1999MNRAS.308...54H

We study the structure of a stationary and axisymmetric charge-deficient region (or potential gap) in the outer magnetosphere of a spinning neutron star. Assuming the existence of global current flow patterns in the magnetosphere, the charge depletion causes a large electric field along the magnetic field lines. This longitudinal electric field accelerates migratory electrons and/or positrons to ultrarelativistic energies. These relativistic electrons/positrons radiate γ-ray photons by curvature radiation. These γ-rays, in turn, produce yet more radiating particles by colliding with ambient X-ray photons, leading to a pair production cascade in the gap. The replenished charges partially screen the longitudinal electric field, which is self-consistently solved together with the distribution of e^± and γ-ray photons. We find the voltage drop in the gap as a function of the soft photon luminosity. It is demonstrated that the voltage drop is less than 3x10¹³V when the background X-ray radiation is as luminous as Vela. However, this value increases with decreasing X-ray luminosity and attains 3x10¹⁵V when the X-ray luminosity is as low as L_X=10³¹erg.s^–1.