We study the effect of laser-induced double-ionization of a helium gas (with inhomogeneous density profile) on vacuum electron acceleration. For enough laser intensity, helium gas can be found doubly ionized and it strengthens the divergence of the pulse. The double ionization of helium gas can defocus the laser pulse significantly, and electrons are accelerated by the front of the laser pulse in vacuum and then decelerated by the defocused trail part of the laser pulse. It is observed that the

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... electrons experience a very low laser-intensity at the trailing part of the laser pulse. Hence, there is not much electron deceleration at the trailing part of the pulse. We found that the inhomogeneity of the neutral gas reduced the rate of tunnel ionization causing less defocusing of the laser pulse and thus the electron energy gain is reduced.