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

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. Such situation is encountered when the gyro-frequency is comparable to the plasma frequency. In addition, it is assumed the plasma density is much bigger than that of the beam. In the regime when the solution propagates in the comoving frame with a velocity that is much smaller than the thermal speed, a nonlinear stationary beam structure is found in which the electron motion in the transverse direction is negligible and whose transverse localization comes from the nonlinearity associated with its 3-D adiabatic expansion. Conversely, when the parallel velocity of the structure is suciently large to prevent the heat convection along the magnetic eld, a helicoidally shaped stationary solution is found that is governed by the transverse convective nonlinearity. The profile of such beam is determined from a nonlinear dispersion relation and depends on the transverse size of the beam and its pitch angle to the magnetic field.