Three-Dimensional Analysis of Wakefields Generated by Flat Electron Beams in Planar Dielectric-Loaded Structures

An electron bunch passing through dielectric-lined waveguide generates $\check{C}$erenkov radiation that can result in high-peak axial electric field suitable for acceleration of a subsequent bunch. Axial field beyond Gigavolt-per-meter are attainable in structures with sub-mm sizes depending on the achievement of suitable electron bunch parameters. A promising configuration consists of using planar dielectric structure driven by flat electron bunches. In this paper we present a three-dimensional analysis of wakefields produced by flat beams in planar dielectric structures thereby extending the work of Reference [A. Tremaine, J. Rosenzweig, and P. Schoessow, Phys. Rev. E 56, No. 6, 7204 (1997)] on the topic. We especially provide closed-form expressions for the normal frequencies and field amplitudes of the excited modes and benchmark these analytical results with finite-difference time-domain particle-in-cell numerical simulations. Finally, we implement a semi-analytical algorithm into a popular particle tracking program thereby enabling start-to-end high-fidelity modeling of linear accelerators based on dielectric-lined planar waveguides.