Z. Jiang et al- X-ray spectroscopy of hot solid density plasmas produced by subpicosecond high contrast laser pulses at 10^18-10^19 W/cm^2

8/3/2019 Z. Jiang et al- X-ray spectroscopy of hot solid density plasmas produced by subpicosecond high contrast laser pulse

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X-ray spectroscopy of hot solid density plasmas produced bysubpicosecond high contrast laser pulses at 1018-1019 W/cm*Z. Jiang,a) J. C. Kieffer, J. P. Matte, ancj M. ChakerInstitut National de la RechercheScientifique,Energie et Mat&-iaux, 1650 Montie Saint Julie, Varennes,Q&bec J3X IS2, Canada0. Peyrusse and D. GiilesCommissariata IEnergie Atomique, Limeil Center, Villeneuve,St. Ceorges,FranceG. Korn,b) A. Maksimchuk, S. Coe, and G. MourouCenter or Ultrafast Optical Science, University of Michigan, Ann Arbor, Michigan 48109(Received 26 October 1994; accepted 25 January 199.5)Analysis is presented of K-shell spectra obtained from solid density pl asmas produced by a highcontrast (1O:l) subpicosecond laser pulse (0.5 pm) at 108-109 W/cm. Stark broadeningmeasurements of He-like and Li-like lines are used to infer the mean electron density at whichemission takes place. The measurements indicate that there is an optimum condition to producex-ray emission at solid density for a given isoelectronic sequence, and that the window of optimumconditions to obtain simultaneously the shortest and the brightest x-ray pulse at a given wavelengthis relatively narrow. Lower intensity produces a short x-ray pulse but low brightness. The x-ray yield(and also the energy fraction in hot electrons) increases with the laser intensity, but above some laserintensity (IOs W/cm* for Al) the plasma is overdriven: during the expansion, the plasma is still hotenough to emit, so that emission occurs at lower density and lasts much longer. Energy transportmeasurements indicate that approximately 6% of the laser energy is coupled to the target at lOI*W/cm* (1% in thermal electrons with T,=O.6 keV and 5% in suprathermal electrons with The25keV). At Zh*= 10s W pm2/cm2 (no prepulse) around 10 photons are emitted per laser shot, in 2nsrd in cold K, radiation (2-9 A, depending on the target material) and up to 2X lo* photons areobtained in 271. rd with the unresolved transition array (UTA) emission from the Ta target. 0 1995American Institute of Physics.

I. INTRODUCTIONDuring the last 15 years, laser-produced plasmas have

been extensively studied for, among other aspects, their po-tential application to inertial confinement fusion (ICF).Nanosecond laser pulses were used to realize laser-drivenablative implosion in which high compression can occur. Inthis scheme a pellet is accelerated inwardly by the reactionforce associated with the outward expanding ablated mate-rial. Very inhomogeneous plasmas with characteristic dimen-sions, the electron density gradient scale length, for instance,very large compared to the laser wavelength are thus pro-duced. Although laser irradiation with Zh2 values up to lOIW ,um2/cm2 has been realized with long-wavelength CO2lasers,* most of the recent experiments of interest for ICFhave been realized with short-wavelength lasers (Xtl pm)at relatively moderate intensity (IX*< lOI W ,um*/cm*) to,among other problems, maximize the collisional absorptionand reduce suprathermal electron preheat.3A recent breakthrough in the laser amplificationtechnique4 has allowed the generation of small-scale lasersystem with a peak power well into the terawatt regime andIA* values greater than 1OJ8W ,um/cm2, and plans for peta-watt class picosecond lasers are actively pursued. This in-crease in peak power and irradiance, which has been madeOn leave from the Shanghai nstitute of Optics and Fine Mechanics, Chi-neseAcademy of Sciences,Shanghai,PeoplesRepublic of China.On leave from Max-Born Institut, Berlin. Germany.

