Electromagnetic Displacements Rotating Inside an Annular Region

Suitable electrodynamical displacements are obtained by solving the vector wave equation for the electric and the magnetic fields. The aim is to characterize domains where the multiplicity of a certain eigenvalue of the vector Laplacian is equal to four. This allows periodic solutions following interesting patterns. Tangential boundary conditions are assumed at the boundaries. We are able to carry out a simplified analysis in the case of annular domains, by playing with the zeros of spherical Bessel’s functions. As a possible application, we show how this preliminary study may help modeling the behavior of electromagnetic fields externally produced by a rotating star, such as our Sun, excited by the movement of the plasma in the corona. Further developments with regard to nonlinear problems may be investigated by adopting the displacements here proposed as a set of basis functions in view of spectral type approximations.