Accurate first-principle equation of state for the one-component plasma

Contributions to Plasma Physics

Volumn 38, Issue 4, 1998, Pages 489-499

  Brilliantov, N V ^a,b  

^a UNIVERSITY OF TORONTO   (Canada)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF STATE; FREE ENERGY; IRON COMPOUNDS; MAGNETOPLASMA;

CORRELATION FUNCTION; EQUATION-OF-STATE; EXCESS FREE ENERGY; FIRST PRINCIPLES; HIGHER ORDER TERMS; HUBBARD; IDEAL GAS; INTERNAL ENERGIES; ONE-COMPONENT PLASMA; REFERENCE SYSTEMS;

HAMILTONIANS;

EID: 0000445634     PISSN: 08631042     EISSN: None     Source Type: Journal    
DOI: 10.1002/ctpp.2150380403     Document Type: Article

References (67)

1. M. Baus and J. P. Hansen Phys.Rep., 59 1 (1980).
2. S. Ichimaru, H. Iyetomi and S. Tanaka, Phys.Rep., 149 91 (1987).
3. H. M. Van Horn, in White Dwarfs ed. by W. J. Luyten, (Springer, Berlin, 1971), p.96.
4. B. Jancovici, J.Stat.Phys., 17 357 (1977).
5. J. P. Hansen Phys.Rev.A, 8 3096 (1973).
6. D. A. Young, E. M. Corey and H. E. DeWitt, Phys.Rev. A 44, 6508 (1991).
7. M. Ross, H. E. DeWitt, and W. B. Hubbard, Phys.Rev. A 24, 1016 (1981); W. H. Young, J.Phys.F: Met.Phys., 12, L19 (1982); N. Montella, G. Senatore, and M. P. Tosi, Physica B+C, 124, 22 (1984); S. Ono, and I. Yokoyama, J.Phys.F: Met.Phys., 14, 2909 (1984); T. Itami, and M. Shimoji, J.Phys.F: Met.Phys., 14, L15 (1984).
8. M. Ross, H. E. DeWitt, and W. B. Hubbard, Phys.Rev. A 24, 1016 (1981); W. H. Young, J.Phys.F: Met.Phys., 12, L19 (1982); N. Montella, G. Senatore, and M. P. Tosi, Physica B+C, 124, 22 (1984); S. Ono, and I. Yokoyama, J.Phys.F: Met.Phys., 14, 2909 (1984); T. Itami, and M. Shimoji, J.Phys.F: Met.Phys., 14, L15 (1984).
9. M. Ross, H. E. DeWitt, and W. B. Hubbard, Phys.Rev. A 24, 1016 (1981); W. H. Young, J.Phys.F: Met.Phys., 12, L19 (1982); N. Montella, G. Senatore, and M. P. Tosi, Physica B+C, 124, 22 (1984); S. Ono, and I. Yokoyama, J.Phys.F: Met.Phys., 14, 2909 (1984); T. Itami, and M. Shimoji, J.Phys.F: Met.Phys., 14, L15 (1984).
10. M. Ross, H. E. DeWitt, and W. B. Hubbard, Phys.Rev. A 24, 1016 (1981); W. H. Young, J.Phys.F: Met.Phys., 12, L19 (1982); N. Montella, G. Senatore, and M. P. Tosi, Physica B+C, 124, 22 (1984); S. Ono, and I. Yokoyama, J.Phys.F: Met.Phys., 14, 2909 (1984); T. Itami, and M. Shimoji, J.Phys.F: Met.Phys., 14, L15 (1984).
11. M. Ross, H. E. DeWitt, and W. B. Hubbard, Phys.Rev. A 24, 1016 (1981); W. H. Young, J.Phys.F: Met.Phys., 12, L19 (1982); N. Montella, G. Senatore, and M. P. Tosi, Physica B+C, 124, 22 (1984); S. Ono, and I. Yokoyama, J.Phys.F: Met.Phys., 14, 2909 (1984); T. Itami, and M. Shimoji, J.Phys.F: Met.Phys., 14, L15 (1984).
12. A. M. Bratkovsky, J.Phys.C: Cond.Matter, 1, 3453 (1989).
13. M. J. Stevens, and M. O. Robbins, Europhys.Lett., 12, 81 (1990).
14. H. Löwen, Phys.Rep., 237, 249 (1994); H. Löwen, P. A. Madden, and J. P. Hansen, Phys.Rev.Lett., 68, 1081 (1992); H. Löwen, J. P. Hansen, and P. A. Madden, J.Chem.Phys. 98, 3275 (1993).
15. H. Löwen, Phys.Rep., 237, 249 (1994); H. Löwen, P. A. Madden, and J. P. Hansen, Phys.Rev.Lett., 68, 1081 (1992); H. Löwen, J. P. Hansen, and P. A. Madden, J.Chem.Phys. 98, 3275 (1993).
