Harmonic decomposition to describe the nonlinear evolution of stimulated Brillouin scattering

An efficient method to describe the nonlinear evolution of stimulated Brillouin scattering(SBS) in long scale-length plasmas is presented in the limit of a fluid description. The method is based on the decomposition of the various functions characterizing the plasma into their long- and short-wavelength components. It makes it possible to describe self-consistently the interplay between the plasmahydrodynamics,stimulated Brillouin scattering, and the generation of harmonics of the excited ion acoustic wave(IAW). This description is benchmarked numerically in one and two spatial dimensions [one dimensional (1D), two dimensional (2D)], by comparing the numerical results obtained along this method with those provided by a numerical code in which the decomposition into separate spatial scales is not made. The decomposition method proves to be very efficient in terms of computing time, especially in 2D, and very reliable, even in the extreme case of undamped ion acoustic waves. A novel picture of the SBS nonlinear behavior arises, in which the IAWharmonics generation gives rise to local defects appearing in the density and velocity hydrodynamics profiles. Consequently, SBS develops in various spatial domains which seem to be decorrelated one from each other, so that the backscattered Brillouin light is the sum of various backscatteredwaves generated in several independent spatial domains. It follows that the SBSreflectivity is chaotic in time and the resulting time-averaged value is significantly reduced as compared to the case when the IAWharmonics generation and flow modification are ignored. From the results of extensive numerical simulations carried out in 1D and 2D, we are able to infer the SBSreflectivity scaling law as a function of the plasma parameters and laser intensity, in the limit where the kinetic effects are negligible. It appears that this scaling law can be derived in the limit where the IAWharmonics generation is modeled simply by a nonlinear frequency shift

Kinetic effects in stimulated Brillouin scattering

The role of ion and electron kinetic effects in the nonlinear evolution of stimulated Brillouin scattering (SBS) is investigated by means of particle-in-cell numerical simulations. The simulations were carried out in one and two spatial dimensions (1D and 2D), with a full PIC code, in which both ions and electrons are kinetic. The full PIC simulations are compared with those obtained from a hybrid PIC code (kinetic ions and Boltzmann electrons), making it possible to determine in which limit the electron kinetic effects are important. The simulation geometry corresponds to a coherent laser beam interacting with an expanding plasma slab. In the 1D simulations, the interaction becomes incoherent, as time goes on, in a domain that spatially begins in the plasma region close to the laser light entrance, and that ends within the plasma at a frontier which moves faster than the ion acoustic wave (IAW) velocity. The higher the laser intensity, the faster moves the frontier of this spatial domain. The SBS reflectivity drops at the very moment when this domain fills entirely the plasma. Two regimes have to be distinguished. In the regimes of low laser intensity, strong sub-harmonic generation of the excited IAW is observed to take place in this moving spatial domain, so that the SBS reflectivity drop is interpreted as being due to sub-harmonic generation. In the opposite regime of high laser intensity, there is no evidence of strong sub-harmonic generation, whereas a strong ion heating is observed, so that the reflectivity drop is interpreted as being due to enhanced ion damping. In the 1D simulations the electron kinetic effects are found to be able to smooth temporally the SBS reflectivity, although the overall picture remains the same when the electrons are taken as a Boltzmann fluid. In the 2D simulations, the SBS reflectivity is observed to drop rapidly in time because of the efficient nonlinear Landau damping on the ions, as previously reported by Cohen et al. [1]. In these 2D simulations, the electron kinetic effects are found to play a negligible role as compared with the ion kinetic effects

Elusive contribution of the experimental surface molecular electrostatic potential and promolecule approximation in the empirical estimate of the crystal density

The aim of this study is to probe the crystal density (Dc) description in terms of pertinent molecular characteristics and properties. In this purpose, the electrostatic potential was derived from available experimental electron density multipole parameters of molecular compounds with different Dc magnitudes. The surface electrostatic potential has been analyzed through the positive and negative statistical variances. The surface of the molecule is here corresponding to particular isodensity values according to Bader’s topological theory. Following the successful Politzer’s method based on quantum mechanics calculations to empirically describe macroscopic properties, the crystal density was regressed on the molecular density and the surface electrostatic potential variance. This latter appears to be a poor statistical descriptor of the crystal density when the experimentally derived electrostatic potential is used and it does not significantly improve the fit of Dc to molecular density alone. Compared to Politzer’s approach based on gas phase isolated molecules, the experimental electrostatic potential is biased by the interactions in the crystal lattice. As an alternative to other sophisticated methods, the promolecule isodensity surface offers a quite useful and straightforward way to define the molecular volumes. The reported description of the crystal density for a set of 50 molecules using the promolecule approach yields satisfactory results

Modeling parametric scattering instabilities in large-scale expanding plasmas

We present results from two-dimensional simulations of long scale-length laser-plasma interaction experiments performed at LULI. With the goal of predictive modeling of such experiments with our code Harmony2D, we take into account realistic plasma density and velocity profiles, the propagation of the laser light beam and the scattered light, as well as the coupling with the ion acoustic waves in order to describe Stimulated Brillouin Scattering (SBS). Laser pulse shaping is taken into account to follow the evolution of the SBS reflectivity as close as possible to the experiment. The light reflectivity is analyzed by distinguishing the backscattered light confined in the solid angle defined by the aperture of the incident light beam and the scattered light outside this cone. As in the experiment, it is observed that the aperture of the scattered light tends to increase with the mean intensity of the RPP-smoothed laser beam. A further common feature between simulations and experiments is the observed localization of the SBS-driven ion acoustic waves (IAW) in the front part of the target (with respect to the incoming laser beam)

Absolute parametric instabilities in inhomogeneous plasmas

The excitation of absolute instabilities in three-wave parametric couplin g processes in inhomogeneous plasmas has been studied analytically . A detailed examination of the full fourth-order set of differential equations describing such processes in infinite media confirms the WKB-criterion that absolute instabilities arise only if d(&#931;<SUB>i</SUB>k<SUB>i</SUB>)/dx=0. A model calculation using the WKB-approximation has also been carried out to study the effects of finite plasma extent and pump depletion; conditions for the excitation of absolute instabilities in this case have also been obtained

Simulations of drastically reduced SBS with laser pulses composed of a Spike Train of Uneven Duration and Delay (STUD pulses)

By comparing the impact of established laser smoothing techniques like Random Phase Plates (RPP) and Smoothing by Spectral Dispersion (SSD) to the concept of “Spike Trains of Uneven Duration and Delay” (STUD pulses) on the amplification of parametric instabilities in laser-produced plasmas, we show with the help of numerical simulations, that STUD pulses can drastically reduce instability growth by orders of magnitude. The simulation results, obtained with the code Harmony in a nonuniformly flowing mm-size plasma for the Stimulated Brillouin Scattering (SBS) instability, show that the efficiency of the STUD pulse technique is due to the fact that successive re-amplification in space and time of parametrically excited plasma waves inside laser hot spots is minimized. An overall mean fluctuation level of ion acoustic waves at low amplitude is established because of the frequent change of the speckle pattern in successive spikes. This level stays orders of magnitude below the levels of ion acoustic waves excited in hot spots of RPP and SSD laser beams