Model pulsar magnetospheres: The perpendicular rotator

Abstract

The simplest model illustrating the effect of the magnetospheric charge-current field on the structure of a pulsar magnetic field has the region within the light-cylinder filled with the Goldreich-Julian charge density which corotates with the neutron star, but has no electric currents along the magnetic field lines. This model has previously been studied for the axisymmetric case, with the rotation and magnetic dipolar axes aligned. The analogous problem is now solved with the two axes mutually perpendicular, so that not only the material current arising from the rotating charges but also the displacement current contributes. Again, the constructed magnetic field B0 crosses the light-cylinder normally, and there is no energy flux to infinity. However, in a more realistic model there is a flow of current along B0, generating a field B1 which has a non-vanishing toroidal component at the light-cylinder, so yielding a finite integrated Poynting flux.