Perturbation analysis and simulation study of the effects of phase on the classical hydrogen atom interacting with circularly polarized electromagnetic radiation

The classical hydrogen atom is examined for the situation where a circularly polarized electromagnetic plane wave acts on a classical charged point particle in a near-circular orbit about an infinitely massive nucleus, with the plane wave normally incident to the plane of the orbit. The effect of the phase alpha of the polarized wave in relation to the velocity vector of the classical electron is examined in detail by carrying out a perturbation analysis and then comparing results using simulation methods. By expanding the variational parts of the radius and angular velocity about their average values, simpler nonlinear differential equations of motion are obtained that still retain the key features of the oscillating amplitude, namely, the gradual increase of the envelope of the oscillating amplitude and the point of rapid orbital decay. Also, as shown here, these key features carry over nicely to conventional quantities of interest such as energy and angular momentum. The phase a is shown here to have both subtle yet very significant effects on the quasistability of the orbital motion. A far wider range of phase conditions are found to provide stability than might intuitively be expected, with the time to orbital decay, t(d), varying by orders of magnitude for any plane wave with an amplitude A above a critical value, A(c).