高温等离子体的状态方程及其热力学性质

汤文辉; 徐彬彬; 冉宪文; 徐志宏

doi:10.7498/aps.66.030505

摘要

高温下等离子体的状态方程及其热力学性质在天体物理、可控核聚变以及武器设计与破坏效应等领域有着广泛应用.本文主要回顾了高温等离子体在不同状态区域的状态方程的理论模型和处理方法.对于理想等离子体，离子之间的相互作用可以忽略，其状态方程较简单，已趋于完善.在超高温下，原子完全电离，离子和电子都可以采用理想气体状态方程描述；当温度不太高时，离子部分电离，可以采用Saha方程及其修正模型描述；原子在高度压缩状态下，其状态方程可以采用Thomas-Fermi模型及其改进模型得到.对于非理想等离子体，离子之间存在强耦合，还没有单一的理论模型能够在任意密度和温度范围内对离子之间的相互作用进行统一描述.量子分子动力学方法原则上可以在较大温度密度范围内给出可靠结果，但由于计算量太大以及高温下的计算存在收敛问题，也较难应用到温度较高的稠密等离子体区域.半经验的经典分子动力学方法虽然简单、计算量小，但只能在一定的区域范围内给出较精确的状态方程结果.在不同温度密度区域内采用不同的计算模型，再在空白区域进行插值从而得到全局状态方程在目前不失为一种简单有效的方法.

关键词:

Abstract

The equations of state (EOS) and the thermodynamics properties of plasma under high temperature are widely applied to the fields of astrophysics, controllable fusion, weapon design and damage. In this paper we mainly review the theoretical model and computing method of the EOS of hot plasma on different density scales and temperature scales. For an ideal plasma, the interaction between ions can be ignored, the EOS is simple and the theories turn matured. Under the condition of extremely high temperature, ions are ionized completely and the EOSs of ions and electrons can be approximated by the EOS of ideal gas. When the temperature is not very high and ions are just partly ionized, the EOS can be obtained by Saha model or its modified model. When atoms are strongly compressed, the EOS can be calculated by Thomas-Fermi model or its modified model. For the non-ideal plasma, there is a strong coupling between ions. No unified theoretical model can completely describe the interaction between ions at arbitrary density and arbitrary temperature. In principle, the quantum molecular dynamics (QMD) can accurately describe the EOS of plasma in large density range and large temperature range. However, due to the enormous computation and the difficulty in converging, it is difficult to apply QMD to the plasma under high temperature. With simple computing method and small computation, classical molecular dynamics using semi-empirical potential can calculate the EOS accurately at high temperature. However, it will produce great error at lower temperature. It is a simple and effective way to obtain a global EOS by using different theoretical models in different density range and different temperature range and by interpolating in the vacant density range and vacant temperature range.

Keywords:

