Buoyancy Waves in Earth's Nightside Magnetosphere: Normal‐Mode Oscillations of Thin Filaments

We derive a coupled pair of differential equations that describe linear oscillations of a thin magnetic filament that slides without friction through a stationary medium that is in equilibrium. Background field lines are assumed to be in the xz plane, and filament motion is confined to that plane. Sample eigenfunctions and eigenfrequencies are computed for a numerical equilibrium that approximately represents the average magnetosphere but departs from exact equilibrium due to finite grid spacing and other numerical inaccuracy. The most important result of the calculation is the value of the eigenfrequency of the lowest even mode for filaments that cross the equatorial plane at y = 0 and −18 < x < −2 RE. The characteristics of the lowest even mode depend on geocentric distances of the field line. For field lines that extend out in the plasma sheet, that mode is characterized as a buoyancy wave but, for the inner magnetosphere, it is best characterized as a long‐wavelength slow mode. Plain Language Summary Bursty bulk flows often move sunward through the Earth's plasma sheet, coming to rest in the inner plasma sheet. Before coming to rest, they often exhibit damped oscillations with periods of a few minutes. These oscillations are very similar to oscillations of Earth's neutral atmosphere; if a small parcel of air is displaced downward a small distance, gravity causes the parcel to bob up and down, executing what atmospheric scientists call “buoyancy oscillations.” The oscillatory motion observed in the plasma sheet is very similar to buoyancy oscillations in the neutral atmosphere, except that buoyancy force in the magnetosphere is caused by the curvature of magnetic fields rather than gravity. The theoretical analogy to the small parcel of air is a thin magnetic filament in the magnetosphere. This paper works out the theory of small amplitude oscillations of a thin magnetospheric filament and calculates the frequency lowest even mode for different field lines in an average magnetosphere. Out in the plasma sheet, these oscillations are best described as buoyancy waves, but in the inner magnetosphere it is a long‐wavelength slow mode. Key Points A theory has been developed for small oscillations of a thin filament in the magnetosphere For the lowest‐frequency even modes, the eigenfunctions are essentially buoyancy waves in the plasma sheet, but they are more like slow modes in the inner magnetosphere For the lowest‐frequency even modes, the eigenfrequencies