Suppression of magnetic islands driven by the neoclassical tearing mode (NTM) is necessary for efficient and sustained operation of tokamak fusion reactors. Compensating for the lack of bootstrap current, due to the pressure profile flattening in the magnetic island, by a localized electron cyclotron current drive (ECCD) has been proved experimentally as an effective method to stabilize NTMs. The effectiveness of this method is limited in practice by the uncertainties in the width of the island, the relative position between the island and the beam, and the ECCD power threshold for NTM stabilization. Heuristic search and suppress algorithms have been proposed and shown effective in improving the alignment of the ECCD beam with the island, using only an estimate of the island width. Making use of this estimate, real-time, non-model-based, extremum-seeking optimization algorithms have also been proposed not only for beam steering but also for power modulation in order to minimize the island-beam misalignment and the time required for NTM stabilization. A control-oriented dynamic model for the effect of ECCD on the magnetic island is proposed in this work to enable both control design and performance analysis of these minimum-seeking type of controllers. The model expands previous work by including the impact of beam modulation parameters such as the island-beam phase mismatch and the beam duty-cycle on the island width dynamics.
Integrated modelling of island growth, stabilization and mode locking: consequences for NTM control on ITER