Locally Monochromatic Approximation To Qed In Intense Laser Fields

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.