Abstract. An MHD theory has been developed for the motion of a thin magnetic flux tube through a two-dimensional stationary medium that is in MHD equilibrium. The flux tube is represented as a one-dimensional filament. Simple properties of the computed time development of the filament are explored analytically, including linear intermediate and slow-mode waves, rotational discontinuities, and slow shocks. One numerical solution is presented in detail for a filament in the Earth's magnetotail that is initially underpopulated relative to its neighbors. The computed filament motion displays the strong earthward flow and reduced field line stretching that characterize bursty bulk flows, which are frequently observed in the plasma sheet of the Earth's magnetosphere. The solutions also display the propagation of MHD waves from the equatorial magnetosphere to the ionosphere, then partial reflection from the conducting ionosphere. The ionospheric end of the bursty-bulk-flow flux tube moves equatorward, but that motion is delayed relative to the earthward motion in the equatorial plane. The simulations illuminate the relationship between the interpretation of a bursty bulk flow (BBF) as an underpopulated flux tube and the fact that BBFs typically do not have significantly lower particle pressure than the neighboring plasma sheet. Though the simulated filament started out with lower particle pressure than its neighbors and thus started out as a "bubble" in the plasma sheet, its particle pressure rose to values comparable to, or sometimes greater than, its neighbors once its strong earthward motion developed.

[1] This paper presents a quantitative theory of "interchange oscillations," which occur as an earthward-moving low-entropy plasma bubble slows and eventually comes to rest. Our theoretical picture is based on an idealized situation where an ideal-MHD magnetic filament moves without friction through a stationary background that represents the plasma sheet. If the relevant region of the background plasma sheet is interchange stable, then the filament usually executes a damped oscillation about an equilibrium position, where its entropy parameter matches the local background. The oscillations are typically dramatic only if the equatorial plasma beta is greater than about one. We derive an approximate analytic formula for the oscillation period, which is not simply related to slow-or intermediate-wave travel times. For an oscillation that Panov and collaborators carefully studied using THEMIS data, our simple theory, though based on an unrealistic 2D background magnetic field, predicted an oscillation period that agrees with the observations within about 40%. The simulations suggest that the ionospheric oscillation should lag behind the magnetospheric one by between 40 and 90 degrees. Ionospheric conductance affects the damping rate, which maximizes for an auroral zone conductance $2 S. Adding a friction force acting between the filament and the background increases the decay rate of the oscillation.