possible by the use of the technique of chirped pulse ampli-fication (CPA),6 gives access o new regimes of interaction oflaser with solid matter.7-g The application of these intensesubpicosecond pulses originates from a few fundamental fea-tures. The first is the short pulse duration, which noticeablylimits pl asma hydrodynamics during the heating phase. Ifthere is negligible energy in the prepulse (high contrast), thenthe electron density gradient scale length is much shorterthan the wavelength and the coupling takes place at nearsolid density. Many works on subpicosecond laser solid mat-ter interaction have concentrated up to now on generatingshort pulses of x rays, l-l5 and the related transient and non-local atomic physics has been explored.6-8 The second fea-ture is the extremely high-energy density and the resultingextremely high radiation pressure of the pulse. Laser inten-sities have long been sufficient to modify the plasma signifi-cantly at the critical density (n,=1.12X102 hT2 cmm3, X isthe laser wavelength in ,um) by what is termed the pondero-motive force. With intense short pulses the radiation pres-sure can be quite large,20 even for electron density wellabove nc , producing craters and going on to hole boring.2Z22These effects are relevant to the concept of fast ignition re-cently introduced by the Lawrence Livermore NationalLaboratory.23 In addition, new phenomena, such as the gen-eration of far-infrared radiation,24 ion collimation,25 andstrongly coupled Raman instability,26 have been observed,and short pulses incident on preformed plasmas have been

1702 Phys. Plasmas 2 (5), May 1995 1070-664)


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used to study Brillouin scattering instabilityZ7 and nonlocaltransport.zsIn this paper we discuss some key issues related to thechallenging probl em of producing one dimension, hot, uni-fomr solid density plasmas. Results are very promising forthe achievement of isochoric heating (the term used to indi-cate heating at constant density) of matter at near solid den-sity? up to extreme temperatures. Production of matter insuch a state will offer a unique way to address experimen-tally in the laboratory some problems of great astrophysicalinterests, namely the opacity of: hot dense matte?9 and thephysics of hot strongly correlated pl asmas.30 Furthermore,this is also of importance for atomic physics, and will give usthe possibility to study, among other aspects, (i) the ioniza-tion dynamics in hot dense plasmas with many electronatoms,31 (ii) the physics of quasimolecular states,3 and (iii)the statistical physics of hot strongly correlated plasmas.These plasmas will be also very interesting as ultrafast andultrabright sources of short-wavelength radiation, which mayhave ap lications in many different fields as x-ray laserphysics, 8 molecular sciences,34and medical research.35II. CRITICAL ELEMENTS FOR SOLID DENSITYPLASMAS

been improved to an estimated 10 in our experiments byusing the second harmonic generation (i.e., conversion to agreen light) in nonlinear crystals, which will not double theweak prepulse. By using a potassium dihydrogen phosphate(KDP) type I crystal, we have been able to obtain a maxi-mum conversion efficiency of 85%.37 The 300 fs green pulsewas focused with a 45 incidence angle off-axis f/3 parabola.An optical system, composed of five dichroic mirrors andone 1 pm filter, has been used to completely reject the un-converted 1 pm radiation that could produce a preplasma.The intensity profile of the focal spo t was measured with amagnifying imaging system (40X) and a digital EG &G two-dimensional charge-coupled-device (CCD) camera. The di-ameter of the spot size was found to be around 8 pm at(l/e)* intensity (that contains 65% of input energy); providedthe laser energy on target is less than 900 mJ. Above thisvalue, the focal spot starts to be degraded by an excessive l3integral effect. Thus, in the present experiments we haveused a maximum energy of 900 mJ in a 300 fs green pulse,giving three terawatts on the target with no prepulse, and amaximum intensity of 4X10i8 W/cm corresponding toIX2= 10 W ,um/cm. To our knowledge, these experimentsare the first in thi s intensity regime, wi th such a high con-trast, short-wavelength subpicosecond laser.

In the present work we try to combine ultrashort gradientscale length plasmas, or solid density, and very high laserintensity. The aim of these experiments is to explore thepossibility of using the radiation pressure of a very highcontrast subpicosecond pulse to balance the dense plasmasthermal pressure during the laser heating. Optimization isrequired: the intensity must be sufficient for the radiationpressure to prevent plasma expansion, but not as high as tolead to hole boring. The ultimate plasma we need to doclean experiments is ideally hot (electron temperature in thekeV range) still (ions at rest) and at solid density(n,=6X 1O23 m- for Li-like solid Al, for instance). Produc-ing such a plasma therefore requi res (i) a strict control ofseveral crucial laser pulse parameters, (ii) de tailed target de-sign, and (iii) an excellent experimental characteri zation ofthe plasma.

