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MHD Turbulence: Scaling Laws and Astrophysical Implications

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Turbulence and Magnetic Fields in Astrophysics

Part of the book series: Lecture Notes in Physics ((LNP,volume 614))

Abstract

Turbulence is the most common state of astrophysical flows. In typical astrophysical fluids, turbulence is accompanied by strong magnetic fields, which has a large impact on the dynamics of the turbulent cascade. Recently, there has been a significant breakthrough on the theory of magnetohydrodynamic (MHD) turbulence. For the first time we have a scaling model that is supported by both observations and numerical simulations. We review recent progress in studies of both incompressible and compressible turbulence. We compare Iroshnikov-Kraichnan and Goldreich-Sridhar models, and discuss scalings of Alfvén, slow, and fast waves. We also discuss the completely new regime of MHD turbulence that happens below the scale at which hydrodynamic turbulent motions are damped by viscosity. In the case of the partially ionized diffuse interstellar gas the viscosity is due to neutrals and truncates the turbulent cascade at ~parsec scales. We show that below this scale magnetic fluctuations with a shallow spectrum persist and discuss the possibility of a resumption of the MHD cascade after ions and neutrals decouple. We discuss the implications of this new insight into MHD turbulence for cosmic ray transport, grain dynamics, etc., and how to test theoretical predictions against observations.

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References

  1. S. M. Andrews, D. M. Meyer, J. T. Lauroesch: Astrophys. J. 552, L73 (2001)

    Article  ADS  Google Scholar 

  2. J. W. Armstrong, B. J. Rickett, S. R. Spangler: Astrophys. J. 443, 209 (1995)

    Article  ADS  Google Scholar 

  3. C. Baccigalupi, C. Burigana, F. Perrotta, G. De Zotti, L. La Porta, D. Maino, M. Maris, R. Paladini: Astron. Astrophys. 372 8 (2001)

    Article  ADS  Google Scholar 

  4. A. Bhattacharjee, C. S. Ng, S. R. Spangler: Astrophys. J. 494, 409 (1998)

    Article  ADS  Google Scholar 

  5. D. Biskamp: Nonlinear Magnetohydrodynamics (Cambridge Uinversity Press, Cambridge, 1993)

    Book  Google Scholar 

  6. D. Biskamp: Phys. Plasmas, 9(4), 1486 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  7. D. Biskamp, E. Schwarz: Phys. Plasmas, 8(7), 3282 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  8. D. Biskamp, E. Schwarz, A. Celani: Phys. Rev. Lett. 81 4855 (1998)

    Article  ADS  Google Scholar 

  9. S. Boldyrev: Astrophys. J. 569, 841 (2002)

    Article  ADS  Google Scholar 

  10. S. Boldyrev, A. Nordlund, P. Padoan Astrophys. J. 573, 678 (2002)

    Article  ADS  Google Scholar 

  11. A. Brandenburg: Astrophys. J. 550, 824 (2001)

    Article  ADS  Google Scholar 

  12. A. Brandenburg, R. L. Jennings, A. Nordlund: J. Fluid Mech. 306, 325 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. M. Brio, C. Wu: J. Comput. Phys. 75, 500 (1988)

