Helical mode localization and mode locking of ideal MHD instabilities in magnetically perturbed tokamak plasmas

In H-mode tokamak plasmas, the achievable pressure-gradient is limited by type-I Edge Localized Modes (ELMs), which are projected to cause severe damage to future fusion devices. There are several approaches aiming to mitigate/suppress the occurrence of ELMs, such as the application of an external non-axisymmetric magnetic perturbation field, which breaks the axisymmetry of the tokamak plasma. In this work we use the CASTOR3D code to investigate helical localization and mode locking of edge-localized ideal MHD instabilities in rotating and flow-free magnetically perturbed tokamak plasmas with N-P = 2 periodicity. Helically localized instabilities are separated into two classes: quasi-locked and strictly locked. In a non-rotating plasma, the localization of quasi-locked modes is determined by an envelope while their precise location under the envelope is arbitrary, whereas strictly locked modes can only occur at a single helical position. Strictly locked modes only rotate if the toroidal plasma rotation exceeds a critical threshold; above the threshold the forced rotation of the strictly locked modes is non-uniform. For quasi-locked modes, no such critical threshold exists; they rotate uniformly beneath their envelope in the case of finite plasma rotation. The helical localization of both quasi-locked and strictly locked instabilities is determined by the energetic decomposition of the instabilities close to the most unstable flux-surface; for example, strongly current-density driven instabilities are aligned with regions of augmented parallel equilibrium current-density. Finally, we compare the computationally determined localization of MHD instabilities to experimental observations. The determined MHD instability is located at the same position as the experimentally measured modes with respect to the equilibrium corrugation, verifying that ideal MHD can describe the experimentally observed instabilities.