Progress in the modelling of 3-D effects on MHD stability with the PB3D numerical code and implications for ITER

Introduction The theory of magnetohydrodynamics (MHD) is valuable because it leads to baseline considerations for toroidal magnetic configurations, even when the parameter ranges in which these configurations are situated often don’t strictly satisfy the assumptions behind the MHD theory. The reason for this lies in the strong anisotropy of these configurations, where the dynamics perpendicular to the magnetic field lines is often indeed well-described by the theory, even though the direction parallel to the magnetic field lines is not. This work is situated in the study of fluted or high-n modes, which are normal modes that fit in the theory of MHD stability, that show very fast variation accross the magnetic field lines, as compared to the behavior along them. High-n MHD stability is important by itself as it can describe phenomena that are known to be important for the current and next generation of nuclear fusion devices, such as ELMs, which can be interpreted as due to two types of high-n instabilities: ballooning modes and peeling modes. In the view of studying these phenomena in enough detail, the two ingredients that this work combines within the world of high-n stability are the inclusion of a possible vacuum perturbation, which is necessary for peeling modes to exist in the absence of resistivity; and the correct treatment of 3-D effects, which are important not only for stellarators, but also for tokamaks. An example thereof can be found in the well-known consequences that toroidal field (TF) ripples can have on confinement [Sai+07; Wey+17]; but also in the application of resonant magnetic perturbation (RMP) coils to control ELMs by destabilizing them [Eva+06]. After briefly summarizing the theory of ideal linear 3-D MHD stability and the advancements of the PB3D (Peeling-Ballooning in 3-D) code over the past year in 2, this work then treats its application to the study of 3-D ballooning stability when applying RMPs in tokamaks in 3 and 4. Finally, in section 5, conclusions are phrased as well as the plans for future work.