CLOSED-FORM SOLUTIONS FOR THE PRODUCTION OF IONS IN THE COLLISIONLESSIONIZATION OF GASES BY INTENSE LASERS

We derive in closed form the solutions to the rate equations for seque ntial 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 s caling laws for the appearance intensity and the saturation intensity of the ion yield. We find that the appearance intensity depends not on ly on the binding energy of the ionized electron but also on the quant um 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 [Phy s. Rev. Lett. 63, 2212 (1989)]. Formulas for five ionization models ar e presented.