"AD-A261 327

laval Research Laboratory ushington, DC 20375-5320

NRIJMJU644O0-92.7I70

Shock-Free Acceleration of Laser Driven Targets

MAu H. EMERY AND JOHN H. GAD.iR

Center for Computational Physics BranchCompuarional Physics and Flguds Lynamyics DiVIsion

DTICS ELECTE .

FEB 2 6 1993

December 10, 1992 C

93-04075

Approved for public release. distribution unlimited

REPORT DOCUMENTATION PAGE

P,.O4. NI~Il on a -*"to" I"* 4A'l#o f a f 'V'l~7*~4 t *"Cf 4.s'a t t.f 's 1 ~ -1.. -'j C" 0 t . ,C.41 .1gr'my, 5,,,i0 1104 AII,1g~w, VA 2 2202 4102 .1 4' 4f- , a- ,. r, . - 4- e n-

I AGENCY USE ONLY Us.~ev &*tan~ REPORT DATE 14 fQAI V Pf A N_'V LA f h

4 TITLE AND SUBTITLE ,

Shock-Frece A ccleration of L.Aer D[.riven Tar`$CV

6 AUTHORIS)

Mark H. Emery and John H, Gardner

7 PERFORMING ORGANIZATION NAMIEIS4 afrg AOORESSIES4 * C* )1',& '. A N '

Naval Research lboratorvWashington. DC 20375-5320

9 SPONSORING/MONITORING AGENCY NAMEISý AND AODRESSIS . t,, • h'

Department of EnergyWashington, DC 20375-5320

I SUPPLEMENTARY NOTES

12a. DISTRIBUTION.AVAILABILITY STATEMENT !;t D 4q**'gi,-',7 4'-:> .

Approved for public release, distribution iS unlimited

13 ABSTRACT WMeritfym 200 waids)

The ability of recently developed laser smoothing technique' to ?roducc uniform ablaii,'n ptrc,%ufc, v. WnnF1% rl 4cntm•r'rn r!,A 't.fdegree of thermal smoothing. Thermal 5moothing is not effective at reducing rc uA! ia~er nonuniflrmatwc jx m.. thc ,tln uIý i'!hat-of a shaped, reactor-like laser pulse The impact of the first shock can be diminihed t% adiahaiicall%1 cImprc . hc W:F"-, ittemporally long, slowly rising laser pulse. This Memorandum Repon dtscu~ses an elastoi-pl,• lact -ratctC, niCrait rn, r a,"_!shows that a shock-free, induced spatial incoherence-smoothed lascr puke can accelerate a targct to nrar: the ondv4wfld1(lf 1uniform implosion.

14. SUBJECT TERMS16

Laser smoothing elastic-plastic

laser-target interaction adiabatic compression pC. CODcE

17, SECURITY CLASSIFICATION 18 SECURITY CLASSIFICATION 19 SECURITY CkASSI!ICATIOI'ZI LMITA4IION OF ARS'4AC;

OF REPORT OF THIS PAGE OF ABSTRACT

UNCLASSIFIED UNCLASSIFI-ED UNCLASSIFIED L

NSN 7540-01-280-5500 1-, -9 9 ICC. 440

t 7944 I0I

SHOCK-FREE ACCELERATION OF LASER DRIVEN TARGETS

A high degree of ablation prr'•-urt, uuf,,rmitv i.- a i.te-,- ,.:., x ao -. ,

laser driven inertial counfieenw~t fusion .-. na~vIz ~etrin., the ,btati,• • , pr,-s:ux, Ibu•:• ,,,,

less than a few percent throughout thi iip, prc,.-.Žý, if hLig gui• v, bI i;,.-

This places a s'.,,ever.. requlrenit't of[ theU: f unLrmitv ,,f •' t LL.-,UI Ihnit~tt i ,; "I il,. t.mv

of the recently developed rand,,m phaŽ,k platt, WIPPl: 1i-oLoh,-ig U t, . r

(SSD) 3 , and induced spatial incoherence (ISI)' kL.er .I.1,Athing t U ,. '

nearly uniform ablation pressurv i strongly •:otwtgnt on thw deg=., ,f Oieriiain ,i . • 4iu

in the ablating plasma.4"s The SSD ,nd ISI technique's [x-:,ufit froni ttmptn ral siij.d, hng, ;v-

a result of the broadband nature of the laser light but re-sidual nA iutlrmitie tp.rsi• witL

all three methods. Nearly all shaped reactor-ike las!-r puaes are co oYm,-d oif four ditstawt

phases : (1) an initial rapid risE to a low - to - moderate intensity, (21 a l iig tcziijxoral.

