Self-consistent model of the electron-positron pair production in the   collision of laser pulses
  Pair production due to the Schwinger mechanism is modeled in a self-consistent approach taking into account the backreaction of the created particles on the field. The model uses the Boltzmann kinetic equation for the electrons and positrons and the Maxwell equations for the electromagnetic field, which are solved numerically in a certain approximation for the case of the linearly polarized plane wave collision. The results indicate three main stages of the collision process: the acceleration of particles, the deceleration of particles, and plasma oscillations. A linear equation describing the oscillations is obtained, the oscillation frequency is related to the frequency of the quasinormal mode of the plasma with the least damping. It is also shown that the oscillation frequency is of the order of the plasma frequency. 
Alexander Tarasenko
physics.plasm-ph