Generation of magnetic hydrodynamic waves in a simplified model of Earth’s magnetosphere tail

The main attention is paid to the construction of a mathematical model and the description of methods for studying magnetic hydrodynamic (MHD) waves propagating in the “tail” of the Earth magnetic field. These waves, in contrast to MHD waves propagating near the closed part of the Earth magnetic field, have been little studied. The complexity of the description of these waves is associated with the configuration of the magnetic field inside the plasma layer of the magnetosphere “tail”. We consider the system “flat plasma layer — an external moving plasma”, which allows the obtaining of analytical results in a complete form. For the model of a “flat” plasma layer, equations of small oscillations are obtained both inside the layer and outside it. Using the theory of singularities of differentiable mappings (catastrophe theory), the question of stability of their existence is considered. The dispersion equation for perturbations of the magnetic field is found, which takes into account the compressibility of the plasma medium. Using this equation, the problem of the propagation of MHD waves inside and outside the plasma layer in the solar wind is analyzed. It was ascertained that in the plasma layer (analog of the magnetosphere) stable waves can be present, which are not connected with the surrounding solar wind. In the flow (the solar wind) surrounding the plasma layer, excitations that are associated with disturbances inside the geomagnetic tail do not occur. This can be explained by the sparseness and huge speed of the solar wind. Thus, the magnetic storms that arise due to the considered perturbations in the Earth atmosphere owe their origin to coronary ejections of the mass of the Sun. © 2019 by Begell House Inc.