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  • Open Access

Scattering with total depletion in strong, focused fields

Tim Adamo1,* and Anton Ilderton2,†

  • *Contact author: t.adamo@ed.ac.uk
  • †Contact author: anton.ilderton@ed.ac.uk
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Phys. Rev. D 111, 125005 – Published 10 June, 2025

DOI: https://doi.org/10.1103/dxl7-m68z

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., focusing). We show here that a solution to one problem can solve the other: even if particle wave functions in a chosen focused background are not known, we show they can be constructed once depletion is accounted for. We demonstrate this by giving the exact wave functions in a flying focus beam for which all energy is absorbed by particles scattering on it. In addition we use the wave functions 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.

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Phys. Rev. D 111, 125005– Published 10 June, 2025
  • Received 15 January 2025
  • Revised 14 March 2025
  • Accepted 27 May 2025
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