HIGHLY EXCITED CHARGED 2-BODY SYSTEMS IN A MAGNETIC-FIELD - A PERTURBATION THEORETICAL APPROACH TO CLASSICAL DYNAMICS

We investigate classical dynamics and properties of highly excited cha rged two-body systems in a magnetic field. We hereby focus on the regu lar 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 t he parameter sigma:=B-1/2 and use a time-averaging method to obtain th e 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 differe nt 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 s pace is classified completely. Finally we arrive at a thorough underst anding of the recently found self-stabilization effect of the center-o f-mass motion of the ion in the context of our perturbation theoretica l investigation.