Influence of an ambient magnetic field on the nonlinear modulational stability of circularly polarized electromagnetic pulses in a two-component neutral plasma

Abstract

This paper extends our previous results (Kates & Kaup 1989) on the nonlinear modulational stability properties of plasma electromagnetic pulses to include the presence of an ambient magnetic field B0 parallel to the direction of propagation. As before, the pulse is assumed to be sufficiently strong to accelerate particles to weakly, but not fully, relativistic velocities. The positive component may consist of either positrons or singly charged ions, and no specific assumptions or approximations are made concerning the mass ratio of the components (previous work assumed a positron—electron plasma). The plasma is assumed to be fully ionized. The effects of a finite temperature are included for generality. Using singular perturbations, we derive approximate solutions that describe the evolution of a circularly polarized pulse. The envelope is shown to evolve over long time scales according to the cubic nonlinear Schrödinger (NLS) equation. Relativistic corrections and pon-deromotive forces both contribute terms cubic in the amplitude. (In contrast with the case studied in Kates & Kaup (1989), harmonic effects vanish identically here because of circular polarization.) A positron-electron plasma without magnetic fields was shown in our previous paper to be modulationally stable, except in the case of finite temperature, where modulational instability is possible near the plasma frequency ωp. Here it is shown that, even for a cold plasma, the presence of an ambient magnetic field makes a decisive difference: modulational instability can arise within a broad range of frequencies and values of B0, in particular for a pure positron-electron plasma. For given B0 and polarization we demonstrate the existence of critical frequencies for the onset of modulational instability. This result has important consequences for observations of pulsar micropulses and possible technological applications.