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arXiv physics/0603230physics.acc-ph
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小不连续性的耦合阻抗:与束流速度的关系

Coupling Impedances of Small Discontinuities: Dependence on Beam Velocity

Sergey S. Kurennoy

摘要:

计算了加速器真空室小不连续性的束耦合阻抗[例如,S.S.库伦诺伊河Gluckstern和G. V. Stupakov,Phys.Rev.E52,4354(1995)]中的方法。在这里,我们将结果推广到任意的光束速度。假设真空室具有任意但沿光束路径均匀的截面。纵向和横向的耦合阻抗推导出在一系列的横截面本征函数,而不连续的形状进入通过其极化率。给出了两种重要特殊情况-圆形和矩形腔室截面-的简单显式公式。阻抗对束流速度的依赖性表现出一些不寻常的特征:例如,在超相对论极限中占主导地位的电抗性阻抗可以在一定的束流速度下消失,或者其幅度可以多次超过超相对论值。此外,我们证明了同样的技术,场展开成一系列的横截面本征函数,是方便的计算空间电荷阻抗的均匀束管与任意截面。

英文摘要:

The beam coupling impedances of small discontinuities of an accelerator vacuum chamber have been calculated [e.g., S.S. Kurennoy, R.L. Gluckstern, and G.V. Stupakov, Phys. Rev. E 52, 4354 (1995)] for ultrarelativistic beams using the Bethe diffraction theory. Here we extend the results to an arbitrary beam velocity. The vacuum chamber is assumed to have an arbitrary, but uniform along the beam path, cross section. The longitudinal and transverse coupling impedances are derived in terms of series over cross-section eigenfunctions, while the discontinuity shape enters via its polarizabilities. Simple explicit formulas for two important particular cases - circular and rectangular chamber cross sections - are presented. The impedance dependence on the beam velocity exhibits some unusual features: for example, the reactive impedance, which dominates in the ultrarelativistic limit, can vanish at a certain beam velocity, or its magnitude can exceed the ultrarelativistic value many times. In addition, we demonstrate that the same technique, the field expansion into a series of cross-section eigenfunctions, is convenient for calculating the space-charge impedance of uniform beam pipes with arbitrary cross section.

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