Action-angle representation of MHD waves and instabilities

Hirota, Makoto

Effects of flows on the MHD instabilities have been drawing considerable attention. The standard energy principle, however, is not applicable to flowing plasmas, because waves with negative energy may be stable in such moving media. The action-angle representation for the MHD waves is useful for studying how negative energy modes occur and trigger instabilities, and we discuss it by taking the resistive wall mode (RWM) as an example. The external kink mode, being stabilized by the wall, assumes negative energy when the Doppler shift due to the flow exceeds a critical value. The energy dissipation at the resistive wall destabilizes this mode. To attain stability condition, another physical mechanism different from dissipation must be taken into account.