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

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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 U S I N G L A S E R - D R I V E N S H O C K S B y Gordon S. Y . C h i u B . A . S c , The University of Brit ish Columbia , 1986 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E DEGREE OF MA S T E R OF AP P L I E D SCIENCE in T H E FACULTY OF GRADUATE STUDIES DEPARTMENT 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 this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6G/81) A b s t r a c t A series of impedance-mismatch experiments with aluminum-gold targets has been per-formed. These experiments are used to probe the equation of state (EOS) 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 in 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 equa-tion of state theoretical models. Our 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 Mbar and temperature of ~ 17500 K also represent the first study of gold under shock melting. n T a b l e of C o n t e n t s A b s t r a c t i i L i s t of Tab le s v L i s t of F i g u r e s v i A c k n o w l e d g e m e n t x i 1 I n t r o d u c t i o n 1 J . l I n t r o d u c t i o n to H i g h Pressure Research 1 1.2 Thes i s O b j e c t i v e 4 1.3 Thes i s O u t l i n e 5 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 6 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 Sol ids 6 2.1.1 Laser E n e r g y D e p o s i t i o n 6 2.1.2 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 8 2.1.3 Shock W a v e G e n e r a t i o n 9 2.2 T h e H u g o n i o t 10 2.3 T h e I m p e d a n c e - M i s m a t c h Techn ique 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 Prehea t 20 2.4 E q u a t i o n of State 23 2.4.1 S E S A M E E q u a t i o n of State 23 i i i 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 26 2.5 C o m p u t e r S i m u l a t i o n s 31 2.5.1 S H Y L A C C o d e 32 2.5.2 H Y R A D C o d e 33 2.5.3 P T C C o d e 36 3 E x p e r i m e n t a l F a c i l i t y , D i a g n o s t i c s , a n d S e t u p 38 3.1 Laser F a c i l i t y 38 3.2 I r r a d i a t i o n C o n d i t i o n s 41 3.3 E x p e r i m e n t a l A r r a n g e m e n t s 45 4 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 ing le and D o u b l e d - L a y e r e d Targe t s 49 4.1 Shock V e l o c i t y S t u d y 49 4.1.1 S ingle Layer A l u m i n u m F o i l 50 4.1.2 A l u m i n u m - G o l d Targets 57 4.2 Br ightnes s T e m p e r a t u r e S t u d y w i t h A l u m i n u m - G o l d Targets ' 69 4.2.1 E x p e r i m e n t a l O b s e r v a t i o n s 71 4.2.2 Computer S i m u l a t i o n s 77 5 S u m m a r y 98 5.1 C o n c l u s i o n s 98 5.2 F u t u r e Research 100 B i b l i o g r a p h y 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 tudy of the effects of r a d i a t i o n t r a n s p o r t on free surface shock parameters for a 19 pm A ] o n 13 pm A u target 84 4.2 c o m p a r a t i v e s t u d y of the effects of our new go ld E O S data on free surface shock parameter s for a 19 pm A l on 13 pm Au target , r ad ia t ion t r anspor t is i n c l u d e d 84 4.3 c o m p a r a t i v e s t u d y of the effects of our new gold E O S d a t a on the shock breakout t imes the compress ion r a t i o (p/po), the shock pressure ( P ) , a n d the shock t e m p e r a t u r e (T) at breakout for various 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 85 v Lis 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 laser-driven shock 7 2.2 A n i l l u s t r a t i o n of the shocked and unshocked regions 11 2.3 T h e a l u m i n u m p r i n c i p a l Hugonio t in the (a) P vs p p lane , a n d (b) T vs p plane , as g iven i n S E S A M E 14 2.4 T h e a l i m i n u m p r i n c i p a l Hugon io t i n the (a) Up vs Us p lane , and (b) Up vs P p lane . A l s o i n c l u d e d in (b) is the p r i n c i p a l H u g o n i o t of go ld . D a t a are f rom S E S A M E 15 2.5 Shock p r o p a g a t i o n and parameters in an i m p e d a n c e - m i s m a t c h e d target . 17 2.6 T h e c a l c u l a t i o n of pressure in the sample us ing the mirror-re f lec t ion m e t h o d . T h e slope ol the straight, l ine involves the measurement of the shock ve-loc i ty Us i n the sample 19 2.7 T h e mirror- re f lec t ion m e t h o d w i t h the sample Hugonio t k n o w n , e l imina t -i n g the need to measure Us 21 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 the seven E O S model s of a l u m i n u m used in S E S A M E 25 2.9 T h e solid and l i q u i d Hugoniot. of gold as ca lcula ted in §2 .4 .2 , tha t in S E S A M E is also i n c l u d e d ; also shown is the m e l t i n g curve 30 3.10 A schematic of the laser and diagnost ics sy s tem 39 3.11 A t y p i c a l laser pulse 40 3.12 A t ime- integra ted laser intens i ty 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 profi le of the laser spot of F i g u r e 3.12 43 v i 3.14 A cross section of the laser spot in F i g u r e 3.12 across (a) the x -coord ina te and (b) the y -coord ina te , each s p a n n i n g the centra l 5 pm of the spot . . 44 3.15 T h e e x p e r i m e n t a l setup i n the luminscence s tudy 46 4.16 Streak records of shock breakout emis s ion (left s treak) and f i d u c i a l s igna l (r ight s treak) i n (a) 38.4 pm a n d (b) 53 pm a l u m i n u m target 51 4.17 T e m p o r a l h i s to ry of the (a) shock breakout and (b) f iduc ia l s treak i n a 38.4 pm A l target 53 4.18 T h e ca lcu la ted abla.tion pressure pulse f r o m H Y R A D (sol id) and the Gaus-sian pressure pulse assumed i n S H Y L A C (dash) 54 4.19 C a l c u l a t e d shock paths by S H Y L A C (dot-dash) , by H Y R A D without , ra-d i a t i o n t r a n s p o r t (dash) , a n d w i t h r a d i a t i o n t ranspor t (sol id) ; also p l o t t e d are the e x p e r i m e n t a l results in various a l u m i n u m targets 56 4.20 Streak record of free surface l u m i n o u s emiss ion (left s treak) and fiducial s ignal (right, s t reak) of a 19 pm a l u m i n u m on 8.4 pm gold target . . . . 58 4.21 Shock pressure profiles in A l - A u targets w i t h the front a l u m i n u m thickness equal to 5 p.m. T h e i n i t i a l profi le corresponds to a t i m e of 1.5 ns before the pressure pulse peak, and subsequent, ones are 0.25 ns apart 60 4.22 Same as F i g u r e 4.21 but a l u m i n u m thickness is 11.5 pm 61 4.23 Same as F i g u r e 4.21 but a l u m i n u m thickness is 19 pm 62 4.24 Same as F i g u r e 4.21 but a l u m i n u m thickness is 50 pm 63 4.25 Shock i n d u c e d pressure in the free surface of gold as a f u n c t i o n of the a l u m i n u m thickness . T h e var ious l ines denote different gold thicknesses : 2 pm ( so l id ) . 8.4 pm (clash), 13 pm (dot-dot-dot-clash) . 20 pm (dot-dash) . A l s o shown is the m a x i m i u m pressure reached somewhere in a go ld layer of in f in i te thickness (dot) 65 v i i 4.26 Shock pressure at the free surface of go ld as a f u n c t i o n of thickness i n the gold layer for various front a l u m i n u m thicknesses : 11.5 fim (dot-dot-dash) , 19 fim (dot-dash) , 34 fi.m ( so l id) , a n d 50 fim (dash) 68 4.27 Shock paths as ca lcu la ted by H Y R A D i n 19 fim A l and 13 fim A u target u s ing S E S A M E E O S (dot-dot-dash) , and us ing new gold E O S (dash) ; i n 26.5 fim A l and 13 fim A u target us ing S E S A M E E O S (dot-dash) , a n d us ing new gold E O S (dot ) . T h e shock p a t h in 53 fim Al (solid) is i n c l u d e d . A l s o p lo t t ed are the e x p e r i m e n t a l po int s for var ious A l - A u targets and pure A l targets 70 4.28 T e m p o r a l l y resolved and integrated p lot of the backs ide emiss ion in tens i ty of a 38.4 fim A l target , w i t h t i m e zero be ing the peak of the laser p u l se. 72 4.29 Same as F i g u r e 4.28except target is 19 fim A l on 13 fim A u 73 4.30 Same as F i g u r e 4.28except target is 19 fim A l on 8.4 fim A u 74 4.31 Same as F i g u r e 4.28except target is 26 .5micron A l on 8.4 fim A u . . . . 75 4.32 Same as F i g u r e 4.28exc.ept target is 26.5 fim A l on 13 fim A u 76 4.33 A snapshot of the h y d r o d y n a m i c profi le i n a 19 fim A l on 13 fim A u target at t = -1.26 ns. R a d i a t i o n t r anspor t process is neglected, and b o t h A l and A u E O S data are f r o m S E S A M E ! 79 4.34 Same as F i g u r e 4.33 except r ad ia t ion t r a n s p o r t process is i n c l u d e d . T h e absorbed X - r a y power is also p lo t t ed 80 4.35 Same as F i g u r e 4.33 except t i m e is at t = 0.24 ns 82 4.36 Same as F i g u r e 4.35 but r a d i a t i o n t r a n s p o r t process is inc luded 83 4.37 Backside, emiss ion f rom a 19 fim A l on 13 ftm A u target us ing S E S A M E (dash) and our new (dot-dot-dot-dash) gold E O S da ta , as well as f r o m a 38.4 fim A l (sol id) target , w i t h t i m e zero cor re spond ing to shock breakout 87 v i i i 4.38 T i m e - i n t e g r a t e d emis s ion in tens i ty of the prev ious F i g u r e 4.37: that of a 19 pm A l on 13 pm A u target us ing S E S A M E (dot) and the new (dash) go ld da ta ; that, of a 38.4 pm A l target (dot-dash) 88 4.39 T i m e - i n t e g r a t e d emis s ion in tens i ty ra t io for a 19 A l on 13 pm A n target to a 38.4 pm A l target : (a) u s ing S E S A M E ( d o t ) , and new gold (dot-dash) E O S da ta ; and (b) bes t - f i t ted t e m p e r a t u r e Tp curve (dot-dot-dash) to an e x p e r i m e n t a l curve (dot-dash) - 89 4.40 S i m i l a r to F i g u r e 4 .39(b) : an e x p e r i m e n t a l t ime- integra ted emiss ion in-tens i ty r a t io is bes t- f i t ted w i t h a shock t e m p e r a t u r e Tp 90 4.41 S i m i l a r to F i g u r e 4 .39(b) : an e x p e r i m e n t a l t ime- integra ted emiss ion in-tens i ty r a t io is best- f i t ted w i t h a shock t e m p e r a t u r e Tp 91 4.42 S i m i l a r to F i g u r e 4 .39(b) : an e x p e r i m e n t a l t ime- integra ted emiss ion i n -tens i ty ra t io is best- f i t ted w i t h a shock t e m p e r a t u r e Tp . . . 92 4.43 T i m e - i n t e g r a t e d emiss ion intens i ty ra t io for a 19 pm A l on 8.4 pm A u target to a 38.4 pm A l target u s i n g S E S A M E (dot) , and the new (1 ong dot-dash) gold 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 ( long dash , so l id , long dot-dot-clot-dash) are i n d i v i d u a l l y best-f i t ted w i t h a shock t e m p e r a t u r e Tp ( short do t -dot -dot -dash , short dash, short dot-dash) 93 4.44 T i m e - i n t e g r a t e d emiss ion intens i ty ra t io for a 26.5 pm A l on 8.4 pm A u target to a 38.4 pm A l target us ing S E S A M E (dot ) , and the new (dot-dash) go ld E O S data . T h e e x p e r i m e n t a l d a t a ( long dash, solid) are i n d i v i d u a l l y bes t- f i t ted w i t h a shock t empera ture Tp (dot-dot-dot-dash , short dash) . 94 IX 4.45 T i m e - i n t e g r a t e d emiss ion in tens i ty r a t io for a 26.5 pm A l on 13 pm A u target to a 38.4 pm A l target us ing S E S A M E (dot ) , and the new ( dot-dash) gold E O S da ta . O n e e x p e r i m e n t a l da ta ( long dash) is best-f i t ted w i t h a shock t e m p e r a t u r e Tp (short dash) whi l e the other (sol id) coincides w i t h the ca lcu la ted curve (dot-dash) 95 4.46 A p lo t of the H u g o n i o t of g o l d f rom S E S A M E (dot-dash) , the l i q u i d Hugo-nio t in our new ca l cu la t ions (dash) and the e x p e r i m e n t a l l y deduced po int s . 97 x A c k n o w l e d g e m e n t I w o u l d l ike to t h a n k m y supervi sor , D r . A n d r e w N g for his gu idance in the present pro ject and for p r o v i d i n g an excel lent e x p e r i m e n t a l f ac i l i ty . M y indebtedness is to D r . B . K . G o d w a l for his m a n y helpful suggestions and assistance in t h e o r e t i c a l ca lculat ions in this thesis . I a m espec ia l ly grateful to L u i z D a S i lva , w h o has he lped me great ly in every phase of the e x p e r i m e n t a l work and thesis p r e p a r a t i o n . T o the other members and v i s i tors of the p l a s m a group , I say t h a n k you for p r o v i d i n g l i v e l y discussions and ins ight fu l c o m m e n t s , work re la ted or o therwise . T h i s work is s u p p o r t e d by the N a t u r a l Sciences and E n g i n e e r i n g Research C o u n c i l of C a n a d a . XI C h a p t e r 1 I n t r o d u c t i o n 1.1 I n t r o d u c t i o n to H i g h P r e s s u r e R e s e a r c h T h e generat ion of h igh pressure ( 1 0 b a tmosphere regime) in m a t t e r not only f inds i m m e d i a t e a p p l i c a t i o n in d r i v i n g implo s ions in i n e r t i a ! confinement fus ion [1, 2], where the t h e r m o n u c l e a r fuel must be brought i n t o an ex t reme state of dens i ty and t empera ture (b rought about by h igh pressure compress ion) to ign i te and susta in the fus ion react ions , b u t also can be of f u n d a m e n t a l interest i n the s tudy of equations of state ( E O S ) of m a t t e r at h i g h pressure[3], the d e t e r m i n a t i o n of s t r u c t u r a l phase t rans i t ions i n crystals[4], a n d the inves t igat ions of in te rmolecu la r forces, e lec t ronic , chemica l , and o p t i c a l propert ies of mater i a l s u n d e r extreme condit ions[5] . M a n y interes t ing phys i ca l p h e n o m e n a such as s-d e lec t ronic transfer l ead ing to i n s u l a t o r - m e t a l l i c t rans i t ion[6 , 7], or shock m e l t i n g f r o m sol id to l i q u i d at h igh pressure[8], have rema ined mos t ly unexp lored a.nd not wel l u n d e r s t o o d (for e x a m p l e , Shaner in reference [9] discusses the var ious diff iculties bese t t ing the measurements i n h igh 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 needed to resolve d iverg ing pred ic t ions among contend ing E O S theories as we l l as to e x t e n d and to establ i sh the ra.nge of a p p l i c a b i l i t y of ex i s t ing ca l cu l a t iona l techniques . Hence h igh pressure s tudy can be seen to be of i m m e n s e i m p o r t a n c e in b o t h a p p l i e d and theore t i ca l s tudies . 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 dynamic . methods[10], i n 1 Chapter 1. Introduction 2 contras t to the stat ic techniques (such as the d i a m o n d a n v i l c e l l j l l ] ) , involves the in t ro-d u c t i o n of a r a p i d impul se (shock wave) t h r o u g h : 1. the d e n o n a t i o n of explos ive systems, e i ther chemical [12, 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 us ing a high-speed pro jec t i l e f r o m a s ingle or two-stage l ight-gas gun[18], 3. the energy depos i t ion by a n intense ion b e a m [ l 9 ] , 4. the ab sorp t ion of an intense pulse of r a d i a t i o n p r o v i d e d by a h igh-power laser[20]. G e n e r a l l y speak ing , the m a i n advantage of dynamic , over s tat ic techniques is tha t h igher pressure can be a t t a ined . T h i s is because the pressure achieved in 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 res tr ic ted by the plastic, de format ion l i m i t of d i a m o n d s . However , for d y n a m i c pressure studies unique a n d fast diagnost ics (e.g. sub-nanosecond re so lu t ion i n la.ser-driven exper iments ) must also be developed. In a d d i t i o n , d y n a m i c methods are u sua l ly much more cost ly in bo th cap i t a l and opera t ion aspects. A brief d i scuss ion on the mer i t s and short comings of the var ious d y n a m i c m e t h o d s is in order here. T h e use of chemica l explosives has been one of the earliest m e t h o d s in h i g h pressure generation[12, 13], but the a t t a inab le pressures have been l i m i t e d to ~ 1 0 M b a r (1 M b a r = 1 0 6 a tmospheres) i n metals[15]. U n d e r g r o u n d nuclear explosions[3, 16, 17] offer the p o s s i b i l i t y to achieve record-set t ing pressures ( read i ly exceeding 100 M b a r , and recently, pressures of >4000 M b a r in a l u m i n u m [ 2 l ] have been repor ted) w i t h good accuracy (<5%), a l though this m e t h o d is vas t ly expensive and obv ious ly inaccess ible to m a n y researchers. O n the other h a n d , the two-stage l ight-gas guns[22] have p r o d u c e d the most precise measurements (< 1% accuracy in pressure[ l8]) , b u t the pressure a t t a ined is somewhat l i m i t e d (up to ~ 5 Mbar[3] ) . W h i l e heavy ion beams are p ro jec ted to be capable 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 Mbar [23] , yet no 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 ser-dr iven shock waves have been shown to be e m i n e n t l y able to span pressures i n the " i n t e r m e d i a t e " reg ion (tens to hundreds of M b a r s [ 2 4 , 25]) p rev ious ly inaccess ible by the more c o n v e n t i o n a l means , thus b r i d g i n g the gap between the low presssure region appropr i a t e to gas g u n s / c h e m i c a l explos ives a n d the h igh pressure region charac ter i s t i c of nuclear explos ions . F u r t h e r m o r e , because of its h i g h r e p e t i t i o n ra te a n d re lat ive ease of o p e r a t i o n , laser has become the sole means of genera t ing pressures in the in te rmed ia te region in l abora tory- sca led exper iments , a l t h o u g h the uncer ta int ie s in the measurements can be s ignif icant (> 10%). A s we w i l l be us ing the la.ser o p t i o n i n the work of the present thesis , we w i l l e laborate fur ther on the ver sa t i l i ty of the use of laser-driven shock waves. A great m a j o r i t y of re-searches in the past decades have been directed towards u n d e r s t a n d i n g the m a n y aspects in l a ser-matter interact ions such as laser absorpt ion efficiency, mass a b l a t i o n rate , target preheat mechan i sms , or t h e r m a l t r a n s p o r t propert ie s , and hence a r r i v i n g at the o p t i m a l cond i t ions for laser-dr iven fusion[26, 27, 28, 29]. Nevertheless i t is soon recognized that the ab i l i ty of laser-driven shock waves to generate h i g h pressures is also ideal for equa t ion of s tate studies of mater ia l s at ex t reme condi t ions of pressure and density[24, 30]. In ad-d i t i o n , e lec t r ica l propert ies such as the p o t e n t i a l difference between surfaces of deformed die lectr ics caused by the m o t i o n of a. shock wave (this is ca l led shock p o l a r i z a t i o n [ 3 l ] ) , or the e lectronic c o n d u c t i v i t y in dense plasma[32] , have also been s tud ied us ing laser-dr iven shock waves. M o r e recent exper iment s of interest in condensed m a t t e r phys ics and a t o m i c physics , a l l us ing laser-dr iven shocks to a,chieve the desired materia.] state, i n c l u d e the measurements of l a t t i ce compress ions a,nd stresses in s ihconj33] , the t e m p o r a l e v o l u t i o n of the K - a b s o r p t i o n edge in shock compressed p o t a s s i u m chloride[34] , or the short range ion cor re l a t ion effects in a l u m i n u m plasma[35]. F i n a l l y we w i l l conc lude the i n t r o d u c t o r y section by d i scuss ing the 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 the p r i n c i p a l areas of studies in th i s thesis. Shock wave p r o p a g a t i o n in a m a t e r i a l leads to the compress ion a n d heat ing of the m a t e r i a l above so l id dens i ty and ambient t e m p e r a t u r e , and somet imes th i s heat ing is sufficient to cause the m a t e r i a l to mel t . K o r m e r et al.