In the generalized Rutherford equation describing the nonlinear evolution of the width of the magnetic island associated with a neoclassical tearing mode, the effect of localized current drive is represented by a term ΔCD′. We investigate oscillations in ΔCD′ originating from the rotation of the island through the electron cyclotron power deposition region and their dependence on the collisional time scale on which the driven current is generated, the rotation period, the island size, and the power deposition width. Furthermore, their consequences for the island growth or the stabilization are analyzed. This work shows that the net result of the oscillations in ΔCD′ is a slight increase in the stabilizing effect of electron cyclotron current drive and consequently, a reduction in the minimum power requirement to fully suppress an island.

Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived previously by Harvey et al, Phys. Rev. Lett. 62 (1989) 426. We study the non-linear electron cyclotron current drive (ECCD) efficiency through bounce-averaged, quasi-linear Fokker-Planck calculations in the magnetic geometry as created by the islands. The calculations are performed for the parameters of a typical NTM stabilization experiment on ASDEX Upgrade. A particular feature of these experiments is that the rays of the EC wave beam propagate tangential to the flux surfaces in the power deposition region. The calculations show significant non-linear effects on the ECCD efficiency, when the ECCD power is increased from its experimental value of 1 MW to a larger value of 4 MW. The nonlinear effects are largest in case of locked islands or when the magnetic island rotation period is longer than the collisional time scale. The non-linear effects result in an overall reduction of the current drive efficiency for this case with absorption of the EC power on the low field side of the electron cyclotron resonance layer. As a consequence of the non-linear effects, also the stabilizing effect of the ECCD on the island is reduced from linear expectations.

Modelling of the experiments on TEXTOR on tearing mode suppression by electron cyclotron resonance heating and current drive based on the generalized Rutherford equation (GRE) is presented. The comparison between the model and the experimental data provides a satisfactory agreement taking into account the experimental uncertainties. Both the model and the experimental observations confirm that in TEXTOR heating is the dominant suppression mechanism above that of current drive. As a conclusion, these experiments provide a positive benchmark for the stabilizing term in the GRE arising from the localized heating.

Abstract. In the presence of electron cyclotron current drive (ECCD), the Ohm's law of single fluid magnetohydrodynamics (MHD) is modified as E + v × B = η(J − J ECCD ). This paper presents a new closure relation for the EC driven current density appearing in this modified Ohm's law. The new relation faithfully represents the nonlocal character of the EC driven current and its main origin in the Fisch-Boozer effect. The closure relation is validated on both an analytical solution of an approximated Fokker-Planck equation as well as on full bounce-averaged, quasi-linear Fokker-Planck code simulations of ECCD inside rotating magnetic islands.