New Results on the Impedance of Resistive Metal Walls of Finite Thickness
New Results on the Impedance of Resistive Metal Walls of Finite Thickness
复制标题
有限厚度电阻金属壁阻抗的新结果
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
B. Zotter
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文献类型：
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作者：
B. Zotter
圆柱形真空室的电阻壁阻抗在40多年前首次计算。原始结果对于金属真空室壁是有效的，金属真空室壁在感兴趣的频率下与趋肤深度相比是厚的。最近，这个问题再次成为重要的束流稳定性在LHC特别是横向阻抗的大量石墨准直器安装可能会严重限制其性能，如果“厚壁”公式是正确的。在这样一个大的机器慢电子感应加速器波的频率是非常低的，因此横向阻抗，原来发现是成正比的频率的平方根倒数，可能会导致不稳定性。然而，当集肤深度超过壁厚时，横向电阻性壁阻抗强烈减小，并且最近发表了许多论文来估计这种减小。然而，所有这些都有有效性的限制。在这里，我们给出了一个一致的推导出的一般表达式的横向阻抗的任意材料制成的墙壁是有效的在所有频率。的结果进行了比较，与以前的LHC准直器的图形中，他们同意相当不错，但也为SPS-MKE踢球者，需要注入到LHC和协议是不太完美的。日内瓦，瑞士
The resistive wall impedance of cylindrical vacuum chambers was first calculated over 40 years ago. The original results were valid for metal vacuum chamber walls which are thick compared to the skin depth at the frequencies of interest. Recently the subject has again become important for beam stability in the LHC where in particular the transverse impedance of the large number of graphite collimators to be installed could severely limit its performance, if the “thick wall” formulae were correct. The frequencies of the slow betatron waves in such a large machine are very low and thus the transverse impedance, originally found to be proportional to the inverse square root of frequency, could lead to instabilities. However, when the skin depth exceeds the wall thickness, the transverse resistive wall impedance is strongly reduced and a number of papers have recently been published to estimate this reduction. However, all of these had restrictions of validity. Here we give a consistent derivation of the general expression for the transverse impedance of walls made of arbitrary materials which are valid at all frequencies. The results are compared with previous ones in the graphs for the LHC collimators where they agree quite well, but also for the SPS-MKE kickers which are required for injection into the LHC and where the agreement is less perfect. Geneva, Switzerland 02/08/2005