Abstract
We study single, double and higher-order nonlinear Compton scattering where an electron interacts nonlinearly with a high-intensity laser and emits one, two or more photons. We study, in particular, how double Compton scattering is separated into one-step and two-step parts, where the latter is obtained from an incoherent product of two single-photon emissions. We include all contributions to double Compton scattering and show that the exchange term, which was not calculated in previous constant-crossed field studies, is in general on the same order of magnitude as the other one-step terms. Our approach reveals practically useful similarities between double Compton scattering and the trident process, which allows us to transfer some of our previous results for trident to double Compton scattering. We provide a new gluing approach for obtaining the dominant contribution to higher-order Compton scattering for long laser pulses. Unlike the standard gluing approach, our new approach does not require the intensity parameter $a_0$ to be much larger than one. For `hard' photons we obtain several saddle-point approximations for various field shapes.
Highlights
In [1] we studied the trident process [2,3,4,5,6,7,8], e− → 2e− þ eþ, in plane-wave background fields, and derived compact expressions for the probability for arbitrary background field shapes
In particular, how double Compton scattering is separated into one-step and two-step parts, where the latter is obtained from an incoherent product of two single-photon emissions
In this paper we identify a term in double Compton scattering that dominates for sufficiently long pulses without assuming a0 ≫ 1 or any particular field shape, and we show that this two-step term can be obtained from an appropriate sum of the incoherent product of two singlephoton emissions
Summary
In [1] we studied the trident process [2,3,4,5,6,7,8], e− → 2e− þ eþ, in plane-wave background fields, and derived compact expressions for the probability for arbitrary background field shapes. In this paper we identify a term in double Compton scattering that dominates for sufficiently long pulses without assuming a0 ≫ 1 or any particular field shape, and we show that this two-step term can be obtained from an appropriate sum of the incoherent product of two singlephoton emissions. We do this for an arbitrary background field. IV we separate the probability into one-step and two-step terms and compare with the incoherent product of two single-photon emissions This comparison helped us to find a new gluing approach, which we confirm in Sec. V for triple and quadruple Compton scattering. In particular, that the exchange term can continue to be on the same order as the direct part of the one-step term for larger χ
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