理想导体圆柱形束管中超相对论带电聚束产生的电磁场能谱
Energy Spectra from Electromagnetic Fields Generated by Ultra-relativistic Charged Bunches in a Perfectly Conducting Cylindrical Beam Pipe
摘要：
本文讨论了满足理想导电边界条件的圆形截面直束流管中电磁场的频谱随各种源模型的变化。其中包括沿管轴以恒定速度移动的带电束团，推导出束管中麦克斯韦方程组初边值问题的精确解。在超相对论极限下，场的所有纵向分量趋于零，并且横向场的谱含量和穿过束管的任何截面的平均总电磁能量与超相对论源的性质直接相关。它示出，对于轴对称的超相对论束干涉效应的发生，显示出惊人的相似，发生由于CSR在循环机，尽管事实上，在这个限制的源不再加速。结果提供了一个分析描述，显示如何增强光谱行为取决于源的几何形状和源内结构的随机分布的细节。它们提供了一个可行的实验手段推断与微结构束团的纵向电荷分布的性质，在超相对论运动的直段的束管从观察相关的电磁能谱。它们也与设计标准有关，这些领域的相干效应发挥着重要作用。
英文摘要：
The spectrum of electromagnetic fields satisfying perfectly conducting boundary conditions in a segment of a straight beam pipe with a circular cross-section is discussed as a function of various source models. These include charged bunches that move along the axis of the pipe with constant speed for which an exact solution to the initial-boundary value problem for Maxwell's equations in the beam pipe is derived. In the ultra-relativistic limit all longitudinal components of the fields tend to zero and the spectral content of the transverse fields and average total electromagnetic energy crossing any section of the beam pipe are directly related to the properties of the ultra-relativistic source. It is shown that for axially symmetric ultra-relativistic bunches interference effects occur that show a striking resemblance to those that occur due to CSR in cyclic machines despite the fact that in this limit the source is no longer accelerating. The results offer an analytic description showing how such enhanced spectral behaviour depends on the geometry of the source and the details of the stochastic distribution of structure within the source. They offer a viable experimental means for inferring properties of the longitudinal charge distribution of bunches with micro-structure in ultra-relativistic motion in straight segments of a beam pipe from observation of the associated electromagnetic energy spectra. They are also of relevance to design criteria where the coherence effects of such fields play a significant role.
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