Ill. K-SHELL Al SPECTROSCOPYPlasma spectroscopy, which contributed to advances ininertial confinement fusion research, provides much of theinformationof these new high-densi ty ultrashort plasmas. Jo-hann and Von H amos crystal spectrometers were used at 45from the laser axis to record the time-integrated keV spectra,

c3.0 I.*.,..,*I....,..I0 a)52.5 *4 af -2.0

.a 5,s intercomblnation$2p1.0--Ic 0.:5

For the particular problem of forming a hot solid densitynearly uniform plasma, the key laser pulse issues are (i) ahigh contrast ratio to avoid any expansion of the matter be-fore the main pulse arrival and (ii) an optimal pulse durationand high intensity (107-109 W/cm).While high intensities for short pulse duration are fea-tures obtained with the technology of chirped pulse amplifi-cation, an undesirab le by-product of this technology i s theproduction, at the wavelength of 1 pm, of a long prepulse atvery low relative intensity (typicall y low6 of the mainpulse).36 This contrast of lo6 is not adequate at the intensityof interest here, where a contrast of something like 10 isrequired to avoid excessive energy deposition at lower den-sity in the preplasma created by the long prepulse.

5IM9

5iii2I5The experiments were carried out with the table top tera-watt (Ts) laser system at the University of Michigan.37 Thelaser delivered up to 2 J in a 400 fs pulse at the wavelengthof 1.053 pm. The intensity peak to background contrast ratiowas measured to be 5 X 10 at 1.053 pm. The contrast has

=02.5.c:2.0El.5$0

%0.5z 0.07.7 7.8 7.9 8.0 0.1 8.2 8.3 8.4Wavelength (A)

FIG. 1. Al spectra n 7.7-8.4 %,obtainedwith a high contrastsubpicosecondlaserpulse ncident on 130pm Al target. a) 20 mJ, IO W/cm; (b) 150 mJ,7.7X10i7 W/cm; and (c) 710 mJ, 3.5X lOI W/cm.

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c0cf

=E0 @(022 *E fwi;5

Al H$

2.5 :2.0 :1.5 :

: Al Hel.O- 7

6.2 6.4 6.6 6.8 7.0 7.2 7.4Wavelength (A)

FIG. 2. He-like and H-like lines in the 6.5 A rangeof Al plasmaproducedby 2.5X 10s W/cm* laser pulse ncident on a 130 pm AI target. The lineratio of L yJHe @ s used o deduce he average lectron emperature,whichis around600 eV in o ur experimentalconditions.

in the l-10 A range, with SB5 and DEF Kodak films. Thethickness of Be filters in front of the film was adjusted as afunction of the wavelength to avoid the saturation of thebrightest line in a given wavelength detection window. Ourcrystal spectrometer s provide high resolution spectra (x/AXof 2000-4000) for detailed studies of line shapes.Figure 1 presents Al spectra (7.7-8.4 A) obtained at lOI7W/cm2 [Fig. l(a), 20 mJ on target], 7.7X lOI W/cm [Fig.1 b), 150 m.T],and 3.5 X 1018W/cm [Fig. l(c), 630 mJ]. Theobserved spectra have been cor rected for the film,38 filter,3gand crystal response.40At lower intensity [Fig. l(a)], thels2-1.~2~ emission (He3 from the thermal plasma is rela-tively low, and the emission is dominated by K, lines. Weobserve both the K, line from cold al uminum (Al+-A14transitions are blended) and shifted K, lines corresponding tovarious ionization states from Al+ to Al+. This spectrumindicates that a low-temperature plasma was produced at lowlaser intensity. As the laser intensity is increased, the tem-perature, and thus the thermal emission, rapidly increases[Figs. l(b) and l(c)]. Above 10 W/cm2, noticeable Ly,H-like emission is observed. A typical spectrum in the 6.5 8,range, including the transitions from He- and H-like ionsstates s shown in Fig. 2 (it-radiance at 2.5X lot8 W/cm2). TheHep and He, line profiles are used to infer the mean electrondensity at which the emissions take place. The LyJH ep lineratio is around 0.35 at this intensity, and can provide a meansof determining the electron temperature. The He- and Li-likeline s hapes and LyJHep intensity ratio are discussed in thenext section.IV. AVERAGE ELECTR ON DENSITY

