e t h e shock p r e s s u r e at t h e free surface is p l o t t e d  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  67  a g a i n s t t h e t h i c k n e s s of t h e g o l d l a y e r , w i t h the a l u m i n u m thicknesses r a n g i n g f r o m 11.5 t o 50 p m .  T h e n o n - u n i f o r m i t y of t h e shock p r e s s u r e i n t h e g o l d layer is e v i d e n t .  For  i n s t a n c e , for a 19 p m a l u m i n u m l a y e r , t h e shock pressure at t h e free surface o f a 2 p m g o l d l a y e r is s m a l l e r t h a n t h a t i n a 8.4 p m g o l d layer, w h i c h i n t u r n is less t h a n t h a t i n a 13 p m g o l d layer.  T h i s s e e m i n g l y strange s i t u a t i o n of i n c r e a s i n g s h o c k p r e s s u r e  w i t h i n c r e a s i n g g o l d layer t h i c k n e s s arises since, n o t w i t h s t a n d i n g the adverse effect of shcok d e c a y w h i c h has b e g u n i n t h e front a l u m i n u m layer (cf.  F i g u r e 4.23), t h e shock  f r o n t c o n t i n u e s to s t e e p e n as i t p r o p a g a t e s i n t h e g o l d l a y e r , c u l m i n a t i n g i n a shock f r o n t o f g r e a t e r a m p l i t u d e . O f c o u r s e , t h i s process c a n n o t c a r r y on i n d e f i n i t e l y as shock a t t e n t u a t i o n m u s t e v e n t u a l l y d o m i n a t e once t h e f r o n t s i d e r a r e f a c t i o n w a v e catches u p w i t h t h e s h o c k , a n d t h e p r e s s u r e is n o t s u s t a i n e d .  T h i s c a n be seen by c o m p a r i n g t h e  p r e s s u r e at t h e free surface i n t h e case of a 11.5 p m A l on 8.4 p m A u t a r g e t w i t h t h a t of a 11.5 p m A l on 13 p m A u t a r g e t ( F i g u r e 4 . 2 2 ) , w h e r e shock d a m p i n g s t a r t s t o t a k e over at a d e p t h of ~ 9 p m i n t h e g o l d layer.  In fact, if t h e front a l u m i n u m layer were  a l r e a d y t o o t h i c k (such as 50 p m i n F i g u r e 4.24), the free surface pressure i n g o l d w i l l decrease m o n o t o n i c a l l y w i t h i n c r e a s i n g gold t h i c k n e s s . T h u s pressure m a x i m a i z a t i o n is a, r a t h e r i n v o l v e d p r o c e s s , a n d one needs to t a k e i n t o a c c o u n t b o t h t h e front a n d b a c k l a y e r t h i c k n e s s e s of the t a r g e t . F i g u r e 4.26  also serves to b r i n g u p a n o t h e r i n t e r e s t i n g p o i n t , n a m e l y t h e role of  shock u n i f o r m i t y in d e t e r m i n i n g o p t i m a l thicknesses.  T h e present c r i t e r i o n of h a v i n g a  m a x i m u m p r e s s u r e at t h e free surface w i l l not b e a p p r o p r i a t e if one's a i m is E O S s t u d y , w h e r e it is m o r e d e s i r a b l e t o have an as u n i f o r m l y c o m p r e s s e d region as p o s s i b l e , i.e. as u n i f o r m a s h o c k as p o s s i b l e .  A nonuniform]}' s h o c k e d m a t e r i a l experiences d e n s i t y a n d  t e m p e r a t u r e g r a d i e n t s , c o n s e q u e n t l y affecting m e a s u r e m e n t s such as shock t r a n s i t t i m e s . F r o m t h i s p o i n t of v i e w a 34 p m a l u m i n u m front layer i n a n a l u m i n u m - o n - g o l d target, y i e l d s t h e m o s t u n i f o r m s h o c k p r e s s u r e i n g o l d e x t e n d i n g f r o m 2 t o 13 p m , a l t h o u g h at  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  68  A 6 8 10 12 DEPTH IN GOLD LAYER (urn)  F i g u r e 4.26:  S h o c k p r e s s u r e at t h e free surface of g o l d as a f u n c t i o n of t h i c k n e s s i n  t h e g o l d layer for v a r i o u s front a l u m i n u m t h i c k n e s s e s : ( d o t - d a s h ) , 34 um ( s o l i d ) , a n d 50 um ( d a s h )  11.5 urn ( d o t - d o t - d a s h ) ,  19 um  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  69  t h e e x p e n s e of l o w e r free surface pressure. In s u m m a r y , we have seen t h a t t h i c k n e s s o p t i m i z a t i o n in a n i m p e d a n c e - m i s m a t c h e d t a r g e t needs to a d o p t different c r i t e r i a d e p e n d i n g o n w h e t h e r t h e free surface pressure • is t o b e m a x i m i z e d , or w h e t h e r t h e s h o c k p r e s s u r e is to be as u n i f o r m as p o s s i b l e .  In  a d d i t i o n , we h a v e f o u n d t h a t b o t h t h e f r o n t a l u m i n u m a n d the rear g o l d layer p l a y a role i n t h e pressure e v o l u t i o n , a n d m u s t b o t h b e t a k e n i n t o a c c o u n t .  4.1.2.B.ii H Y R A D  Simulations  I n this p a r t of the s i m u l a t i o n s , we c a l c u l a t e t h e  s h o c k t r a j e c t o r i e s i n 19 or 26.5 fim a l u m i n u m o n 8.4 or 13 p m g o l d u s i n g H Y R A D i n c l u d i n g t h e process of r a d i a t i o n t r a n s p o r t . W e h a v e p e r f o r m e d t h e s i m u l a t i o n s u s i n g t w o different E O S m o d e l s of g o l d : S E S A M E a n d t h e n e w c a l c u l a t i o n i n c o p o r a t i n g m e l t i n g transition.  F i g u r e 4.27 shows t h e c a l c u l a t e d shock t r a j e c t o r i e s together w i t h the mea-  s u r e d shock transit, t i m e s for v a r i o u s t a r g e t s . T h e agreement, b e t w e e n e x p e r i m e n t a l d a t a a n d b o t h c a l c u l a t e d shock p a t h s is g o o d , i n d i c a t i n g t h e v a l i d i t y of b o t h E O S m o d e l s for g o l d , at least i n s o f a r as s h o c k v e l o c i t y is c o n c e r n e d .  