Extending the space of edge harmonic oscillations by magnetic symmetry breaking external coils in tokamaks

This work presents numerical and analytic approaches for calculating the amplitude of edge harmonic oscillations (EHOs) associated with QH-modes in the presence of external magnetic coils. The analytic approach uses a linear ideal MHD model for edge harmonic oscillations and external kink modes subject to a given boundary condition defined by an externally applied helical field. The imposed 3D field is found to extend the parameter space of unstable external kink modes and EHOs, also providing an amplitude for the MHD perturbation, including the edge corrugation. The saturated states obtained using the linear time-invariant MHD equations are compared with those obtained with the VMEC nonlinear free boundary code, where the Error Field Correction Coils (EFCCs) in JET-like geometry were added to obtain a self-consistent equilibrium solution including the plasma response. Quantitative and qualitative agreement is found between the saturated amplitude calculated analytically and with VMEC for the case of the external kink modes. Only qualitative agreement was found for the most complex case of the EHO amplitude, though saturated amplitudes in both approaches are of the same order of magnitude and follow a similar linear trend with applied current to the EFCCs. The results obtained in this paper may help the modeling of the plasma response for external saturated modes, as well as offer an attractive route for scenario development and control in tokamak devices.