High Intensity Compton Scattering in a strong plane wave field of general form

TL;DR

This paper provides a comprehensive theoretical analysis of photon emission by electrons in arbitrary plane wave electromagnetic fields, deriving a general formula for transition probabilities applicable to various field configurations.

Contribution

It derives an exact, general expression for photon emission probabilities in arbitrary plane wave fields using Volkov solutions, extending previous specific case analyses.

Findings

Derived a general transition probability formula for photon emission in arbitrary plane wave fields.

Validated the formula with specific cases like circular polarization and crossed fields.

Numerically analyzed photon emission in two phase-separated circularly polarized fields.

Abstract

Photon emission by an electron embedded in a strong external field of general form is studied theoretically. The external field considered is a plane wave electromagnetic field of any number of components, period and polarisation. Exact, Volkov solutions of the Dirac equation with the 4-potential of the general external field are obtained. The photon emission is considered in the usual perturbation theory using the Volkov solutions to represent the electron. An expression for the transition probability of this process is obtained after the usual spin and polarisation sums, trace calculation and phase space integration. The final transition probability in the general case contains a single sum over contributions from external field photons and an integration over one of the phase space components. The validity of the general expression is established by considering specific external fields. Known specific analytic forms of the transition probability are obtained after substitution of the 4-potential for a circularly polarised and constant crossed external field. As an example usage of the general result for the transition probability, the case of two phase separated, circularly polarised external fields is studied both analytically and numerically.