4.2  Brightness  Temperature Study with A l u m i n u m - G o l d Targets  A n o t h e r i m p o r t a n t t h e r m o d y n a m i c a l p a r a m e t e r c h a r a c t e r i z i n g the e q u a t i o n of state of a s h o c k e d m a t e r i a l is t h e shock t e m p e r a t u r e T ( w h i c h is related to t h e i n t e r n a l energy  E of e q u a t i o n (2.7).) A s suggested i n §1.1 and § 2 . 4 . 2 , the m e a s u r e m e n t s of T is e x p e c t e d t o c l a r i f y o u r u n d e r s t a n d i n g of shock m e l t i n g i n g o l d , a n d also t o place a c o n s t r a i n t on t h e p r e d i c t i o n s b a s e d o n v a r i o u s t h e o r e t i c a l E O S m o d e l s . H e r e we s h a l l refer t o the shock  Chapter  4.  Luminescence  ~1 15  Measurements  in Single  and Doubled-Layered  Targets  70  1  1  1  1  1  1  1  1—  20  25  30  35  40  45  50  55  Lagrangian Coordinate (/mi)  F i g u r e 4 . 2 7 : S h o c k p a t h s as c a l c u l a t e d b y H Y R A D i n 19 um A l a n d 13 um A u t a r g e t u s i n g S E S A M E E O S ( d o t - d o t - d a s h ) , a n d u s i n g n e w g o l d E O S (dash); i n 26.5 um A l a n d 13 um A u t a r g e t u s i n g S E S A M E E O S ( d o t - d a s h ) , a n d u s i n g new g o l d E O S ( d o t ) . T h e s h o c k p a t h i n 53 um A l ( s o l i d ) is i n c l u d e d . A l s o p l o t t e d are t h e e x p e r i m e n t a l p o i n t s for various A l - A u targets a n d pure A l targets.  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-La.ye.red  Targets  71  t e m p e r a t u r e as t h e b r i g h t n e s s t e m p e r a t u r e b e c a u s e i t is o b t a i n e d f r o m t h e i n t e n s i t y of the shock-induced luminous emission. T h i s measurement  t e c h n i q u e has p r e v i o u s l y b e e n  used t o y i e l d t e m p e r a t u r e d a t a i n a l u m i n u m [ l 0 9 ] a n d l i q u i d  4.2.1  Experimental  argon[115].  Observations  I n t h i s e x p e r i m e n t , the b r i g h t n e s s t e m p e r a t u r e is i n f e r r e d f r o m m e a s u r e m e n t s of t h e i n t e n s i t y of the s h o c k - i n d u c e d l u m i n e s c e n c e at t h e free surface of t h e t a r g e t . T h e e m i s s i o n is r e c o r d e d by t h e streak c a m e r a at a faster streak speed t h a n t h a t used i n t h e shock t r a n s i t t i m e m e a s u r e m e n t s i n §4.1 since we are p r i m a r i l y c o n c e r n e d w i t h t h e m e a s u r e m e n t of t h e l u m i n o u s e m i s s i o n at v e r y early t i m e s to r e d u c e t h e effect of t h e o p a c i t y of t h e p l a s m a e x p a n d i n g f r o m t h e free surface i n t o the s u r r o u n d i n g v a c u u m . M e a s u r e m e n t s are m a d e i n t a r g e t s w i t h a 19 or 26.5 um a l u m i n u m layer o n e i t h e r an 8.4 o r 13 um g o l d l a y e r . T h e s e f o u r t a r g e t s are e x p e c t e d to achieve a l m o s t the h i g h e s t shock p r e s s u r e i n g o l d (see F i g u r e 4.25). W e have also o b t a i n e d d a t a for 38.4 um  pure  a l u m i n u m t a r g e t s , w h i c h w i l l serve as t h e E O S s t a n d a r d . F i g u r e s 4.28 t o 4.32 show t h e t y p i c a l t i m e - r e s o l v e d and t i m e - i n t e g r a t e d e m i s s i o n f r o m a p u r e 38.4 um A l f o i l , a 19 um A l o n 13 um A u t a r g e t , a 19 urn A l o n 8.4 um A u t a r g e t , a 26.5 um A l o n 8.4 um A u t a r g e t , a n d a 26.5 / / m A l on 13 um A u t a r g e t r e s p e c t i v e l y . are o b s e r v e d i n t h e shock b r e a k o p u t r e g i o n s .  N o significant, h o t spots  T h e t y p i c a l rise t i m e s i n t h e i n t e n s i t y of  the s h o c k - i n d u c e d l u m i n o u s e m i s s i o n are f o u n d t o b e ~ 2 5 0 ps, w h i c h c a n be a t t r i b u t e d to t h e c o m b i n e d effects of surface roughness ( ~ 6 0 p s ) , i r r a d i a t i o n n o n u m i f o r m i t y ( ~ 6 0 0 ps), a n d streak c a m e r a e n t r a n c e slit h e i g h t (~8'0 ps). The. s u b s e q u e n t r a p i d decrease i n t h e i n t e n s i t y results f r o m t h e r e a r s i d e m a t e r i a l b e i n g released by t h e r a r e f a c t i o n wave, w h i c h f o r m s an o p t i c a l l y t h i c k m e d i u m a t t e n t u a t i n g t h e r a d i a t i o n f r o m t h e hot m a t e r i a l behind[116]. In o u r stud}?, we have t a k e n a d v a n t a g e o f t h e fact t h a t b o t h o u r m e a s u r e m e n t s  on  F i g u r e 4.28: T e m p o r a l l y r e s o l v e d a n d i n t e g r a t e d p l o t of t h e b a c k s i d e e m i s s i o n i n t e n s i t y of a 38.4 um A l t a r g e t , w i t h t i m e zero b e i n g t h e p e a k of t h e laser p u l s e .  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  1100-p 1000900-  (a)  eoo•5 700s  600>Co 500c £ 400-  ^—  3002001000-  1.0 h2 TIME (nsecs)  200000-  (b) 150000  c  50000H  —I— 0.6  0.8  1.0 1.2 T i m e (nsecs)  F i g u r e 4.29: S a m e as F i g u r e 4.28except t a r g e t is 19 p m A l o n 13 p m A u  73  a.pter 4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  700  1.0  1.2 TIME (nsecs)  1  1  100000-1  0.6  -i  0.8  1.0  1  1.2 1.4 Time (nsecs)  1  1.6  1-  1.8  F i g u r e 4.30: S a m e as F i g u r e 4.28except t a r g e t is 19 p m A l o n 8.4 p m A u  Chapter  4.  