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温稠密物质的物性参数在惯性约束聚变能源、Z箍缩等高能量密度物理领域的实验结果分析和物理过程数值模拟等方面有着重要的应用价值. 本文应用部分电离等离子体模型, 在理想自由能的基础上考虑了库仑相互作用、排斥体积作用和极化作用等非理想特性, 开展了温稠密等离子体物态方程和电离平衡的研究. 计算了温稠密铝等离子体的压强等物态方程数据和在密度为1.0 × 10–4—3.0 g/cm3, 温度为1.0 × 104—3.0 × 104 K范围内的粒子组分. 计算结果显示, 铝等离子体的平均电离度在临界密度区域内随着密度的增加而突然增大. 根据非理想Saha方程中有效电离能这一关键参数, 分析了铝等离子体平均电离度在临界密度区域内随密度迅速增大的现象.Warm dense matter is widely found in the high-energy-density-physics researches, such as inertial confinement fusion, X-ray source and wire-array Z-pinch. The equation of state and ionization equilibrium of material in warm dense matter regime play a significant role in explaining experimental results and simulations of physical process. In this paper, the Coulomb interaction between charged particles, and the excluded volume effect due to high density and polarization effect between neutral atoms and charged particles are considered in the equation of state for aluminum in warm dense matter regime. A non-ideal Saha equation is used to account for the ionization equilibrium. The data for pressure and concentration of particles of aluminum plasma are derived by iteration between equation of state and ionization equilibrium model. The pressure and average ionization degree of aluminum plasma are consistent with the calculation results from other models and relevant experimental data. The Coulomb interaction, which dominants the non-ideal effects, is insensitive to temperature and increases with density rising especially near the region of critical density. The excluded volume effect peaks at a density of ～0.5 g/cm3. The polarization effect first becomes stronger with density increasing and then decreases at a density of ～0.4 g/cm3. The ionization equilibrium results with density ranging from 1.0 × 10–4 g/cm3 to 3.0 g/cm3 and temperature ranging from 1.0 × 104 K to 3.0 × 104 K reveal that the average ionization degree increases with density sharply increasing near the critical density. The non-ideal effects, which lead the ionization energy to decline and the effective ionization potential of specific ions in aluminum plasma to decrease substantially, are responsible for the sharp increase of average ionization degree near the region of critical density. When the temperature is lower than 12000 K, first and second stage of ionization occur in aluminum plasma, and the system is mainly composed of Al1+, Al2+ and electrons. The average ionization degree can reach 2 at critical density. The third stage of ionization is dominant in the aluminum plasma when plasma temperature is higher than 12000 K. And then, the charged particles in the plasma are composed of Al3+ and electrons, allowing the average ionization degree to reach 3 at critical density.
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Keywords:
- equation of state /
- ionization equilibrium /
- warm dense matter
[1] 付志坚, 贾丽君, 夏继宏, 唐可, 李召红, 权伟龙, 陈其峰 2016 65 065201
Google Scholar
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Google Scholar
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Google Scholar
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Graziani F, Desjarlais M P, Redmer R, Trickey S B (translated by Chen Q F) 2018 Frontiers and Challenges in Warm Dense Matter (Beijing: Atomic Energy Press) ppvii−x (in Chinese)
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Xu X S, Zhang W X 1986 Introduction to the Theory of Equation of State (Beijing: Science Press) pp1−5 (in Chinese)
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[9] 于继东, 李平, 王文强, 吴强 2014 63 116401
Google Scholar
Yu J D, Li P, Wang W Q, Wu Q 2014 Acta Phys. Sin. 63 116401
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[11] Fu Z J, Quan W L, Zhang W, Li Z G, Zheng J, Gu Y J, Chen Q F 2017 Phys. Plasmas 24 013303
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[12] 汤文辉, 徐彬彬, 冉宪文, 徐志宏 2017 66 030505
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Google Scholar
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Google Scholar
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Tian Q Y 2015 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese)
[38] Son S K, Thiele R, Jurek Z, Ziaja B, Santra R 2014 Phys. Rev. X 4 031004
[39] Ebeling W, Föster A, Fortov V E, Gryaznov V K, Polishuk A Y 1991 Thermophysical Properties of Hot Dense Plasmas (Stuttgar-Leipzig: Teubner Verlagsgesellshaft) pp39—42
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图 1 在密度为0.1 g/cm3时, 不同模型计算的铝等离子体压强随温度的变化
Fig. 1. The pressure of aluminum plasma calculated by different models as a function of temperature at density of 0.1 g/cm3.