作者及机构信息

1.
国防科学技术大学理学院, 长沙 410073

通信作者: 汤文辉, wenhuitang@163.com

Authors and contacts

1.
College of Science, National University of Defense Technology, Changsha 410073, China

Corresponding author: Tang Wen-Hui, wenhuitang@163.com

参考文献

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[62]	Desjarlais M P, Kress J D, Collins L A 2002 Phys. Rev. E 66 025401
[63]	Mazevet S, Clérouin J, Recoules V, Anglade P M, Zérah G 2005 Phys. Rev. Lett. 95 085002
[64]	Mazevet S, Desjarlais M P, Collins L A, Kress D, Magee N H 2005 Phys. Rev. E 71 016409
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[66]	Holst B, Redmer R 2008 Phys. Rev. B 77 184201
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[68]	Kohn K, Sham L J 1965 Phys. Rev. 140 A1133
[69]	Born M, Huang K 1954 Dynamical Theory of Crystal Lattice (Oxford:Oxford University Press)
[70]	Hohenberg P, Kohn W 1964 Phys. Rev. B 136 864
[71]	Hansen J P, McDonald I R 1976 Theory of Simple Liquids (Lodon:Academic Press)
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[73]	Lambert F, Clérouin J, Zérah G 2006 Phys. Rev. E 73 016403
[74]	More R M, Warren K H, Young D A, Zimmerman G B 1988 Phys. Fluids 31 3059
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[80]	Atzeni S, Meyer-ter-Vehn J 2004 The Physics of Inertial Fusion (New York:Oxford University Press)
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[82]	Ragan C E 1982 Phys. Rev. A 25 3360
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[84]	Mitchell A C, Nellis W J 1981 J. Appl. Phys. 52 3363
[85]	Hou Y 2009 Ph. D. Dissertation (Changsha:National University of Defence Technology) (in Chinese)[侯永2009博士学位论文(长沙:国防科学技术大学)]
[86]	Letter R 1955 Phys. Rev. 99 1854
[87]	Perrot F, Dharma-wardana M W C, Benage J 2002 Phys. Rew. E 65 046414
[88]	Hou Y, Yuan J 2009 Phys. Rev. E 79 016402
[89]	Dai J Y 2009 Ph. D. Dissertation (Changsha:National University of Defence Technology) (in Chinese)[戴佳钰2010博士学位论文(长沙:国防科学技术大学)]
[90]	Lambert F, Clérouin J, Mazevet S 2006 Europhys. Lett. 75 681
[91]	Fromy P, Deutsh C, Maynard G 1996 Phys. Plasmas 3 714
[92]	Piron R, Blenski T 2011 Phys. Rev. E 83 026403
[93]	Batani D, Morelli A, Tomasini M, Benuzzi-Mounaix A, Philippe F, Koenig M, Marchet B, Masclet I, Rabec M, Reverdin C, Cauble R, Celliers P, Collins G, Silva L D, Hall T, Moret M, Sacchi B, Baclet P, Cathala B 2002 Phys. Rev. Lett. 88 235502