Luminescence  Measurements  m Single  and Douhled-Layered  Targets  800  TIME (nsecs)  1  200000-.  (b)  Time (nsecs)  F i g u r e 4 . 3 1 : S a m e as F i g u r e 4 . 2 S e x c e p t t a r g e t is 26.5mic.ron A l on S.4 p m A u  75  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  400  TIME (nsecs)  120000-  (b) 100000-  80000-  k_  '</) c  60000-  40000-  20000 4  L4  MS  l!g  2!0  2*2  2T4  2~6  Time (nsecs)  F i g u r e 4.32: S a m e as F i g u r e 4.28except t a r g e t is 26.5 um A l on 13 um A u  76  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  77  t h e s i n g l e a n d d o u b l e l a y e r e d t a r g e t s are done u s i n g t h e s a m e i m a g i n g s y s t e m , a n d t h a t t h e s h o c k b r e a k o u t regions i n b o t h t y p e s o f targets are s i m i l a r . T h e r e f o r e , k n o w i n g t h e t e m p e r a t u r e of t h e s h o c k - h e a t e d a l u m i n u m , the b r i g h t n e s s t e m p e r a t u r e of g o l d c a n be o b t a i n e d b y c o m p a r i n g t h e i n t e n s i t y of e m i s s i o n f r o m g o l d t o t h a t f r o m a l u m i n u m , w i t h o u t t h e need for an a b s o l u t e i n t e n s i t y c a l i b r a t i o n of t h e s t r e a k c a m e r a a n d o p t i c s s y s t e m . F r o m F i g u r e s 4.28 t o 4.32, it c a n be seen t h a t t h e i n s t a n t a n e o u s e m i s s i o n i n t e n s i t y is h i g h l y s p i k y a n d m o d u l a t e d , c o n s e q u e n t l y t h e r a t i o of t h e e m i s s i o n i n t e n s i t y c a n n o t p r o d u c e a n y m e a n i n g f u l results. O n the o t h e r h a n d , t h e r a t i o of t h e t i m e - i n t e g r a t e d i n t e n s i t y does a l l o w for an o b j e c t i v e a n d u m a m b i g u o u s a n a l y s i s of t h e d a t a .  4.2.2  Computer Simulations  T h e s i m u l a t i o n of t h i s e x p e r i m e n t is p e r f o r m e d i n t w o steps. F i r s t , we use t h e H Y R A D c o d e t o f o l l o w t h e e n t i r e h i s t o r y o f t h e t a r g e t f r o m the onset of the laser p u l s e t o the t i m e of s h o c k a r r i v a l at t h e free surface. T h e n , t o s i m u l a t e p r o p e r l y t h e m e a s u r e m e n t of t h e s h o c k - i n d u c e d l u m i n o u s e m i s s i o n f r o m t h e target rear surface, the P U C code is used to c a l c u l a t e t h e e m i s s i o n i n t e n s i t y f r o m t h e r a r e f y i n g p l a s m a at t h e rear side of t h e target as d e t e c t e d b y t h e streak c a m e r a .  4.2.2.A H Y R A D  Simulations  H Y R A D is u s e d since it a l l o w s for n o t o n l y a m o r e c o m p l e t e t r e a t m e n t of t h e lasert a r g e t i n t e r a c t i o n s , b u t also t h e p o s s i b i l i t y of accessing t h e effect of r a d i a t i o n t r a n s p o r t i n t h e e x p e r i m e n t . I n t h e c o d e , t h e E O S of a l u m i n u m is o b t a i n e d f r o m the S E S A M E d a t a l i b r a r y , a n d t h e a t o m i c p h y s i c s m o d e l has b e e n d e s c r i b e d i n § 2 . 4 . 1 . F o r g o l d , t h e a t o m i c and  o p a c i t y d a t a used are t a k e n f r o m t h e S E S A M E l i b r a r y , b u t t w o sets of E O S d a t a  ( S E S A M E a n d t h e n e w s o l i d / l i q u i d s t a t e c a l c u l a t i o n ) are used. T h e s p a t i a l r e s o l u t i o n i n these s i m u l a t i o n s is less t h a n 0.25 / m i .  Chapter  4.  4.2.2.A.i  Luminescence  Measurements  in Single  E f f e c t of R a d i a t i o n T r a n s p o r t  and Doubled-Layered  Targets  78  In t h i s s e c t i o n we c o n s i d e r t h e effects  of r a d i a t i o n t r a n s p o r t i n m o r e d e t a i l , a n d e x a m i n e t h e shock profiles i n a 19 p m A l o n 13 p m A u t a r g e t u s i n g S E S A M E E O S d a t a , e m p h a s i z i n g o n h o w r a d i a t i v e transfer m a y affect t h e s h o c k t e m p e r a t u r e .  R a d i a t i v e h e a t i n g is e x p e c t e d t o p l a y o n l y a m i n o r role  i n t h e g o l d l a y e r as a l r e a d y r e m a r k e d i n section § 2 . 3 . 2 . F i g u r e s 4.33 shows t h e s p a t i a l profiles of d e n s i t y , pressure, a n d t e m p e r a t u r e at a t i m e of 1.26 ns before t h e laser p e a k w h e n t h e p r o c e s s of r a d i a t i o n t r a n s p o r t is n e g l e c t e d ( h e n c e f o r t h referred t o as case [A]). F i g u r e 4.34 shows s i m u l a r profiles i n t h e presence of r a d i a t i o n t r a n s p o r t (case [B]). s h o c k front is m a r k e d b y a s h a r p increase i n d e n s i t y , p r e s s u r e a n d t e m p e r a t u r e o c c u r s at a. d e p t h of ~ 1 0 p m i n t h e t a r g e t i n figures 4.33 a n d 4.34). t h e different i n i t i a l t e m p e r a t u r e s ,  (which  W e note  that  4 0 0 K i n A l a n d 1 3 0 K i n A u , are necessary due t o  l i m i t a t i o n s i n t h e m o d e l s of t h e g r o u n d s t a t e t e m p e r a t u r e i n t h e S E S A M E d a t a , are c h o s e n so t h a t t h e i n i t i a l pressures i n b o t h m a t e r i a l s are t h e s a m e .  and  Therefore the  i n i t i a l t e m p e r a t u r e difference i n t h e t w o m a t e r i a l s does not signify a r e a l d i s c o n t i n u i t y at t h e i r i n t e r f a c e .  