Effects of a static electric field on nonsequential double ionization

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Using a three-dimensional semiclassical method, we perform a systematic analysis of the effects of an additional static electric field on nonsequential double ionization (NSDI) of a helium atom in an intense, linearly polarized laser field. It is found that the static electric field influences not only the ionization rate, but also the kinetic energy of the ionized electron returning to the parent ion, in such a way that, if the rate is increased, then the kinetic energy of the first returning electron is decreased, and vice versa. These two effects compete in NSDI. Since the effect of the static electric field on the ionization of the first electron plays a more crucial role in the competition, the symmetric double-peak structure of the ${\mathrm{He}}^{2+}$ momentum distribution parallel to the polarization of the laser field is destroyed. Furthermore, the contribution of the trajectories with multiple recollisions to the NSDI is also changed dramatically by the static electric field. As the static electric field increases, the trajectories with two recollisions, which start at the time when the laser and the static electric field are in the same direction, become increasingly important for the NSDI.