low intensity "foot", (3) a moderately rapid (power law-lik-ei rifs, to high iitensot, and

(4) the main drive portion of the pulse., See Figure 1 The first two regimes aret usually

referred to as the start-up phase, and the ratio of the final driv, po1wýer to thl, footi polwer L.-

termed the dynamic range. The details of the actual pulse shape (initial rise tin,. duratii,,i

of the "foot", dynamic range, and final drive intensity) are dictated by the targt design

(material composition, lavered/nonlayered, target thickness) and the desired final velocitv

of the target; but, in general, the pulse is designed ., that the initial shock- kip the

target on a low adiabat and breaks out through the rear of the targft as thf, laser 1itnsityi NTIS -CRA&I

reaches the beginning of the drive portion of the pulse WDC TAB

Manuscript approved October 20, 1992. m . -

-JI4Y fi6- 1)7E 3 R

I )",t~1co~

,V ib 1ir fode

Thernial smoothing is not 'tfttctit- at rt•lucinKg av aL• ht-r•-it L,.M'Z la ,

ties during the -foot" pirtion of thit pul:ke and tht- sh,,tk Structm, •Ue e-rati ! u• U h,

start-up phas. will nlurror any re-sidual la.-er n,.nunrforutirie 5 The, re-uhiu •It L ,

mass perturbations can linearly grow a ord,-r .,of Inagnirtud, or mtorv d,-ii., th,

target thickness, as a result of th' Frichtmv,-r-,\h4kOv Wt abdhty• bei,,•,e he t ,-& i,-.

the rapid acceleration pha.se 5 It is the ma11wss variations t,-ar tL, tOgianlrg of the- drlvv,

portion of the laser pulse which will provide the .•-eds foir ftayl-igh-Tavior T lIt,,wlh

during the acceleration pha.w For a target to implodht uniforndv, tht maiss ,-var ,atlo

at this point must be --,< 17/ Recent numerical results' indicate that co,lt, lo w density

foam layers, multiple wavelength lasers and initia. x-ray fl.ashe:, can signficantlv r,-d ce-

the mass perturbation level stemming from thte initial imprint of an ISl-srnooth,•t h ;id , lr

beam. There is also expermental evidence that an initial x-ray flash can eliminat, pla.,rwm

jetting generated by the initial imprint of an ISI-srnoothed laser.' However, the nurmerwal

results indicate that the perturbation level at the beginning of the drive po'IIJ of thef

pulse (several percent) is still too large to enable the targl't to implod, uuiformlv , Silc,

it is the first shock which is the culprit here, it may be possible to comtpress thet tarxgt

adiabatically - without any shocks except for the final drive portion of the pulse - and cir-

cumvent the problem. This would entail a very long. slowly rising la4e-r puLse A pulse of

this shape would generatc kilobar-like pressures in the target and thus compressive, strt-•s,

shear stress, elastic response and plastic flow become important conwiderations. We, have

modified our numerical model to account for these phenomena and report on tuhos. reisults

in this Memorandum Report.

2

Our two-dimensional, Cartesian, fully coit-ssibi•- hvivariw~ ,id- wt i

Eulerian grid with variable grid spacing and real k-quatiiL ,,f tatt- hý,v- ,

incorporate elastic, e(lastic-plastic, and hydrodynamic Hfw in a uiauxi s11iaa l .

developed by Wilkins The metdia is asun•ilt to, b,- isotrpic nd li,- ! t111, - .-

conservation equations fur olluivnturiil alnd tne'r, ar` 1ist'd f k -t•- .

a hydrostatic pressure and a stress associatted with the- reslstanc, of tht mater'a. 1' >L-•

distortion. Hooke's law provides the linear corrspoidence, lsetwri strfs.- a;trid h

an elastic material through the Lame' constants which art, nat,.rial -mi,-ni tla:. ,

flow begins where the elastic distortion energy texceeds the vo'11 Mi'se -i. y -,ld ovit.

Plastic flow is described by maintaining the stress deviators at the #-a.-stic hlnit soy ti;aa

the material flows plastically under a constant stress without work hairderiixi WVt:i

enough work has been done to melt the material, the yield str(es is set to 7er, and !i'A'

hydrodynamnic description follows automatically- The particulars of the niodel wil. 11

detailed in a forthcoming report."

As a test of the model we simulate the response of a target impacte-d with a I 1n--

FWVHM Gaussian 1/4 Arm laser pulse with a peak intensity of 10 W/crn2 The t; ."et Vs

composed of 35 pm of polystyrene (P'H = 1.04gm/cm3 ) with a 45 Mm thick layer 14f b:

density foam-like material (" = O.08gm/cni 3m3) on the front surface 'se.-1r-sideýý Th-

artificial foam-like material has material properties similar to a niix' ire of polystyrfen ,, anib4

frozen DT. As the absorption characteristics of low intensity lasers is not well undersi,

and is further complicated by the problems of material tiansparency and shn-thruizh1 '.

