Finite Element Method for the Electromagnetic Field Computation in Cylindrically Symmetric RF Structures

Abstract

In this article a finite element method with special third-order elements for the computation of the TM 0np resonance modes and fields of cylindrically symmetric radio frequency (RF) structures is presented. The structure can be either an axially symmetric cavity resonator or a segment of a coaxial or a cylindrical waveguide, possibly with ceramic windows. In the closed cavity resonators the field computation problem can be reduced to an eigenvalue problem. In waveguides the computation domain is first closed by properly placed electric and magnetic walls. Then the field problem can be considered similarly as in the case of a cavity resonator, and any special boundary conditions at the ends of the waveguide are not needed. Thereafter, all possible wave forms, standing, traveling, and mixed waves, are obtained by appropriately combining these two resonant solutions. The locations of the walls are found by an iterative algorithm so that the given frequency of the electromagnetic field is the eigenvalue of the resulting cavity resonator. The developed methods are applied for the field computation in the TESLA accelerator structures.