Experimental study of the interaction of two laser-driven radiative shocks at the PALS laser

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Experimental study of the interaction of two

laser-driven radiative shocks at the PALS laser

R. Singh, C. Stehlé, F. Suzuki-Vidal, M. Kozlova, Jean Larour, U.

Chaulagain, T. Clayson, R. Rodriguez, M. Gil, J. Nejdl, et al.

To cite this version:

R. Singh, C. Stehlé, F. Suzuki-Vidal, M. Kozlova, Jean Larour, et al.. Experimental study of the

interaction of two laser-driven radiative shocks at the PALS laser. High Energy Density Physics,

Elsevier, 2017, 23, pp.20 - 30. �10.1016/j.hedp.2017.03.001�. �hal-01496020�

radiative sho ks at the PALS laser R.L.Singh a,d,

∗

,C.Stehlé a , F.Suzuki-Vidal b ,M.Kozlova ,f ,J.Larour d ,U. Chaulagain a,e ,T.Clayson b ,R.Rodriguez j ,J.M.Gil j ,J.Nejdl ,f ,M.Krus f, ,J. Dostal f, ,R. Dudzak ,f ,P.Barroso g ,O.A ef h ,M.Cotelo i ,P. Velarde i a

LERMA,ObservatoiredeParis,UPMC,CNRS,ENS,UCG,Paris,Fran e b

ImperialCollegeLondon,London,UK

Instituteof Physi softheCze hA ademyof S ien es,NaSlovan e1999/2,18221 Prague,Cze hRepubli

d

LPP,CNRS,E olepolyte hnique, UPMCUnivParis06,Univ. Paris-Sud,Observatoire deParis,UniversitéParis-Sa lay,SorbonneUniversités,PSLResear hUniversity,75252

Paris,Fran e e

ELIBeamlines,InstituteofPhysi sASCR,NaSlovan e1999/2,Prague,18221,Cze h Republi

f

Instituteof PlasmaPhysi sof theCze hA ademyofS ien es,ZaSlovankou1782/3,182 00Prague,Cze hRepubli

g

GEPI,ObservatoiredeParis,PSLResear hUniversity,CNRS,UniversitéParisDiderot, SorbonneParisCité,Paris,Fran e

h

SYRTE,ObservatoiredeParis,UPMC,CNRS,Paris,Fran e i

InstitutodeFusionNu lear,UPM,Madrid,Spain j

UniversidaddelasPalmasde GranCanaria,LasPalmas, Spain

Abstra t

Radiativesho ks(RS)are omplexphenomenawhi hareubiquitousin astrop-hysi al environments. The studyof su h hypersoni sho ksin the laboratory, under ontrolled onditions, is of primary interest to understand the physi s atplayandalsoto he ktheabilityofnumeri alsimulationsto reprodu ethe experimentalresults.

Inthis ontext, we ondu ted,at thePrague AsterixLaserSystem fa ility (PALS),therstexperimentsdedi atedtothestudyoftwo ounter-propagating radiativesho kspropagatingatnon-equalspeedsupto25-50km/sinnoble ga-sesatpressuresrangingbetween0.1and0.6bar. Theseexperimentshighlighted theintera tionbetweenthetworadiativepre ursors. This intera tionis quali-tativelybutnotquantitativelydes ribedby1Dsimulations. Preliminaryresults

∗

andion hargeoftheplasmaarealsopresented.

Keywords: radiativesho ks,hydrodynami slaser-plasmas,spe tros opy, laboratoryastrophysi s

1. Introdu tion

Radiativesho ksarestrong sho ks(i.e. theMa h number,M

>>

1), whi h rea h high temperatures and thus are the sour e of intense radiation [1, 2, 3℄. Depending on the opa ity, the radiation emitted from the sho k may be absorbed by the pre-sho k region, indu ing its pre-heating. Su h pre-heated zone is termed as the radiative pre ursor (i.e. a radiative ionization wave) [1, 4, 5℄. Radiative sho k waveshavebeen studied experimentallysin e more thanade ade,mostlyonlarge-s alelaserfa ilities[4,5,6,7,8,9,10,11,12,13℄, in noblegasesand with dierenttargets geometries. With laserintensitieson thetarget omprisedbetween

10

14

and

10

15

W/ m

2

,theseexperimentsallowed tore ordsho kspeedsrangingbetween40and150km/s.

Tubulartargetshavebeenusedin manysho kexperiments. Hen e,in this ase,thesho ktendstollthetubeandinarstapproximation,maybe assu-medtobehaveas1D.Theexperiments anbethenusedfor odeben hmarking. Inthis onguration,severalstudieshavebeenfo usedonthe hara terization of the radiativepre ursor [4, 8, 6℄ for sho k speeds

∼

60 km/s. In su h ex-periments, ele tron densities up to

10

19

m

−3

have been re orded by visible interferometry. Theradiativelossesat thetubeboundarieshavebeenpointed outleading to a strong diminution of the ele tron density when ompared to theresultsfrom1Dsimulations[4,14, 6℄. Su hradiativelossesdependon the wallsmaterialandhavebeenestimatedtobe40%forAluminumandSili a[6℄. Thelossesleadto asmall urvature oftheionization front andto aredu tion of its longitudinal extension [14, 15℄. At higher speeds (

∼

200 km/s), x-ray radiography pointed out a ollapse of the post-sho k [7℄ due to the radiation losses. Finally, for these high-speed onditions, the wall heating leads to the

[16℄,andwhi hhavenotbeenobservedatlowerspeeds.

Contrarytothe asedis ussedabove,ifthesho kwavedoesnotllthetube, 2Dee ts are morepronoun edasshown in are entexperimentdedi ated to XUVimagingofboththepost sho kandtheradiativepre ursorofaRS wave propagatingat45km/sinXenonat0.3bar[5℄.

