The axisymmetric pulsar magnetosphere

We present, for the first time, the structure of the axisymmetric force-fre e magnetosphere of an aligned rotating magnetic dipole, in the case in whic h there exists a sufficiently large charge density (whose origin we do not question) to satisfy the ideal MHD condition, E.B = 0, everywhere. The uniq ue distribution of electric current along the open magnetic field lines tha t is required for the solution to be continuous and smooth is obtained nume rically. With the geometry of the field lines thus determined, we compute t he dynamics of the associated MHD wind. The main result is that the relativ istic outflow contained in the magnetosphere is not accelerated to the extr emely relativistic energies required for the flow to generate gamma rays. W e expect that our solution will be useful as the starting point for detaile d studies of pulsar magnetospheres under more general conditions, namely, w hen the force-free and/or the ideal MHD condition, E.B = 0, are not valid i n the entire magnetosphere. Based on our solution, we consider that the mos t likely positions of such an occurrence are the polar cap, the crossings o f the zero space charge surface by open field lines, and the return current boundary, but not the light cylinder.