Theory of modulational interactions in collisional plasmas

The modulational instability development of Langmuir and electromagnetic waves is reviewed in highly collisional plasmas where the characteristic frequency Ω of the modulated perturbations is much less than v eff , the effective electron collision frequency. All calculations are based on Braginskii's system of hydrodynamic equations in collision-dominated plasmas and use a simple and universal formalism including new methods developed for description of the modulational effects in arbitrary media. It is demonstrated that the modulational instability for the situation considered is mostly determined by collisional effects (differential Joule heating nonlinearity), in contrast to the wellknown modulational instability in collisionless plasmas (where ponderomotive force nonlinearity dominates). Rates and thresholds of the instabilities are found in various limits. Coupled nonlinear Langmuir and sound waves are presented. Theory taking into account combined effect of the differential Joule heating, ponderomotive force and relativistic electron mass variation on the instability of electromagnetic waves is presented. Effects of magnetic fields are briefly discussed.