All previousexperimental studieshavebeenfo usedonthe aseofisolated radiativesho ks. However,inastrophysi al onditions,theradiativesho koften intera ts with a denser medium, leading to the development of ree ted and transmittedsho ks. Afewrepresentativeexamplesofsu hphenomenaare the intera tion of supernovae remnants with dense mole ular louds [17, 18℄, the a retionsho kson thephotosphere ofT-Tauristars [19℄ andthe bowsho ks at the head of stellar jets [20, 21℄. The ollision (or the intera tion) of two radiativesho kwavesisobviouslyarareastrophysi al eventand thetemplate aseofsupernovaremnantDEML316(see g. 1of[22℄)isstill thesubje tof debates[23,24,25℄astheobservationofthesetwodierentsho ks anbealso interpretedas thesuperposition of two blastwavesin the eld of view of the teles ope. Inthis ontext,thedevelopmentofdedi atedlaboratoryexperiments tothestudyofpropagationandintera tionof ounter-propagatingsho kwaves isimportantto hara terizesu heventsthroughtheirspe i signatures.

Inthispaper,wepresenttheresultsofexperimentsperformedatthePrague AsterixLaserSystem(PALS)fa ility[26℄onthestudyoftheintera tionoftwo radiativesho kwavesinXenonatlowpressure(

<

1

bar). Thesesho kwavesare laun hedbytwolaserbeamswithdierentenergyandwavelengthandtherefore thesho kwaveshavedierentspeeds,whi hare omprisedbetween

∼

20and 50km/s.

Se tion 2 presentsnumeri al studies of the intera tion of two sho k waves withidenti al(50- 50km/s)anddierent(50- 20km/s)speeds. The experi-mentalsetupisthenpresentedin se tion3. Itin ludesades riptionofthetwo maindiagnosti snamely,time-dependentopti allaserinterferometry,toprobe theradiativepre ursorsbefore the ollisiontime, and time andspa e

integra-relevantspe tralsignatures. Se tion 4dis ussestheresults derivedfrom these diagnosti s. Con ludingremarksarepresentedinthelastse tion.

2. Intera ting sho k waves

Weinvestigateherethe hara teristi parametersanddynami softwo ounter-streamingsho ks,and ofasinglesho k,through1Dsimulations. These simu-lations were performed employing the Lagrangian numeri al ode `HELIOS', usingtheasso iated PROPACEOSequationofstateand opa ity[27℄. Forthe opa ity, we have used, for the Xe gas, a multiplier

×

20 (to adjust with our own opa ities [28℄, see Appendix). For our qualitative study, the number of groupsis setto be1. Thetarget ell,with a4-mm length,is lledwith Xeat 0.1bar. Twogold oated-CHfoils(totalthi kness11.6

µ

m)arepla edatboth ends losingthe ell.

Wepresenttheresultsofthreerepresentativesetsofsimulationsperformed inXe at0.1 (massdensity=5.4

×

10

−4

g/ m

−3

)barnamely,(I): forasingle RS at

∼

50 km/smovingfrom theleft end ofthetarget ellto therightend, aswellasfortwoidenti alRSat

∼

50km/spropagatinginoppositedire tions (i.e. startingfromtheleftandrightend, respe tively,Fig.1),(II):forthesame onditionsbut withoutany oupling with radiation(Fig.2) and, (III): for two ounter-propagatingradiativesho ksofdierentspeedsin whi h, one sho kis propagating with the speed of

∼

50 km/s from the left end of the ell while anothersho kpropagateswiththespeedof

∼

20km/sfromtherightendofthe ell(Fig. 3). Toa hievetheaforementionedspeedsinthesimulation, wehave usedontheleftandrightsidestwolaserbeams(

λ

=438nm)withtheadequate uen es. Thepulsedurationissetto0.3ns (peakat0.15ns)toreprodu ethe experimental onditionsdetailed laterinthepaper.

Firstly, wedis uss the aseof two ounter-propagatingidenti al RS. Fig.1 showsthe variationsof theele trondensity (

N

e

)and temperature(

T

e

)in the Xenon layers. This a ademi ase is fully symmetri aland it is equivalent to

(b)

Figure1:Ele trondensity

N

e

(a)andele trontemperature

T

e

(b)versusaxialposition(along a0.4 mlongsho ktube)at3,10,20,30and38nsfromHELIOSsimulationsforthe ases ofsinglesho kof

∼

50km/s(dashedline)andtwo identi al ounter-propagatingsho ksof

∼

50km/s(solidlines). Theverti aldottedlinesshowthepositionoftheinterfa ebetween pistonandba kingXenongas.

radiation) in the middle of the tube. The two sho ks appear in Xenon at

∼

2ns and the ollisiono urs at

∼

38 ns. At 3ns, the pre ursor extension is

∼

0.08 m, whereasthe post-sho k ele trondensity and ele trontemperature are7.8

×

10

20

m

−3

and 14eV respe tively. The lengthof pre ursorin reases rapidly with time and the twopre ursors merge suddenly at

∼

8ns. As the time progresses, the merging ee t in reases signi antly. It is hara terized byaat ommonpre ursor, whose ele tron density and ele trontemperature arein reasingwithtime. Atthetimeofthe ollision(

∼

38ns), thepost-sho k massdensityand ele trondensity jump from 0.011 to0.14 g/ m

−3

and 6.7

×

10

20

to 6.6

×

10

21

m

−3

, whereasthe ele trontemperature risesupto 39 eV. The ollisionleadstothedevelopmentof tworeversesho kwavespropagating ba kinXenonandinthedierentlayersofthepiston,withaspeedof15km/s. These reverse sho ks lead to a dense plasma (

N

e

>

10

21

m

−3

) whi h is not a essibletothepresentexperimentandwillnotbedetailedhere.