The  temperature  W e h a v e also i n d i c a t e d e d t h e X - r a y p o w e r a b s o r p t i o n  profile i n the target i n F i g u r e 4.34.  W e see t h a t a l t h o u g h m o s t of t h e X - r a y energy is  d e p o s i t e d i n t h e first 7 p m of t h e a l u m i n u m l a y e r , s o m e r a d i a t i o n is d e p o s i t e d well i n t o t h e t a r g e t also, even a h e a d of t h e s h o c k front a n d h e n c e p r e h e a t i n g t h e a l u m i n u m ( n o t e the. slight, t e m p e r a t u r e a n d p r e s s u r e increase a b o v e a m b i e n t t e m p e r a t u r e a n d p r e s s u r e i n a l u m i n u m a h e a d of t h e s h o c k ) . C o n s e q u e n t l y , t h e t e m p e r a t u r e g r a d i e n t is less i n case [B] t h a n [A], T h i s p r e h e a t i n g of the c o l d a l u m i n u m layer a h e a d of the shock front w i l l not ha.ve been d e s i r a b l e i n E O S studies since t h e p r e - s h o c k e d s t a t e of a m a t e r i a l w i l l d e p e n d on t h e r a d i a t i o n t r a n s p o r t p r o c e s s . A l s o , due to t h e l a r g e o p a c i t y i n c r e a s e of g o l d over a l u m i n u m (e.g. at 1 k e V , o p a c i t y of g o l d is five t i m e s t h a t of a l u m i n u m ) , g o l d is a m u c h b e t t e r a b s o r b e r of r a d i a t i o n t h a n a l u m i n u m a n d t h e r e m a i n i n g X - r a d i a t i o n is d e p o s i t e d i n t h e first 2 t o 3 p m of t h e g o l d l a y e r . T h e r e is s t i l l p r e h e a t i n g i n g o l d , b u t t h e l e v e l is  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  79  Lagrangian Coordinate (/im)  F i g u r e 4 . 3 3 : A s n a p s h o t of t h e b y d r o d y n a m i c p r o f i l e i n a 19 p m A l o n 13 p m A u t a r g e t at t = - 1 . 2 6 ns. R a d i a t i o n t r a n s p o r t process is n e g l e c t e d , a n d b o t h A l a n d A u E O S d a t a are f r o m S E S A M E .  Chapter  4.  F i g u r e 4.34:  Luminescence  Measurements  S a m e as F i g u r e 4.33 except  a b s o r b e d X - r a y p o w e r is also p l o t t e d .  in Single  and Doubled-Layered  Targets  r a d i a t i o n t r a n s p o r t process is i n c l u d e d .  80  The  Chapter  4.  Luminescence  Measurements  in Single  and Double.d-La.ye.red  Targets  81  v e r y l o w since m o s t of t h e r a d i a t i o n have been a b s o r b e d i n a l u m i n u m , a n d the e x t e n t of t h e p r e h e a t e d r e g i o n is v e r y s m a l l . N e x t , we show i n figures 4.35 a n d 4.36 t h e c o r r e s p o n d i n g t w o cases at 0.24 ns after t h e laser peak w h e n t h e shock has crossed t h e a l u m i n u m - g o l d i n t e r f a c e i n t o t h e g o l d layer.  A s before, t h e g r a d i e n t i n t h e t e m p e r a t u r e profile i n case [B] is m o r e g r a d u a l  t h a n i n case [A] due to r a d i a t i o n d e p o s i t i o n . W e also n o t e t h e pressure c o n t i n u i t y across t h e i n t e r f a c e , as r e q u i r e d b y t h e b o u n d a r y c o n d i t i o n . A decrease of t h e s h o c k p r e s s u r e , t e m p e r a t u r e , a n d to a lesser e x t e n t , d e n s i t y , i n case [B] c a n also be o b s e r v e d as a r e s u l t of r a d i a t i v e energy loss f r o m t h e h o t p l a s m a l e a d i n g t o a l o w e r a b l a t i o n pressure.  Finally,  t h e shock f r o n t has p r o p a g a t e d p a s t t h e first few m i c r o n s of t h e g o l d l a y e r w h e r e t h e r e is X - r a y energy a b s o r p t i o n .  A s a r e s u l t , r a d i a t i o n t r a n s p o r t no l o n g e r c o n s t i t u t e s  p r e h e a t p r o b l e m , a n d t h e subsequent  a  shock s t r u c t u r e b e c o m e m u c h m o r e w e l l - d e f i n e d ,  c o m p a r a b l e to t h a t i n case [A]. In t h i s m a n n e r we have a c h i e v e d a " c l e a n " shock, i.e. a q u a s i - steady shock e n t e r i n g t h e c o l d m a t e r i a l w i t h o u t s i g n i f i c a n t p r e h e a t . T h e a d v a n t a g e of t h e i m p e d a n c e m i s m a t c h m e t h o d i n r a d i a t i v e p r e h e a t s u p p r e s s i o n i n h i g h - Z m a t e r i a l is r e a l i z e d . T a b l e 4.1 s u m m a r i z e s results of t h e s i m u l a t i o n s at t h e t i m e of s h o c k b r e a k o u t t h e free surface of g o l d .  W e s h o u l d e m p h a s i z e t h e s i g n i f i c a n t d r o p i n shock  at  temper-  a t u r e (—23%) as r a d i a t i o n transport, is t a k e n i n t o a c c o u n t , a n d t h i s s h o u l d lead t o a c o r r e s p o n d i n g decrease i n t h e rear surface e m i s s i o n .  4.2.2.A.ii  EOS  Models  In t h i s section we w i l l c o m p a r e t h e effects of t h e t w o i n t h e same 19 um  A l o n 13  T h e t w o E O S m o d e l s of g o l d are r e s p e c t i v e l y t h e S E S A M E  tabulated  different. E O S m o d e l s o f g o l d o n t h e shock p a r a m e t e r s  um A u t a r g e t .  d a t a a n d t h e n e w c a l c u l a t i o n i n c o p o r a t i n g t h e m e l t i n g t r a n s i t i o n . T a b l e 4.2 presents t h e s i m u l a t i o n r e s u l t s . W e see s i m i l a r q u a l i t i v e b e h a v i o r i n t h e shock p r o p a g a t i o n , b u t t h e  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  LASER 10 t 8  IO1IO 2 .  10 7  10  io-i  6  w < u a.  2  u H  10 -10" 4  3  IQ3 J a o - J I i o - J  Lagrangian Coordinate (jim)  F i g u r e 4 . 