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温稠密钛电导率计算

付志坚 贾丽君 夏继宏 唐可 李召红 权伟龙 陈其峰

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Citation:

温稠密钛电导率计算

付志坚, 贾丽君, 夏继宏, 唐可, 李召红, 权伟龙, 陈其峰

A simple and effective simulation for electrical conductivity of warm dense titanium

Fu Zhi-Jian, Jia Li-Jun, Xia Ji-Hong, Tang Ke, Li Zhao-Hong, Quan Wei-Long, Chen Qi-Feng
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  • 温稠密物质是惯性约束核聚变、重离子聚变、Z箍缩动作过程中物质发展和存在的重要阶段. 其热力学性质和辐射输运参数在聚变实验和内爆驱动力学模拟过程中有至关重要的作用. 本文通过建立非理想Saha方程, 结合线性混合规则的理论方法模拟了温稠密钛从10-5-10 gcm-3, 104 K到3104 K区间的粒子组分分布和电导率随温度密度的变化, 其中粒子组分分布由非理想Saha方程求解得到. 线性混合规则模型计算温稠密钛的电导率时考虑了包括电子、原子和离子之间的多种相互作用. 钛的电导率的计算结果与已有的爆炸丝实验数据相符. 通过电导率随温度密度变化趋势判断, 钛在整个温度区间, 密度0.56 gcm-3时发生非金属相到金属相相变. 对于简并系数和耦合系数的计算分析, 钛等离子体在整个温度和密度区间逐渐从弱耦合、非简并状态过渡到强耦合部分简并态.
    A linear mixture rule has been used to calculate the electrical conductivity of warm dense titanium plasmas in the density and temperature ranges of 10-510 gcm-3 and 1043104 K, in which the interactions among electrons, atoms, and ions are considered systemically. In the first place, the coupling and degeneracy parameters of titanium plasma are shown as a function of density and temperature in the warm dense range. The warm dense titanium plasmas span from weakly coupled, nondegenerate region to strongly coupled, degenerate domain in the whole density and temperature regime. The titanium plasma becomes strongly coupled plasma at higher than 0.22 gcm-3 and almost in the whole temperature range where the coupling parameter ii 1. In particular, the Coulomb interactions become stronger at higher than 0.56 gcm-3 where 10 ii 216. At the same time, the titanium plasma is in the degenerate regime at higher than 0.35 gcm-3 where the degeneracy parameter 1, and is in the nondegenerate or partial degenerate regime at lower than 0.35 gcm-3 where 1. The influence of temperature on the coupling and degeneracy parameters is less than that of the density, and the plasma composition is calculated by the nonideal Saha equation felicitously. Thus the ionization degree decreases with increasing density at lower density, which is due to the thermal ionization in that regime where the free electrons have sufficiently high thermal energy. Meanwhile, the ionization degree increases with the increase of density at higher than 0.1 gcm-3, in which the pressure ionization takes place in the region where the electrons have sufficiently high density and the collisions increase rapidly. There is a minimum for the ionization degree at about 0.1 gcm-3, while the maximum ionization degree reaches 4 at 10 gcm-3. In the whole temperature regime, the titanium plasma is mostly in the partial plasma domain at lower than 1 gcm-3, and becomes completely ionized at higher than 1 gcm-3. The calculated conductivity is in reasonable agreement with the experimental data. At a fixed temperature, there is a minimum in each of the ionization curves at lower than 3104 K. And the position of the minimum is shifted towards decreasing density with increasing temperature. The conductivity monotonously increases as the density increases at a temprature of 3104 K. At a constant density, the conductivity increases with increasing temperature for lower than 0.56 gcm-3, while it decreases with increasing temperature for higher than 0.56 gcm-3. This behavior is connected with the nonmetal to metal transition in a dense plasma regime. So the nonmetal to metal transition in dense titanium plasma occurs at about 0.56 gcm-3 and its corresponding electrical conductivity is 1.5105 -1m-1. Finally, the contour of electrical conductivity of titanium plasma is shown as a function of density and temperature in the whole range. Its electrical conductivity spans a range from 103 to 106 -1m-1. It can be seen that the titanium plasma gradually approaches the semiconducting regime as temperature increases. When the order of magnitude of the electrical conductivity reaches 105 -1m-1, the plasma almost becomes conducting fluid in the higher density range. This also demonstrates that a nonmetal-metal transition has taken place in the warm dense titanium plasma.
      通信作者: 付志坚, jianzhifu@126.com
    • 基金项目: 国家自然科学基金(批准号: 11074266, 11071025)、中国工程物理研究院科技发展基金(批准号: 2013 A0101001)、中国工程物理研究院冲击波物理和爆轰物理国家重点实验室基金(批准号: 9140 C670103150 C67289)、重庆市教育委员会科学技术研究项目(批准号: KJ131222, KJ121209)、中国博士后科学基金 (批准号: 2015 M572497)和重庆文理学院项目(批准号: R2012DQ05)资助的课题.
      Corresponding author: Fu Zhi-Jian, jianzhifu@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11074266, 11071025), the Scientific Research Fund of Chongqing Municipal Education Commission of China (Grant Nos. KJ131222, KJ121209), the Science and Technology Development Foundation of China Academy of Engineering Physics (Grant No. 2013 A0101001), the foundation of Laboratory of Shock Wave and Detonation Physics, CAEP (Grant No. 9140 C670103150 C67289), the China Postdoctoral Science Foundation (Grant No.2015 M572497), and the Chongqing University of Arts and Sciences Foundation, China (Grant No. R2012DQ05).
    [1]

