In a rotating toroidal plasma surrounded by a resistive wall, it is shown that linear MHD instabilities can be excited by couplings between the resistive wall mode (RWM) and stable ideal MHD modes. In particular, it is shown that the RWM can couple not only with stable external kink modes but also with Alfvén eigenmodes that are ordinarily in the stable continuum of a toroidal plasma. The RWM growth rate is shown to peak whenever the Doppler shift caused by the plasma rotation cancels the frequency of an ideal MHD mode, so that the mode appears to have zero frequency in the laboratory frame. At these values of the rotation frequency, the RWM can overcome the stabilizing effects of plasma rotation, continuum damping, and ion Landau damping.
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