Steady-state magnetic trap configurations for the axially symmetric free electromagnetic field in vacuum

In this paper we deduce and obtain a set of exact axially symmetric independent solutions of the free Maxwell equations in vacuum that represent stable electromagnetic field configurations containing (i) spherical and conical surfaces where there is only time-dependent tangential magnetic field and no electric field, and (ii) ring-shaped formations with the time-dependent tangential electric field and zero magnetic fields. The magnetic surfaces are combined in such a way that they form magnetic traps, that is, these magnetic surfaces are the border of closed spatial regions, with the particularity that an electric ring is always contained within each magnetic trap. We carry out a detailed study of the spatial distribution of the energy density and the energy flux density.