  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.
