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Nonlinear dynamics of radiative condensations in optically thin plasmas
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)
- Akhromeyeva, T.S., S.P. Kurdyumov, G.G. Malinetskii, and A.A. Samarsky, 1989, Phys. Rep. 176, 189
- Alfimov, G.L., V.M. Eleonsky, N.E. Kulagin, L.M. Lerman, and V.P. Silin, 1990, Physica D 44, 168
- Alladro, F., R. Bartiromo, B. Casali, P. Buratti, and F. De-Marco, 1982, Phys. Lett. A 90, 405
- Antiochos, S.K., and A.J. Klimchuk, 1991, Astrophys. J. 378, 372
- Aranson, I., B. Meerson, and P.V. Sasorov, 1993, Phys. Rev. E 47, 4337
- Aranson, I., B. Meerson, and P.V. Sasorov, 1995, Phys. Rev. E 52, 948
- 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
- Ashby, D.E.T.F., and M.H. Hughes, 1981, Nucl. Fusion 21, 911
- Baker, D.R., R.T. Snider, and N. Nagami, 1982, Nucl. Fusion 22, 807
- Balbus, S.A., 1988, Astrophys. J. 328, 395
- 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)]
- Barenblatt, G.I., 1979, Similarity, Self-Similarity and Intermediate Asymptotics (Consultants Bureau, New York)
- Batchelor, G.K., 1970, An Introduction to Fluid Dynamics (Cambridge University, Cambridge, England), p. 244
- Bazdenkov, S.V., A.V. Gruzinov, and O.P. Pogutse, 1990, Plasma Phys. Controlled Fusion 32, 1061
- Begelman, M.C., and C.F. McKee, 1990, Astrophys. J. 358, 375
- 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)]
- Blinnikov, S.I., and P.V. Sasorov, 1996, Phys. Rev. E (in press)
- 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)
- Bogoyavlenskii, O.I., 1985, Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics (Springer, Berlin)
- Boody, F.P., C.E. Bush, S.S. Medley, H. Park, and J. Schivell, 1985, Bull. Am. Phys. Soc. 30, 1518
- Braginskii, S.I., 1957, Zh. Éksp. Teor. Fiz. 33, 645 [Sov. Phys. JETP 6, 494 (1958)]
- Brown, L.C., 1989, Acta Metall. 37, 71
- Brown, L.C., 1990, Scr. Metall. Mater. 24, 963, 2231
- Brown, L.C., 1992, Acta Metall. Mater. 40, 1293
- Brown, L.C.Burton, W.B., B.G. Elmegreen, and R. Genzel, 1992, Eds., The Galactic Interstellar Medium (Springer, Berlin)
- Chaplygin, S.A., 1976, Izbrannye Trudy, Selected Works (Nauka, Moscow), p. 94 (in Russian)
- Chen, M.K., and P.W. Voorhees, 1993, Model. Simul. Mater. Sci. Eng. 1, 591
- Chiuderi, C., and G. Van Hoven, 1979, Astrophys. J. 232, L69
- Choe, G.S., and L.C. Lee, 1992, Sol. Phys. 138, 291
- Choudhury, S.R., and P.K. Kaw, 1989, Phys. Fluids B 1, 1646
- Cross, M.C., and P.C. Hohenberg, 1993, Rev. Mod. Phys. 65, 851
- Dalgarno, A., and R.A. McCray, 1972, Annu. Rev. Astron. Astrophys. 10, 375
- Defouw, R.J., 1970a, Astrophys. J. 160, 659
- Defouw, R.J., 1970b, Astrophys. J. 161, 55
- Deshpande, S., 1994, Phys. Plasmas 1, 127
- Dimits, A.M., and B. Meerson, 1991, Phys. Fluids B 3, 1420
