Conservation laws and theorems of confinement and stability for a charged equatorial disk in a pulsar magnetosphere

CEA/DSM/DAPNIA, Service d'Astrophysique (CNRS FRE 2591), CE Saclay, 91191 Gif-sur-Yvette Cedex, France e-mail: jjaly@discovery.saclay.cea.fr

Received: 21 July 2004
Accepted: 14 December 2004

Abstract

For studying the nonaxisymmetric stability of the bounded electrosphere of an “aligned pulsar” (Michel's structure with polar domes and equatorial belt), Pétri et al. (2002) recently introduced a simplified but useful model in which all the charge-separated plasma located outside the magnetized rotating star is concentrated into a thin equatorial disk. In this paper, some aspects of this model are investigated analytically. It is shown that the equations governing the behaviour of the disk – in the case where there are no sources of particles feeding it – imply a series of conservation laws (for energy, angular momentum,...), and that there is a non-canonical Hamiltonian structure hidden behind them. The conservation laws are used to prove that: (i) for any initial conditions imposed on the disk, its evolution cannot lead to charges escaping to infinity (confinement theorem); (ii) a disk steady state with a possibly rotating pattern is nonlinearly stable if the charge density per unit of magnetic flux is a decreasing function of the electrostatic potential in the rotating frame (stability theorem).