On the stability of Saturn's rings: A quasi-linear kinetic theory

Monthly Notices of the Royal Astronomical Society

Volumn 342, Issue 4, 2003, Pages 1102-1116

  Griv, Evgeny ^a   Gedalin, Michael ^a   Yuan, Chi ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b INSTITUTE OF ASTRONOMY AND ASTROPHYSICS   (Taiwan)

Author keywords

InstabilitiesWavesPlanets: rings; Planets and satellites: individual: Saturn

Indexed keywords

BOLTZMANN EQUATION; DRAG; INTEGRAL EQUATIONS; KINETIC THEORY; ORBITS; PLANETS; POISSON EQUATION; SATELLITES;

BOLTZMANN KINETIC EQUATIONS; COOLING MECHANISM; GRAVITY PERTURBATIONS; INSTABILITIESWAVESPLANET: RING; LINEAR KINETICS; OPTICAL DEPTH; PLANETS AND SATELLITES: INDIVIDUAL: SATURN; QUASI-LINEAR; SATURN RINGS; VELOCITY OF PARTICLES;

OPTICAL PROPERTIES;

EID: 0142137158     PISSN: 00358711     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-8711.2003.06608.x     Document Type: Article

References (144)

1. Alexandrov A.F., Bogdankevich L.S., Rukhadze A.A., 1984, Principles of Plasma Electrodynamics. Springer-Verlag, Berlin
2. Araki S., 1988, Icarus, 76, 182
3. Araki S., 1991a, Am. Sci., 79, 44
4. Araki S., 1991b, Icarus, 90, 139
5. Araki S., Tremaine S., 1986, Icarus, 65, 83
6. Bertin G., 1980, Phys. Rep., 61, 1
7. Bertin G., Lin C.C., 1996, Spiral Structure in Galaxies: a Density Wave Theory. MIT, Cambridge MA
8. Bertin G., Mark J.W.-K., 1978, A&A, 64, 389
9. Bhadra D.K., 1971, Phys. Fluids, 14, 977
10. Bhatnagar P.L., Gross E.P., Krook M., 1954, Phys. Rev., 94, 511
11. Binney J., Tremaine S., 1987, Galactic Dynamics. Princeton Univ. Press, Princeton
12. Borderies N., Goldreich P., Tremaine S., 1985, Icarus, 63, 406
13. Bridges F.G., Hatzes A., Lin D.N.C., 1984, Nat, 309, 333
14. Brophy T.G., Esposito L.W., 1989, Icarus, 78, 181
15. Camichel H., 1958, Ann. Astrophys, 21, 231
16. Colombo G., Goldreich P., Harris A., 1976, Nat, 264, 344
17. Cook A.F., Franklin F.A., 1964, AJ, 69, 173
18. Cuzzi J.N., Lissauer J.J., Esposito L.W., Holberg J.B., Marouf E.A., Tyler G.L., Boishchot A., 1984, in Greenberg R., Brahic A., eds, Planetary Rings. Univ. of Arizona, Tucson AZ, p. 73
19. Daisaka H., Ida S., 1999, Earth Planets Space, 51, 1195
20. Dones L., Cuzzi J.N., Showalter M.R., 1993, Icarus, 105, 184
21. Drummond J.E., 1958, Phys. Rev., 110, 293
22. Drummond J.E., Pines D., 1962, Nuclear Fus. Suppl., 3, 1049
23. Durisen R.H., 1995, Icarus, 115, 66
24. Esposito L.W., 1986, Icarus, 67, 345
25. Esposito L.W., 1993, ARE&PS, 21, 487
26. Esposito L.W., 2002, Rep. Prog. Phys, 65, 1741
27. Esposito L.W., Colwell J.E., McClintock W.E., 1998, Planet. Space Sci., 46, 1221
28. Ferrari C., Brahic A., 1997, Planet. Space Sci., 45, 1051
29. Franklin F.A., Colombo G., 1978, Icarus, 33, 279
30. Franklin F.A., Cook A. F., Barrey R.T.F., Roff C.A., Hunt G.E., de Rueda H. B., 1987, Icarus, 69, 280
31. French R.G., Nicholson P.D., 2000, Icarus, 145, 502
32. Galeev A.A., Sagdeev R.Z., 1983, in Rosenbluth M.N., Sagdeev R.Z., eds, Basic Plasma Physics, Vol. 1. North-Holland, Amsterdam, p. 679
33. Gammie C., 2001, ApJ, 553, 174
34. Genkin I.L., Safronov V.S., 1975, SvA, 19, 189
35. Goertz C.K., Morfill G., 1988, Icarus, 74, 325
36. Goldreich P., Lynden-Bell D., 1965, MNRAS, 130, 125
37. Goldreich P., Tremaine S., 1978, Icarus, 34, 227
38. Goldreich P., Tremaine S., 1982, ARA&A, 20, 249
39. Griv E., 1996, Planet. Space Sci., 44, 579
40. Griv E., 1998, Planet. Space Sci., 46, 615
