Universal expressions for 3d electric and magnetic potentials which are uniform in Euler terms

Electric and magnetic fields which are uniform in Euler terms are a useful instrument to design the systems of charge particle optics. The similarity principle for charged particle trajectories in these fields which was realized by Yu.K. Golikov for the first time enables to create spectrographic charge particle optical systems in a more systematic and intelligence way by using the fields which are uniform in Euler terms. As a result the analytical expressions for the Laplace potentials which are uniform in Euler terms are a useful tool to design optical systems of this type. This paper considers general expressions of an algebraic-differential type which produces 3D harmonic functions which are uniform in Euler’ terms and can be used as potentials of corresponding electric and magnetic fields.