On the Existence of Resistive Instabilities of Line-Tied Modes in Cylindrical Geometry

Summary form only given. Linear MHD stability with line-tying boundary conditions has been the subject of intense research in the solar physics community for the past twenty years, in an attempt to understand the dynamics of solar flares and the related mechanisms of energy release. Recently, there has been a renewed interest line-tying mainly due to two set of experiments. The present work investigates the role of resistivity on linetied kink modes because of the importance of resistivity in laboratory experiments and in simulations. We use the method recently proposed by Evstatiev et al. (2006) to analyze the linear stability of line-tied kink modes in cylindrical geometry. The method consists of summing up a number of one-dimensional (radial) eigenfunctions to obtain the lull two-dimensional solution of the problem and has been successfully applied to both ideal and resistive MHD. Resistivity affects the problem in two ways. First, it disallows perfect line-tying at the two end-plates of the cylinder. Second, some of the radial eigenfunctions used to construct the full solution of the problem can be unstable tearing modes instead of stable ideal modes, thus opening the possibility of tearing-like instabilities in line-tied configurations. In order to address these two issues, we will use our new method to study different equilibria where the field line pitch as a function of radius can be monotonicallv increasing (tokamak-like), monotonicallv decreasing (RFP-like) or constant. We will show the existence of slowly growing resistive modes below the threshold for ideal stability. These modes, however, grow at a rate proportional to resistivity and there is no evidence of tearing-like scaling in the line-tied system. Consistently, we do not observe current sheets. These resistive modes are due to imperfect line-tying, where resistivity acts globally on the plasma column and not in resistive layers.