On the MHD stability of the

We revisit the ideal MHD stability of the $m = 1$ kink mode in configurations representative of coronal loops, using a stability code. We adopt different magnetic force-free equilibria defined by the twist function that are embedded into an outer potential field situated at a radial distance r0 from the magnetic axis. In the limit $r_0 \gg l_0$, l0 being the axis pitch length, the configurations are driven unstable by the kink mode when the twist exceeds the classical critical value of $2.5 \pi$ on the axis. However, the critical axis twist strongly depends on the equilibrium in the opposite limit, with sharply increasing values when r0 becomes of the order or smaller than l0. We interpret these results in terms of the stability criterion $\langle\Phi\rangle_l = 2.5 \pi$, where $\langle\Phi\rangle_l$ is the twist value averaged over a radial length l. It is found that l is of the order of 3-4 times l0, provided $r_0/l_0 \ga 5$; otherwise it depends on the twist profile via the existence of magnetic resonances