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

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.

17 pages, 6 figures, 2 tables

Cited by in corpus (6)

• Stability condition for the drive bunch in a collinear wakefield accelerator
• Analytical treatment of the wakefields driven by transversely shaped beams in a planar slow-wave structure
• Analytical model of a 3D beam dynamics in a wakefield device
• On "Efficiency versus Instability in plasma accelerators"
• Analytical theory of the skewed wake effect
• Bounds on geometric wakefields in collimators and step transitions of arbitrary cross sections