ATI as a source for multiply charged ion production in a laser field

A theory for the many-electron multi-photon process is presented. It is shown that after single-electron excitation into some level in the continuum (ATI) an inelastic collision of the excited electron with the parent atomic particle can result in an excitation of the ion. It may be the continuum state excitation giving the doubly charged ion or the discrete state which also greatly enhances the doubly charged ion production. The probability of these phenomena greatly exceeds that of the direct ionization of a single-charged ion. The single-electron ATI makes possible the two-electron process even in the moderate field. The example of two-electron excitations of He atom in a 780 nm laser field with intensity above $\approx 10^{14}$W/cm$^2$ is discussed.