Pair formation above pulsar polar caps - Structure of the low altitude acceleration zone

Solutions are presented for a steady space-charge-limited flow of an electron beam above the polar cap of a pulsar in the case where the vector product of the neutron star's angular velocity and surface magnetic field is greater than zero over the whole polar-cap region and the flow is shorted out by pair creation. The flow has the characteristics of a space-charge-limited diode, with the stellar surface acting as a cathode and the lower boundary of the pair plasma acting as a conducting anode at a finite height above the surface. Reasons are given for believing that this flow is stable. The minimum photon energy absorbed in the hypothesized magnetic-field structure is computed and used to calculate the maximum period for pair creation in a dipole field. The maximum period for pair creation in more compex geometries is also estimated. It is shown that the dynamical structure of the plasma layer at the anode surface is such as to lead to a small reversed positron flux. Implications of this theory for understanding and predicting pulsar observations are discussed.