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

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

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