Driven phase space holes and synchronized Bernstein, Greene, and Kruskal modes

The excitation of synchronized Bernstein, Greene, and Kruskal (BGK) modes in a pure electron plasma confined in Malmberg–Penning trap is studied. The modes are excited by controlling the frequency of an oscillating external potential. Initially, the drive resonates with, and phase-locks to, a group of axially bouncing electrons in the trap. These initially phase-locked electrons remain phase-locked (in “autoresonance”) during a subsequent downward chirp of the external potential’s oscillation frequency. Only a few new particles are added to the resonant group as the frequency, and, hence, the resonance, moves to lower velocities in phase space. Consequently, the downward chirp creates a charge density perturbation (a hole) in the electron phase space distribution. The hole oscillates in space, and its associated induced electric field constitutes a BGK mode synchronized with the drive. The size of the hole in phase space, and thus the amplitude of the mode, are largely controlled by only two external parameters: the driving frequency and amplitude. A simplified kinetic theory of this excitation process is developed. The dependence of the excited BGK mode amplitude on the driving frequency chirp rate and other plasma parameters is discussed and theoretical predictions are compared with recent experiments and computer simulations. © 2004 American Institute of Physics. [DOI: 10.1063/1.1781166]