Kinetic model of pair cascades in pulsar polar caps

Electron-positron pairs have been proposed as a primary ingredient to explain the nature of pulsar radio emission, a longstanding open problem in high-energy astrophysics. During these discharges - positive feedback loops of gamma-ray emission via curvature radiation by TeV electrons and positrons and pair production -, the plasma self-consistently develops waves that couple to EM modes capable of escaping the pulsar dense plasma. A simple kinetic model that can predict the growth rate of the cascade, the screening time, and the subsequent emissions is yet to be known. We show how simplified kinetic equations can be used to provide such predictions in two setups: an uniform electric field and a space-time dependent electric field. All analytical results are illustrated with particle-in-cell simulations performed with OSIRIS. These results are used to interpret new multidimensional simulations including an ab initio description of the Quantum Electrodynamics effects responsible for hard photon emission and pair production in pair discharges. It is shown that the electromagnetic modes generated during pair discharges present direct imprints of QED and plasma kinetic effects in properties (frequency, polarisation and Poynting flux) that are consistent with observations.