  An axisymmetric space-localized solution of nonlinear electrodynamics is
considered as massive charged particle with spin and magnetic moment. The
appropriate solution for nonlinear electrodynamics with ring singularity is
investigated. In view of this problem the system of toroidal waves in linear
electrodynamics is considered. The problem with boundary conditions on the
singular ring of the toroidal coordinate system is investigated. The boundary
conditions are taken taking into account the conformity between the toroidal
and cylindrical waves on the ring. In this case the singular ring looks like
convolute axis of cylindrical system. The appropriate system of wave modes are
obtained in an integral form with the help of source function.