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    Zaghloul M 2008 Phys. Plasmas 15 042705

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    Clrouin J, Renaudin P, Laudernet Y, Noiret P, Desjarlais M 2005 Phys. Rev. B 71 064203

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    Renaudin P, Blancard C, Faussurier G, Noiret P 2002 Phys. Rev. Lett. 88 215001

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    [6]

    Chen Y Q 2014 Acta Phys. Sin. 63 205201 (in Chinese) [陈艳秋 2014 物理学报 63 205201]

    [7]

    Faussurier G, Blancard C, Renaudin P, Silvestrelli P 2006 Phys. Rev. B 73 75106

    [8]

    Recoules V, Crocombette J 2005 Phys. Rev. B 72 104202

    [9]

    Kim D, Kim I 2003 Phys. Rev. E 68 56410

    [10]

    Recoules V, Renaudin P, Clrouin J, Noiret P, Zrah G 2002 Phys. Rev. E 66 056412

    [11]

    Desjarlais M, Kress J, Collins L 2002 Phys. Rev. E66 025401

    [12]

    Krisch I, Kunze H 1998 Phys. Rev. E 58 6557

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    Mostovych A, Chan Y 1997 Phys. Rev. Lett. 79 5094

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    DeSilva A, Kunze H 1994 Phys. Rev. E 49 4448

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    DeSilva A, Katsouros J 1998 Phys. Rev. E 57 5945

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    Tkachenko I, Fernandez de Cordoba P 1998 Phys. Rev. E 57 2222

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    Kuhlbrodt S, Redmer R 2000 Phys. Rev. E 62 7191

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    Grinenko A, Gurovich V T, Saypin A, Efimov S, Krasik Y E, Oreshkin V 2005 Phys. Rev. E 72 066401

    [20]

    Barysevich A E, Cherkas S L 2011 Phys. Plasmas 18 052703

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    Sheftman D, Krasik Y E 2010 Phys. Plasmas 17 112702

    [22]

    Haun J, Kunze H, Kosse S, Schlanges M, Redmer R 2002 Phys. Rev. E 65 46407

    [23]

    Haun J, Kosse S, Kunze H, Schlanges M, Redmer R 2001 Contrib. Plasma Phys. 41 275

    [24]

    Haun J 2000 Contrib. Plasma Phys. 40 126

    [25]

    Kloss A, Motzke T, Grossjohann R, Hess H 1996 Phys. Rev. E 54 5851

    [26]

    Likalter A 1997 Phys. Scr. 55 114

    [27]

    Saleem S, Haun J, Kunze H 2001 Phys. Rev. E 64 56403

    [28]

    Saleem S 2001 Ph. D. Dissertation (Bochum: Ruhr-Universitat)

    [29]

    Desjarlais M 2001 Contrib. Plasma Phys. 41 267

    [30]

    Redmer R, Ropke G, Beule D, Ebeling W 1999 Contrib. Plasma Phys. 39 25

    [31]

    Adams J, Reinholz H, Redmer R, Mintsev V, Shilkin N, Gryaznov V 2007 Phys. Rev. E 76 36405

