| The double-photoionization process of helium was investigated widely in past years. Recent progress has led to a satisfactory agreement between experimental and theoretical data. In helium, even though the"single active electron"(SAE) based calculation can give a highly accurate fit to the single ionization yield, it systematically underestimates the double ionization yield. In the absence of electron correlation one would expect a sequential double ionization mechanism, i.e., the electrons are ionized one after the other by their subsequent independent interaction with intense electric fields. But in experiments, it has been found that the probabilities of double ionization by linearly polarized lasers exceed the expectations based on this sequential mechanism by many orders of magnitude. In earlier studies, two possible mechanisms have been suggested to explain the experimental observation of the non-sequential ionization (NSI). Fittinghoff et al. suggested a"shake off"model that one electron is thought to ionize very fast and then the second electron ionizes due to the sudden change of the binding potential and consequently''shaken off''the atom. Corkum proposed a rescattering model that the first electron ionizes first and revisit the core, and then frees the second electron by inelastic collision. Recently, the ab initio method is adopted to calculate the ionization of two-electron atoms including the electron correlation beyond one-dimensional approximation by intense laser pulses, and the corresponding results are in good agreement with the experimental results. In principle, the treatment of the laser-matter interaction including atoms and molecules needs quantum theory. However, it has been demonstrated that a classical treatment is valid in the case of the superintense and ultrashort laser pulse, in which the Planck constant ? is negligible when compared with the amount of the system's action . Recently, classical simulations of He have also been studied and the results are in agreement with quantum calculations qualitatively. Particularly, Eberly and his co-workers do very excellent work of non-sequential double ionization (NSDI) studies of atoms using the classical simulation.In this paper, the classical dynamics of helium in intense fields are studied by the classical ensemble method. The initial conditions are chosen by ensemble method in the field-free case, and then the Hamiltonian canonical equations of helium in intense laser fields are solved numerically by means of symplectic method under these initial conditions. It turns out that classical simulations are adequate to study strong two-electron correlation, such as NSDI.Firstly, we implement the classical simulation of the ionization dynamics of a 1D model of helium atom in intense laser pulses Three different laser envelopes are used and the result shows that the ionization probability is the largest in a trapezoidal envelope. Besides, our classical simulations have the contributed to a detailed picture of how NSDI and SDI work in terms of one-particle energy. The numerical results are in good agreement with both experimental results and quantum calculations.Secondly, we demonstrate the double ionization in the case of two-dimensional (2D) model helium interacting with elliptically polarized laser pulse using classical ensemble simulations. Compared with the case of linear polarization, the kinematics caused by an elliptically polarized field are genuinely two dimensions. Fortunately, the z component does not influence the ionization probability. We also illustrate the double ionization under the influence of elliptically polarized light. The classical ensemble results show the strong ellipticity dependence. The double ionization probability is also studied for linearly and circularly polarized laser pulse, respectively. Although the classical trajectory method can't describe some quantum effects, it is in agreement with quantum-mechanical calculations in many cases and may be extended to larger molecular system.
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