Scattering with total depletion in strong, focussed fields

TL;DR

This paper develops a method to include depletion effects in quantum electrodynamics scattering calculations within focused laser fields, enabling analytic solutions and advancing understanding of strong-field interactions.

Contribution

It introduces a way to construct particle wavefunctions in focused fields accounting for depletion, solving a key challenge in strong-field QED.

Findings

Exact wavefunctions for a flying focus beam with energy absorption

Derived a simple expression for nonlinear Compton scattering amplitude in focused fields

Demonstrated simultaneous treatment of depletion and focusing effects

Abstract

Theoretical approaches to QED scattering in strong fields typically treat the field as a fixed background with simple spacetime dependence, such as a plane wave. Two major challenges are therefore the inclusion of backreaction (e.g. depletion of the field) and spatial geometry (e.g. focussing). We show here that a solution to one problem can solve the other: even if particle wavefunctions in a chosen focussed background are not known, we show they can be constructed once depletion is accounted for. We demonstrate this by giving the exact wavefunctions in a flying focus beam for which all energy is absorbed by particles scattering on it. In addition we use the wavefunctions to obtain a simple expression for the nonlinear Compton scattering amplitude, comparing with the plane wave case. Our methods thus open a new avenue of investigation in which two previously challenging effects are simultaneously brought under analytic control.