Vs. Beskin et Lm. Malyshkin, ON THE SELF-CONSISTENT MODEL OF AN AXISYMMETRICAL RADIO PULSAR MAGNETOSPHERE, Monthly Notices of the Royal Astronomical Society, 298(3), 1998, pp. 847-853
We consider a model of axisymmetric neutron star magnetospheres. In ou
r approach, the current density in the region of open field lines is c
onstant and the returning current flows in a narrow layer along the se
paratrix. In this case, the stream equation describing the magnetic he
ld structure is linear both in the open and closed regions; the main p
roblem is matching the solutions along the separatrix, 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 poin
t of magnetic field is shown to be located near the light cylinder. Mo
reover, the hypothesis of the existence of the non-linear Ohm's Law, c
onnecting the potential drop in the pair creation region and the longi
tudinal electric current flowing in the magnetosphere, is confirmed.