Closed system of equations for description of the e+e– γ plasma generated from vacuum by strong electric field

We develop a self-consistent kinetic description of a e + e– γ plasma, generated from vacuum in a focal spot of counterpropagating laser pulses. Our model assumes purely time-dependent external (laser) field, but properly takes into account the semiclassical internal (plasma) field, as well as quantum radiation. While nonperturbative kinetic description of e + e– -pair production from vacuum and the simplest variant of backreaction problem have been previously addressed, quantum radiation is included in such a model for the first time. To achieve this goal we derived coupled kinetic equations for the electron, positron, and photon plasma species and the Maxwell equation for the internal electric field. Photon subsystem is included systematically using the BBGKY chain, which we truncate at the second order of perturbation theory by taking into account the annihilation and radiation channels. An important application of our results would be consideration of laser field depletion due to cascade production beyond the locally constant field approximation.