dorsal/arxiv
View SchemaImpedance of a Rectangular Beam Tube with Small Corrugations
| Authors | K. L. F. Bane, G. Stupakov |
|---|---|
| Categories | |
| ArXiv ID | physics/0209042 |
| URL | https://arxiv.org/abs/physics/0209042 |
| DOI | 10.1103/PhysRevSTAB.6.024401 |
| Journal | Phys.Rev.ST Accel.Beams 6 (2003) 024401 |
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 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 $v_g$, and loss factor $\kappa$ for the lowest (the dominant) mode which, when compared with the results of the complete numerical solution, agreed well. We find: if $w\sim a$, where $w$ is the beam pipe width and $a$ is the beam pipe half-height, then one mode dominates the impedance, with $k\sim1/\sqrt{w\delta}$ ($\delta$ is the depth of corrugation), $(1-v_g/c)\sim\delta$, and $\kappa\sim1/(aw)$, which (when replacing $w$ by $a$) is the same scaling as was found for small corrugations in a {\it round} beam pipe. Our results disagree in an important way with a recent paper of Mostacci {\it et al.} [A. Mostacci {\it et al.}, Phys. Rev. ST-AB, {\bf 5}, 044401 (2002)], where, for the rectangular structure, the authors obtained a synchronous mode with the same frequency $k$, but with $\kappa\sim\delta$. 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.
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"abstract": "We consider the impedance of a structure with rectangular, periodic\ncorrugations on two opposing sides of a rectangular beam tube. Using the method\nof field matching, we find the modes in such a structure. We then limit\nourselves to the the case of small corrugations, but where the depth of\ncorrugation is not small compared to the period. For such a structure we\ngenerate analytical approximate solutions for the wave number $k$, group\nvelocity $v_g$, and loss factor $\\kappa$ for the lowest (the dominant) mode\nwhich, when compared with the results of the complete numerical solution,\nagreed well. We find: if $w\\sim a$, where $w$ is the beam pipe width and $a$ is\nthe beam pipe half-height, then one mode dominates the impedance, with\n$k\\sim1/\\sqrt{w\\delta}$ ($\\delta$ is the depth of corrugation),\n$(1-v_g/c)\\sim\\delta$, and $\\kappa\\sim1/(aw)$, which (when replacing $w$ by\n$a$) is the same scaling as was found for small corrugations in a {\\it round}\nbeam pipe. Our results disagree in an important way with a recent paper of\nMostacci {\\it et al.} [A. Mostacci {\\it et al.}, Phys. Rev. ST-AB, {\\bf 5},\n044401 (2002)], where, for the rectangular structure, the authors obtained a\nsynchronous mode with the same frequency $k$, but with $\\kappa\\sim\\delta$.\nFinally, we find that if $w$ is large compared to $a$ then many nearby modes\ncontribute to the impedance, resulting in a wakefield that Landau damps.",
"arxiv_id": "physics/0209042",
"authors": [
"K. L. F. Bane",
"G. Stupakov"
],
"categories": [
"physics.acc-ph"
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"doi": "10.1103/PhysRevSTAB.6.024401",
"journal_ref": "Phys.Rev.ST Accel.Beams 6 (2003) 024401",
"title": "Impedance of a Rectangular Beam Tube with Small Corrugations",
"url": "https://arxiv.org/abs/physics/0209042"
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