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(ρ)≥1 for which the internal kink is unstable in the latter case, even at β=0. The nonlinear evolution is dominated by ideal magnetohydrodynamics (MHD), and the instability saturates, giving a quasihelical shift to the magnetic axis. The nonlinear saturation is caused by increased field line bending. Time scales of 103 τHp and axis shifts of 20% are reached when changes in q on the order of 3×10−3 from the marginal profile are produced.