Toinvestigatetheee tsoftheintera tion,we omparethepreviousresults with those obtained for a single radiative sho k, moving from the left to the right dire tion in the ell(plotted by dotted lines in Fig 1). The singlesho k propagatesidenti ally to the ase (I) until 10ns. After this time, the proles ofthe ele trontemperature anddensitydier stronglyfrom theprevious ase andtheirvaluesarelowerthanforthe2RS.Thepost-sho kextensionisslightly smallerthanforthe2RS.Thislastee tisduetothefa tthatthesho kwave propagates in a warmer medium, whi h modies the opa ity and the sound speed.

Inordertohighlighttheee toftheradiation,weperformedanother simu-lation with the same set of parameters asof the above, however, putting the Xenonopa ityequaltozero. TheresultofthesimulationispresentedinFig.2. The ollisiontime is now40 ns and thepost-sho kis nomore ompressedby radiation ooling. Its ompressionat 10nsis10 insteadof 35. There isno ra-diativepre ursor. Moreover,therearenodieren esin the

N

e

,and

T

e

proles ofthe singlesho kand that of thetwo ounter-propagatingsho ksbefore the

In theset (III), we performed the simulationsfor the ase of two ounter-propagatingsho ksofdierentspeeds,i.e. 50and20km/sstartingfromtheleft andtherightendsof the ell,respe tively. Likepreviously,wealso performed thesimulation forthe twosinglesho ksof respe tivespeeds50 (from theleft end) and20 km/s (from the right end). This more ompli ated asestudy is primarily motivated by our experimental setup. However, it is interesting to omparethese resultswith thesimplerprevious aseoftwo ounter-streaming identi alsho ks. Thespatialandtemporalvariationsof

N

e

and

T

e

areplotted attimes3,10, 30,38and 49ns inFig. 3aand3b.

Theleftandtherightsho ksappearinXenonat

∼

2and3ns,respe tively. Later,at10ns,thetwopre ursorextensionsarerespe tivelyequalto0.18and 0.034 m. The mergingof thetwopre ursors startsat

∼

15 ns. As expe ted from the values of sho k speeds, the ollision time o urs at 49 ns, whi h is delayedin omparisontothe ase(I).Itmaybenotedthat,uptothis ollision time,thepost-sho k onditionsareidenti al forthe asesof asingleRS at50 km/sand thepresent leftsho kat the samespeed. Thisrevealsthat there is no noti eableee t of the rightRS with speed20 km/son the left RS of 50 km/s. Onthe ontrary,wenoteadieren einextensionoftherightpostsho k fromthe ounter-propagating ase omparedwiththesinglesho kpropagating from the right at 20 km/s (Fig. 3a). The two radiative pre ursors merging resultsinaplateaufortheele trondensityandtemperature. Thetemperature at ollisiontimeis now28eVinsteadof39eV inthe ase(I),andtheele tron densityrea hesupto3.1

×

10

21

m

−3

insteadof6.6

×

10

21

m

−3

.

Thisnumeri alstudygivesthemain hara teristi softheintera tionoftwo ounter-propagatingsho kwavespropagatingin Xenonat 0.1barwithspeeds equalto 50-50km/s and 50-20 km/s. The ase of identi al speeds is simpler dueto thesymmetryoftheproblem. However,whateverthespeeds,themost importantsignatureoftheintera tionisthemergingofthepre ursorat8nsfor 50-50km/sandat 15ns for50-20km/s. Thismergingis followedbyaregular in reasewith time of theele tron density and the temperature. The ollision

(b)

Figure2: Variationsof

N

e

(a)and

T

e

(b)versusaxialpositionforthe aseoftwoidenti al ounter-propagatingsho ks(ofspeeds

∼

50km/s)at3,10, 20,30,38and40nsasderived fromHELIOSsimulations. Forthesesimulationswehavenegle tedtheee tofradiationin HELIOSbykeepingtheopa itytobezero.Theverti aldottedlinesshowthepositionofthe interfa ebetweenthepistonandba kingXenongas.

(b)

Figure3: Variationsof

N

e

(a)and

T

e

(b)withaxialpositionforthe aseoftwonon-identi al ounter-propagatingsho ks(ofspeeds

∼

50

&

20km/s)andtwosinglesho k(dottedlines) ofspeeds

∼

50

&

20km/srespe tivelyat3,10, 30,38and 49ns asderivedfromHELIOS simulations. Theverti al dottedlinesshowthepositionoftheinterfa ebetweenpistonand ba kingXenongas.

ofmagnitude, rea hing6.6

×

10

21

and 3.1

×

10

21

m

−3

respe tively, whereas thetemperaturein reasesupto39and28eV.

3. Experimental Setup

Asmentionedinthepreviousse tion,thetwolaserbeams,whi hhavebeen usedto drivethetwo ounter streamingsho ksare notidenti aland thus will drivesho kwavesat dierentspeeds. Therstbeam,at 438nm,also termed asMAIN laser beam, hasa nominal energy of

∼

120J (measured on target) whereas the se ond laser beam, at 1315 nm, hereafter AUX laser beam, has alower energy

∼

60 J (measured before the entran e window of the va uum hamber). Thetwolaser beamsare fo used by lenses(f =564mmfor MAIN and1022mmforAUX)ontheoppositesidesofthemillimetri sizedtargetin theva uum hamber.

