  We consider a model of axisymmetric neutron star magnetosphere. In our
approach, the current density in the region of open field lines is constant and
the returning current flows in a narrow layer along the separatrix. In this
case, the stream equation describing the magnetic field structure is linear
both in the open and closed regions, the main problem lying in matching the
solutions along the separatrix (Okamoto 1974; Lyubarskii 1990). We demonstrate
that it is the stability condition on the separatrix that allows us to obtain a
unique solution of the problem. In particular, the zero point of magnetic field
is shown to locate near the light cylinder. Moreover, the hypothesis of the
existence of the nonlinear Ohm's Law (Beskin, Gurevich & Istomin 1983)
connecting the potential drop in the pair creation region and the longitudinal
electric current flowing in the magnetosphere is confirmed.
