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Non-linear cascade scattering of intense, tightly focused laser pulses byrelativistic electrons is studied numerically in the classical approximationincluding the radiation damping for the quantum parameter hwx-ray/E<1 and anarbitrary radiation parameter Kai. The electron energy loss, along with itsside scattering by the ponderomotive force, makes the scattering in thevicinity of high laser field nearly impossible at high electron energies. Theuse of a second, co-propagating laser pulse as a booster is shown to solve thisproblem.

Radiation Reaction Effects in Cascade Scattering of Intense, Tightly Focused Laser Pulses by Relativistic Electrons