Abstract
A review is given of the basic results of modern theory of instabilities in a rotating plasma. Both axisymmetric and nonaxisymmetric perturbations are considered. Main attention is given to the magnetorotational instability (MRI), discovered earlier by Velikhov, and the rotational-convective instability (RCI) discussed in a number of papers of astrophysical trend. For qualitative explanation of the results, a local approach is used which, with equilibrium plasma pressure gradient and/or nonsymmetry of perturbations, requires operation with nonlocal azimuthal perturbed magnetic field. The gravity and effects of pressure anisotropy are taken into account. In addition to hydrodynamic, the electrodynamic approach is formulated. The drift effects are considered. Analyzed are the ideal instabilities and those depending on the dissipative effects: viscosity and heat conductivity. The MRI is considered at presence of the charged dust particles. Besides the local approach, the nonlocal approach is formulated for the plasma model with a steplike profile of angular rotation frequency. Alongside with perturbations which frequencies are small compared to the ion cyclotron frequency, the perturbations are analyzed with frequencies larger than the ion cyclotron frequency. The latter corresponds to the Hall regime and subregime of nonmagnetized plasma.
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References
A. A. Vedenov, E. P. Velikhov, and R. Z. Sagdeev, Usp. Fiz. Nauk 73, 701 (1961) [Sov. Phys. Usp. 4, 332 (1961)].
M. N. Rosenbluth and A. Simon, Phys. Fluids 8, 1300 (1965).
A. B. Mikhailovskii, Theory of Plasma Instabilities (Atomizdat, Moscow, 1971; Consultants Bureau, New York, 1974), Vol. 2: Instabilities in an Inhomogeneous Plasma.
