Locally monochromatic approximation to QED in intense laser fields

Abstract

We derive an approximation to QED effects in intense laser fields which can be employed in 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 apply to nonlinear Compton scattering in circularly and linearly polarized backgrounds and to nonlinear Breit-Wheeler pair production. We provide the explicit link between the LMA and QED, and benchmark against exact QED results. The LMA is particularly useful for high-energy, intermediate-intensity collisions, where, unlike the ``locally constant field'' approximation, the LMA correctly describes the position and amplitude of harmonic features and exactly reproduces the low energy limit. We show that in the limit of high-intensity and large harmonic order, the locally constant field approximation is recovered from the LMA.