    [32]

    Redmer R 1997 Phys. Rep. 282 35

    [33]

    Recoules V, Lambert F, Decoster A, Canaud B, Clrouin J 2009 Phys. Rev. Lett. 102 075002

    [34]

    Glenzer S, Redmer R 2009 Rev. Mod. Phys. 81 1625

    [35]

    Kress J, Cohen J, Kilcrease D, Horner D, Collins L 2011 Phys. Rev. E 83 026404

    [36]

    Kress J, Cohen J, Horner D, Lambert F, Collins L 2010 Phys. Rev. E 82 036404

    [37]

    Zaghloul M 2004 Phys. Rev. E 69 026702

    [38]

    Kim D, Kim I 2007 Contrib. Plasma Phys. 47 173

    [39]

    Zaghloul M, Bourham M, Doster J 2000 Phys. Lett. A 266 34

    [40]

    Zaghloul M, Bourham M, Doster J, Powell J 1999 Phys. Lett. A 262 86

    [41]

    Bespalov I M, Polishchuk A Y 1989 Sov. Tech. Phys. Lett. 15 39

    [42]

    Salzmann D, Krumbein A 1978 J. Appl. Phys. 49 3229

    [43]

    Reinholz H, Redmer R, Nagel S 1995 Phys. Rev. E 52 5368

    [44]

    Kietzmann A, Holst B, Redmer R, Desjarlais M, Mattsson T 2007 Phys. Rev. Lett. 98 190602

  • [1]

    DeSilva A, Vunni G 2011 Phys. Rev. E 83 037402

    [2]

    Zaghloul M 2008 Phys. Plasmas 15 042705

    [3]

    Clrouin J, Renaudin P, Laudernet Y, Noiret P, Desjarlais M 2005 Phys. Rev. B 71 064203

    [4]

    Renaudin P, Blancard C, Faussurier G, Noiret P 2002 Phys. Rev. Lett. 88 215001

    [5]

    Fan D, Huang Z C, Huang J K, Wang X X, Huang Y 2015 Acta Phys. Sin. 64 108102 (in Chinese) [樊丁, 黄自成, 黄健康, 王新鑫, 黄勇 2015 物理学报 64 108102]

    [6]

    Chen Y Q 2014 Acta Phys. Sin. 63 205201 (in Chinese) [陈艳秋 2014 物理学报 63 205201]

    [7]

    Faussurier G, Blancard C, Renaudin P, Silvestrelli P 2006 Phys. Rev. B 73 75106

    [8]

    Recoules V, Crocombette J 2005 Phys. Rev. B 72 104202

    [9]

    Kim D, Kim I 2003 Phys. Rev. E 68 56410

    [10]

    Recoules V, Renaudin P, Clrouin J, Noiret P, Zrah G 2002 Phys. Rev. E 66 056412

    [11]

    Desjarlais M, Kress J, Collins L 2002 Phys. Rev. E66 025401

    [12]

    Krisch I, Kunze H 1998 Phys. Rev. E 58 6557

    [13]

    Mostovych A, Chan Y 1997 Phys. Rev. Lett. 79 5094

    [14]

    DeSilva A, Kunze H 1994 Phys. Rev. E 49 4448

    [15]

    DeSilva A, Katsouros J 1998 Phys. Rev. E 57 5945

    [16]

    Tkachenko I, Fernandez de Cordoba P 1998 Phys. Rev. E 57 2222

    [17]

    Redmer R 1999 Phys. Rev. E 59 1073

    [18]

    Kuhlbrodt S, Redmer R 2000 Phys. Rev. E 62 7191

    [19]

    Grinenko A, Gurovich V T, Saypin A, Efimov S, Krasik Y E, Oreshkin V 2005 Phys. Rev. E 72 066401

    [20]

    Barysevich A E, Cherkas S L 2011 Phys. Plasmas 18 052703

    [21]

    Sheftman D, Krasik Y E 2010 Phys. Plasmas 17 112702

    [22]

    Haun J, Kunze H, Kosse S, Schlanges M, Redmer R 2002 Phys. Rev. E 65 46407

    [23]

    Haun J, Kosse S, Kunze H, Schlanges M, Redmer R 2001 Contrib. Plasma Phys. 41 275

    [24]

    Haun J 2000 Contrib. Plasma Phys. 40 126

    [25]