3 5 : S a m e as F i g u r e 4.33 e x c e p t t i m e is at t = 0.24 ns  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  <= LASER  Lagrangian Coordinate (^m)  F i g u r e 4 . 3 6 : S a m e as F i g u r e 4.35 b u t r a d i a t i o n t r a n s p o r t process is i n c l u d e d  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  84  Targets  No Radiation Transport  W i t h Radiation Transport  0.88±0.02  0.85±0.02  s h o c k b r e a k o u t t i m e (ns)  1.08±0.02  1.19±0.02  shock breakout  1.86±0.05  1.80±0.05  7.1±0.2  6.0±0.2  2.46±0.04  2.00±0.04  $ = 2.3 x 1 0 1 3  W/cm2  s t e a d y shock v e l o c i t y i n g o l d (x 1 0  6  cm/s)  compression ratio shock breakout  pressure  in gold ( M b a r ) shock breakout  temperature  in g o l d ( e V )  T a b l e 4.1: c o m p a r a t i v e s t u d y of t h e effects of r a d i a t i o n t r a n s p o r t on free surface shock p a r a m e t e r s for a 19 p m A l on 13 p m A u t a r g e t  S E S A M E G o l d d a t a (2700)  N e w G o l d d a t a (2788)  0.85±0.02  0.95±0.02  shock b r e a k o u t t i m e (ns)  1.19±0.02  1.04±0.02  shock b r e a k o u t  1.80±0.05  1.71 ± 0 . 0 5  6.0 ± 0 . 2  6.1±0.2  2.00±0.04  1.54±0.04  $ = 2.3 x 1 0 1 3  W/cm2  s t e a d y shock v e l o c i t y i n g o l d (x 1 0  6  cm/s)  compression ratio shock breakout  pressure  in gold ( M b a r ) shock b r e a k o u t  temperature  in gold (eV)  T a b l e 4.2:  c o m p a r a t i v e s t u d y of t h e effects of o u r new g o l d E O S d a t a on free  surface  s h o c k p a r a m e t e r s for a 19 p m A l o n 13 p m A u t a r g e t , r a d i a t i o n t r a n s p o r t is i n c l u d e d  Chapter  4.  Luminescence  Measurements  in Single  <S> = 2.3 x 1 0 1 3 W / c m 2 19 um A l + 8.4 um A u  New Gold E O S  0.58±0.02  0.55±0.02  1.79±0.05  1.70±0.05  5.8±0.2  5.9±0.2  (eV)  1.83±0.04  1.46±0.04  / i , (ns)  1.03±0.02  1.02±0.02  p/Po P (Mbar)  1.76±0.05  1.68±0.05  5.4±0.2  5.4±0.2  T(eV).  1.68±0.04  1.28±0.04  / f . (ns)  1.51±0.02  1.48±0.02  p/po P (Mbar)  1.75±0.05  1.62±0.05  5.3±0.2  5.3±0.2  T(eV)  1.67±0.04  1.20±0.04  h  T  26.5 um A l + 13 um A u  Table 4.3:  Targets  S E S A M E Gold E O S (ns)  p/Po P (Mbar) 2 6 . 5 um A l -f 8.4 um A u  and Doubled-Layered  c o m p a r a t i v e stud}? of the effects of o u r n e w g o l d E O S d a t a on t h e shock  b r e a k o u t t i m e s (t-b), t h e c o m p r e s s i o n r a t i o (p/po), t e m p e r a t u r e (T)  the s h o c k p r e s s u r e ( P ) . and t h e shock  at b r e a k o u t for v a r i o u s A l - A u targets. R a d i a t i o n t r a n s p o r t is i n c l u d e d .  shock b r e a k s o u t sooner (see F i g u r e 4.27) a n d t h e shock t e m p e r a t u r e is decreased T a b l e 4.2).  85  (see  T h i s r e s u l t we a t t r i b u t e to t h e "softer'" n a t u r e o f t h e l i q u i d , as t h e l i q u i d  p h a s e c a n a t t a i n a g r e a t e r shock v e l o c i t y u n d e r the s a m e p r e s s u r e t h a n the s o l i d .  The  lower t e m p e r a t u r e is also e x p e c t e d since energy is e x p e n d e d d u r i n g m e l t i n g w i t h o u t a c o r r e s p o n d i n g t e m p e r a t u r e increase.  Table. 4.3 presents the s i m u l a t i o n results for t h e  r e m a i n i n g three t a g e t s , w h i c h are 19 pm A l o n 8.'4 pm A u , 26.5 p m A l on 8.4 p m A u , a n d 26.5 p m A l o n 13 p m A u .  4.2.2.B P U C Simulations T h e s e c o n d s t e p of t h e s i m u l a t i o n for t h e b r i g h t n e s s t e m p e r a t u r e s t u d y uses P U C to c a l c u l a t e t h e t i m e e v o l u t i o n of t h e i n t e n s i t y of e m i s s i o n f r o m t h e target rear surface at a n d s u b s e q u e n t t o shock b r e a k o u t . T h e shock d e n s i t y , p r e s s u r e , a n d t e m p e r a t u r e at the rear surface of t h e target ( a l u m i n u m o r g o l d ) at b r e a k o u t as c a l c u l a t e d by H Y R A D  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  86  i n § 4 . 1 . 1 . B a n d § 4 . 1 . 2 . B . i i are u s e d as t h e i n i t i a l c o n d i t i o n s of t h e s h o c k e d m e d i u m i n P U C w h i c h t h e n c a l c u l a t e s t h e r a d i a t i o n e m i t t e d at 4 3 0 0 A as t h e target rarefies i n t o t h e v a c u u m . T h e s p a t i a l r e s o l u t i o n i n these c a l c u l a t i o n s is less t h a n 0.05 p m . A p l o t of t h e rearside e m i s s i o n f r o m g o l d ( f r o m a 19 p m A l o n 13 p m A u t a r g e t ) a n d a l u m i n u m ( f r o m a 38.4 p m A l t a r g e t ) is s h o w n i n F i g u r e 4.37. H e r e t i m e z e r o c o r r e s p o n d s t o t h e t i m e of s h o c k b r e a k o u t at t h e free surface. W e have also used b o t h t h e S E S A M E a n d o u r n e w g o l d E O S d a t a . W e see t h a t t h e r e a r s i d e e m i s s i o n decreases r a p i d l y ( d r o p p i n g 2 o r d e r s of m a g n i t u d e i n t h e first 30 p s ) . T h i s is because as t h e rear surface u n l o a d s , t h e e x p a n d i n g c o o l e r m a t e r i a l r a p i d l y shields t h e h o t p l a s m a b e h i n d , so t h a t t h e i n t e n s i t y of t h e e m i s s i o n t h a t c a n b e d e t e c t e d also d r o p s r a p i d l y . F i g u r e 4.38 is a p l o t of t h e t i m e - i n t e g r a t e d e m i s s i o n f o r t h e s a m e t w o t a r g e t s . W e see t h a t t h e i n i t i a l r a p i d rise i n t h e e m i s s i o n reflects t h e laxge a m o u n t of r a d i a t i o n at the b e g i n n i n g of t h e shock u n l o a d i n g . A n a b s o l u t e c o m p a r i s o n of t h e rearside e m i s s i o n i n t e n s i t y between e x p e r i m e n t a l a n d s i m u l a t i o n r e s u l t s c a n n o t b e m a d e since a n a b s o l u t e i n t e n s i t y c a l i b r a t i o n of the streak c a m e r a is n o t m a d e . W e ha.ve i n s t e a d c o m p a r e d t h e r a t i o of t h e t i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t i e s for g o l d t o a l u m i n u m . T h e results for 19 p m A l o n 13 p m A u a n d 38.4 p m A l t a r g e t s are p l o t t e d i n F i g u r e 4 . 