Closed-form solutions for the production of ions in the collisionless ionization of gases by intense lasers

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Abstract
We derive in closed form the solutions to the rate equations for sequential field ionization of gases by a focused laser beam. We obtain the low-intensity and the high-intensity limits of the ion yield for each charge state produced by the laser pulse. Furthermore we derive the scaling laws for the appearance intensity and the saturation intensity of the ion yield. We find that the appearance intensity depends not only on the binding energy of the ionized electron but also on the quantum numbers of the shell from which the electron ionizes. We interpret this dependence on the quantum number to be the species dependence in the appearance intensities discussed by Meyerhofer and co-workers [Phys. Rev. Lett. 63, 2212 (1989)]. Formulas for five ionization models are presented.