The non-sequential double ionization (NSDI) of Mg atom is investigated in both linearly and circularly polarized laser fields with different kinds of potentials. The numerical results indicate that the "knee" structure still exist in circularly polarized laser fields in 800 nm case with different potentials, which can be well explained by the corresponding momentum and position distribution of electrons. Moreover, the ionized electron energy of Mg atom at the end of pulse also shows the

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... of rescattering electrons is different between linearly and circularly polarized cases. Besides, we also look into the angular distribution at the end of pulse with different kind of potentials to illustrate the difference of double ionization mechanism between linearly and circularly polarized case.