Non-Linear Interaction Mechanisms of an Ultra-lntense Laser Pulse with an Underdense Plasma

Transcription

1 J. Plasma Fusin Res. SRS, Yl2 (1999) Nn-Linear nteractin Mechanisms f an Ultra-lntense Laser Pulse with an Underdense Plasma ADAM Jean C., HRON Anne, LAVAL Guy and MORA Patrick Centre de Physique Thdrique, CNRS-cle Plytechnique, Palaiseau, France (Received: 26 January 1999 / Accepted: 11 August 1999) Abstract The interactin f an intense beam (1Ore < / < l020wcm2; with mderately dense plasmas has been investigated by using theretical analysis as well as numerical simulatins. The parametric instabilities f a plane intense light wave have been theretically studied in this strngly cupled case, with a particular emphasis n filamentatin and the generalizatin f the TPD instability. Then these results are used t discuss numerical simulatins. A 2D PC cde is used t study the prpagatin f picsecnd pulses. The theretical cnclusins may be cmpared with present experimental results. These experiments shw that the plasma strngly absrbs the intense radiatin fr densities where it wuld be expected t be transparent r reflective via Raman instabilities. Mrever, very high electrn temperatures are achieved and multi-mev particles are generated. These behavirs result frm the strng nn-linear interactin f the radiatin with the plasma. Keywrds: relativistic plasma, laser-plasma interactin, absrptin, MeV electrns 1. lntrductin The chirped pulse amplificatin f laser light has pened a new field f investigatin fr plasma physicists. Laser peak pwers have reached up t ne petawatt. By fcusing this light beam, intensities larger than l020wcm2 are nw available. n this intensity range, the electrns are brught t relativistic energies by the mere scillatin in the laser electric field. Cnsequently, the physics f laser plasma interactin is strngly mdified. The electrn mass depends n the light intensity and the usual picture f wave prpagatin des nt apply any mre t this relativistic plasma. A large number f ultra-high intensity lasers have been built t generate high energy particles fr several purpses. Amng them, the fast ignitin f fusin targets raised great hpes by lwering the laser required energy t btain the fuel burning and a thermnuclear gain. The fast ignitin principle relies upn the C rre s pndin g aut h r' s e - mail : c p ht. p ly t e c hnique Jr assumptin that the scillating electrns can be cnverted int a high energy particle beam which will heat the dense cre f a cmpressed pellet. Preliminary experiments and numerical simulatins shw that the cnversin des ccur when the ultra-intense laser beam interacts with a very verdense plasma. Hwever, several physics issues have t be examined befre being able t make a realistic assessment f the methd. Amng them, the channeling f the ultra-intense pulse thrugh the underdense crna is challenging. The shrt intense pulse has t prpagate thrugh the lng crnal plasma withut deviatin, filamentatin and absrptin. The current slutin implies that a lng intense prepulse will drill a channel in the crnal plasma. Once this channel frmed, the ultra-intense pulse will reach safely the dense cre. n rder t define the desirable parameters f by The Japan Sciety f Plasma Science and Nuclear Fusin Research t9

