Stability properties of a thin relativistic beam propagation in a magnetized plasma

Abstract

A self-consistent nonlinear hydrodynamic theory is presented of the propagation of a long and thin relativistic electron beam through a plasma that is relatively strongly magnetized, $|\Omega_e|\sim\omega_{pe}$ and whose density is much bigger than that of the beam. In the regime when the parallel phase velocity in the comoving frame is much smaller than the thermal speed and the beam electrons are thermalized, a stationary solution for the beam is found when the electron motion in the transverse direction is negligibile and the transverse localization comes from the nonlinearity of its 3-D adiabatic expansion. Conversely, when the parallel phase velocity is sufficiently large to prevent the heat convection along the magnetic field, a helicoidally shaped stationary beam is found whose transverse profile is determined from a nonlinear dispersion relation and depends on the transverse size of the beam and its pitch angle.