Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Nonlinear dynamics of radiative condensations in optically thin plasmas

Baruch Meerson

Baruch Meerson

  • Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel

Rev. Mod. Phys. 68, 215 – Published 1 January, 1996

DOI: https://doi.org/10.1103/RevModPhys.68.215

Abstract

Plasmas that cool by radiation may become unstable to the formation of localized regions of lower temperature and increased density. Such radiative condensations are common in astrophysical and laboratory plasmas that are optically thin. Some perspective of the rapidly developing theoretical understanding of the dynamics of radiative condensations can be given in the framework of simple models. Radiative condensations are closely related to the condensation mode of the thermal instability, first studied by G. B. Field. Progress in the analysis of the nonlinear stage of this instability, achieved recently, employs the hierarchy of time and length scales of the problem. Sets of reduced equations, which describe the nonlinear dynamics of the radiative condensation, have been developed separately in the long-, intermediate-, and short-wavelength limits. Being quite different, all these reduced models predict radiation-driven segregation of the unstable plasma into two different states ("phases") on an intermediate time scale. Subsequent long-time evolution of radiative condensation may strongly depend on the type of boundary condition for the plasma. Radiative condensations usually disappear on a longer (thermal conduction related) time scale, if an inflow/outflow of the plasma is allowed. In this case, regions occupied by one of the "phases" expand until they occupy the whole plasma. On the contrary, in confined plasmas (no inflow/outflow of the plasma is allowed), radiative condensations can persist "forever." Similarities have been explored between radiative condensations and a number of instabilities of growth, such as the Darrieus-Landau instability and Ostwald ripening. A new type of shock wave with a nonmonotonic pressure profile, resulting from radiative condensation dynamics, is described. The role of magnetic fields in radiative condensations is briefly discussed.

References (147)

