Abstract
The electrodynamics and dispersion properties of a magnetized dusty plasma containing elongated and rotating charged dust grains are examined. Starting from an appropriate Lagrangian for dust grains, a kinetic equation for the dust grain and the corresponding equations of motion are derived. Expressions for the dust charge and dust current densities are obtained with the finite size (the dipole moment) of elongated and rotating dust grains taken into account. These charge and current densities are combined with the Maxwell-Vlasov system of equations to derive dispersion relations for the electromagnetic and electrostatic waves in a dusty magnetoplasma. The dispersion relations are analyzed to demonstrate that the dust grain rotation introduces new classes of instabilities involving various low-frequency waves in a dusty magnetoplasma. Examples of various unstable low-frequency waves include the electron whistler, the dust whistler, dust cyclotron waves, AlfvÉn waves, electromagnetic ion-cyclotron waves, as well as lower-hybrid, electrostatic ion cyclotron, modified dust ion-acoustic waves, etc. Also found is a new type of unstable waves whose frequency is close to the dust grain rotation frequency. The present results should be useful in understanding the properties of low-frequency waves in cosmic and laboratory plasmas that are embedded in an external magnetic field and contain elongated and rotating charged dust grains.
Similar content being viewed by others
References
N. N. Rao, P. K. Shukla, and M. Y. Yu, Planet. Space Sci. 38, 345 (1990).
P. K. Shukla, Phys. Scr. 45, 504 (1992).
P. K. Shukla and V. P. Silin, Phys. Scr. 45, 508 (1992).
A. Barkan, R. L. Merlino, and N. D’Angelo, Phys. Plasmas 2, 3563 (1995); C. Thomson, A. Barkan, N. D’Angelo, and R. L. Merlino, Phys. Plasmas 4, 2331 (1997); R. L. Merlino, A. Barkan, C. Thompson, and N. D’Angelo, Phys. Plasmas 5, 1607 (1998).
H. R. Prabhakara and V. L. Tanna, Phys. Plasmas 3, 3176 (1996).
E. Thomas, Jr. and M. Watson, Phys. Plasmas 6, 4111 (1999); V. E. Fortov, A. G. Kharpak, S. A. Kharpak, et al., Phys. Plasmas 7, 1374 (2000); V. I. Molotkov, A. P. Nefedov, V. M. Torchinskii, et al., Zh. Éksp. Teor. Fiz. 116, 902 (1999) [JETP 89, 477 (1999)].
A. Barkan, N. D’Angelo, and R. L. Merlino, Planet. Space Sci. 44, 239 (1996).
Y. Nakamura, H. Bailung, and P. K. Shukla, Phys. Rev. Lett. 83, 1602 (1999).
P. K. Shukla, in Frontiers in Dusty Plasmas, Ed. by Y. Nakamura, T. Yokota, and P. K. Shukla (Elsevier, Amsterdam, 2000), p. 3.
F. Verheest, Waves in Dusty Plasmas (Kluwer, Dordrecht, 2000).
M. Harwit, Astrophysical Concepts (Springer-Verlag, New York, 1988), p. 405.
L. Spitzer, Jr., Physical Processes in Interstellar Medium (Wiley, New York, 1977; Mir, Moscow, 1981), p. 182.
U. Mohideen, H. U. Rahman, M. A. Smith, et al., Phys. Rev. Lett. 81, 349 (1998); H. U. Rahman, U. Mohideen, M. A. Smith, et al., Phys. Scr. T 89, 186 (2000).
V. I. Molotkov, A. P. Nefedov, M. Yu. Putsyl’ink, et al., Pis’ma Zh. Éksp. Teor. Fiz. 71, 152 (2000) [JETP Lett. 71, 102 (2000)].
D. Tskhakaya and P. K. Shukla, Phys. Lett. A 279, 243 (2001).
N. V. Voshchinnikov and D. A. Semenov, Pis’ma Astron. Zh. 26, 789 (2000) [Astron. Lett. 26, 679 (2000)].
J. Mahmoodi, P. K. Shukla, N. L. Tsintsadze, and D. D. Tskhakaya, Phys. Rev. Lett. 84, 2626 (2000). We have noted an error in Eq. (27), which must contain an addition term (k⊥/k 2)Ω 2r (ω+Ω0)2, respectively, on its right-hand side. However, this term does not affect our final finding [viz. our Eq. (31) remains intact], as we have dealt with the resonance case ω≅Ω 0.
L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Nauka, Moscow, 1973; Pergamon, Oxford, 1975).
