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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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[1] Jha J, Krishnamurthy M 2008 J. Phys. B 41 041002
[2] Sumeruk H A, Kneip S, Symes D R, Churina I V, Belolipetski A V, Dyer G, Landry J, Bansal G, Bernstein A, Donnelly T D, Karmakar A, Pukhov A, Ditmire T 2007 Phys. Plasmas 14 062704
[3] Ditmire T, Smith R A, Marjoribanks R S, Kulcsár G, Hutchinson M H R 1997 Appl. Phys. Lett. 71 166
[4] Li S H, Wang C, Liu J S, Wang X X, Li R X, Ni G Q, Xu Z Z 2005 Acta Phys. Sin. 54 636 (in Chinese)[李邵辉, 王成, 刘建胜, 王向欣, 李儒新, 倪国权, 徐至展 2005 物理学报 54 636]
[5] Sun Y Q, Chen L M, Zhang L, Mao J Y, Liu F, Li D Z, Liu C, Li W C, Wang Z H, Li Y J, Wei Z Y, Zhang J 2012 Acta Phys. Sin. 61 075206 (in Chinese)[孙彦乾, 陈黎明, 张璐, 毛婧一, 刘峰, 李大章, 刘成, 李伟昌, 王兆华, 李英骏, 魏志义, 张杰 2012 物理学报 61 075206]
[6] Cang Y, Dong Q L, Wu H C, Sheng Z M, Yu W, Zhang J 2004 Chin. Phys. Lett. 21 2414
[7] Liu H J, Gu Y Q, Wang H B, Zheng Z J, Ge F F, Wen X L, Jiao C Y, He Y L, Wen T S, Huang W Z, Wang G C, Zhou W M, Zhang S G, Wang X X, Zhou K N, Wang X D, Huang X J, Ni G Q 2005 Chin. Phys. Lett. 22 1174
[8] Zheng L, Wang C, Li S H, Liu B C, Ni G Q, Li R X, Xu Z Z 2006 Chin. Phys. 15 697
[9] Li S H, Wang C, Liu J S, Wang X X, Zhu P P, Li R X, Ni G Q, Xu Z Z 2004 Chin. Phys. Lett. 21 481
[10] Li S H, Wang C, Zhu P P, Wang X X, Li R X, Ni G Q, Xu Z Z 2003 Chin. Phys. Lett. 20 1247
[11] Lin J Q, Zhang J, Li Y J, Chen L M, L T Z, Teng H, Man B Y, Zhao L Z 2001 Chin. Phys. Lett. 18 211
[12] Wang Q, Cheng Y L, Zhao Y P, Xia Y Q, Chen J, X, Xiao Y F 2003 Chin. Phys. Lett. 20 1309
[13] Du H C, Wang H Q, Liu Z Y, Sun S H, Li L, Ma L L, Hu B T 2010 Chin. Phys. B 19 035202
[14] Li H Y, Liu J S 2010 Acta Phys. Sin. 59 7850 (in Chinese)[李洪玉, 刘建胜 2010 物理学报 59 7850]
[15] Li H Y, Liu J S, Wang C, Ni G Q, Li R X, Xu Z Z 2006 Chin. Phys. Lett. 23 2956
[16] Rose-Petruck C, Schafer K J, Wilson K R, Barty C P J 1997 Phys. Rev. A 55 1182
[17] McPherson A, Thompson B D, Borisov A B, Boyer K, Rhodes C K 1994 Nature 370 631
[18] Ditmire T, Donnelly T, Rubenchik A M, Falcone R W, Perry M D 1996 Phys. Rev. A 53 3379
[19] Wang W G, Li H Y, Niu D M, Wen L H, Zhang N Z 2008 Chem. Phys. 352 111
[20] Niu D M, Li H Y, Liang F, Luo X L, Wen L W 2005 Appl. Phys. Lett. 87 034103
[21] Niu D M, Li H Y, Liang F, Wen L H, Luo X L, Wang B, Qu H B 2005 J. Chem. Phys. 122 151103
[22] Zhang N Z, Wang W G, Cang H W, Wang H L, Li H Y 2009 Chem. Phys. Lett. 469 14