  1. Akhromeyeva, T.S., S.P. Kurdyumov, G.G. Malinetskii, and A.A. Samarsky, 1989, Phys. Rep. 176, 189
  2. Alfimov, G.L., V.M. Eleonsky, N.E. Kulagin, L.M. Lerman, and V.P. Silin, 1990, Physica D 44, 168
  3. Alladro, F., R. Bartiromo, B. Casali, P. Buratti, and F. De-Marco, 1982, Phys. Lett. A 90, 405
  4. Antiochos, S.K., and A.J. Klimchuk, 1991, Astrophys. J. 378, 372
  5. Aranson, I., B. Meerson, and P.V. Sasorov, 1993, Phys. Rev. E 47, 4337
  6. Aranson, I., B. Meerson, and P.V. Sasorov, 1995, Phys. Rev. E 52, 948
  7. Arnold, V. I., Ya. B. Zel'dovich, and S. F. Shandazin, 1981, Preprint No. 100, Institute for Applied Mathematics, Academy of Sciences of the U.S.S.R., Moscow
  8. Ashby, D.E.T.F., and M.H. Hughes, 1981, Nucl. Fusion 21, 911
  9. Baker, D.R., R.T. Snider, and N. Nagami, 1982, Nucl. Fusion 22, 807
  10. Balbus, S.A., 1988, Astrophys. J. 328, 395
  11. Barelko, V.V., V.M. Beĭbutyan, Yu.E. Volodin, and Ya.B. Zel'dovich, 1981, Dokl. Akad. Nauk SSSR 257, 339 [Sov. Phys. Dokl. 26, 335 (1981)]
  12. Barenblatt, G.I., 1979, Similarity, Self-Similarity and Intermediate Asymptotics (Consultants Bureau, New York)
  13. Batchelor, G.K., 1970, An Introduction to Fluid Dynamics (Cambridge University, Cambridge, England), p. 244
  14. Bazdenkov, S.V., A.V. Gruzinov, and O.P. Pogutse, 1990, Plasma Phys. Controlled Fusion 32, 1061
  15. Begelman, M.C., and C.F. McKee, 1990, Astrophys. J. 358, 375
  16. Belova, N.G., A.A. Galeev, R.Z. Sagdeev, and Yu.S. Sigov, 1980, Pis'ma Zh. Éksp. Teor. Fiz. 31, 551 [JETP Lett. 31, 518 (1980)]
  17. Blinnikov, S.I., and P.V. Sasorov, 1996, Phys. Rev. E (in press)
  18. Blinnikov, S.I., P.V. Sasorov, and S.E. Woosley, 1995, "Self-acceleration of nuclear flames in supernovae," in Proceedings of the Jubilee Gamov Seminar, St. Petersburg, Russia, September 1994, edited by A. Bykov, Space Sci. Rev. (in press)
  19. Bogoyavlenskii, O.I., 1985, Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics (Springer, Berlin)
  20. Boody, F.P., C.E. Bush, S.S. Medley, H. Park, and J. Schivell, 1985, Bull. Am. Phys. Soc. 30, 1518
  21. Braginskii, S.I., 1957, Zh. Éksp. Teor. Fiz. 33, 645 [Sov. Phys. JETP 6, 494 (1958)]
  22. Brown, L.C., 1989, Acta Metall. 37, 71
  23. Brown, L.C., 1990, Scr. Metall. Mater. 24, 963, 2231
  24. Brown, L.C., 1992, Acta Metall. Mater. 40, 1293
  25. Brown, L.C.Burton, W.B., B.G. Elmegreen, and R. Genzel, 1992, Eds., The Galactic Interstellar Medium (Springer, Berlin)
  26. Chaplygin, S.A., 1976, Izbrannye Trudy, Selected Works (Nauka, Moscow), p. 94 (in Russian)
  27. Chen, M.K., and P.W. Voorhees, 1993, Model. Simul. Mater. Sci. Eng. 1, 591
  28. Chiuderi, C., and G. Van Hoven, 1979, Astrophys. J. 232, L69
  29. Choe, G.S., and L.C. Lee, 1992, Sol. Phys. 138, 291
  30. Choudhury, S.R., and P.K. Kaw, 1989, Phys. Fluids B 1, 1646
  31. Cross, M.C., and P.C. Hohenberg, 1993, Rev. Mod. Phys. 65, 851
  32. Dalgarno, A., and R.A. McCray, 1972, Annu. Rev. Astron. Astrophys. 10, 375
  33. Defouw, R.J., 1970a, Astrophys. J. 160, 659
  34. Defouw, R.J., 1970b, Astrophys. J. 161, 55
  35. Deshpande, S., 1994, Phys. Plasmas 1, 127
  36. Dimits, A.M., and B. Meerson, 1991, Phys. Fluids B 3, 1420
  37. Doroshkevich, A.G., and Ya.B. Zel'dovich, 1981, Zh. Éksp. Teor. Fiz. 80, 801 [Sov. Phys. JETP 53, 405 (1981)]