3 9 ( a ) . W e c o n s i d e r t h o s e d a t a b e t w e e n 50 t o 300 ps to be m o r e r e l i a b l e , since at v e r y e a r l y t i m e s we are l i m i t e d b y e x p e r i m e n t a l u n c e r t a i n t i e s i n d e t e r m i n i n g t h e t i m e s of s h o c k b r e a k o u t , w h i l e at l a t e times t h e effects of t h e r a r e f a c t i o n wave a n d t h e i n c r e a s i n g a b s o r p t i o n b y the released p l a s m a b e c o m e i n c r e a s i n g l y m o r e dominant.  In a d d i t i o n , we h a v e also b e s t - f i t t e d a m e a s u r e d e m i s s i o n r a t i o b y v a r y i n g  t h e shock t e m p e r a t u r e i n P U C . T h e results are s h o w n in F i g u r e s 4 . 3 9 ( b ) . o t h e r t a r g e t sots a,re p r e s e n t e d i n F i g u r e s 4.40 to 4.42.  Results from  T h e results for t h e r e m a i n i n g  19 p m A l on 8.4 p m A u , as w e l l as 26.5 p m A l on 19 a n d 8.4 p m A u t a r g e t s are p l o t t e d r e s p e c t i v e l y in figures 4.43 t o 4 5 .  Chapter  4.  F i g u r e 4.37:  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  B a c k s i d e e m i s s i o n f r o m a 19 p m A l o n 13 p m A u t a r g e t u s i n g  (dash) and our new (dot-dot-dot-dash)  87  SESAME  g o l d E O S d a t a , as well as f r o m a 38.4 p m A l  (solid) target, w i t h t i m e zero c o r r e s p o n d i n g to shock breakout  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  88  150  ioo H  50 H  200  300  400  500  Integration Time (ps)  F i g u r e 4.38: T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y of t h e p r e v i o u s F i g u r e 4.37: t h a t of a 19 p m A l on 13 p m A u t a r g e t u s i n g S E S A M E ( d o t ) a n d t h e n e w ( d a s h ) g o l d d a t a ; t h a t of a 38.4 p m A l t a r g e t  (dot-dash).  Chapter  4.  Luminescence  Measurements  in Single  8-1  and Doubled-Layered  Targets  89  T = 21800 K  5-  T - 17B50 K  1-  100  200  300  400  Integration Time (ps)  500  6-1  5-  T = 15500 K F  100  200  300  Integration Time (ps)  400  500  F i g u r e 4.39: T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y r a t i o for a 19 um A l on 13 um A u target t o a 38.4 um A l t a r g e t : (a) u s i n g S E S A M E ( d o t ) , a n d new g o l d ( d o t - d a s h ) E O S d a t a : a n d (b) b e s t - f i t t e d t e m p e r a t u r e Tp c u r v e ( d o t - d o t - d a s h ) to an e x p e r i m e n t a l c u r v e ( d o t - d a s h ) .  Chapter  4  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  90  F i g u r e 4.40: S i m i l a r t o F i g u r e 4 . 3 9 ( b ) : an e x p e r i m e n t a l t i m e - i n t e g r a t e d e m i s s i o n i n t e n sity r a t i o is b e s t - f i t t e d w i t h a s h o c k t e m p e r a t u r e TF.  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  91  6-1  O  H  i  0  i 100  i  200  i 300  i 400  i 500  i 200  1 300  1 400  1 500  Integration Time (ps)  6-1  (b) 5-  o  H  i 0  i 100  Integration Time (ps)  F i g u r e 4.41: S i m i l a r t o F i g u r e 4 . 3 9 ( b ) : an e x p e r i m e n t a l t i m e - i n t e g r a t e d e m i s s i o n i n t e n sity r a t i o is b e s t - f i t t e d w i t h a s h o c k t e m p e r a t u r e T p .  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  .  92  (a) 5H  H  4  <  H  TF» 17500 K 2  7L  w  100  200  300  400  500  Integration Time (ps)  \  (b)  \ H  f  /  oo  X  T -19250K  4  2H  100  200  300  400  500  Integration Time (ps)  F i g u r e 4.42: S i m i l a r t o F i g u r e 4 . 3 9 ( b ) : an e x p e r i m e n t a l t i m e - i n t e g r a t e d e m i s s i o n i n t e n sity 7 r a t i o is b e s t - f i t t e d w i t h a shock t e m p e r a t u r e  Tp.  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  93  T-2H00K  5-  T =19000K F  <  \  .  in W H  3 -  2-  1-  100  200  300  400  500  Integration Time (ps)  F i g u r e 4.43:  T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y r a t i o for a 19 / / m A l o n 6.4 um  Au  target to a 38.4 um A l t a r g e t u s i n g S E S A M E ( d o t ) , a n d t h e n e w ( l o n g d o t - d a s h ) g o l d E O S d a t a . T h e e x p e r i m e n t a l d a t a ( l o n g d a s h , s o l i d , l o n g d o t - d o t - d o t - d a s h ) are i n d i v i d u a l l y b e s t - f i t t e d w i t h a shock t e m p e r a t u r e 7> (short d o t - d o t - d o t - d a s h , short d a s h , short dot-dash)  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  94  T=19800K  4-  < H  T = 17000 K F  <L U  2-  T=14970 K 1-  100  200  300  400  500  Integration Time (ps)  Au target, t o a 38.4 fim A l t a r g e t u s i n g S E S A M E ( d o t ) , a n d t h e n e w ( d o t - d a s h ) g o l d E O S d a t a . T h e e x p e r i m e n t a l d a t a ( l o n g d a s h , s o l i d ) are i n d i v i d u a l l y b e s t - f i t t e d w i t h a shock t e m p e r a t u r e TF ( d o t - d o t - d o t - d a s h , short d a s h ) F i g u r e 4.44:  T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y r a t i o for a 26.5 fim A l on 6.4 fim  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  95  6 -i  5-  T= 19200K  14500K 2-  T = 14000K  100  200  300  400  500  Integration Time (ps)  F i g u r e 4.45:  T i m e - i n t e g r a t e d e m i s s i o n i n t e n s i t y r a t i o for a 26.5 fim A l o n 13 fim A u  target, to a. 38.4 fim A l t a r g e t u s i n g S E S A M E ( d o t ) , a n d t h e new ( d o t - d a s h ) g o l d E O S data.  