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We discuss intensity effects in collisions between beams of optical photons from a high-power laser and relativistic electrons. Our main focus are the modifications of the emission spectra due to realistic finite-beam geometries. By carefully analysing the classical limit we precisely quantify the distinction between strong-field QED Compton scattering and classical Thomson scattering.A purely classical, but fully covariant, calculation of the bremsstrahlung emitted by an electron in a plane wave laser field yields radiation into harmonics, as expected. This result is generalised to pulses of finite duration and explains the appearance of line broadening and harmonic substructure as an interference phenomenon. The ensuing numerical treatment confirms that strong focussing of the laser leads to a broad continuum while higher harmonics become visible only at moderate focussing, hence lower intensity. We present a scaling law for the backscattered photon spectral density which facilitates averaging over electron beam phase space. Finally, we propose a set of realistic parameters such that the observation of intensity induced spectral red-shift, higher harmonics, and their substructure, becomes feasible.

Based on strong-field QED in the Furry picture we use the Dirac-Volkov propagator to derive a compact expression for the differential emission probability of the two-photon Compton process in a pulsed intense laser field. The relation of real and virtual intermediate states is discussed, and the natural regularization of the on-shell contributions due to the finite laser pulse is highlighted. The inclusive two-photon spectrum is two orders of magnitude stronger than expected from a perturbative estimate.Comment: 5 pages, 3 figure

The locally constant field approximation (LCFA) has to date underpinned the numerical simulation of quantum processes in laser-plasma physics and astrophysics, but its validity has recently been questioned in the parameter regime of current laser experiments. While improvements are needed, literature corrections to the LCFA show inherent problems. Using nonlinear Compton scattering in laser fields to illustrate, we show here how to overcome the problems in LCFA corrections. We derive an "LCFA+ " which, comparing with the full QED result, shows an improvement over the LCFA across the whole photon emission spectrum. We also demonstrate an implementation of our results in the type of numerical code used to design and analyse intense laser experiments.