图 2 铝等离子体的平均电离度随密度与温度变化等值线分布
Fig. 2. Contour map of average ionization degree of aluminum plasma as a function of density and temperature.
图 3 等离子体中不同粒子的相对粒子分数在密度为0.1 g/cm3时随温度的变化
Fig. 3. Dependence of relative particle fraction of different particles on temperature at density of 0.1 g/cm3.
图 4 不同模型计算的铝等离子体平均电离度在不同温度下随密度的变化 (a) 10000 K; (b) 15000 K
Fig. 4. Average ionization degree of aluminum plasma calculated by different models as a function of density at different temperatures: (a) 10000 K; (b) 15000 K.
图 5 不同温度下非理想效应自由能密度以及电子、原子相对粒子分数随密度的变化 (a) 库仑相互作用; (b) 排斥体积作用; (c) 极化作用; (d) 电子、原子相对粒子分数
Fig. 5. Free energy density of different non-ideal effects and relative particle fraction for electrons and atoms as a function of density at different temperatures: (a) Coulomb interaction; (b) excluded volume effect; (c) polarization effect; (d) relative particle fraction for electrons and atoms.
图 6 温度为15000 K时等离子体中不同粒子化学势的非理想部分随密度的变化
Fig. 6. Dependence of non-ideal chemical potential of particles on density at temperature of 15000 K.
图 7 温度为15000 K时不同模型计算的电离能的降低∆E随密度的变化(黑色曲线, 非理想Saha方程; 红色曲线, DmEK模型)
Fig. 7. Depression of ionization potential calculated by different models as a function of density at 15000 K. Black lines correspond to nonideal Saha equation; red lines correspond to DmEK model.
表 1 物态方程及电离平衡模型参数列表
Table 1. Parameters of equation of state and ionization equilibrium model.
参数 值 参数 值 参数 值 R0 2.5714 R6 0.4167 E3 2.0909 R1 2.3377 rc 1.7712 E4 8.8192 R2 2.1429 mk 24597 E5 11.3059 R3 0.4678 αD 46.281 E6 14.0008 R4 0.4494 E1 0.4400 R5 0.4324 E2 1.3839 
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[1] 付志坚, 贾丽君, 夏继宏, 唐可, 李召红, 权伟龙, 陈其峰 2016 65 065201
Google Scholar
Fu Z J, Jia L J, Xia J H, Tang K, Li Z H, Quan W L, Chen Q F 2016 Acta Phys. Sin. 65 065201
Google Scholar
[2] Wallace M S, Haque S, Neill P, Pereira N R, Presura R 2018 Rev. Sci. Instrum. 89 015106
Google Scholar
[3] Oreshkin V I, Artyomov A P, Chaikovsky S A, Oreshkin E V, Rousskikh A G 2017 Phys. Plasmas 24 012703
Google Scholar
[4] 格拉齐亚尼F, 德斯贾莱斯M P, 雷德默R, 特里基S B 著 (陈其峰 译) 2018 温稠密物质研究的前沿和挑战 (北京: 原子能出版社) 第vii−x页
Graziani F, Desjarlais M P, Redmer R, Trickey S B (translated by Chen Q F) 2018 Frontiers and Challenges in Warm Dense Matter (Beijing: Atomic Energy Press) ppvii−x (in Chinese)
[5] 徐锡申, 张万箱 1986 实用物态方程理论导引 (北京: 科学出版社) 第1−5页
Xu X S, Zhang W X 1986 Introduction to the Theory of Equation of State (Beijing: Science Press) pp1−5 (in Chinese)
[6] Shi Z Q, Wang K, Li Y, Shi Y J, Wu J, Jia S L 2014 Phys. Plasmas 21 032702
Google Scholar
[7] Eliezer S, Ghatak A, Hora H, Teller E 2002 Fundamentals of Equations of State (Singapore: World Scientific) pp153−164
[8] 陈其峰, 顾云军, 郑君, 李江涛, 李治国, 权伟龙, 付志坚, 李成军 2017 科学通报 62 812
Google Scholar
Chen Q F, Gu Y J, Zheng J, Li J T, Li Z G, Quan W L, Fu Z J, Li C J 2017 Chin. Sci. Bull. 62 812
Google Scholar
[9] 于继东, 李平, 王文强, 吴强 2014 63 116401
Google Scholar
