The principle of similarity of trajectories for the motion of charged particles with different masses in electric and magnetic fields that are homogeneous in Euler terms

An electric field with potentials that is homogeneous in Euler terms satisfies the principle of similarity of trajectories that was derived by Yu.K. Golikov. Such fields are a useful tool for the development of electron and ion optical systems with unique properties. In this paper, the principle of similarity of trajectories is generalized to the case of a magnetic field and a combined electric and magnetic field that are homogeneous in Euler terms.