Stability of three-dimensional electron holes

Abstract

A self-consistent kinetic model of three-dimensional (3D) electron holes in a strongly magnetized collisionless plasma is presented. A stability study of these localized electrostatic structures has been carried out. The analysis of the motion of trapped particles in the 3D potential structure suggests using the Hamiltonian approach to describe how electron holes interact with an external electrostatic perturbation. Using 3D action-angle variables and perturbation theory, it is shown that, in addition to standard Landau resonance of passing (i.e., untrapped) particles, trapped particles resonate with the perturbation in such a way that they amplify it. A growth rate for this process is derived and application to magnetospheric plasma conditions shows that the stability of 3D electron holes is strongly dependent on the anisotropy of the underlying potential structure. Possible production of electrostatic whistler waves by a train of electron holes in the auroral region of the Earth’s magnetosphere is emphasized.