Stimulated Brillouin Backscattering for Laser-Plasma Interaction in the Strong Coupling Regime

Stimulated Brillouin Backscattering For Laser-Plasma Interaction In The Strong Coupling Regime S. Weber1;2;3;?, C. Riconda1;2, V.T. Tikhonchuk1 1Centre Lasers Intenses et Applications, UMR 5107 CNRS-Université Bordeaux 1-CEA, Université Bordeaux 1, 33405 Talence, France 2Laboratoire pour l'Utilisation Lasers Intenses/Physique Atomique des Plasmas Denses, UMR 7605 CNRS-CEA-Ecole Polytechnique-Université Paris VI, Université Paris VI, 75252 Paris, France 3 Centre de Physique Théorique, UMR 7644 CNRS-Ecole Polytechnique, Ecole Polytechnique, 91128 Palaiseau, France ? email: [email protected] The strong coupling (sc) regime of stimulated Brillouin backscattering (SBS) is characterized by relatively high laser intensities and low electron temperatures. In this regime of laser plasma interaction (LPI) the pump wave determines the properties of the electrostatic wave. The present contribution intends to present several aspects of this regime. Up to now sc-SBS has received little attention due to the fact that research on LPI was dominated by standard inertial confinement fusion (ICF) relevant parameters. However, sc-SBS has several interesting applications and might also open up new approaches to ICF. One application is plasma-based optical parametric amplification (POPA) which allows for the creation of short and intense laser pulses. POPA has several advantages with respect to other approaches, such as Raman-based amplification, and overcomes damage threshold limitations of standard OPA using optical materials. Recent experiments are approaching the sc-regime even for short laser wavelengths. Simula- tions operating above the quarter-critical density have shown that new modes (e.g. KEENs, electron- acoustic modes, solitons etc.) can be excited which couple to the usual plasma modes and provide new decay channels for SBS. 1. Introduction Stimulated Brillouin scattering plays an important role in laser-plasma interaction in general and ICF in particular [1]. It has been studied in a regime of relatively low laser intensities for a long time. At low intensities SBS is characterized by an eigenmode of the plasma. However, interesting new effects arise if one operates in the so-called strong coupling regime (see following section). This sc-SBS regime is very rich in physics phenomena, some of which might have application in laser-plasma interaction in general and some also in ICF-schemes. In the time of CO2-lasers this regime was already attained [2] due to the much longer laser wavelength of λo 10 µm. The determining parameter for 2 ≈ most effects is Iλo and as present-day laser systems operate with wavelengths in general one order of magnitude smaller, λo 1 µm, much higher laser intensities are required, which, however, have become available.≈ 2. The Strong Coupling Regime The sc-SBS regime [3] is characterized by low plasma temperatures, in general a few hundred electronvolts, and high laser intensities, albeit non-relativistic. In this regime the plasma response is no longer an eigenmode but a quasimode characterized by 1 + ip3 ! = (k2v2 !2 =! )1=3: (1) sc 2 o osc pi o One enters this regime provided 2 vosc 2 > 4kocs!o=!pi: (2) ve Here ko and !o are wavevector and frequency of the laser light. In the above two formulae the functional dependencies of the relevant parameters, !pi pni, vosc pIo and v pT , allow to access this regime by adjusting density n ,∼electron temp∼erature T e ∼ e e e and laser intensity Io. Under these conditions the Brillouin instability has a much faster growth rate and a strongly modifies frequency of the excited ion-acoustic wave. In all the subsequent results presented the plasma density was chosen above the quarter- critical density in order to exclude Raman backscattering and therefore have the possibility to study \pure" Brillouin effects. In a recent series of papers [4; 5; 6] the strong coupling SBS-regime has been explored in some detail using 1D and 2D full-PIC simulations. The simulations performed indicate a series of new effects which were unknown up to now in the context of SBS and non- relativistic intensities: 1. The SBS-reflectivity in the sc-regime exhibits a bursty, quasi-regular structure which is the precursor state for the subsequent phenomena occurring. The final state is a quasi-stationary, low-level saturated reflectivity. 2. The appearance of solitons in the wake of a relativistically strong and ultrashort laser pulse propagating in a plasma is a well-known phenomena. The present work has shown that solitons can also be created with the help of SBS for incident laser intensities which are not relativistic. 3. The creation of solitons, whether transient or stationary, are accompagnied by strong local density depletions (cavities). 4. At the same time energy is transferred to the plasma: the electrons are heated and the ions are accelerated. 