Double Compton scattering in a constant crossed field

Two-photon emission of an electron in an electromagnetic plane wave of vanishing frequency is calculated. The unpolarised probability is split into a two-step process, which is shown to be exactly equal to an integration over polarised subprocesses, and a one-step process, which is found to be dominant over the formation length. The assumptions of neglecting spin and simultaneous emission, commonly used in numerical simulations, are discussed in light of these results.