Transverse operator method for wakefields in a rectangular dielectric loaded accelerating structure

Abstract

Cherenkov radiation generated by a relativistic electron bunch in a rectangular dielectric-loaded waveguide is analyzed under the assumption that the dielectric layers are inhomogeneous normal to the beam path. We propose a method that uses eigenfunctions of the transverse operator applied to develop a rigorous full solution for the wakefields that are generated. The dispersion equation for the structure is derived and the wakefield analysis is carried out. The formalism developed here allows the direct solution of the inhomogeneous system of Maxwell equations, an alternative analytic approach to the analysis of wakefields in contrast to the previously used impedance method for rectangular structure analysis. The formalism described here was successfully applied to the analysis of rectangular dielectric-lined structures that have been recently beam tested at the Argonne (ANL/AWA) and Brookhaven (BNL/ATF) accelerator facilities.

Cherenkov Radiation from Short Relativistic Bunches: General Approach

“…The same equivalence of the loss factor can be found for noncylindrical structures as well [14]. In a planar or rectangular all-metal waveguide with resistive walls [16,22], small corrugations [14,15], or a thin dielectric liner [24,25] the loss factor would be the same for structures with equal apertures: it is a constant that is dependent on transverse dimensions but independent of the material properties.…”

“…Also, at first the loss factor formula (20), Table I, was derived here for a waveguide with the square cross section metal wall completely lined with the slowdown layer. This formula can be used for dielectric wakefield acceleration or THz generation devices [2, 25,27,28]. In addition to the resistance and roughness, the waveguide wall may have an oxide layer, which is usually a dielectric.…”

“…The total loss factor κ is usually defined as (1). In the case of a thin corrugation layer [14,[16][17][18][19][20][21] or dielectric [14,19,21,25] the total loss factor is equal to the loss factor of the fundamental mode of the structure. The expression for the loss factor of a conductive cylindrical pipe [ Fig.…”

General solutions for the fields generated by a relativistic electron beam propagating in a rectangular dielectric waveguide

“…These radiation fields can also used for acceleration of a witness electron beam passing through the same structure at a specific delay with respect to the drive beam [5]. While the original work in this area focused on cylindrical structures, rectangular structures have recently come under intensive scrutiny in recent years both in testing new methods of acceleration and for studying the electronic properties of the dielectric itself [6,7].…”

“…Analytic expressions for the fields were obtained using a modification of the transverse operator method [6]. This approach allows us to obtain a complete analytical solution for the eigenfunctions and therefore solve the problem of the generation of radiation in a rectangular dielectric loaded structure.…”