Twophaseplatesarepla edbeforeea hlaserlens. TheMAINphaseplate, su essfullyusedinpreviousexperiments[6,8℄isdesignedtoprodu eauniform intensitydistributionovera ir ularse tionof diameter 0.5mm, whereasitis 0.25mmfortheAUX phaseplate. Theexpe tedfra tionofthelaserenergyin thefo alspotsisabout80%. TwokeVpinhole amerasareemployedtomonitor the laser's impa t on the twopistons. These time integrated re ords provide estimatesofthelaserspotdiametersrangingbetween500-600

µ

m forMAIN, and250-300

µ

m forAUX.

3.1. Targets

Thetargets arepla ed inside thePALSva uum hamberand lledin situ withXeorXe+He(90-10%) mixtureat0.1-0.6bar. Thetargets onsistsof a hannelof aparallelpipe shapehavingthe dimensionof0.9

×

0.6

×

4mm, pla ed at the top of an aluminum stru ture (Fig. 4). The hannel is losed laterally by two fused sili a (SiO

2

) windows of 500

µ

m thi kness. From the top,itis losed witha100-nmthin Si

3

N

4

membrane,whi h issupported bya

Parylene-N (11

µ

m) and oated withAu (0.6

µ

m) are pla edat bothends to losethe hannel(Fig. 5)to a taspistonstodrivethesho ksfrombothsides insidethetarget. Whereas theParylene layerwill beablated bythelaser, the gold oatingaimsatblo kingthex-raysgenerated duringablation, preventing thepreheatingofgasinthe hannel. Asa onsequen eoftheablationpro ess, the twofoils will be propelled in the tube. These foils are glued on 0.1 mm thi kNi keldisks,whi hinternaldiameter of1mm. Thisdisk aimsathelping theassemblingofthetargets. It also ontributesto preventradiationfrom the laserimpa tonthefoiltorea hthegasinthetube.

Figure4:S hemati softhetargetshowingthetwoAu-CHpistons losingthetube(ontheir respe tiveNidisks),thehorizontalSi

3

N

4

windowitsaSili onframeandthetwoverti alSiO

2

windowswhi haresupportedbyanAlbase.Figureisnotdrawntos ale.

3.2. VisibleInterferometry

Avisibleinterferometrydiagnosti isusedtoestimatethespeedofthesho ks and the pre ursorele tron density. The Ma h-Zehnder setup is shown at the bottom of the hamber in Fig. 5. The target is pla ed in one arm of the interferometer (Fig. 5) and is illuminated by a probing EVOLUTION laser (beamdiameter

∼

1 m,wavelength527nm,duration

∼

200ns). Thefringes arere ordedonaHAMAMATSU C7700visiblestreak amera(CCDpixelsize 24

µ

m). Thetargetisimagedontheslitofthis amerawithamagni ationof

Figure5: S hemati ofexperimentalsetup. MAINbeam: E

∼

120 Jat 438nmand AUX beam: E

∼

60Jat1315nm.

Thesweepingiskepteither50or200ns,andtheslitopeningis setto200

µ

m (100

µ

m on the target). In the longitudinal onguration, the horizontal line whi h onne tsthe entersoftheMAINandAUXlaserspotsisimagedonthe slitofthestreak amera(i.e. nominallyat adistan eof 300

µ

m fromthebase ofthe hannel). Inthetransversemode,theslitre ordstheimagesofaverti al line lo ated at a given distan e from the pistons. This is doneusing a Dove prism,whi hallowsmakingarotationoftheimageby90degrees.

3.3. XUVSpe tros opy

Time and spa e integrated XUV emission spe tra between 15 and 35 nm havebeenre ordedemployingaateldXUVspe trometer(showninside the red dotted box in Fig. 5), using a ylindri al gold oated grating ( urvature radiusof5649mm,1200grovespermm,e ientgratingareaof45

×

27mm, blazeangle3.7degrees). Thisspe trometerisinstalledonthetopoftheva uum hamber,fa ingthe

Si

3

N

4

window. A ooledAndorDX440CCDisatta hedto thespe trometertore ordthespe trumoftheXUVradiation. TwoAlltersof thi kness0.8and1.6

µ

m,respe tivelyprote tthegratingandtheCCD amera fromdebrisandvisiblelight. Thewavelength alibrationisperformedusingthe L-edgeofAllterat17nmintherstandse ondorders. ThegoaloftheXUV spe tros opi analysisistoprovideinformationabouttheplasmatemperature. To make this interpretation easier, tra esof Helium (10% in number) an be introdu edin Xenonforsomeshots.

4. Results

There ordsobtainedfromtheexperimentshavebeenpro essedtoestimate the sho k se tion, speed, ele tron temperature and density. We shall briey presenttheresultsobtainedwiththetransverseinterferometry,astheyprovide qualitative information about the urvature and transverse extension of the radiative pre ursor. Then, we shall fo us on the results of the longitudinal

ele tron density. The spe tros opi re ords will then omplete this analysis withestimatesof theele trontemperature.

4.1. TransverseInterferometry

Figure6: Transverse interferometri imagesfor(a): shot#48111 (MAIN sho konly). (b): shot#48130(AUXsho konly). Thetimeismeasuredafteranoset equalto14and 23ns respe tively. Theposition`zero'onthe x-axisofea himage orresponds tothe baseof the target.

