The pair plasma can be created when a seed gamma-ray photon encounters the very high magnetic fields in the polar cap region. One photon can produce two leptons; each lepton can produce more photons, which can in turn produce more particles . . . leading to a cascade. The occurence of this cascade can be estimated analytically, based on existing models of the polar cap. Surprisingly, we find that these models are missing something. Old pulsars should not have strong pair cascades at all; and yet they still shine. Young pulsars shoud have pair cascades, but the pairs should be distributed around the edge of the polar cap, which is not where the radio emission comes from in these objects. Thus, we are still missing something!
In another approach, my colleagues and I are developing a numerical code to follow the detailed development of the pair cascade. This code follows the cascade in physical space and in momentum space. We will use the results of this code to elaborate the analytic results on the onset and spatial distribution of the pair cascade, and also as input to future numerical modelling of the plasma instabilities by which this pair plasma can radiate.
