Optical Approximation in the Theory of Geometric Impedance
Optical Approximation in the Theory of Geometric Impedance
复制标题
几何阻抗理论中的光学逼近
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
I. Zagorodnov
中科院分区：
文献类型：
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作者：
G. Stupakov;K. Bane;I. Zagorodnov
本文将光学近似引入到阻抗计算理论中，该近似在高频极限下是有效的。这种近似忽略了辐射过程中的衍射效应，在概念上等同于电磁理论中的几何光学近似。利用这个近似，我们推导出源粒子和测试粒子相对于参考轨道任意偏移的纵向阻抗方程。在Panofsky-Wenzel定理的帮助下，我们还得到了横向阻抗的表达式（也适用于任意偏移量）。对于实际应用中典型的小偏移量，我们进一步简化了这些表达式。我们最后的阻抗表达式，在一般情况下，涉及到在各种过渡截面上的二维积分。对于几个已知的轴对称例子，我们进一步演示了如何将我们的方法应用于阻抗的计算。最后，讨论了阻抗理论中光学近似的精度及其与衍射状态的关系。
In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually equivalent to the approximation of geometric optics in electromagnetic theory. Using this approximation, we derive equations for the longitudinal impedance for arbitrary offsets, with respect to a reference orbit, of source and test particles. With the help of the Panofsky-Wenzel theorem we also obtain expressions for the transverse impedance (also for arbitrary offsets). We further simplify these expressions for the case of the small offsets that are typical for practical applications. Our final expressions for the impedance, in the general case, involve two dimensional integrals over various cross-sections of the transition. We further demonstrate, for several known axisymmetric examples, how our method is applied to the calculation of impedances. Finally, we discuss the accuracy of the optical approximation and its relation to the diffraction regime in the theory of impedance.