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| The helical (m=1) kink instability is one of many ideal MHD instabilities. It occurs in a twisted magnetic flux rope if the twist (i.e. the winding of the magnetic field lines about the rope axis) exceeds a critical value and leads to a helical deformation of the flux rope. The critical value depends on the details of the model considered, but is of the order of 1-2 windings for most flux rope models. The figure above shows snapshots from a numerical simulation of the kink instability by Török, Kliem, and Titov, A&A 413, L27 (2004). A force-free coronal flux rope model, developed by Titov & Démoulin (A&A 351, 707, 1999), is used as initial condition for the simulation (with a twist of 2.5 windings). The figure shows isosurfaces of current density at the beginning (left) and during (right) the simulation. The flux rope current is shown in red. In the course of the instability, a helical current sheet, wrapped about the rising flux rope (purple), and a vertical current sheet below the flux rope (yellow) are formed. Due to the relatively strong magnetic field overlying the flux rope, its rise comes to a stop at roughly two times its initial height. See the animation for the time evolution of the instability. |
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| In confined eruptions, a filament or prominence starts to rise, but does not succeed to escape from the Sun. We reproduced the rise characteristics and morphology of such an event in a numerical simulation similar to the one described at the top of the page. The animation above shows a comparison of this event (left) with the numerical simulation (right). The filament eruption was observed by the TRACE satellite in extreme ultraviolet light (EUV). The simulation images show magnetic field lines outlining the core of the kink-unstable flux rope as well as the normal component of the magnetic field in the bottom plane ("photospheric magnetogram"). The remarkable similarity between the observation and the simulation strongly indicates that the destabilization of the filament was due to a kink instability. See Török and Kliem, ApJ 630, L97 (2005) for details. See also Nature Physics Research Highlight. |
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| In ejective or full eruptions, a filament or prominence succeeds to escape from the Sun and evolves as part of a coronal mass ejection (CME). The animation above shows a numerical simulation of such a full eruption, triggered by the kink instability. The difference to the simulation of the confined eruption is that the magnetic field initially overlying the flux rope is chosen significantly weaker here. This allows the flux rope to escape, indicating that the drop of the overlying field with height is an important parameter in deciding whether an eruption becomes ejective or stays confined (see Török and Kliem, ApJ 630, L97 (2005) for details). As in the animation of the confined eruption, the core of the flux rope is shown in rainbow colors. The additional green field lines outline the potential field initially overlying the flux rope. Note the strong reconnection below the rising flux rope which leads to cusp-shaped field lines, resembling the morphology of soft X-ray cusps often observed in the late phase of solar eruptions. The rise profile of the flux rope could be scaled with very good agreement to two well-observed ejective filament eruptions (see Török and Kliem, ApJ 630, L97 (2005) and Williams et al., ApJ 628, L163 (2005)). |