Trapped-particle diocotron modes

Recent experiments have characterized trapped-particle modes on a non-neutral plasma column [A. A. Kabantsev, C. F. Driscoll, T. J. Hilsabeck, T. M. O'Neil, and J. H. Yu, Phys. Rev. Lett. 87, 225002 (2001)], and in this paper we present a theoretical model of the modes. Theoretical predictions for the mode frequency, damping rate, and eigenmode structure are compared to experimental observation. The modes are excited on a non-neutral plasma column in which classes of trapped and passing particles have been created by the application of a potential barrier. The column resides in a Malmberg-Penning trap, and the barrier is created by applying a voltage to an azimuthally symmetric section of the wall near the axial mid-point of the column. Low energy particles near the edge of the column (where the barrier is strong) are trapped in one end or the other, while high energy particles near the center of the column transit the entire length. The modes have azimuthal variation l=1,2,..., and odd z-symmetry. The trapped particles on either side of the barrier execute ExB drift oscillations producing density perturbations that are 180 deg. out of phase with each other, while passing particles run back and forth along the field lines attempting to Debye shield the perturbed charge density. The mode is damped by collisional scattering across the separatrix between trapped and passing particles. The damping rate is calculated using a boundary layer analysis of the Fokker-Planck equation. It is also shown that the damping is associated with the radial transport of plasma particles