Landau-fluid simulation of laser filamentation

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Abstract
The Landau‐fluid model is a recently introduced fluid‐moment closure scheme [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)] that was designed to include kinetic dissipative effects like Landau damping in fluid calculations. The fluid‐moment hierarchy is terminated by assuming linear relationships among the retained moments in Fourier‐transform space, with coefficients determined by matching the plasma response to that obtained from a kinetic analysis. This paper generalizes the technique to the full range of ion and electron collisionality and applies it to a new fluid simulation code constructed to study laser filamentation in underdense plasmas [Berger et al., Phys. Fluids B 5, 2243 (1993)]. By matching the ion‐acoustic complex frequency derived from the fluid model with that predicted by collisional, Fokker–Planck, and kinetic analyses, the specific heat ratio, thermal conductivity coefficient, and viscosity coefficient for ions and the thermal conductivity coefficient for electrons are determined as functions of the wave number k. For frequencies much less than the pump frequency this leads to a fourth‐order polynomial dispersion relation whose spectrum includes damped ion‐acoustic waves as well as filamentation modes whose stability depends on the pump strength. An analytic instability threshold condition on the laser intensity is derived from which the relative importance of ponderomotive and thermal drives can be assessed. Expressions for the linear susceptibilities in the presence of a finite‐amplitude pump are also given, which might prove useful for understanding spectral linewidths for Thomson scattering.