The Dynamics of Excited Hydrogen Atoms in Strong Electric and Magnetic Fields

Rath, Orsola (1990). The Dynamics of Excited Hydrogen Atoms in Strong Electric and Magnetic Fields. PhD thesis The Open University.



This thesis concerns the study of dynamical systems whose classical dynamics exhibit chaotic motion. Two systems in which classical chaos plays an important role are investigated in this work. Both involve highly excited hydrogen atoms in strong external fields, in one case a periodic electric field and in the other a uniform magnetic field. These examples are chosen for their particular relevance to the study of the relationship between classical and quantum dynamics when the motion is irregular.

A three-dimensional classical simulation of the hydrogen atom in a microwave field is developed. This is then used for a study of the mechanism of ionisation and for an extensive comparison with experimental results. For this purpose a regularising transformation is developed, together with an asymptotic approximation for the case when the electron moves far from the atom. This reveals many interesting new features of the dynamics. Some explanations of the ionisation mechanism in different frequency ranges are given.

The hydrogen atom in a magnetic field is studied by using the adiabatic method, which is shown to be reliable for very accurate calculations of the energy levels even when the external field is very strong and most of the orbits are irregular. This system has both librational and rotational motion. Although the zero-frequency motion on the separatrix contradicts the assumption of adiabatic invariance, it is shown that in practice the adiabatic method may still be applied. A similar problem occurs because one of the fundamental frequencies is initially zero, but this is overcome by choosing the initial conditions appropriately.

An extensive review of the literature is given for both of these problems.

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