Electric-field effects on the closed orbits of the diamagnetic Kepler problem

The nonrelativistic closed orbits of an electron interacting with a unit positive charge in the presence of homogeneous magnetic and electric fields are investigated. A simplified theoretical model is proposed utilizing appropriate initial conditions in semiparabolic coordinates for arbitrary magnetic-and electric-field alignments. The evolution of both the angular spectrum of orbits and the shape and duration of individual orbits, as the electric-field intensity and scaled energy are increased, is shown for the cases of both parallel and crossed fields. Orbit mixing in the high-field regime is investigated in the case of parallel fields, giving an indication of the system moving from the quasi-Landau chaotic regime to the electric-field-induced (Stark effect) regular regime. For crossed fields, it is shown that the Garton-Tomkins orbits lead to a pair of orbits that have opposite behaviors as a function of the electric-field intensity.