Numerical approach to the semiclassical method of radiation emission for arbitrary electron spin and photon polarization

TL;DR

This paper presents a numerically efficient reformulation of semiclassical radiation emission formulas for electrons with arbitrary spins and photon polarization, validated against quantum solutions, and explores polarization transfer in laser-electron interactions.

Contribution

The paper introduces a quickly converging numerical form of semiclassical radiation formulas for arbitrary spins and polarizations, validated against Dirac equation solutions, and applies it to laser-electron interactions.

Findings

Finite laser pulse duration reduces circular polarization transfer compared to monochromatic predictions.

Increased laser intensity in nonlinear regime deteriorates polarization transfer, but collimation recovers it.

Formulas enable analysis of radiative polarization, with applications to bent crystals and high-energy positrons.

Abstract

We show how the semiclassical formulas for radiation emission of Baier, Katkov and Strakhovenko for arbitrary initial and final spins of the electron and arbitrary polarization of the emitted photon can be rewritten in a form which numerically converges quickly. We directly compare the method in the case of a background plane wave with the result obtained by using the Volkov state solution of the Dirac equation, and confirm that we obtain the same result. We then investigate the interaction of a circularly polarized short laser pulse scattering with GeV electrons and see that the finite duration of the pulse leads to a lower transfer of circular polarization than that predicted by the known formulas in the monochromatic case. We also see how the transfer of circular polarization from the laser beam to the gamma ray beam is gradually deteriorated as the laser intensity increases, entering the nonlinear regime. However, this is shown to be recovered if the scattered photon beam is collimated to only allow for passage of photons emitted with angles smaller than $1/\gamma$ with respect to the initial electron direction, where $\gamma$ is the approximately constant Lorentz factor of the electron. The obtained formulas also allow us to answer questions regarding radiative polarization of the emitting particles. In this respect we briefly discuss an application of the present approach to the case of a bent crystal and high-energy positrons.