Model pulsar magnetospheres: the perpendicular rotator

The simplest model illustrating the effect of the magnetospheric charge-cur rent field on the structure of a pulsar magnetic field has the region withi n the light-cylinder filled with the Goldreich-Julian charge density which corotates with the neutron star, but has no electric currents along the mag netic field lines. This model has previously been studied for the axisymmet ric case, with the rotation and magnetic dipolar axes aligned, The analogou s problem is now solved with the two axes mutually perpendicular, so that n ot only the material current arising from the rotating charges but also the displacement current contributes. Again, the constructed magnetic field B- 0 crosses the light-cylinder normally, and there is no energy flux to infin ity. However, in a more realistic model there is a flow of current along B- 0, generating a field B-1 which has a non-vanishing toroidal component at t he light-cylinder, so yielding a finite integrated Poynting flux.