Free-electron lasers (FELs) can emit light with different optical polarizations including linear, elliptic and circular polarizations corresponding to the characteristics of the undulators used. X-ray FELs depend upon long undulator lines consisting of a sequence of short undulators. Linearly polarized undulators are most commonly used; hence the optical output is linearly polarized. Alternately, APPLE-II, Delta undulator designs, or a sequence of linearly polarized undulators with alternating orientations can be used to produce undulating magnetic fields with arbitrary polarizations. We present a three-dimensional, time-dependent formulation that self-consistently includes two optical orientations and, therefore, treats any given sequence or combination of undulator including undulator imperfections and degradation There are two principal characteristics of the formulation that underpin this capability. First, particles are tracked using the full Newton–Lorentz force equations with analytic models of the undulators fields. This permits an accurate model of the interaction of the electrons with a large variety of undulator fields and orientations. Second, the electrons can couple simultaneously to two independent electromagnetic polarizations and, therefore, the optical polarization evolves self-consistently along the undulator line. We present the numerical model and give some examples using prevailing undulator configurations.

自由电子激光器 (FEL) 可以根据所使用的波荡器的特性发射具有不同光学偏振的光，包括线偏振、椭圆偏振和圆偏振。X 射线 FEL 依赖于由一系列短波荡器组成的长波荡器线。线极化波荡器是最常用的；因此光输出是线偏振的。或者，可以使用 APPLE-II、Delta 波动器设计或一系列具有交替方向的线性极化波动器来产生具有任意极化的波动磁场。我们提出了一个三维的、与时间相关的公式，它自洽地包括两个光学方向，因此，处理任何给定的波动器序列或组合，包括波动器缺陷和退化 支持此功能的配方有两个主要特征。首先，使用完整的牛顿-洛伦兹力方程和波动场的解析模型跟踪粒子。这允许电子与各种波动场和方向的相互作用的准确模型。其次，电子可以同时耦合到两个独立的电磁极化，因此，光极化沿着波荡器线自洽地演变。我们展示了数值模型并给出了一些使用流行波荡器配置的例子。使用完整的牛顿-洛伦兹力方程和波动场的解析模型跟踪粒子。这允许电子与各种波动场和方向的相互作用的准确模型。其次，电子可以同时耦合到两个独立的电磁极化，因此，光极化沿着波荡器线自洽地演变。我们展示了数值模型并给出了一些使用流行波荡器配置的例子。使用完整的牛顿-洛伦兹力方程和波动场的解析模型跟踪粒子。这允许电子与各种波动场和方向的相互作用的准确模型。其次，电子可以同时耦合到两个独立的电磁极化，因此，光极化沿着波荡器线自洽地演变。我们展示了数值模型并给出了一些使用流行波荡器配置的例子。光偏振沿着波荡器线自洽地演变。我们展示了数值模型并给出了一些使用流行波荡器配置的例子。光偏振沿着波荡器线自洽地演变。我们展示了数值模型并给出了一些使用流行波荡器配置的例子。