Numerical Analysis of the Interaction between a Tubular Beam of Charged Particles and a Dielectric Cylinder

Abstract

The effect of nonlinear stabilization of the instability of a tubular electron beam when it moves along the surface of a solid dielectric cylinder is investigated theoretically. It is assumed that the beam is nonrelativistic, infinitely thin in the radial direction, and moves along the surface of the cylinder parallel to the lines of force of an external constant magnetic field, which prevents the transverse motion of the beam electrons. The mechanism of nonlinear stabilization of azimuthally symmetric E-type electromagnetic waves with different values of radial mode indices is studied by the method of slowly varying amplitudes and phases. The physical cause of excitation of such waves is the Vavilov–Cherenkov resonance, and the nonlinear stabilization mechanism is based on the trapping of beam particles by the field of the excited wave. It is shown that, as the radial mode index of the excited wave increases, the saturation time of instability and the maxima and the “period” of amplitude oscillations at the nonlinear stage of instability saturation decrease. It is shown that, at the nonlinear stage of instability, the waves excited by the beam have elliptical polarization. Moreover, in the vacuum region, the directions of rotation of the electric field vectors of E01 and E02 waves turn out to be opposite.