Calculation of the electrostatic field in a dielectric-loaded waveguide due to an arbitrary charge distribution on the dielectric layer

The goal of this paper is to study the electrostatic field due to an arbitrary charge distribution on a dielectric layer in a dielectric-loaded rectangular waveguide. In order to obtain this electrostatic field, the potential due to a point charge on the dielectric layer is solved in advance. The high computational complexity of this problem requires the use of different numerical integration techniques (e.g., Filon, Gauss-Kronrod, Lobatto, ...) and interpolation methods. Using the principle of superposition, the potential due to an arbitrary charge distribution on a dielectric layer is obtained by adding the individual contribution of each point charge. Finally, a numerical differentiation of the potential is carried out to obtain the electrostatic field in the waveguide. The results of this electrostatic problem are going to be extended to model the multipactor effect, which is a problem of great interest in the space industry.