Approximate method for electromagnetic analysis of a dielectric-loaded coupler used in accelerating structures

Abstract

In this paper, a theoretical analysis of a dielectric-loaded coupler based on the transmission line model is proposed. One of the major challenges in the design of dielectric-loaded accelerating (DLA) structures is the proper coupling of high-power RF into the dielectric-loaded tube. The considered X-band coupler consists of a tapered dielectric-loaded tube converting TM 01 mode in a conventional circular waveguide to the one in a uniform dielectric-loaded tube. To analyze the coupler with an approximation based on the transmission line model, the coupler is divided into a large number of sections in the propagation direction. Every section is considered as a short-length uniform transmission line with its own characteristic impedance and propagation constant. Then, scattering matrix parameters of the coupler are calculated by the total transmission matrix of the structure. To investigate the accuracy of the proposed method, two coupler prototypes with different dielectric materials are considered and their scattering matrix parameters are obtained by the proposed method and full-wave simulation. Overall, it is shown that the analytical results are sufficiently close to the simulation and optimizations performed by the proposed method can be used as the starting point for full-wave or numerical optimization.

Enhancement of transmission line model to analyze the matching section of a dielectric-loaded accelerator with sharp discontinuities

“…Although DLAs and their dielectric-loaded couplers are mostly single-mode structures, the radial inhomogeneity limits the transmission line model to analyze such structures because it is not possible to define a single value for the characteristic impedance of a dielectric-loaded waveguide (DLW). To solve this problem in [22,23] an approximation formula as a linear combination of the characteristic impedances of dielectric and vacuum regions is used to dedicate a single value to the characteristic impedance of the DLW. By employing this formula, a uniform standing-wave DLA and a non-uniform dielectric-loaded coupler are analyzed with transmission line model in [22] and [23], respectively and it is shown the proposed method is fast and has acceptable accuracy.…”

“…To solve this problem in [22,23] an approximation formula as a linear combination of the characteristic impedances of dielectric and vacuum regions is used to dedicate a single value to the characteristic impedance of the DLW. By employing this formula, a uniform standing-wave DLA and a non-uniform dielectric-loaded coupler are analyzed with transmission line model in [22] and [23], respectively and it is shown the proposed method is fast and has acceptable accuracy.…”

“…in which 𝛼 𝑧 and 𝛽 𝑧 are the phase constant and attenuation constant, respectively. For a uniform DLW with the inner radius of 𝑟 = 𝑎, the outer radius of 𝑟 = 𝑏, and perfect electric conductor (PEC) body, the propagation constant can be extracted from the following dispersion equation [22][23][24]:…”

“…Due to the inhomogeneity of the DLW structure, the characteristic impedance of the 𝑇 𝑀 01 mode is different in the dielectric and vacuum regions. In [22,23] a linear combination of the characteristic impedance of vacuum and dielectric mediums is introduced as single value estimation of the characteristic impedance of the DLW. In this formula, the characteristic impedance of each region is weighted by the ratio of the power flow in that region to the total power flow of the DLW.…”

“…The total transmission matrix of the matching section can be obtained by cascading the transmission matrix of the stratified segments. Then, using some mathematical formulas, S-parameters can be achieved from the total transmission matrix [23,24,26].…”