    Article  MathSciNet  Google Scholar 

  14. C. Brunt, M. Heyer: Astrophys. J. 566, 276 (2002)

    Article  ADS  Google Scholar 

  15. F. Cattaneo, D. W. Hughes: Phys. Rev. E. 54, R4532 (1996)

    Article  ADS  Google Scholar 

  16. C. Cesarsky: Annu. Rev. Astro. Astrophys. 18, 289 (1980)

    Article  ADS  Google Scholar 

  17. B. Chandran: Phys. Rev. Lett. 85(22), 4656 (2001)

    Article  ADS  Google Scholar 

  18. S. Chandrasekhar, E. Fermi: Astrophys. J. 118, 113 (1953)

    Article  ADS  MathSciNet  Google Scholar 

  19. J. Cho, E. T, Vishniac: Astrophys. J. 538, 217 (2000a)

    Article  ADS  Google Scholar 

  20. J. Cho, E. T. Vishniac: Astrophys. J. 539, 273 (2000b)

    Article  ADS  Google Scholar 

  21. J. Cho, A. Lazarian: Phys. Rev. Lett. accepted (2002) astro-ph/0205282

    Google Scholar 

  22. J. Cho, A. Lazarian: Astrophys. J., 575, L63 (2002) astro-ph/0205284

    Article  ADS  Google Scholar 

  23. J. Cho, A. Lazarian, E. T. Vishniac: Astrophys. J. 564, 291 (2002a) (CLV02a)

    Article  ADS  Google Scholar 

  24. J. Cho, A. Lazarian, E. T. Vishniac: Astrophys. J. 566, L49 (2002b)

    Article  ADS  Google Scholar 

  25. L. Del Zanna, M. Velli, P. Londrillo: Astron. Astrophys. 367, 705, (2001)

    Article  ADS  Google Scholar 

  26. N. F. Derby: Astrophys. J. 224, 1013, (1978)

    Article  ADS  Google Scholar 

  27. A. A. Deshpande: Monthly Not. Roy. Astron. Soc. 317, 199 (2000)

    Article  ADS  Google Scholar 

  28. A. A. Deshpande, K. S. Dwarakanath, W. M. Goss: Astrophys. J. 543, 227 (2000)

    Article  ADS  Google Scholar 

  29. P. H. Diamond, G. G. Craddock: Comments on the Plasma Physics of Controlled Fusion, 13, 287 (1990)

    Google Scholar 

  30. J. M. Dickey, N. M. McClure-Griffiths, S. Stanimirovic, B. M. Gaensler, A. J. Green: Astrophys. J. 561, 264 (2001)

    Article  ADS  Google Scholar 

  31. R. L. Dickman: in Protostars and Planets II, ed. by D. C. Black, M. S. Mathews (Tucson: Univ. Arizona Press, 1985) p. 150

    Google Scholar 

  32. N. H. Dieter, W. J. Welch, J. D. Romney: Astrophys. J. 206, L113 (1976)

    Article  ADS  Google Scholar 

  33. B. T. Draine: 1985, in Protostars and Planets II, ed. by D. C. Black, M. S. Matthews (Tucson: Univ. Arizona Press, 1985) p. 621

    Google Scholar 

  34. B. T. Draine, Lazarian, A.: Astrophys. J. 512, 740 (1999)

    Article  ADS  Google Scholar 

  35. B. G. Elmegreen: in From Darkness to Light, ed. by T. Montmerle, P. Andre (ASP Conf. Series, 2002, p. 255) (astro-ph:0010582)

    Google Scholar 

  36. M. D. Faison, W. M. Goss: Astron. J. 121, 2706 (2001)

    Article  ADS  Google Scholar 

  37. E. Falgarone, G. Pineau des Forets, E. Roueff: Astron. Astrophys. 300, 870 (1995)

    ADS  Google Scholar 

  38. E. Falgarone, J. L. Puget, Astron. Astrophys. 293, 840 (1995)

    ADS  Google Scholar 

  39. J. Fournier, P. Sulem, A. Pouquet: J. Phys. A, 15, 1393 (1982)

    Article  ADS  MATH  Google Scholar 

  40. P. Fosalba, A. Lazarian, S. Prunet, J. A. Tauber: Astron. J. 564, 762 (2002)

    ADS  Google Scholar 

  41. U. Frisch: Turbulence: the legacy of A.N. Kolmogorov, (Cambridge Univ. Press, New York, 1995)

    MATH  Google Scholar 

  42. S. Galtier, S. V. Nazarenko, A. C. Newell, A. Pouquet: J. Plasma Phys. 63, 447 (2000)

    Article  ADS  Google Scholar 

  43. G. Giardino, A.J. Banday, P. Fosalba, K.M. Górski, J.L. Jonas, W. O’Mullane, J. Tauber: Astron. Astrophys. 371 708 (2001)

