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Register a new userFrom quantum to classical modelling of radiation reaction: a focus on stochasticity effects
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Radiation-reaction in the interaction of ultra-relativistic electrons with a strong external electromagnetic field is investigated using a kinetic approach in the weakly quantum regime ($chi lesssim 1$, with $chi$ the electron quantum parameter). Three complementary descriptions are considered, their domain of applicability discussed and their predictions on average properties of an electron population compared. The first description relies on the radiation reaction force in the Landau and Lifschitz (LL) form. The second relies on the linear Boltzmann equation for the electron and photon distribution functions. It is valid for any $chi lesssim 1$, and usually implemented numerically using a Monte-Carlo (MC) procedure. The third description relies on a Fokker-Planck (FP) expansion and is rigorously derived for any ultra-relativistic, otherwise arbitrary configuration. Our study shows that the evolution of the average energy of an electron population is described with good accuracy in many physical situations by the leading term of the LL equation with the so-called quantum correction, even for large values of the $chi$. The leading term of the LL friction force (with quantum correction) is actually recovered naturally by taking the FP limit. The FP description is necessary to correctly describe the evolution of the energy variance (second order moment) of the distribution function, while the full linear Boltzmann (MC) description allows to describe the evolution of higher order moments whose contribution can become important when $chi rightarrow 1$. This analysis allows further insight on the effect of particle straggling in the deformation of the particle distribution function. A general criterion for the limit of validity of each description is proposed, as well as a numerical scheme for inclusion of the FP description in Particle-In-Cell codes.
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Soon available multi petawatt ultra-high-intensity (UHI) lasers will allow us to probe high-amplitude electromagnetic fields interacting with either ultra-relativistic electron beams or hot plasmas in the so-called moderately quantum regime. The correct modelling of the back-reaction of high-energy photon emission on the radiating electron dynamics, a.k.a. radiation reaction, in this regime is a key point for UHI physics. This will lead to both validation of theoretical predictions on the photon spectrum emitted during the laser-particle interaction and to the generation of high energy photon sources. In this paper we analyse in detail such emission using recently developed models to account for radiation reaction. We show how the predictions on the spectrum can be linked to a reduced description of the electron distribution function in terms of the first energy moments. The temporal evolution of the spectrum is discussed, as well as the parameters for which quantum effects induce hardening of the spectrum.
Impacts of quantum stochasticity on the dynamics of an ultra-relativistic electron beam head-on colliding with a linearly polarized ultra-intense laser pulse are theoretically investigated in a quasi-classical regime. Generally, the angular distribution of the electron beam keeps symmetrically in transverse directions in this regime, even under the ponderomotive force of the laser pulse. Here we show that when the initial angular divergence $Delta theta_i lesssim 10^{-6} a_0^2$ with $a_0$ being the normalized laser field amplitude, an asymmetric angular distribution of the electron beam arises due to the quantum stochasticity effect, via simulations employing Landau-Lifshitz, quantum-modified Landau-Lifshitz equations, and quantum stochastic radiation reaction form to describe the radiative electron dynamics respectively. The asymmetry is robust against a variety of laser and electron parameters, providing an experimentally detectable signature for the nature of quantum stochasticity of photon emission with laser and electron beams currently available.
The Landau-Lifshitz equation provides an efficient way to account for the effects of radiation reaction without acquiring the non-physical solutions typical for the Lorentz-Abraham-Dirac equation. We solve the Landau-Lifshitz equation in its covariant four-vector form in order to control both the energy and momentum of radiating particle. Our study reveals that implicit time-symmetric collocation methods of the Runge-Kutta-Nystrom type are superior in both accuracy and better maintaining the mass-shell condition than their explicit counterparts. We carry out an extensive study of numerical accuracy by comparing the analytical and numerical solutions of the Landau-Lifshitz equation. Finally, we present the results of simulation of particles scattering by a focused laser pulse. Due to radiation reaction, particles are less capable for penetration into the focal region, as compared to the case of radiation reaction neglected. Our results are important for designing the forthcoming experiments with high intensity laser fields.
Radiation losses in the interaction of superintense circularly polarized laser pulses with high-density plasmas can lead to the generation of strong quasistatic magnetic fields via absorption of the photon angular momentum (so called inverse Faraday effect). To achieve the magnetic field strength of several Giga Gauss laser intensities $simeq 10^{24}$W/cm$^2$ are required which brings the interaction to the border between the classical and the quantum regimes. We improve the classical modeling of the laser interaction with overcritical plasma in the hole boring regime by using a modified radiation friction force accounting for quantum recoil and spectral cut-off at high energies. The results of analytical calculations and three-dimensional particle-in-cell simulations show that, in foreseeable scenarios, the quantum effects may lead to a decrease of the conversion rate of laser radiation into high-energy photons by a factor 2-3. The magnetic field amplitude is suppressed accordingly, and the magnetic field energy - by more than one order in magnitude. This quantum suppression is shown to reach a maximum at a certain value of intensity, and does not grow with the further increase of intensities. The non monotonic behavior of the quantum suppression factor results from the joint effect of the longitudinal plasma acceleration and the radiation reaction force. The predicted features could serve as a suitable diagnostic for radiation friction theories.
This work is dedicated to the study of radiation reaction signatures in the framework of classical and quantum electrodynamics. Since there has been no distinct experimental validation of radiation reaction and its underlying equations so far and its impact is expected to be substantial for the construction of new experimental devices, e.g., quantum x-free electron lasers, a profound understanding of radiation reaction effects is of special interest. Here, we describe how the inclusion of quantum radiation reaction effects changes the dynamics of ultra-relativistic electron beams colliding with intense laser pulses significantly. Thereafter, the angular distribution of emitted radiation is demonstrated to be strongly altered in the quantum framework, if in addition to single photon emission also higher order photon emissions are considered. Furthermore, stimulated Raman scattering of an ultra-intense laser pulse in plasmas is examined and forward Raman scattering is found to be significantly increased by the inclusion of radiation reaction effects in the classical regime. The numerical simulations in this work show the feasibility of an experimental verification of the predicted effects with presently available lasers and electron accelerators.
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