Numerical modeling of nonlinear growth and saturation of neoclassical tearing modes

Numerical modeling results of the nonlinear growth and saturation of neoclassical tearing modes are presented and compared with analytical theories. The saturated magnetic island width obtained numerically in most cases approximately agrees with that derived from generalized Rutherford equation. For a high bootstrap current density fraction and/or a small magnetic shear at the rational surface, however, the change of the local magnetic shear due to the loss of the bootstrap current inside the island should be taken into account in calculating the saturated island width. At island saturation the tearing mode stability index, Δ′, is found to approximately agree with that found from the linear outer region equation of the tearing mode and to linearly decrease with the saturated island width. During the growth of the island, however, the value of Δ′ depends not only on the island width but also on other parameters which affect the plasma current density profile.