The heating of toroidal plasmas by resonant absorption of Alfvén waves is considered in the framework of ideal MHD. A theory is developed which closely parallels that of ideal-MHD stability. Computations are performed by using the numerical methods known from stability theory. It is shown that the overall picture of Alfvén wave heating in a torus with circular cross-section does not fundamentally differ from that in a cylinder. This type of plasma may be efficiently heated internally when a collective mode of the plasma response is excited. In contrast, plasmas with elongated cross-sections are shown to suffer from edge heating due to substantial linear mode-coupling. Alfvén wave heating of two specific tokamaks, TCA and JET, is discussed.
Low-frequency heating revisited