Infinite wavelength kink instabilities in uniform current cylindrical plasmas with rectangular cross sections

The magnetohydrodynamic stability of a free-boundary straight plasma column with a slightly elongated rectangular cross section, carrying a uniform axial current, is investigated analytically. Axisymmetric modes (n = 0), for which the circular cross section case is marginally stable (m = 1), are considered. Stability is found for a rigid vertical displacement, in good agreement with numerical results. However, a vertical displacement with a small additional m = 3 like perturbation, localized near the plasma surface, leads to instability