16. H. Löwen, Phys.Rep., 237, 249 (1994); H. Löwen, P. A. Madden, and J. P. Hansen, Phys.Rev.Lett., 68, 1081 (1992); H. Löwen, J. P. Hansen, and P. A. Madden, J.Chem.Phys. 98, 3275 (1993).
17. R. Penfold, B. Jonsson, and C. E. Woodward, J.Chem.Phys. 92, (1990); R. Penfold, B. Jonsson, and S. Nordholm, J.Chem.Phys. 99, 497 (1993); R. Penfold, S. Nordholm, B. Jonsson, and C. E. Woodward, J.Chem.Phys. 95, 2048 (1991).
18. R. Penfold, B. Jonsson, and C. E. Woodward, J.Chem.Phys. 92, (1990); R. Penfold, B. Jonsson, and S. Nordholm, J.Chem.Phys. 99, 497 (1993); R. Penfold, S. Nordholm, B. Jonsson, and C. E. Woodward, J.Chem.Phys. 95, 2048 (1991).
19. R. Penfold, B. Jonsson, and C. E. Woodward, J.Chem.Phys. 92, (1990); R. Penfold, B. Jonsson, and S. Nordholm, J.Chem.Phys. 99, 497 (1993); R. Penfold, S. Nordholm, B. Jonsson, and C. E. Woodward, J.Chem.Phys. 95, 2048 (1991).
20. H.E. De Witt, J.Math.Phys., 3, 1216 (1962); G. Kelbg, Ann.Physik, 12, 1216 (1963); H.J. Hoffmann and W. Ebeling, Physica , 39, 593 (1968); C. Deutsch and M. Lavaud, Phys.Lett.A, 39, 253 (1972), 43, 193 (1973) ; W. Ebeling and A. Föerster, in Condensed Matter and Plasma in Physics and Astronomy, eds. S. Ichimaru and S. Ogata (Addison-Wesley, Reading (MA), 1994; H. Lehmann and W. Ebeling, Phys.Rev. E 54, 2451 (1996).
21. H.E. De Witt, J.Math.Phys., 3, 1216 (1962); G. Kelbg, Ann.Physik, 12, 1216 (1963); H.J. Hoffmann and W. Ebeling, Physica , 39, 593 (1968); C. Deutsch and M. Lavaud, Phys.Lett.A, 39, 253 (1972), 43, 193 (1973) ; W. Ebeling and A. Föerster, in Condensed Matter and Plasma in Physics and Astronomy, eds. S. Ichimaru and S. Ogata (Addison-Wesley, Reading (MA), 1994; H. Lehmann and W. Ebeling, Phys.Rev. E 54, 2451 (1996).
22. H.E. De Witt, J.Math.Phys., 3, 1216 (1962); G. Kelbg, Ann.Physik, 12, 1216 (1963); H.J. Hoffmann and W. Ebeling, Physica , 39, 593 (1968); C. Deutsch and M. Lavaud, Phys.Lett.A, 39, 253 (1972), 43, 193 (1973) ; W. Ebeling and A. Föerster, in Condensed Matter and Plasma in Physics and Astronomy, eds. S. Ichimaru and S. Ogata (Addison-Wesley, Reading (MA), 1994; H. Lehmann and W. Ebeling, Phys.Rev. E 54, 2451 (1996).
23. H.E. De Witt, J.Math.Phys., 3, 1216 (1962); G. Kelbg, Ann.Physik, 12, 1216 (1963); H.J. Hoffmann and W. Ebeling, Physica , 39, 593 (1968); C. Deutsch and M. Lavaud, Phys.Lett.A, 39, 253 (1972), 43, 193 (1973) ; W. Ebeling and A. Föerster, in Condensed Matter and Plasma in Physics and Astronomy, eds. S. Ichimaru and S. Ogata (Addison-Wesley, Reading (MA), 1994; H. Lehmann and W. Ebeling, Phys.Rev. E 54, 2451 (1996).
24. H.E. De Witt, J.Math.Phys., 3, 1216 (1962); G. Kelbg, Ann.Physik, 12, 1216 (1963); H.J. Hoffmann and W. Ebeling, Physica , 39, 593 (1968); C. Deutsch and M. Lavaud, Phys.Lett.A, 39, 253 (1972), 43, 193 (1973) ; W. Ebeling and A. Föerster, in Condensed Matter and Plasma in Physics and Astronomy, eds. S. Ichimaru and S. Ogata (Addison-Wesley, Reading (MA), 1994; H. Lehmann and W. Ebeling, Phys.Rev. E 54, 2451 (1996).
