Effect of radiation back-reaction on the interaction of super-strong laser fields with plasmas.

We analyze the effect of self-force on a single electron and on plasma electrons giving attention to the electromagnetic energy generated by non-linear Thomson scattering. The effect is essential if the scattered energy is comparable with the rest-mass energy of the electron in the frame of reference where the electron was initially at rest. We develop a method for solving the Lorentz-Abraham-Dirac equation and accounting for radiation in a self-consistent manner. The solution is then applied to the interactions of super-strong laser fields with an electron and a plasma layer including the presence of strong charge separation fields. This scheme allows a simulation of resulting radiation with spatial and spectral distributions, and demonstrates the possibility of efficient conversion (up to several {\%}) of incident radiation to $\gamma $-ray emission at intensities of $\sim $10$^{22}$W/cm$^{2}$, recently achieved in experiments.