O n e e x p e r i m e n t a l d a t a ( l o n g d a s h ) is b e s t - f i t t e d w i t h a shock t e m p e r a t u r e  (short dash) while the other (solid) coincides w i t h the calculated curve  (dot-dash).  T>  Chapter  4.  Luminescence  Measurements  in Single  and Doubled-Layered  Targets  96  It c a n b e seen t h a t c a l c u l a t i o n s u s i n g t h e S E S A M E E O S da.ta for g o l d s e e m t o overe s t i m a t e t h e o b s e r v e d t i m e - i n t e g r a t e d i n t e n s i t y r a t i o , w h i l e t h o s e u s i n g t h e n e w E O S for g o l d a p p e a r to be i n m u c h closer agreement  w i t h experimental observations.  Since the  l a t t e r c a l c u l a t i o n i n c l u d e s t h e l i q u i d p h a s e of g o l d , t h e m e l t i n g p h e n o m e n a is t r e a t e d i n t h e s i m u l a t i o n . T h e e x p e r i m e n t a l results t h u s c l e a r l y i n d i c a t e t h a t g o l d e x i s t s i n t h e l i q u i d p h a s e at h i g h pressure. F i g u r e 4.46 shows t h e H u g o n i o t of g o l d f r o m S E S A M E a n d t h a t f r o m t h e n e w E O S c a l c u l a t i o n s , as w e l l as t h e d e d u c e d shock points i n the studies.  pressure-temperature  T h e s e p o i n t s are o b t a i n e d as f o l l o w s . T h e pressures are t h e free  surface p r e s s u r e s as c a l c u l a t e d i n t h e s i m u l a t i o n s b y H Y R A D i n § 4 . 2 . 2 . A , u s i n g t h e n e w gold E O S data.  T h e y are, r e s p e c t i v e l y , 6.1 M b a r i n t h e 19 um A l o n 13 um A u t a r g e t ,  5.9 M b a r i n t h e 19 p m A l on 8.4 p m A u t a r g e t , 5.5 M b a r i n t h e 26.5 p m A l o n 8.4 p m A u t a r g e t , a n d 5.3 M b a r i n t h e 26.5 p m A l o n 13 p m A u t a r g e t . T h e c o r r e s p o n d i n g t e m p e r a t u r e s are t h e b e s t - f i t t e d t e m p e r a t u r e s to each set of e x p e r i m e n t a l t i m e - i n t e g r a t e d i n t e n s i t y r a t i o c u r v e s . T h e a g r e e m e n t of these e x p e r i m e n t a l p o i n t s w i t h t h e l i q u i d H u g o niot is v e r y g o o d .  Chapter  4.  Luminescence  25000  Measurements  in Single  and Doubled-Layered  Targets  97  n  22500H  0) 20000H "5 Q_ E  17500  .<i>  s  B  15000 H  12500  5.25  5.50  5.75  6  6.25  6.50  Pressure (Mbar)  F i g u r e 4.46: A p l o t o f t h e H u g o n i o t of g o l d f r o m S E S A M E ( d o t - d a s h ) , t h e l i q u i d H u g o n i o t in our new calculations (dash) and the e x p e r i m e n t a l l y deduced points.  Chapter 5  Summary  5.1  Conclusions W e w i l l n o w s u m m a r i z e s o m e of t h e m a j o r results i n these l a s e r - d r i v e n s h o c k ex-  p e r i m e n t s . W e have u t i l i z e d t h e i m p e d a n c e - m i s m a t c h t e c h n i q u e t o s t u d y t h e p r o p e r t i e s of s h o c k c o m p r e s s e d g o l d u s i n g a l u m i n u m as t h e reference s t a n d a r d .  O u r s t u d i e s ha.ve  i n v o l v e d b o t h e x p e r i m e n t a l m e a s u r e m e n t s a n d c o m p u t e r s i m u l a t i o n s of t h e s h o c k t r a n s i t t h r o u g h t a r g e t s of v a r i o u s t h i c k n e s s e s . In p a r t i c u l a r , t h e p y r o m e t r i c t e c h n i q u e i n w h i c h we m e a s u r e t h e l u m i n o u s e m i s s i o n i n t e n s i t y f r o m t h e free, surface of t h e t a r g e t is used to t o detect t h e onset t i m e of s h o c k b r e a k o u t and also to d e d u c e t h e shock t e m p e r a t u r e . W e have s h o w n how a p r o p e r design of an i m p e d a n c e - m i s m a t c h e d l a y e r e d target (lowi m p e d a n c e a l u m i n u m i n f r o n t of h i g h - i m p e d a n c e g o l d ) can l e a d to pressure e n h a n c e m e n t a n d also r e d u c t i o n of r a d i a t i v e p r e h e a t i n t h e h i g h - Z g o l d layer. In a d d i t i o n , t h e m a x i m a z a t i o n of t h e free surface pressure is f o u n d to be d e p e n d e n t on t h e t h i c k n e s s e s of b o t h layers of t h e t a r g e t , a n d t h a t i t i n v o l v e s an o p t i m i z a t i o n between an i n c o m p l e t e b u i l d u p of t h e shock w h e n t h e t a r g e t is t o o t h i n a n d shock a t t e n t u a t i o n w h e n t h e target is t o o t h i c k . O n t h e o t h e r h a n d , we h a v e s h o w n t h a t t h e r e q u i r e m e n t of m a x i m u m free surface pressure is n o t n e c e s s a r i l y c o m m e n s u r a t e w i t h that, in h i g h pressure E O S s t u d i e s , w h e r e it is m o r e i m p o r t a n t to a c h i e v e an u n i f o r m a n d s t e a d y s h o c k . In t h e shock v e l o c i t y s t u d y , we have m a p p e d out the. s h o c k t r a j e c t o r y i n a t a r g e t b y m e a s u r i n g the shock b r e a k o u t t i m e s i n v a r i o u s t h i c k n e s s e s .  