Nonlinear dynamics of drift structures in a magnetized dissipative plasma
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MA DYNAMICS
Nonlinear Dynamics of Drift Structures in a Magnetized Dissipative Plasma G. D. Aburjaniaa, c, D. L. Rogavaa, b, and O. A. Kharshiladzeb, c a
I. Vekua Institute of Applied Mathematics, Tbilisi State University, University str. 2, Tbilisi, 0143 Georgia b Ivane Javakhishvili Tbilisi State University, Chavchavadze ave. 1, Tbilisi, 0128 Georgia c Nodia Institute of Geophysics, Aleksidze str. 1, Tbilisi, 0193 Georgia Received August 11, 2010; in final form, October 7, 2010
Abstract—A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous mag netized dissipative plasma. A nonlinear transport equation for longwavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the mag netic 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 secondorder 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 smallscale vortices and dissipation hastens this process. It is found that the relax ation 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 struc tures. It is shown that, as the instability develops, the init
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