N. N. Bogolyubov, Dynamic Problems of Statistical Physics (Gostekhizdat, Moscow, 1946).
Yu. L. Klimontovich, Kinetic Theory of Nonideal Gases and Nonideal Plasmas (Nauka, Moscow, 1975; Pergamon, Oxford, 1982).
L. D. Landau and E. M. Lifshitz, Statistical Physics (Nauka, Moscow, 1976; Pergamon, Oxford, 1989).
A. F. Alexandrov, L. S. Bogdankevich, and A.A. Rukhadze, Principles of Plasma Electrodynamics (Vysshaya Shkola, Moscow, 1988; Springer-Verlag, Berlin, 1984).
A. B. Mikhailovskii, Theory of Plasma Instabilities: Instabilities of a Homogenous Plasma (Atomizdat, Moscow, 1971; Consultants Bureau, NewYork, 1974), Vol. 1.
M. Rosenberg and D. A. Mendis, IEEE Trans. Plasma Sci. 20, 929 (1992); D. A. Mendis and M. Rosenberg, Annu. Rev. Astron. Astrophys. 32, 410 (1994).
P. K. Shukla and H. U. Rahman, Phys. Plasmas 3, 430 (1996).
P. K. Shukla, Phys. Lett. A 252, 340 (1999).
P. K. Shukla, Phys. Rev. E 61, 7249 (2000).
O. Havnes, J. Troim, T. Blix, et al., J. Geophys. Res. 101, 10839 (1996).
M. Horányi, B. Walch, S. Robertson, et al., J. Geophys. Res. 103, 8575 (1998).
J. E. Howard, H. R. Dullin, and M. Horányi, Phys. Rev. Lett. 84, 3244 (2000).
V. W. Chow, D. A. Mendis, and M. Rosenberg, IEEE Trans. Plasma Sci. 22, 179 (1994); M. Rosenberg and D. A. Mendis, IEEE Trans. Plasma Sci. 23, 177 (1995); M. Rosenberg, D. A. Mendis, and D. P. Sheehan, IEEE Trans. Plasma Sci. 27, 239 (1999).
V. E. Fortov, A. P. Nefedov, O. F. Petrov, et al., Phys. Lett. A 219, 89 (1996).
V. E. Fortov, A. P. Nefedov, and O. S. Vaulina, Zh. Éksp. Teor. Fiz. 114, 2004 (1998) [JETP 87, 1087 (1998)]; V. Fortov, V. I. Molotkov, A. P. Nefedov, and O. F. Petrov, Phys. Plasmas 6, 1759 (1999).
A. A. Samaryan, O. S. Vaulina, A. P. Nefedov, et al., Zh. Éksp. Teor. Fiz. 118, 119 (2000) [JETP 91, 106 (2000)]; A. A. Sickafoose, J. W. Colwell, M. Horányi, and S. Robertson, Phys. Rev. Lett. 84, 6034 (2000).
H. Fujiyama, H. Kawasaki, S. C. Yang, and Y. Matsuda, Jpn. J. Appl. Phys. 33, 4216 (1994); S. Nunomura, N. Ohno, and S. Takamura, Jpn. J. Appl. Phys. 36, 877 (1997).
G. Uchida, R. Ozaki, S. Iizuka, and N. Sato, in Proceedings of the International Congress on Plasma Physics, European Physical Society, Prague, 1998, Ed. by P. Pavlo, p. 2557; N. Sato, G. Uchida, R. Ozaki, S. Iizuka, and T. Kamimura, in Frontiers in Dusty Plasmas, Ed. by Y. Nakamura, T. Yokota, and P. K. Shukla (Elsevier, Amsterdam, 2000), p. 329.
D. W. Law, H. Steel, B. M. Annaratone, and J. E. Allen, Phys. Rev. Lett. 80, 4189 (1998).
U. Konopka, D. Samsonov, A. V. Ivlev, et al., Phys. Rev. E 61, 1890 (2000).
Author information
Authors and Affiliations
Additional information
From Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 120, No. 2, 2001, pp. 340–352.
Original English Text Copyright © 2001 by Tskhakaya, Shukla, Tsintsadze.
This article was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Tskhakaya, D.D., Shukla, P.K. & Tsintsadze, N.L. Electrodynamics and dispersion properties of a magnetoplasma containing elongated and rotating dust grains. J. Exp. Theor. Phys. 93, 301–312 (2001). https://doi.org/10.1134/1.1402731
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1402731