3.2 Titov–Démoulin equilibrium

Another approach for computing axisymmetric NLFFF solutions has been developed in Titov and Démoulin (1999Jump To The Next Citation Point). This model active region contains a current-carrying flux-tube, which is imbedded into a potential field. A motivation for such an approach is that solar active regions may be thought of as composed of such flux tubes. The method allows to study a sequence of force-free configurations through which the flux tube emerges. Figure 6View Image shows how the equilibrium is built up. The model contains a symmetry axis, which is located at a distance d below the photosphere. A line current I0 runs along this symmetry axis and creates a circular potential magnetic field. This potential field becomes disturbed by a toroidal ring current I with the minor radius a and the major radius R, where a ≪ R is assumed. Two opposite magnetic monopoles of strength q are placed on the axis separated by distance L. These monopoles are responsible for the poloidal potential field. This field has its field lines overlying the force-free current and stabilizes the otherwise unstable configuration. Depending on the choice of parameters one can contain stable or unstable nonlinear force-free configurations. The unstable branch of this equilibrium has been used to study the onset of coronal mass ejections; see Section 5.5. Stable branches of the Titov–Démoulin equilibrium are used as a challenging test for numerical NLFFF extrapolation codes (see, e.g., Wiegelmann et al., 2006a; Valori et al., 2010).
View Image

Figure 6: Construction of the Titov–Démoulin equilibrium. Image reproduced by permission from Figure 2 of Titov and Démoulin (1999), copyright by ESO.

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