施引文献

[1]	Fortov V E 2016 Extreme States of Matter (Berlin:Springer) p9
[2]	Xu J A, Mao H K, Bell P M 1986 Science 232 1404
[3]	Ming L C, Bassett W A 1974 Rev. Sci. Instrum. 45 1115
[4]	Nellis W J 2006 Rep. Prog. Phys. 69 1479
[5]	Qian X S 2007 Lectures on Physics (Shanghai:Shanghai Jiaotong University Press) (in Chinese)[钱学森2007物理力学讲义(上海:上海交通大学出版社)]
[6]	Fortov V E 2007 Phys. Uspek. 50 333
[7]	Lindl J D, Amendt P, Berger R L, Glendinning S G, Glenzer S H, Haan S W, Kauffman R L, Landen O L, Suter L J 2004 Phys. Plasmas 11 339
[8]	Saha M N, Srivastava B N 1965 A Treatise on Heat (Allahabad:The India Press)
[9]	Debye P, Hckel E 1923 Physik Z 24 185
[10]	Thomas L H 1927 Proc. Cambridge Philos. Soc. 23 542
[11]	Fermi E 1928 Z. Phys. 48 73
[12]	Xu X S, Zhang W X 1986 Theory Guide of Practical Equations of State (Beijing:Science Press) (in Chinese)[徐锡申, 张万箱1986实用物态方程理论导引(北京:科学出版社)]
[13]	Feynman R P, Metropolis N, Teller E 1949 Phys. Rev. 75 1561
[14]	Car R, Parrinello M 1985 Phys. Rev. Lett. 55 2471
[15]	Letter R 1955 Phys. Rev. 99 1854
[16]	Dirac P A M 1930 Proc. Camb. Phil. Soc. 26 376
[17]	Cowan R D, Ashkin J 1957 Phys. Rev. 105 144
[18]	Bloch F 1929 Zeits. F Phys. 57 545
[19]	McCarthy S L 1965 Lawrence Livermore Laboratory Report UCRL-14364
[20]	Kirzhnits D A 1957 Sov. Phys. JETP 5 64
[21]	Tang W H, Zhang R Q 2008 Introduction to the Theory and Compution of Equations of State (Beijing:Higher Education Press) (in Chinese)[汤文辉, 张若棋2008物态方程理论及计算概论(北京:高等教育出版社)]
[22]	Bell A R 1980 Rutherford and Appleton Laboratories Report RL-80-091
[23]	Zink J W 1968 Phys. Rev. 176 279
[24]	Lee C M, Thorsos B I 1978 Phys. Rev. A 17 2073
[25]	Rozsnyai B F 1972 Phys. Rev. A 5 1137
[26]	Rozsnyai B F 1982 J. Quant. Spectrosc. Radiat. Transf. 27 211
[27]	Rozsnyai B F, Lamoureux M 1990 J. Quant. Spectrosc. Radiat. Transf. 43 381
[28]	Bauche-Arnoult C, Bauche J, Klapisch 1978 M. J. Opt. Soc. Am. 68 1136
[29]	Bauche-Arnoult C, Bauche J, Klapisch M 1979 Phys. Rew. A 20 2424
[30]	Bar-Shalom A, Oreg J, Goldstein W H, Shvart D, Zigler A 1989 Phys. Rev. A 40 3183
[31]	Oreg J, Goldstein W H, Bar-Shalom A, Klapisch M 1990 J. Comput. Phys. 91 460
[32]	Iglesias C A, Rogers F J, Wilson B G 1987 Astrophys. J. 322 45
[33]	Kurten K E, Ristig M L, Clark J W 1977 Lett. Al Nuovo Cimento 20 313
[34]	Kang H S, Ree F H 1998 Phys. Rev. E 57 5988
[35]	Rose D V, Genoni T C, Welch D R, Clark R E, Campbell R B, Mehlhorn T A, Flicker D G 2009 Phys. Plasams 16 102105
[36]	Dror O, Nardi E, Rosenfeld Y 1988 Phys. Rev. A 38 5801
[37]	Furukawa H, Nishihara K 1992 Phys. Rev. A 46 6596
[38]	Zérah G, Clérouin J G, Pollock E L 1992 Phys. Rev. Lett. 69 446
[39]	Clérouin J G, Pollock E L, Zérah G 1992 Phys. Rev. A 46 5130
[40]	Flavien L, Gilles Z 2006 Phys. Rev. E 73 016403
[41]	Danel J F, Kazandjian L, Zérah G 2006 Phys. Plasmas 13 092701
[42]	Dharma-wardana M W C, Francois P 1982 Phys. Rev. A 26 2096
[43]	Dharma-wardana M W C, Murillo M S 2008 Phys. Rev. E 77 026401
[44]	Danel J F, Kazandjian L, Zérah G 2009 Phys. Rev. E 79 066408
[45]	Horner D A, Lambert F, Kress J D, Collins L A 2009 Phys. Rev. B 80 024305
[46]	Hou Y, Jin F T, Yuan J M 2006 Phys. Plasmas 13 093301
[47]	Hou Y, Jin F T, Yuan J M 2007 J Phys.:Condens. Matter 19 425204
[48]	Dai J, Yuan J 2009 Europhys. Lett. 88 20001
[49]	Dai J, Hou Y, Yuan J 2010 Phys. Rev. Lett. 104 245001