The average electron density at which the emission takesplace is inferred from various line profiles calculated by us-ing the standard hypotheses of Stark line broadening byplasma,4* i.e., quasistatic approximations for the ions andimpact approximation for the electrons. One aspect of ourline shape calculations is the use of analytic fits of theplasma microfield distribution function, deduced from a large

number of Monte Carlo simulations,42 performed with aYukaw a potential and a linearized Thomas-Fermi electronscreening. In the range of plasma conditions where K-shelllines are emitted, this formulation of the ion-ion potentialagrees very well with a more sophisticated self-consistentformulation?3 The analytic fit that we use depends on theionic correlation pa rameter (depending on ri) and on thescreening parameter (depending on T,), and thus are a two-temperature formulation of the microfield distribution func-tion, As noted elsewhere,& this detail is important, since themicrofield can be very sensiti ve to the temperature ratioT,ITi. Then the profile depends mainly on two unknownparameters, the electron densi ty ~1,) and the ion temperatureTi , if the density range is such (typically n,< 1O23 me3) thatthe thermal relaxation rate is lower than the radiative rate ofthe upper state of the transition of interest. A previous studyof the He, ( s2- 1~4~) line profile in similar experimentalconditions (201 rradiation, no prepulse, 5 X 10 W/cm2)45 n-dicated an ion temperature much lower than the electrontemperature and a relatively high densi ty at which He,, emis-

1.0 l...1L~II,.Ten600 eV

0.62d 0.6A.z!t 0.4dr

0.2

-.v6.60 6.61 6.62 6.63 6.64 6.65 6.66 6-67WavelengthA)

0.80.60.40.20.06.28 6.29 6.30 6.31 6.32 6.33 6.34

Wavelength (A)FIG. 3. Profilesof He-like ines of a 130pm AI target.The laser ntensity s3X10s W/cm. The open dots are experimentaldata. The best fit (solidlines) to the data are using standardStark broadening alculation (see hetext) with the following parameters:T,=600 eV, T,=30-60 eV, andn,=5-7X 102cm-. (a) He @ ine and (b) He, line.

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0.82-22 0.6t2 0.4

0.2

0.0 *7.81 7.83 7.85 7.87 7.89 7.91Wavelength (A) Wavelength (A)

1.2 ,,1(,,,,,1,, ,1 ,,,, ,,,,

0.0Lg -.81 7.63 7.85 7.87 7.89 73

0.8

0.6

0.07.81 7.83 7.85 7.87 7.89

Wavelength (A) Wavelength (A)FIG. 4. The profiles of Li-like lines of 130 pm Al target obtainedwith different laser ntensities.The experimentaldata opendots) are itted (solid lines) withLTE L&like line profile calculation and the inferred averageelectron densitiesare denoted n the figures. (a) 3X10L7W/cm*; (b) 7X lOI W/cm*; (c) 10W/cm; and (d) 2X lOI w/cm.

sion was taking place (n,=6X1022 cmm3). Here, we simul-taneously fit two lines (HeP and He, lines) in order to fix thetwo free parameters, ~1, and T,, from the line profiles. Al-though the error bar on Ti evaluation remains large, thisprocess gives an interesting information on the Ti behavior.A rough estimate of the time-integrated electron temperatureT, is obtained from a nonstationary calculation of theLyJI-IeP line intensity ratio, assuming an optically thinplasma. The temperature is supposed to grow linearly up to agiven value at which we extract the population, and the in-tensity line ratio calculated by the multicell time-dependentcollisional radiative code TRANSPEC.46 Calculations wereperformed for a fixed ion density ni=5X102 cmm3, and fora temperature increasing from 0 to T, in 300 fs. For laserintensity around 3 X lo* Wlcm2, we infer T, =600 eV fromLyJHeP line ratio with such a calculation. Any changes inthe conditions of the calculations (ni, nonlinear temperatureramp, opacity) should affect the T, evaluation. However, thelarge uncertainty in T, does not strongly affect the line pro-file, which is mainly sensitive to ~1,and Ti . Figure 3 presentsthe Hep [Fig. 3(a)] and He,, [Fig. 3(b)] experimental linePhys. Plasmas, Vol. 2, No. 5, May 1995 Jiang et a/. 1705

