Ideal kink instability of a magnetic loop equilibrium.pdf

a r X i v : a s t r o - p h / 0 3 1 1 1 9 8 v 1 9 N o v 2 0 0 3 Astronomy Astrophysics manuscript no. Fi252 February 2, 2008 (DOI: will be inserted by hand later) Ideal kink instability of a magnetic loop equilibrium T. To?ro?k 1,2 , B. Kliem 1 , and V. S. Titov 3 1 Astrophysikalisches Institut Potsdam, 14482 Potsdam, Germany 2 School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife KY16 9SS, UK 3 Theoretische Physik IV, Ruhr-Universita?t Bochum, 44780 Bochum, Germany Received 25 September 2003 / Accepted 3 November 2003 Abstract. The force-free coronal loop model by Titov De?moulin (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 Φ ～ 3.5π (at a loop aspect ratio of ≈ 5). The threshold of instability increases with increasing major loop radius, primarily because the aspect ratio then also increases. 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. Key words. Instabilities – Magnetic fields – MHD – Sun: activity – Sun: corona – Stars: coronae 1. Introduction Magnetic loops are the elementary building block of the solar corona and of low-plasma-beta environments of astrophysical objects in general. Understanding their instabilities is one of the fundamental problems in corona physics. Due to the small plasma beta (β = Pkin/Pmag ～ 10?3 . . . 10?2 in the inner so- lar corona), the magnetic configuration