Pair-Starved Pulsar Magnetospheres
  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. 
Alex G. Muslimov and Alice K. Harding