Highly excited charged two-body systems in a magnetic field: A perturbation theoretical approach to classical dynamics

We investigate classical dynamics and properties of highly excited charged two-body systems in a magnetic field. We hereby focus on the regular regime which can be described by perturbation theoretical methods. After introducing the exact constants of motion as canonical momenta we apply a perturbation theoretical series expansion with respect to the parameter σ:=${\mathit{B}}^{1/2}$ and use a time-averaging method to obtain the long-time dynamical behavior of the system. This procedure allows us to identify approximate constants of motion and enables us to derive effective Hamiltonians which describe the averaged dynamics on different time scales. The doubly averaged equations of motion are in fourth-order perturbation theory integrable. The solutions of these equations in terms of rotators and librators are given analytically and phase space is classified completely. Finally we arrive at a thorough understanding of the recently found self-stabilization effect of the center-of-mass motion of the ion in the context of our perturbation theoretical investigation. © 1996 The American Physical Society.