Global constant field approximation for radiation reaction in collision of high-intensity laser pulse with electron beam

In the laser --- electron beam head-on interaction electron energy can decrease due to radiation reaction, i.e. emission of photons. For 10--100~fs laser pulses and for the laser field strength up to the pair photoproduction threshold, it is shown that one can calculate the resulting electron and photon spectra as if the electron beam travels through a constant magnetic field. The strength of this constant field and the interaction time are found as functions of the laser field amplitude and duration. Using of constant field approximation can make a theoretical analysis of stochasticity of the radiation reaction much simpler in comparison with the case of alternating laser field, also, it allows one to get electron and photon spectra much cheaper numerically than by particle-in-cell simulations.