Effects of line-tied boundary conditions on internal current-driven kink mode

MHD kink instabilities caused by current passing though high temperature plasma in magnetic field is a topic of importance to astrophysical and lab plasmas. Recent theoretical study of external kink mode stability in line-tied geometry[1] has shown the existence of complex axial wave numbers k$_{z}$ in spatial spectrum of the system. Similar to the external kink mode complex k$_{z}$ were found in numerical calculations performed at LANL for line-tied internal kink instability. We are developing an analytical model for internal mode in line-tied cylindrical geometry to follow transition from the case of periodic cylinder where all axial wave numbers are real to line-tied boundary conditions (BC). The model allows us to determine whether line-tying BC change axial modes globally or their effect is ``shielded'' in long systems in the vicinity of the end-plates. This is important for mode structure and, specifically, for perturbed current profile (``current sheet'') which is localized on the resonance surface in periodic case and is broadened due to superposition of ``quasi-resonances'' in line-tied geometry. [1] V.V.Mirnov et al., Bull. of the APS, v.50, No 8, p.238, DPP Meeting, Oct. 24-28, 2005