Impedance of a rectangular beam tube with small corrugations

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Abstract

We consider the impedance of a structure with rectangular, periodic corrugations on two opposing sides of a rectangular beam tube. Using the method of field matching, we find the modes in such a structure. We then limit ourselves to the case of small corrugations, but where the depth of corrugation is not small compared to the period. For such a structure we generate analytical approximate solutions for the wave number k, group velocity vg, and loss factor êfor the lowest (the dominant) mode which, when compared with the results of the complete numerical solution, agreed well. We find if w ∼ a, where w is the beam pipe width and a is the beam pipe half-height, then one mode dominates the impedance, with k ∼ 1 / √wδ (δ is the depth of corrugation), (1 - vg/c) ∼ δ, and κ ∼ 1 /(aw), which (when replacing w by a) is the same scaling as was found for small corrugations in a round beam pipe. Our results disagree in an important way with a recent paper of Mostacci et al. [A. Mostacci et al., Phys. Rev. ST Accel. Beams 5, 044401 (2002)], where, for the rectangular structure, the authors obtained a synchronous mode with the same frequency k, but with κ ∼ δ. Finally, we find that if w is large compared to a then many nearby modes contribute to the impedance, resulting in a wakefield that Landau damps. © 2003 The American Physical Society.

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Bane, K. L. F., & Stupakov, G. (2003). Impedance of a rectangular beam tube with small corrugations. Physical Review Special Topics - Accelerators and Beams, 6(2), 45–54. https://doi.org/10.1103/PhysRevSTAB.6.024401

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