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Application of the fictitious components method to the computation of the principal mode of a complex-shape RF cavity resonator

The problem of computing the minimal eigenfrequency and the corresponding electro-magnetic field is treated for a cavity resonator of special shape. This problem is approximated by a finite difference technique on shifted grids in the cylindrical coordinate system. A two-stage iterative process employing the ideas of the fictitious components technique is suggested for the solution of the resultant algebraic problem. The results of numerical experiments are given. Eigenvalue problems of electrodynamics, namely, the computation of eigenfrequencies and the corresponding eigenmodes of cavity resonators and waveguides, constitute an urgent problem in numerical mathematics. A large number of papers have been devoted to this field of study but attention was focused mostly on situations which are in some way reducible to two-dimensional cases. 'Essentially three-dimensional' problems have been much less analysed. Realization of the numerical methods suggested up to now for such problems [15] requires a very large number of arithmetic operations and memory locations. As a result, precise computation of eigenmodes for complex-shape cavities can be implemented only on very high performance computers. This paper treats the problem of computing the minimal eigenfrequency, and the eigenmode corresponding to it, of a special-shape cavity resonator. A finite difference approximation is constructed in the cylindrical coordinate system and the obtained grid problem is solved using an approach based on the fictitious components method [4,7, 11] which yields a very efficient algorithm. The paper is concluded with the results of numerical experiments with a specific cavity, the results are compared with experimental data. 1. DIFFERENTIAL PROBLEM Let Ω <= R represent the interior domain of a cavity resonator with ideally conductive surface 3Ω. Assume that the medium inside the cavity is a vacuum. The electromagnetic field in Ω is described by the system of Maxwell's equations [9], IdH rot£= --— c dt