Single and double nonlinear Compton scattering

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 a0 to be much larger than one. For "hard" photons we obtain several saddle-point approximations for various field shapes. * dinu@barutu.fizica.unibuc.ro † greger.torgrimsson@uni-jena.de 1 Note that we do not use "direct" as synonymous to the one-step term. By "direct" we mean instead the non-exchange part. The two-step term only has a direct part while the one-step term has both direct and exchange parts.

Trident process in laser pulses

“…For a field with longer pulse length we have explicitly demonstrated that, unless b 0 is large or a 0 small, the one-step terms become negligible and so the two-step can indeed be used to approximate the probability. This is evidence in support of using our new gluing approximation [27,46] for studying other higher-order processes in long laser pulses with moderately high intensity a 0 1.…”

“…A negligible twostep term will also occur if b 0 is not large, but a 0 is small. However, in that case we have no reason to neglect P 22 ex , which can be comparable to the other terms, as seen in The P 22→1 dir dominance is also interesting from a conceptual point of view, because, together with the twostep P 22→2 dir it can be obtained from our gluing approach [27,46]. The only difference consists in what step-function combination is put in the lightfront time integrand, see (B6).…”

“…The "glued-up" term P 22 dir (s) is the most important, clearly dominates for a long pulse unless a 0 is subunitary. Our interest in the gluing techniques comes from the conjecture that this can generalize to other processes, see [27,46], including the ones involving the emission of hard photons. While good in the LCF limit, the division into steps Integrating over s smooths out the former.…”

“…This maximizes the importance of P 22→1 dir (s) compared to P 22 dir (s), whose oscillations are partially washed out by the different choice of step functions that sever the Θ ij integrals. Check [27] for the oscillations shown by the Compton spectra for linear polarization.…”

“…This, however, will likely change soon, given the great deal of interest in this process in itself [14][15][16][17] and as a first step towards production of many particles in cascades [18][19][20]. A related second-order process is double nonlinear Compton scattering [21][22][23][24][25][26][27][28], where the electron instead produces two photons.…”