25. H.E. De Witt, J.Math.Phys., 3, 1216 (1962); G. Kelbg, Ann.Physik, 12, 1216 (1963); H.J. Hoffmann and W. Ebeling, Physica , 39, 593 (1968); C. Deutsch and M. Lavaud, Phys.Lett.A, 39, 253 (1972), 43, 193 (1973) ; W. Ebeling and A. Föerster, in Condensed Matter and Plasma in Physics and Astronomy, eds. S. Ichimaru and S. Ogata (Addison-Wesley, Reading (MA), 1994; H. Lehmann and W. Ebeling, Phys.Rev. E 54, 2451 (1996).
26. H.E. De Witt, J.Math.Phys., 3, 1216 (1962); G. Kelbg, Ann.Physik, 12, 1216 (1963); H.J. Hoffmann and W. Ebeling, Physica , 39, 593 (1968); C. Deutsch and M. Lavaud, Phys.Lett.A, 39, 253 (1972), 43, 193 (1973) ; W. Ebeling and A. Föerster, in Condensed Matter and Plasma in Physics and Astronomy, eds. S. Ichimaru and S. Ogata (Addison-Wesley, Reading (MA), 1994; H. Lehmann and W. Ebeling, Phys.Rev. E 54, 2451 (1996).
27. R. Abe, Progr.Theor.Phys., 22, 213 (1959); see also C. Deutsch, Y. Furutani and M.M. Combert, Phys.Rep., 69 85 (1981).
28. R. Abe, Progr.Theor.Phys., 22, 213 (1959); see also C. Deutsch, Y. Furutani and M.M. Combert, Phys.Rep., 69 85 (1981).
29. W.L. Slattery, G.D. Doolen and H.E. De Witt, Phys.Rev.A, 21 2087 (1980).
30. E.G.D. Cohen and T.J. Murphy, Phys.Flitids, 12, 1404 (1969).
31. J.F. Springer, M.A. Pokrant and F.A. Stevens, J.Chem.Phys., 58, 4863 (1973); P. Hutchinson and W.R. Conkie, Mol.Phys., 3, 567 (1972); K.C. Ng, J.Chem.Phys., 61, 2680 (1974).
32. J.F. Springer, M.A. Pokrant and F.A. Stevens, J.Chem.Phys., 58, 4863 (1973); P. Hutchinson and W.R. Conkie, Mol.Phys., 3, 567 (1972); K.C. Ng, J.Chem.Phys., 61, 2680 (1974).
33. J.F. Springer, M.A. Pokrant and F.A. Stevens, J.Chem.Phys., 58, 4863 (1973); P. Hutchinson and W.R. Conkie, Mol.Phys., 3, 567 (1972); K.C. Ng, J.Chem.Phys., 61, 2680 (1974).
34. Y. Rosenfeld and N.W. Aschcroft, Phys.Rev.A, 20, 1208 (1979); 2162 (1979); Y. Rosenfeld Phys.Rev.Lett., 20, 1208 (1980); Y. Rosenfeld and W. Gelbart J.Chem.Phys., 61, 2680 (1985). A.A. Broyles, H.L. Sahlin and D.D. Carley Phys.Rev.Lett., 10, 319 (1963).
35. Y. Rosenfeld and N.W. Aschcroft, Phys.Rev.A, 20, 1208 (1979); 2162 (1979); Y. Rosenfeld Phys.Rev.Lett., 20, 1208 (1980); Y. Rosenfeld and W. Gelbart J.Chem.Phys., 61, 2680 (1985). A.A. Broyles, H.L. Sahlin and D.D. Carley Phys.Rev.Lett., 10, 319 (1963).
36. Y. Rosenfeld and N.W. Aschcroft, Phys.Rev.A, 20, 1208 (1979); 2162 (1979); Y. Rosenfeld Phys.Rev.Lett., 20, 1208 (1980); Y. Rosenfeld and W. Gelbart J.Chem.Phys., 61, 2680 (1985). A.A. Broyles, H.L. Sahlin and D.D. Carley Phys.Rev.Lett., 10, 319 (1963).
37. Y. Rosenfeld and N.W. Aschcroft, Phys.Rev.A, 20, 1208 (1979); 2162 (1979); Y. Rosenfeld Phys.Rev.Lett., 20, 1208 (1980); Y. Rosenfeld and W. Gelbart J.Chem.Phys., 61, 2680 (1985). A.A. Broyles, H.L. Sahlin and D.D. Carley Phys.Rev.Lett., 10, 319 (1963).
38. S.G. Brush, H.L. Sahlin and E. Teller, J.Chem.Phys., 45, 2102 (1966).
39. W.L. Slattery, G.D. Doolen and H.E. De Witt, Phys.Rev.A, 26 2255 (1982).
40. G.S. Stringfellow, H.E. De Witt and W.L. Slattery, Phys.Rev.A, 41 1105 (1990).
41. R.T. Farouki and S. Hamaguchi, Phys.Rev.E. 47 4330 (1993).
42. H.E. De Witt, W.L. Slattery and G.S. Stringfellow, in Strongly Coupled Plasma Physics, ed. S. Ichimaru (Elsevier, Amsterdam, 1990), p.635. see also H.E. De Witt, Contr.Plasma Phys. 33, 399 (1993).