profiles (open dots) at 3X 101* W/cm2, and the best fits (solidlines) calculated for T, =600 eV. The inferred electron den-sity and ion temperature are n,=5-7X1022 cmm3 andTi=30-60 eV. While He, measurements and calculations inFig. 3(b) agree quite well, it is more difficult to fit the Hepline profile [Fig. 3(a)]. In particular, no evidence of a centraldip is observed in our data, in contrast to the calculated lineshapes, also shown in Fig. 3(a). It was recently shown thation dynamics could reduce the central dip47 (in the case of ahigh-2 emitter embedded in a hot low-Z perturbing me-dium). However, we believe that, here, the temporal integra-tion effects (variation of the emitting density and densitygradients and eventual shifts in line position due to perturb-ing electrons) contribute to the filling in of the central dipand to the observed HeP profile.The density at which the Li-like emission (dielectronicsatellites) takes place, has been inferred from thels2121-ls2Z line spectra.t6 Our calculations67 show thatthis line spectrum could be strongly affected by non-steady-state population kinetics and also by the non-Maxwelliancharacters of the electron distribution function when pro-


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I * *,a , * ~~*~, - 1 Cl Li-like

- Solid density

,o=t.,.,l1 ot6 10 10Laser ntensity Wcti*)

FIG. 5. Variation f the average lectron ensity nferred rom ine profilesas a functionof laser ntensity. he full do ts (He-likeemission) nd opendots Li-likeemission) ave een btained ithAl targets. hesquare ot sobtainedrom Cl Li-l ike line shape shown n Fig. 6).

duced at intermediate density (n ,3X lOI W/cm2 up to some maxi mumvalue of 4X lo* crne3 which is close to the solid density ofa Li-like Al plasma (&=p,, Z*= 10, and n,=6X 1O23 mm3).For I, above 10s W/cm2, the Li-like density dramaticallydecreases.

These results suggest that the radiative pressure plays avery important role at these laser intensities. Indeed, at lowlaser intensity the gradient scale length is very short, andenergy deposition is realized at near solid density. In theabsence of any ponderomotive pressure, when the intensityincreases, the gradient scale length increases while the den-sity n, at which energy deposition takes place decreases49(n, scales roughly as Z4). Thus, the densities of the emittingHe-like and Li-like radiations are expected to decrease whenIt increases. However, at higher intensities the radiationpressure could eventual ly balance the thermal pressure,maintaining a very steep electron density gradient during theenergy deposition, and producing a deep penetration of thethermal wave in the solid, thus causing the emission to beproduced at near solid density.The behavior of Al Li-like density at intensity larger thanlOI* W/cm2 is interesting. Recent calculations indicate thatshort pulse emission, and thus solid density plasma, can beobtained if the plasma heating is in some optimum range setby target materials.50 Two alternative scenarios can explainthe lower emission density of the Li-like Al K-shell emissionat intensities above 10s W/cm2: (a) the prepulse effect couldbe larger than estimated, so that the pulse would interact withpreformed, lower-density plasma: (b) the plasma is over-heated, that is, after the laser pulse, as it expands and cools,it is still sufficiently hot to emit Li-like K-shell x-ray lines,Both scenarios are also compatible with the observation ofstrong Ly, emission when I,> 10s W/cm2, scaling as 12,indicating a high electron temperature. To decide betweenthe two scenarios, we observed Li-like Cl l ines (C114+) roma sodium chloride (NaCl) target irradiated at 3X lOus W/cm2,The choice of NaCl was dictated by (i) the possibility tomeasure the density of emission from higher atomic numbermaterial that are matched more appropriately to high tem-perature; (ii) the fact that in Li-like Cl and Li-like Al soliddensity plasmas (using solid NaCl and Al targets) the elec-tron densities are the same (6X 102 cme3). Figure 6 presentsthe ls2121-1~~21 Cl line spectrum measured at 3X1018W/cm*. The best fit between experimental and calculationresults indicates that this emission is produced at around6X 1O23 me3 which is the Li-like solid density (Fig. 5). Fur-thermore, no thermal He-like and Li-like emissi ons (keVrange) was observed at 3X 10s W/cm with a Ti target (Z=22). These results (i) demonstrate that there is no prepulsein our experiments, even at the highest intensities; (ii) high-light a very important aspect for the generation of emitti ngsolid density plasma: it is essential to match the emittingtarget to T, for a given isoelectronic sequence. It is alsointeresting to note that the Cl Li-like emission should be veryshort, because it is produced at a very large density.