    Article  ADS  Google Scholar 

  44. G. Giardino, A.J. Banday, K.M. Górski, K. Bennett, J.L. Jonas, J. Tauber: Astron. Astrophys. astro-ph/0202520 (2002)

    Google Scholar 

  45. P. Goldreich, S. Sridhar: Astrophys. J. 438, 763 (1995) (GS95)

    Article  ADS  Google Scholar 

  46. P. Goldreich, S. Sridhar: Astrophys. J. 485, 680 (1997)

    Article  ADS  Google Scholar 

  47. M. L. Goldstein: Astrophys. J. 219, 700 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  48. M. L. Goldstein, D. A. Roberts: Annu. Rev. Astron. Astrophys. 33, 283, (1995)

    Article  ADS  Google Scholar 

  49. J. Goodman, R. Narayan: Monthly Not. Roy. Astron. Soc. 214, 519 (1985)

    ADS  Google Scholar 

  50. S. Ghosh, W. M. Matthaeus, D. C. Montgomery: Phys. Fluids, 31, 2171 (1988)

    Article  ADS  Google Scholar 

  51. J. R. Gott, C. Park, R. Juskiewicz, W. Bies, F. Bouchet, A. Stebbins: Astrophys. J. 352, 1 (1990)

    Article  ADS  Google Scholar 

  52. D. A. Green: Monthly Not. Roy. Astron. Soc. 262, 328 (1993)

    ADS  Google Scholar 

  53. A. V. Gruzinov, P. H. Diamond: Phys. Rev. Lett. 72, 1671 (1994)

    Article  ADS  Google Scholar 

  54. C. Heiles: Astrophys. J. 481, 193 (1997)

    Article  ADS  Google Scholar 

  55. M. H. Heyer, F. P. Schloerb: Astrophys. J. 475, 173 (1997)

    Article  ADS  Google Scholar 

  56. J. C. Higdon: Astrophys. J. 285, 109 (1984)

    Article  ADS  Google Scholar 

  57. T. S. Horbury: in Plasma Turbulence and Energetic particles, ed. by M. Ostrowski, R. Schlickeiser (Cracow, Poland, 1999) p. 28

    Google Scholar 

  58. T. S. Horbury, A. Balogh: Nonlin. Proc. Geophys. 4, 185 (1997)

    Article  ADS  Google Scholar 

  59. S. von Horner: Zs.F. Ap. 30, 17 (1951)

    ADS  Google Scholar 

  60. M. Hossain, P. C. Gray, D. H. Pontius, W. H. Matthaeus: Phys. Fluids, 7, 2886 (1995)

    Article  MATH  ADS  Google Scholar 

  61. P. Iroshnikov: Astron. Zh. 40, 742 (1963) (English: Sov. Astron. 7, 566 (1964))

    ADS  Google Scholar 

  62. V. Jayanti, J. V. Hollweg: J. Geophys. Res. 98, 13247 (1993)

    Article  ADS  Google Scholar 

  63. K. Joulain, E. Falgarone, G. Pineau des Forets, D. Flower: Astro. Astrophys. 340, 241 (1998)

    ADS  Google Scholar 

  64. J. Kampé de Fériet: in: Gas Dynamics of Cosmic Clouds (Amsterdam: North-Holland, 1955) p. 134

    Google Scholar 

  65. S. A. Kaplan, S. B. Pickelner: The Interstellar Medium (Harvard Univ. Press, 1970)

    Google Scholar 

  66. L. Klein, R. Bruno, B. Bavassano, H. Rosenbauer: J. Geophys. Res. 98, 17461 (1993)

    Article  ADS  Google Scholar 

  67. R. S. Klessen: Astrophys. J. 556, 837 (2001)

    Article  ADS  Google Scholar 

  68. A. Kolmogorov: Dokl. Akad. Nauk SSSR, 31, 538 (1941)

    Google Scholar 

  69. J. Kota, J. R. Jokipii: Astrophys. J. 531, 1067 (2000)

    Article  ADS  Google Scholar 

  70. R. Kraichnan: J. Fluid Mech. 5, 497 (1959)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  71. R. Kraichnan: Phys. Fluids 8, 1385 (1965)

