Resonant axisymmetric modes in tokamak fusion plasmas

The impact of divertor X-points on axisymmetric modes (toroidal mode number n=0) in tokamak plasmas is discussed. Axisymmetric perturbations, such as vertical displacements, can lead to current sheets localized in the vicinity of magnetic X-points and extending along the magnetic divertor separatrix, likely to have a profound impact on disruptions and MHD edge stability. When a nearby resistive wall is present, the vertical mode can still grow on the relatively slow resistive wall time scale. Active feedback control is then required for complete stabilization. However, it is shown that the resistive growth rate can be significantly faster, scaling with fractional powers of wall resistivity, if the wall position satisfies the criterion for ideal-MHD marginal stability, thus posing more stringent conditions for active feedback stabilization. Furthermore, it is shown that so-called Vertical Displacements Oscillatory Modes (VDOM) can be excited. These modes have a frequency of oscillation scaling with the poloidal Alfvén frequency. They are normally damped by wall resistivity, but can be driven unstable by the resonant interaction with fast ions, leading to a new type of fast ion driven mode. Instability requires a fast ion distribution with a positive slope, or with a significant anisotropy, in velocity space. Scenarios for the required fast ion population are discussed. Numerical simulations of VDOM using the NIMROD extended-MHD code are presented. This theory may explain the observation of saturated n=0 fluctuations in recent JET experiments.