[23] Kong X L, Luo X L, Niu D M, Li H Y 2004 Chem. Phys. Lett. 388 139
[24] Luo X L, Li H Y, Niu D W, Wen L H, Liang F, Wang B, Xiao X 2005 Phys. Rev. A 72 013201
[25] Zhao W D, Wang W G, Qu P C, Hou K Y, Li H Y 2012 Chem. Phys. Lett. 543 55
[26] Sharma P, Vatsa R K, Kulshreshtha S K, Jha J, Mathur D, Krishnamurthy M 2006 J. Chem. Phys. 125 034304
[27] Das S, Badani P M, Sharma P, Vatsa R K 2011 Curr. Sci. 100 1008
[28] Saalmann U, Siedschlag C, Rost J M 2006 J. Phys. B 39 R39
[29] Krainova V P, Smirnov M B 2002 Phys. Rep. 370 237
[30] Döppner T, Mller J P, Przystawik A, Göde S, Tiggesbäumker J, Meiwes-Broer K H, Varin C, Ramunno L, Brabec T, Fennel T 2010 Phys. Rev. Lett. 105 053401
[31] Niu D M, Li H Y, Liang F, Wen L H, Luo X L, Wang B, Hou K Y, Zhang X X 2005 Chem. Phys. Lett. 403 218
[32] Xiao X, Li H Y, Luo X L, Niu D M, Wen L H, Wang B 2005 Acta Phys. Sin. 54 5098 (in Chinese) [肖雪, 李海洋, 罗晓琳, 牛冬梅, 温丽华, 王宾 2005 物理学报 54 5098]
[33] Qu P C, Wang W G, Zhao W D, Zhang G Q, Li H Y 2012 Acta Phys. Sin. 61 182101 (in Chinese) [曲丕丞, 王卫国, 赵无垛, 张桂秋, 李海洋 2012 物理学报 61 182101]
[34] Niu D M, Li H Y, Luo X L, Liang F, Cheng S, Li A L 2006 Chin. Phys. 15 1511
[35] Luo X L, Kong X L, Niu D M, Qu H B, Li H Y 2005 Acta Phys. Sin. 54 606 (in Chinese) [罗晓琳, 孔祥蕾, 牛冬梅, 渠洪波, 李海洋 2005 物理学报 54 606]
[36] Xiao X, Li H Y, Luo X L, Niu D M, Wen L H, Wang B 2006 Acta Phys. Sin. 55 661 (in Chinese) [肖雪, 李海洋, 罗晓琳, 牛冬梅, 温丽华, 王宾 2006 物理学报 55 661]
[37] Zhang N Z, Cang H W, Wang W G, Miao S Y, Jin F, Wu Q H, Hua L, Li H Y 2009 Acta Phys. Sin. 58 4556 (in Chinese) [张娜珍, 仓怀文, 王卫国, 苗书一, 金峰, 吴庆浩, 花磊, 李海洋 2009 物理学报 58 4556]
[38] Karras G, Kosmidis C 2010 Int. J. Mass Spectrom. 290 133
[39] Dawson J, Oberman C 1962 Phys. Fluids 5 517
[40] Decker C D, Mori W B, Dawson J M, Katsouleas T 1994 Phys. Plasmas 1 4043
[41] Kostyukov I Y 2001 JETP Lett. 73 393
[42] Wang X L, Zhang N, Zhao Y B, Li Z L, Zhai H C, Zhu X N 2008 Acta Phys. Sin. 57 354 (in Chinese) [王晓雷, 张楠, 赵友博, 李智磊, 翟宏琛, 朱晓农 2008 物理学报 57 354]
[43] Lotz W 1967 Z. Phys. 206 205
[44] Lotz W 1968 Z. Phys. 216 241
[45] Hilse P, Moll M, Schlanges M,Bornath T 2009 Laser Phys. 19 428
[46] Zhang N Z, Wang W G, Zhao W D, Han F L, Li H Y 2010 Chem. Phys. 373 181
[47] Hagena O F 1992 Rev. Sci. Instrum. 63 2374
[48] Seki T, Matsuo J, Takaoka G H, Yamada I 2003 Nucl. Instrum. Meth. Phys. Res. B 206 902
[49] Yang S, Daineka D V, Chatelet M 2003 Chem. Phys. Lett. 377 595
[50] Last S, Schek L, Jortner J 1997 Chem. Phys. 107 6685
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