  The dipolar magnetic field structure of the neutron star is modified by the
plasma originating in the pulsar magnetopshere. In the simplest case of a
stationary axisymmetric force-free magnetosphere, a self-consistent description
of the fields and currents is given by the well-known pulsar equation. Here we
revise the commonly used boundary conditions of the problem in order to
incorporate the plasma-producing gaps and to provide a framework for a truly
self-consistent treatment of the pulsar magnetosphere. The generalized
multipolar solution of the pulsar equation is found, which, as compared to the
customary split monopole solution, is suggested to better represent the
character of the dipolar force-free field at large distances. In particular,
the outer gap location entirely inside the light cylinder implies that beyond
the light cylinder the null and critical lines should be aligned and go
parallel to the equator at a certain altitude. Our scheme of the pulsar
force-free magnetosphere, which will hopefully be followed by extensive
analytic and numerical studies, may have numerous implications for different
fields of pulsar research.