    Article  MathSciNet  ADS  Google Scholar 

  72. F. Krause, & K.H. Radler: Mean-Field Magnetohydrodynamics and Dynamo Theory (Oxford: Pergamon Press 1980)

    Google Scholar 

  73. R. M. Kulsrud, S. W. Anderson: Astrophys. J. 396, 606 (1992)

    Article  ADS  Google Scholar 

  74. T. Kusaka, T. Nakano, C. Hayashi: Prog. Theor. Phys.44, 1580 (1970)

    Article  ADS  Google Scholar 

  75. R. B. Larson: Monthly Not. Roy. Astron. Soc. 194, 809 (1981)

    ADS  Google Scholar 

  76. A. Lazarian: Astron. and Astrophys. Transactions, 3, 33 (1992)

    Article  ADS  Google Scholar 

  77. A. Lazarian: Astron. Astrophys. 293, 507 (1995)

    ADS  Google Scholar 

  78. A. Lazarian: in Interstellar Turbulence, ed. by J. Franco, A. Carraminana (Cambridge Univ. Press, 1999a) p. 95 (astro-ph/9804024)

    Google Scholar 

  79. A. Lazarian: in Plasma Turbulence and Energetic Particles, ed. by M. Ostrowski, R. Schlickeiser (Cracow, 1999b) p. 28, (astro-ph/0001001)

    Google Scholar 

  80. A. Lazarian: 2000, in Cosmic Evolution and Galaxy Formation, ASP v. 215, ed. by J. Franco, E. Terlevich, O. Lopez-Cruz, I. Aretxaga (Astron. Soc. Pacific, 2000) p. 69 (astro-ph/0003414)

    Google Scholar 

  81. A. Lazarian, G. Chibisov: Sov. Astron. Lett. 17(3), 208 (1991)

    ADS  Google Scholar 

  82. A. Lazarian, A. Goodman, P. Myers: Astrophys. J. 490, 273 (1997)

    Article  ADS  Google Scholar 

  83. A. Lazarian, V. R. Shutenkov: Sov. Astron. Lett. 16(4), 297 (1990)

    ADS  Google Scholar 

  84. A. Lazarian, D. Pogosyan: Astrophys. J. 537, 720L (2000)

    Article  ADS  Google Scholar 

  85. A. Lazarian, D. Pogosyan: (2002), in preparation

    Google Scholar 

  86. A. Lazarian, D. Pogosyan, A. Esquivel: 2002, in Seeing Through the Dust, ed. by R. Taylor, T. Landecker, A. Willis (ASP Conf. Series, 2002), in press (astroph/ 0112368) (LPE02)

    Google Scholar 

  87. A. Lazarian, D. Pogosyan, E. Vazquez-Semadeni, B. Pichardo: Astrophys. J. 555, 130 (2001)

    Article  ADS  Google Scholar 

  88. A. Lazarian, S. Prunet: in Astrophysical Polarized Backgrounds, ed. by S. Cecchini, S. Cortiglioni, R. Sault, C. Sbarra (2002) (astro-ph/0111214)

    Google Scholar 

  89. A. Lazarian, E. T. Vishniac: Astrophys. J. 517, 700 (1999)

    Article  ADS  Google Scholar 

  90. A. Lazarian, E. T. Vishniac: in Astrophysical Plasmas: Codes, Models, and Observations, eds. by J. Arthur, N. Brickhouse, & J. Franco, RevMexAA (Serie de Conferencias), Vol. 9, 55

