The structure of ionizing electron trajectories for hydrogen in parallel fields

Classical trajectories of an electron escaping from a hydrogen atom in parallel electric and magnetic fields exhibit strikingly diverse and complex behavior. We study the classification and qualitative structure of these trajectories. Specifically, (i) we develop a symbolic phase space labeling for ionizing trajectories; (ii) we describe the trajectories in configuration space using a second symbolic encoding that records the sequence of electron oscillations and electron orbits around the nucleus; and (iii) we establish an algorithm that connects the phase space labeling of a trajectory to its configuration space description.