Kinetic model of pair discharges in pulsar polar caps

Time-dependent discharges of electron-positron pairs have recently 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 photon emission via curvature radiation by TeV electrons and positrons and pair production -, the plasma self-consistently develops inductive waves that couple to electromagnetic modes capable of escaping the pulsar dense plasma. In this work, we present an analytical description of pair cascades relevant in pulsars, including their onset, exponential growth and saturation stages. We show that the plasma is set to inductively oscillate at the relativistic plasma frequency after the cascade saturates. These oscillations are found to be unstable to a new kinetic instability, that converts the energy in the inductive oscillations into an infinite number of electrostatic modes. 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 (QED) 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 (e.g. frequency, polarisation and Poynting flux angular distribution) that are consistent with observations.