  We propose a simple analytic model for the innermost (within the light
cylinder of canonical radius) structure of open-magnetic-field lines of a
rotating neutron star (NS) with relativistic outflow of charged particles
(electrons/positrons) and arbitrary angle between the NS spin and magnetic
axes. We present the self-consistent solution of Maxwell's equations for the
magnetic field and electric current in the pair-starved regime where the
density of electron-positron plasma generated above the pulsar polar cap is not
sufficient to completely screen the accelerating electric field and thus
establish the E \cdot B = 0 condition above the pair-formation front up to very
high altitudes within the light cylinder. The proposed model may provide a
theoretical framework for developing a refined model of the global pair-starved
pulsar magnetosphere.

Astrophysics