  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.