41. Griv E., Chiueh T., 1997, A&A, 311, 1033
42. Griv E., Chiueh T., 1998, ApJ, 503, 186
43. Griv E., Peter W., 1996, ApJ, 469, 84
44. Griv E., Chiueh T., Peter W., 1994, Physica A, 205, 299
45. Griv E., Gedalin M., Yuan C., 1997, A&A, 328, 531
46. Griv E., Gedalin M., Eichler D., Yuan C., 2000a, Planet. Space Sci., 48, 679
47. Griv E., Gedalin M., Eichler D., Yuan C., 2000b, Phys. Rev. Lett., 84, 4280
48. Griv E., Gedalin M., Eichler D., 2001a, ApJ, 555, L29
49. Griv E., Gedalin M., Liverts E., Eichler D., Kimhi Y., 2001b, A&A Trans., 20, 151
50. Griv E., Gedalin M., Yuan C., 2002, A&A, 383, 338
51. Griv E., Gedalin M., Yuan C., 2003, A&A, 400, 375
52. Griv E., Liverts E., Gedalin M., Yuan C., 2003b, in Makino J., Hut P., eds, Proc. IAU Symp. 208, Astrophysical Supercomputing Using Particle Simulations. Astron. Soc. Pac., San Francisco, in press
53. Griv E., Rosenstein B., Gedalin M., Eichler D., 1999, A&A, 347, 821
54. Grivnev E.M., 1988, SvA, 32, 139
55. Hohl F., 1978, AJ, 83, 768
56. Holberg J.B., Forrester W.T., Lissauer J.J., 1982, Nat, 297, 115
57. Horn L.J., Cuzzi J.N., 1996, Icarus, 119, 285
58. Jeffreys H., 1947, MNRAS, 107, 263
59. Julian W.H., Toomre A., 1966, ApJ, 146, 810
60. Krall N.A., Rosenbluth M.N., 1963, Phys. Fluids, 6, 254
61. Krall N.A., Trivelpiece A.W., 1986, Principles of Plasma Physics. San Francisco Press, San Francisco
62. Kulsrud R.M., 1972, in Lecar M., ed., IAU Colloq. 10, Gravitational N-Body Problem. Reidel, Dordrecht, p. 337
63. Lane A.L. et al., 1982, Sci, 215, 537
64. Lau Y.Y., Bertin G., 1978, ApJ, 226, 508
65. Lewis M.C., Stewart G.R., 2000, AJ, 120, 3295
66. Lifshitz E.M., Pitaevskii L.P., 1981, Physical Kinetics. Pergamon, Oxford
67. Lin C.C., Bertin G., 1984, Adv. Appl. Mech., 24, 155
68. Lin D.C.N., Bodenheimer P., 1981, ApJ, 248, L83
69. Lin C.C., Lau Y.Y., 1979, SIAM Stud. Appl. Math., 60, 97
70. Lin C.C., Shu F.H., 1966, Proc. Nat. Acad. Sci. USA, 55, 229
71. Lin C.C., Yuan C., Shu F.H., 1969, ApJ, 155, 721
72. Lissauer J.J., 1984, Icarus, 57, 63
73. Lissauer J.J., 1989, in Sellwood J.A., ed., Dynamics of Astrophysical Discs, Vol. 1. Cambridge Univ. Press, Cambridge
74. Lissauer J.J., Cuzzi J.N., 1982, AJ, 87, 1051
75. Lissauer J.J., Shu F.H., Cuzzi J.N., 1981, Nat, 292, 707
76. Liverts E., Griv E., Eichler D., Gedalin M., 2000, Ap&SS, 274, 315
77. Longaretti P.-Y, Rappaport N., 1995, Icarus, 116, 376
78. Lovelace R.V.E., Jore K.P., Haynes M.P., 1997, ApJ, 475, 83
79. Lukkari J., 1981, Nat, 292, 433
80. Lynden-Bell D., Kalnajs A.J., 1972, MNRAS, 157, 1
81. Lynden-Bell D., Pringle J.E., 1974, MNRAS, 168, 603
82. Mark J.W.-K., 1971, Proc. Nat. Acad. Sci. USA, 68, 2095
83. Marochnik L.S., 1966, SvA, 10, 442
84. Maxwell J.C., 1859, in Niven W.D., ed., Science Papers, Vol. 1 (1960). Dover, New York, p. 288
85. Mikhailovskii A.B., 1974, Theory of Plasma Instabilities. Plenum, New York
86. Mishurov Yu. N., Peftiev V.M., Suchkov A.A., 1976, SvA, 20, 152
87. Morozov A.G., 1978, SvA Lett., 4, 115
88. Morozov A.G., 1980, SvA, 24, 391
89. Morozov A.G., 1981a, SvA Lett., 7, 109
90. Morozov A.G., 1981b, SvA, 25, 421
91. Morozov A.G., Torgashin Yu. M., Fridman A.M., 1985, SvA Lett., 11, 94
92. Nakamura T., Takahara F., Ikeuchi S., 1975, Prog. Theor. Phys., 53, 1348
93. Nicholson P.D., French R. G., Tollestrup E., Cuzzi J. N., Harrington J., Matthews K., Perkovic O., Stover R. J., 2000, Icarus, 145, 474
94. Ohtsuki K., Emori H., 2000, AJ, 119, 403
