Analytical results for non-linear Compton scattering in short intense laser pulses

TL;DR

This paper provides analytical expressions for non-linear Compton scattering spectra in short intense laser pulses, revealing how the spectrum depends on pulse shape and identifying universal features at high harmonics.

Contribution

It introduces a novel analytical framework expressing the spectrum dependence on pulse shape through three-parameter master integrals.

Findings

Spectrum dependence on pulse shape is encapsulated in three master integrals.

Analytical formulas for the non-linear Compton spectrum are derived.

Universal behavior of high harmonic lines spectrum is analyzed.

Abstract

We study in detail the strong-field QED process of non-linear Compton scattering in short intense plane wave laser pulses of circular polarization. Our main focus is placed on how the spectrum of the back-scattered laser light depends on the shape and duration of the initial short intense pulse. Although this pulse shape dependence is very complicated and highly non-linear, and has never been addressed explicitly, our analysis reveals that all the dependence on the laser pulse shape is contained in a class of three-parameter master integrals. Here we present completely analytical expressions for the non-linear Compton spectrum in terms of these master integrals. Moreover, we analyse the universal behaviour of the shape of the spectrum for very high harmonic lines.