Dynamic chaos in the tunnelling ionization produced by a strong low-frequency electromagnetic field

Ionization of atoms by a strong low-frequency linearly polarized electromagnetic field (the photon energy is small compared to the atomic ionization potential) is considered under new conditions compared to the well known Keldysh approach. The field strength is supposed to be small in comparison to the atomic field strength. But the Coulomb interaction of an electron with atomic core is assumed to be of the same order of magnitude as the interaction between an electron and the external electromagnetic field. It was shown that then classical electron motion in the continuum becomes chaotic (this is so-called dynamic chaos). Using the averaging procedure of Chirikov about the chaotic variation of the phase of motion, the considered Newton problem is transformed into the problem of nonlinear electron diffusion over energy scale. In this work we derive the classical electron energy averaged over fast chaotic oscillations of an electron in the final continuum state which takes into account both the Coulomb field and electromagnetic field. This energy is used for analytic calculation of the ionization rate of the ground atomic state into the low lying continuum state based on the Landau-Dykhne approximation (with exponential accuracy). We found that the ionization rate depends significantly on the field frequency. When field frequency decreases, the well known tunnelling limit has been obtained, and then the ionization rate does not depend on the field frequency.