[36] have suggested the measurement of shock t e m p e r a t u r e to detect the onset of m e l t i n g and to resolve different predic t ions forwarded by so l id a n d l i q u i d states E O S theories . For e x a m p l e , the observat ions of shock mel t-i n g a long the H u g o n i o t i n mater i a l s have been prev ious ly r e p o r t e d . T h e earliest studies of Kormer [36 ] measured the br ightness t e m p e r a t u r e of the shock front a n d determined the h igh-pressure m e l t i n g curve i n a n u m b e r of t ransparent a lka l i halides ( N a C l , K B r , L i F , e tc . ) . T h e Livermore[37] and Los A l a m o s group[38]- have ca lcula ted the m e l t i n g b e h a v i o r o n the H u g o n i o t of a n u m b e r of a lkal i meta l s as wel l as a l u m i n u m , and have e x p e r i m e n t a l l y de te rmined the shock m e l t i n g range in a l u m i n u m t h r o u g h sound speed measurements . T h e recent inves t iga t ions of R a d o u s k y et.al.[39] also use shock temper-ature measurements to d e t e r m i n e the onset of m e l t i n g in C'sl . In p a r t i c u l a r , they found that the i r da.ta were suff ic iently sensi t ive detect an inadequacy in the sol id H u g o n i o t c a l c u l a t i o n , and have shown the v a l i d i t y of us ing a. l i q u i d theory in the m e l t i n g regime. H e n c e , the acqui sa t ion of e x p e r i m e n t a l da.ta is c r u c i a l in h e l p i n g to differentiate between the p r e d i c t i o n s of different theories . 1.2 T h e s i s O b j e c t i v e T h e p r i n c i p a l a i m of th i s thesis is to u t i l i ze intense laser pulses to generate s t rong shock waves for equat ion of state inves t igat ions in h i g h - Z mater i a l s . A s an example , we Cha.pt.er 1. Introduction 5 w i l l focus on the behav ior of go ld at h igh pressure a n d specif ical ly, the process of shock m e l t i n g . F r o m t ime-resolved measurements of s h o c k - i n d u c e d l u m i n o u s emiss ions, we w i l l d e t e r m i n e the t empera ture of go ld at ~ 6 M b a r , above i ts pred ic ted m e l t i n g t r ans i t i on at —2 M b a r . T h e result w i l l be used to assess ex i s t ing equat ion of state models and to p r o v i d e an e x p e r i m e n t a l basis for new models . ' A second but s t rongly re la ted object ive is to employ the i m p e d a n c e - m i s m a t c h techniquef ] 2, 14, 15, 22] in the s tudy of h i g h - Z mater i a l s u s ing laser-dr iven shock waves. T h e i m p e d a n c e - m i s m a t c h technique involves the p r o d u c t i o n of a shock wave in a low-Z (low dens i ty and low acoust ic impedance) m a t e r i a l , w h i c h then propagates in to the h i g h - Z (h igh density a n d high acoust ic impedance) m a t e r i a l of interest . In this s tudy, go ld a n d a l u m i n u m have been chosen as the h i g h - Z and l o w - Z mater i a l s respectively. W e w i l l demons t ra te the advantages of this technique , namely , pressure enhancement and r e d u c t i o n of r ad i a t ive preheat . W e w i l l e x a m i n e the proper design of an impedance-m i s m a t c h e d target and identi fy the c r i t i ca l c r i t e r i o n for o p t i m a l pressure generat ion in the h i g h - Z m a t e r i a l of interest . 1.3 T h e s i s O u t l i n e T h i s thesis is organized as fo l lows: C h a p t e r 2 gives a review of the theory on shock waves and the technique 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 fac i l i ty , d iagnost ics , and the e x p e r i m e n t a l setup. T h e exper i -m e n t a l results and c o m p a r i s o n w i t h computer s imula t ions w i l l be presented i n chapter 4. F i n a l l y , the m a j o r conclus ions are s u m m a r i z e d in chapter 5. C h a p t e r 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 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 So l id s T h e process for generat ing laser-driven shocks has been e x a m i n e d i n detai ls i n ref-erences [l] and [2]. Here we sha l l briefly rev iew the three p r i n c i p a l phys ics processes i n v o l v e d : 1. laser energy absorp t ion i n a laser-heated target , 2. e lectron t h e r m a l c o n d u c t i o n w h i c h carries the heat flux f r o m the ab sorp t ion region i n t o the target in te r io r , effecting a b l a t i o n , and 3. shock wave generat ion by the o u t w a r d expans ion of the ab la ted m a t e r i a l . 2.1.1 L a s e r E n e r g y D e p o s i t i o n F i g u r e 2.1 shows a s chemat ic d i a g r a m of a l a ser- i r radia ted sol id target , where the outer layer of the target is heated by 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 inverse brem,sstTahlung[AO], or free-free absorp t ion . T h i s process can be v i sua l i zed a.s electrons o s c i l l a t i n g in the electr ic f ield of the inc ident laser l ight and thereby absorb ing the energy of the p h o t o n . T h e electrons subsequently transfer the i r energies to the rest of the target (i.e. ions) via e lectron- ion col l i s ions . In this m a n n e r , part ic les in the target absorb the laser energy and become heated , ionized and e x p a n d in to the v a c u u m , f o r m i n g a low dens i ty blow-off p l a s m a , ca l led the corona. For short wavelength (<1 / i in ) 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: Schemat ic d i a g r a m of a l a ser-dr iven shock Chapter 2. Theory oi Laser-driven Shocks 8 thi s process is the d o m i n a n t absorp t ion m e c h a n i s m . T h e laser energy can be absorbed up to the c r i t i c a l dens i ty surface where the e lectron o sc i l l a t ion frequency equals the f requency of the laser r a d i a t i o n a n d the laser l ight is reflected. A c c o r d i n g l y , the c r i t i ca l dens i ty nCTli is defined by ncrir =  u L £ ° m [MKS units] (2.1) e-where u.^ is the laser frequency, m and e are the electron mass and charge respectively, and e 0 is the p e r m i t t i v i t y of space. S ince the p l a s m a densi ty scale l e n g t h ( ^ = ( ^ f f ) - 1 i where n is the e lec tron densi ty) i n the c o r o n a is invar i ab ly m u c h larger t h a n the laser wavelength[40] , a n d since, the e lec tron- ion energy transferr ing process becomes more and m o r e efficient as e lectron densi ty increases ( the e lectron-ion co l l i s iona l f requency 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 lectron density[40]) , therefore essential ly a l l of the laser energy is absorbed in the corona before" it reaches the c r i t i c a l surface. Consequent ly , the corona l p l a s m a is very hot (~- 1 keV)[41] . 2.1.2 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 T h e la.ser energy absorbed on the surface of the target is t r a n s p o r t e d inward due to large t e m p e r a t u r e gradient between the ho i corona and the cold in te r io r of the target. T h e depos i t ion of th i s intense heat f lux in the so-called conduction or ablation zone (see F i g u r e 2.1 ) causes the target m a t e r i a l to be ab la ted (i.e., vapor ized f r o m the solid) w h i c h then expands r a p i d l y o u t w a r d in to the corona . T h e heat c o n d u c t i o n is m a i n l y carr ied out by the e lectrons , first s tud ied by Spi tzer and Harm[42] . T h e y assumed electron t h e r m a l c o n d u c t i o n to follow the class ical Four ier heat l aw, (2.2) Chapter 2. Theory oi Laser-driven Shocks 9 where Ke is the Sp i tzer 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 the form[43] q 0 . 0 9 5 ( £ + 0.24) ThJ2 K e = 1.955 • 1CT 9 - — „ >-A 2.3 1 + 0 . 2 4 Z Z l n A K 1 where Z is the m a t e r i a l a t o m i c n u m b e r , Te is the e lectron t e m p e r a t u r e , and In A is the C o u l o m b l o g a r i t h m . A s a resul t , the specific heat flux w i l l be He = - - V • K e V T e (2.4) p where p is the density. It has been observed that at h igh enough in tens i ty ( > 1 0 1 4 W / c n r ) the S p i t z e r - H a r m t ranspor t m o d e l breaks down[27, 44, 45], so that the ac tua l heat c o n d u c t i o n is m u c h less t h a n pred ic ted . ( T h i s is because for large t e m p e r a t u r e gradient , eq u a t ion (2.3) predict s an excessively large heat flux.) T h i s decrease in heat flux is ca l led e lectron t h e r m a l flux i n h i b i t i o n , and one usua l ly remedies it a r t i f i ca l ly i n s imula t ions by ass igning a " f lux-l i m i t e r , ; / , so that the ac tua l flux Ha = / • H£ is no more than a f r ac t ion of the Sp i tzer flux. F u r t h e r m o r e , at h igh intensi t ies energet ic electrons cal led s u p r a t h e r m a l or hot electrons[2S, 46] w i t h energies much greater t h a n the t h e r m a l e lectrons of the p l a s m a corona, are p r o d u c e d . These s u p r a t h e r m a l electrons represent another means of energy t ransport in a d d i t i o n to the diffusive heat flow discussed above. These electrons have long mean free paths and w i l l '"preheat" the target (i.e. heat up the target before the shock arr ives) . These two aspects w i l l be fur ther addressed in §2 .5 .2 and it w i l l be shown that they are negl ig ib le in our exper iments 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 expans ion of the ab la ted m a t e r i a l f r o m the 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 conservat ion , this produces a large abla-t i o n pressure w h i c h drives a shock wave i n t o the in te r ior of the so l id target ( F i g u r e 2.1). Chapter 2. Theory of Laser-driven Shocks 10 So long as the a b l a t i o n pressure increases (due to the increas ing laser in tens i ty , for exam-ple , i n the r i s i n g edge of a G a u s s i a n pulse) , shock waves of increa s ing a m p l i t u d e s w i l l be l a u n c h e d in to the target . N o w the first l aunched shock wave travels at s l i ght ly exceeding the speed of s o u n d , and be ing a compres s iona l d i s turbance , w i l l compress the sol id a l i t t l e . T h e second s tronger shock wave w i l l therefore t ravel near the c o r r e s p o n d i n g sound speed of the compressed reg ion , w h i c h is greater t h a n tha t i n an u n d i s t u r b e d m e d i u m , a n d w i l l recompress the target s t i l l fur ther . ( T h e sound speed c = yjdP/dp (P,p is the pressure and dens i ty ) equals , in the case of an idea l ad i aba t i c gas for e x a m p l e , ^JfP/p, where 7 is the r a t i o of specific heat. Hence c — c0(p/po) J~°' 5 {po- Co is some reference den-s i ty and c o r r e s p o n d i n g sound speed) oc / i 7 - 0 5 = p 1 - 1 ' for a m o n a t o m i c gas.) E v i d e n t l y , the l a t ter waves, p r o p a g a t i n g at h igher speeds, w i l l t end to ca tch up w i t h the preceeding ones. T h i s leads to a " s teepening" of the wave front , or the coalescence of a sequence of m u l t i p l e shock waves in to a single s teady shock front . T h e compres s ive effects of the i n d i v i d u a l shock waves also accumula te , and this shock front is charac te r i zed by a sharp d i s c o n t i n u i t y in pressure, density, and t e m p e r a t u r e between the shocked and unshocked regions. 2.2 T h e H u g o n i o t C o n s i d e r a p l a n a r , steady state s t rong shock wave and fur ther assume tha t the m e d i u m ahead of the shock is at rest whereas the state b e h i n d the shock is u n i f o r m l y compressed 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 , conservat ion of mass , m o m e n t u m , a n d energy across the shock front in the l a b o r a t o r y frame leads to the R a n k i n e - H u g o n i o t Chapter 2. Theory of Laser-driven Shocks 11 F i g u r e 2.2: A n i l l u s t r a t i o n of the shocked and unshocked regions Chapter 2. Theory of Laser-driven Shocks 12 equat ions (see e.g.[47, 48]): PoUs = pi{Us ~ Up) (2.5) Pi-P0 = PoUsUp (2.6) E1-E0 = l/2(P1+P0)(l/p0-l/pi) (2.7) w h e r e p, P , and P are the density , pressure a n d in te rna l energy respect ively. T h e sub-scr ipts 0 and 1 denote the unshocked and shocked regions, w h i l e Us a n d Up are the shock wave ve loc i ty and the par t ic le ve loc i ty in the compressed region. In the l i m i t i n g case w h e n P j ^ P 0 . equa t ion (2.6) reduces to w h i c h is a s t ra ight l ine on the P vs Up p lane w i t h slope PoUs- T h i s c o n d i t i o n is easi ly satisf ied w h e n P i is of the o r d e r of M b a r whi le PQ is at a tmospher ic pressure i n our e x p e r i m e n t . 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, Po, and Pi, or some other shock parameter describ-i n g the s t rength of the shock wave) , there are five u n k n o w n parameters ( p 3 , Eo, E\, Us, Up) and three equat ions (Eqs . (2.5) to (2.7)) . Therefore two quant i t ie s need to be measured e x p e r i m e n t a l l y i n order to specify complete ly the t h e r m o d y n a m i c a l state in the shocked reg ion . For example , the f requent ly measured quant i t ie s in 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 the shock speed and par t i c le speed. In laser-dr iven shock exper iments , the. shock speed and t e m p e r a t u r e have been measured[49]. A l t e r n a t i v e l y , if the equa-t i o n of state (such as E = E(p.P)) of the 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 , then one can ca lcu la te all the u n k n o w n quant i t ies . A n y h o w , a set of five shock parameters (pi, Pi, Ei, U$, Up) corresponds to a f ina l state of a shock-compressed mater i a ] , and the locus of the final states tha t can be reached by e m p l o y i n g shock waves of different s t rength f r o m the same i n i t i a l state, p lo t t ed us ing any two of the five shock parameters , is k n o w n Pi = PoUsUp (2.8) Chapter 2. Theory of Laser-driven Shocks 13 as the shock adiabat or the Hugoniot curve. T h a t p a r t i c u l a r curve for w h i c h the m a t e r i a l is i n i t i a l l y at s t a n d a r d t e m p e r a t u r e ( O K ) and pressure (1 bar ) is ca l led the p r i n c i p a l H u g o n i o t . T h e p r i n c i p a l H u g o n i o t s of a l u m i n u m us ing various shock parameters are presented i n F igures 2.3 and 2.4. W e note the essential ly l inear re l a t ionsh ip between U$ a n d f/p[47, 48]. For a l u m i n u m , i t is[50] Us = 0.58 + \.22UP (2.9) where b o t h Us and Up are g iven in 10 6 c m / s . In F i g u r e 2.4(b) the p r i n c i p a l H u g o n i o t of gold is also inc luded as a c o m p a r i s o n to tha t of a l u m i n u m . These d a t a are a l l t aken f r o m the S E S A M E l i b r a r y (detai l s are presented be low i n § 2 . 4 . 1 ) . 2.3 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 h e i m p e d a n c e - m i s m a t c h technique has been var ious ly cal led the ref lect ion m e t h o d , the decelerat ion 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 in gas gun experiments[22] . W e shal l restr ict our discussions of this technique as i t applies to laser-dr iven shock wave studies , a l t h o u g h it is o b v i o u s l y not l i m i t e d to laser applic.ation[3, 15, 17]. T h e i m p e d a n c e - m i s m a t c h technique refers to the p r o p a g a t i o n of a shock wave t h r o u g h a target b o u n d together by two (or more) layers of mater ia l s of d i f ler ing shock impedances . In genera l , the q u a n t i t y pv represents the characterist ic , i m p e d a n c e of a m a t e r i a l , where p is the dens i ty of the m a t e r i a l and v the p r o p a g a t i o n ve loc i ty of the d i s t o r t i o n a l wave t h r o u g h the m a t e r i a l . F o r e x a m p l e , if one replaces v by the sound speed c, t h e n pc is k n o w n as the acoustic i m p e d a n c e , and if one replaces v by Us, the resul tant q u a n t i t y Density in g/cm**3 tOOOOOn (b) ^ 10000 c £ "5 i_ 0) Q_ E 1000-) 100-y / / / / / 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 in the (a) P vs p p lane , a n d (b) T vs p p lane , as g iven in S E S A M E . Chapter 2. Theory of Laser-driven Shocks 15 (a) 2.5-1 o CO * O 1.5 o 1 $ -¥ o o 5 0.5 — I — 0.2 —r-0.4 — I — 0.6 0.8 1 Particle Velocity in 10**6 cm/s -r— 1.2 1.4 —I 1.6 10 (b) L. o 3 V< 4 0_ L e g e n d + Aluminum X Gold — i — 0.8 0.6 Particle Velocity in — i 1— 1 1.2 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 the (a) Up vs Us p lane , and (b) Up vs P plane . A l s o i n c l u d e d in (b) is the p r i n c i p a l H u g o n i o t of go ld . D a t a are f r o m S E S A M E . Chapter 2. Theory of Laser-driven Shocks 16 pUs is k n o w n as the shock im.peda.nce. A s m e n t i o n e d i n § 2 . 