- Doroshkevich, A.G., and Ya.B. Zel'dovich, 1981, Zh. Éksp. Teor. Fiz. 80, 801 [Sov. Phys. JETP 53, 405 (1981)]
- Drake, J.F., 1987, Phys. Fluids 30, 2429
- Drake, J.F., Y. Mok, and G. Van Hoven, 1993, Astrophys. J. 413, 416
- Drake, J.F., L. Sparks, and G. Van Hoven, 1988, Phys. Fluids 31, 813
- Dyakov, S.P., 1954, Zh. Éksp. Teor. Fiz. 27, 288
- Elmer, F.J., 1992, Z. Phys. B 87, 377
- Elphick, C., O. Regev, and N. Shaviv, 1992, Astrophys. J. 392, 106
- Engvold, O., and E. Jensen, 1977, Sol. Phys. 52, 37
- Ferrara, A., and Yu. Shchekinov, 1993, Astrophys. J. 417, 595
- Field, G.B., 1965, Astrophys. J. 142, 531
- Field, G.B., D.W. Goldsmith, and H.J. Habing, 1969, Astrophys. J. Lett. 155, L149
- Fife, P., 1979, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics, Vol. 28 (Springer, New York)
- Filyand, L., G.I. Sivashinsky, and M.L. Frankel, 1994, Physica D 72, 110
- Finn, R., 1986, Equilibrium Capillary Surfaces (Springer, New York), p. 133
- Fisher, P., 1936, Ann. Eugenics 7, 355
- Frankel, M. L., 1990, Phys. Fluids A 2, 1879
- Frank-Kamenetskii, D.A., 1969, Diffusion and Heat Transfer in Chemical Kinetics (Plenum, New York), p. 99
- Gibson, A., 1976, Nucl. Fusion 16, 546
- Goldsmith, D.W., 1970, Astrophys. J. 161, 41
- Gostintsev, Ya.A., A.G. Istratov, and Yu.V. Shulenin, 1988, Combust. Explos. Shock Waves 24, 70
- Gray, A., 1993, Modern Differential Geometry of Curves and Surfaces (CRC, Boca Raton), p. 280
- Gurevich, A.Vl., and R.G. Mints, 1987, Rev. Mod. Phys. 59, 941
- Haken, H., 1978, Synergetics. An Introduction, Springer Series in Synergetics Vol. 1 (Springer, Berlin/Heidelberg)
- Haken, H., 1987, Advanced Synergetics, Springer Series in Synergetics Vol. 20 (Springer, Berlin/Heidelberg)
- Heyvaerts, J., 1974, Astron. Astrophys. 37, 65
- Hildner, E., 1974, Sol. Phys. 35, 123
- Hildner, E.Hollenbach, D.J., and H.A. Thronson, Jr., 1987, Eds., Interstellar Processes, Astrophysics and Space Science Library, Vol. 134 (Reidel, Dordrecht)
- 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)]
- Kaplan, S.A., and S.B. Pikel'ner, 1979, Physics of the Interstellar Medium (Nauka, Moscow; in Russian)
- Kaptsov, O.V., 1988, Dokl. Akad. Nauk SSSR 298, 597 [Sov. Phys. Dokl. 32, 44 (1988)]
- Karpen, J.T., S.K. Antiochos, J.M. Picone, and R.B. Dahlburg, 1989, Astrophys. J. 338, 493
- Karpen, J.T., J.M. Picone, and R.B. Dahlburg, 1988, Astrophys. J. 324, 590
- Kaw, P.K., S. Deshpande, K. Avinash, and S. Rath, 1990, Phys. Rev. Lett. 65, 2873
- Kittel, C., and H. Kroemer, 1980, Thermal Physics (Freeman, San Francisco), p. 290
- Klimchuk, J.A., S.K. Antiochos, and J.T. Mariska, 1987, Astrophys. J. 320, 409
- 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)]
- Krasheninnikov, S.I., 1988, Pis'ma Zh. Éksp. Teor. Fiz. 48, 287 [JETP Lett. 48, 320 (1988)]
