Dynamical screening of the electric field in pair discharges and its implications for pulsar radio luminosity and spectrum

Pulsar radio luminosity is a factor of $10^{-6}$ to $10^{-4}$ smaller than spindown luminosity, but has negligible dependence on spindown luminosity. The radio spectrum is roughly $S_\omega \sim \omega^{-1.4 \pm 1.0} $. In this talk, we will discuss how these characteristics may arise partially from the nonlinear, relativistic, collisionless physics of the pair plasma discharge that screens the polar cap electric field. During the early stages of the discharge, the electric field experiences strong damping due to large displacements in the momenta of newly added pairs. This strong damping ceases when the displacement of newly injected particles in the electric field is small. Quantitative statement of the resulting condition on electric field amplitude yields an expression for radio luminosity that is roughly consistent with observation. After this point, the discharge experiences a linear phase which only slightly decreases the emission amplitude but creates a relationship between emission amplitude and frequency which may contribute to the observed radio spectrum.