95. Osterbart R., Willerding E., 1995, Planet. Space Sci., 43, 289
96. Papaloizou J.C.B., Lin D.N.C., 1988, ApJ, 331, 838
97. Pitaevskii L.P., 1963, Sov. Phys. - JETP, 17, 658
98. Richardson D.C., 1994, MNRAS, 269, 493
99. Rohlfs K., 1977, Lectures on Density Wave Theory. Springer-Verlag, Berlin, section 5
100. Rosen P.A., Lissauer J.J., 1988, Sci, 241, 690
101. Rosenbluth M.N., Rostoker N., 1959, Phys. Fluids, 2, 23
102. Rukhadze A.A., Silin V.P., 1969, Sov. Phys. - Usp., 11, 659
103. Safronov V.S., 1960, Ann. Astrophys., 23, 979
104. Safronov V.S., 1980, in Lal D., ed., Early Solar System Processes and the Present Solar System. North-Holland, Amsterdam, p. 73
105. Sagdeev R.Z., Galeev A.A., 1969, in O'Neil T.M., Book D.L., eds, Nonlinear Plasma Theory. Benjamin, New York
106. Salo H., 1991, Icarus, 90, 254
107. Salo H., 1992, Nat, 359, 619
108. Salo H., 1995, Icarus, 117, 287
109. Salo H., Schmidt J., Spahn F., 2001, Icarus, 153, 295
110. Sandel B.R. et al., 1982, Sci, 215, 548
111. Schmidt J., Salo H., Spahn F., Petzschmann O., 2001, Icarus, 153, 316
112. Schmit U., Tscharnuter W.M., 1995, Icarus, 115, 304
113. Schmit U., Tscharnuter W.M., 1999, Icarus, 138, 173
114. Sellwood J.A., Carlberg R.G., 1984, ApJ, 282, 61
115. Shapiro V.D., Shevchenko V.I., 1964, Sov. Phys. - JETP, 18, 1109
116. Shapiro V.D., Shevchenko V.I., 1965, in Sinelnikov K.D., ed., Plasma Physics and Controlled Thermonuclear Fusion. Naukova Dumka, Kiev, p. 149
117. Showalter M.R., Nicholson P.D., 1990, Icarus, 87, 285
118. Shu F.H., 1970, ApJ, 160, 99
119. Shu F.H., 1984, in Greenberg R., Brahic A., eds, Planetary Rings. Univ. of Arizona, Tucson, p. 513
120. Shu F.H., Cuzzi J.N., Lissauer J.J., 1983, Icarus, 53, 185
121. Shu F.H., Dones L., Lissauer J.J., Yuan C., Cuzzi J.N., 1985, ApJ, 299, 542
122. Shu F.H., Stewart G.R., 1985, Icarus, 62, 360
123. Shukhman I.G., 1984, SvA, 28, 574
124. Smith B.A. et al., 1982, Sci, 215, 504
125. Spahn F., Sremcevic M., 2000, A&A, 358, 368
126. Spahn F., School H., Hertzsch J.-M., 1994, Icarus, 111, 514
127. Spitzer L., Schwarzschild M., 1953, ApJ, 118, 106
128. Sterzik M.F., Herold H., Ruder H., Willerding E., 1995, Planet. Space Sci., 43, 259
129. Stewart G., Lin D.N.C., Bodenheimer P., 1984, in Greenberg R., Brahic A., eds, Planetary Rings. Univ. of Arizona Press, Tucson, p. 447
130. Swanson D.G., 1989, Plasma Waves. Academic, Boston
131. Thompson W.T., Lumme K., Irvine W.M., Baum W.A., Esposito L.W., 1981, Icarus, 46, 187
132. Toomre A., 1964, ApJ, 139, 1217
133. Toomre A., 1981, in Fall S.M., Lynden-Bell D., eds, Structure and Evolution of Normal Galaxies. Cambridge Univ. Press, Cambridge, p. 111
134. Toomre A., 1990, in Wielen R., ed., Dynamics and Interactions of Galaxies. Springer-Verlag, Heidelberg, p. 292
135. Tremaine S., 1989, in Sellwood J.A., ed., Dynamics of Astrophysical Discs. Cambridge Univ. Press, Cambridge, p. 231
136. Tremaine S., 2003, AJ, 125, 894
137. Vandervoort P.O., 1970, ApJ, 161, 87
138. Vedenov A.A., Velikhov E.P., Sagdeev R.Z., 1962, Nucl. Fus. Suppl., 2, 465
139. Ward W.R., 1976, in Avrett E.H., ed., Frontiers of Astrophysics. Harvard Univ. Press, Cambridge, p. 3
140. Ward W.R., 1981, J. Geophys. Res. Lett., 8, 641
141. Willerding E., 1992, Earth Moon Planets, 56, 173
142. Wisdom J., Tremaine S., 1988, AJ, 95, 925
143. Yuan C., 1969, ApJ, 158, 871
144. Zebker H.A., Marouf E.A., Tyler G.L., 1985, Icarus, 64, 531