  Using the correspondence between solutions of gravitational and gauge
theories (the so-called classical double copy conjecture) some electromagnetic
fields with vortices are constructed, for which the Lorentz force equations are
analytically solvable. The starting point is a certain class of plane
gravitational waves exhibiting the conformal symmetry. The notion of the
Niederer transformation, crucial for the solvability, is analysed in the case
of the Lorentz force equation on the curved spacetimes as well as its
derivation by means of integrals of motion (associated with conformal
generators preserving these vortices) is presented. Furthermore, some models
discussed recently in the context of the intense laser beams are constructed
from their gravitational counterparts, with the special emphasis put on the
focusing property, and new solvable examples are presented.