3

we assume that the targets are opaque to th' laser light anld tLir hLs"x IIt , aK -

through inverse Bremsstrahlung absorption witI! !UWK of thet lav'cr 1h01? 1hat 1,-,I k ,"•

deposited in three cells that surround the critical surfac in di> cLa•s t ht- targ, ,'

Figure 2 is an x-t diagram iliustrating the t.-lastic ,npr,.'.sP m ald t,-iim ti , i ,

gating through the two ruateriab; A 2-D pe.rsp,•ctive,, pi, t he ,i, tv ;f ,,

is plotted separately for clarity and the density is norrmalized to 1 0 u4 ,ach , i,,

the laser "pings" the foamn layer, an elastic comprt-ssion wa vi ,,-zt it utfirigh L '.

When this wave reaches the plastic-foim interface, a portio, L; Transniitted thr1tig.L it?.,1

plastic and a portion is reflected back through the foam. As thetoimipre,, t ý .V,--

reach the front and rear free surfaces, they are reflected as elastic teusin wave, ani fh,

cycle continues. Note that once the compres-sion/tension wave has propagated thjr,,1;i,

the material, the material relaxes back to its original density, there is httlfk disslpatlI, ,,!

the wave amplitude and little mass diffusion as evidenced by the steep gradirents at th:,

front surface of the target and at the material interface after 42 nwec. or 5 transits ''f II,

elastic waves. The maximum amplitude of the stress wave as in propagates through •th,

media is approximately 5 kbar. See Figure 3. The yield strength of the foamolike nat,,lrid

is 4.7 kbar and 40.8 kilobar for the plastic. The computational results yield an elast Pi wav,

velocity in the foamn (plastic) of 5.42 x 10• cm/s (2.20 x 105 crn/s) as compar.ed t,, tIO,

theoretical/experimental values of 5.39 x 105 cmr/s (2.19 x 1if5 cris) 13 At th, nrerfa,

between two dissimilar materials, the amplitude of the transmitted stress wave, (at) sh, ,ifl

equal the sum of the amplitudes of the incident (a,) and reflected (a, i stress- wavsP F,,

4

stresses measured at the interface, the cumputatiaial rtýsalt• g Coo, a, zr 4 kha•i t ,i

at = 5.5 kbar. The conmputational results art in .xc!llent ag-norerlw with ,hI4v

For the adiabatic, slowly rising, high iutew'•itv iiLser put•; ut. w(--h,.,• %t%* tLk-

nesses and maximum laser intensities similar to those UvLF dnil fr th,- NIKL I.-,

System 14 For the first case, the ISI-smoothed lawr pulse has., the: cawnmcwal ;,wr-iaw

profile with a 1/2 nsec rise to 1012 W/cm 2 , a t-5/ 4 rise, to 3 x 1WOa \Vcito at 6isv.,

followed by a 3 nsec drive at this intensity. See Figure 1. The targft Ls 6W rn ,of ('CH ai, l

the laser wavelength is 1/4 Am with a coherence time of 1 psec* Thet target ntamss vart Ik •I

at the beginning of the drive portion of the pulste 6 nsec) is 3.67 This is omarab,. t,,

the mass variation (3.8%) attained with the pure hydrodyuarnic version of the c,,d, u1d.0r

the same pulse shape conditions. This is to be expected as the first shock stemming fr,,1

this laser pulse is 0(1 Mbar) and the elasticity/plasticity of the material dies noit play a

role. The target would soon fracture as a result of the RT instability with ar initial rna.,•

perturbation of this magnitude. The total energy density of the laser pulse (9 nsec t is 970i

kJ/cm2 and the target velocity at 9 nsec is 2.5 x 107 cm/s.

