Magnetohydrodynamic equilibria of compressible plasma with mass flow in an axisymmetric tokamak

In the present work the problem of ideal MHD equilibria of compressible plasma with mass flow in axisymmetric tokamak is investigated. The generalized Grad-Shafranov equation is derived for an arbitrary coordinate system. Two equations of equilibrium are derived by means of an expansion with respect to the inverse aspect ratio from this equation. It is shown that the Shafranov shift is essentially effected by the toroidal velocity for a conventional tokamak

Magnetospheric ULF waves driven by external sources

The multi-spacecraft missions (Cluster and THEMIS) observations allowed to collect large data base for Ultra Low Frequency (ULF) waves properties, their localization, and sources. Here we focused mainly on these recent results. Studies of the source and characteristics of ULF waves can help in the understanding of the interaction and energy transport from the solar wind to the magnetosphere. In the presented paper peculiarities of the ULF waves are presented in depends of their generation source: surface magnetopause instabilities, magnetospheric cavity modes, and solar wind sudden impulses (SI). Permanent observations of the ULF waves involve existence of the permanent source and, as the previous studies showed, the contributions to Pc4-Pc5 ULF wave power from the external sources are larger than the contribution from internal magnetosphere sources. The Kelvin-Helmholtz instability (KHI) can generate classical ULF resonant waves with spatially localized amplitude maximum on the magnetosphere flanks. As observations show the constraint satisfaction of KHI development is quite rare. SI in the solar wind dynamic pressure generate ULF waves with different polarization and frequency close to the frequency of the local field line resonance (FLR). Wide range of temporal and amplitude characteristics of the solar wind dynamics can generate magnetosphere cavity modes and magnetosonic perturbations which penetrate through the magnetosphere and can couple with the local FLR modes. The observed dependence of ULF waves properties on their localization corresponds well to these sources and their occurrence

The transformation of long scale Alfven waves in space dusty plasma

A nonlinear mechanism of the generation of kinetic Alfv´en waves (KAW) on dust plasma with small plasma parameter β is proposed. As the generation mechanism, the parametric instability where a pumping wave is the MHD Alfv´en wave is considered. On the basis of the three-fluid MHD, the nonlinear dispersion equation describing the three-wave interaction is deduced and its solution is derived. Obtained instability growth rate is determined by parameters of dust plasma particles. The nonlinear process under consideration can take place both in laboratory and in space plasma with small plasma parameter β. As an application of theoretical results, we consider Saturn’s F-ring

Structures of vortexes near the poles of planets of the solar system

In the vicinity of the poles of the planets of the solar system, ordered crystals of vortices and intermittency are observed. The formation of vortex structures in the vicinity of the poles of the planets of the solar system is investigated. The conditions for the formation of vortexes are considered. A nonlinear equation was found describing the vortex dynamics and structures were studied.В околицях полюсів планет Сонячної системи спостерігаються впорядковані кристали вихрів і перемежування. Досліджено утворення вихрових структур поблизу полюсів планет Сонячної системи. Розглянуто умови утворення вихорів. Знайдено нелінійне рівняння, що описує динаміку вихорів, досліджено їх структури