Line-tied kink modes in cylindrical equilibria with magnetic shear.

The method described by Evstatiev et al. [Phys. Plasmas 13, 072902 (2006)] to study the linear stability of line-tied modes in cylindrical geometry is applied to screw pinch equilibria with magnetic shear. The method is based on an expansion in eigenfunctions which depend on radius, and for ideal magnetohydrodynamics (MHD) the inclusion in the expansion of singular eigenfunctions (originating from a continuum) is necessary. The method is also applied to study scaling laws for large cylinder lengths L. It is found that the width of the internal layer of the radial displacement for the line-tied mode scales asymptotically as L-2, consistent with the so-called two-mode approximation. This result is valid in the context of both ideal and resistive MHD and is obtained both analytically and numerically. [ABSTRACT FROM AUTHOR]