Energetics of resistive wall modes in flowing plasmas

Stabilization/destabilization of magnetohydrodynamic (MHD) waves are formulated in terms of wave energy, where the waves are subject to Alfvén and sound resonances and also influenced by small resistivity at conductive wall. Negative energy wave, which may exist in the presence of mean flow, is shown to be destabilized by the resistive wall, where its growth rate is characterized by the energy dissipation rate. The effect of resonance is examined as well based on a recent knowledge of wave energy for Alfvén and sound continuum modes. Resonant coupling between an eigenmode and a continuum mode having the same sign of energy results in phase mixing (or continuum) damping. In contrast, if their signs are opposite, such resonance triggers an instability.