Interchange instability analysis based on magnetosphere-ionosphere coupling theory

A localized flux tube with reduced entropy (PV^5/3, where P and V stand for the plasma pressure and flux tube volume, respectively) as compared to its neighbors is defined as a plasma-sheet bubble. Bubbles are susceptible to interchange instability. The interchange instability plays a key role in the transport of plasma from the magnetotail to the near-Earth region. A strong dawn-to-dusk electric field is formed inside the bubble which creates a shear flow. The E×B drift causes the bubble to grow earthward and the magnetic tension force drives it towards the equilibrium location where its total entropy matches the entropy of the surrounding area. According to the Vasyliunas equation, when the angle (α) between ∇V and ∇PV^5/3 is either 0 (being parallel) or 180^° (being antiparallel), the Birkeland current cannot be flown between the plasma sheet and the ionosphere. In this study, using the linear instability analysis we investigate the excitation and development of interchange modes in the low-beta plasma sheet (β<<1) when 0<α<180^°. To this end, a boundary layer (with thickness δ) separating regions of higher and lower entropy is assumed in a small region of the ionosphere. The first-order electric potential (Φ) within this layer is numerically calculated based on time-sequence technique. The complete analytical solution for the temporal variation of Φ clearly shows that the unstable interchange modes with large wavelengths compared to the boundary layer (i.e., λ>>δ) can be generated.