Extended locally monochromatic approximations of strong-field QED processes

Strong-field QED (SFQED) probability rates in the locally monochromatic approximation (LMA) have become an indispensable tool for simulations of processes like gamma-ray emission or electron-positron pair production in laser-particle collisions. We revisit the LMA derivation and explicitly demonstrate that it is based on the separation of timescales, neglect of the long-range interference effects, and subsequent averaging over the cycle scale. Doing so, we obtain unambiguously LMA rates for arbitrary polarizations of the plane-wave background. Additionally, we partially restore the finite bandwidth effects that are lost in the LMA derivation. We refer to the bandwidth-restored result as the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msup><a:mrow><a:mi>LMA</a:mi></a:mrow><a:mo>+</a:mo></a:msup></a:math> and show that it agrees with the full SFQED predictions better than the standard LMA. We use <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msup><b:mrow><b:mi>LMA</b:mi></b:mrow><b:mo>+</b:mo></b:msup></b:math> to address previously inaccessible observables and formulate an additional limitation on the applicability of locally monochromatic approximations in general. We provide analytical results for the angular-integrated <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msup><c:mrow><c:mi>LMA</c:mi></c:mrow><c:mo>+</c:mo></c:msup></c:math> probability rate and the fully differential probability that account for the finite bandwidth effects.