2 , it is general ly necessary to measure two independent shock variables i n order to de te rmine the H u g o n i o t state of the shocked m e d i u m . O n the o ther h a n d , for the i m p e d a n c e - m i s m a t c h technique i n v o l v i n g t w o different mater ia l s , the H u g o n i o t of one m a t e r i a l (the sample) can be d e t e r m i n e d f rom measurement s of on ly one shock parameter i f the equa t ion of state of the other m a t e r i a l is k n o w n . T h e la t ter t h e n serves as a refernence s t a n d a r d . In the context of equa t ion of state s tudies , a single H u g o n i o t is by i tsel f insufficient to describe the comple te E O S of a m a t e r i a l ; nevertheless , it serves as a good v a l i d a t i n g m e c h a n i s m for theore t ica l E O S e jaculat ions and also as a useful e m p i r i c a l r e l a t i on at h i g h pressure. In an 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 , the laser generated shock often, t h o u g h not necessari ly , first passes t h r o u g h the s t andard m a t e r i a l a n d then i n t o the adjacent sample of interest, as i l lu s t r a ted in F i g u r e 2.5. In close analogy to other compress iona l d is tur-bances (see e.g. [51]), the shock impedance can be used to de termine the behav ior of a shock pressure pulse at the interface where the two mater ia l s are j o i n e d together . For the l a ser-dr iven shock wave propa.gating t h r o u g h the s t a n d a r d in to the sample , w h e n it rea,ches the interface, it w i l l s imul t aneous ly generate a b a c k w a r d - m o v i n g , reflected wave i n t o the 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 into the sample . One can then deduce the shock p r o p e r t y of the sample m a t e r i a l as fol lows. A s s u m i n g again the p r o p a g a t i o n of a. p l a n a r a n d s teady shock front , there are a t o t a l of ten u n k n o w n s (p, P, E, Up, and Us for each of the two mater i a l s ) . A p p l y i n g the m a t c h i n g condi t ions of pressure and par t i c l e ve loc i ty at the interface of the two mater ia l s reduces the 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 three conservat ion equat ions (Eqs . (2.5) to (2.7)) govern ing each of the shocked states in the s t a n d a r d and the sample, p l u s ( t h e E O S for the s t andard m a t e r i a l , g i v i n g a to ta l of seven equat ions . Therefore one needs to measure o n l y one parameter , u s u a l l y a shock ve loc i ty i n e i ther one of the two mater ia l s , i n order to comple te ly specify the final shock-compressed 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 17 A Interface Material 1: Standard Pi, Pi, El Materia] 2: Sample Pi, P 2 , E2 Interface Matching Conditions: PQ + Pi = P2 Upi = Up2 F i g u r e 2.5: Shock p r o p a g a t i o n and parameters in an 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 mater i a l s . 2.3.1 P r e s s u r e E n h a n c e m e n t A s m e n t i o n e d before, a reflected wave a n d a t r a n s m i t t e d wave are generated at the interface of the target . W h e t h e r the reflected a n d t r a n s m i t t e d waves are ei ther a rarefac-t i o n or second shock depends u p o n the re la t ive shock impedance s of the two mater i a l s . Speci f ica l ly , i f P0 is the a m p l i t u d e of the i n c o m i n g pressure pulse , a n d Pi and 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) respect ively , then[52] = ( ^ - ; ^ ) . P o ( 2 . 1 0 ) P , = .p (2.11) " (pUsh + (pUs)i where the subscr ipt s 1,2 denote the regions in front and back of the interface. Tn any case, the resu l tant pressure and pa r t i c l e ve loc i ty must be cont inuous across the interface. It can be seen that pressure enhancement i n the sample can be achieved by us-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 the sample (so that 2(pUs)2 is greater t h a n {pUs)? -f (pUs)i in e q u a t i o n (2.11).) T h e t r a n s m i t t e d shock pressure can therefore be great ly increased u s ing this technique . T h e v a l i d i t y of such pressure enhancement was first, d e m o n s t r a t e d in la ser-dr iven shocks by Vesser et al.[30] w i t h a l u m i n u m - g o l d targets us ing 1.06 pm laser i r r a d i a t i o n . Subsequent 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 targets i r r a d i a t e d w i t h 1.06 pm laser l i gh t and Cot te t et al.[25] for 0.26 pin laser r a d i a t i o n on a l u m i n u m - g o l d targets. T h e a m o u n t of pressure enhancement, can be easi ly ca l cu l a t ed f r o m the H u g o n i o t of the s t a n d a r d by u t i l i z i n g the mir ror - re f l ec t ion m e t h o d , and is g r a p h i c a l l y i l lu s t r a ted i n F i g u r e 2.6. T h e i n c o m i n g shock first produces an i n t e r m e d i a t e state at the point (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 in the sample us ing the mir ror - re f l ec t ion m e t h o d . T h e slope of the straight l ine involves the measurement of the shock ve loc i ty Us in the sample . Chapter 2. . Theory of Laser-driven Shocks 20 i n the s t a n d a r d . T h e reflected shock then takes the s t andard f r o m the new i n i t i a l state (UPO,PQ) to a f i n a l s tate on 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 the pressure-part ic le ve loc i ty plane f r o m a m i r r o r ref lect ion of the p r i n c i p a l H u g o n i o t of the s t a n d a r d about a v e r t i c a l l ine t h r o u g h the po int (Up0, P 0 ) [ 2 5 , 48], T h e p o i n t of in ter sec t ion of the reflected H u g o n i o t of the s t a n d a r d and the s t ra ight l ine w i t h s lope polls (where pQ is the i n i t i a l dens i ty of the sample as governed by e q u a t i o n (2.8)) a s suming t h a t U$ is measured for the sample , const i tutes the state reached i n the sample. T h e m e t h o d so descr ibed is an a p p r o x i m a t e one since the reflected shock in the s tandard or ig inates f r o m the p o i n t {Upo,Po) ra ther t h a n f rom n o r m a l cond i t ions . Such re-shocked states are more i sent rop ic t h a n the states a t t a ined i n a single shock[3, 48, 54]. However , the difference is n e g l i g i b l y s m a l l for low values of P0 ( < several Mbar [17] ) . O f course, the m e t h o d becomes exact if one takes the reflected H u g o n i o t to be that w h i c h originates f rom the i n t e r m e d i a t e po in t ( Up0, P0) but this involves the knowledge of another Hugon io t curve . A l t e r n a t i v e l y , one can assume knowledge of the p r i n c i p a l H u g o n i o t of the sample m a t e r i a l and uses the exper iment for ver i f i ca t ion . U n d e r such a s s u m p t i o n , the final state achieved in the sample is given by the intersect ion of the reflected H u g o n i o t of the s t a n d a r d and the p r i n c i p a l H u g o n i o t of the sample as i n d i c a t e d i n F i g u r e 2.7. T h e in ter sec t ion p o i n t then gives the pressure Pf and par t i c le ve loc i ty Upj in the sample, w h i c h can be used to corre la te w i t h exper iment s . For example , the shock speed in the s ample can be ca l cu l a t ed u s ing a re la t ion s imi l a r to E q . (2.9), and can be compared 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 rac t ive in E O S studies of h i g h - Z ma-ter ia ls since it reduces the undes i rab le effect of r ad i a t ive prehea t ing ahead of the shock Chapter 2. Theory of Laser-driven Shocks 21 P Pi • / 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 mirror-re f lec t ion m e t h o d w i t h the sample H u g o n i o t k n o w n , e l i m i n a t i n g the need to measure Us-Chapter 2. Theory of Laser-driven Shocks 22 front[55]. A s is wel l demonstrated[29 , 56, 57, 58], the convers ion f r o m laser l ight to X - r a d i a t i o n arises due to the var ious e lec tronic de-exc i ta t ion and r e c o m b i n a t i o n i n a par-t i a l l y i o n i z e d p l a sma . T h e r a d i a t i o n may be due to free-free (b remss t rah lung) , free-bound or b o u n d - b o u n d emissions[59]. T h e first two processes lead to c o n t i n u u m r a d i a t i o n whi le the last process to l ine r a d i a t i o n . In general , f ree-bound and b o u n d - b o u n d rad ia t ion d o m i n a t e over free-free r a d i a t i o n . T h a t the corona and c o n d u c t i o n zone are not i n a f u l l y i on ized state is especia l ly t rue as the a t o m i c n u m b e r of the target increases and these regions become a s t rong source of X - r a y . T h e energetic, components of these X-rays ( those whose energies exceed ~ 1 k e V ) , w i t h cor re spond ing long mean free, pa ths , w i l l pass u n i m p e d e d t h r o u g h the c o r o n a and ab la t ion zone w h i c h are o p t i c a l l y t h i n (i.e. transpar-ent to th i s r ad i a t ion ) and deposi t their energy in the m a t e r i a l ahead of the shock front. S u c h preheat of the unshocked region of the target m a y affect the shock process and obscure the s tudy of shock- induced phenomena . T h i s di f f iculty can be c i r cumvented in an i m p e d a n c e - m i s m a t c h e d target where the shock is p r o d u c e d by la ser-dr iven ab la t ion in the l o w - Z materia] before it propagates in to the h i g h - Z m a t e r i a l of interest . T h e laser is then incident, on a l o w - Z m a t e r i a l and the re su l t ing p l a s m a is more l ike ly to be ful ly ion-i z e d , hence reduc ing the generat ion of X - r a y . M o r e o v e r , it takes a lower laser irradia.nce to achieve a given shock pressure i n the h i g h - Z m a t e r i a l in an impeda ,nce-mismatched target, t h a n that is requ i red by d i r e c t l y p r o d u c i n g the shock i n the h i g h - Z m a t e r i a l , since the i m p e d a n c e m i s m a t c h technique yields the benefit of pressure enhancement at the inter face . A lower laser in tens i ty can fur ther d i m i n i s h the p r o d u c t i o n of h a r m f u l X- rays . Chapter 2. Theory of Laser-driven Shocks 23 2.4 E q u a t i o n of S t a t e An equa t ion of state ( E O S ) is a r e l a t ion g o v e r n i n g the t h e r m o d y n a m i c a l propert ies (pressure, t e m p e r a t u r e , density , etc.) of a subs tance in 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 prov ides the i n f o r m a t i o n i n p r e d i c t i n g such diverse p h e n o m e n a as phase t rans i t ions 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 ) u n d e r various e x t e r n a l cond i t ions . G o o d rev iew art ic les of the E O S at h igh pressure can be found i n references [47] and [48]. Here we w i l l brief ly descr ibe the c a l c u l a t i o n a l procedures used in two different E O S mode l s . 2.4.1 S E S A M E E q u a t i o n of S t a te T h e S E S A M E E O S l i b r a r y f rom the Los A l a m o s N a t i o n a l Labora tory [50 ] is an ex-tens ive c o m p i l a t i o n of E O S propert ies (specific i n t e r n a l energy, pressure, average charge state.) and other a t o m i c d a t a (such as t h e r m a l and e lectr ica l c o n d u c t i v i t y , opac i ty) of m a n y different mater ia l s over a wide range of dens i ty and 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 imula t ions in m a n y laser-dr iven shock studies (see, e.g. [25, 60, 61]). W e w i l l descr ibe some of the theore t ica l m e t h o d s i n S E S A M E as they a p p l y to gold a n d a l u m i n u m . T h e S E S A M E ca l cu l a t ions of the t o t a l i n t e r n a l energy E of gold 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) where the three terms descr ibe the co ld (OK) c r y s t a l l ine sol id (i.e. the t h e r m o d y n a m i c states of the sol id is on the zero degree i s o t h e r m ) , the ionic t h e r m a l v i b r a t i o n , and the e lec t ronic t h e r m a l c o n t r i b u t i o n respect ively . T h e co ld curve ca l cu la t ions are based on an e m p i r i c a l modi f i ed M o r s e p o t e n t i a l model[63] , whose pressure t e r m is of the form P = a77 2 / 3 (r /e^" - eh*v) (2.13) Chapter 2. Theory of Laser-driven Shocks 24 "where ?/ = pjp0, v = 1 — 7 / - 1 / 3 , ba — 3 -j- bT — 3 .B 0 , Bo is the b u l k m o d u l u s at O K , and a, 6 r are two parameters to be fitted by m a t c h i n g o n to the co ld curve i n the T F D (Thomas-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 based on an i n t e r p o l a t i o n be tween the low t e m p e r a t u r e (<1 e V ) Debye model[65] and the high 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 , the e lectronic c o n t r i b u t i o n is also based on the T F D m o d e l . T h e S E S A M E E O S ca lcu la t ions for a l u m i n u m also account for its m e l t i n g t r ans i t i on at h igh pressure. In fact , seven different theore t i ca l models are used to complete the E O S over a w i d e range of dens i ty and t e m p e r a t u r e . F i g u r e 2.8 shows the dens i ty- temperature regions where each m o d e l is app l ied and expec ted to be v a l i d . T h e seven regions are then 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 ( shaded 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 employed i n the various regions are: 1. A C T E X [ 6 6 ] for a s t rongly coupled p l a s m a ( in w h i c h the p o t e n t i a l energy of the p l a s m a is m u c h larger than its k i n e t i c energy) . It is based on a m a n y - b o d y pertur-b a t i o n e x p a n s i o n . 2. For the low dens i ty low tempera ture case, Young ' s soft sphere m o d e l for metals[67] is used. T h i s is a s emi-empi r i ca l m o d e l where free parameters are adjusted to reproduce e x p e r i m e n t a l i sobar ic da ta . 3. Sana's i o n i z a t i o n model[6S] is used i n the low dens i ty in te rmed ia te tempera ture reg ion. 4. G R A Y [ 6 9 ] is a s emi-empir i ca l mode l to treat the region between l i q u i d to two-fold sol id dens i ty at t e m p e r a t u n r e s under 1 e V . T h e sol id E O S ut i l izes the Dugale-M a c D o n a l d form[70] of the G r i i n e i s e n theory . T h e m e l t i n g t r a n s i t i o n is e s t imated a c c o r d i n g to the 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 long the 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 the seven E O S models of a l u m i n u m used i n S E S A M E 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 ed . W e emphas ize that i t is in this region where the m e l t i n g of a l u m i n u m is t aken i n t o cons idera t ion . 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 by the self-consistent aug-m e n t e d p lane wave ( A P W ) method[72] , 6. T F N U C [ 7 3 , 75] is used i n the non-zero temperatures and h igh densi ty case. It adds to the co ld so l id part ( region 5) an e lec t ronic t h e r m a l c o n t r i b u t i o n us ing the T h o m a s - F e r m i - K i r z h n i t s theory [73, 74] and an ion ic t h e r m a l c o n t r i b u t i o n using a Gr i ine i s en- l ike theory at low temperatures[75] and a one-component p l a s m a theory at h i g h tempera tures [7.5]. 7. T h e E O S for the 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 cu la ted by a var ia-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 theory 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 our new ca lcu la t ions of the gold E O S . T h i s work is per formed by D r . B . K . G o d w a l (on leave f r o m the B h a b h a A t o m i c Research Center , Ind ia ) . T h e new E O S m o d e l is developed f r o m b o t h sol id a n d l i q u i d state theories . T h e sol id phase 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 the model[62] i n w h i c h the tota l i n t e r n a l energy E is g iven by eq. (2.12) and the to ta l pressure P of the mate r i a l at a g iven v o l u m e V a n d t e m p e r a t u r e T is P =-P, + -yEi/V + ieEJV (2.14) w i t h the 7's be ing the G r i i n e i s e n parameters . For the' evaluat ions of Ec and P c on the co ld curve (OK i so therm) as a func t ion of V , a first p r inc ip l e energy b a n d s t ructure m e t h o d , n a m e l y , the l inear i zed-muf fm- t in-orb i t a l ( L M T O ) method[77] , is used. T h i s is a self-consistent c a l c u l a t i o n capable of eva lua t ing the g r o u n d state propert ie s , namely , Chapter 2. Theory of Laser-driven Shocks 27 the energy eigenvalue and wavefunct ion of a n ordered c ry s t a l l ine m e t a l (a m a n y b o d y sys tem) by so lv ing the effective one-electron Schrodinger equa t ion . In c o m p a r i s o n w i t h the m o r e sophis t ica ted e lectron b a n d m e t h o d such as the self-consistent augmented plane wave ( A P W ) m e t h o d , the L M T O m e t h o d is at least a h u n d r e d t imes faster w i t h l i t t le loss of accuracy. It is therefore adopted here to ca lcu la te the 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 the frame w o r k of the H o h e n b e r g - K o h n -S h a m ( H K S ) loca l dens i ty formal ism[78] , w h i c h provides the theore t i ca l basis for using a. v a r i a t i o n a l approach to evaluate the g r o u n d state energy in the context of a density f u n c t i o n a l theory. T h e muf f in- t in orbi ta l s ( w h i c h are spec ia l ized forms of the basis wave-funct ions ) are cons t ructed us ing the von B a r t h - H e d i n exchange c o r r e l a t i o n potential[79] w i t h the ground state of go ld assumed to be i n a fee (face center cub ic ) s t ruc ture and 5 d 1 0 6 s 1 e lectronic conf igura t ion . T h e energy and pressure 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 angular m o m e n t u m states up to 1 = 3 (i.e. s ,p,d,f states) i n the frozen-core a p p r o x i m a t i o n (i.e. a s ta t ic la t t ice w i t h i m m o b i l e atoms) 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 inc lude correct ions due to the in terce l lu la r C o u l o m b i n t e r a c t i o n based on the m o d e l of G l o t z e l and McM.ahan[80] as