Magnetic-field-caused narrowing of hydrogenic spectral lines under a circularly polarized electromagnetic wave: the analytical solution

Abstract

In the literature, there was an exact analytical result for the splitting of hydrogen spectral lines in an electric field E rotating with a constant angular velocity Ω. In the reference frame rotating with the angular velocity of the field, the problem was reduced to a hydrogen atom in the static electric field crossed with a fictitious static magnetic field, the latter problem having an exact analytical solution. From the physical point of view, this was achieved by using the O₄ symmetry of hydrogen atoms. In the present paper we provide an analytical solution for the splitting of hydrogen-like spectral lines in the situation where the rotating field represents a circularly polarized electromagnetic wave, but there is also a true, relatively strong magnetic field B that can be parallel or antiparallel to the angular velocity vector Ω. We show that by varying the true magnetic field, it is possible to diminish the splitting of hydrogenic spectral lines, which is a counterintuitive result. The most interesting case is where the true magnetic field completely cancels out the effect of the fictitious magnetic field, thus minimizing the splitting. In this case, the total intensity of the spectral line diminishes by 40%. This is yet another counterintuitive result. One important practical application could be the spectroscopic diagnostic of the electron cyclotron waves used as an additional heating method for plasmas in magnetic fusion machines. Another practical embodiment could relate to the configuration that can occur during relativistic laser plasma interactions where strong magnetic fields are predicted.