2 Adam J.C. er al., Nn-Linear nteractin Mechanisms f an Ultra-ntense Laser Pulse with an Underdense Plasma residual plasma inside the channel, it is necessary t knw hw the ultra-intense pulse will interact with it. This is the purpse f several experiments in which an ultra-intense pulse interacts with a prefrmed underdense r slightly verdense plasma. n these experiments, anmalus absrptin has been bserved [] as well as a strng reductin f the transmissin thrugh mderately underdense plasmas. Fr the same parameters, high energy electrns have been detected. n this paper, the interactin f an ultra-intense pm laser pulse with mderately dense plasmas will be investigated by using mainly 2D numerical particle simulatins. The transmissin, reflectin and absrptin f the pulse will be studied fr densities in the range nl n" = and fr intensities frm 1016 t 1020W/ cm2. The results will then be discussed in the light f theretical calculatins, mainly abut the parametric instabilities in the strngly relativistic regime. t will be shwn that the interactin is strngly nn-linear and may be understd by assuming that the laser plasma interactin leads t a bulk electrn heating t relativistic energies. Calculatins f parametric instabilities in such ht plasma will be necessary in rder t understand the numerical results. been perfrmed with 0.O5 < nln" < 0.4 and 1016 < 1, < 1020W/cm2 where f. is the maximum intensity f the pulse. n this range f intensities, the relativistic mass factr 7f an electrn scillating in the laser field varies frm 1.01 t 6.1 fr a pm radiatin. The transmissin and the reflectin cefficients were btained by cmputing the utging flux f the Pynting vectr thrugh the simulatin bx bundaries and the absrptin cefficient was given by the verall energy flux balance. One run lasts 15 hurs n the 64 prcessrs f a T3. Figures 1-a,b,c are plts f the transmissin, s^(a) r " a ^ t i-t a (w 1cm27 2. Numerical Simulatins n the numerical simulatins, the electrmagnetic field is prpagated by integrating the full Maxwell equatins. The electrmagnetic wave is linearly plarized with the electric field in the plane f incidence. n rder t simulate a fcused beam, the intensity prfile is assumed t be gaussian with the same?' sz 0.1 a te 5,l,e full width at half maximum (FWHM) fr all cases, where,l,s is the vacuum wavelength. Fr the plasma, 2D particle-in-cell simulatins are used [2-3]. The simulatin bx initially cntains a plasma slab, with sharp edges nrmal t the directin f incidence f the laser. The slab width is and in the transverse directin, nrmal t the directin f incidence, the simulatin bx is 73.l,s wide. There are 74 millin particles and 8.4 millin grid pints. The bundary cnditins are peridic in the transverse directin. n rder t avid interactin between the simulatin and its peridic images, the particles are cled as they crss the transverse bundary. n frnt f the plasma slab, the length f the vacuum regin is 35 2eThe electrn/in mass rati is l/1836 and the initial temperature is KeV. The tempral pulse shape is apprximately gaussian with a full width at half maximum LT = l2oo rrlq- 1 ftcll. A series f simulatins have ,016 1'0rt J0r6 fre ia iu r (w/cms) (n /cmz) YO Fig. 1 a) Transmissin cefficient as a functin f flux fr three different densities f plasma ll) n/n. = 0.1,* nln.=0.2,o nln.=9.4,y nln"= 0.4and fixed ins), b) Reflectin cefficient as a functin f flux fr the same parameters as figure 1a), c) Absrptin cefficient as a functin f flux fr the same parameters as figure 1a). 0 (c) 20

3 Adam J.C. er a/., Nn-Linear nteractin Mechanisms f an Ultra-ntense Laser Pulse with an Underdense plasma reflectin and absrptin cefficients as a functin flm fr three different density rutis nlnc. These results shw that the transmissin initially decreases with 1., becming very lw at 1m - 10reWcm2 fr nln. = 0.2 r nln" = Q.4 and increasing again fr 1, > l0rewcm2, t reach 30V fr 1* = l02wcm2. The rather large transmissin at very high intensities culd result frm the actin f the pndermtive frce which creates a hllw density u channel where the laser prpagates withut interactin with the plasma. n rder t check this interpretatin, simulatins have been perfrmed with fixed ins fr 1. > l01ewcm2. t is seen, n figure l-a, that there is n significant mdificatin f the transmissin in this case n/ \" Cnsequently, this simple interpretatin des nt seem t apply. nstead, it suggests that the lw transmissin results frm an interactin taking place in the frnt f the pulse where the electrns have nt yet been evacuated. The reflectin cefficient reaches 0.25 fr fluxes in the l0r7 Wcm2 range and falls dwn fr higher fluxes t negligible values fr 1, = l020wcm2. The behavir f the reflectin cefficient fr n/n" = 0.4 is enlightening: fr 1, < l017wcm2, the reflectin cefficient is much smaller than fr lwer densities, as it is expected since backward Raman instabilities are frbidden. At higher intensities, relativistic effects allw again Raman instabilities [4] and the reflectin cefficient behaves in the same way as fr lwer densities. The absrptin cefficient brings ut the surprisingly strng energy transfer between the electrmagnetic wave and the plasma in the relativistic regime 1, > l0l8wcm2, whereas, at lwer fluxes and in this density range, the absrptin is very lw, as predicted frm the linear prpagatin thery. The anmalus absrptin is nt mdified if the ins are fixed, at least fr 1, > l018wcm2. t rules ut the radial acceleratin f ins by the pndermtive ptential as the rigin f the anmalus absrptin. The main purpse f this wrk is t try t understand this relativistic induced pacity. Figures 2-a,b,c are plts f the transmissin, reflectin and absrptin cefficients as a functin f n/ n" fr three different values f 1, in the relativistic regime. The very fast grwth f the absrptin cefficient with density excludes a direct acceleratin f electrns by the laser since it wuld lead t a linear grwth f the absrptin cefficient with the density. t implies that the heating prcess is very sensitive t the plasma density. t als shws that experimental results t. d.4! v. _B trg n/n. n/n Fig. 2 a) Transmissin cefficient as a functin f density f plasma fr tw different fluxes (! Wcm'z, * 1020Wcm'?), b) Reflectin cefficient as a functin f density f plasma fr the same parameters as figure 2a), c) Absrptin cefficient as a functin f density f plasma fr the same parameters as figure 2a). can be widely scattered if the plasma density is nt cntrlled with a sufficient precisin. The imprtance f transverse effects is clear n figure 3 where the distributin f the laser intensity has been pltted at a given time. As already nticed [5], it is seen that strng self-fcusing may ccur and filamentatin takes place even fr such narrw beams. (c) 2l