wel l as correct ions due to l a t t i ce v i b r a t i o n s (i.e. core is not frozen but can become a valence b a n d state) us ing a p rocedure by S i k k a a n d G o d w a l [ 8 l ] . Secondly , we have used the classical D u l o n g and P e t i t law for the l a t t i ce t h e r m a l energy : E-t = 3fcgT per a t o m , where kp is B o l t z m a n n ' s constant . T h e corre sponding pressure is ~yEJV. F i n a l l y , the e lectronic t h e r m a l energy is der ived us ing a free e lectron gas m o d e l (see, e.g. [47]): Ee = \(3T 2 where j3 is the e lectronic specific heat coeffi-cient and is equal to \>ir 2k 2BN (e f) w i t h N{ej) be ing the densi ty of states at the F e r m i level . T h e Gr i ine i s en parameters used above are ca l cu la ted w i t h D u g a l e and M a c D o n a l d ' s express ion [70], V d 2(PcV 2' 3)/dV 2 1 7 ( V ) = ~ i d{PcVW)/dV " 3 ( 2 - 1 5 ) Chapter 2. Theory of Laser-driven Shocks 28 where the co ld pressure PC(V) is o b t a i n e d f r o m previous results of the OK i s o t h e r m ca l cu l a t ions us ing the L M T O m e t h o d . O n the other h a n d , the l i q u i d phase is mode l l ed by the corrected r i g i d spheres ( O R I S ) method[82] . T h i s is a first order 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 the E O S of a fluid f r o m the zero-degree i s o t h e r m of the c o r r e s p o n d i n g so l id . L i k e m a n y o ther p e r t u r b a t i o n theor ies , the basic reference sys tem in the O R I S m e t h o d is tha t of a h a r d sphere f lu id (a h a r d sphere fluid is one w i t h " b r i c k - w a l l " pa i r p o t e n t i a l , i.e. the p o t e n t i a l U(r) — +oo i f r < <j0 and 0 o therwi se , where a0 = a0(p,T) is the h a r d sphere d i ameter ) whose prop-erties are k n o w n . Y e t , the O R I S m e t h o d is d i s t ingu i shed by the fact t h a t i ts first order p e r t u r b a t i o n t e r m is an average over the O K - i s o t h e r m ra ther t h a n the pa i r in te rac t ion po-t e n t i a l , w h i c h is more di f f icul t to a scer ta in . There fore , the c a l c u l a t i o n of the zero-degree i s o t h e r m us ing the L M T O m e t h o d in the sol id par t can be employed conven ient ly in the l i q u i d c o m p u t a t i o n . B r i e f l y speaking , the m e t h o d evaluates the H e l m h o l t z free energy F of the l i q u i d w i t h F = F 0 + A ' < < £ > o (2.16) where F0 is the free energy of the h a r d sphere f l u i d , N the to ta l n u m b e r of part ic les , a n d < <p > the p o t e n t i a l energy of a par t i c l e in the field of its ne ighbors , averaged over a l l conf igurat ions . T h e ca l cu l a t ions of the t h e r m o d y n a m i c propert ies then proceed in two steps. F i r s t of a l l , the free energy and c o r r e s p o n d i n g pressure of a h a r d sphere fluid are g iven by[82] ( - £ - ) o = - 3 1 n ( l - - ) + E A „ ( ^ f (2.17) NkT rlc ^ r)c a n d ( ^ ^ I f - ^ + E ^ f (2.18) where r\ = TTNO~Q/6V is the p a c k i n g f rac t ion and 7] c(=0.6452) that for r a n d o m l y close-packed spheres. T h e coefficients A ' K are o b t a i n e d f r o m a v i r i a l ex pans ion a n d are also Chapter 2. Theory of La.ser-driven Shocks 29 g iven i n [82]. T h e second step is to ca lcula te <</>>0, w h i c h is the average value of the p o t e n t i a l in the h a r d sphere sy s tem. W e note that w i t h i n the C R I S m o d e l , each par t ic le is located i n a spher i ca l cell of r ad ius R f o r m e d by its ne ighbors . If one further assumes that on ly the c o n t r i b u t i o n s f r o m the nearest neighbors are s ignif icant, then < (f)>o is re lated to the O K - i s o t h e r m energy £" c [82] v i a 3 J<?0 < & >0= It f m Ec(NR 3/V2)gs0(R)R2dR (2.19) 3 J (7r, where Rm, the cutoff rad ius and gso{P), the nearest ne ighbor c o n t r i b u t i o n to the r ad 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 the h a r d sphere f l u i d ( R D F is a measure of the neighbors ' 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 ted a n a l y t i c a l l y in reference [82]. T h e resultant i n t e r n a l energy and pressure are accord ing ly , E = F - T ( ^ ) (2.20) and 8F Las t ly , the m e l t i n g curve P m ( T m ) is c a l cu l a t ed by s t i p u l a t i n g that m e l t i n g occurs at pressures and t empera ture s where the two phases have equal G i b b s free energies, i.e. G solid Pm • Tm ) = Gijguid(Pm,Tm). Resu l t s of th i s new equat ion of state ca lcu la t ion are p l o t t e d in F i g u r e 2.9, w i t h the 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 compar i son . T h e ca l cu la ted sol id H u g o n i o t agrees well w i t h tha t in S E S A M E - , but the new E O S pre-dicts that m e l t i n g of go ld w i l l beg in at ~ 1 . 3 M b a r and be comple ted at —2.2 M b a r . There fore i t is expected that under a shock pressure of over 2.2 M b a r , the pressure-t e m p e r a t u r e p a t h w i l l be a long the 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 tha t for go ld at h igh pressure, say 7 M b a r , the solid and l i q u i d Chapter 2. Theory of Laser-driven Shocks 30 0 1 2 3 4 5 6 7 Pressure (Mbar) F i g u r e 2.9: T h e so l id (sol id l ine) and l i q u i d (dash) H u g o n i o t of go ld as ca lcu la ted in § 2 . 4 . 2 , t h a t in S E S A M E (dot-dash) is also i n c l u d e d ; also shown is the m e l t i n g curve (dot-dot-dot-dash) Chapter 2. Theory of Laser-driven Shocks 31 phases are respect ive ly at a t empera ture of 25600 K (2.20 e V j and 22400 K (1.93 e V ) , a difference tha t s h o u l d be d i scernible i n exper iment s . 2.5 C o m p u t e r S imula t ions T h e genera l ly t i m e dependent nature of a laser-dr iven shock wa.ve renders the steady state 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 , the m a n y phys i ca l processes invo lved in the i n t e r a c t i o n of a. laser and a p l a sma , and the fact that the governing p a r t i a l differential equat ions are c o u p l e d and nonl inear m a k e a n a l y t i c a l ca lcu la t ions e x t r e m e l y res tr ic t ive and often unrea l i s t i c . C o m p u t e r s imula t ions offer a v iable a l t e rna t ive i n p r o v i d i n g the-ore t i ca l suppor t for exper iment s . T h r e e different codes, S H Y L A C , H Y R A D , and P U C are used in our studies . B o t h S H Y L A C and H Y R A D str ive to m o d e l the hydrodyna .mic and t h e r m o d y n a m i c evo lu t ions 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 they differ by the i r level of sophis-t i c a t i o n . Br ie f ly , S H Y L A C is a pure ly f l u i d code, w h i l e H Y R A D incoporat.es laser-matter in te rac t ions . B o t h are one-d imens iona l , Lagrangia.n codes. (A L a g r a n g i a n system is one in w h i c h the f l u i d elements or cells are assigned coordinates w h i c h do not vary w i t h t ime . In a d i t i o n , each cell moves w i t h its l oca l f lu id (par t i c le ) ve loc i ty , so that the mass in each cel l is conserved. For th i s reason, a L a g r a n g i a n sys tem is sometimes ca l led a c o m o v i n g sys tem.) Es sent i a l ly , the two codes integrate the three conservat ion equat ions of mass, m o m e n t u m , a n d to ta l energy, as wel l as the r a d i a t i o n t r a n s p o r t equat ion (in H Y R A D o n l y ) , as they a p p l y to e i ther part ic les (ions or electrons) or r a d i a t i o n f ie ld in our one-d i m e n s i o n a l p l a n a r geometry . O n the other h a n d , the codes differ by the degree as to how Chapter 2. Theory of Laser-driven Shocks 32 these equat ions axe s impl i f i ed and the var ious te rms i m p l e m e n t e d . F o r instance, bo th treat the p l a s m a as a s ingle, i n v i s c i d and compress ib le fluid of i n t e r p e n e t r a t i n g ions and electrons , b u t S H Y L A C is one- tempera ture (i .e. it assumes the same tempera ture for the ions and electrons) whereas H Y R A D , in its m o r e comple te d e s c r i p t i o n , assigns different t empera ture s to the ions and electrons i n v i e w of the finite energy e q u i p a r t i t i o n t ime between ions a n d electrons[83] due to the k n o w n dominant , inverse b r e m s s t r a h l u n g ab-sorp t ion m e c h a n i s m w h e r e b y the laser energy is first depos i ted i n the electrons and later t ransferred to the ions (as discussed brief ly i n § 2 . 1 . 1 ) . In general S H Y ' L A C is s impler and thus re l a t ive ly fast, w h i l e H Y R A D is more c o m p l e x but more comple te in its t reatment of l a ser-p lasma 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 in chapter .4 to s imula te the shock b e h a v i o r in s ingle and m u l t i - l a y e r e d targets . 2.5.1 S H Y L A C C o d e S H Y ' L A C is developed by C o t t e t and Mar ty [84 ] at U n i v e r s i t e de P o i t i e r s , France. In S H Y L A C , the la ser- induced a b l a t i o n pressure is subs t i tu ted by an equivalent pressure pulse . T h i s is done a c c o r d i n g to the e x p e r i m e n t a l sca l ing l aw between the laser intens i ty and the a b l a t i o n pressure[85] Pabl ~ 1.4 ( y j ^ . ) a 8 [Mbar] (2.22) where §A ( in W / c m 2 ) is the absorbed laser i r r a d i a n c e averaged over an area equal to tha t of the shock breakout reg ion , tha t is, the area of the shock front . F u r t h e r m o r e , this code incoporates an a r t i f i c a l v i scos i ty , as wel 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 ) equat ion of state. A l t h o u g h the a s s u m p t i o n of an i n v i s i d fluid (i.e. no viscous stress) is u sua l ly v a l i d , i t has been shown[86] that the absence of v i scos i ty in a h y d r o d y n a m i c t reatment of shock waves renders the pressure and dens i ty d i scont inuous at the shock front . 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 rong osc i l l a t ions in the densi ty or pressure profiles[87] Chapter 2. Theory of Laser-driven Shocks 33 (i.e. par t ic le s t e n d i n g to leave their cell) a n d thus be n u m e r i c a l l y uns tab le . A f ict i t ious t e r m - the a r t i f i c i a l viscosity[88] - is therefore used to in t roduce e x p l i c i t l y some amount of d i s s i p a t i o n a r o u n d the shock front in order to " smear o u t " the shock front , thereby 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 the form P = ~E (2.23) (where 7 is the G r i i n e i s e n parameter and V the specific vo lume) has been best fitted w i t h e x i s t i n g high-pressure H u g o n i o t da ta to m a k e i t m o r e real i s t ic . These approx imat ions - the r e d u c t i o n of the c o m p l i c a t e d laser-matter in terac t ions in to a pressure pulse, the a s s u m p t i o n that the state of the m a t e r i a l b e h i n d the shock lies on the H u g o n i o t , together w i t h the neglect of r a d i a t i o n t r anspor t - m a k e S H Y L A C a pure ly fluid code and therefore m u c h faster and less cost ly to r u n . 2.5.2 H Y R A D C o d e 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 code) is developed at U B C . Deta i l s of the code can be found in t h e theses of Celliers[89] a n d D a Silva[90]. It is an extens ively m o d i -fied version of the h y d r o d y n a m i c code M E D U S A [ 9 1 ] . 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 , and L a g r a n g i a n in t r e a t m e n t . It models the d y n a m i c s of laser-target in terac t ions and solves for the 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 trans-p o r t in 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 the usual set of cou-p led di f ferentia l equat ions represent ing the conservat ion of mass, m o m e n t u m , and energy of the ions and electrons in one d i m e n s i o n : Chapter 2. Theory of Laser-driven Shocks 34 De, _ dV - m = - p - m + Q ' ( 2 ' 2 7 ) where D j Dt = d j dt -f ud/dx is the L a g r a n g i a n t i m e der iva t ive , Pt = P% + Pt the t o t a l pressure, V — l/p the specific v o l u m e , e the specific i n t e r n a l energy, and Q the energy source t e r m due to various energy depos i t i on and d i s s ipa t ion processes. For instance , the e lectron heat f lux t e r m Oe inc ludes c o n t r i b u t i o n s f rom Sp i tzer heat c o n d u c t i o n (see E q . (2.4)) , e lec t ron- ion energy exchange (not present i n one t e m p e r a t u r e descr ip t ion) , laser energy d e p o s i t i o n , and 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) to (2.27) give the t em-p o r a l e v o l u t i o n of density, f lu id ve loc i ty , and ion and e lectron t e m p e r a t u r e respect ively . T h e i o n i z a t i o n m o d e l is that of the co l l i s iona l - rad ia t ive e q u i l i b r i u m ( C R E ) type[92], w h i c h has been shown to best descr ibe laser-produced plasma[58, 93], especia l ly that i n the corona. In thi s m o d e l , the average i o n i z a t i o n and the associated r a d i a t i v e power are ob ta ined by so lv ing a sys tem of rate equat ions of the f o r m where A/,- is the p o p u l a t i o n density of state i , and WZJ the rate coefficients of var ious mechan i sms w h i c h change the sys tem f r o m state j to i a n d f r o m state i to j respect ively. Hence , the first t e r m in E q . (2.28) represents the p o p u l a t i o n of state i f rom al l o ther states, and the second t e r m the d e p o p u l a t i o n of state i into the other states. T h e var ious mechan i sms affecting state p o p u l a t i o n s i n c l u d e rad ia t ive or co l l i s iona l i o n i z a t i o n , recom-b i n a t i o n , and e x c i t a t i o n . T h e c o m p l e x i t y of C R E lies i n the fact tha 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 and t r ans i t i ons , and consequently a large number of rate equat ions , need to be considered self-consistently. In the l i m i t of h igh- tempera ture a n d low-dens i ty , r a d i a t i v e processes are faster t h a n co l l i s iona l ones and we w i l l recover the f a m i l i a r c o r o n a l model[59] . O n the o ther h a n d , in the h igh-dens i ty l i m i t where co l l i s iona l Chapter 2. Theory of Laser-driven Shocks 35 processes d o m i n a t e , the p l a s m a w i l l be i n L T E ( loca l t h e r m o d y n a m i c equi l ibr ium ) [94] . T h e h y d r o d j r n a m i c s and i o n i z a t i o n m o d e l are coup led as fol lows. T h e t empera ture a n d dens i ty p r o d u c e d by the h y d r o d y n a m i c par t of the c a l c u l a t i o n are needed to c o m p u t e the level p o p u l a t i o n s and emiss ion of r a d i a t i o n (since the rate coefficients are density and t e m p e r a t u r e dependent ) . T h e emiss ion power then enters as an energy source t e r m i n the Oe 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 d iv ides the r a d i a t i o n energy s p e c t r u m into a discrete set of frequency g roup , each w i t h its own group-averaged opac i ty and mean free p a t h , is used to solve the r a d i a t i v e transfer e q u a t i o n , dl„ r --^ + ~ = SV-XI, (2.29) c at ox where / is the r a d i a t i o n intens i ty , 5 the emiss ion source t e r m , \ the opac i ty , and subscr ipt v the g roup frequency. T h e Sv t e r m represents r ad ia t ive emis s ion , and the \IX, t e r m represents a b s o r p t i o n . O f course, the way r a d i a t i o n is t r a n s p o r t e d is inf luenced by the t h e r o m o d y n a m i c state of the fluid, w h i c h is in t u r n affected by the rad ia t ive energy c o n t r i b u t i o n . T h e process of r a d i a t i o n transport , can also be " s w i t c h e d off" i n H Y R A D . T h i s may be done 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 extens ively tested in the simula.t ions of shock behav ior in b o t h a luminum[95] a n d fused silica[96]. H Y R A D n o r m a l l y incorpora te s the 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 governed by Spitzer[42j c o n d u c t i o n . T h e n u m e r i c a l scheme is that of the P P M (piecewise p a r a b o l i c m e t h o d ) type[97]. T h i s is a second order extens ion of the G o d u n o v ' s method[98] , b u t improves upon it by i n t r o d u c i n g the parabolae as the basic, spa t i a l i n t e r p o l a t i o n funct ions , w h i c h al lows for a steeper representat ion of d i scont inu i t i e s . T h e P P M has been shown to be the most accurate method[99] in the t reatment of shock h y d r o d y n a m i c s . S t i l l , some processes are not i n c l u d e d i n H Y R A D : supra/thermal e lec t ron 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 lux l i m i t e r . It can be seen ( in chapter 3) t h a t our e x p e r i m e n t a l condi t ions fa l l w i t h i n the ' c l a s s i ca l ' laser-matter c o u p l i n g regime [20, 100] where IX2 < 1 0 1 4 p m 2 - W / c m 2 (7 is the i r r a d i a t i o n in tens i ty and A the laser f requency) and effects such as e lectron flux i n h i b i t i o n or hot e lectron generat ion are negl ig ib le . A l t h o u g h we are not speci f ica l ly s t u d y i n g r a d i a i o n i n this thes i s , the 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 ranspor t by r a d i a t i o n m a y p lay an i m p o r t a n t role p a r t i c u -l a r ly i n e x p e r i m e n t s us ing a r e l a t ive ly long laser pulse[58, 101]. A x i a l r ad i a t ive t ranspor t can lead to p rehea t ing in the target as discussed in §2 .3 .2 , w h i l e l a tera l r a d i a t i o n trans-por t leads to t h e r m a l losses, a n d w i l l thus m o d i f y the h y d r o d y n a m i c and t h e r m o d y n a m i c profi le of the m a t e r i a l (see e.g. [61, 102, 103, 104]). There fore it may affect our s tudy of t e m p e r a t u r e due to shock hea t ing and fur ther discussions w i l l be presented in chapter 4. 