Double Compton scattering in a constant crossed field

TL;DR

This paper calculates two-photon emission by an electron in a zero-frequency electromagnetic wave, revealing the dominance of the one-step process over the formation length and discussing common simulation assumptions.

Contribution

It provides an exact calculation of two-photon emission in a constant crossed field and analyzes the validity of typical simulation assumptions.

Findings

The unpolarised probability splits into two processes: two-step and one-step.

The one-step process dominates over the formation length.

Neglecting spin and simultaneous emission assumptions are critically examined.

Abstract

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.