Magneto-parametric instabilities in the Crab Nebula: II.

Results of a previous linear analysis of parametric instabilities of electromagnetic waves in a one-fluid cold-plasma model with immobile ions are extended by relaxing the assumption of immobile ions, treating the ion motion in a fully relativistic way, and examining the nonlinear evolution of the magnetoparametric instabilities computed in the linearized analysis. Two types of two-fluid model are considered: electron-proton and electron-positron. A dispersion relation is derived which describes the evolution of mixed electromagnetic and space-charge perturbations to a strong circularly polarized electromagnetic wave propagating along a magnetostatic field in a two-fluid cold plasma, assuming that the perturbations propagate parallel to the driving field. The dispersion relation is shown to result in a twelfth-order polynomial, which is investigated for instabilities. The nonlinear development of these instabilities is analyzed by means of a numerical simulation, the linear and nonlinear analyses are compared, and the results are discussed in the context of the Crab Nebula where applicable. The two-fluid results are then extensively compared with those for the one-fluid model.