In the presence of a homogeneous magnetic field, the center of mass and electronic motion of an atom cannot be separated. For an atomic ion, the residual coupling is a Stark term with an oscillating electric field that is determined by the collective motion of the system. We investigate the effects and phenomena that occur due to this coupling in the classical dynamics of the highly excited ion. In particular, a permanent exchange of energy between the center of mass and the internal degrees of freedom is shown to take place. This leads, in the regular regime, in spite of an initially vanishing center-of-mass velocity, to the self-stabilization of the ion on a circular orbit. For small center-of-mass velocities and energies close to the ionization threshold, the motion of the atom is governed by its intermittent behavior. The most interesting dynamics occurs for rapidly moving ions for which the energy transfer from the center of mass to the internal degrees of freedom becomes strong enough to allow the atom to ionize. The statistics of this dynamical self-ionization process is studied for different center-of-mass velocities as well as internal energies. © 1995 The American Physical Society.