5. The result is a very irregular plasma with strong density fluctuations. Such a plasma induces a loss of spatial and temporal coherence. 6. Finally, the effect of bursty reflectivity was exploited in a controlled way in order to amplify short laser pulses in a very efficient way. The interest generated by these numerical experiments has induced the experimental com- munity to perform a series of experiments on the sc-SBS (section 6). 3. Bursty Reflectivity, Saturation, Formation Of Solitons, Heating And Cavi- tation In the PIC-simulations performed [4; 5] the intensity was of the order of 1016 Wµm2=cm2, the plasma density was set to 0:3 nc and a realistic mass ratio of mi=me = 1836 was used. The most striking feature of the sc-SBS regime is the behaviour of the backscattered intensity: the reflectivity exhibits a spiky evolution in time, composed of short pulse with intensities of several tens of the incident laser intensity (see Fig. 1). It was shown [6] that above a certain threshold these high-intensiy pulses inside the plasma invoke a new 3-wave coupling decay process where a transverse electromagnetic wave is decomposed into a stationary transverse mode with zero group velocity and an electrostatic mode. Figure 1: Bursty reflectivity in the strong coupling regime: at a given location inside the plasma slab (red) and in vacuum in front of the plasma slab (blue). The stationary transverse mode develops into a transverse soliton [7] associated with a strong plasma depletion, a cavity. The soliton- and cavity-formation process go along with a strong heating of the electrons and acceleration of the ions. It was found hat in one dimension the so created solitons are stationary structures which survive for tens of picoseconds. The main difference between 1D and 2D is the dynamics of the soliton. Whereas solitons are stable in 1D they are only transient in 2D [6]. However, in both cases the plasma heating, the saturation of the reflectivity and the cavitation process are present. The limited life-time of the solitons implies that the heating of the plasma is equally limited in time and that in due course laser transmission fully recovers. Figure 2 displays the transversally averaged reflectivity and transmission of the laser in the two- dimensional case. The initially spatially coherent laser beams breaks up and temporal coherence is lost due to IAW-perturbations. Figure 3 gives a corresponding 3D view of the reflectivity and its clear saturation everywhere in the plasma at late times. The saturation of the reflectivity has also important consequences for standard ICF- applications as in single speckles the intensity might well reach the values used in the numerical simulations and therefore help to contribute to the ongoing discrepancy concerning the reflectivity in experiments, simulation and analytical analysis. 4. The Issue of Laser Beam Smoothing And Coherence Loss Figure 4 shows the how the plasma evolves from a cavity-dominated phase to a very irregular state with the remnants of the cavities still visible. An electromagnetic plane wave passing through such a plasma is submitted to a strong loss of spatial and temporal coherence. This is due to the plasma density varying strongly across the computational volume on a characteristic length scale of a few times the laser wavelength and the plasma per- turbation which have their origin in the IAW-activity generated by the Brillouin process 2.5 2 1.5 o I/I 1 0.5 0 0 2000 4000 6000 8000 10000 12000 14000 t [ω−1] o Figure 2: Reflectivity (blue) and transmission (red) averaged over the transverse direction of the laser. The appearnce of the \white" areas means that in the transverse direction the elctro- magnetic wave no longer oscillates in phase due to the strong plasma density variations. Figure 3: Bird's eye view of the spatio-temporal evolution of the backscattered intensity. Figure 4: The appearance of cavities and the final strongly perturbed state of the plasma and their effect on a plane electromagnetic wave traversing it. evolve on a typical time scale of a few picoseconds. In summary, such a plasma induces a smoothing of the laser beam. Basically this is just another example of self-induced smoothing of a laser beam as was shown already to exist for much lower intensities below the self-focusing threshold [8]. The same happens here just in a more violent way. The standard ICF-schemes propose a limit to the intensity of the order of 1015 Wµm2=cm2. This has its origin in the fact that the reflectivity was expected to be too high and correspondingly the energy losses unacceptable. However, these analysis were done with- out taking proper account of kinetic effects. Only the advent of multi-dimensional and large-scale full-PIC simulations allowed to correct erroneous conceptions concerning the reflectivity at higher intensities.

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