2.5.3 P U C C o d e W e now descr ibe 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 developed at U B C . It is an i m p r o v e d ( in the n u m e r i c a l scheme) vers ion of the P E C ( P l a s m a E x p a n s i o n C o d e ) descr ibed i n the thesis of Par feniuk[85] . S ince a l l of the measurements presented in th i s work are m a d e at the back or free surface of a target as the shock wave emerges f rom this surface, a specific code ( P U C ) is developed in order to o b t a i n an accurate c a l c u l a t i o n w i t h h i g h spa t i a l and t e m p o r a l re so lu t ion of the p l a s m a profiles at the rear surface of the target . In p a r t i c u l a r , P U C is used to access the effect of shock u n l o a d i n g on the free surface emiss ion measurements d u r i n g and subsequent to shock breakout . T h e one-d imens iona l h y d r o d y n a m i c code P U C treats o n l y the h y d r o d y n a m i c s of a compressed target rare fy ing into the v a c u u m . T h e process of l a ser-matter in te rac t ions is not i n c l u d e d . T h e s i m u l a t i o n begins at t i m e t = 0, w h i c h is def ined to be the t i m e of shock breakout at the free surface. A t t = 0, the t a r g e t - v a c u u m interface is a s sumed to be a d i s c o n t i n u i t y w i t h the shocked state of the target specif ied to have the dens i ty a n d t e m p e r a t u r e cor re spond ing Chapter 2. Theory of Laser-driven Shocks 37 to the shocked c o n d i t i o n as ca l cu la ted by, for example , H Y R A D . Therefore , P U C can be regarded as a "post-processor" to be used in t a n d e m w i t h H Y R A D . P U C is a L a g r a n g i a n , one t e m p e r a t u r e code a n d uses the same P P M n u m e r i c a l scheme as in H Y R A D . It also solves the h y d r o d y n a m i c equat ions for mass, m o m e n t u m and t o t a l i n t e r n a l energy, and uses E O S d a t a f r o m either S E S A M E or the new equat ion of state of go ld w h i c h incopora te s the 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 the u n l o a d i n g m a t e r i a l is assumed to or ig inate l o c a l l y f r o m a b l a c k b o d y source, i .e. , the e m i t t e d r a d i a t i o n is in 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 loca l ) of the compressed mat te r . Hence , the emis s ion in tens i ty Ix of wavelength A at t i m e t by 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 empera ture T(x,t) i s [ l05] 2 fee2 1 h(x, t) = — (2.30) A b exp[h.c/Xkl [x,t)\ — 1 W e have to account for the fact tha t the 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 way to the detector 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 ra re fy ing p l a s m a w i l l absorb its own 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{ detected by a. remote detector is thus Ixit)= <r(x)p{x)h(x,t)exp[- j ° a(x')p{xr)dx'} dx (2.31) where cr(x) is the o p a c i t y and p(x) the density a long the detector l ine of sight. P U C w i l l be used in the br ightness t e m p e r a t u r e s tudy to s imula te the t ime evo lut ion of the rear surface emis s ion in tens i ty (see § 4 .2 .2 .B) . C h a p t e r 3 E x p e r i m e n t a l F a c i l i t y , D i a g n o s t i c s , a n d S e t u p 3.1 L a s e r F a c i l i t y A schemat ic d i a g r a m of the laser system a long w i t h the b e a m diagnost ics is shown i n F i g u r e 3.10. T h e Quante l neodymium-g la s s laser sys tem includes a N d - Y A G ( n e o d y m i u m -d o p e d y t t r i u m a l u m i n u m garnet ) osc i l la tor , a N d - Y A G preaml i f ier , four Nd-glass a m p l i -fiers, a n d associated b e a m expanders and steering opt ic s . T h e b e a m d iameter at the exit of the f i n a l ampl i f ier rod is 45 m m . T h e laser osc i l l a tor is pass ively Q-swi tched w i t h a dye-cel l and produces a single pulse at 1.064 p m in the T E M 0 o mode . T h r e e spa t i a l f i lters are also d i s t r i b u t e d w i t h i n the laser cha in . T h e y consist, essential ly of two lenses and 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 remove the h igher spa t i a l f requency intens i ty m o d u u l a t i o n s in the la.ser pulse. F o r our present exper iments , the laser b e a m is f requency-doubled to y ie ld 0.532 p m green l ight us ing a K D * P (deuterated p o t a s s i u m d ihydrogen phosphate ) c r y s t a l . T h e sys tem is operated to deliver up to 7 joules at 0.532 p m , and the energy can be c o n t i n u o u s l y var ied by adjust ing, the ampl i f ier p u m p i n g level . T h e energy of the o u t p u t b e a m is m o n i t o r e d by a, Gentec energy meter[106], whi l e a fast (350 ps rise t ime) Hamamat . su photod iode [ l07 ] records the laser pulse shape. A t y p i c a l 0.53 p m laser pulse as measured w i t h the p h o t o d i o d e is shown i n F i g u r e 3.11. It is seen that the pulse, shape is a p p r o x i m a t e l y Gaus s i an t e m p o r a l l y w i t h a ful l w i d t h ha l f m a x i m u m (FWHM) of 2.3 ns. 38 Chapter 3. Experimental Facility, Diagnostics, and Setup 39 OSC = OSCILLATOR S F = S P A T ] A L F ] L T £ R PA = PRE-AMPLIFIER BE = BEAM EXPANDER A = AMPLIFIER SHG = SECOND HARMONIC GENERATOR Figure 3.10: A schematic of the laser and diagnostics system Chapter 3. Experimental Facility, Diagnostics, and Setup 40 F i g u r e 3.11: A t y p i c a l laser pulse Chapter 3. Experimental Facility, Diagnostics, and Setup 41 3.2 I r r a d i a t i o n C o n d i t i o n s W e determine the laser intens i ty d i s t r i b u t i o n on target by i m a g i n g the laser focal spot onto a streak camera i n its focus (i.e. s ta t ic , non-s treak) m o d e . T h e H a m a m a t s u u l t ra fas t ( re so lut ion l i m i t of 10 ps) c a m e r a inc ludes a t e m p o r a l disperser m o d e l C 9 7 9 and a t e m p o r a l analyser C1440[108]. T h e c a m e r a is sensit ive i n the o p t i c a l a n d n e a r - U V s p e c t r u m . T h e overa l l m a g n i f i c a t i o n of the o p t i c a l sys tem is f o u n d by p l a c i n g a gr id of k n o w n spacings i n the target p lane. T h e m a g n i f i c a t i o n is then c a l c u l a t e d by re l a t ing the spacings of the image of the g r id as d i sp layed on the v ideo m o n i t o r of the streak camera to that of the. ob ject . T h e laser is f ired at fu l l energy and a p p r o p r i a t e l y a t tentua ted by N D (neutra l dens i ty ) f i l ters pla.ced before the f inal focuss ing lens. T h e laser is also focussed at the target p lane to give the most u n i f o r m in tens i ty d i s t r i b u t i o n . F i g u r e 3.12 shows an in tens i ty d i s t r i b u t i o n of the laser focal spot , t i m e integrated over the entire laser pulse. T h e spa t i a l re so lut ion in this measurement is ~ 2 . 5 p.m. It shows the laser spot to be conf ined in a. region 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 this laser spot 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 , the same d i s t r i b u t i o n is p lo t ted into an equivalent 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 profi le i n F i g u r e 3.13. F i g u r e 3.14 shows the cross-section of the laser spot of F i g u r e 3.12 across the x- a n d y-coordinates s p a n n i n g the centra l 5 p m of the spot . T h e laser profi le is a p p r o x i m a t e l y t r apezo ida l spat ia l ly , and we ca lcu la te the intens i ty $5 by cor re l a t ing w i t h the shock breakout region as fol lows. F r o m §4 .1 .1 .A it w i l l be shown tha t the shock breakout, region corresponds to an area of ~ 8 0 p m in d iameter , and the laser intens i ty in this area, w i l l be ca lcu la ted . O n the other h a n d , i t is seen f rom F i g u r e 3.13 that 80% of the laser energy is conta ined w i t h i n a. radius R&0 of ~ 4 2 p m . There fore , the effective in tens i ty $5 cor re sponding to the area of shock breakout is $ s = 0.80 _ ^ £ £ 1 _ (3.32) Chapter 3. Experimental Facility, Diagnostics, and Setup 42 X_Posit.ion (Junri) F i gure 3.12: A time-integrated laser intensity distribution 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 prof i le of the laser spot of F i g u r e 3.12 Chapter 3. Experimental Facility, Diagnostics, and Setup 44 o n 1 1 — 1 1 1 0 20 40 60 80 100 Y-Coord inate ( urn ) F i g u r e 3.14: A cross sect ion of the laser spot in F i g u r e 3.12 across (a) the x -coord ina te and (b) the y - c o o r d i n a t e , each s p a n n i n g the centra l 5 um of the spot Chapter 3. Experimental Facility. Diagnostics, and Setup 45 where Eiaser is the t o t a l laser energy, T\ASER the F W H M of the laser t e m p o r a l profi le , a n d ^4-80 ( = TT-PCSO) the area where 8 0 % of the laser energy is conta ined . T h e laser i r rad iance ca l cu l a t ed u s ing this p rocedure has been successfully used as an i n p u t parameter i n p rev ious h y d r o c o d e s i m u l a t i o n s , where the ab la t ion pressure and shock t r a j e c t o r y thereby p r e d i c t e d agree wel l w i t h e x p e r i m e n t a l results (see [ 4 9 , 5 5 , 1 0 9 ] ) . In our exper iments , the intens i ty 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 , and us ing equat ion ( 3 . 3 2 ) ( w i t h Eiaser — 4 . 2 ± 0 . 4 J , rlaser = 2 . 3 ± 0.2ns), the inc ident in tens i ty is therefore 2 . 6 ± 0 . 7 x 1 0 1 3 W / c m 2 . T h e ab sorp t ion of 0 . 5 3 p m laser on a l u m i n u m targets has been measured i n prev ious s t u d i e s [ l l O , 1 1 1 ] . Based on those measurements , the absorbed i r rad iance is $A = fa- $s = - 2 . 3 ± 0 . 6 x 1 0 1 3 W / c m 2 , where fa is the absorpt ion f r a c t i o n ] ! 1 0 ] . 3.3 E x p e r i m e n t a l A r r a n g e m e n t s F i g u r e 3 . 1 5 shows the exper imenta l arrangement ins ide the target chamber and the i m a g i n g opt ics for observat ion of the taget rear surface. T h i s setup is used to record the 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 the rear surface of the target as the shock wave emerges f r o m thi s free surface. T h e target chamber is m a i n t a i n e d at a pressure of about 6 0 mtorr s . In the e x p e r i m e n t , p l a n a r targets of a l u m i n u m foils or doubled- layered a l u m i n u m - g o l d targets are i r r a d i a t e d -with 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 rected in to the c h a m b e r w i t h a series of three d i chor i c m i r r o r s , and is focussed onto the front a l u m i n u m surface of the target w i t h f / 6 . 7 opt ics at n o r m a l inc idence . T h e rear surface of the target is imaged onto the entrance sl it of the streak c a m e r a w i t h f/1.4 a c h r o m a t i c opt ic s placed at target n o r m a l . T h e rear surface l u m i n o u s emis s ion apter 3. Experimental Facility. Diagnostics, and Setup 46 F i g u r e 3.15: T h e e x p e r i m e n t a l setup i n the luminscence s t u d y Chapter 3. Experimental Facility, Diagnostics, and Setup 47 is observed t h r o u g h a l O O A - b a n d p a s s interference f i l ter centered at A 0 = 4 3 0 0 A (re ject ion r a t i o outs ide the b a n d between 0 .82A 0 a n d 1.1 A 0 is 0.01%) p l a c e d at the streak c a m e r a entrance . T h i s e l iminates laser stray l i ght f r o m enter ing the camera . T h e t e m p o r a l h i s t o r y of the s p a t i a l d i s t r i b u t i o n of the l u m i n o u s emis s ion is recorded by the streak c a m e r a and t h e n d i sp l ayed on the v ideo m o n i t o r . A s there is a t i m e j i t t e r of up to 50 ps between the t i m e the streak camera is t r iggered by a laser pulse der ived f r o m the m a i n b e a m to the t i m e w h e n i t a c tua l ly begins i t s " s t r e a k i n g " o p e r a t i o n , the t i m i n g of the free surface emis s ion w i t h respect to the laser pulse can on ly be d e t e r m i n e d us ing a reference laser pulse or f i d u c i a l w h i c h is recorded s imul taneous ly by the streak camera . Such a f iduc i a l is der ived f r o m the m a i n laser b e a m as i n d i c a t e d in F i g u r e 3.15. T h e o p t i c a l p a t h l e n g t h of the f i d u c i a l f rom the exit of the laser cha in (i.e. after the K D * P crys ta l ) to the entrance of the streak camera is made near ly equal to that of the m a i n laser b e a m go ing t h r o u g h the target and the i m a g i n g opt ics at the target rear side. Hence , the f iduc ia l s ignal becomes an "effective" m a i n laser pulse and the t i m i n g of the l u m i n o u s emiss ion f r o m the free surface of the target can be corre lated u n a m b i g u o u s l y w i t h the inc ident laser pulse. O u r e x p e r i m e n t a l setup yields a fiducial reference w h i c h leads the m a i n b e a m by 375+75 ps. T h i s is taken into account i n the analys is of shock ve loc i ty da ta . In a d d i t i o n , the fiducial also prov ides a measure of the laser pulse shape on the streak camera m o n i t o r . A l t h o u g h the streak camera, has a lower d y n a m i c range (< 100) than that of the p h o t o d i o d e (>1000) , the pulse shape recorded by the streak c a m e r a nevertheless r e a d i l y identif ies the t i m e of peak laser in tens i ty^ w h i c h is needed as the t i m e reference ( taken as t i m e zero here) for any shock-re lated p h e n o m e n o n under s tudy. D e p e n d i n g on the type of measurements , the d u r a t i o n of the streak m a y be set at 5.42 or 1.26 ns. T h e slower streak m o d e (5.42 ns) is used for shock ve loc i ty measurements where the ent ire fiducial pulse can be recorded . In the case of t e m p e r a t u r e measurements , Chapter 3. Experimental Facility, Diagnostics, and Setup 48 i n w h i c h the laser fiducial is not necessary, the faster s treak speed (1.26 ns) is chosen ins tead to i m p r o v e the t e m p o r a l r e so lu t ion of the measurement . In the e x p e r i m e n t , an appropr i a t e n u m b e r of n e u t r a l dens i ty f i lters are inserted in to the o p t i c a l p a t h of the fiducial pulse . T h i s helps to reduce the l i gh t intens i ty to an acceptable level so as not to saturate the streak c a m e r a t u b e , w h i c h can lead to premature t u b e d e t e r i o r a t i o n . C h a p t e r 4 L u m i n e s c e n c e M e a s u r e m e n t s i n S ing le a n d D o u b l e d - L a y e r e d T a r g e t s 4.1 S h o c k V e l o c i t y S t u d y A s a shock wave propagates t h r o u g h the target the region b e h i n d the shock front is heated. W h e n the shock front reaches the back or free surface of the target , the l u m i n o u s emiss ion f r o m the heated m a t e r i a l can to be detected by a streak camera . Since the target is i n i t i a l l y co ld (i .e. at r o o m t e m p e r a t u r e ) a n d opaque, no r a d i a t i o n w i l l be observed f r o m the sample u n t i l the t i m e of shock emergence. A c t u a l l y , the r a d i a t i o n w i l l become v i s ib le when the shock front is w i t h i n a d i s tance of several o p t i c a l mean free paths / f r o m the free surface. For e x a m p l e , for r a d i a t i o n at 4300A(2 .88 e V ) , the mass absorpt ion coefficient (opac i ty ) K of a l u m i n u m under n o r m a l cond i t ions is ~ 5 x l 0 4 c m 2 / g and 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. There fore , the t i m e of shock breakout at the free surface is s ignif ied by a sudden occurence of l u m i n o u s emiss ion. B y measur ing the shock breakout t imes i n targets of different thicknesses , one can m a p out the shock t r a j ea to ry f rom w h i c h the shock speed Us can be d e t e r m i n e d d . S u c h measurments can therefore be used as a d iagnost ics to s tudy the la ser-dr iven shock wave. A s discussed i n chapter 2, equat ion of state studies us ing the i m p e d a n c e - m i s m a t c h technique requires the 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 ve loc i ty i n e i ther the s t a n d a r d m a t e r i a l , or that in the sample of interest . However , in shock- induced l u m i n o u s emiss ion measurements w i t h i m p e d a n c e - m i s m a t c h e d targets , one is res tr ic ted to measure the shock a r r i v a l t imes at the free surface of the sample only. T h i s by itself is not sufficient 49 Chapter 4. Luminescence Measurements in Single and Douhled-La.ye.red Targets 50 to y i e l d the shock speed i n either the s t a n d a r d or the sample , s ince i t represents the t o t a l shock t rans i t t i m e t h r o u g h the t w o mater ia l s of the target . O n the other h a n d , one can first charac ter ize the shock p r o d u c e d i n the s t a n d a r d . In our 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 the low-i m p e d a n c e s t a n d a r d i n the a l u m i n u m - o n - g o l d targets (gold as the h igh- impedance sam-ple , w i t h Z = 79, p 0 = 19.3 g / c m 3 ) i n the i m p e d a n c e - m i s m a t c h study. A l u m i n u m is selected as o u r s t andard since its E O S da ta are w e l l t a b u l a t e d , bo th in terms of theoret-i c a l calculat ions[50] and e x p e r i m e n t a l measurements[49]. 4.1.1 S i n g l e L a y e r A l u m i n u m F o i l 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 ] of various thicknesses r ang ing f r o m 25 to 53 p m are used. T h e l u m i n o u s emis s ion associated w i t h shock breakout at the free surfaces of the targets are. recorded b y the streak camera . T h e overal l m a g n i f i c a t i o n of the d iagnos t ic sys tem ( i n c l u d i n g the i m a g i n g opt ics a n d the streak c a m e r a opt ics ) is measured by p l a c i n g a fine wire m e s h of k n o w n spac ing at the target p lane , focuss ing it onto the streak camera , a n d n o t i n g the spacing of the magni f i ed image d i sp layed on the camera 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 , the spa t i a l resolut ion achieved is a p p r o x i m a t e l y 8 p m . T h e entrance sl it of the c a m e r a is set at 200 p m . T h i s produces a streak image w i t h g o o d s ignal-to-noise ra t io of ~ 5 0 , however i t degrades the t i m e reso lut ion to —50 ps. T h i s far exceeds ' the i d e a l streak c a m e r a re so lu t ion of 10 ps. A s discussed in chapter 3, the l u m i n o u s emiss ion is observed t h r o u g h a 100 A band-pass filter centered at 4300 A . F i g u r e 4.16 shows spa t i a l ly resolved streak records of the emiss ion f r o m the shock breakout regions in 38.4 a n d 53 p m a l u m i n u m targets. A fiducial s i gna l is also recorded to a l low d e t e r m i n a t i o n of the shock breakout t ime w i t h respect to Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 51 F i g u r e 4.16: Streak records of shock breakout emiss ion (left s treak) and fiducial s ignal (r ight s t reak) i n (a) 38.4 p m and (b) 53 p m a l u m i n u m target . Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 52 the m a i n laser pulse. T i m e zero corresponds to the peak of the laser pulse. T h e shock is observed to emerge at the free surface in a region of ~ 8 0 ± 1 0 um d i ameter . N o hot spots (regions of very h i g h intens i t ies ) are observed. In the analys i s of the emiss ion intensity , we consider the emiss ion spa t i a l l y in tegra ted over the centra l 45 um span i n the shock breakout reg ion w h i c h is w i d e enough to y i e l d a suff ic iently good s igna l to noise ra t io , but n a r r o w enough 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 the t e m p o r a l h i s t o r y of the shock- induced l u m i n o u s emiss ion i n t e n s i t y and the fud ic i a l for a 38.4 um a l u m i n u m target . T h e rise t imes (between the 10% to 90% in tens i ty of the i n i t i a l peak) of the emiss ion for a l l the targets are t y p i c a l l y 2 3 0 ± 7 0 ps. T h e shock breakout t imes in 25, 29.3, 38.4, and 53 um a l u m i n u m are found to be respect ive ly 0 . 0 ± 0 . 1 , 0 . 3 0 ± 0 . 0 6 , 1 . 0 3 ± 0 . 0 5 , and 1 . 8 9 ± 0 . 1 1 ns after the t i m e of the laser peak. N o target preheat is observed as i n d i c a t e d by the fast rise t imes in the emis s ion intens i ty . 4.1.1.B Computer Simulations T o m o d e l the d y n a m i c s of the shock, the pure ly 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 this code does not incopora te the la ser-matter in te rac t ion processes, it is nevertheless fast, a n d inexpens ive . 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 pulse of 2.5 ns F W H M w i t h a peak pressure of 3.5 M b a r . T h i s is to a p p r o x i m a t e the a b l a t i o n pressure generated by our 0 .53 /mi , 2.3 ns F W H M laser pulse at an absorbed i r r a d i a n c e of $A = 2.3 x 1 0 1 3 W / c m J a ccord ing to the prev ious ly ob ta ined e x p e r i m e n t a l sca l ing la.w i n equat ion (2.22). T h i s a p p r o x i m a t i o n of the a b l a t i o n pressure appears to be reasonable as seen f r o m results of the more e laborate H Y R A D s imula t ions w h i c h inc lude the la ser- induced a b l a t i o n process . A c o m p a r i s o n of the ca lcu la ted a b l a t i o n pressure f rom H Y R A D and the G a u s s i a n pressure pulse assumed i n S H Y L A C ' is shown in F i g u r e 4.18. T h e r i s i n g por t ions of the t w o pulses ( w h i c h dr ive the shock) agree reasonably w e l l , but the a b l a t i o n pressure pulse has a longer F W H M (2.9 ns) than the assumed pressure pulse Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 53 F i g u r e 4.17: T e m p o r a l h i s t o r y of the (a) shock breakout a n d (b) fiducial streak i n a 38.4 p m A l target Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 54 TIME (ns) F i g u r e 4.18: T h e ca lcu la ted a b l a t i o n pressure pulse f r o m H Y R A D (sol id) a n d the Gaus-sian pressure pulse assumed i n S H Y L A C (dash) Chapter 4. Luminescence Measurements in Single and Doubled-La.yered Targets 55 used i n S H Y L A C (2.5 ns) . F i g u r e 4.19 shows the measured shock t rans i t t i m e as a f u n c t i o n of target thickness for the given absorbed irra,diance as wel l as the ca l cu la ted shock t r a j e c t o r y us ing S H Y -L A C . T o test the accuracy of the S H Y L A C s i m u l a t i o n , we have also ca l cu la ted the shock t r a j e c t o r y us ing H Y R A D . T w o different, cases are cons idered i n the H Y R A D s imula t ions , one where the process of r a d i a t i o n t ranspor t is t a k e n i n t o account , and the other where r a d i a t i o n t r a n s p o r t is neglected . (In this and subsequent s imula t ions where the 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 , the r a d i a t i o n is d i v i d e d into 10 energy groups f rom 0.3 to 10 k e V , as descr ibed i n the d i scuss ion 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 the s i m u l a t i o n s , we note tha t the shock is acce lerat ing (i .e. non-s teady) at ear ly t imes. T h e shock then reaches a quas i-s teady state w h e n it has propaga ted to a dep th of approx i -m a t e l y 20 p m in the target . T h e quasi-steady shock speed is f o u n d to be (1.5 ± 0.1) x 10 6 c m / s . T h e agreement a m o n g the three ca lcu la ted shock paths and e x p e r i m e n t a l d a t a are equa l ly good , and there is no i n d i c a t i o n that one s i m u l a t i o n is m o r e preferable to another . T h u s , the shock t rans i t t i m e measurement is not sensit ive enough 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, another ( H Y R A D ) or to ident i fy the s ignif icance of r a d i a t i o n t r a n s p o r t in the shock process . It appears that S H Y L A C is adequate in the p r e d i c t i o n of shock p a t h and veloci ty . H o w e v e r , we shal l use H Y R A D i n c l u d i n g the r a d i a t i o n t ranspor t process to s imula te our subsequent exper iments , a.s i t has the m o s t comple te t rea tment of the laser-matter in te rac t ions . It should be noted that the shock pressure can also be e s t imated by c o m p a r i n g the measured shock ve loc i ty w i t h H u g o n i o t da ta . F r o m the S E S A M E E O S l i b r a r y , the mea-sured shock speed of (] .5 ± 0.1) x 10c"' c m / s corresponds to a pressure of 3.1 ± 0.5 M b a r . T h i s is in agreement w i t h the pressure of 3.5 M b a r used 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 shock paths by S H Y L A C (dot-dash) , by H Y R A D w i t h o u t r a d i -a t ion t r a n s p o r t (dash) , and w i t h r a d i a t i o n t r a n s p o r t ( so l id) ; also p lo t t ed are the exper i -m e n t a l resul t s in var ious a l u m i n u m targets Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 57 4.1.2 A l u m i n u m - G o l d Targe t s 4 . 1 . 2 . 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 T h e layered targets used m this exper iment 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 by vapor d e p o s i t i o n , i.e. e v a p o r a t i o n of go ld onto a l u m i n u m substrate . T h e s e targets i n c l u d e a c o m b i n a t i o n of e i ther 19 or 26.5 p m of a l u m i n u m layers w i t h e i ther 8.4 or 13 p m of gold layers. In order to o b t a i n pressure enhancement , the targets are i r rad ia ted on the a l u m i n u m side. For these targets , the shock a r r iva l t imes at the back surfaces ( the free surfaces of the gold layer) are measured by the same technique as descr ibed i n § 4 .1 .1 .A . F i g u r e 4.20 shows a sample streak record of the shock- induced l u m i n o u s emiss ion and the 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 gold target . W e see s imi l a r qua l i t a t ive behaviors in the backs ide l u m i n o u s emiss ion as those in pure a l u m i n u m targets ; again, no target preheat or hot spots are observed. T h e shock breakout t imes 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 in 26.5 p m a l u m i n u m on 8.4 p m g o l d , and 1.89 ns i n 26.5 p m a l u m i n u m o n 13 p m go ld . T h e uncer ta in i t i e s in the measured breakout t imes are ± 0 . 1 ns. 4 .1 .2 .B C o m p u t e r S i m u l a t i o n s T h e s imula t ions are per formed in two part s . T h e first part is to examine the various issues and criteria, govern ing the 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 targets of different thicknesses need to be cons idered, we have selected the S H Y L A C code because it is speedy to r u n a n d conta ins the relevant physics of shock p r o p a g a t i o n . H Y R A D is used in the second par t of the s imula t ions to prov ide deta i led ca l cu l a t ions for the 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 and a l i m i t e d n u m b e r of target conf igurat ions . Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 58 F i g u r e 4.20: Streak record of free surface l u m i n o u s emiss ion (left s t reak) and fiducial s igna l ( r ight s treak) of a 19 um a l u m i n u m on 8.4 um gold target Chapter 4. Luminescence Measurements in Single, and Doubled-Layered Targets 59 4.1 .2 .B. i S H Y L A C s imula t ions for Targe t O p t i m i z a t i o n In S H Y L A C , the M i e -G r i i n e i s e n eq ua t ion of s tate model s for a l u m i n u m and gold are used a n d the shock pres-sure is c o m p u t e d accord ing ly . A s before, we have assumed that a G a u s s i a n pressure pulse of 2.5 ns ( F W H M ) a n d peak pressure of 3.5 M b a r is app l ied o n the front surface of the a l u m i n u m layer. In the s i m u l a t i o n s , the thicknesses of the gold layer are taken to be t h i c k enough so t h a t the shocks do not reach the free surfaces d u r i n g the s imula t ion per iods . E q u i v a l e n t l y , the gold layer thickness i n these smula t ions can be taken to be i n f i n i t y so tha t no free surface exists i n the 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 and no free surface rarefact ions 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 imes in a l u m i n u m - g o l d targets for a l u m i n u m layers w i t h thicknesses r ang ing f r o m 5 um to 50 um are p l o t t e d in F i g u r e s 4.21 to 24. O n e can c lear ly see the l ead ing edge of the s t rong shock wave, represented b y the sharp increase i n pressure, and the " d y n a m i c " na ture of the shock as i t propagates in to the target . T h e pressure at the shock f ront represents the shock breakout pressure i f a free surface were at that p o s i t i o n . For e x a m p l e , in the case of a 19 um A l on 13 um A u target ( F i g . 4.23), the free surface pressure at shock breakout (i .e. when the shock front reaches a target d i s tance of 32 um) would be approx imate ly 7.3 M b a r . A n u m b e r of conc lus ions can i m m e d i a t e l y be d r a w n f r o m the figures. F i r s t of a l l , pressure enhancement can indeed be achieved at. the interface w i t h appropr i a te choices of the front a l u m i n u m thicknesses . Secondly , by no means is the shock t r u l y steady. T h i s is due to the fact tha t the d r i v i n g pressure pulse is t ime-dependent . Shock b u i l d u p takes p lace d u r i n g the t i m e w h e n the pressure pulse is increas ing 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 s ingle s t rong shock front, has a lready been discussed in §2 .1 .3 . F u r t h e r m o r e , as the pressure of the. d r i v i n g pulse drops and eventua l ly ceases, a rare fac t ion or un load ing wave develops at the front surface of the target . T h i s propagates into the shocked m e d i u m w i t h the v e l o c i t y of sound in the shocked reg ion , w h i c h is faster t h a n the shock speed. Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 60 F i g u r e 4 .21: Shock pressure profi les in A l - A u targets w i t h the front a l u m i n u m thickness equal to 5 p m . T h e i n i t i a l prof i le corresponds to a t i m e of 1.5 ns before the pressure pulse peak , and subsequent ones are 0.25 ns apart . Chapter 4. Luminescence Measurements in Single and Doubled-La.yereci Targets 61 DISTANCE IN TARGET ( pm) F i g u r e 4.22: Same as F i g u r e 4.21 but a l u m i n u m thickness is 11.5 p m pter 4. Luminescence Measurements in Single and Doubied-Layered Targets DISTANCE IN TARGET ( jjm) F i g u r e 4.23: Same as F i g u r e 4.21 b u t a l u m i n u m thickness is 19 p m pter 4. Luminescence Measurements in Single and Doubled-Layered Targets DISTANCE IN TARGET (jjm) F i g u r e 4.24: Same as F i g u r e 4.21 but a l u m i n u m thickness is 50 p m Chapter 4. Luminescence Measurements in Single and Douhled-Layered Targets 64 W h e n it catches up w i t h the shock front , the pressure at the sock front w i l l be reduced . T h i s is ca l l ed shock a t t e n t u a t i o n or d a m p i n g . T h u s i f the a l u m i n u m layer is too th ick ( F i g u r e 4.24), the shock w i l l be a t tentuated before i t reaches the interface; hence the t r a n s m i t t e d pressure in to the gold layer w i l l not be as h igh as it can be. O n the other h a n d , i f the a l u m i n u m layer is too 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 formed shock f ront w i l l i m p i n g e too ear ly on the interface to benefit s igni f icant ly f r o m the pressure enhancement by shock re f lect ion. F u r t h e r m o r e , i f the shock waves reach the interface too soon , the 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 into the a l u m i n u m layer, 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 the a l u m i n u m layer (F igure 4.22), a n d again one w i l l not have der ived the 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 the go ld layer, if i t is too t h i n , then the t r a n s m i t t e d shock may not have been c o m p l e t e l y formed (cf. the process of shock s teepening in gold i n figures 4.22 a n d 22) whereas i f it is too t h i c k , shock a t tentua t ion w i l l o ccur before the shock reaches the free surface. F i g u r e 4.25 i l lus trates the effects of the a l u m i n u m a n d gold thicknesses on the free surface pressure induced in go ld . These effects are c o m p l i c a t e d , and the final free surface pressures ce r t a in ly cannot be ca lcu la ted on the basis of equat ion (2.11) alone. ( N . B . In the case of an idea l steady shock, the t r a n s m i t t e d shock pressure as given in eq. (2.11) equals the. free surface pressure in gold.) A l s o p l o t t e d in the figure is the m a x i m u m pressure JPsw w h i c h can be induced in the gold layer for the given i n i t i a l pressure pulse i f the inc ident shock.were idea l , i .e. a steady shock of 3.5 M b a r . A s s ta ted in previous discuss ions , the shock- induced pressure, in the gold layer is in f lu-enced by the thicknesses of b o t h the front a l u m i n u m layer and the rear gold layer. Hence pressure o p t i m i z a t i o n , or a l t e rna t ive ly thickness 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 between incomple te shock b u i l d u p in t h i n targets and shock a t t en tua t ion in t h i c k ones. P r e v i o u s studies u s ing computer s imula t ions i n c l u d e the work 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: Shock induced pressure in the free surface of gold as a funct ion of the a l u m i n u m thickness . T h e various lines denote different go ld thicknesses : 2 um ( so l id) , 8.4 um (dash) , 13 urn (dot-dot-dot-dash) , 20 um (dot-dash) . A l s o shown is the m a x i m i u m pressure reached somewhere in a gold layer of in f in i te thickness (dot ) Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 66 on C H 2 - a l u m i n u m targets i r r a d i a t e d by m o d i f i e d G a u s s i a n pulses of 1.06 um as we l l as tha 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 targets and 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 tha t pressure m a x i m i z a t i o n at the interface can be achieved by o p t i m i z i n g the th ickness of the s t andard . H o w e v e r , as i t is not poss ib le to measure d i rec t ly the pressure at the interface, we sha l l in s tead adopt another c r i t e r i o n . T a k i n g the 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 pressure at the free surface of the gold layer and referr ing to F i g u r e 4.25, one can see that for every go ld layer th ickness , there exists a c o r r e s p o n d i n g o p t i m a l thickness in the a l u m i n u m layer . For example , the o p t i m a l a l u m i n u m thickness for a 2 p m go ld layer is about 40 p m , w h i l e i n the case of an 8.4 p m gold layer , 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 tha t the peak pressures achieved at the free surfaces i n the above two cases are never as h igh as ?sw- T h i s is because the front a l u m i n u m layers are a l ready t h i c k enough to al low shock a t t e n t u a t i o n to o c c u r . S i m i l a r l y , if the gold layer is 20 p m t h i c k , t h e n the o p t i m a l a l u m i n u m thickness is a r o u n d 23 p m . Once aga in , Psw is not reached at the free surface since, in this case, the rear go ld layer is too th ick a n d shock d a m p i n g dominate s . Is the best o p t i m i z a t i o n then achieved w h e n the f o r m a t i o n of the strong shock occurs at the i n s t a n t w h e n it reaches the interface? If so, the best s o l u t i o n would seem to be solely dependent on the front a l u m i n u m thickness , g iven an i n i t i a l d r i v i n g pulse . T h i s w o u l d be the case if one were to derive the m a x i m u m interface p re s sure [ l l 4 ] , and is satisfied (i .e. P$w is reached) w h e n the a l u m i n u m thickness a p p r o x i m a t e l y equals to 19 p m as seen in F i g u r e 4.23. However , f rom F i g u r e 4.25, i t is clear that se t t ing the a l u m i n u m th ickness to be 19 p m is no guarantee t h a t the o p t i m a l pressure Psw w o u l d be i n d u c e d at the free surface of the gold layer . T h i s is because the gold layer also plays a. s igni f icant role i n d e t e r m i n i n g the f ina l pressure a t t a i n e d at its free surface. T h i s po int is best i l l u s t r a t e d in F i g u r e 4.26, where the shock pressure at the free surface is p l o t t e d Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 67 against the thickness of the gold layer , 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 to 50 p m . T h e n o n - u n i f o r m i t y of the shock pressure i n the gold layer is ev ident . For in s t ance , for a 19 p m a l u m i n u m layer , the shock pressure at the free surface of a 2 p m g o l d layer is smal ler t h a n tha t i n a 8.4 p m gold layer, w h i c h in t u r n is less t h a n that i n a 13 p m gold layer. T h i s seemingly strange s i tua t ion of increas ing shock pressure w i t h i n c r e a s i n g gold layer thickness arises since, n o t w i t h s t a n d i n g the adverse effect of shcok decay w h i c h has begun in the front a l u m i n u m layer (cf. F i gure 4.23), the shock front cont inues to steepen as i t propagates in the gold layer , c u l m i n a t i n g i n a shock front of greater a m p l i t u d e . O f course, this process cannot ca r ry on indef in i te ly as shock a t t e n t u a t i o n must eventua l ly d o m i n a t e once the fronts ide rarefact ion wave catches up w i t h the shock , and the pressure is not susta ined. T h i s can be seen by c o m p a r i n g the pressure at the free surface in the case of a 11.5 p m A l on 8.4 p m A u target w i t h that of a 11.5 p m A l on 13 p m A u target ( F i g u r e 4.22), where shock d a m p i n g starts to take over at a d e p t h of ~ 9 p m in the go ld layer. In fact, i f the front a l u m i n u m layer were a l ready too t h i c k (such as 50 p m in F i g u r e 4.24), the free surface pressure in gold w i l l decrease m o n o t o n i c a l l y w i t h increa s ing gold thickness . 