- Kurz, W., and D.J. Fisher, 1992, Fundamentals of Solidification (Trans Tech, Aedermannsdorf, Switzerland)
- Lamb, H., 1932, Hydrodynamics (Cambridge University Press, Cambridge)
- Landau, L.D., 1944, Acta Physicochim. URSS 19, 77 (see also a reprinted version in Pelcé, 1988)
- Landau, L.D., and E.M. Lifshitz, 1987, Fluid Mechanics (Pergamon, Oxford)
- Lawson, J.D., 1959, J. Nucl. Energy, Part C 1, 31
- Lepp, S., R. McCray, J.M. Shull, D.T. Woods, and T. Kallman, 1985, Astrophys. J. 288, 58
- Lifshitz, I.M., and V.V. Slezov, 1958, Zh. Éksp. Teor. Fiz. 35, 479 [Sov. Phys. JETP 8, 331 (1959)]
- Lin̄án, A., and F.A. Williams, 1993, Fundamental Aspects of Combustion (Oxford University Press, New York)
- Lipshultz, B., 1987, J. Nucl. Mater. 145-147, 15
- Lipshultz, B., B. LaBombard, E.S. Marmar, M.M. Pickrell, J.L. Terry, R. Watterson, and S.M. Wolfe, 1984, Nucl. Fusion 24, 977
- Manneville, P., 1990, Dissipative Structures and Weak Turbulence, Perspectives in Physics, edited by H. Araki, A. Libchaber, and G. Parisi (Academic, Boston)
- Marder, M., 1987, Phys. Rev. A 36, 858
- McCarthy, D., and J.F. Drake, 1991, Phys. Fluids B 3, 22
- Meerson, B., 1989, Astrophys. J. 347, 1012
- Meerson, B., E. Megged, and T. Tajima, 1996, Astrophys. J. 457, 321
- Meerson, B., N. Petviashvili, and T. Tajima, 1995, Phys. Plasmas 2, 414
- Meerson, B., E.R. Priest, and C.D.C. Steele, 1993, Geophys. Astrophys. Fluid Dyn., 71, 243
- Meerson, B., and I.M. Rutkevich, 1994, unpublished
- Meerson, B.I., and P.V. Sasorov, 1987, Zh. Éksp. Teor. Fiz. 92, 531 [Sov. Phys. JETP 65, 300 (1987)]
- Meerson, B., and P.V. Sasorov, 1996, Phys. Rev. E (in press)
- Meerson, B., C.D.C. Steele, A.M. Milne, and E.R. Priest, 1993, Phys. Fluids B 5, 3417
- Middya, U., M. Sheintuch, M.D. Graham, and D. Luss, 1993, Physica D 63, 393
- Mikhailov, A.S., 1990, Foundations of Synergetics I. Distributed Active Systems, Springer Series in Synergetics Vol. 51 (Springer, Berlin)
- Mok, Y., J.F. Drake, D.D. Schnack, and G. Van Hoven, 1990, Astrophys. J. 359, 228
- Morozov, D.Kh., 1992, Fiz. Plazmy 18, 564 [Sov. J. Plasma Phys. 18, 294 (1992)]
- Murakami, M., J.D. Callen, and L.A. Berry, 1976, Nucl. Fusion 16, 347
- Murray, J.D., 1989, Mathematical Biology (Springer, Berlin)
- Nedospasov, A.V., and V.D. Khait, 1979, Oscillations and Instabilities in Low-Temperature Plasmas (Nauka, Moscow; in Russian)
- Neudachin, V.V., and P.V. Sasorov, 1991, Nucl. Fusion 31, 1053
- Neuhauser, J., S. Schneider, and R. Wunderlich, 1986, Nucl. Fusion 26, 1679
- Ohyabu, N., 1979, Nucl. Fusion 19, 1491
- Oran, E.S., J.T. Mariska, and J.P. Boris, 1982, Astrophys. J. 254, 349
- Ostwald, W., 1900, Z. Phys. Chem. 34, 495
- Parker, E.N., 1953, Astrophys. J. 117, 431
- Pease, R.S., 1957, Proc. R. Soc. London Ser. B 70, 11
- Pelcé, P., 1988, Dynamics of Curved Fronts (Academic, Boston)