  38. Drake, J.F., 1987, Phys. Fluids 30, 2429
  39. Drake, J.F., Y. Mok, and G. Van Hoven, 1993, Astrophys. J. 413, 416
  40. Drake, J.F., L. Sparks, and G. Van Hoven, 1988, Phys. Fluids 31, 813
  41. Dyakov, S.P., 1954, Zh. Éksp. Teor. Fiz. 27, 288
  42. Elmer, F.J., 1992, Z. Phys. B 87, 377
  43. Elphick, C., O. Regev, and N. Shaviv, 1992, Astrophys. J. 392, 106
  44. Engvold, O., and E. Jensen, 1977, Sol. Phys. 52, 37
  45. Ferrara, A., and Yu. Shchekinov, 1993, Astrophys. J. 417, 595
  46. Field, G.B., 1965, Astrophys. J. 142, 531
  47. Field, G.B., D.W. Goldsmith, and H.J. Habing, 1969, Astrophys. J. Lett. 155, L149
  48. Fife, P., 1979, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics, Vol. 28 (Springer, New York)
  49. Filyand, L., G.I. Sivashinsky, and M.L. Frankel, 1994, Physica D 72, 110
  50. Finn, R., 1986, Equilibrium Capillary Surfaces (Springer, New York), p. 133
  51. Fisher, P., 1936, Ann. Eugenics 7, 355
  52. Frankel, M. L., 1990, Phys. Fluids A 2, 1879
  53. Frank-Kamenetskii, D.A., 1969, Diffusion and Heat Transfer in Chemical Kinetics (Plenum, New York), p. 99
  54. Gibson, A., 1976, Nucl. Fusion 16, 546
  55. Goldsmith, D.W., 1970, Astrophys. J. 161, 41
  56. Gostintsev, Ya.A., A.G. Istratov, and Yu.V. Shulenin, 1988, Combust. Explos. Shock Waves 24, 70
  57. Gray, A., 1993, Modern Differential Geometry of Curves and Surfaces (CRC, Boca Raton), p. 280
  58. Gurevich, A.Vl., and R.G. Mints, 1987, Rev. Mod. Phys. 59, 941
  59. Haken, H., 1978, Synergetics. An Introduction, Springer Series in Synergetics Vol. 1 (Springer, Berlin/Heidelberg)
  60. Haken, H., 1987, Advanced Synergetics, Springer Series in Synergetics Vol. 20 (Springer, Berlin/Heidelberg)
  61. Heyvaerts, J., 1974, Astron. Astrophys. 37, 65
  62. Hildner, E., 1974, Sol. Phys. 35, 123
  63. Hildner, E.Hollenbach, D.J., and H.A. Thronson, Jr., 1987, Eds., Interstellar Processes, Astrophysics and Space Science Library, Vol. 134 (Reidel, Dordrecht)
  64. Kadomtsev, B.B., 1963, in Voprosy Teorii Plazmy, edited by M.A. Leontovich (Atomizdat, Moscow), Vol. 2, p. 173 [Rev. Plasma Phys. 2, 195 (1966)]
  65. Kaplan, S.A., and S.B. Pikel'ner, 1979, Physics of the Interstellar Medium (Nauka, Moscow; in Russian)
  66. Kaptsov, O.V., 1988, Dokl. Akad. Nauk SSSR 298, 597 [Sov. Phys. Dokl. 32, 44 (1988)]
  67. Karpen, J.T., S.K. Antiochos, J.M. Picone, and R.B. Dahlburg, 1989, Astrophys. J. 338, 493
  68. Karpen, J.T., J.M. Picone, and R.B. Dahlburg, 1988, Astrophys. J. 324, 590
  69. Kaw, P.K., S. Deshpande, K. Avinash, and S. Rath, 1990, Phys. Rev. Lett. 65, 2873
  70. Kittel, C., and H. Kroemer, 1980, Thermal Physics (Freeman, San Francisco), p. 290
  71. Klimchuk, J.A., S.K. Antiochos, and J.T. Mariska, 1987, Astrophys. J. 320, 409
  72. Kolmogorov, A.N., I.G. Petrovskii, and N.S. Piskunov, 1937, Byull. Mosk. Gos. Univ., Sekt. Matematika i Mekhanika 1, No. 6, p. 1 [Bull. Univ. Moscow, Ser. Internat., Sec. A 1, 1 (1937)]
  73. Krasheninnikov, S.I., 1988, Pis'ma Zh. Éksp. Teor. Fiz. 48, 287 [JETP Lett. 48, 320 (1988)]
  74. Kurz, W., and D.J. Fisher, 1992, Fundamentals of Solidification (Trans Tech, Aedermannsdorf, Switzerland)
  75. Lamb, H., 1932, Hydrodynamics (Cambridge University Press, Cambridge)