    Google Scholar 

  91. A. Lazarian, E. T. Vishniac, J. Cho: 2002, in preparation

    Google Scholar 

  92. A. Lazarian, H. Yan: Astrophys. J. 566, L105 (2002)

    Article  ADS  Google Scholar 

  93. R. J. Leamon, C. W. Smith, N. F. Ness, W. H. Matthaeus: J. Geophys. Res. 103, 4775 (1998)

    Article  ADS  Google Scholar 

  94. C. W. Lee, P. C. Myers, M. Tafalla: Astrophys. J. Supp. 136, 703 (2001)

    Article  ADS  Google Scholar 

  95. M. Lesieur: Turbulence In Fluids (Dordrecht: Kluwer, 1990)

    MATH  Google Scholar 

  96. Y. Lithwick, P. Goldreich: Astrophys. J. 562, 279 (2001)

    Article  ADS  Google Scholar 

  97. V. S. L’vov, Y. V. L’vov, A. Pomyalov: Phys. Rev. E, 61, 2586 (2000)

    Article  ADS  Google Scholar 

  98. M. Mac Low: Phys. Rev. Lett. 80, 2754 (1998)

    Article  ADS  Google Scholar 

  99. M. Mac Low: Astrophys. J. 524, 169 (1999)

    Article  ADS  Google Scholar 

  100. J. Maron, S. Cowley: astro-ph/0111008 (2001)

    Google Scholar 

  101. J. Maron, P. Goldreich: Astrophys. J. 554, 1175 (2001)

    Article  ADS  Google Scholar 

  102. A. P. Marscher, E. M. Moore, T. M. Bania: Astrophys. J. 419, L101 (1993)

    Article  ADS  Google Scholar 

  103. W. M. Matthaeus, M. L. Goldstein, D. C. Montgomery: Phys. Rev. Lett. 51, 1484 (1983)

    Article  ADS  Google Scholar 

  104. W. M. Matthaeus, S. Oughton, S. Ghosh, M. Hossain: Phy. Rev. Lett. 81, 2056 (1998)

    Article  ADS  Google Scholar 

  105. W. M. Matthaeus, S. Ghosh, S. Oughton, D. A. Roberts: J. Geophys. Res. 101, 7619 (1996)

    Article  ADS  Google Scholar 

  106. C. F. McKee: in The Origin of Stars and Planetary Systems, ed. by J. L. Charles, D. K. Nikolaos (Dordrecht: Kluwer, 1999) p. 29

    Google Scholar 

  107. M. Meneguzzi, U. Frish, A. Pouquet: Phys. Rev. Lett. 47, 1060 (1981)

    Article  ADS  Google Scholar 

  108. D. M. Meyer, J. C. Blades: Astrophys. J. 464, L179 (1996)

    Article  ADS  Google Scholar 

  109. L. J. Milano, W. H. Matthaeus, P. Dmitruk, D. C. Montgomery: Phys. Plasmas, 8(6), 2673 (2001)

    Article  ADS  Google Scholar 

  110. A. Minter, S. Spangler: Astrophys. J. 485, 182 (1997)

    Article  ADS  Google Scholar 

  111. H. K. Moffatt: Magnetic Field Generation in Electrically Conducting Fluids (Cambridge: Cambridge Univ. Press, 1978)

    Google Scholar 

  112. A. S. Monin, A. A. Yaglom: Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 2 (Cambridge: MIT Press, 1975)

    Google Scholar 

  113. D. C. Montgomery: Physica Scripta, T2/1, 83 (1982)

    Article  ADS  Google Scholar 

  114. D. C. Montgomery, W. H. Matthaeus: Astrophys. J. 447, 706 (1995)

    Article  ADS  Google Scholar 

  115. D. C. Montgomery, L. Turner: Phys. Fluids 24(5), 825 (1981)

    Article  MATH  ADS  Google Scholar 

  116. W.-C. Müller, D. Biskamp: Phys. Rev. Lett. 84(3) 475 (2000)

    Article  ADS  Google Scholar 

  117. G. Munch: Rev. Mod. Phys. 30, 1035 (1958)

    Article  ADS  Google Scholar 

  118. P. C. Myers: Astrophys. J. 270, 105 (1983)

    Article  ADS  Google Scholar 

  119. P. C. Myers: in The Origin of Stars and Planetary Systems, ed. by J. L. Charles, D. K. Nikolaos (Dordrecht: Kluwer, 1999) p. 67