- Penston, M.V., and F.E. Brown, 1970, Mon. Not. R. Astron. Soc. 150, 373
- Pikel'ner, S.B., 1967, Astron. Zh. 44, 915 [Sov. Astron. 11, 737 (1968)]
- Pikel'ner, S.B., 1971, Sol. Phys. 17, 44
- Pismen, L., 1979, Chem. Eng. Sci. 34, 563
- Poland, A.I., and J.Y. Mariska, 1986, Sol. Phys. 104, 303
- Priest, E.R., and E.A. Smith, 1979, Sol. Phys. 64, 267
- Priest, E.R., 1984, Solar Magnetohydrodynamics (Reidel, Dordrecht), p. 91
- Priest, E.R.Priest, E.R., 1989, Ed., Dynamics and Structure of Quiescent Solar Prominences, Astrophysics and Space Science Library, Vol. 150 (Kluwer, Dordrecht)
- Raju, P.K., 1968, Mon. Not. R. Astron. Soc. 139, 479
- Rebut, P.H., and B.J. Green, 1977, Nucl. Fusion., Suppl., 2, 3
- Ribes, E., and W. Unno, 1980, Astron. Astrophys. 91, 129
- Rosner, R., W.H. Tucker, and G.S. Vaiana, 1978, Astrophys. J. 220, 643
- Rubinstein, J., and P. Sternberg, 1992, IMA J. Appl. Math. 48, 249
- Rubinstein, J.P. SternbergRuždjak, V., and E. Tandberg-Hanssen, 1989, Eds., Dynamics of Quiescent Prominences (Springer, Berlin)
- Sasorov, P.V., 1975, Astron. Zh. 52, 106 [Sov. Astron. 19, 62 (1975)]
- Sasorov, P.V., 1988, Pis'ma Astron. Zh. 14, 306 [Sov. Astron. Lett. 14, 129 (1988)]
- Scheffler, H., and H. Elsässer, 1987, Physics of the Galaxy and Interstellar Matter (Springer, Berlin)
- Schwarz, J., R. McCray, and R.F. Stein, 1972, Astrophys. J. 175, 673
- 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
- Shercliff, J.A., 1977, J. Fluid Mech. 82, 687
- Sivashinsky, G.I., 1977, Acta Astronautica 4, 1177
- Slezov, V. V., 1978, J. Phys. Chem. Solids 39, 367
- Slezov, V.V., and V.V. Sagalovich, 1987, Usp. Fiz. Nauk 151, 67 [Sov. Phys. Usp. 30, 23 (1987)]
- Sparks, L., G. Van Hoven, and D.D. Schnack, 1990, Astrophys. J. 353, 297
- Spitzer, L., 1978, Physical Processes in the Interstellar Medium (Wiley, New York), p. 2
- 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
- Stuart, J.T., 1967, J. Fluid Mech. 29, 417
- Tandberg-Hanssen, E., 1974, Solar Prominences (Reidel, Dordrecht)
- 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)
- Terry, J.L., E.S. Marmar, and S.M. Wolfe, 1981, Bull. Am. Phys. Soc. 26, 886
- Trubnikov, B.A., and S.K. Zhdanov, 1987, Phys. Rep. 155, 137
- Van der Linden, R.A.M., M. Goossens, and J.P. Goedbloed, 1991, Phys. Fluids B 3, 866
- Vershkov, V.A., and S.V. Mirnov, 1974, Nucl. Fusion 14, 383
- Wagner, C., 1961, Z. Elektrochem. 65, 581
- Yao, J.H., K.R. Elder, H. Guo, and M. Grant, 1993, Phys. Rev. B 47, 14 110
- 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)
- Zel'dovich, Ya.B., and I.D. Novikov, 1983, The Structure and Evolution of the Universe, Relativistic Astrophysics Vol. 2 (University of Chicago, Chicago)
- Zel'dovich, Ya.B., and S.B. Pikel'ner, 1969, Zh. Éksp. Teor. Fiz. 56, 310 [Sov. Phys. JETP 29, 170 (1969)]