A nonlinear diocotron mode

Abstract

A perturbation procedure for the construction of a nonlinear diocotron mode of an infinite length cylindrical pure electron plasma column is presented. The plasma is modeled as a cold fluid executing E×B drift in a strong axial magnetic field. The mode has no axial variation and depends on θ (azimuthal angle) and t (time) through the combination θ−Ωt. Thus the potential and the density are stationary in the frame rotating with angular frequency Ω. In this frame, the potential satisfies the relation ∇2φ=F(φ) where F is a function of φ only. This equation is solved perturbatively to determine a nonlinear mode supported by a cylindrically symmetric equilibrium density profile. The properties of the mode depend only on the offset of the plasma column from the axis of the bounding conducting cylinder and the frequency of the mode is larger than the value predicted by linear theory by an amount roughly proportional to the square of the offset.