The Compton and Thomson radiation spectra, generated in collisions of an electron beam with a powerful laser beam, are studied in the framework of quantum and classical electrodynamics, respectively. We show that there are frequency regimes where both radiation spectra are nearly identical, which for Compton scattering relates to the process which preserves the electron spin. Although the radiation spectra are nearly identical, the corresponding probability amplitudes exhibit different global phases. This has pronounced consequences, which we demonstrate by investigating temporal power distributions in both cases. We show that, contrary to Thomson scattering, it is not always possible to synthesize short laser pulses from Compton radiation. This happens when the global phase of the Compton amplitude varies in a nonlinear way with the frequency of emitted photons. We also demonstrate that while the Compton process driven by a non-chirped laser pulse can generate chirped bursts of radiation, this is not the case for the Thomson process. In principle, both processes can lead to a generation of coherent frequency combs when single or multiple driving laser pulses collide with electrons. Once we synthesize these combs into short bursts of radiation, we can control them, for instance, by changing the time delay between the driving pulses.
The Sauter-Schwinger process of electron-positron pair creation from vacuum, driven by a sequence of time-dependent electric-field pulses, is studied in the framework of quantum-field theoretical approach. As demonstrated by our numerical results, the probability distributions of produced pairs exhibit intra-and inter-pulse interference structures. We show that such structures can be observed beyond the regime of applicability of the WKB theory, which was the focus of earlier investigations. Going beyond these developments, we perform the analysis of the time-evolution operator for an arbitrary eigenmode of the fermionic field. This shows that a perfect coherent enhancement of the inter-pulse peaks can never be reached. A nearly perfect coherence, on the other hand, is due to nonadiabatic transitions at avoided crossings of the phases defining the unitary time evolution. This analysis allows us to determine the conditions under which the nearly perfect coherence is lost.
Nonlinear Thomson and Compton processes, in which energetic electrons collide with an intense optical pulse, are investigated in the framework of classical and quantum electrodynamics. Spectral modulations of the emitted radiation, appearing as either oscillatory or pulsating structures, are observed and explained. It is shown that both processes generate a bandwidth radiation spanning the range of few MeV, which occurs in a small cone along the propagation direction of the colliding electrons. Most importantly, these broad bandwidth structures are temporarily coherent which proves that Thomson and Compton processes lead to generation of a supercontinuum. It is demonstrated that the radiation from the supercontinuum can be synthesized into zeptosecond (possibly even yoctosecond) pulses. Thus, confirming that Thomson and Compton scattering can be used as novel sources of an ultra-short radiation, opening routes to new physical domains for strong laser physics.
Abstract. The paper presents a number of definitions of variable order difference and discusses duality among some of them. The duality is used to improve the performance of the least squares estimation when applied to variable order difference fractional systems. It turns out, that by appropriate exploitation of duality one can reduce the estimator variance when system identification is carried out.
Spectra of Thomson and Compton radiation, emitted during electron scattering off an intense laser beam, are calculated using the frameworks of classical and strong-field quantum electrodynamics, respectively. Both approaches use a plane-wave-fronted pulse approximation regarding the driving laser beam. Within this approximation, a very good agreement between Thomson and Compton frequency distributions is observed provided that frequencies of the emitted radiation is relatively low. The dependence of frequency spectra on the laser pulse envelope is analyzed. This becomes important in the context of ultra-short pulse generation, as illustrated by numerical examples.The lecture presented during the 22nd International Laser Physics Workshop, Prague, July 15-19, 2013.
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