Canonical perturbation treatment of a Rydberg electron in combined electric and magnetic fields

We analyze the motion of a Rydberg electron in combined external electric and magnetic fields using different levels of classical perturbation theory. Important dynamical properties of these systems are captured analytically through adiabatic invariants, and three widely different time scales for motion are identified. The hydrogen atom in tilted electric and magnetic fields, the hydrogen atom in combined magnetic and circularly polarized microwave fields, and the generalized van der Waals interaction are among the cases we examine.