Conservation laws and theorems of confinement and stability for a charged equatorial disk in a pulsar magnetosphere
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).
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- May 2005
- DOI:
- 10.1051/0004-6361:20041707
- Bibcode:
- 2005A&A...434..405A
- Keywords:
-
- pulsars: general;
- magnetic fields;
- plasmas