For the shock-free pulse, the laser intensity starts at 10' W/cmn and increa.es vfry

slowly reaching 3 x 10"4 W/cm2 at 28 nsec. See Figure 4a. Shown in Figure 4b is aii x -

t - p plot illustrat.ig the target response. A small compression wave begins propagatim,

through the target at : 20 nsec; the total stress has reached an amplitude of z 2(1 kbar

at this time. The peak compressed density is 8.2 gm/cm3 which is 12'7 laxger than for

the 6 nsec pulse case. Figure 5 illustrates the target isodensity contours at 28 nsec

5

the beginning of the drive portion of the- pulse The- amplitudor of thte il•Laxum iun.>-

variation is only 0.5%. This is close to the requirrient (00f1, 1K) f,,r unifrau mplt,,,4

Note that a portion of this growth, an e-folding or 4•o. is due to, RT •Nwth av th- ttlr't:

begins to rapidly accelerate at - 27 nsec For this cas,. thr tI tit• energV di,:1>itv ,f hL,

laser pulse (31 usec) is 120•1 kJ/cnc 2 and the targ.-t v citv at '31 iv,,, 2 x !')- ('1, :1

In summary, we have shown that it is possible to iinirinze the impart of tLe residu.t

nonuniformities inherent in a nonperfect laser beam during the start-up phas,., Thi- I.

done by eliminating the first shock in the laser pulse by designing a tempolrally ulog.

slowly rising, truly adiabatic laser pulse. In order to model this phenomenia. we developd

an elastic, elastic-plastic, hydrodynamic code. A small price- ii paid in laser enecrg'y arid

hydrodynamic efficiency, but the net result is that the perturbation level Ls rtduced bty

nearly an order of magnitude below the level attained with the canonical Tpower-law pulse,

or with other target designs.5

Acknowledgements

This work was supported by the US DoE and ONR.

6

REFERENCES

1. S. E. Bodner. J. Fusion Energy 1. 221(1981).

2. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y Kitagawa. NI NaLit-.u.ki. oi (i

Yamanaka, Phys. Rev. Lett. 53, 1057(1984).

3. S. Skupsky, R. W. Short, T. Kessler. R. S. Craxton, S. Letzring, and .J IM. Swlrf, .1

Appl. Phys. 66, 3456 (1989).

4. R. H. Lehmberg and S. P. Obenschain, Opt. Commun, 46, 27(19S3): R H Lhxzer•.

A. I. Schmitt, and S. E. Bodner, I. App. Phys. 62, 2680 (1987).

5. M. H. Emery, J. H. Gardner, R. H. Lehmberg. and S. P. Obenschain, Phys. Fluid, B,

3, 2640 (1992).

6. R. D. Richtmyer, Commun. Pure Appl. Math. 13. 297 (1960) .Ye Nf,.ke,

NASA Technical Translation NASA TT F-13, 074 (1970).

7. Lord Rayleigh, Theory of Sound, 2nd. ed. (Dover. New York. 19i45. %,)1 2). G;

Taylor, Proc. R. Soc. London Ser. A 201, 192 (1950).

8. M. Desselberger, T. Afshar-rad, F. Khattak, S. Viana, and . Willi. Phvsl Rev L,-tt

68, 1539 (1992).

7

9. Mark L. Wilkins, Meth, Comp Physics 3. 211 (1964)

10. R. von Mises, Z. Angew. Math. u. Mech. 8 "Eng trans. UCRL Traw. $72, L.'

(1928).

11. M. H. Emery, in preparation.

12. J. Delettrez, D. K. Bradley, P. A. Jaanimagi, and C. P. Verdon, Phvys Rf,, A. 41.

5583 (1990).

13. LASL Shock Hugoniot Data , edited by Stanley P. Marsh, (URniv. Cal Press., Lw->

Angeles, 1980).

14. J. H. Gardner, J. P. Dahlburg, M. H. Emery, and S. E. Bodner. Bull. Am Phvs. S,-

35, 1969 (1990).

8

o[ aS o l_ ____

___ 0

(Z**O/Mi )dIN ~I-

If-4

Ag

cua/ua 901-

~ ~ 960 4- I-10

SI• ' I , T • .. .' V ... ,- It • '.. . . .. .. ...

4 I 4I i I i

2

IDFr•-Surfiv c .

-2 Plastic -'Foam

0 20 40 60 80

Figure 3. Plot of the amnplitude of the ev.t w ,r, wav: ioi , 2 I, K, >,

the waves propagate through the f, p;,i- zz- Ti,

propagation.

11

"0.0 8.0 16.0 24.0 32.0

TK (ns)

8.2gm/cml - (b)

i.04v/cm, 4

• %

Figure 4. (a) luteusity profile for the tempoIral ly,. I lwl.v risiimi laser ImpIsc x-t-O p,

for the 60 4tm thick plastic target (ii th, li#.t'ter-,.4-mazs frame) fitr the slowly ri••ii :.,.'

pulse.

12

- -.

H -4- -4

-~-.4

I I

0 70/umFigure 5. Isodensity contours of the 60 •m thick CHi target at. 28 nse:c iimpacted with th,, sbiwlv

rising laser pulse. The maximum ma~ss variation at this time is 0•5%.

13