    Google Scholar 

  120. P. C. Myers, A. Lazarian: Astrophys. J. Lett. 507, 157 (1998)

    Article  ADS  Google Scholar 

  121. R. Narayan, J. Goodman: Monthly Not. Roy. Astron. Soc. 238, 963 (1989)

    ADS  Google Scholar 

  122. C. S. Ng, A. Bhattacharjee: Astrophys. J. 465, 845 (1996)

    Article  ADS  Google Scholar 

  123. A. Nordlund, A. Brandenburg, R. Jennings, M. Rieutord, J. Ruokolainen, R. Stein, I. Tuominen: Astrophys. J. 392, 647 (1992)

    Article  ADS  Google Scholar 

  124. V. Ossenkopf: Astron. Astrophys. 280, 617 (1993)

    ADS  Google Scholar 

  125. E. C. Ostriker, C. F. Gammie, J. M. Stone: Astrophys. J. 513, 259 (1999)

    Article  ADS  Google Scholar 

  126. E. C. Ostriker, J. M. Stone, C. F. Gammie: Astrophys. J. 546, 980 (2001)

    Article  ADS  Google Scholar 

  127. B. Otte, R.-J. Dettmar: Astron. Astrophys. 343, 705 (1999)

    ADS  Google Scholar 

  128. B. Otte, R. J. Reynolds, J. S. Gallagher III, A. M. N. Ferguson: Astrophys. J. 560, 207O (2001)

    Article  ADS  Google Scholar 

  129. S. Oughton, E. R. Priest, W. H. Matthaeus: J. Fluid Mech. 280, 95 (1994)

    Article  MATH  ADS  Google Scholar 

  130. P. Padoan, A. Nordlund: Astrophys. J. 526, 279 (1999)

    Article  ADS  Google Scholar 

  131. P. Padoan, A. Goodman, B. T. Draine, M. Juvela, A. Nordlund, O. Rognvaldsson: Astrophys. J. 559, 1005 (2001)

    Article  ADS  Google Scholar 

  132. E. N. Parker: Cosmical magnetic fields: Their origin and their activity (Oxford University Press, New York, 1979)

    Google Scholar 

  133. T. Passot, A. Pouquet, P. Woodward: Astron. Astrophys. 197, 228 (1988)

    ADS  MATH  Google Scholar 

  134. T. Passot, E. Vazquez-Semadeni, A. Pouquet: Astrophys. J. 455, 536 (1995)

    Article  ADS  Google Scholar 

  135. H. Politano, A. Pouquet: Phys. Rev. E 52(1), 636 (1995)

    Article  ADS  Google Scholar 

  136. H. Politano, A. Pouquet, V. Carbone: Europhys. Lett. 43(5), 516 (1995)

    Article  ADS  Google Scholar 

  137. H. Politano, A. Pouquet, P. L. Sulem: Phys. Plasmas 2(8), 2931 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  138. D. Porter, P. Woodward, A. Pouquet: Phys. Fluids 10, 237 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  139. A. Pouquet, U. Frish, J. Léorat: J. Fluid Mech. 77, 321 (1976)

