Quasi-dipole magnetic fields

This paper describes the development of an analytical technique for includi ng the modification to the poloidal magnetic field that is generated by the toroidal component of motion of the charged particles in the axisymmetric pulsar magnetosphere model of Mestel and co-workers. This 'quasi-dipole' te chnique, and its 'distorted dipole' case: are developed in such a way as to retain as much as possible of the earlier formalism in which the poloidal magnetic field was taken to be the dipole field of the star. The field is d escribed in terms of a 'magnetic Stokes stream function', which is constant on each poloidal field line. The technique involves using the cylindrical polar radial coordinate and this stream function (in preference to the axia l coordinate) as the independent variables, forming a non-orthogonal coordi nate set in meridian planes. The field contains an unspecified function, wh ich represents the modification to the dipole field of the star generated b y the toroidal magnetospheric currents. Expressions are calculated for the curl of the poloidal magnetic field, which must be matched to an expression obtained for the toroidal electric current density from a magnetosphere mo del, thus determining the unspecified function.