The production of multiply charged ions by the interaction of intense femtosecond laser with clusters has been widely reported. Recently, many groups discovered the multiply charged ions when the cluster was irradiated by a 532 nm nanosecond laser with the intensity as low as 1010 W/cm2. Although this interesting phenomenon could be explained by the mechanism of“multiphoton ionization triggered-inverse bremsstrahlung heating-electron impact ionization”, there is a lack of numerical simulation to explain the generation of multiply charged ions. In this paper, numerical simulation is performed to study the generation process of multiply charged ions in the moderate intensity laser. Firstly, the electron energy is calculated according to ponderomotive potential. Secondly, the cross section of electron impact ionization is calculated on the basis of Lotz formula. Finally, the evolution of multiply charged ions in the cluster is calculated with the kinetic reaction rate equation. The effects of cluster size and electron density on multiply charged ions are investigated in detail. Simulation results show that the ionization process is completed and the balance among C2+, C3+and C4+ is achieved in 0.7 ns. The relative intensity sequence of multiply charged ions is C2+ > C3+ > C4+, which is consistent with the experimental results. In addition, numerical simulation results show that the charge state of ions is increased with the increase of cluster size, which is consistent with the experimental results.%飞秒强激光与团簇相互作用产生多价离子的现象已被广泛报道，然而近期多个研究小组发现当功率密度低至1010 W/cm2的纳秒激光照射团簇时，同样也观察到了多价离子的存在.虽然可以用“多光子电离引发-逆韧致吸收加热-电子碰撞电离”电离机理对这种现象进行解释，但是缺乏相应的数值模拟.建立了一个简化的数值模型，根据有质动力势Up计算团簇内电子能量，再由Lotz公式计算出相应的电离截面，最后由动力学反应速率方程计算出团簇内多价碳离子随时间的演变.详细分析了团簇尺寸、电子密度等关键参数对多价离子产生的影响.数值模拟结果表明：团簇电离在小于0.7 ns时间尺度内完成， C2+， C3+和C4+多价离子强度达到平衡后，离子相对强度由大到小依次为C2+， C3+， C4+，这与实验结果相一致；多价离子的价态随着团簇尺寸的增加而升高，半径为5.6 nm的苯团簇比半径为3 nm的苯团簇更容易产生高价态的离子，这也与实验结果相一致.
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