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 process , and one needs to take into account both the front and back layer thicknesses of the target . F i g u r e 4.26 also serves to b r i n g u p another interes t ing p o i n t , n a m e l y the 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 cr i ter ion of h a v i n g a m a x i m u m pressure at the free surface w i l l not be appropr i a te if one's a i m is E O S study, where it is m o r e desirable to have an as u n i f o r m l y compressed region as poss ib le , i.e. as u n i f o r m a shock as poss ib le . A nonuniform]} ' shocked m a t e r i a l experiences dens i ty and t e m p e r a t u r e gradients , consequent ly affecting measurements such as shock t rans i t t imes . F r o m th i s p o i n t of v iew a 34 p m a l u m i n u m front layer in a n a l u m i n u m - o n - g o l d target, y ie lds the mos t u n i f o r m shock pressure in gold e x t e n d i n g f r o m 2 to 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: Shock pressure at the free surface of go ld as a funct ion of thickness in the gold layer for var ious front a l u m i n u m thicknesses : 11.5 urn (dot-dot-dash) , 19 um (dot-dash) , 34 um ( so l id) , and 50 um (dash) Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 69 the expense of lower free surface pressure. In s u m m a r y , we have seen that thickness o p t i m i z a t i o n in an i m p e d a n c e - m i s m a t c h e d target needs to adopt different c r i t e r i a depend ing on whether the free surface pressure • is to be m a x i m i z e d , or w h e t h e r the shock pressure is to be as u n i f o r m as possible . In a d d i t i o n , we have found tha t b o t h the front a l u m i n u m and the rear go ld layer p lay a role i n the pressure e v o l u t i o n , a n d must b o t h be t a k e n i n t o account. 4 . 1 . 2 . B . i i H Y R A D S i m u l a t i o n s In this p a r t of the s imula t ions , we ca lcula te the shock t ra jec tor ies i n 19 or 26.5 fim a l u m i n u m on 8.4 or 13 p m gold us ing H Y R A D i n -c l u d i n g the process of r a d i a t i o n t r a n s p o r t . W e have performed the s imula t ions using two different E O S model s of go ld : S E S A M E and the new ca lcu la t ion i n c o p o r a t i n g m e l t i n g t r a n s i t i o n . F i g u r e 4.27 shows the ca lcu la ted shock tra jectories together w i t h the mea-sured shock transit, t imes for var ious targets . T h e agreement, between e x p e r i m e n t a l da ta and b o t h ca lcu la ted shock pa ths is good , i n d i c a t i n g the va l id i ty of b o t h E O S models for g o l d , at least insofar as shock ve loc i ty is concerned . 4.2 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 w i t h A l u m i n u m - G o l d Targe t s 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 parameter charac ter i z ing the equa t ion of state of a shocked m a t e r i a l is the shock t e m p e r a t u r e T ( w h i c h is related to the i n t e r n a l energy E of equa t ion (2.7).) A s suggested in §1.1 and §2 .4 .2 , the measurements of T is expected to c lar i fy our u n d e r s t a n d i n g of shock m e l t i n g in g o l d , and also to place a constra int on the p r e d i c t i o n s based on var ious theoret ica l E O S model s . Here we shal l refer to the shock Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 70 ~1 1 1 1 1 1 1 1 1— 15 20 25 30 35 40 45 50 55 Lagrangian Coordinate (/mi) F i g u r e 4.27: Shock pa ths as ca l cu l a t ed by H Y R A D in 19 um A l and 13 um A u target u s i n g S E S A M E E O S (dot-dot-dash) , a n d us ing new go ld E O S (dash); i n 26.5 um A l and 13 um A u target us ing S E S A M E E O S (dot-dash) , and u s i n g new gold E O S (dot ) . T h e shock p a t h in 53 um A l ( sol id) is i n c l u d e d . A l s o p l o t t e d are the exper imenta l po int s for var ious 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 the brightness t e m p e r a t u r e because i t is o b t a i n e d f r o m the intens i ty of the shock- induced l u m i n o u s emiss ion . T h i s measurement technique has p r e v i o u s l y been used to y i e l d t empera ture d a t a i n a l u m i n u m [ l 0 9 ] and l i q u i d argon[115]. 4.2.1 E x p e r i m e n t a l Observa t ions In th i s e x p e r i m e n t , the brightness t e m p e r a t u r e is inferred f rom measurements of the in tens i ty of the shock- induced luminescence at the free surface of the target . T h e emiss ion is recorded by the streak c a m e r a at a faster streak speed t h a n tha t used in the shock t rans i t t i m e measurements i n §4.1 since we are p r i m a r i l y concerned w i t h the measurement of the l u m i n o u s emiss ion at very early t imes to reduce the effect of the opac i ty of the p l a s m a e x p a n d i n g f r o m the free surface in to 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 made in targets w i t h a 19 or 26.5 um a l u m i n u m layer on e i ther an 8.4 or 13 um gold layer . These four targets are expected to achieve a lmost the highest shock pressure in go ld (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 targets , w h i c h w i l l serve as the E O S s t a n d a r d . F igures 4.28 to 4.32 show the t y p i c a l t ime-reso lved and t ime- integra ted emiss ion f r o m a pure 38.4 um A l f o i l , a 19 um A l on 13 um A u target , a 19 urn A l on 8.4 um A u target , a 26.5 um A l on 8.4 um A u target , a n d a 26.5 / / m A l on 13 um A u target respect ively. N o significant, hot spots are observed i n the shock breakoput regions. T h e t y p i c a l rise t imes in the intens i ty of the shock- induced l u m i n o u s emiss ion are found to be ~ 2 5 0 ps, w h i c h can be a t t r i b u t e d to the c o m b i n e d effects of surface roughness ( ~ 6 0 ps) , 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), and streak c a m e r a entrance sl it height (~8'0 ps) . The. subsequent r a p i d decrease in the in tens i ty results f rom the rears ide m a t e r i a l be ing released by the rare fac t ion wave, w h i c h forms an o p t i c a l l y th ick m e d i u m a t t e n t u a t i n g the r a d i a t i o n f r o m the hot m a t e r i a l behind[116] . In our stud}?, we have t aken advantage of the fact t h a t b o t h our measurements on F i g u r e 4.28: T e m p o r a l l y resolved and in tegra ted p lo t of the backs ide emiss ion in tens i ty of a 38.4 um A l target , w i t h t ime zero b e i n g the peak of the laser pulse. Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 73 (a) 1100-p 1000-900-eoo-•5s 700-600->-—^ Co c 500-£ 400-300-200-100-0-1.0 h2 TIME (nsecs) (b) 200000-150000 c 50000H —I— 0.6 0.8 1.0 1.2 Time (nsecs) F i g u r e 4.29: Same as F i g u r e 4.28except target is 19 p m A l on 13 p m A u a.pter 4. Luminescence Measurements in Single and Doubled-Layered Targets 700 1.0 1.2 TIME (nsecs) 100000-1 -i 1 1 1 1 1-0.6 0.8 1.0 1.2 1.4 1.6 1.8 Time (nsecs) F i g u r e 4.30: Same as F i g u r e 4.28except target is 19 p m A l on 8.4 p m A u Chapter 4. Luminescence Measurements m Single and Douhled-Layered Targets 75 800 TIME (nsecs) 200000-. (b) 1 Time (nsecs) F i g u r e 4.31: Same as F i g u r e 4.2Sexcept target is 26.5mic.ron A l on S.4 p m A u Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 76 400 TIME (nsecs) 120000-(b) 100000-80000-k_ 60000-'</) c 40000-20000 4 L4 MS l!g 2!0 2*2 2T4 2~6 Time (nsecs) F i g u r e 4.32: Same as F i g u r e 4.28except target is 26.5 um A l on 13 um A u Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 77 the s ingle and d o u b l e layered targets are done us ing the same i m a g i n g sys tem, and that the shock breakout regions in b o t h types of targets are s imi l a r . Therefore , k n o w i n g the t e m p e r a t u r e of the shock-heated a l u m i n u m , the brightness t empera ture of go ld can be o b t a i n e d by c o m p a r i n g the in tens i ty of emiss ion f rom go ld to that f r o m a l u m i n u m , w i t h -out the need for an absolute in tens i ty c a l i b r a t i o n of the streak camera and opt ics system. F r o m F i g u r e s 4.28 to 4.32, it can be seen that the ins tantaneous emiss ion in tens i ty is h i g h l y s p i k y and m o d u l a t e d , consequent ly the ra t io of the emiss ion in tens i ty cannot pro-duce any m e a n i n g f u l results . O n the other h a n d , the r a t i o of the t ime- integra ted intens i ty does a l l o w for an ob jec t ive a n d u m a m b i g u o u s analysis of the da ta . 4.2.2 C o m p u t e r S i m u l a t i o n s T h e s i m u l a t i o n of this exper iment is per formed i n two steps. F i r s t , we use the H Y R A D code to fol low the entire h i s to ry of the target f rom the onset of the laser pulse to the t i m e of shock a r r iva l at the free surface. T h e n , to s imulate p r o p e r l y the measurement of the s h o c k - i n d u c e d l u m i n o u s emiss ion f rom the target rear surface, the P U C code is used to ca l cu l a te the emis s ion in tens i ty f r o m the rare fy ing p l a s m a at the rear side of the target as detected by the streak camera . 4 . 2 . 2 . A H Y R A D S i m u l a t i o n s H Y R A D is used since it a l lows for not only a more complete t rea tment of the laser-target in te rac t ions , but also the pos s ib i l i ty of accessing the effect of r a d i a t i o n t ranspor t in the e x p e r i m e n t . In the code, the 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 the a t o m i c phys ics m o d e l has been descr ibed i n § 2 . 4 . 1 . For go ld , the a tomic and o p a c i t y d a t a used are t aken f rom the S E S A M E l i b r a r y , but two sets of E O S d a t a ( S E S A M E and the new s o l i d / l i q u i d state ca lcu la t ion) are used. T h e spa t i a l reso lut ion 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. Luminescence Measurements in Single and Doubled-Layered Targets 78 4 . 2 . 2 . A . i Ef fect of R a d i a t i o n T r a n s p o r t In this sect ion we consider the effects of r a d i a t i o n t r anspor t i n m o r e d e t a i l , and examine the shock profiles i n a 19 p m A l on 13 p m A u target us ing S E S A M E E O S da ta , e m p h a s i z i n g on how r a d i a t i v e transfer may affect the shock tempera ture . R a d i a t i v e hea t ing is expec ted to p l ay o n l y a m i n o r role i n the gold layer as a lready remarked i n section §2 .3 .2 . F igure s 4.33 shows the spa t i a l profi les of density , pressure, and t e m p e r a t u r e at a t i m e of 1.26 ns before the laser peak w h e n the process of r a d i a t i o n t r a n s p o r t is neglected (henceforth referred to as case [A]). F i g u r e 4.34 shows s imular profiles in the presence of r a d i a t i o n t r a n s p o r t (case [B]). T h e shock front is m a r k e d by a sharp increase i n density, pressure and t e m p e r a t u r e ( w h i c h occurs at a. d e p t h of ~ 1 0 p m i n the target in figures 4.33 and 4.34). W e note that the different i n i t i a l t empera tures , 4 0 0 K in A l and 130K in A u , are necessary due to l i m i t a t i o n s in the models of the g r o u n d state t e m p e r a t u r e i n the S E S A M E da ta , a n d are chosen so tha t the i n i t i a l pressures in b o t h mater i a l s are the same. Therefore the i n i t i a l t e m p e r a t u r e difference i n the t w o mater ia l s does not signify a real t empera ture d i s c o n t i n u i t y at their interface. W e have also i n d i c a t e d e d the X - r a y power ab sorp t ion profi le in the target i n F i g u r e 4.34. W e see tha t a l t h o u g h most of the X - r a y energy is depos i ted i n the first 7 p m of the a l u m i n u m layer , some r a d i a t i o n is depos i ted wel l i n t o the target also, even ahead of the shock front and hence prehea t ing the a l u m i n u m (note the. slight, t empera ture and pressure increase above ambient t e m p e r a t u r e a n d pressure i n a l u m i n u m ahead of the shock) . Consequent ly , the t e m p e r a t u r e gradient is less i n case [B] t h a n [A], T h i s prehea t ing of the cold a l u m i n u m layer ahead of the shock front w i l l not ha.ve been desirable in E O S studies s ince the pre-shocked state of a m a t e r i a l w i l l depend on the r a d i a t i o n t ranspor t process. A l s o , due to the large opac i ty increase of gold over a l u m i n u m (e.g. at 1 k e V , o p a c i t y of go ld is five t imes that of a l u m i n u m ) , go ld is a m u c h be t t e r absorber of r a d i a t i o n t h a n a l u m i n u m and the r e m a i n i n g X - r a d i a t i o n is depos i ted i n the first 2 to 3 p m of the gold layer . T h e r e is s t i l l p rehea t ing i n g o l d , but the level is Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 79 Lagrangian Coordinate (/im) F i g u r e 4 .33: A snapshot of the b y d r o d y n a m i c profi le in a 19 p m A l on 13 p m A u target at t = - 1 . 2 6 ns. R a d i a t i o n t r anspor t process is neglected , and b o t h A l and A u E O S data are f r o m S E S A M E . Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 80 F i g u r e 4.34: Same as F i g u r e 4.33 except r a d i a t i o n t r anspor t process is i n c l u d e d . T h e absorbed X - r a y power is also p l o t t e d . Chapter 4. Luminescence Measurements in Single and Double.d-La.ye.red Targets 81 very low since most of the r a d i a t i o n have been absorbed i n a l u m i n u m , a n d the extent of the preheated region is very s m a l l . N e x t , we show in figures 4.35 and 4.36 the c o r r e s p o n d i n g two cases at 0.24 ns after the laser peak w h e n the shock has crossed the a l u m i n u m - g o l d interface into the gold layer . A s before, the gradient in the t e m p e r a t u r e profi le i n case [B] is more 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 depos i t i on . W e also note the pressure c o n t i n u i t y across the interface, as requ i red by the b o u n d a r y c o n d i t i o n . A decrease of the shock pressure, t e m p e r a t u r e , and to a lesser extent , density, in case [B] can also be observed as a result of r a d i a t i v e energy loss f r o m the hot p l a s m a l ead ing to a lower ab la t ion pressure. F i n a l l y , the shock front has p ropaga ted past the first few microns of the gold layer where there is X - r a y energy a b s o r p t i o n . A s a resul t , r a d i a t i o n t r a n s p o r t no longer const i tutes a preheat p r o b l e m , and the subsequent shock s t ruc ture become m u c h m o r e wel l-def ined, c o m p a r a b l e to tha t in case [A]. In this m a n n e r we have achieved a " c l e a n " shock, i.e. a quas i- steady shock enter ing the co ld m a t e r i a l w i t h o u t s ignif icant preheat . T h e advantage of the i m p e d a n c e m i s m a t c h m e t h o d in r ad i a t ive preheat suppress ion i n h i g h - Z m a t e r i a l is r ea l i zed . T a b l e 4.1 summar ize s results of the s imula t ions at the t i m e of shock breakout at the free surface of go ld . W e should emphas ize the s ignif icant drop i n shock temper-a ture (—23%) as r a d i a t i o n transport, is taken in to account , and this shou ld lead to a c o r r e s p o n d i n g decrease i n the rear surface emis s ion . 4 . 2 . 2 . A . i i E O S M o d e l s In this section we w i l l compare the effects of the two different. E O S models of go ld on the shock parameter s in the same 19 um A l on 13 um A u target . T h e two E O S models of go ld are respect ively the S E S A M E t a b u l a t e d d a t a and the new c a l c u l a t i o n i n c o p o r a t i n g the 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 the s i m u l a t i o n results . W e see s imi l a r qua l i t i ve b e h a v i o r in the shock p r o p a g a t i o n , but the Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets LASER 1 0 8 t IO1IO 2. 10 7 -106 w < u a. 2 u H i o - i 104-10"3-IQ3 J a o - J I i o - J Lagrangian Coordinate (jim) F i g u r e 4.35: Same as F i g u r e 4.33 except 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 4.36: Same as F i g u r e 4.35 b u t r a d i a t i o n t ransport process is inc luded Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 84 $ = 2.3 x 1 0 1 3 W / c m 2 N o R a d i a t i o n T r a n s p o r t W i t h R a d i a t i o n T r a n s p o r t s teady shock v e l o c i t y 0 . 8 8 ± 0 . 