Diocotron instability in pulsar electrospheres

I. Linear analysis

¹ Observatoire de Strasbourg, 11 rue de l'Université, 67000 Strasbourg, France
² DARC, Observatoire de Meudon, Place Jules Janssen, 92195 Meudon, France

Corresponding author: J. Pétri, petri@newbr.u-strasbg.fr

Received: 22 October 2001
Accepted: 8 March 2002

Abstract

In a previous work, we have shown that the electrospheric plasma of a pulsar's magnetosphere with vacuum gaps is subject to differential rotation in the equatorial belt. Here we examine the stability of a simplified model of this belt. The model consists of a charged thin plasma disc in differential rotation, embedded in a dipolar magnetic field 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 different disc models, which differ by the total charge of the disc-star system. Velocity and electric field perturbations are also shown in the disc plane for a few fast-growing modes. Increasing the total charge has a stabilizing effect, 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 efficient in causing particles to migrate across magnetic surfaces.