4 Adam J.C. et cl., Nn-Linear nteractin Mechanisms f an Ultra-ntense Laser Pulse with an Underdense Plasma These transverse prcesses have t be taken int accunt in any explanatin f the strng absrptin since ld simulatins exhibit a much higher transparency [6]. F 44.?0. s 40. p0.! {1{3 Fig. 3 lsvalues f the flux f the Pynting vectr acrss the y directin in dimensinless units lr nln. = 0.2 and 1021&/cm2 at tw different times a) 500fs, b) 840fs. lna 3. Parametric nstabilities n the relativistic regime, parametric instabilities cannt be studied by using the resnant weak cupling apprximatin. The laser wave prpagatin is nn-linear and simple slutins are available nly fr circular plarizatin. n such a case and fr a cld plasma, the stability f the slutin with respect t lngitudinal perturbatin has been thrughly investigated [4]. n the relativistic regime and fr 0.O5 < nln" < 0.4, the usual frward and backward branches f the Raman stimulated scattering merge int a mixed instability in which the Stkes and the anti-stkes waves are strngly cupled. The grwth rate peaks fr mdes such that the Stkes cmpnent is backscattered. Mrever the grwth rate is very high as indicated n figure 4. n this figure, the maximum grwth rate is pltted as a functin f the intensity as well as the crrespnding plasma wave number /<, its frequency rat and its phase velcity v6. The grwth rates and frequency unit is the laser pulsatin ab, the wavenumber unit is the laser light wavenumber in vacuum fte and the phase velcity unit is the velcity f light c. n these units, the frequency f the Stkes cmpnent is l-ar and its wavenumber is 1-ft. Fr intensities larger than l01e Wcm2, it is seen that ft = i 15 i.? ts 0.1 a i 0. J01. lr. iz r(w/cm'),0.5 F n f. 0.4.!.r,(u / cmz). l0t6 l0rr lr0r5 lte (f,/cm") Fig. 4 Slutins f the cld dispersin relatin as a functin f flux fr three different densities f plasma (l) nln. = 9.1, * nln.= 0.2, A, nln. = 0.4), a) the maximum f the grwth rate, b) the wave number crrespnding t the maximum grmh rate, c) the real part f the frequency crrespnding t the maximum grwth rate, d) the phase velcity crrespnding t the maximum grwth rate. 22

5 Adam J.C. et a/., Nn-Linear nteractin Mechanisms f an Ultra-ntense Laser Pulse with an Underdense Plasma 2 while a and v becme very small. These features are thse f the backward Raman instability in a very lw density plasma. t can be understd by nticing that the relativistic increase f the electrn mass brings dwn the effective plasma frequency. Hwever and n the cntrary, the grwth rate is very high since it peaks at 0.4 fr nln"- O.4 and reaches 0.26 fr n/n" = tit values are larger than the effective plasma frequency a4l 7. t implies that the Raman instability is in the direct Cmptn regime. t is als seen that the absrptin cefficient fllws nicely the grwth rate dependence n the intensity. Cnsequently, it is natural t link the bserved large absrptin t the parametric instability in the relativistic regime. 4. lectrn Heating f the reflectivity is nw cnsidered, the picture des nt fit s well the results, since the instability is essentially a stimulated backward scattering which shuld generate a strng reflectin. n rder t explain this discrepancy, the very fast grwth f the instability and the very lw phase velcity f the plasma wave have t be taken int accunt. These features shw that, after a few femtsecnds, wavebreaking will ccur fr the lngitudinal perturbatin, leading t an efficient lngitudinal heating f the electrns. This heating shuld stabilize the backward mdes with lw phase velcity. Such stabilizatin f the backward Raman scattering has already been bserved in experiments [7], where the bursting f the reflected light was interpreted as signs f the wavebreaking fr the lngitudinal perturbatin. n rder t settle this pint in a mre quantitative way, the parametric instability dispersin equatin has been established fr lngitudinally heated plasmas [4] and slved numerically. The unperturbed electrn distributin functin in mmentum space is assumed t be cld in the transverse directin. As regards the lngitudinal velcity dependence, the distributin functin is the sum f a dirac functin and f a gaussian with a zer average mmentum and a rms mmentum d in mc units, which is suppsed t take int accunt the frmatin f ht tail. t has been fund that a ht tail des nt mdify the instability, even when it cntains 20V f the particles. Cnsequently, nly distributins with 1007 ht particles will be cnsidered here. Figure 5 shws that fr an intensity = 3 x l0r8w cm2 and nln" - 0.2, the maximum grwth rate is nly l - r-1 A a tt ' 33 O,1.8 - r.6 H r.4 3 r.a ^ a "' (b) qp a- (w/cm2) (rvtcme) x l. t 1. u t 0.4 8! ^9s ^ ^ na s ata" a g 02 3.e 3u.. (tylcm2) e$t /cm?) Fig. 5 Slutin f the warm dispersin relatin as a functin f flux fr nln. = 0.2 and different values f the <thermal> spread(46=0.,*6=1.,!6=2..o6=4.),a)themaximumfthegrwthrate,b)thewavenumber crrespnding t the maximum grwth rate, c) the real part f the frequency crrespnding t the maximum grwth rate, d) the phase velcity crrespnding t the maximum grwth rate. z3

