GLOBAL STRUCTURE OF THE PULSAR AXISYMMETRIC FORCE-FREE MAGNETOSPHERE ALLOWING FOR CURRENT CLOSURE ON THE NEUTRON STAR SURFACE

Abstract

The stationary axisymmetric force-free magnetosphere of a pulsar
is considered. The well-known pulsar equation is generalized
so as to allow for the sheet of closing current at the neutron star
surface. As a result of simplification of the pulsar equation close
to the magnetic axis we find the axial magnetic flux function,
which links the neutron star interior to the force-free magnetosphere
up to infinity. Using this function as a starting approximation,
we solve the complete pulsar equation in the polar region,
obtain the self-consistent current and magnetic flux functions
at infinity and show their uniqueness. With the current
function obtained we find the self-consistent flux function at the
top of the current sheet and demonstrate its distinctness from
the dipolar function inside the neutron star. This result implies
the necessity to reconsider the standard set of boundary conditions
in the problem of the pulsar force-free magnetosphere.