4.3 Oscillations of line current models

A completely different approach, based on line current models of filaments, was taken by van den Oord and Kuperus (1992Jump To The Next Citation Point), Schutgens (1997aJump To The Next Citation Point,bJump To The Next Citation Point), and van den Oord et al. (1998Jump To The Next Citation Point) in order to study filament vertical oscillations. They used the model introduced by Kuperus and Raadu (1974), in which the prominence is treated as an infinitely thin and long line, i.e., without internal structure. The interaction of the filament current with the surrounding magnetic arcade and photosphere was taken into account. Furthermore, both normal (NP) and inverse polarity (IP) configurations were considered. When a perturbation displaces the whole line current representing the filament, that remains parallel to the photosphere during its motion, the coronal magnetic field is also disturbed and the photospheric surface current is modified. This restructuring affects the magnetic force acting on the filament current. As a consequence, either this force enhances the initial perturbation and the original equilibrium becomes unstable, or the opposite happens and the system is stable against the initial disturbance. As a further complication, van den Oord and Kuperus (1992Jump To The Next Citation Point), Schutgens (1997aJump To The Next Citation Point,bJump To The Next Citation Point), and van den Oord et al. (1998Jump To The Next Citation Point) took into account the finite travel time of the perturbations between the line current and the photosphere and investigated the effect of these time delays on the filament dynamics. For both NP and IP configurations, exponentially growing or decaying solutions were found, which means that perturbations are amplified and the equilibrium becomes unstable, or that oscillations are damped in time and the equilibrium is stable.

Schutgens and Tóth (1999Jump To The Next Citation Point) considered an IP magnetic configuration in which the prominence is not infinitely thin but is represented by a current-carrying cylinder. They solved numerically the magnetohydrodynamic equations assuming that the temperature has a constant value (106 K) everywhere. The inner part of the filament is disturbed by a suitable perturbation that causes the prominence to move like a rigid body in the corona, both vertically and horizontally, undergoing exponentially damped oscillations. Horizontal and vertical motions can be studied separately since they are decoupled. It turns out that the period and damping time of horizontal oscillations are much larger than those of vertical oscillations. Some remarks about the damping mechanism at work in these models is presented in Section 5.6.


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