Yu J D, Li P, Wang W Q, Wu Q 2014 Acta Phys. Sin. 63 116401
Google Scholar
[10] Danel J F, Kazandjian L, Zérah G 2008 Phys. Plasmas 15 072704
Google Scholar
[11] Fu Z J, Quan W L, Zhang W, Li Z G, Zheng J, Gu Y J, Chen Q F 2017 Phys. Plasmas 24 013303
Google Scholar
[12] 汤文辉, 徐彬彬, 冉宪文, 徐志宏 2017 66 030505
Google Scholar
Tang W H, Xu B B, Ran X W, Xu Z H 2017 Acta Phys. Sin. 66 030505
Google Scholar
[13] 张颖, 陈其峰, 顾云军, 蔡灵仓, 卢铁城 2007 56 1318
Google Scholar
Zhang Y, Chen Q F, Gu Y J, Cai L C, Lu T C 2007 Acta Phys. Sin. 56 1318
Google Scholar
[14] Chen Q F, Cai L C, Gu Y J, Gu Y 2009 Phys. Rev. E 79 016409
Google Scholar
[15] Chen Q F, Zheng J, Gu Y J, Chen Y L, Cai L C 2011 Phys. Plasmas 18 112704
Google Scholar
[16] Quan W L, Chen Q F, Fu Z J, Sun X W, Zheng J, Gu Y J 2015 Phys. Rev. E 91 023106
Google Scholar
[17] Apfelbaum E M 2015 Phys. Plasmas 22 092703
Google Scholar
[18] Apfelbaum E M 2017 High Temp. 55 1
Google Scholar
[19] Kuhlbrodt S, Holst B, Redmer R 2005 Contrib. Plasma Phys. 45 73
Google Scholar
[20] Moldabekov Z A, Groth S, Dornheim T, Bonitz M, Ramazanov T S 2017 Contrib. Plasma Phys. 57 532
Google Scholar
[21] Stolzmann W, Blöcker T 1996 Astron. Astrophys. 314 1024
[22] Fortov V E, Altshuler L V, Trunin R F, Funtikov A I 2004 High-Pressure Shock Compression of Solids VII (New York: Springer) pp437−489
[23] 付志坚, 陈其峰, 陈向荣 2011 60 055202
Google Scholar
Fu Z J, Chen Q F, Chen X R 2011 Acta Phys. Sin. 60 055202
Google Scholar
[24] Redmer R, Rother T, Schmidt K, Kraeft W D, Röpke G 1988 Contrib. Plasma Phys. 28 41
Google Scholar
[25] Apfelbaum E M 2011 Phys. Rev. E 84 066403
Google Scholar
[26] Karakhtanov V S, Redmer R, Reinholz H, Röpke G 2011 Contrib. Plasma Phys. 51 355
Google Scholar
[27] More R M, Warren K H, Young D A, Zimmerman G B 1988 Phys. Fluids 31 3059
Google Scholar
[28] Iyetomi H, Ichimaru S 1986 Phys. Rev. A 34 433
Google Scholar
[29] Kresse G, Hafner J 1993 Phys. Rev. B 47 558
Google Scholar
[30] Zaghloul M R 2018 High Energy Density Phys. 26 8
Google Scholar
[31] Wu B, Shin Y C 2006 Appl. Phys. Lett. 89 111902
Google Scholar
[32] Morel V, Bultel A, Chéron B G 2009 Int. J. Thermophys. 30 1853
Google Scholar
[33] Preston T R, Vinko S M, Ciricosta O, Chung H K, Lee R W, Wark J S 2013 High Energy Density Phys. 9 258
Google Scholar
[34] Stransky M 2016 Phys. Plasmas 23 012708
Google Scholar
[35] Kemp A J, Meyer-Ter-Vehn J 1998 Nucl. Instrum. Methods Phys. Res., Sect. A 415 674
Google Scholar
[36] Krisch I, Kunze H J 1998 Phys. Rev. E 58 6557
Google Scholar
[37] 田庆云 2015 硕士学位论文 (长沙: 国防科学技术大学)
Tian Q Y 2015 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese)
[38] Son S K, Thiele R, Jurek Z, Ziaja B, Santra R 2014 Phys. Rev. X 4 031004
[39] Ebeling W, Föster A, Fortov V E, Gryaznov V K, Polishuk A Y 1991 Thermophysical Properties of Hot Dense Plasmas (Stuttgar-Leipzig: Teubner Verlagsgesellshaft) pp39—42
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