Harmonic decomposition to describe the nonlinear evolution of stimulated Brillouin scattering

Abstract

An efficient method to describe the nonlinear evolution of Stimulated Brillouin Scattering in long scale-length plasmas is presented. The method is based on a decomposition of the hydrodynamics variables in long-and short-wavelength components. It makes it possible to describe the selfconsistent coupling between the plasma hydrodynamics, Stimulated Brillouin Scattering, and the generation of harmonics of the excited ion acoustic wave (IAW). This description is benchmarked numerically and proves to be reliable even in the case of an undamped ion acoustic wave. The momentum transferred from the electromagnetic waves to the plasma ions is found to induce a plasma flow which modifies the resonant three wave coupling between the IAW and the light waves.A novel picture of SBS arises, in which both IAW harmonics and flow modification reduce the coherence of SBS by inducing local defects in the density and velocity profiles. The spatial domains of Stimulated Brillouin activity are separated by these defects and are consequently uncorrelated, resulting in a broad and structured spectrum of the scattered light and in a temporally chaotic reflectivity.PACS numbers: 52.38. Bv, 52.35.Mw, 42.65.Es * Permanent address : Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester NY 14623, USA 1The description of parametric instabilities in laser-produced plasmas using simple coupled mode equations for three wave interaction is no longer sufficient whenever the longitudinal plasma waves are driven to large amplitudes. Then the nonlinearities of the longitudinal wave can induce detuning with respect to the three wave resonance. This is one of the reasons usually invoked to explain why these simplified models overestimate the scattering levels of Stimulated Brillouin Scattering (SBS). In this article we concentrate on SBS, which is the process by which the incident laser wave couples to an ion acoustic wave (IAW) togive rise to a scattered transverse wave. The generation of the harmonics due to the IAW fluid-type nonlinearity [1, 2, 3, 4, 5] is already known to be able to reduce significantly the SBS reflectivity when compared with the results involving simply a linearized IAW.However, the previous fluid-type models for SBS in Refs. [1, 2, 3, 4], aimed at taking into account the IAW nonlinearity, were incomplete because they did not properly describe the flow modification [6, 7] caused by the incident transverse wave momentum deposition. All the mentioned models [1, 2, 3, 4, 5] also ignored multi-dimensional effects. On the other hand, kinetic effects associated with particle trapping [8] give also rise to a nonlinear IAW frequency shift and therefore modify the SBS nonlinear behavior.In the present Letter, we reconsider the effect of the IAW nonlinearities on SBS by accounting properly for the flow modification caused by SBS. We first derive approximate equations describing simultaneously the plasma hydrodynamics (i.e. the long wavelength density and flow profiles), SBS, and the harmonic g...

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

“…This guarantees sufficiently good speckle statistics and can be run for upwards of a 100 ps at moderate computational expense. With the help of numerical simulations using the code Harmony [3], we have compared the evolution of this instability to cases where the driving laser is RPP, SSD, and 50% duty cycle STUD pulses with changing speckle patters with each spike, STUD5010×1, and with nonchanging speckle patterns, STUD5010×Inf. Harmony solves two paraxial wave equations for the incident light field with the complex-valued amplitude E 0 (with principal frequency and wavenumber 05010-p. 2 …”

“…(2) for c s u 1,x . The IAW density perturbation n 1 = (U + + U − )/2c s is then used for the 3-wave coupling terms for the paraxial equations for E 0 and E 1 (see [3]). The usual 1st order equation for n 1 for 'weak coupling', when temporal growth is slower than the ion acoustic oscillations, corresponds to the case when the counter-propagating wave U − is not excited.…”

Laser plasma interaction physics on the LIL facility

“…Then, from a direct analysis of the plasma profiles coming from FCI2, the postprocessor Piranah gave us the SBS/SRS spectrum and helped us to validate the hydrodynamic simulation by a direct comparison with the experimental spectrum. On a second step, the SBS evolution and laser propagation can be more correctly described using the code HERA, which describes in 2D/3D the propagation of the incident and backscattered fields, and the evolution of the ion acoustic waves (IAW) in an expanding plasma by means of the decomposition method [12]. Plasma profiles are extracted from FCI2 simulations and given as an input in HERA, which can, with a realistic description of the laser (including the smoothing technique) give us a SBS reflectivity.…”

Modeling of energy transfer between two crossing smoothed laser beams in a plasma with flow profile

“…We have computed the energy transfer with two approaches, namely a time-dependent paraxial code, coupled to fluid equations for the plasma fluid, with the code Harmony [9,10] and with the paraxial geometrical optics approach, based on a stationary CBET model [2,11,12]. The amplification in power, T = P probe,out /P probe,in , of the probe beam at the right-hand-side boundary ("out") with respect to its incident power ("in") is shown in Fig.…”