0 2 0 . 8 5 ± 0 . 0 2 i n go ld (x 10 6 c m / s ) shock breakout t i m e (ns) 1 . 0 8 ± 0 . 0 2 1 . 1 9 ± 0 . 0 2 shock breakout 1 . 8 6 ± 0 . 0 5 1 . 8 0 ± 0 . 0 5 compres s ion ra t io shock breakout pressure 7 . 1 ± 0 . 2 6 . 0 ± 0 . 2 i n go ld ( M b a r ) shock breakout t e m p e r a t u r e 2 . 4 6 ± 0 . 0 4 2 . 0 0 ± 0 . 0 4 in go ld ( e V ) T a b l e 4.1: c o m p a r a t i v e s tudy of the effects of r a d i a t i o n t ranspor t on free surface shock parameter s for a 19 p m A l on 13 p m A u target $ = 2.3 x 1 0 1 3 W / c m 2 S E S A M E G o l d da ta (2700) N e w G o l d da ta (2788) steady shock v e l o c i t y i n go ld (x 10 6 c m / s ) 0 . 8 5 ± 0 . 0 2 0 . 9 5 ± 0 . 0 2 shock breakout t i m e (ns) 1 . 1 9 ± 0 . 0 2 1 . 0 4 ± 0 . 0 2 shock breakout compress ion ra t io 1 . 8 0 ± 0 . 0 5 1.71 ± 0 . 0 5 shock breakout pressure in go ld ( M b a r ) 6.0 ± 0 . 2 6 . 1 ± 0 . 2 shock breakout t e m p e r a t u r e i n go ld ( e V ) 2 . 0 0 ± 0 . 0 4 1 . 5 4 ± 0 . 0 4 T a b l e 4.2: c o m p a r a t i v e s tudy of the effects of o u r new gold E O S d a t a on free surface shock parameter s for a 19 p m A l o n 13 p m A u target , 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 and Doubled-Layered Targets 85 <S> = 2.3 x 1 0 1 3 W / c m 2 S E S A M E G o l d E O S N e w G o l d E O S 19 um A l + 8.4 um A u h (ns) 0 . 5 8 ± 0 . 0 2 0 .55±0 .02 p/Po 1 . 7 9 ± 0 . 0 5 1 . 7 0 ± 0 . 0 5 P ( M b a r ) 5 . 8 ± 0 . 2 5 . 9 ± 0 . 2 T ( e V ) 1 . 8 3 ± 0 . 0 4 1.46±0.04 26.5 um A l -f 8.4 um A u / i , (ns) 1 . 0 3 ± 0 . 0 2 1.02±0.02 p/Po 1 . 7 6 ± 0 . 0 5 1 . 6 8 ± 0 . 0 5 P ( M b a r ) 5 . 4 ± 0 . 2 5 . 4 ± 0 . 2 T ( e V ) . 1 . 6 8 ± 0 . 0 4 1.28±0.04 26.5 um A l + 13 um A u / f. (ns) 1 . 5 1 ± 0 . 0 2 1 . 4 8 ± 0 . 0 2 p/po 1 . 7 5 ± 0 . 0 5 1 . 6 2 ± 0 . 0 5 P ( M b a r ) 5 . 3 ± 0 . 2 5 . 3 ± 0 . 2 T ( e V ) 1 . 6 7 ± 0 . 0 4 1 . 2 0 ± 0 . 0 4 Tab le 4 .3 : c o m p a r a t i v e stud}? of the effects of our new gold E O S d a t a on the shock breakout t imes (t-b), the compress ion ra t io (p/po), the shock pressure ( P ) . and the shock t e m p e r a t u r e (T) at breakout for var ious 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 breaks out sooner (see F i g u r e 4.27) and the shock t e m p e r a t u r e is decreased (see Tab le 4.2) . T h i s result we a t t r i b u t e to the "softer'" na ture of the l i q u i d , as the l i q u i d phase can a t t a i n a greater shock ve loc i ty under the same pressure than the so l id . T h e lower t e m p e r a t u r e is also expected since energy is expended d u r i n g me l t ing w i t h o u t a cor re spond ing 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 the r e m a i n i n g three tagets , w h i c h are 19 pm A l on 8.'4 pm A u , 26.5 p m A l on 8.4 p m A u , and 26.5 p m A l on 13 p m A u . 4 .2 .2 .B P U C S i m u l a t i o n s T h e second step of the s i m u l a t i o n for the brightness t e m p e r a t u r e s tudy uses P U C to ca l cu l a te the t i m e evo lu t ion of the in tens i ty of emiss ion f r o m the target rear surface at and subsequent to shock breakout . T h e shock density , pressure, and temperature at the rear surface of the target ( a l u m i n u m or go ld) at breakout as ca lcu la ted by H Y R A D Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 86 i n § 4 . 1 . 1 . B and §4 .1 .2 .B . i i are used as the i n i t i a l condi t ions of the shocked m e d i u m i n P U C w h i c h t h e n calculates the r a d i a t i o n e m i t t e d at 4300A as the target rarefies into the v a c u u m . T h e spa t i a l re so lu t ion i n these ca lcu la t ions is less t h a n 0.05 p m . A p lo t of the rearside emis s ion f r o m gold ( f r o m a 19 p m A l o n 13 p m A u target) a n d a l u m i n u m ( f rom a 38.4 p m A l target ) is shown i n F i g u r e 4.37. Here t i m e zero corresponds to the t i m e of shock breakout at the free surface. W e have also used b o t h the S E S A M E a n d our new gold E O S d a t a . W e see that the rears ide emiss ion decreases r a p i d l y (drop-p i n g 2 orders of m a g n i t u d e i n the first 30 ps) . T h i s is because as the rear surface unloads , the e x p a n d i n g cooler m a t e r i a l r a p i d l y shields the hot p l a sma b e h i n d , so t h a t the inten-s i ty of the emis s ion tha t c a n be detected also drops rap id ly . F i g u r e 4.38 is a p lot of the t ime- in tegra ted emiss ion for the same two targets. W e see tha t the i n i t i a l r a p i d rise i n the emiss ion reflects the 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 the shock un load-ing . A n abso lute c o m p a r i s o n of the rearside emis s ion in tens i ty 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 results cannot be m a d e since an abso lute intens i ty c a l i b r a t i o n of the streak c a m e r a is not made . W e ha.ve ins tead c o m p a r e d the ra t io of the t ime- integra ted emiss ion intens i t ies for go ld to a l u m i n u m . T h e results for 19 p m A l on 13 p m A u and 38.4 p m A l targets are p l o t t e d i n F i g u r e 4.39(a) . W e consider those d a t a between 50 to 300 ps to be more re l iab le , since at very ear ly t imes we are l i m i t e d by e x p e r i m e n t a l uncerta int ies i n d e t e r m i n i n g the t imes of shock breakout , whi l e at la te t imes the effects of the rarefact ion wave and the increas ing a b s o r p t i o n by the released p l a s m a become increas ing ly more d o m i n a n t . In a d d i t i o n , we have also best-f i tted a measured emiss ion r a t i o by v a r y i n g the shock t e m p e r a t u r e in P U C . T h e results are shown in F i g u r e s 4.39(b) . Resu l t s f rom other target sots a,re presented in F igure s 4.40 to 4.42. T h e results for the r e m a i n i n g 19 p m A l on 8.4 p m A u , as we l l as 26.5 p m A l on 19 and 8.4 p m A u targets are p l o t t e d re spec t ive ly in figures 4.43 to 45. Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 87 F i g u r e 4.37: B a c k s i d e emiss ion f r o m a 19 p m A l on 13 p m A u target us ing S E S A M E (dash) and our new (dot-dot-dot-dash) gold E O S da ta , as well as f r o m a 38.4 p m A l ( sol id) 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 Integration Time (ps) 400 500 F i g u r e 4.38: T i m e - i n t e g r a t e d emiss ion in tens i ty of the prev ious F i g u r e 4.37: tha t of a 19 p m A l on 13 p m A u target u s ing S E S A M E (dot ) and the new (dash) gold da ta ; tha t of a 38.4 p m A l target (dot-dash) . Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 89 8-1 5-1-T = 21800 K T - 17B50 K 100 200 300 400 Integration Time (ps) 500 6-1 5-TF= 15500 K 100 200 300 400 Integration Time (ps) 500 F i g u r e 4.39: T i m e - i n t e g r a t e d emiss ion in tens i ty r a t i o for a 19 um A l on 13 um A u target to a 38.4 um A l target : (a) u s ing S E S A M E (dot ) , a n d new gold (dot-dash) E O S data : and (b) best- f i t ted t e m p e r a t u r e Tp curve (dot-dot-dash) to an e x p e r i m e n t a l curve (dot-dash) . 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 to F i g u r e 4 .39(b) : an e x p e r i m e n t a l t ime- in tegra ted emiss ion in ten-sity r a t io is best- f i t ted w i t h a shock 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 i i i i i 0 100 200 300 400 500 Integration Time (ps) 6-1 (b) 5-o H i i i 1 1 1 0 100 200 300 400 500 Integration Time (ps) F i g u r e 4.41: S i m i l a r to F i g u r e 4.39(b) : an e x p e r i m e n t a l t ime- in tegra ted emiss ion inten-sity r a t i o is best- f i t ted w i t h a shock 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) 5 H H 4 < H 2 7L w TF» 17500 K 100 200 300 400 Integration Time (ps) 500 (b) H 4 oo X 2H \ \ / Tf-19250K 100 200 300 400 Integration Time (ps) 500 F i g u r e 4.42: S i m i l a r to F i g u r e 4.39(b) : an e x p e r i m e n t a l t ime- integra ted emis s ion in ten-sity7 r a t i o is best-f i t ted 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 < in W H 5-3 -2-1-T - 2 H 0 0 K TF=19000K \ . 100 200 300 Integration Time (ps) 400 500 F i g u r e 4.43: T i m e - i n t e g r a t e d emis s ion intens i ty r a t io for a 19 / /m A l on 6.4 um A u target to a 38.4 um A l target u s ing S E S A M E (dot ) , and the new ( long dot-dash) gold 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 ( long dash , so l id , long dot-dot-dot-dash) are i n d i v i d -u a l l y best-f i t ted w i t h a shock t e m p e r a t u r e 7> (short do t -dot -dot -dash , short dash , short dot-dash) Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 94 < H <L U 4-2-1-T=19800K TF= 17000 K T=14970 K 100 200 300 Integration Time (ps) 400 500 F i g u r e 4.44: T i m e - i n t e g r a t e d emiss ion in tens i ty r a t io for a 26.5 fim A l on 6.4 fim Au target, to a 38.4 fim A l target us ing S E S A M E (dot ) , and the new (dot-dash) gold 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 ( long dash , sol id) are i n d i v i d u a l l y best-f i t ted w i t h a shock t e m p e r a t u r e TF (dot -dot-dot-dash , short dash) Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 95 6 -i 5-T= 19200K 2-14500K T = 14000K 100 200 300 Integration Time (ps) 400 500 F i g u r e 4.45: T i m e - i n t e g r a t e d emiss ion in tens i ty r a t i o for a 26.5 fim A l on 13 fim A u target, to a. 38.4 fim A l target us ing S E S A M E (dot ) , and the new (dot-dash) go ld E O S d a t a . O n e e x p e r i m e n t a l d a t a ( long dash) is best- f i t ted w i t h a shock t e m p e r a t u r e T> ( short dash) w h i l e the o ther (sol id) coincides w i t h the ca lcu la ted curve (dot-dash) . Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 96 It can be seen tha t ca l cu la t ions us ing the S E S A M E E O S da.ta for gold seem t o over-es t imate the observed t ime- in tegra ted intens i ty r a t io , w h i l e those u s ing the new E O S for go ld appear to be i n m u c h closer agreement w i t h e x p e r i m e n t a l observat ions . S ince the l a t ter c a l c u l a t i o n includes the l i q u i d phase of g o l d , the m e l t i n g p h e n o m e n a is t rea ted i n the 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 thus c lear ly i n d i c a t e tha t gold exists i n the l i q u i d phase at h i g h pressure. F i g u r e 4.46 shows the H u g o n i o t of go ld f r o m S E S A M E a n d that f r o m the new E O S ca l cu l a t ions , as wel l as the deduced shock pres sure- temperature points i n the studies . These po int s are ob ta ined as fo l lows . T h e pressures are the free surface pressures as ca lcu la ted i n the s imula t ions by H Y R A D in § 4 . 2 . 2 . A , u s ing t h e new gold E O S da ta . T h e y are, respect ive ly , 6.1 M b a r in the 19 um A l on 13 um A u target , 5.9 M b a r i n the 19 p m A l on 8.4 p m A u target , 5.5 M b a r in the 26.5 p m A l on 8.4 p m A u target , and 5.3 M b a r in the 26.5 p m A l on 13 p m A u target. T h e c o r r e s p o n d i n g tempera tures are the best-f i tted tempera tures to each set of e x p e r i m e n t a l t ime- in tegra ted intens i ty r a t i o curves . T h e agreement of these e x p e r i m e n t a l po int s w i t h the l i q u i d Hugo-niot is very good . Chapter 4. Luminescence Measurements in Single and Doubled-Layered Targets 97 25000 n 0) "5 Q_ E .<i> 22500H 20000H 17500 15000 H 12500 s B 5.25 5.50 5.75 6 Pressure (Mbar) 6.25 6.50 F i g u r e 4.46: A p lo t of the H u g o n i o t of gold f r o m S E S A M E (dot-dash) , the l i q u i d H u g o n i o t i n our new ca l cu l a t ions (dash) and the e x p e r i m e n t a l l y deduced p o i n t s . Chapter 5 S u m m a r y 5.1 Conclusions W e w i l l now s u m m a r i z e some of the m a j o r results in these la ser-dr iven shock ex-per iment s . W e have u t i l i z e d the i m p e d a n c e - m i s m a t c h technique to s t u d y the propert ies of shock compressed go ld us ing a l u m i n u m as the reference s t a n d a r d . O u r studies 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 measurements and c o m p u t e r s imula t ions of the shock t rans i t t h r o u g h targets of var ious thicknesses . In p a r t i c u l a r , the p y r o m e t r i c t echn ique i n w h i c h we measure the l u m i n o u s emiss ion in tens i ty f r o m the free, surface of the target is used to to detect the onset t i m e of shock breakout and also to deduce the shock t e m p e r a t u r e . W e have shown 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 layered target ( low-i m p e d a n c e a l u m i n u m in front of h igh- impedance gold) can lead to pressure enhancement a n d also r e d u c t i o n of r a d i a t i v e preheat i n the h i g h - Z gold layer. In a d d i t i o n , the m a x i -m a z a t i o n of the free surface pressure is found to be dependent on the thicknesses of b o t h layers of the target , and t h a t i t involves 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 the shock when the target is too t h i n and shock a t t e n t u a t i o n when the target is too t h i c k . O n the other h a n d , we have shown that the requirement of m a x i m u m free surface pressure is not necessari ly c o m m e n s u r a t e w i t h that, in h igh pressure E O S studies , where it is more i m p o r t a n t to achieve an u n i f o r m and steady shock. In the shock ve loc i ty s tudy, we have m a p p e d out the. shock t r a j ec tory i n a target b y measur ing the shock breakout t imes in var ious thicknesses . However , these d a t a are 98 Chapter 5. Summary 99 not accura te enough to d i s c r i m i n a t e a m o n g various equa t ion of s tate predic t ions , and are u n a b l e to assess the s igni f icance of the process of r a d i a t i o n t r anspor t i n the target. Nonethe les s , these s i m u l a t i o n s have i n d i c a t e d the adequacy of us ing a one-dimensional and p u r e l y f l u i d code i n p r e d i c t i n g the shock tra jector ies . T h e use of a less complex (hence faster and cheaper to 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 to those faced w i t h l i m i t e d c o m p u t i n g resources. In the shock t e m p e r a t u r e s tudy , we have in i t i a t ed a. new E O S ca l cu la t ion of gold i n c o p o r a t i n g b o t h so l id and l i q u i d state theories , and therefore a c c o u n t i n g for shock m e l t i n g i n go ld . It is found tha t the measurement of shock t e m p e r a t u r e is m u c h more sensi t ive to the e qua t ion of state, in o ther words , we are able to d i s c r i m i n a t e between two e q u a t i o n of state pred ic t ions . O u r measurements of the br ightness t empera ture i n gold favor the new E O S p r e d i c t i o n over that o b t a i n e d f rom the S E S A M E E O S l i b r a r y where the process of shock m e l t i n g is absent. In p a r t i c u l a r , we have found that whereas those s imula t ions us ing the S E S A M E E O S have overes t imated the t ime- integra ted l u m i n o u s emiss ion (and hence t empera ture ) of the target rear surface, the s imula t ions us ing the new gold are in m u c h be t t e r agreement w i t h the exper imenta l measurements . W e therefore conc lude tha t shock m e l t i n g of go ld has occured . T h e present measurement of gold ( in its l i q u i d phase) at a pressue of ~ 6 M b a r and ~ 1 7 5 0 0 K represents a first repor ted measurement of gold under shock m e l t i n g . Chapter 5. Summary 100 5.2 F u t u r e Research A n a t u r a l extension 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 exper iments on h i g h - Z ma-ter ia l s o ther t h a n gold in order to de termine the i r equat ion of state under shock com-pres s ion . It is also expected tha t by us ing a s t andard w i t h a lower i m p e d a n c e t h a n that of a l u m i n u m , a higher pressure enhancement at the m a t e r i a l interface can be a t t a i n e d . F u r t h e r m o r e , t r ip le- layered targets m a y be considered and the ir thicknesses o p t i m i z e d to the laser i rradiance. and pulse c o n d i t i o n i n order to achieve perhaps s t i l l h igher pressure and compres s ion . 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 the o p t i m a l thickness of a p a r t i c u l a r layer should s t i l l be v a l i d in mul t i - l ayered targets , i.e. the thickness of a target layer in front of the interface should be th ick enough so that the p r o p a g a t i n g shocks have t i m e to coalesce in to a s t rong shock front when they reach the interface, a n d the thickness of the layer b e h i n d the interface s h o u l d be t h i n enough so that shock d a m p i n g w i l l not cause the shock to decay s ign i f i cant ly w h e n it encounters the free surface (or another inter face) . Nevertheless , one should also be careful to ensure tha t the re su l t ing shock prof i le shou ld be as steady a n d u n i f o r m as possible i n order 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 the E O S d a t a . T h e br ightness t e m p e r a t u r e s tudy can be extended to invo lve intens i ty measurements as a f u n c t i o n of wavelength . For e x a m p l e , the peak of 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 these h i g h temperatures (17500 K ) is a p p r o x i m a t e l y 1650A, and spectra l measurements m a d e at a r o u n d this wavelength should y ie ld a m u c h higher s ignal . However , one must t h e n develop an i m a g i n g a n d detector sys tem w h i c h is sensit ive i n this spec t ra l range. In a d d i t i o n , the brightness t e m p e r a t u r e over a wider range of pressure should be measured so to ga in a bet ter u n d e r s t a n d i n g of the range of a p p l i a b i l i t y of the theore t i ca l E O S m e t h o d . It w o u l d be espec ia l ly in teres t ing , for ins tance , i f one can ob ta in t empera ture measurement s i n the pressure range where m e l t i n g of gold occurs . B i b l i o g r a p h y [1] J . 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