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A singular perturbation problem for an envelope equation in plasma physics

We report on two-dimensional simulations of parametric instabilities excited by a single, intense (2 × 1016 W cm−2), wavelength-sized laser speckle immersed in a nonuniform CH plasma close to the quarter-critical density. A first set of simulations is performed using a Zakharov-type reduced model. This newly developed simulation tool, which we present in detail, describes Stimulated Raman Scattering (SRS), Two-Plasmon Decay (TPD), Stimulated Brillouin Scattering, and secondary decays involving ion acoustic waves. Because of the high speckle intensity considered, strong electron plasma waves (EPWs) are driven via TPD, whose beating induces fast-collapsing ion cavities. Yet, Zakharov equations are notoriously incapable of modeling collapse arrest due to their neglect of kinetic processes dissipating energy from small-scale EPW packets, thus resulting in nonphysical density evolution. Transit-time damping is such a process, and we show that its inclusion in the reduced model allows for a self-consistent description of all phases of the collapse. The accuracy of our model is checked against a second simulation, performed using a particle-in-cell (PIC) code run under similar conditions. Good qualitative agreement is obtained, particularly in regard to the cavities' dynamics. Still, an excessive SRS reflectivity is predicted by the reduced model, which we ascribe to missing kinetic effects. The influence of electron trapping and heating on the decay of EPWs and saturation of SRS is assessed based on the PIC simulation.

Comprehensive Zakharov-type model for parametric instabilities in the corona of direct-drive targets

Two spherically symmetric versions of a self-similar collapse are investigated within the framework of the Zakharov equations, namely, one relative to a vectorial electric field and the other corresponding to a scalar modeling of the Langmuir field. Singular solutions of both of them depend on a linear time contraction rate Ξ( t ) = V( t * – t ), where t * and V = – Ξ denote, respectively, the collapse time and the constant collapse velocity. We show that under certain conditions, only the scalar model admits self-similar solutions, varying regularly as a function of the control parameter V from the subsonic ( V ≪ 1) to the supersonic ( V ≫ 1) regime.

G. Pelletier

Papers

Self-similar Langmuir collapse at critical dimension

Self-similar regimes of anisotropic collapses

Collapsing solutions of the Zakharov equations with anisotropic contraction rates