EQUILIBRIA OF CHARGE-SEPARATED RIGIDLY ROTATING RELATIVISTIC MAGNETOSPHERES

In this paper, we present the results of self-consistent numerical calculations of equilibria of rotating relativistic magnetospheres, generally considered as relevant for the modelling of pulsar magnetospheres. We assume that the central body (e.g., a neutron star) is a highly conducting charged sphere with an intrinsic magnetic dipole field aligned with the rotation axis (aligned or parallel rotator model). This assumption allows for the existence of axisymmetric stationary states of the magnetosphere.

We describe the collisionless plasma of the magnetosphere by prescribing a distribution function depending on the constants of motion, the particle energy and the angular momentum. In this paper, we will focus on trapped particle populations. For a correct treatment of trapped particles in the framework of collisionless theory, it is necessary to investigate the phase space regions accessible to a particle with given energy and angular momentum. This will be carried out numerically for the vacuum fields, thereby providing evidence that a distribution function of trapped particles should have a cut-off at high energies for all field configurations.

Specifying a suitable example of a distribution function, it is then possible to solve the appropriate Maxwell equations for the electromagnetic fields self-consistently. In the present paper, we specialize to magnetospheres of small radial extent so that the deformation of the magnetic dipole field by the toroidal current is negligible.

The resulting magnetospheres are completely charge-separated and contain large vacuum gaps. The numerical method we use starts with the vacuum solution and then calculates successively more populated magnetospheres. It is found that as the local particle density increases, a) it approaches the Goldreich-Julian density almost everywhere in the plasma-filled region; b) the parallel electric field is drastically diminished in the plasma-filled regions.