  76. Landau, L.D., 1944, Acta Physicochim. URSS 19, 77 (see also a reprinted version in Pelcé, 1988)
  77. Landau, L.D., and E.M. Lifshitz, 1987, Fluid Mechanics (Pergamon, Oxford)
  78. Lawson, J.D., 1959, J. Nucl. Energy, Part C 1, 31
  79. Lepp, S., R. McCray, J.M. Shull, D.T. Woods, and T. Kallman, 1985, Astrophys. J. 288, 58
  80. Lifshitz, I.M., and V.V. Slezov, 1958, Zh. Éksp. Teor. Fiz. 35, 479 [Sov. Phys. JETP 8, 331 (1959)]
  81. Lin̄án, A., and F.A. Williams, 1993, Fundamental Aspects of Combustion (Oxford University Press, New York)
  82. Lipshultz, B., 1987, J. Nucl. Mater. 145-147, 15
  83. Lipshultz, B., B. LaBombard, E.S. Marmar, M.M. Pickrell, J.L. Terry, R. Watterson, and S.M. Wolfe, 1984, Nucl. Fusion 24, 977
  84. Manneville, P., 1990, Dissipative Structures and Weak Turbulence, Perspectives in Physics, edited by H. Araki, A. Libchaber, and G. Parisi (Academic, Boston)
  85. Marder, M., 1987, Phys. Rev. A 36, 858
  86. McCarthy, D., and J.F. Drake, 1991, Phys. Fluids B 3, 22
  87. Meerson, B., 1989, Astrophys. J. 347, 1012
  88. Meerson, B., E. Megged, and T. Tajima, 1996, Astrophys. J. 457, 321
  89. Meerson, B., N. Petviashvili, and T. Tajima, 1995, Phys. Plasmas 2, 414
  90. Meerson, B., E.R. Priest, and C.D.C. Steele, 1993, Geophys. Astrophys. Fluid Dyn., 71, 243
  91. Meerson, B., and I.M. Rutkevich, 1994, unpublished
  92. Meerson, B.I., and P.V. Sasorov, 1987, Zh. Éksp. Teor. Fiz. 92, 531 [Sov. Phys. JETP 65, 300 (1987)]
  93. Meerson, B., and P.V. Sasorov, 1996, Phys. Rev. E (in press)
  94. Meerson, B., C.D.C. Steele, A.M. Milne, and E.R. Priest, 1993, Phys. Fluids B 5, 3417
  95. Middya, U., M. Sheintuch, M.D. Graham, and D. Luss, 1993, Physica D 63, 393
  96. Mikhailov, A.S., 1990, Foundations of Synergetics I. Distributed Active Systems, Springer Series in Synergetics Vol. 51 (Springer, Berlin)
  97. Mok, Y., J.F. Drake, D.D. Schnack, and G. Van Hoven, 1990, Astrophys. J. 359, 228
  98. Morozov, D.Kh., 1992, Fiz. Plazmy 18, 564 [Sov. J. Plasma Phys. 18, 294 (1992)]
  99. Murakami, M., J.D. Callen, and L.A. Berry, 1976, Nucl. Fusion 16, 347
  100. Murray, J.D., 1989, Mathematical Biology (Springer, Berlin)
  101. Nedospasov, A.V., and V.D. Khait, 1979, Oscillations and Instabilities in Low-Temperature Plasmas (Nauka, Moscow; in Russian)
  102. Neudachin, V.V., and P.V. Sasorov, 1991, Nucl. Fusion 31, 1053
  103. Neuhauser, J., S. Schneider, and R. Wunderlich, 1986, Nucl. Fusion 26, 1679
  104. Ohyabu, N., 1979, Nucl. Fusion 19, 1491
  105. Oran, E.S., J.T. Mariska, and J.P. Boris, 1982, Astrophys. J. 254, 349
  106. Ostwald, W., 1900, Z. Phys. Chem. 34, 495
  107. Parker, E.N., 1953, Astrophys. J. 117, 431
  108. Pease, R.S., 1957, Proc. R. Soc. London Ser. B 70, 11
  109. Pelcé, P., 1988, Dynamics of Curved Fronts (Academic, Boston)
  110. Penston, M.V., and F.E. Brown, 1970, Mon. Not. R. Astron. Soc. 150, 373
  111. Pikel'ner, S.B., 1967, Astron. Zh. 44, 915 [Sov. Astron. 11, 737 (1968)]
  112. Pikel'ner, S.B., 1971, Sol. Phys. 17, 44
  113. Pismen, L., 1979, Chem. Eng. Sci. 34, 563
  114. Poland, A.I., and J.Y. Mariska, 1986, Sol. Phys. 104, 303
  115. Priest, E.R., and E.A. Smith, 1979, Sol. Phys. 64, 267
  116. Priest, E.R., 1984, Solar Magnetohydrodynamics (Reidel, Dordrecht), p. 91
