发表机构
Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究推导了适用于不等束流管道与任意束流速度的纵向和横向尾场势间接积分公式，经数值测试验证了方法的正确性，可用于尾场计算。
AI 中文摘要
间接积分将尾场计算中长的均匀束流管道部分替换为管道横截面上的场问题。早期的超相对论方法主要针对纵向尾场，而横向尾场通常通过Panofsky-Wenzel定理得到。我们推导了间接公式，用于补充时域计算中已累积的横向洛伦兹力积分。在β=1时，每个半无限尾由两个泊松问题求解：一个是由Ez驱动的狄利克雷泊松问题，描述TM贡献；另一个是由cBz驱动的诺伊曼泊松问题，描述TE贡献。我们针对输入和输出管道相等或不等的情况，得到了固定时间移动窗口表示和固定平面时间历程表示。随后将该方法扩展到以0<βc<c的恒定速度运动的刚性束团，纵向修正满足(x,y,s)中的各向异性椭圆方程，并为横向TM问题提供额外源。在双端口有限参考约定中，包含空间电荷的完整场在两个固定平面之间直接积分，而半无限尾场则在减去各管道内的稳态场后计算。所得Panofsky-Wenzel关系包含两个端口处稳态横向电场的差值。对β=1和β=0.8时不等矩形阶跃结构的数值测试，验证了横向间接积分和不等管道边界项的正确性。
英文摘要
Indirect integration replaces the long uniform beam-pipe parts of a wakefield calculation by field problems in the pipe cross sections. Earlier ultrarelativistic methods were developed mainly for the longitudinal wake, whereas the transverse wake was usually obtained from the Panofsky--Wenzel theorem. We derive indirect formulas that complete a transverse Lorentz-force integral already accumulated in a time-domain calculation. At $β=1$, each semi-infinite tail is found from a Dirichlet Poisson problem driven by $E_z$ and a Neumann Poisson problem driven by $cB_z$, describing the TM and TE contributions, respectively. We obtain both a fixed-time moving-window representation and a fixed-plane time-history representation for equal or unequal input and output pipes. The method is then extended to a rigid bunch moving with constant velocity $0<βc<c$. The longitudinal correction satisfies an anisotropic elliptic equation in $(x,y,s)$ and provides an additional source for the transverse TM problem. In a two-port finite-reference convention, the complete fields, including space charge, are integrated directly between two fixed planes, while the semi-infinite tails are calculated after subtraction of the stationary field in each pipe. The resulting Panofsky--Wenzel relation contains the difference of the stationary transverse electric fields at the two ports. Numerical tests for an unequal rectangular step-out at $β=1$ and $β=0.8$ confirm the transverse indirect integration and the unequal-pipe boundary term.
Comments14 pages, 4 figures