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1.2 I I . ( I I I , , , , , , , , 1.6 . . ..I... t....., . . . . . . . . ..T--Cl 1.4 e) He, 7Li-iike lines

0.8

0.6

0.04.47 4.48 4.49 4.50 4.51WaLelength (A)

FIG. 6. The profile of Li-like Cl lines (open dots). The NrFZl target isirradiatedby a 3X IO W/cm laser pulse.The best profile fitting &lid line)indicates he emitting density s around6X 10 cm 3, which is solid densityfor Li-like Cl of NaCI.

V. THERMAL TRANSPORTAdditional understanding of the high-intensity regimefor Al targets, can be obtained from~thermal transport mea-surements. Thermal conduction may drive the density atwhich Li-like emission is produced. During the laser pulse,when radiation pressure is effective, thermal conduction canalso play a very importan t role in plasma cooling, and wiIleventually limit the temperature. However , at these high in-tensities the pIasma expansion is another important coolingmechanism that cannot be neglected, particularly when theplasma is overdriven.We use multilayer targets composed of polished Si sub-strate coated with 0.01-S ,um Al layers, and we follow theintensity of Si and Al lines as a function of the Al thickness.Figure 7 presents a spectrum (6.2-7.2 A) recorded with a Sitarget coated with 1000 A Al irradiated at 3.4X10 W/cm2.

5mo- Si HeuI9E

5 lA5id wE 5Wb cc.c-0.L

6.2 6.5 6.7 7.0 7.3Wavelength (i\)

FIG. 7. Spectrum n the 6.2-7.2 8, range recordedwith a Si target coatedwith 1000A Al irradiated at 3.4X10 W/cm*. The different lims are ndi-cated n the figure. The %/He, will disappearwhen the Al layer is 3000 8,thick or a bove at this laser intensity.

130pm Al

El.0 - b) intercombination.$50.8 _00.6 -80.4:

130pm Ali! :20.2 -5 :,,,,

: c) Li-iikel.O-0.8:0.6:0.4: 90.2;

10 100 1000 10000 100000Al Thickness (A)

FIG. 8. The variation of Al line intensity as a function of the Al layerthickness in multilayer ta rget experiment at laser intensities of 2X10W/cm2. The penet rationdepth of thermal energy (temperaturearound 600eV) is about 2000 A. (a) He, line, (b) intercombination ine, and (c) Li-likelines.

We observe Al lines (Hep and He, and Ly,) and Si HeU,Li-like, and K, lines. As the thickness of the Al layer isincreased, the Al line intensity increases up to a saturationlevel, which is the intensity obtained with a thick (130 ,um)target. The depth at which the saturation occurs is usuallyconsidered as a measure of the penetration of the thermalfront. At 2X lOI W/cm2, the very quick saturation of AIHe,line seems to indicate a limited penetration (Cl00 A) of thehigher temperature thermal front [Fig. 3(a)]. However, theintercombination line [Fig. S(b)] and the Li-like satellitesemission [Fig. 8(c)] have a much larger penetration depththan resonance line. These lines (intercombination and satel-lites) give a thermal penetration depth of around 2000 A.Thus, the heating of the Al target by conduction occurswithin the 2000 A layer, where the plasma density remainsnear solid and the temperature is around 600 eV. At suchhigh temperature the He-like ions population should domi-nate, but due to the rapid dielectronic recombination andionization delay, the Li-like populati on is large within the hotplasma. Furthermore, the different behaviors of the reso-nance and intercombination lines seems to indicate that theeffects of autoabsorption are very strong and limit the ob-served emission depth of He, line. The same situation isobserved for Ly, line.This penetration of thermal energy is in qualitativeagreement with simple scaling laws, representing the pen-etration of a heat wave by classical electron thermal conduc-tion in a constant solid density plasma [no hydrodynamicexpansion and assuming a given energy flux at one end).51

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13510o-#EuPtd6E 10234

L

f * * ~~**~*1 s * *,~*~I s + at*fl108wlcm

I

T /

l

130pm Al

I I , , , , , , , , * t , L

10 1000Al thickness A)

100000

FIG. 9. The averagedensity of Li-like AI lines as a function of Al layerthickness at a laser intensity of 1O8W/cm, deduced rom line profilessimilar to that show n n Fig. 5.

