The problem of own values and own functions in the toroidal cavity

In this work the problem of definition of electromagnetic fields in the toroidal cavity is discussed and is given the analysis of the comparison of the own values and the own functions obtained by different methods. Three methods are discussed to define the own frequencies in the toroidal cavity — the uniform short wave asymptotic method, where the variables are separated partially in the Helmholtz equation when the toroid is filled by an inhomogenious medium with a toroidal symmetry and then are constructed the uniform short wave asymptotic solutions of Maxwell equations, then the successful approximate method based on the perturbation theory and at last a digital method by the package $FEMLAB$ using the finite element method. Then it is defined the own frequencies of the toroidal cavity by these three methods. It is shown that the results show a good coincidence for the large torus.