On the self-consistent description of axisymmetric pulsar magnetospheres

The general structure of the system of pulsar equations derived in an earlier paper for the magnetosphere of a parallel rotator including particle inertia is investigated. The complete system reduces to one parabolic and two elliptic differential equations. The characteristics are found to be the streamlines. Appropriate variational principles are specified and a method for solving the pulsar equations numerically is proposed. Complete boundary conditions are given. First results for the solution within the corotating zone are presented. (author)