Nonlinear growth of the tearing mode

The resistive tearing mode is analyzed in the nonlinear regime; nonlinearity is important principally in the singular layer around k·B = 0. In the case where the resistive skin time τs is much longer than the hydromagnetic time τ H, exponential growth of the field perturbation is replaced by algebraic growth like t2 at an amplitude of order (τ H / τ S )4/5. Application of the theory to the unstable tearing modes of a tokamak with a shrinking current channel yields good agreement with the observed amplitudes of the m ≥ 2 oscillations. The analysis excludes the very long wavelength mode, and m = 1 in the tokamak, for which the “constant-Ψ” approximation is invalid.