Nonlinear Stabilization of Resistive Instability of a Tubular Charged Particle Beam Moving above a Solid-State Plasma Cylinder

Abstract

Nonlinear stabilization of instability of an infinitely thin tubular electron beam moving along the surface of a solid-state plasma cylinder is analyzed. It is assumed that the electron collision frequency in the plasma cylinder is much higher than the frequency of plasma eigenmodes (oscillations). The beam is assumed to be nonrelativistic, and, thus, the problem is solved in the electrostatic approximation. It is shown that the growth of the wave amplitude is stabilized nonlinearly due to the self-trapping of the beam electrons by the field of the electrostatic wave excited in the beam itself. It is found that the saturation time of instability and the maximum amplitude of the excited wave depend on the radius of the plasma cylinder. It is established that the larger the radius of the plasma cylinder, the later the nonlinear stage of instability begins and the larger the maximum amplitude of the excited wave.