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arXiv · 1507.03901

Calculation of the Cherenkov fields in the cross-section of a short relativistic bunch

S. S. Baturin
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Abstract

Recently, a new method for calculating the Cherenkov field acting on a point-like electron bunch passing through longitudinally homogeneous structures lined with arbitrary slowdown layers was proposed, where the formalism was obtained though consideration of a general integral relation that allows calculation of the fields at the vicinity of a point-like bunch. It demonstrates that the Cherenkov field at the point of the short relativistic bunch does not depend on the waveguide system material and is a constant for any given transverse dimensions and cross-section shapes of waveguides. With this paper we present a strict derivation of the fields formulas valid at the cross-section of a bunch on the basis of a conformal mapping method. We generalize the results of the previous paper to the case of transversely distributed bunch by deriving a two-dimensional Green function at the cross-section of a bunch. Comparison of the results proving validity of the method is given in the appendix.

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S. S. Baturin. 2015-07-14. Calculation of the Cherenkov fields in the cross-section of a short relativistic bunch. https://doi.org/10.1103/physrevaccelbeams.19.051001

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