Nonlinear evolution of the internal kink mode in toroidal geometry for shaped tokamak plasmas

The nonlinear evolution of the internal kink mode is studied in toroidal geometry for noncircular cross section tokamak plasmas. The study is focused on very low shear and hollow q profiles with q(rho) greater than or equal to 1 for which the internal kink is unstable, in the latter case even at ..beta.. - 0. The nonlinear evolution is dominated by ideal magnetohydrodynamics (MHD), and the instability saturates, giving a quasi-helical shift to the magnetic axis. The nonlinear saturation is caused by increased field line bending. Time scales of 10/sup 3/ tau/sub Hp/ and axis shifts of 20% are reached when changes in q on the order of 3 x 10/sup -3/ from the marginal profile are produced. 25 refs., 27 figs.