Mass-separation by waves near the cyclotron frequency in the presence of electrostatic self-fields

The ponderomotive force by standing waves near the ion cyclotron frequency pushes ions along the axial steady magnetic field. The direction of this axial force depends on the ion mass, what can be used for ion mass separation, a much-needed process for various applications. We calculate single-particle trajectories under forces by standing waves, where there is an axial ponderomotive force, and compare them to the trajectories under traveling waves, where the axial ponderomotive force is absent. The equations of motion are solved for the case that the particle displacement is much smaller than a quarter wavelength. In that case we present analytical solutions that show the particle pushing along the magnetic field with the mass-dependent direction as well the growth of particle perpendicular velocity. We find numerically the particle trajectories when the particle displacement is close to a quarter wavelength and show when the trajectory deviates from the analytical solution. We then examine theoretically the possible role of electrostatic self- fields in a plasma. We show that, under certain conditions, the self-fields can be used to enhance the process of ion mass separation.