Vertical displacements close to ideal-MHD marginal stability in tokamak plasmas

Elongated tokamak plasmas are prone to instability, initiated by vertical displacement perturbations, which can be suppressed if a perfectly conductive wall is placed near the plasma boundary, providing passive feedback stabilization. For the more realistic case of a resistive wall, the vertical mode can still grow on the relatively slow resistive wall time scale. Active feedback control is then required for complete stabilization. However, the slow growth is far from ideal-MHD marginal stability on the stable side, i.e., provided that the wall is sufficiently close to the plasma. 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.