Analytical infrared limit of nonlinear Thomson scattering including radiation reaction

A Di Piazza

doi:10.1016/j.physletb.2018.05.081

Abstract

If an electric charge is accelerated by a sufficiently intense electromagnetic field, the effects of the radiation emitted by the charge on the charge dynamics (radiation reaction) cannot be ignored. Here we show that classical radiation-reaction effects alter qualitatively and quantitatively the infrared behavior of the spectrum of the radiation emitted by an electron in the presence of an intense electromagnetic plane wave (nonlinear Thomson scattering). An analytical expression of the infrared limit of nonlinear Thomson scattering is provided, which includes radiation-reaction effects and is valid for an arbitrary plane wave. Apart from their own conceptual importance and as a signature of classical radiation reaction, these results provide the limiting expression of the corresponding and yet unknown exact infrared behavior of strong-field QED in an intense plane wave.

Highlights

The definitive foundation of classical electrodynamics culminated with the formulation of Maxwell’s equations, which, together with the Lorentz equation, allow in principle to describe self-consistently the dynamics of electric charges and their electromagnetic field
In the present Letter we focus on the established equivalence between solving the LAD/LL equation for an electron in an external electromagnetic field and solving the coupled Maxwell’s and Lorentz equations, i.e., determining the exact electron’s dynamics in that field
We have derived analytically the infrared limit of nonlinear Thomson scattering, which is valid to all orders in the classical parameter RC = αχ0ξ0, to leading order in the classical parameters αη0 and αχ0, and for an arbitrary plane wave

Summary

Introduction

The definitive foundation of classical electrodynamics culminated with the formulation of Maxwell’s equations, which, together with the Lorentz equation, allow in principle to describe self-consistently the dynamics of electric charges and their electromagnetic field. In the present Letter we focus on the established equivalence between solving the LAD/LL equation for an electron in an external electromagnetic field and solving the coupled Maxwell’s and Lorentz equations, i.e., determining the exact electron’s dynamics in that field (in the case of the LL equation, short of effects much smaller than quantum effects) By exploiting this idea, we derive analytically the classical infrared limit of the energy spectrum emitted by an electron driven by an arbitrary plane wave (nonlinear Thomson scattering) including radiation-reaction effects. We derive analytically the classical infrared limit of the energy spectrum emitted by an electron driven by an arbitrary plane wave (nonlinear Thomson scattering) including radiation-reaction effects It is known, that according to the Lorentz equation, the asymptotic momentum of the electron after exiting an arbitrary plane wave with no dc component coincides with the asymptotic one before the electron enters the plane wave (Lawson-Woodard theorem [31, 32]).

Infrared behavior of classical radiation

Analytical infrared limit of nonlinear Thomson scattering

Conclusions