98  H o w e v e r , these d a t a are  Chapter  5.  Summary  99  not a c c u r a t e e n o u g h t o d i s c r i m i n a t e a m o n g v a r i o u s e q u a t i o n of s t a t e p r e d i c t i o n s , a n d are u n a b l e t o assess t h e s i g n i f i c a n c e of t h e process of r a d i a t i o n t r a n s p o r t i n the target. N o n e t h e l e s s , these s i m u l a t i o n s h a v e i n d i c a t e d the a d e q u a c y of u s i n g a o n e - d i m e n s i o n a l a n d p u r e l y f l u i d c o d e i n p r e d i c t i n g t h e shock t r a j e c t o r i e s .  T h e use of a less c o m p l e x  (hence faster a n d c h e a p e r t o r u n ) h y d r o c o d e is of course a t t r a c t i v e t o those faced w i t h l i m i t e d c o m p u t i n g resources. In t h e s h o c k t e m p e r a t u r e s t u d y , we h a v e i n i t i a t e d a. new E O S c a l c u l a t i o n of gold i n c o p o r a t i n g b o t h s o l i d a n d l i q u i d s t a t e t h e o r i e s , a n d therefore a c c o u n t i n g for shock m e l t i n g i n g o l d . It is f o u n d t h a t t h e m e a s u r e m e n t of s h o c k t e m p e r a t u r e is m u c h m o r e s e n s i t i v e t o t h e e q u a t i o n of s t a t e , i n o t h e r w o r d s , we are a b l e to d i s c r i m i n a t e between t w o e q u a t i o n of s t a t e p r e d i c t i o n s . O u r m e a s u r e m e n t s of t h e b r i g h t n e s s t e m p e r a t u r e i n g o l d favor t h e new E O S p r e d i c t i o n over t h a t o b t a i n e d f r o m t h e S E S A M E E O S l i b r a r y where t h e p r o c e s s of shock m e l t i n g is a b s e n t . In p a r t i c u l a r , we h a v e f o u n d t h a t whereas  those  simulations using the S E S A M E E O S have overestimated the time-integrated luminous e m i s s i o n ( a n d h e n c e t e m p e r a t u r e ) of the t a r g e t rear surface, t h e s i m u l a t i o n s u s i n g t h e new g o l d are i n m u c h b e t t e r agreement w i t h t h e e x p e r i m e n t a l m e a s u r e m e n t s .  W e therefore  c o n c l u d e t h a t shock m e l t i n g of g o l d has o c c u r e d . T h e present m e a s u r e m e n t of g o l d ( i n its l i q u i d p h a s e ) at a p r e s s u e of ~ 6  M b a r and ~17500  m e a s u r e m e n t of g o l d u n d e r s h o c k m e l t i n g .  K represents  a first r e p o r t e d  Chapter  5.2  5.  Summary  100  Future Research  A n a t u r a l e x t e n s i o n is to p e r f o r m i m p e d a n c e - m i s m a t c h e x p e r i m e n t s o n h i g h - Z m a t e r i a l s o t h e r t h a n g o l d i n o r d e r t o d e t e r m i n e t h e i r e q u a t i o n of s t a t e u n d e r shock c o m p r e s s i o n . It is also e x p e c t e d t h a t b y u s i n g a s t a n d a r d w i t h a l o w e r i m p e d a n c e t h a n t h a t of a l u m i n u m , a h i g h e r p r e s s u r e e n h a n c e m e n t at t h e m a t e r i a l i n t e r f a c e c a n be a t t a i n e d . F u r t h e r m o r e , t r i p l e - l a y e r e d t a r g e t s m a y b e c o n s i d e r e d a n d t h e i r thicknesses o p t i m i z e d to t h e laser i r r a d i a n c e . and p u l s e c o n d i t i o n i n order to achieve p e r h a p s still h i g h e r pressure and compression.  T h e c r i t e r i o n used here for d e t e r m i n i n g t h e o p t i m a l t h i c k n e s s of a  p a r t i c u l a r layer s h o u l d s t i l l b e v a l i d i n m u l t i - l a y e r e d t a r g e t s , i.e. t h e t h i c k n e s s of a target l a y e r i n f r o n t of t h e interface s h o u l d b e t h i c k e n o u g h so t h a t t h e p r o p a g a t i n g shocks have t i m e t o coalesce i n t o a s t r o n g shock f r o n t w h e n t h e y r e a c h t h e i n t e r f a c e , a n d t h e t h i c k n e s s of t h e l a y e r b e h i n d the i n t e r f a c e s h o u l d be t h i n e n o u g h so t h a t shock d a m p i n g w i l l n o t cause t h e s h o c k t o decay s i g n i f i c a n t l y w h e n it e n c o u n t e r s t h e free surface (or a n o t h e r interface).  N e v e r t h e l e s s , o n e s h o u l d also be careful to ensure t h a t t h e r e s u l t i n g shock  p r o f i l e s h o u l d be as steady a n d u n i f o r m as p o s s i b l e i n o r d e r to o b t a i n an u n a m b i g u o u s i n t e r p r e t a t i o n of t h e E O S d a t a . T h e b r i g h t n e s s t e m p e r a t u r e s t u d y c a n be e x t e n d e d to i n v o l v e i n t e n s i t y m e a s u r e m e n t s as a f u n c t i o n of w a v e l e n g t h . F o r e x a m p l e , the p e a k o f the P l a n c k b l a c k b o d y d i s t r i b u t i o n at t h e s e h i g h t e m p e r a t u r e s (17500 K ) is a p p r o x i m a t e l y 1 6 5 0 A , a n d s p e c t r a l m e a s u r e m e n t s m a d e at a r o u n d t h i s w a v e l e n g t h s h o u l d y i e l d a m u c h h i g h e r s i g n a l . H o w e v e r , one m u s t t h e n d e v e l o p an i m a g i n g a n d d e t e c t o r s y s t e m w h i c h is sensitive i n t h i s s p e c t r a l range. 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