dorsal/arxiv
View SchemaOptical approximation in the theory of geometric impedance
| Authors | G. Stupakov, K. L. F. Bane, I. Zagorodnov |
|---|---|
| Categories | |
| ArXiv ID | physics/0703171 |
| URL | https://arxiv.org/abs/physics/0703171 |
| DOI | 10.1103/PhysRevSTAB.10.054401 |
| Journal | Phys.Rev.STAccel.Beams10:054401,2007 |
Abstract
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.
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"abstract": "In this paper we introduce an optical approximation into the theory of\nimpedance calculation, one valid in the limit of high frequencies. This\napproximation neglects diffraction effects in the radiation process, and is\nconceptually equivalent to the approximation of geometric optics in\nelectromagnetic theory. Using this approximation, we derive equations for the\nlongitudinal impedance for arbitrary offsets, with respect to a reference\norbit, of source and test particles. With the help of the Panofsky-Wenzel\ntheorem we also obtain expressions for the transverse impedance (also for\narbitrary offsets). We further simplify these expressions for the case of the\nsmall offsets that are typical for practical applications. Our final\nexpressions for the impedance, in the general case, involve two dimensional\nintegrals over various cross-sections of the transition. We further\ndemonstrate, for several known axisymmetric examples, how our method is applied\nto the calculation of impedances. Finally, we discuss the accuracy of the\noptical approximation and its relation to the diffraction regime in the theory\nof impedance.",
"arxiv_id": "physics/0703171",
"authors": [
"G. Stupakov",
"K. L. F. Bane",
"I. Zagorodnov"
],
"categories": [
"physics.acc-ph"
],
"doi": "10.1103/PhysRevSTAB.10.054401",
"journal_ref": "Phys.Rev.STAccel.Beams10:054401,2007",
"title": "Optical approximation in the theory of geometric impedance",
"url": "https://arxiv.org/abs/physics/0703171"
},
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