LULI, UPMC Université Paris 06: Sorbonne Universités, CNRS, École Polytechnique, CEA, Université Paris-Saclay, F-75252 Paris cedex 05, France.
CEA, DAM, DIF, F-91297 Arpajon, France.
Phys Rev E. 2018 Apr;97(4-1):043209. doi: 10.1103/PhysRevE.97.043209.
Radiation reaction in the interaction of ultrarelativistic electrons with a strong external electromagnetic field is investigated using a kinetic approach in the nonlinear moderately quantum regime. Three complementary descriptions are discussed considering arbitrary geometries of interaction: a deterministic one relying on the quantum-corrected radiation reaction force in the Landau and Lifschitz (LL) form, a linear Boltzmann equation for the electron distribution function, and a Fokker-Planck (FP) expansion in the limit where the emitted photon energies are small with respect to that of the emitting electrons. The latter description is equivalent to a stochastic differential equation where the effect of the radiation reaction appears in the form of the deterministic term corresponding to the quantum-corrected LL friction force, and by a diffusion term accounting for the stochastic nature of photon emission. By studying the evolution of the energy moments of the electron distribution function with the three models, we are able to show that all three descriptions provide similar predictions on the temporal evolution of the average energy of an electron population in various physical situations of interest, even for large values of the quantum parameter χ. The FP and full linear Boltzmann descriptions also allow us to correctly describe the evolution of the energy variance (second-order moment) of the distribution function, while higher-order moments are in general correctly captured with the full linear Boltzmann description only. A general criterion for the limit of validity of each description is proposed, as well as a numerical scheme for the inclusion of the FP description in particle-in-cell codes. This work, not limited to the configuration of a monoenergetic electron beam colliding with a laser pulse, allows further insight into the relative importance of various effects of radiation reaction and in particular of the discrete and stochastic nature of high-energy photon emission and its back-reaction in the deformation of the particle distribution function.
利用非线性中度量子 regime 中的动力学方法，研究了超相对论电子与强外电磁场相互作用中的辐射反应。讨论了三种互补的描述，考虑了任意的相互作用几何形状：一种依赖于 Landau 和 Lifschitz (LL) 形式的量子修正辐射反作用力的确定性描述，一种电子分布函数的线性 Boltzmann 方程，以及在发射光子能量相对于发射电子能量较小时的福克-普朗克 (FP) 展开。后一种描述等效于随机微分方程，其中辐射反作用力的影响以对应于量子修正 LL 摩擦力的确定性项的形式出现，并以考虑光子发射随机性的扩散项的形式出现。通过研究电子分布函数能量矩随三个模型的演化，我们能够表明，所有三种描述在各种感兴趣的物理情况下，对于电子群体的平均能量的时间演化都提供了相似的预测，即使对于大的量子参数 χ 也是如此。FP 和完整的线性 Boltzmann 描述还允许我们正确描述分布函数的能量方差（二阶矩）的演化，而高阶矩通常只能通过完整的线性 Boltzmann 描述正确捕获。提出了每种描述的有效性限制的一般准则，以及在粒子在细胞代码中包含 FP 描述的数值方案。这项工作不仅限于单能电子束与激光脉冲碰撞的配置，它进一步深入了解了辐射反作用力的各种效应的相对重要性，特别是高能光子发射的离散性和随机性及其在粒子分布函数变形中的反作用。