During the laser pulse the surface temperature To and theheat front penetration depth X0 are given by the followingexpressions?7-,=3.2X 10-714i9?9,aX0= 1.8x 10-81;9~79,

where To is in hundreds of eV, X0 in cm, I, is the absorbedintensity (in e rg/cm2 s), and 7 is the laser duration (in s).Assuming 1% absorption (I,= lOI W/cm) and r-300 fs,we obtain To=880 eV, in relative agreement with the T,value inferred from the time-dependent Ly&ep ratio, andX0= 1900 A, consistent with the thermal penetration deducedfrom the intercombination line and Li-like lines [Figs. 8(b)and 8(c)]. Recent kinetic simulations of this regime indicatean absorption of around l%, an electron temperature T,around I keV, and a thermal penetration of 2500 A.53However, the hot surface layer will decompress, duringthe cooling after the laser pulse, due to some hydrodynamics,leading to a relatively lower time-integrated densiiy at whichHe-like emission takes place. The same part of Li-like emis-sion is also produced in this decompressing plasma but isdue to the very large Li-like production thickness at soliddensity (larger penetration of the lower-temperature front)the density at which total Li-like emission takes place re-mains close to solid density (Fig. 5). This is illustrated byFig. 9, which presents the average Li-like density (deducedfrom the shape of the Li-like spectrum as previously de-scribed) as a function of the Al thickness at lOI W/cm2.Thus, at very high intensity, the very hot surface layer ofthe Al target will cool on a time scale larger than the pulseduration, leading to x-ray emission during the plasma de-compression. A quantitative understanding of these processeswould require hydrodynamics or kinetics calculationscoupled to atomic physics modeling. Such simulations arepresently in progress.53

6.0 , , , , , ,~, (, , f,, , ., , , , , , ,Vanadium

4SB-iit2 ; 3.0p?

2a:, 1.5c

I2.503 2.506 2.509 2.512Wavelength (A)

FIG. 10. The cord K, spectrumof vanadiumobtained at lase r ntensity of3~ 10 W/cm (obtainedhith Von Hamoscrystal spectrometer perated tseconddiffraction order).

VI. SUPRATHERMAL TRANSPORTComparison between thermal transport measurementsand simple analytic estimates for the heat propagation, aspreviously discussed, require the use of a very low absorp-tion value (consistent with the results of a more elaboratecalculation performed at various laser intensities).53 How-ever, recent experiments with sub-ps lasers at intensitiesaround lOI7 W/cm2 suggest absorption is between IO%-30%of the laser energy and also that an important fraction of thelaser energy is carried by hot electrons.5J.ssHere we used K,yield measurements in order to obtain information on the hotelectron energy content and deposition profile. The K, emis-

sion is recorded with the Von Hamos crystal spectrometerand with PIN diodes (with magnets in front to avoid hotelectron fluorescence). Scandium (50 pm) and titanium (25,um) foils are used as Ross filters with the diodes to obtainthe K, emission of a Vanadium target.56 The difference be-tween the signals obtained with the SC and Ti filters is pre-dominantly due to V K, emission, the continuum emission inthe Ross filter window being a small fraction of the totalsignal (as verified with various 2 targets). The K, yield mea-sured with the diodes can be used to calibrate the crystalspectrometer. the V K, spectrum measured at 3X lo* W/cm*with the crystal spectrometer (second diffraction order) ap-pears in Fig. IO. We observed the K,t and K, doublet (tran-sitions from the K shell to respectively the L, and L, levels),with the expected relative intensities (the K,,/K,, intensityratio should be 0.5). In these conditions the K, yield mea-sured with the Ross diodes is 2X IO- mJ/srd, for 600 mJlaser energy, corresponding to a conversion efficiency of3.3X IO-% srd. The energy in fast electrons is calculatedfrom the energy in K, emission by using a conversion effi-ciency R(T,,) deduced from the K, yield per electron56(which was measured for monoenergetic electrons incidenton thick targets). For these calculations we assume that hotelectrons (spatially integrated) angular distribution is semi-isotropic and that the energy distribution has the followingform:

