Thin Filament Oscillations: Pure Interchange in a Bubble

Buoyancy waves are an important low-frequency wave mode in the Earth's magnetosphere that is akin to gravity waves in the Earth's atmosphere, but where gravity is replaced by magnetic tension. We have recently computed the eigenfrequencies and eigenfunctions of buoyancy waves using two different approaches: classic interchange theory and MHD ballooning. Interchange waves are not MHD waves, but rather assume a constant pressure $p$ along each field line. We found that in an average magnetosphere the ballooning and interchange modes are very similar for field lines that extend into the plasma sheet but differ somewhat in the inner magnetosphere [Toffoletto et al., 2022]. We found that the determining factor that controls whether a buoyancy wave is an interchange oscillation is the gradient of entropy $pV^\gamma$, where $V$ is the flux tube volume. Low entropy bubbles, which are ubiquitous in the magnetosphere, have a small entropy gradient, so one would expect very different buoyancy waves within the bubble compared to the background even in the inner magnetosphere. In the bubble scenario, we use a localized small negative entropy-gradient region which is unstable adjacent to a region where the entropy gradient is near-vanishing within which low frequency waves can occur. We find that inside the bubble the buoyancy frequencies are much lower and resemble pure interchange modes.