MHD-instability of the magnetotail: Global modes

A hydromagnetic stability problem is solved for the magnetospheric tail inside the solar wind plasma flow. A model magnetotail is used in the form of a plasma cylinder which is inhomogeneous over the radius. For a qualitative analysis of the problem the solution is obtained analytically, in the WKB approximation. The plasma cylinder boundary is assumed to have the form of a tangential discontinuity. A numeric solution was found for a more realistic model, with the boundary in the form of a smooth transition layer. This model cannot simulate such a feature of the actual magnetotail as its being divided into two lobes with opposite magnetic fields. It is capable, however, of simulating the finiteness of the magnetotail cross-section and the inhomogeneous plasma distribution over the radius. It is shown, analytically, that a local instability develops in the boundary when the velocity of the plasma flowing round the magnetosphere exceeds the Alfvén speed at the magnetotail boundary. This conclusion is supported by a numerical solution of the problem for a model with its boundary in the form of a smooth transition layer. The instability increment, however, is much smaller in the latter case. Apart from a local instability of the boundary, unstable global modes are discovered whose amplitude practically does not vary over the magnetotail cross-section. These modes remain unstable for any, however, slow velocities of the plasma flowing round the magnetosphere. When the plasma flow velocity reaches a critical magnitude the global modes of the MHD oscillations become stable. Unstable global modes may be a source of ultra-low-frequency (∼1mHz) oscillations observed in the Earth's nightside magnetosphere.

Research highlights
► A hydromagnetic stability problem is theoretically solved for the magnetospheric tail inside the solar wind plasma flow.
► It is shown that a local instability develops in the boundary when the velocity of the plasma flowing round the magnetosphere exceeds the Alfv’en speed at the magnetotail boundary.
► Apart from a local instability of the boundary, unstable global modes are discovered whose amplitude practically does not vary over the magnetotail cross-section.