The Axisymmetric Pulsar Magnetosphere

We present the structure of the axisymmetric force-free magnetosphere of an aligned rotating magnetic dipole, in the case in which there exists a sufficiently large charge density (whose origin we do not question) to satisfy the ideal MHD condition, E (raised dot) B = 0, everywhere. The unique distribution of electric current along the open magnetic field lines which is required for the solution to be continuous and smooth is obtained numerically. We expect that our solution will be useful as the starting point for detailed studies of pulsar magnetospheres under more general conditions, namely when either the force-free and/or the ideal MHD condition E (raised dot) B = 0 are not valid in the entire magnetosphere. Based on our solution, we consider that the most likely positions of such an occurrence are the polar cap, the crossings of the zero space charge surface by open field lines, and the return current boundary, but not the light cylinder.