[50]	Dai J, Hou Y, Yuan J 2010 Astrophys. J. 721 1158
[51]	Militzer B 2009 Phys. Rev. B 79 155105
[52]	Wunsch K, Vorberger J, Gericke D O 2009 Phys. Rev. E 79 010201
[53]	Gericke D O, Wunsch K, Grinenko A, Vorberger J 2010 J. Phys.:Conf. Ser. 220 012001
[54]	Peyrusse O, Mazevet S, Recoules V, Dorchies F, Harmand M, Levy A, Fuchs J, Mancic A, Nakatsutsumi M, Renaudin P, Audebert P 2009 CP, Atomic Processes in Plasmas 1161 200
[55]	Frenkel D, Smit B 1996 Understanding Molecular Simulation (San Diego:Acedemic Press)
[56]	Morse P M 1929 Phys. Rev. 34 57
[57]	Born M, Mayer J E 1931 Z. Phys. 75 1
[58]	Daw M S, Baskes M I 1983 Phys. Rev. Lett. 50 1285
[59]	Finnis M W, Sinclair J E 1984 Philosophic Magazine A 50 45
[60]	Abell G C 1985 Phys. Rev. B 31 6184
[61]	Collins L, Kwon I, Kress J, Troullier N, Lynch D 1995 Phys. Rev. E 52 6202
[62]	Desjarlais M P, Kress J D, Collins L A 2002 Phys. Rev. E 66 025401
[63]	Mazevet S, Clérouin J, Recoules V, Anglade P M, Zérah G 2005 Phys. Rev. Lett. 95 085002
[64]	Mazevet S, Desjarlais M P, Collins L A, Kress D, Magee N H 2005 Phys. Rev. E 71 016409
[65]	Clérouin J, Noiret P 2008 Phys. Rev. B 78 224203
[66]	Holst B, Redmer R 2008 Phys. Rev. B 77 184201
[67]	Mazevet S, Zérah G 2008 Phys. Rev. Lett. 101 155001
[68]	Kohn K, Sham L J 1965 Phys. Rev. 140 A1133
[69]	Born M, Huang K 1954 Dynamical Theory of Crystal Lattice (Oxford:Oxford University Press)
[70]	Hohenberg P, Kohn W 1964 Phys. Rev. B 136 864
[71]	Hansen J P, McDonald I R 1976 Theory of Simple Liquids (Lodon:Academic Press)
[72]	Perdew J P, Kieron B, Matthias E 1996 Phys. Rev. Lett. 77 3865
[73]	Lambert F, Clérouin J, Zérah G 2006 Phys. Rev. E 73 016403
[74]	More R M, Warren K H, Young D A, Zimmerman G B 1988 Phys. Fluids 31 3059
[75]	Lyon S P, Johnson J D 1992 SESAME:The Los Alamos National Laboratory Equation of State Database Report No. LA-UR-92-3407
[76]	Bushman A V, Fortov V E 1983 Soviet Phys. Uspek. 26 465
[77]	Godval B K, Sikka S K 1983 Phys. Rep. 102 121
[78]	Basko M M. Metallic 1985 Soviet High Temperat. Phys. 23 388
[79]	Kemp A J, Meyer-ter-Vehn J 1998 Nucl. Instrum. Meth. Phys. Res. A 415 674
[80]	Atzeni S, Meyer-ter-Vehn J 2004 The Physics of Inertial Fusion (New York:Oxford University Press)
[81]	Altshuler L 1965 Soviet Phys. Uspek. 8 52
[82]	Ragan C E 1982 Phys. Rev. A 25 3360
[83]	Vladimirov A S, Voloshin N P, Nogin V N, Petrovtsev A V, Simonenko V A 1984 JETP Lett. 39 82
[84]	Mitchell A C, Nellis W J 1981 J. Appl. Phys. 52 3363
[85]	Hou Y 2009 Ph. D. Dissertation (Changsha:National University of Defence Technology) (in Chinese)[侯永2009博士学位论文(长沙:国防科学技术大学)]
[86]	Letter R 1955 Phys. Rev. 99 1854
[87]	Perrot F, Dharma-wardana M W C, Benage J 2002 Phys. Rew. E 65 046414
[88]	Hou Y, Yuan J 2009 Phys. Rev. E 79 016402
[89]	Dai J Y 2009 Ph. D. Dissertation (Changsha:National University of Defence Technology) (in Chinese)[戴佳钰2010博士学位论文(长沙:国防科学技术大学)]
[90]	Lambert F, Clérouin J, Mazevet S 2006 Europhys. Lett. 75 681
[91]	Fromy P, Deutsh C, Maynard G 1996 Phys. Plasmas 3 714
[92]	Piron R, Blenski T 2011 Phys. Rev. E 83 026403
[93]	Batani D, Morelli A, Tomasini M, Benuzzi-Mounaix A, Philippe F, Koenig M, Marchet B, Masclet I, Rabec M, Reverdin C, Cauble R, Celliers P, Collins G, Silva L D, Hall T, Moret M, Sacchi B, Baclet P, Cathala B 2002 Phys. Rev. Lett. 88 235502

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