We propose a new approach, based on statistical mechanics, to predict the saturated state of a single-pass, high-gain free-electron laser (FEL). In analogy with the violent relaxation process in self-gravitating systems and in the Euler equation of 2D turbulence, the initial relaxation of the laser can be described by the statistical mechanics of an associated Vlasov equation. The Laser field intensity and the electron bunching parameter reach quasi-stationary values that are well fitted by a Vlasov stationary state if the number of electrons $N$ is sufficiently large. Finite $N$ effects (granularity) finally drive the system to Boltzmann-Gibbs statistical equilibrium, but this occurs on times that are unphysical (i.e. excessively long undulators). All theoretical predictions are successfully tested in finite $N$ numerical experiments. Our results may provide important hints to the optimization of the length of the FEL undulator.
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机译:我们提出了一种基于统计力学的新方法来预测单通,高增益自由电子激光器(FEL)的饱和状态。与自重力系统中的剧烈弛豫过程类似,在二维湍流的欧拉方程中,激光的初始弛豫可以通过相关的Vlasov方程的统计力学来描述。如果电子的数量$ N $足够大,则激光场强度和电子聚集参数达到准静态值,该静态值很好地适合于Vlasov稳态。有限的$ N $效应(粒度)最终使系统达到Boltzmann-Gibbs统计平衡,但这发生在非物理时间(即过长的波动器)上。所有的理论预测均已在有限的$ N $数值实验中成功进行了测试。我们的结果可能为优化FEL波动器的长度提供重要提示。
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