Capture into resonance in dynamics of a classical hydrogen atom in an oscillating electric field

We consider a classical hydrogen atom in a linearly polarized electric field of slow changing frequency. When the system passes through a resonance between the driving frequency and the Kepler frequency of the electron's motion, a capture into the resonance can occur. We study this phenomenon in the case of 2:1 resonance and show that the capture results in growth of the eccentricity of the electron's orbit. The capture probability for various initial values of the eccentricity is defined and calculated.