    Kloss A, Motzke T, Grossjohann R, Hess H 1996 Phys. Rev. E 54 5851

    [26]

    Likalter A 1997 Phys. Scr. 55 114

    [27]

    Saleem S, Haun J, Kunze H 2001 Phys. Rev. E 64 56403

    [28]

    Saleem S 2001 Ph. D. Dissertation (Bochum: Ruhr-Universitat)

    [29]

    Desjarlais M 2001 Contrib. Plasma Phys. 41 267

    [30]

    Redmer R, Ropke G, Beule D, Ebeling W 1999 Contrib. Plasma Phys. 39 25

    [31]

    Adams J, Reinholz H, Redmer R, Mintsev V, Shilkin N, Gryaznov V 2007 Phys. Rev. E 76 36405

    [32]

    Redmer R 1997 Phys. Rep. 282 35

    [33]

    Recoules V, Lambert F, Decoster A, Canaud B, Clrouin J 2009 Phys. Rev. Lett. 102 075002

    [34]

    Glenzer S, Redmer R 2009 Rev. Mod. Phys. 81 1625

    [35]

    Kress J, Cohen J, Kilcrease D, Horner D, Collins L 2011 Phys. Rev. E 83 026404

    [36]

    Kress J, Cohen J, Horner D, Lambert F, Collins L 2010 Phys. Rev. E 82 036404

    [37]

    Zaghloul M 2004 Phys. Rev. E 69 026702

    [38]

    Kim D, Kim I 2007 Contrib. Plasma Phys. 47 173

    [39]

    Zaghloul M, Bourham M, Doster J 2000 Phys. Lett. A 266 34

    [40]

    Zaghloul M, Bourham M, Doster J, Powell J 1999 Phys. Lett. A 262 86

    [41]

    Bespalov I M, Polishchuk A Y 1989 Sov. Tech. Phys. Lett. 15 39

    [42]

    Salzmann D, Krumbein A 1978 J. Appl. Phys. 49 3229

    [43]

    Reinholz H, Redmer R, Nagel S 1995 Phys. Rev. E 52 5368

    [44]

    Kietzmann A, Holst B, Redmer R, Desjarlais M, Mattsson T 2007 Phys. Rev. Lett. 98 190602

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出版历程
  • 收稿日期:  2015-08-24
  • 修回日期:  2015-11-06
  • 刊出日期:  2016-03-05

温稠密钛电导率计算

  • 1. 重庆文理学院电子电气工程学院, 重庆 402160;
  • 2. 中国工程物理研究院流体物理研究所, 冲击波物理与爆轰物理国防科技重点实验室, 绵阳 621900;
  • 3. 重庆文理学院图书馆, 重庆 402160
  • 通信作者: 付志坚, jianzhifu@126.com
    基金项目: 国家自然科学基金(批准号: 11074266, 11071025)、中国工程物理研究院科技发展基金(批准号: 2013 A0101001)、中国工程物理研究院冲击波物理和爆轰物理国家重点实验室基金(批准号: 9140 C670103150 C67289)、重庆市教育委员会科学技术研究项目(批准号: KJ131222, KJ121209)、中国博士后科学基金 (批准号: 2015 M572497)和重庆文理学院项目(批准号: R2012DQ05)资助的课题.

摘要: 温稠密物质是惯性约束核聚变、重离子聚变、Z箍缩动作过程中物质发展和存在的重要阶段. 其热力学性质和辐射输运参数在聚变实验和内爆驱动力学模拟过程中有至关重要的作用. 本文通过建立非理想Saha方程, 结合线性混合规则的理论方法模拟了温稠密钛从10-5-10 gcm-3, 104 K到3104 K区间的粒子组分分布和电导率随温度密度的变化, 其中粒子组分分布由非理想Saha方程求解得到. 线性混合规则模型计算温稠密钛的电导率时考虑了包括电子、原子和离子之间的多种相互作用. 钛的电导率的计算结果与已有的爆炸丝实验数据相符. 通过电导率随温度密度变化趋势判断, 钛在整个温度区间, 密度0.56 gcm-3时发生非金属相到金属相相变. 对于简并系数和耦合系数的计算分析, 钛等离子体在整个温度和密度区间逐渐从弱耦合、非简并状态过渡到强耦合部分简并态.

English Abstract

参考文献 (44)

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