Ideal kink instability of a magnetic loop equilibrium

By Tibor Török, B. Kliem, V. Titov. 2003

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The force-free coronal loop model by Titov & Demoulin (1999) is found to be unstable with respect to the ideal kink mode, which suggests this instability as a mechanism for the initiation of flares. The long-wavelength ( m= 1) mode grows for average twists � > 3.5� (at a loop aspect ratio of≈ 5). The threshold of instability increases with increasing major loop radius, primarily because the aspect ratio then also increa ses. Numerically obtained equilibria at subcritical twist are very close to the approximate analytical equilibrium; they do not show indications of sigmoidal shape. The growth of kink perturbations is eventually slowed down by the surrounding potential field , which varies only slowly with radius in the model. With this field a global eruption is not obtained in the ideal MHD limit. Kink perturbations with a rising loop apex lead to the formation of a vertical current sheet below the apex, which does not occur in the cylindrical approximation.

Subfields: Astronomy and Astrophysics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/ebec2bca10a7709a7b8fc02aef08c9bae5aae273

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Citations in the corpus

Tracking Vector Magnetograms with the Magnetic Induction Equation (2008, background): “…flux cancellation of the overlying coronal field (Linker et al. 2001), flux injection (Chen 1989, 1996), the kink instability of filaments (Rust & Kumar 1996; Török et al. 2004; Kliem et al. 2004), and photospheric footpoint shearing (Amari et al. 2000, 2003a, 2003b; Schrijver et al. 2005).”
Generalized Squashing Factors for Covariant Description of Magnetic Connectivity in the Solar Corona (2007, background): “…seems to be quite natural that this HFT is pinched into a vertical current sheet below the flux rope by its upward movement when the kink or torus instability is developed in the configuration at a sufficiently large twist of the field lines in the rope (Török et al. 2004; Roussev et al. 2003).”
X-ray sources and magnetic reconnection in the X3.9 flare of 2003 November 3 (2006, background): “When the sheet gets long enough, fast reconnection starts (Furth et al. 1963; Ugai 1987; Vršnak et al. 2003; see also Török et al. 2004, and references therein).”
The standard flare model in three dimensions - III. Slip-running reconnection properties (2013, background): “S R ] 1 7 M ay 2 01 3 flux ropes (Shibata et al. 1995; Shiota et al. 2005; Priest & Forbes 2002; Amari et al. 2003a,b), and unstable flux ropes (Török et al. 2004; Aulanier et al. 2010).”
Photospheric flux cancellation and associated flux rope formation and eruption (2010, background): “Expressing the average twist angle in the flux rope as Θ = πΦpol/Φaxi, the rope is expected to be stable against the helical kink mode for a poloidal flux of (typically) up toΦpol ∼ 3Φaxi (Török et al. 2004; Fan & Gibson 2004).”