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E2 10 -0Yiii032~ IOI=iitz

1 bPAl Thickness (A)

FIG. Il. The line intensity ratio of Si K, andAl K, as a function of Al layerthicknessat 2X 10s W/IX?, from which we infer a hot electron emperatureof 25 keV. The absorption f Si K, emissiondue o the Al layer is taken ntoaccount.

f(E)=AE2 exp(-E/kTh),where kT,; is the hot electron temperature. The hot electrontemperature is deduced from the variations of the Al and SiK, intensities as a function of Al thickness (Fig. 11). Fromthese, and using previously published calculation for hotelectron penetration in Al, s9 we found that at 2X 1Ot8W/cm2kT,* is about 25 keV. For vanadium, R(T,) is relatively in:dependent of T,, when 10 keV


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the obtention of around 10 photons in 27~ srd (Fig. 13)down to very short wavelength (3-9 w range).The x-ray yiel d increases as the laser intensity increases.However, it is worthy to note that there are some optimumconditions for the obtention of high-density plasma, since theshortest x-ray pulse is produced for the highe$t emittingplasma density. This highl ights a very important and novelpoint, which is that there are some optimal windows for theproduction of simultaneously the shortest and brightest x-raypulse for a given wavelength. For instance, taking into ac-count the results described in Sec. IV, the simultaneouslybrightest and shortest Li-like lines of the Al target should beproduced at laser intensity of 7-9X lOI W/cm*.VIII. CONCLUSlON

The generation of solid density emitting plasma can beachieved with subpicosecond high contrast laser pulses at anintensity of IO*- lOI W/cm2 by using the radiation pressureto balance the dense slab thermal pressure during the laserheating and maintain a very deep thermal front penetrationinto the solid. Our experiments show that there is an opti-mum condition to produce emission at solid density. At veryhigh laser intensity (larger than 1018W/cm2 for Al), the elec-tron temperature may be very high resulting in an overdrivenAl plasma. Thus, for a given pulse duration and intensity it isessential to match the target to the electron temperature togenerate emitting plasma at solid density. The energy bal-ance, deduced from thermal and suprathermal penetrationdepths, and from K, yield measurements, indicates thatabout 6% of laser energy is coupled to the target at 2X IO*W/cm2 (1% E, in therma electrons at a temperature of 600eV and 5% EL in hot electrons with a hot temperatureT,, =25 keV). Interesting conversion efficiencies are obtainedin various line emissions in these conditions. These resultsalso highlight a very importan t and novel point, whi ch is thatthere is some optimal window for the production of simulta-neously the shortest and brightest x-ray pulse for a givenwavelength (about lo* W/cm2 for Li-like Al emission). Thex-ray yield (and also the energy fraction in hot electrons)increases with the driven laser intensity, but above some la-ser intensity the plasma is overdriven and the thermal radia-tion is produced at a lower-density region, and there is sig-nificant increase of the x-ray pulse duration. At laserintensity around a few times IO* W/cm2, by usingmoderate-Z targets (Ti, for example) and high-Z targets (Ta,for example) we obtained up to 10 photons/Zrr srd per shotin cold K, emission (Ti, narrow bandwidth) and 2X IOphotonsf2r srd per shot in unresolved transition array (Ta,larger bandwidth), which is very encouraging for the appli-cation of ultrafast bright x-ray sources.ACKNOWLEDGMENTS

The authors would like to thank H. P&pin and D. Ums-tadter for many helpful discussions, C. Y. Coti for help indata analysis, C. Y. Chien for laser operation, and C. Siroisand F. Poitras for technical support.This work was supported by the Natural Sciences andEngineering Research Council of Canada, le Fonds pour la

Formation de Chercheurs et IAide i la Recherche and Min-istere de liducation du Quibec. One of the authors (2.Jiang) would like to acknowledge the support from the Chi-nese Academy of Sciences.

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Z. Jiang et al- X-ray spectroscopy of hot solid density plasmas produced by subpicosecond high contrast laser pulses at 10^18-10^19 W/cm^2