Diocotron instability in pulsar electrospheres

Abstract

In a previous work, we have shown that the electrospheric plasma of a pulsar's magnetosphere with vacuum gaps is subject to dierential rotation in the equatorial belt. Here we examine the stability of a simplied model of this belt. The model consists of a charged thin plasma disc in dierential rotation, embedded in a dipolar magnetic eld anchored in the neutron star. In the linearized electrostatic perturbation approximation, this disc appears to be unstable to the so-called diocotron instability. We present several eigenspectra and eigenfunctions for dierent disc models, which dier by the total charge of the disc-star system. Velocity and electric eld perturbations are also shown in the disc plane for a few fast-growing modes. Increasing the total charge has a stabilizing eect, in the sense that the growth rate of the fastest-growing eigenvalue decreases with total charge and eventually vanishes. When the system is unstable, the growth rates are of the order of the azimuthal rotation rate. This means that the diocotron instability, which develops in a few pulsar's periods, should be very ecient in causing particles to migrate across magnetic surfaces.