Abstract

Undulator radiation (UR) in an undulator with field harmonics in two orthogonal planes is theoretically studied taking nonperiodic magnetic components and off-axis effects into account. New analytical expressions for the UR spectrum and UR intensity are written explicitly in terms of the generalized Bessel function and Airy function. In limiting cases, they describe the radiation of a two-frequency planar undulator, a helical undulator, and an elliptical undulator. The influence of the finite size of the electron beam, the emittance, electron beam deflection from the axis, the spread of the electron energy, and the influence of the constant components of the magnetic field are taken into account analytically. The expressions make it possible to distinguish the contributions of each field component and characteristics of the beam and undulator to the generation of UR harmonics. The phenomenological FEL model is used to study the evolution of harmonic power in the FEL experiments of LCLS and LEUTL. The influence of the beam parameters and undulator parameters on the harmonic generation is analyzed. The theoretical results of the power and radiation spectrum of the FEL are in agreement with experiments. It is shown that the second harmonic in the X-ray FEL of LCLS can be due to the beam deflection from the axis by \({\sim}12\) \(\mu\)m, and the second harmonic in the UV-A FEL of LEUTL is due to wide (\({\sim}0.2\) mm) beams of electrons and photons.

中文翻译：

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非周期性磁场和偏轴效应对X射线FEL和其他FEL辐射的影响分析

摘要

从理论上考虑了非周期磁分量和离轴效应，研究了在两个正交平面中具有场谐波的波荡器中的波荡器辐射（UR）。UR谱和UR强度的新解析表达式是根据广义Bessel函数和Airy函数明确编写的。在有限的情况下，它们描述了两频平面波荡器，螺旋波荡器和椭圆波荡器的辐射。分析地考虑了电子束的有限尺寸，发射率，电子束从轴偏转，电子能量的散布以及磁场的恒定分量的影响。这些表达式可以区分每个场分量以及光束和波荡器特性对UR谐波的产生的影响。现象学的FEL模型用于研究LCLS和LEUTL的FEL实验中谐波功率的演变。分析了光束参数和波荡器参数对谐波产生的影响。FEL的功率和辐射光谱的理论结果与实验一致。结果表明，LCLS的X射线FEL中的二次谐波可能是由于光束偏离轴 分析了光束参数和波荡器参数对谐波产生的影响。FEL的功率和辐射光谱的理论结果与实验一致。结果表明，LCLS的X射线FEL中的二次谐波可能是由于光束偏离轴 分析了光束参数和波荡器参数对谐波产生的影响。FEL的功率和辐射光谱的理论结果与实验一致。结果表明，LCLS的X射线FEL中的二次谐波可能是由于光束偏离轴\（{\ sim} 12 \） \（\ mu \） m，而LEUTL的UV-A FEL中的二次谐波是由于电子和光子的束宽（\（{\ sim} 0.2 \） mm） 。