Magnetic double gradient mechanism for flapping oscillations of a current sheet

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Abstract
A new kind of magnetohydrodynamic waves are analyzed for a current sheet in a presence of a small normal magnetic field component varying along the sheet. As a background, two simplified models of a current sheet are considered with a uniform and nonuniform current distributions in the current sheet. On a basis of these two models, the flapping‐type waves are obtained which are related to a coexistence of two gradients of the tangential and normal magnetic field components along the normal and tangential directions with respect to the current sheet. A stable situation for the current sheet is associated with a positive result of the multiplication of the two magnetic gradients, and unstable (wave growth) condition corresponds to a negative result of the product. In the stable region, the “kink”‐like wave mode is interpreted as so called flapping waves observed in the Earth's magnetotail current sheet.

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