The locally monochromatic approximation to QED in intense laser fields

We derive an approximation to QED effects in strong background fields which can be employed to improve numerical simulations of laser-particle collisions. Treating the laser as a plane wave of arbitrary intensity, we split the wave into fast (carrier) and slow (envelope) modes. We solve the interaction dynamics exactly for the former while performing a local expansion in the latter. This yields a `locally monochromatic' approximation (LMA), which we compare with exact spectra for nonlinear Compton scattering and nonlinear Breit-Wheeler pair production, for realistic laser pulse durations. We show that, as an improvement over the commonly used `locally-constant field' approximation, the LMA exactly reproduces the correct low energy behaviour of particle spectra, as well as the position and amplitude of harmonic features.