Dipole-mode wakefields in dielectric-loaded rectangular waveguide accelerating structures

Abstract

By applying different symmetric boundary conditions, we found that the transverse wakefields generated by an electron bunch traveling through a partially loaded rectangular dielectric structure at an off center position can be decomposed into corresponding orthogonal longitudinal section electric (LSE) and longitudinal section magnetic (LSM) modes for guided waves as in the case of longitudinal wakefields treated previously. The wakefields are characterized using the normalized shunt impedance R/Q, a function of the geometry of the accelerating structure, for both LSE and LSM modes. A numerical example is given for an X-band waveguide structure and detailed results are given for the several leading transverse wakefield terms. The analytic results obtained are in agreement with the results from the time domain simulation tool MAFIA.

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

“…Finally, (i) the proposed method does not require any assumptions on the form of the beam's Coulomb field (in contrast to the impedance method [25,26], where it is often assumed that the field of the beam is essentially flat, an assumption that is valid only at ultrarelativistic energies); (ii) we also did not use the mode decomposition for the problem formulation and its subsequent solution; the mode series obtained as a solution emerges in a natural way as a result of solving the problem; (iii) as a consequence of (ii), and the use of the transverse operator formalism the series of modes of the solution is uniformly convergent. This is not obvious for the solution obtained by the impedance method [25,26] and requires additional analysis and proof.…”

“…Theoretical analyses of dielectric accelerating structures with rectangular geometries have been reported in a number of publications [23,[25][26][27][28][29][30][31]. To determine the amplitudes of individual Cherenkov radiation modes excited in a rectangular waveguide with dielectric slabs, the impedance matching technique was used in the earlier papers [23,25,26].…”

“…To determine the amplitudes of individual Cherenkov radiation modes excited in a rectangular waveguide with dielectric slabs, the impedance matching technique was used in the earlier papers [23,25,26]. When that formalism is used instead of the direct solution of the nonhomogeneous system of Maxwell equations (the standard analytic approach in analysis of wakefields in cylindrical structures [20,21]), the amplitudes of the wakefields needs to be expressed in terms of the shunt impedance (or integrated loss factor) for each mode of the structure [23,25,26]. The approach involves certain approximations, while the direct solution of the inhomogeneous system of Maxwell's equations without intermediate approximations is always preferable for analyzing the wakefield generation problem in DWA structures.…”

Three-dimensional analysis of wakefields generated by flat electron beams in planar dielectric-loaded structures

“…This paper is pedagogical in the sense that it is about the method of derivation rather than the results, which have been derived in previous papers, most extensively in Ref. [24]. However, this paper provides close-form formulas for the eigenfrequencies and electromagnetic fields excited in planar DLWs.…”

“…Therefore, the design of the DLW structures must compromise between a small transverse size to maximize the intensity of the wakefield, and a longer interaction length to maximize the energy gain of the test charge. An appealing solution consists of using flat electron beams passing through slab-geometry DLWs [14,[23][24][25]. This possibility has become more attractive since the recent advances toward generating flat beams directly in photoinjectors [26,27].…”