Calculation of the resonance frequency of a toroidal plasma

In this research, we obtain the resonance frequency of the toroid cold plasma, by calculating the related electric potential in two different states of polarization of the incident electric field. In the first case, we consider the incident electric field parallel to the axis of the torus and in the second case, we consider it perpendicular to the axis of the torus. By solving the Laplace equation and using the appropriate boundary conditions in the toroidal coordinates, we calculate the electrical potential inside and outside the torus and the resonance frequency of the toroidal plasma. Furthermore, the electrical field inside the torus is calculated. Then, we plot the resonance frequency and the amplitude of the potential in different sta.