Plasma Physics Reports

, Volume 37, Issue 6, pp 477–497

# Nonlinear dynamics of drift structures in a magnetized dissipative plasma

• G. D. Aburjania
• D. L. Rogava
Plasma Dynamics

## Abstract

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.

## Keywords

Vortex Cyclone Vortex Structure Plasma Physic Report Plasma Medium
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1.
A. B. Mikhailovskii, Theory of Plasma Instabilities, Vol. 2: Instabilities of an Inhomogeneous Plasma (Atomizdat, Moscow, 1971; Consultants Bureau, New York, 1974).Google Scholar
2. 2.
V. S. Mukhovatov, Itogi Nauki Tekh., Ser. Fiz. Plazmy 1, 6 (1980).
3. 3.
W. Horton, in Basic Plasma Physics, Ed. by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983; Energoatomizdat, Moscow, 1984), Vol. 2.Google Scholar
4. 4.
B. B. Kadomtsev, Collective Phenomena in Plasma (Nauka, Moscow, 1976) [in Russian].Google Scholar
5. 5.
S. Migliuolo, J. Geophys. Res. A 89, 11023 (1984).
6. 6.
Handbook of the Solar-Terrestrial Environment, Ed. by Y. Kamie and A. Chian (Springer-Verlag, Berlin, 2007).Google Scholar
7. 7.
B. B. Kadomtsev, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Atomizdat, Moscow, 1964; Consultants Bureau, New York, 1968), Vol. 4.Google Scholar
8. 8.
V. I. Petviashvili and O. A. Pokhotelov, Fiz. Plazmy 12, 1127 (1986) [Sov. J. Plasma Phys. 12, 651 (1986)].Google Scholar
9. 9.
W. Horton and A. Hasegawa, CHAOS 4, 227 (1994).
10. 10.
G. D. Aburjania, Self-Organization of Nonlinear Vortex Structures and Vortex Turbulence in Dispersive Media (KomKniga, Moscow, 2006) [in Russian].Google Scholar
11. 11.
G. D. Aburdjania, Fiz. Plazmy 16, 70 (1990) [Sov. J. Plasma Phys. 16, 40 (1990)].Google Scholar
12. 12.
G. D. Aburjania, Kh. Z. Chargazia, L. M. Zelenyi, and G. Zimbardo, Nonlin. Processes Geophys. 16, 11 (2009).
13. 13.
G. D. Aburjania, A. B. Mikhailovskii, and S. E. Sharapov, Plasma Phys. Controlled Fusion 26, 603 (1984).
14. 14.
G. D. Aburjania, V. N. Ivanov, F. F. Kamenetz, and A. M. Pukhov, Phys. Scr. 35, 677 (1987).
15. 15.
T. D. Kaladze, G. D. Aburjania, O. A. Kharshiladze, et al., J. Geophys. Res. 109, A05302 (2004).
16. 16.
G. D. Aburjania, Kh. Z. Chargazia, and O. A. Kharshiladza, J. Atmos. Sol.-Terr. Phys. 72, 971 (2010).
17. 17.
A. B. Mikhailovskii, V. P. Lakhin, and L. A. Mikhailovskaya, Fiz. Plazmy 11, 836 (1985) [Sov. J. Plasma Phys. 11, 487 (1985)].Google Scholar
18. 18.
G. P. Williams and T. Yamagata, J. Atmos. Sci. 41, 453 (1984).
19. 19.
M. V. Nezlin and G. P. Chernikov, Fiz. Plazmy 21, 975 (1995) [Plasma Phys. Rep. 21, 922 (1995)].Google Scholar
20. 20.
W. Horton, Phys. Rep. 192, 1 (1990).
21. 21.
M. V. Nezlin, CHAOS 4, 187 (1994).
22. 22.
G. D. Aburdjania, Fiz. Plazmy 22, 954 (1996) [Plasma Phys. Rep. 22, 864 (1996)].Google Scholar
23. 23.
P. C. Liewer, Nucl. Fusion 25, 543 (1985).
24. 24.
A. B. Mikhailovskii, V. P. Lakhin, G. D. Aburjania, et al., Plasma Phys. Controlled Fusion 29, 1 (1987).
25. 25.
V. D. Larichev and G. M. Reznik, Dokl. Akad. Nauk SSSR 231, 1077 (1976) [Sov. Phys. Doklady 21, 531 (1976)].Google Scholar
26. 26.
O. G. Onishchenko, O. G. Pokhotelov, V. P. Pavlenko, et al., Phys. Plasmas 8, 59 (2001).
27. 27.
A. G. Litvak and A. M. Sergeev, in High-Frequency Plasma Heating, Ed. by A. G. Litvak (IPF AN SSSR, Gorki, 1983; AIP, New York, 1991).Google Scholar
28. 28.
V. I. Pistunovich and G. E. Shatalov, Itogi Nauki Tekh., Ser. Fiz. 2, 138 (1981).Google Scholar
29. 29.
L. A. Hajkowicz, Planet. Space Sci. 39, 583 (1991).
30. 30.
Atmospheric and Ionospheric Electromagnetic Phenomena Associated with Earthquakes, Ed. by M. Hayakawa (Terra Scientific, Tokyo, 1999).Google Scholar
31. 31.
V. I. Drobzhev, G. F. Moloetov, M. P. Rudina, et al., Ionos. Issled., No. 39, 61 (1986).Google Scholar
32. 32.
L. D. Shaefer, D. R. Rock, J. P. Lewis, et al., Preprint No. 94550 (Lawrence Livermore Laboratory, Livermore, CA, 1999).Google Scholar
33. 33.
V. I. Karpman, Nonlinear Waves in Dispersive Media (Nauka, Moscow, 1973; Pergamon, Oxford, 1975).Google Scholar
34. 34.
G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974; Mir, Moscow, 1977).
35. 35.
V. P. Starr, Physics of Negative Viscosity Phenomena (McGraw-Hill, New York, 1968; Mir, Moscow, 1971).Google Scholar
36. 36.
P. K. Shukla, M. Y. Yu, and N. L. Tsintsadze, Phys. Lett. A 121, 131 (1987).
37. 37.
A. B. Mikhailovskii, Instabilities in a Confined Plasma (Atomizdat, Moscow, 1978; IOP, Bristol, 1998).Google Scholar
38. 38.
T. Taniuti and A. Hasegawa, Phys. Scr. T2B, 529 (1982).
39. 39.
V. I. Petviashvili and A. P. Smirnov, Dokl. Akad. Nauk SSSR 277, 88 (1984).
40. 40.
V. P. Pavlenko and V. B. Taranov, Fiz. Plazmy 10, 1303 (1984) [Sov. J. Plasma Phys. 10, 754 (1984)].Google Scholar
41. 41.
V. D. Larichev and G. M. Reznik, Dokl. Akad. Nauk SSSR 264, 229 (1982).Google Scholar
42. 42.
M. Makino, T. Kamimura, and T. Taniuti, J. Phys. Soc. Jpn. 50, 980 (1981).
43. 43.
J. C. McWilliams, G. R. Flierl, V. D. Larichev, and G. M. Reznik, Dyn. Atm. Ocean 5, 219 (1981).
44. 44.
L. A. Mikhailovskaya, Fiz. Plazmy 12, 879 (1986) [Sov. J. Plasma Phys. 12, 507 (1986)].Google Scholar
45. 45.
L. J. Campbell and S. A. Maslowe, J. Math. Comput. Simul. 55, 365 (2001).
46. 46.
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961; Nauka, Moscow, 1971).

## Authors and Affiliations

• G. D. Aburjania
• 1
• 3
• D. L. Rogava
• 1
• 2