43. H.E. De Witt, W.L. Slattery and G.S. Stringfellow, in Strongly Coupled Plasma Physics, ed. S. Ichimaru (Elsevier, Amsterdam, 1990), p.635. see also H.E. De Witt, Contr.Plasma Phys. 33, 399 (1993).
44. B. Brami, J.P. Hansen and F. Joly, Physica A 95, 505 (1979).
45. T. Kahlbaum, in Physics of Strongly Coupled Plasma, ed. W.D. Kraeft and M. Schlanges (World Scientific, 1996), p.99.
46. H.E. De Witt and Y. Rosenfeld, Phys.Lett.A, 75, 79 (1979).
47. S. Nordholm, Chem.Phys.Lett., 105, 302 (1984).
48. W. Ebeling, On the Thermodynamic Functions of the One-Component Nonideal Plasma, preprint.
49. The term with k = 0 conceals with the terms describing the self-interaction of the compensating background and interaction of the background with particles.
50. J. Hubbard, and P. Schofield, Phys. Lett., A40, 245 (1972).
51. N.V. Brilliantov and J.P. Valleau, J.Chem.Phys., 108, 1123 (1998); N.V. Brilliantov, Phys.Rev. E, in press.
52. N.V. Brilliantov and J.P. Valleau, J.Chem.Phys., 108, 1123 (1998); N.V. Brilliantov, Phys.Rev. E, in press.
53. -k is used.
54. R. Kubo, J.Phys.Soc. Jap., 17, 1100 (1962).
55. N. Goldenfeld, Lectures on Phase Transittons and the Renormalization Group, Addison-Wesley Publishing Company, NY, 1992; S.-K. Ma, Modern Theory of Critical Phenomena (Benjamin, New York, 1976).
56. N. Goldenfeld, Lectures on Phase Transittons and the Renormalization Group, Addison-Wesley Publishing Company, NY, 1992; S.-K. Ma, Modern Theory of Critical Phenomena (Benjamin, New York, 1976).
57. The ideal-gas cumulants, Eq.(11), may be easily computed using the standard technique; in application to fluids, see, e.g. T. Morita, and K. Hiroike, Progr.Theor.Phys., 25, 537 (1961), or I. R. Yukhnovskii and M. F. Golovko, Statistical Theory of Classical Equilibrium Systems, (in Russian) (Naukova Dumka, Kiev, 1980), where these are explicitely given.
58. The ideal-gas cumulants, Eq.(11), may be easily computed using the standard technique; in application to fluids, see, e.g. T. Morita, and K. Hiroike, Progr.Theor.Phys., 25, 537 (1961), or I. R. Yukhnovskii and M. F. Golovko, Statistical Theory of Classical Equilibrium Systems, (in Russian) (Naukova Dumka, Kiev, 1980), where these are explicitely given.
59. A.L. Kholodenko, A.L. Beyerlein, Phys.Rev. A, 34, 3309 (1986).
60. J. Ortner, private communication.
61. J. Glimm and A. Jaffe, Quantum Physics (Springer-Verlag, New York, 1981).
62. N. V. Brilliantov, C. Bagnuls, and C. Bervillier, Phy.Lett.A, in press.
63. The self-energy is equal to the energy of interactions of two charges at vanishing distance. This divergency does not affect the final result and may be removed considering the lattice version of the problem [36, 38], or (equivalently) implying an infinitesimally small hard-core for interacting particles.
64. N. Krall and A. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, New York, 1973).
65. J.M. Ziman, Principles of the Theory of Solids. (Clarendon Press, Oxford, 1964).
66. k* does not reduce the total number of physically different modes, since the modes with the wave-vectors k and -k correspond to that spreading in the opposite directions.
67. A.S. Kakljugin, Teplofizika Visokih Temperatur, 23, 217 (1985).