  117. Priest, E.R.Priest, E.R., 1989, Ed., Dynamics and Structure of Quiescent Solar Prominences, Astrophysics and Space Science Library, Vol. 150 (Kluwer, Dordrecht)
  118. Raju, P.K., 1968, Mon. Not. R. Astron. Soc. 139, 479
  119. Rebut, P.H., and B.J. Green, 1977, Nucl. Fusion., Suppl., 2, 3
  120. Ribes, E., and W. Unno, 1980, Astron. Astrophys. 91, 129
  121. Rosner, R., W.H. Tucker, and G.S. Vaiana, 1978, Astrophys. J. 220, 643
  122. Rubinstein, J., and P. Sternberg, 1992, IMA J. Appl. Math. 48, 249
  123. Rubinstein, J.P. SternbergRuždjak, V., and E. Tandberg-Hanssen, 1989, Eds., Dynamics of Quiescent Prominences (Springer, Berlin)
  124. Sasorov, P.V., 1975, Astron. Zh. 52, 106 [Sov. Astron. 19, 62 (1975)]
  125. Sasorov, P.V., 1988, Pis'ma Astron. Zh. 14, 306 [Sov. Astron. Lett. 14, 129 (1988)]
  126. Scheffler, H., and H. Elsässer, 1987, Physics of the Galaxy and Interstellar Matter (Springer, Berlin)
  127. Schwarz, J., R. McCray, and R.F. Stein, 1972, Astrophys. J. 175, 673
  128. Sergienko, G., K. Höthker, A. Nedospasov, A. Pospieszczyk, D. Rusbüldt, U. Samm, B. Schweer, and M. Tokar, 1993, in 20th European Conference on Controlled Fusion and Plasma Physics, Contributed Papers, Part II, Lisboa, edited by J.A. Costa Cabral, M.E. Manso, F.M. Serra, and F.C. Schüller (European Physical Society, Lisboa), p. 667
  129. Shercliff, J.A., 1977, J. Fluid Mech. 82, 687
  130. Sivashinsky, G.I., 1977, Acta Astronautica 4, 1177
  131. Slezov, V. V., 1978, J. Phys. Chem. Solids 39, 367
  132. Slezov, V.V., and V.V. Sagalovich, 1987, Usp. Fiz. Nauk 151, 67 [Sov. Phys. Usp. 30, 23 (1987)]
  133. Sparks, L., G. Van Hoven, and D.D. Schnack, 1990, Astrophys. J. 353, 297
  134. Spitzer, L., 1978, Physical Processes in the Interstellar Medium (Wiley, New York), p. 2
  135. Stringer, T.E., 1985, in 12th European Conference on Controlled Fusion and Plasma Physics, Budapest, Hungary, 1985, edited by L. Pocs and A. Montvai (European Physical Society, Budapest), Part 1, p. 86
  136. Stuart, J.T., 1967, J. Fluid Mech. 29, 417
  137. Tandberg-Hanssen, E., 1974, Solar Prominences (Reidel, Dordrecht)
  138. Tandberg-Hanssen, E.Tenorio-Tagle, G., M. Moles, and J. Melnik, 1989, Eds., Structure and Dynamics of the Interstellar Medium, Lecture Notes in Physics Vol. 350 (Springer, Berlin)
  139. Terry, J.L., E.S. Marmar, and S.M. Wolfe, 1981, Bull. Am. Phys. Soc. 26, 886
  140. Trubnikov, B.A., and S.K. Zhdanov, 1987, Phys. Rep. 155, 137
  141. Van der Linden, R.A.M., M. Goossens, and J.P. Goedbloed, 1991, Phys. Fluids B 3, 866
  142. Vershkov, V.A., and S.V. Mirnov, 1974, Nucl. Fusion 14, 383
  143. Wagner, C., 1961, Z. Elektrochem. 65, 581
  144. Yao, J.H., K.R. Elder, H. Guo, and M. Grant, 1993, Phys. Rev. B 47, 14 110
  145. Zel'dovich, Ya.B., G.I. Barenblatt, V.B. Librovich, and G.M. Makhviladze, 1985, The Mathematical Theory of Combustion and Explosions (Consultants Bureau, New York)
  146. Zel'dovich, Ya.B., and I.D. Novikov, 1983, The Structure and Evolution of the Universe, Relativistic Astrophysics Vol. 2 (University of Chicago, Chicago)
  147. Zel'dovich, Ya.B., and S.B. Pikel'ner, 1969, Zh. Éksp. Teor. Fiz. 56, 310 [Sov. Phys. JETP 29, 170 (1969)]

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation