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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.
Chen et al. (1999) studied this question.