A transverseinterferometri re ordfor theMAIN sho k alonein Xeat 0.2 barisreportedinFig. 6(a). Thesetuphereimagesonthe ameraatransverse se tionofthetubewhi hislo atedatadistan ed

slit

equalto 3mmfrom the initialpositionoftheMAINpiston. Takingintoa ounttheosetof14ns, the timeofsho karrivalisre ordedat72nsafterthetime

t

0

oflaserarrivalonthe targetandthesho kspeedisestimatedto be

∼

35km/s. Dueto thepresen e ofglueononelateralwindow(ontherightpartofthegure),only6fringesare visible. Thelateralextensionofthesho kstru tureatthistimeisderivedtobe

thesho kisestimatedto beat

∼

350mi ronsfrom thebaseofthetarget(i.e. 50

µ

mabovethenominalvalueof300

µ

m).

Are ordfortheAUXsho kaloneisshowninFig. 6(b), whi h orresponds toagateopeningof50ns. Thestarttimeoftheimagehasanosetof+23ns from

t

0

andthedistan e d

slit

is setto 700mi ronsfromtheinitial positionof theAUXpiston. TheAUXsho kdurationextendsfrom30nstoatleast34ns after

t

0

. The sho k speed isthen estimated to beranging between 23and 20 km/s. Thestru tureofthepre ursorisstronglybent. Itmayfurtherbenoted thatthelateralspreadofthesho kisranging between250-300

µ

m(whi his alsoin agreementwiththespe i ationsoftheAUXphaseplate)andthat the axisofsymmetryofthesho ksystemisalsolo atedatabout350

µ

mfrom the bottomofthe ell.

4.2. Longitudinal Interferometry

The interferometri images havebeen pro essed with a frequen yltering s hemeintheIntera tiveDataLanguage(IDL)toenhan ethefringes ontrast. Thelo ations of the maximum intensity in ea h fringe are used to derive the sho k speed (Fig. 7) and the average ele tron density (Fig. 8) as presented below.

4.2.1. Sho kSpeed

Atypi allongitudinalinterferometri re ordisshowninFig. 7forXenonat 0.1barand two ounterstreaming sho ksdrivenbylaser beamswith energies 133and 68 J for the MAIN and the AUX sho ks respe tively. Toderive the sho ks speeds, we determinethe position of the last visible end pointsof the fringes,wheretheele trondensityrea hesthemaximumvaluea essibletothe diagnosti . The fringes are strongly bent, as expe ted due to the presen e of theradiativepre ursors. Weassumethesho kfronttobe loseto thelo ation ofthese last visibleend points. A linearregressionofthe onne tingpointsis

thenusedtomeasurethesho kspeed,whi h,inthis ase,is54

±

3and23

±

3 km/sforMAIN andAUX sho kwaves,respe tively. Thisspeeddetermination isbasedontheabsorptionbehavioroftheplasmaandnotontherealposition ofthefrontdis ontinuity,whi hisnotvisibleduetothestrongabsorption. The ollisionof thetwosho ksis lo atedat

∼

2800

µ

m (t= 47ns afterthestart ofthesho kpropagation).

Figure7: Interferometri imagere ordedfor theshot #48055inXeat0.1 bar. Thesho k speedsfor thesho ksdrivenbyMAINlandAUXlasers arerespe tively equalto

∼

54and 23km/s. Thetimeoflaser arrivalon the pistonisat 146ns. Thepositionsof theAu-Xe interfa eonthere ordarerespe tively950

±

50and4950

±

50mi rons.

4.2.2. Averagedele trondensity

Theaverageoftheele trondensityalongthepathof theprobelaserbeam (lineaveragedele trondensity)intheplasma anbeestimatedfromthere ord. Forthispurpose,we omparetherelativevariationofthephaseshiftwithtime at ea h fringe maxima with its value at the time of laser arrival. The phase

∆φ ≈ −

πd

λN

c

< N

e

>

(1)

where

λ

=527nmisthewavelengthoftheprobinglaser,

N

c

=4

×

10

21

m

−3

the riti al density at this wavelength, and

< N

e

>

, is the ele tron density averagedoverthelaserpath

d

inthe ell,denedas:

< N

e

>=

Z

d

0

N

e

(z, t)dy

d

(2)

Inthefollowing,weshalltaked =600

µ

m,whi h orrespondstothe hori-zontal transversese tionof thesho k hannel. Foraplasmawhi h isuniform withinthisse tion,

< N

e

>

is losetothereallo alvalueoftheele trondensity. As seenfrom the transverse interferometri re ord, this is rather truefor the MAIN sho kwave, whereasitis notthe aseforthe AUX sho k,whi h hasa smallerse tion(

∼

300

µ

m,see4.1)andwhi hisobviouslynotuniform.

Shot Gas Pressure MAINlaser AUXSho k MAINSho k AUX Sho k number (bar) Energy (J) Energy(J) Speed(km/s) Speed(km/s)

48055 Xe 0.1 133 68 54

±

3 23

±

3 48132 Xe+He 0.2 118 57 41

±

4 18

±

2 48138 Xe+He 0.2 121 0 45

±

4 Nosho k

Table1: Experimentaldetailsof the interferometri re ords. Thespeed isdedu ed bythe methodofthelastfringeexplainedinthetext(seesubse tion4.2.1).

Toanalysetheintera tionofthesho ks,weshalldis ussbelowthree repre-sentativeinterferometri re ordsforXenon. The onditionsofthesere ordsare presentedinTable1andthere ordsareshowninFig. 8. Twoshots on ernthe propagationof tworadiativesho kwavesat 0.1 and 0.2bar. For omparison, one re ord is dedi ated to the propagation of one sho k (MAIN) only at 0.2 bar. The twore ords at 0.2bar areperformed in theXe-Hemixture (90 -10 %in numbersofatoms). Atthepre isionofourre ords,we onsider thatthis impurity on entrationhasonlyanegligibleee t onthesho k speedand the

pre ursorele trondensity. Thelimitofdete tionof

< N

e

>

overthese tionof thetube(0.6 mm)is orrespondsrespe tivelyto 9

×

10

17

, 6

×

10

17

and6

×

10

17

m

−3

fortheFigures8(a),(b)and( ).

