On the kinetic treatment of pair production strong electric fields

We investigate the behavior of the electron-positron plasma created by a strong electric field using a kinetic approach. Assuming a uniform and unbound field, the system under consideration is uniform and homogeneous in the physical space and axially symmetric in the momentum space with the axis of symmetry given by the direction of the initial field. The relativistic Boltzmann-Vlasov equation for pairs is solved numerically for different starting values of the field with particular attention to the momentum distribution of pairs produced from the field. Then we solve the system of coupled Vlasov-Boltzmann equation for pairs and Boltzmann equation for photons including collision terms for all the two-particle interactions between pairs and photons: electron-positron annihilation into two photons and its inverse process, Compton and Coulomb scatterings. We compare the two cases and discuss the role of the interactions.