Nonlinear stability of the internal m=1 modes in a pure Z-pinch

According to linear, ideal MHD theory the internal region of a pure Z-pinch (i.e. a pinch having no axial magnetic field) is strongly unstable with respect to m=1 (kink) modes. However, various fusion devices based on the Z-pinch often show experimental lifetimes much longer than the characteristic Alfven time. While numerous attempts have been made to explain this anomalous stability in terms of various non-ideal phenomena, the nonlinear evolution of these instabilities does not seem to have been calculated previously. In the present work the result of such a calculation, based on bifurcation theory, is presented. (author) 5 refs., 2 figs