Five olors (white, red, blue, green and magenta) are used in Fig. 8 to identifydierentphaseand lineintegrateddensitiesasfollowing:

•

bin1:

≤

0.6

π

;

N

e

≤

3.9

×

10

18

m

−3

(white),

•

bin2: 0.6

π

-0.8

π

;3.9-5.7

×

10

18

m

−3

(red),

•

bin3: 0.8

π

-1.1

π

;5.7-7.5

×

10

18

m

−3

(blue),

•

bin4: 1.1

π

-1.3

π

;7.5-9.3

×

10

18

m

−3

(green),

•

bin5:

>

1.3

π

;

>

9.3 10

19

m

−3

(magenta).

Thevariationsof

< N

e

>

withthedistan ealongthesho ktubearereported in theright panelofFig. 8at 10ns (in red),20ns (in blue), 30ns (in green) and40ns(inmagenta).

Theintera tionbetweenthetwopre ursorsis learlyvisibleat0.1bar(Fig. 8(a)): at10ns,theintera tionofthe ounter-propagatingsho kshaseithernot yet startedorisbelowthesensitivityof thediagnosti . Theintera tiono urs atlatertimes,withatypi alsignaturewhi hisasfollows: theslopeof

< N

e

>

isde reasingfrom the left (MAIN pre ursor),passes througha minimumand in reasesat theright (AUX). Theminimum itselfin reaseswith time upto 7

×

10

18

m

−3

at40ns.

At0.2bar,thetwore ords(withMAINonlyandwiththetwosho kwaves) indi ate a pre ursor for MAIN, with aslopewhi h de reases from the left to therightinFig. 8(b). Upto40ns,thepre ursorsfortheMAINsho karevery similarwithandwithout(Fig. 8( ))thepresen eofAUXsho kwaveandthere isnoobviousindi ationaboutapre ursorforAUX inthe aseoftwo ounter-propagatingsho k waves(Fig. 8(b)). Atthispressureand omparedwith the previous aseat 0.1bar, theabsen e ofpre ursor forAUX maybeattributed to: i) a lower sho k speed (18km/s) ombined with a largerpressure (hen e

at0.2bar(b)and#48138inXe+Heat0.2bar( ). Rightpanel: ele tron densityat10,20, 30and40nsversusdistan eforthesere ords. Thepositionsofmaximahavebeenidentied on the re ords inthe left panel. The timet =0, orresponds tothe timeof laser arrival onthe target and the positionx=0 orresponds tothe interfa ebetween the piston (Au layer)andthe gas. Itsdeterminationispre isewithin100mi rons. Thedistan esbetween twounperturbedfringes forre ords#48055,#48132and#48138are159, 244and244

µ

m respe tively. The

< N

e

>

un ertainty(

±

2pixels)isindi atedbytheerrorbarinthe right panels. It orrespondsrespe tivelyto

±

9

×

10

17

,

±

6

×

10

17

and

±

6

×

10

17

m

−3

forthe

tinylongitudinalextension oftheeventualpre ursor(seeFig. 8(b)) ompared withtheresolutionof20mi rons(2pixels). Our1Dnumeri alsimulationswith Xenonopa itymultiplier

×

20(not presentedhere),indi ate asmallpre ursor for AUX sho k. At 15 ns, its extension is 50

µ

m (900

µ

m for MAIN sho k) withatypi alele trondensity

∼

3.5

×

10

19

m

−3

(2.3

×

10

19

m

−3

forMAIN sho k),whi h doesnotagreewiththere ord. At42nsthepre ursorofMAIN rea hes theAUX sho k frontand the prole is similar to the prole at 20 ns showninFig. 3aat 0.1bar,withaplateauofalmost onstantele trondensity betweenthe twofronts. This might be ompatible with small bending of the 4

th

fringe(fromtheright)between45and50ns. As1Dsimulationsareknown tooverestimatethepre ursorele trondensity,2Dsimulationsarene essaryfor amorepre iseinterpretationoftheexperimental result.

4.3. XUVSpe tros opy

Spe tros opyisanadequatetooltomonitorthetemperatureoftheplasma. It is thus appropriate for identifying the sho ks ollision by omparing the spe traforsingleand ounter-propagatingsho kwaves. Unfortunately,onlya few re ordswereobtained during the experimentpreventing to at h the ol-lision with this diagnosti . Among the shots re orded, the XUV spe trum of theshot#48143 is presented herein detail. Thisshot wasperformedfor [Xe (90%)+He (10%)℄ mixture at 0.6 bar with laser energies of 123 J for MAIN and63JforAUX.Theinterferometri re ordofthisshotisshowninFig. 9a. The MAIN sho k speed is estimated to be 39

±

4 km/s. The estimation of theAUX speed(18

±

5km/s)isimpre ise,due tothepresen eof glueon the right se tion of the re ord. In this interferometri re ord, weare not able to retrieve the ollisiontime. However, if weextrapolateit for the speeds

∼

39 km/s(MAIN) and

∼

18km/s(AUX),this ollisionshould happenbetween60 to65nswithanin reaseofthetemperatureupto30eV.

Therawspe trumwasre ordedforthewavelengthrangeof15-35nmwith theL edgeofAluminumat 17nm(34nmin se ondorder). Thenetspe trum

orre tedfrom thetransmission[29℄ofthe100nmthi k

Si

3

N

4

window(3mm

×

0.4mm)ispresentedinFig. 9b. Aremarkablefeatureisastrongabsorption dipbetween19and22nm. Thisabsorptionprobably omesfromthe oldlayer (thi kness300

µ

m) betweenthe sho k heated plasmaand the

Si

3

N

4

window. FewlinesofXeVII-VIIIareidentiedthroughNISTdatabase

1

asalsoOxygen IV and V lines. Lyman lines of He II (from 1-2 to 1-7) are also present in thespe trum. Theseinformations will beuseful forestimation ofthe ele tron temperature(se tion4.4).

