High resolution numerical modeling of the force-free pulsar   magnetosphere
  We consider the force-free magnetosphere of an aligned rotator. Its structure is well described by a Grad-Shafranov equation for poloidal magnetic field, the so-called "pulsar equation". We solve this equation by a multigrid method with high numerical resolution. On the fine numerical grid current layer along the last closed field line could be accurately incorporated into the numerical procedure and all physical properties of the solution such as Goldreich-Julian charge density, drift velocity, energy losses etc. could be accurately calculated. Here we report results of the simulations. Among other interesting properties, the solution is not unique, i.e. the position of the last closed field line, and hence the pulsar energy losses, are not determined by the global magnetosphere structure and depend on kinetic of electromagnetic cascades. We discuss the properties of the solutions and their implications for pulsars. A model for pulsar magnetosphere evolution is proposed. In the frame of this model values of the pulsar braking index less than 3 have natural explanation. 
Andrey Timokhin (Sternberg Astronomical Institute, Moscow, Russia)