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

Abstract

In this paper, a compact and single-mode X-band dielectric-loaded matching section with constant tilt angle, blended edges, and two discontinuities at both ends is analyzed by the transmission line model. This matching section is designed as a high-power injection coupler to a dielectric-loaded accelerating structure (DLA). Although the transmission line model is a powerful tool for single-mode structures, because of radial inhomogeneity and lack of single value for characteristic impedance in dielectric-loaded structures, this method is not applicable in non-uniform dielectric-loaded structures. To solve this problem, it is shown that a dielectric-loaded waveguide (DLW) can be modeled by a dielectric-filled waveguide (DFW) with the same parameters of the phase constant, power flow, and dielectric loss. The characteristic impedance of a dielectric-filled waveguide can be determined by three structural parameters of the real and imaginary parts of the dielectric material and inner radius. These structural parameters can be found by solving a non-linear equation system made by equality of the parameters of the dielectric-loaded and dielectric-filled waveguides. To analyze the matching section, it is stratified to low thickness and uniform DLWs in the propagation direction and every segment is substituted by its equal DFW model. However, because of sharp variation in dielectric region at two ends of the flared section, solving the non-linear equation system is difficult at these points due to the lack of a proper initial point for the answer. Therefore, two virtual sections are added at the discontinuities to smoothen the variation of the dielectric region. Then, the total transmission matrix and scattering matrix parameters can be obtained without considering the added virtual sections. Moreover, the matching section is simulated by a full-wave electromagnetic software and the results of the scattering matrix parameters are compared with the ones of the proposed method. It is shown that there is a good agreement between the total behavior of the simulation and analytical results and the proposed method has acceptable accuracy.