The MHD spectrum of circular cross-section tokamak plasmas with small aspect ratio is studied for low mode numbers. Particular attention is given to the continuous part of the ideal MHD spectrum of such plasmas. Poloidal mode coupling in finite aspect ratio tokamaks yields gaps in the Alfven continuum. Global Alfven modes are found with a frequency inside these gaps. By interaction with the continuum branches the global Alfven modes experience damping via phase-mixing. This damping is computed in resistive MHD. It is shown that for asymptotically small resistivity the damping is finite and independent of eta .
On Alfvén wave heating and transit time magnetic pumping in the guiding-centre model of a plasma