E. P. Velikhov, Zh. Éksp. Teor. Fiz. 36, 1398 (1959) [Sov. Phys. JETP 9, 995 (1959)].
S. Chandrasekhar, Proc. Nat. Acad. Sci. U.S.A. 46, 253 (1960).
S. A. Balbus and J. F. Hawley, Astrophys. J. 376, 214 (1991).
N. I. Shakura and R. A. Sunyaev, Astron. Astrophys. 24, 337 (1973).
S. A. Balbus and J. F. Hawley, Rev. Mod. Phys. 70, 1 (1998).
J. F. Hawley and S. A. Balbus, Astrophys. J. 376, 223 (1991).
J. F. Hawley and S. A. Balbus, Astrophys. J. 400, 595 (1992).
S. A. Balbus and J. F. Hawley, Astrophys. J. 400, 610 (1992).
J. F. Hawley and S. A. Balbus, Ann. N. Y. Acad. Sci. 675, 9 (1992).
S. A. Balbus, Astrophys. J. 413, L137 (1993).
S. A. Balbus and J. F. Hawley, Mon. Not. R. Astron. Soc. 266, 769 (1994).
O. M. Blaes and S. A. Balbus, Astrophys. J. 421, 163 (1994).
B. Coppi, Plasma Phys. Controlled Fusion 36, B107 (1994).
J. F. Hawley, C. F. Gammie, and S. A. Balbus, Astrophys. J. 440, 742 (1995).
S. H. Lubow and H. C. Spruit, Astrophys. J. 445, 337 (1995).
R. Matsumoto and T. Tajima, Astrophys. J. 445, 767 (1995).
H. C. Spruit, R. Stehle, and J. C. B. Papaloizou, Mon. Not. R. Astron. Soc 275, 1223 (1995).
W. T. Kim and E. C. Ostriker, Astrophys. J. 540, 372 (2000).
E. Quataert, W. Dorland, and G. W. Hammett, Astrophys. J. 577, 524 (2002).
D. A. Shalybkov, G. Rudiger, and M. Schultz, Astron. Astrophys. 395, 339 (2002).
P. Sharma, G. W. Hammett, and E. Quataert, Astrophys. J. 596, 1121 (2003).
F. Yamoto and M. Sekiya, Icarus 170, 180 (2004).
V. Urpin and G. Rudiger, Astron. Astrophys. 437, 23 (2005).
C. P. Dullemond and C. Dominik, Astron. Astrophys. 434, 971 (2005).
L. Barriere_Forchet, J. F. Gonzales, J. R. Murray, et al., Astron. Astrophys. 443, 185 (2005).
M. Pessah and D. Psaltis, Astrophys. J. 628, 901 (2005).
P. Sharma, G. W. Hammett, E. Quataert, et al., Astrophys. J. 637, 952 (2006).
K. Ferriere, Space Sci. Rev. 122, 247 (2006).
H. Nomura and Y. Nakagawa, Astrophys. J. 640, 1099 (2006).
J. H. Krolik and E. G. Zweibel, Astrophys. J. 644, 651 (2006).
N. M. Ferraro, Astrophys. J. 662, 512 (2007).
C. W. Ormel, M. Spaans, and A. G. G. M. Tielens, Astron. Astrophys. 461, 215 (2007).
E. Quataert, Astrophys. J. 673, 758 (2008).
S. H. Hong and H. E. Wilhelm, J. Appl. Phys. 47, 906 (1976).
H. Ji, G. Goodman, and A. Kageyama, Mon. Not. R. Astron. Soc. 325, 11 (2001).
K. Noguchi, V. I. Pariev, S. A. Colgate, et al., Astrophys. J. 575, 1151 (2002).
G. Rudiger, M. Schultz, and D. Shalybkov, Phys. Rev. E 67, 046312 (2003).
D. R. Sisan, N. Mujica, W. A. Tillotson, et al., Phys. Rev. Lett. 93, 114502 (2004).
E. P. Velikhov, A. A. Ivanov, V. P. Lakhin, and K. S. Serebrennikov, Phys. Lett. A 355, 357 (2006).
E. P. Velikhov, A. A. Ivanov, S. V. Zakharov, et al., Phys. Lett. A 358, 216 (2006).
I. V. Khal’zov, V. I. Ilgisonis, A. I. Smolyakov, and E. P. Velikhov, Phys. Fluids 18, 124107 (2006).
V. P. Lakhin and E. P. Velikhov, Phys. Lett. A 360, 98 (2007).
V. I. Ilgisonis and I. V. Khal’zov, Pis’ma Zh. Éksp. Teor. Fiz. 86, 815 (2007) [JETP Lett. 86, 705 (2007)].
E. P. Velikhov, Pis’ma Zh. Éksp. Teor. Fiz. 82, 789 (2005) [JETP Lett. 82, 690 (2005)].
A. Y. Aydemir, Phys. Plasmas 11, 5065 (2004).
Y. M. Huang and A. B. Hassam, Phys. Plasmas 10, 204 (2003).
S. W. Ng and A. B. Hassam, Phys. Plasmas 12, 064504 (2005).
E. Frieman and N. Rotenberg, Rev. Mod. Phys. 32, 898 (1960).
E. Hameiri, J. Math. Phys. 22, 2080 (1981).
A. Bondeson, R. Iacono, and A. Bhattacharjee, Phys. Fluids 30, 2167 (1987).
R. Keppens, F. Casse, and J. P. Goedbloed, Astrophys. J. 569, L121 (2002).
H. Ji, P. Kronberg, S. C. Prager, et al., Phys. Plasmas 15, 058 302 (2008).
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Zh. Éksp. Teor. Fiz. 133, 183 (2008) [JETP 106, 154 (2008)].
A. B. Mikhailovskii, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Gosatomizdat, Moscow, 1963; Consultants Bureau, New York, 1967), Vol. 3.
B. B. Kadomtsev, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Atomizdat, Moscow, 1964; Consultants Bureau, New York, 1968), Vol. 4.
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Fiz. Plazmy 34, 908 (2008) [Plasma Phys. Rep. 34, 837 (2008)].
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Phys. Lett. A 372, 3274 (2008).
A. B. Mikhailovskii, J. G. Lominadze, R. M. O. Galvao, et al., Phys. Plasmas 15, 052 103 (2008).
A. B. Mikhailovskii, Instabilities in a Confined Plasma (IOP, Bristol, 1998).
R. Kulsrud, in Handbook of Plasma Physics, Ed. by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1984; Énergoatomizdat, Moscow, 1983, 1984), Vol. 1.
A. B. Mikhailovskii, J. G. Lominadze, A. I. Smolyakov, et al., Phys. Plasmas 15, 062 904 (2008).
G. I. Budker, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Ed. by M. A. Leontovich (Izd. Akad. Nauk SSSR, Moscow, 1958; Pergamon, New York, 1959), Vol. 1.
A. Schluter, Z. Naturforsch. A 12, 822 (1957).
V. S. Tsypin, Zh. Tekh. Fiz. 42, 727 (1972) [Sov. Phys. Tech. Phys. 17, 573 (1972)].
A. B. Mikhailovskii, Electromagnetic Instabilities in an Inhomogeneous Plasma (Énergoatomizdat, Moscow, 1991; IOP, Bristol, 1992).
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Phys. Lett. A 372, 3846 (2008).
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Zh. Éksp. Teor. Fiz. 134, 1238 (2008) [JETP 107, 1061 (2008)].
A. A. Vedenov and R. Z. Sagdeev, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Ed. by M. A. Leontovich (Izd. Akad. Nauk SSSR, Moscow, 1958; Pergamon, New York, 1959), Vol. 3.
L. A. Rudakov and R. Z. Sagdeev, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Ed. by M. A. Leontovich (Izd. Akad. Nauk SSSR, Moscow, 1958; Pergamon, New York, 1959), Vol. 3.
