New insights into the generalized Rutherford equation for nonlinear neoclassical tearing mode growth from 2D reduced MHD simulations

Two dimensional reduced MHD simulations of neoclassical tearing mode growth and suppression by ECCD are performed. The perturbation of the bootstrap current density and the EC drive current density perturbation are assumed to be functions of the perturbed flux surfaces. In the case of ECCD, this implies that the applied power is flux surface averaged to obtain the EC driven current density distribution. The results are consistent with predictions from the generalized Rutherford equation using common expressions for $\Delta^\prime_{\rm bs}$ and $\Delta^\prime_{\rm ECCD}$. These expressions are commonly perceived to describe only the effect on the tearing mode growth of the helical component of the respective current perturbation acting through the modification of Ohm's law. Our results show that they describe in addition the effect of the poloidally averaged current density perturbation which acts through modification of the tearing mode stability index. Except for modulated ECCD, the largest contribution to the mode growth comes from this poloidally averaged current density perturbation.