    Article  MATH  ADS  Google Scholar 

  140. A. Pouquet, G. S. Patterson: J. Fluid Mech. 85, 305 (1978)

    Article  MATH  ADS  Google Scholar 

  141. A. Pouquet: in Interstellar Turbulence, ed. by J. Franco, A. Carraminana (Cambridge Univ. Press, 1999) p. 87

    Google Scholar 

  142. R. J. Rand, S. R. Kulkarni, J. J. Hester: Astrophys. J. 352, 1 (1990)

    Article  ADS  Google Scholar 

  143. R. J. Rand: Pub. Astro. Soc. Aust. 15, 106 (1998)

    ADS  Google Scholar 

  144. R. J. Reynolds: Astrophys. J. 333, 341 (1988)

    Article  ADS  MATH  Google Scholar 

  145. R. J. Reynolds, L. M. Haffner, S. L. Tufte: Astrophys. J. 525, 21 (1999)

    Article  ADS  Google Scholar 

  146. M. N. Rosenbluth, D. A. Monticello, H. R. Strauss, R. B. White: Phys. Fluids 19, 1987 (1976)

    Article  ADS  Google Scholar 

  147. D. Ryu, T. W. Jones: Astrophys. J. 442, 228 (1995)

    Article  ADS  Google Scholar 

  148. J. Saur, H. Politano, A. Pouquet, W. H. Matthaeus: American Geophysical Union, Fall Meeting (2001)

    Google Scholar 

  149. J. M. Scalo: Astrophys. J. 277, 556 (1984)

    Article  ADS  Google Scholar 

  150. J. M. Scalo: in Interstellar Processes, ed. by D. J. Hollenbach, H. A. Thronson (Dordrecht: Reidel, 1987) p. 349

    Google Scholar 

  151. A. Schlickeiser, J. A. Miller: Astrophys. J. 492, 352 (1998)

    Article  ADS  Google Scholar 

  152. Z.-S. She, E. Leveque: Phys. Rev. Lett. 72(3), 336 (1994) (S-L)

    Article  ADS  Google Scholar 

  153. J. V. Shebalin, W. H. Matthaeus, D. C. Montgomery: J. Plasma Phys. 29, 525 (1983)

    Article  ADS  Google Scholar 

  154. J. H. Simonetti, J. M. Cordes: in Radio wave scattering in the interstellar medium; Proceedings of the AIP Conference (American Institute of Physics, New York, 1988) p. 134

    Google Scholar 

  155. J. H. Simonetti: Astrophys. J. 386, 170 (1992)

    Article  ADS  Google Scholar 

  156. S. R. Spangler: Astrophys. J. 376, 540 (1991)

    Article  ADS  Google Scholar 

  157. S. R. Spangler, C. R. Gwinn: Astrophys. J. 353, L29 (1990)

    Article  ADS  Google Scholar 

  158. S. Sridhar, P. Goldreich: Astrophys. J. 432, 612 (1994)

    Article  ADS  Google Scholar 

  159. S. Stanimirovic, A. Lazarian: Astrophys. J. 551, L53 (2001)

    Article  ADS  Google Scholar 

  160. J. M. Stone, E. C. Ostriker, C. F. Gammie: Astrophys. J. 508, L99 (1998)

    Article  ADS  Google Scholar 

  161. H. R. Strauss: Phys. Fluids, 19, 134 (1976)

    Article  ADS  Google Scholar 

  162. J. Stutzki: in Plasma Turbulence and Energetic particles, ed. by M. Ostrowski, R. Schlickeiser (Cr acow, 1999) p. 48