S. Chandrasekhar, A. N. Kaufman, and K. M. Watson, Proc. Roy. Soc. London A 245, 435 (1958).
E. N. Parker, Phys. Rev. 109, 1874 (1958).
A. B. Kitsenko and K. N. Stepanov, Zh. Éksp. Teor. Fiz. 38, 1840 (1960) [Sov. Phys. JETP 11, 1323 (1960)].
A. B. Mikhailovskii, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Atomizdat, Moscow, 1972; Consultants Bureau, New York, 1975), Vol. 6.
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Zh. Éksp. Teor. Fiz. 133, 429 (2008) [JETP 106, 371 (2008)].
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Plasma Phys. Controlled Fusion 50, 085 012 (2008).
J. G. Lominadze, A. B. Mikhailovskii, A. P. Churikov, et al., Bull. Georg. Nat. Acad. Sci. 2(4) (2008).
J. G. Lominadze, A. B. Mikhailovskii, A. I. Smolyakov, et al., Bull. Georg. Nat. Acad. Sci. 3 (2009) (in press).
A. B. Mikhailovskii, A. I. Smolyakov, J. G. Lominadze, et al., Fiz. Plazmy 35 (2009) (in press).
J. G. Lominadze, E. A. Pashitskii, A. B. Mikhailovskii, et al., Bull. Georg. Nat. Acad. Sci. 2(3), 48 (2008).
S. I. Braginskii, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Gosatomizdat, Moscow, 1963; Consultants Bureau, New York, 1965), Vol. 1.
S. A. Balbus, Astrophys. J. 562, 909 (2001).
A. B. Mikhailovskii, S. V. Vladimirov, J. G. Lominadze, et al., Phys. Plasmas 15, 014 504 (2008).
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Plasma Phys. Controlled Fusion 50, 085015 (2008).
N. F. Cramer and S. V. Vladimirov, Phys. Plasmas 3, 4740 (1996).
N. F. Cramer, L. K. Yeung, and S. V. Vladimirov, Phys. Plasmas 5, 3126 (1998).
M. Kruskal and M. Schwartzschild, Proc. Roy. Soc. A 233, 348 (1954).
A. B. Mikhailovskii, Theory of Plasma Instabilities (Atomizdat, Moscow, 1971; Consultants Bureau, New York, 1974), Vol. 1: Instabilities in a Homogeneous Plasma.
A. B. Mikhailovskii, J. G. Lominadze, R. M. O. Galvao, et al., Phys. Plasmas 15, 052109 (2008).
A. B. Mikhailovskii, V. D. Pustovitov, R. M. O. Galvao, C. H. S. Amador, et al., Brazil. J. Phys. 39, 73 (2009).
M. Wardle, Mon. Not. Roy. Astron. Soc. 307, 849 (1999).
S. A. Balbus and C. Terquem, Astrophys. J. 552, 235 (2001).
A. I. Akhiezer, I. A. Akhiezer, R. V. Polovin, et al., Plasma Electrodynamics (Nauka, Moscow, 1974; Pergamon, Oxford, 1975).
V. D. Shafranov, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Gosatomizdat, Moscow, 1963; Consultants Bureau, New York, 1967), Vol. 3.
N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (Academic, New York, 1973; Mir, Moscow, 1975).
A. B. Mikhailovskii, J. G. Lominadze, R. M. O. Galvao, et al., Phys. Plasmas 14, 112108 (2007).
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Phys. Lett. A 372, 49 (2007).
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Fiz. Plazmy 34, 736 (2008) [Plasma Phys. Rep. 34, 768 (2008)].
E. S. Weibel, Phys. Rev. Lett. 2, 83 (1959).
A. B. Mikhailovskii, J. G. Lominadze, R. M. O. Galvao, et al., Fiz. Plazmy 34, 589 (2008) [Plasma Phys. Rep. 34, 538 (2008)].
A. B. Mikhailovskii, J. G. Lominadze, A. P. Churikov, et al., Phys. Plasmas 14, 112104 (2007).
A. B. Mikhailovskii, A. M. Fridman, A. P. Churikov, et al., Dokl. Akad. Nauk 424, 181 (2009) [Phys. Dokl. 54, 6 (2009)].
A. B. Mikhailovskii, A. M. Fridman, A. P. Churikov, et al., Plasma Phys. Controlled Fusion 51, 045 003 (2009).
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Original Russian Text © A.B. Mikhailovskii, J.G. Lominadze, A.P. Churikov, V.D. Pustovitov, 2009, published in Fizika Plazmy, 2009, Vol. 35, No. 4, pp. 307–350.
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Mikhailovskii, A.B., Lominadze, J.G., Churikov, A.P. et al. Progress in theory of instabilities in a rotating plasma. Plasma Phys. Rep. 35, 273–314 (2009). https://doi.org/10.1134/S1063780X09040035
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DOI: https://doi.org/10.1134/S1063780X09040035