Scaling Law of Nonlinear Compton Scattering

We show that there are two mechanisms responsible for the net energy exchange between an intense pulsed laser and an electron in vacuum, namely, stimulated Compton scattering and nonlinear Compton scattering(NLCS). For NLCS, being the only effect in a mono-frequency continuous laser beam, its contribution is also independently determined. The characteristics of these two mechanisms in connection with the net energy exchange are studied. For the case of a pulsed laser field, it is found that the maximum net energy exchange by NLCS is approximately proportional to Q²₀(Q₀ ≡ eE₀/(m_e ωc)) for Q₀ ≥100. In addition, the relative importance of these two mechanisms to the net energy exchange at different intensities is explored.