4.4. 1Dsimulationsbasedon experimentalresults

Now,we omparetheexperimentalsho k hara teristi swiththeresultsof HELIOS1DsimulationsusingthePROPACEOSequationofstateandopa ity (limited to 1 group). This opa ity is multiplied by 20 for Xenon. As our interestistounderstandthesho kstru tureinXenonandnotthelasermatter intera tion on the piston, we adjusted the uen es in order to reprodu e the experimentalspeeds.

Toanalyse the results from the shot #48055 (Fig. 8(a)), we thus set the uen es to 32000 and 7500 J/ m

2

. This allowed produ ing the experimental sho kspeeds54and23km/sinXenonat0.1barfortheMAINandAUXbeams, respe tively. Thetwosho ksappearedin Xenonat2and3ns respe tivelyfor MAINandAUX.Themergingofthetwopre ursorsstartedat

∼

15nsandthe sho k ollisiontimeo uredat47ns. InFig.10,wepresenttheele trondensity prolesfrom the simulation (dotted lines) and the experiment(solid lines) at 10,20,30and40ns.

At10ns,thetwosimulatedpre ursorextensionsare0.165and0.022 mfor MAINandAUXrespe tively. Theele trondensityislargerbyafa torof4than intheexperiment. Theshapesofthepre ursorsarealsoverydierent. However, thesimulationsupposesthat theplasmaisuniform in thetransversedire tion (i.e.perpendi ular to the sho k propagation) whereas, in the experiment, N

e

1

onsequen e,thevaluesoftheexperimentallineaveragedN

e

shouldbesmaller than the numeri al ones and the orresponding proles should be smoother. It is also important to note that, for AUX sho k, the average

< N

e

>

value underestimatesthelo al valueat the entre ofthetubebyat leastafa torof about2(asitwasaveragedover0.6mminsteadof0.3mm). Moreover,our1D simulationsuersfromaninexa topa ityand2Dee tsareprobablyimportant espe iallyforAUX. Thuswehavehereonlyaqualitativeinterpretationof the experimentalresults.

Theintera tionbetweenthetwoHELIOSradiativepre ursorsstartsbetween 10and 20 ns, likein the experiment. However,the shape, aswellasabsolute valuesofthe simulatedele trondensity urves,arenotin agreementwith the experimental results and the intera tion is strongerin the simulation than in theexperiment.

Figure10: Re orded ele tron density(shot #48055) together withthe HELIOSresults at dierenttimes.

In order to interpret the spe tros opi data presented in se tion 4.3, we performedanother1DsimulationinXenonat0.6bar,andadaptedtheuen es to generate two ounter-propagatingsho ks with the speeds36 and 18 km/s, lose to the experiment. The time evolutions of the ele tron density, mean

(b)

( )

Figure11: Timeevolutionofthemassdensity(a),ele trontemperature(b)andmean harge ( )at56,57,58,60,64and65nswithinthesho ktubederivedfromtheHELIOSsimulations (withXenonopa itymultiplier

×

20),fortwo ounterstreamingsho ksof

∼

39and18km/s.

inFig. 11.

Thetwosho ksappearedinXenonat2and3nsrespe tivelyforMAINand AUX.Con erningAUX,the ombinationofasmallspeedandarelativelyhigh pressuredoesnotallowtodeveloparadiativepre ursor,inagreementwiththe experimental results(Fig. 9a), whereasthe MAIN sho k hasa pre ursorand itslengthisin reasingwithtime. Thepost-sho ktemperatureoftheMAINis

∼

21 eVand theion harge

∼

9. At57ns, thepre ursorof MAINrea hesthe AUXsho kfront. Thistimeisoutofourre ord(seeFig. 9a)whi hmeansthat theintera tion ee tiseither absentoro ursatlatertimes. Thestru tureof the AUX post sho k is modied by the intera tion with the MAIN pre ursor (Fig. 11b). The sho k ollision o urs at 65 ns (Fig. 11a) resulting in the development of two reserve sho k waves. At the ollision time, the ele tron density,massdensity,ele trontemperatureandion hargerea hrespe tively

∼

1.4

×

10

21

m

−3

,0.034g/ m

−3

,26eVand10.

Inordertointerpretthespe tros opi results,qualitativepreliminary om-putationsof theXUV spe traemerging froma600

µ

m thi k plasmawithtwo representativevaluesofthemassdensity,

ρ

=3.2

×

10

−2

and3.3

×

10

−3

g/ m

3

wereperformedatdierenttemperatures,usingthemethodsdes ribedin [28℄. Theyshow that thelines of HeII anonly be observedat atemperatureof

∼

15eVandforthelowestdensity,i.e. intheradiativepre ursor. Ontheanother side,the presen eof lines ofXe VII-VIII in there ordis ompatible with our 1Dsimulations.

5. Dis ussionand on lusions

This paper reports therst experimental study of the intera tionbetween tworadiativesho kwavespropagatingat twodierentspeedsin Xenon. This intera tionisanalysed byopti alinterferometry,XUV spe tros opyand inter-pretedby1Dsimulations.

mergingofthetworadiativepre ursorsat20ns. The ollisiontimeisre ordedat 47ns. Su hbehaviorisreprodu edbythesimulation. However,theintera tion ee tislargerinthesimulationthanin theexperiment.