6 Adam J.C. et al., Nn-Linear nteractin Mechanisms f an Ultra-ntense Laser Pulse with an Underdense Plasma 0.06 fr 6= and there is n mre backscattering. Fr larger 6, the grwth rate decreases and it becmes negligible fr 6 > 3. t is nticed that, fr 6 = the phase velcity is in c units, which implies that the lngitudinal wave is strngly damped. n this case and fr htter plasmas, the laser pulse is scattered and absrbed by a strng kinetic stimulated Cmptn scattering with a large frequency shift. At high intensity, the backscattering is ruled ut and the grwth rate becmes negligible fr much higher values f 6. This is cnfirmed by the PC simulatins which shw that the average electrn energy, in the pulse, is 3 MeV fr 1= 3 x 10r8Wcm2, while it peaks at 20 MeV fr 1= 1020W cmz. 5. Transverse ffects Transverse effects have been studied theretically in the cld plasma case [8]. t has been shwn that the instability features f the ld case extends in the transverse directin, s that instabilities with large transverse mde numbers are expected t be excited at the same level as the purely lngitudinal mdes. Hwever, the grwth rate peaks always fr purely lngitudinal wavenumbers. n the simulatins, these blique mdes are fund t have amplitudes lwer than the parallel nes but they are respnsible fr the bserved transverse heating which is slightly smaller than in the lngitudinal directin. The absrptin is much larger in 2D simulatins than in ld siniulatins. This increase cannt be explained nly by the transverse heating. The blique mdes culd have als an efficient effect n the lngitudinal heating by destrying the distributin functin plateau which wuld be frmed in a shrt time with purely ld lngitudinal mdes, avidine then a saturatin f the heatine mechanism and allwing t reach very high average energies. 6. Cnclusins Numerical simulatins have shwn that mderately dense plasmas absrb efficiently shrt pulses f laser light in the relativistic regime. This anmalus absrptin seems t be linked t the excitatin f strng Raman-type parametric instabilities. These instabilities lead t a bulk heating f the electrns which stabilizes the backward scattering instability and leaves stimulated Cmptn scattering instabilities t further heat the electrns t relativistic energies. The intensity, the pulse duratin and the plasma density have been chsen in ranges crrespnding t present experiments and fitting the current capacity f the numerical simulatins. t is nt yet pssible t draw cnclusins fr the cnditins f fast ignitin. Hwever, it indicates already that the main pulse may lse energy if the prefrmed channel still cntains a lw density plasma. References [1] J.A. Cbble et al.,phys. Plasmas 4, 3006 (1996). [2] A.B. Langdn, B. Lasinski, in Methds f Cmputatinal Physics (Academic Press, New Yrk, 1976) Vl.9, p.327. [3] J.C. Adam et al., J. f Cmput. Phys. 47, 2 (1982). [4] S. Guerin et al.,phys. Plasmas 2,2807 (1995). l5l A. Pukhv and J. Meyer-ter-Vehn, Phys. Rev. Lett. 76,3975 (1996). [6] J.C. Adam et c/., Phys. Rev. Lett. 78,4765 (1997). t7l C.A. Cverdale et al., Phys. Rev. Lett. 74, 4659 (1995); A. Mdena et al., Nature,377, 606 (1995). t8l B. Quesnel et al.,phys. Rev. Lett. 78,2132 (1997). 24