Instability of Kelvin-Helmholtz and magnetohydrodynamic modes on the boundary of geomagnetic tail

1Cheremnykh, OK, 1Cheremnykh, SO, 2Kozak, LV, 3Kronberg, EA
1Space Research Institute of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Kyiv, Ukraine
2Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
3Max Planck Institute, Göttingen, Germany
Space Sci. & Technol. 2019, 25 ;(2):43-59
Publication Language: Russian
The paper focuses on the description of mathematical and theoretical methods for studying the longitudinal and oblique MHD modes generated by the solar wind, which are  localized near the boundary of the geomagnetic tail. On the contrary to the MHD modes propagating in the inner part of the Earth’s magnetic field, these modes have hardly been studied either theoretically or experimentally. It is shown that the problem of MHD oscillations on the boundary between two relatively moving plasma media is reduced to finding and studying the equation of small variations, as well as finding its boundary conditions. We present the procedure for obtaining the dispersion equation for MHD modes localized on the boundary between moving and stationary plasma media.
           The analysis revealed that one of the eight possible MHD modes could be unstable due to the development of the Kelvin-Helmholtz instability for both weak and strong magnetic field. It is shown that oblique perturbations propagating at an angle to the velocity vector of the medium play a dominant role in the development of this instability. Moreover, the generation of a large number of stable MHD modes at the plasma boundary can lead to the realization of a turbulent plasma state. The results of the work can be applied in the description of wave processes at the boundary of the geomagnetic tail and in the explanation of the generation of ULF disturbances on the night side of the Earth’s magnetosphere.
Keywords: Kelvin-Helmholtz instability, longitudinal and oblique MHD modes, the tail of the Earth’s magnetosphere, waves in a compressible magnetized medium
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