  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.
