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The local-constant-field approximation (LCFA) is an essential theoretical
tool for investigating strong-field QED phenomena in background electromagnetic
fields with complex spacetime structure. In [1] we have analyzed the shortcomings
of the LCFA in nonlinear Compton scattering for the case of a background plane-wave
field. Here, we generalize that analysis to background fields, which can feature a
virtually arbitrary spacetime structure [2]. In addition, we provide an explicit and simple
implementation of an improved expression of the nonlinear Compton scattering
differential probability that solves the main shortcomings of the standard LCFA, and
is suitable for background electromagnetic fields with arbitrary spacetime structure
such as those of particle-in-cell (PIC) codes. Finally, we carry out a systematic procedure
to calculate the probability of nonlinear Compton scattering per unit of emitted photon
light-cone energy and of nonlinear Breit-Wheeler pair production per unit of produced
positron light-cone energy beyond the LCFA in a plane-wave background field, which
allows us to identify the limits of validity of this approximation quantitatively.
[1] A. Di Piazza, M. Tamburini, S. Meuren, and C. H. Keitel, Phys. Rev. A vol. 98, 012134 (2018)
[2] A. Di Piazza, M. Tamburini, S. Meuren, and C. H. Keitel, arXiv:1811.05834
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