Weinvestigatedthisintera tionatlargerpressure,0.2bar,withthefollowing speeds

∼

41km/sforMAIN and

∼

18km/sforAUXsho kwaves. Wedonot re ordany experimentalsignature oftheradiativepre ursor forAUX, andwe donot at hexperimentallythe ollisiontime. There ordedpre ursorofMAIN isnotinuen edbytheAUXwaveupto40ns(Fig. 8(b)and( ))whi hwasthe limitofthere ord. Onitsside, the1Dsimulationpredi tsatinypre ursorfor AUX.At42ns thepre ursorofMAIN rea hestheAUXsho kfront,resulting inaatproleofN

e

.

Theresultsofthetransverseinterferometryat 0.2bar,with speedsof

∼

40 and20km/sindi atethattheMAINpre ursorhasalateralextensionof

∼

600

µ

mwhereasit is300

µ

mfor AUX. Thepre ursorof MAINis almostatwith aprobablesmallbendingattheedgesofthetube,whereastheAUXpre ursor is more urved. This means that the 2D ee ts are moreimportantfor AUX thanforMAIN.

Oursimulationsgiveaqualitativedes riptionofthesho ksintera tionwhen thelaseruen eisadjusted togivethe orre t sho kvelo ities. However,itis nowwellknownthat2Dsimulations(togetherwithstateoftheartopa ities)t better withexperiments[15, 14,8℄. Forthesamelaserenergy,2D simulations leadtoadiminutionofthesho kspeed omparedto1Dasalsotoadiminution ofthe ele trondensity. Forinstan e, in the aseof asho kwavelaun hedby alaserbeamat 1315nminXenonat0.3 baratPALSandwithalaseruen e of 85000 J/ m

2

, ARWEN 2D simulations give a sho k speed of 44 km/s in agreementwiththeexperimental one[30℄. 1Dsimulationwouldrequirein this aseauen eof 30000J/ m

2

toa hievethesame.

Thespa eandtimeintegratedXUVre ordsat0.6bar,forrespe tivespeeds whi hareequalto

∼

39and18km/s,indi atethatthetemperatureofthesho k rea hedupto15eVandthattheXenonmeanion hargealsorea hedvaluesof

harge5 -10 (Fig. 11 ). A moredetailed study, based on2D simulationand radiativetransferpost-pro essingwillbene essarytorenetheanalysis.

6. Appendix

ThequalityoftheLTEPlan kandRosselandopa itiesis ru ialfora pre- ise numeri al modeling of the radiativesho ks, espe ially those presenting a developed pre ursor. The al ulationof these fun tions requires the determi-nationofthemono hromati opa ityin therelevantpartofthetwoweighting fun tions entering in the average,whi h peak at 2.8 and 3.8 kT respe tively. Forourexperimental radiativepre ursors,havinga onstantmassdensity

ρ

= 5.1

×

10

−4

g/ m

3

,thetwomaximumexpe tedtemperaturesarearound15and 7eV, whi hmeansthattheopa itieshavetobea uratebetweenfeweVto15 eV. The ontinuum loweringisintrodu edwithin theionspheremodel[31℄for temperatureslowerthan6eVandaStewart-Pyatt[32℄modelforhigher tempe-ratures. Wefound agood agreementwith ATOMIC[33,34℄ resultsespe ially atthelowesttemperatures,wherethemodeling remainsdeli ate. Moredetails maybefoundin [28℄.

The mean ion harges, omputed by the two methods, are in ex ellent agreement,ex eptat verylowtemperature(Fig.12). However,thePlan kand Rosselandopa itiesdiernoti eablyas anbeseenfromtheFig. 13aand13b. Near10eV, whi h orrespondsto thepre ursorplateau,ouropa ityisgreater thanthe PROPACEOS oneby afa tor of 7forthe Rosseland and 25 for the Plan k.

Inordertokeepthisdieren eintoa ount,theonlypossibilitywastouse amultipli ativefa tor for thetwo opa ities,whi h was then taken

×

20. We are then aware that the present HELIOS results have to be used only for a qualitativeinterpretation.

Figure12:meanion hargeforXenonat5.1

×

10

−4

g/ m

3

,forPROPACEOSandourmodel. Theratio

< z >

ourmodel

/

< z >

P ROP ACEOS

isalsoplottedinblue.

(b)

We are grateful to J. Golasowski,J. Hrebi ek, T. Medrikfor theirhelp in the diagnosti s, to S. Cro e, T. Mesle, F. Reix, Y. Younes, and P. Jagourel, from Pole Instrumental de l`Observatoirede Parisfor the targets manufa tu-ring, to Chris Spindloe (S ite h) for the gilt parylene foils, to Roland Smith (Imperial College) for the Dove prism, and to J. Skala, E. Krousky and M. Pfeifer from PALS for their assistan e. Finally, we a knowledge the support oftheS ienti Coun ilof ObservatoiredeParis,theFren h CNRS/INSU Pro-gramme PNPS, the PICS 6838 of CNRS, the Labex PLASPAR (ANR-11-IDEX-0004-02),theUFRdePhysiqueofUPMCasalsoofEXTREMELIGHT INFRASTRUCTURE proje t no. CZ.1.05/1.1.00/02.0061 and EC OP pro-je tsno. CZ.1.07/2.3.00/30.0057and CZ.1.07/2.3.00/20.0279,whi h were o-nan ed 285 by the European So ial Funds and the Ministry of Edu ation, YouthandSportsoftheCze hRepubli -proje tsLM2010014andLM2015083 (PALS RI), andthe LASERLABEUROPE(grantagreementno. 284464,ECs SeventhFrameworkProgramme).

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