    Google Scholar 

  163. J. Stutzki, F. Bensch, A. Heithausen, V. Ossenkopf, M. Zielinsky: Astron. Astrophys. 336, 697 (1998)

    ADS  Google Scholar 

  164. M. Tafalla, D. Mardones, P. C. Myers, P. Caselli, R. Bachiller, B. J. Benson: Astrophys. J. 504, 900 (1998)

    Article  ADS  Google Scholar 

  165. A. Ting, W. M. Matthaeus, D. C. Montgomery: Phys. Fluids, 29, 3261 (1986)

    Article  ADS  Google Scholar 

  166. H. J. Volk, F. C. Jones, G. E. Morfill, S. Roser: Astron. Astrophys. 85, 316 (1980)

    ADS  MathSciNet  Google Scholar 

  167. S. J. Weidenschilling, T. V. Ruzmaikina: Astrophys. J. 430, 713 (1994)

    Article  ADS  Google Scholar 

  168. E. Vazquez-Semadeni, T. Passot, A. Pouquet: Astrophys. J. 441, 702 (1995)

    Article  ADS  Google Scholar 

  169. E. Vazquez-Semadeni, T. Passot, A. Pouquet: Astrophys. J. 473, 881 (1996)

    Article  ADS  Google Scholar 

  170. E. Vazquez-Semadeni: in Seeing Through the Dust, ed. by R. Taylor, T. Landecker, A. Willis (ASP: San Francisco, 2002) (astro-ph/0201072)

    Google Scholar 

  171. A. Warhaft: Annu. Rev. Fluid Mech. 32, 203 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  172. O. C. Wilson, G. Munch, E. M. Flather, M. F. Coffeen: Astrophys. J. Supp. 4, 199 (1959)

    Article  ADS  Google Scholar 

  173. S. I. Vainstein, F. Cattaneo: Astrophys. J. 393, 165 (1992)

    Article  ADS  Google Scholar 

  174. M. K. Verma: Phys. Plasmas, 6(5), 1455, (1999)

    Article  ADS  MathSciNet  Google Scholar 

  175. M. K. Verma, G. Dar, V. Eswaran: Phys. Plasmas, 9(4), 1484 (2002)

    Article  ADS  Google Scholar 

  176. E. T. Vishniac, J. Cho: Astrophys. J. 550, 752 (2001)

    Article  ADS  Google Scholar 

  177. J. C. Weingartner, B. T. Draine: Astrophys. J. Supp. 134, 263 (2001)

    Article  ADS  Google Scholar 

  178. H. Yan, A. Lazarian: Phys. Rev. Lett. submitted (2002) astro-ph/0205285

    Google Scholar 

  179. H. Yan, A. Lazarian: in preparation (2002)

    Google Scholar 

  180. V. E. Zakharov: Sov. Phys. JETP, 24, 455 (1967)

    ADS  Google Scholar 

  181. V. E. Zakharov, A. Sagdeev: Sov. Phys. Dokl. textbf15, 439 (1970)

    Google Scholar 

  182. G. P. Zank, W. H. Matthaeus: J. Plasma Phys. 48, 85 (1992)

    Article  ADS  Google Scholar 

  183. G. P. Zank, W. H. Matthaeus: Phys. Fluids A 5(1), 257 (1993)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  184. M. Zielinsky, J. Stutzki: Astron. Astrophys. 347, 630 (1999)

    ADS  Google Scholar 

  185. E. G. Zweibel, C. Heiles: Nature, 385, 131 (1997)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Univ. of Wisconsin, WI53706, Madison, USA

    Jungyeon Cho & Alex Lazarian

  2. Johns Hopkins Univ., MD21218, Baltimore, USA

    Ethan T. Vishniac

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  1. Jungyeon Cho
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  2. Alex Lazarian
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  3. Ethan T. Vishniac
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  1. Laboratoire de Radioastronomie, Ecole Normale Supérieure, 24, Rue Lhomond, 75231, Paris Cedex 05, France

    Edith Falgarone

  2. Observatoire de la Côte d’azur, CNRS, B.P.4229, 06304, Nice Cédex 4, France

    Thierry Passot

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Cho, J., Lazarian, A., Vishniac, E.T. (2003). MHD Turbulence: Scaling Laws and Astrophysical Implications. In: Falgarone, E., Passot, T. (eds) Turbulence and Magnetic Fields in Astrophysics. Lecture Notes in Physics, vol 614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36238-X_3

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  • DOI: https://doi.org/10.1007/3-540-36238-X_3

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