Alfvén wave heating in general toroidal plasmas

A variational formulation is presented within the framework of linearized ideal magnetohydrodynamics of the problem of the heating of a general toroidal plasma by Alfvén waves. The extremal value of the functional yields directly the impedance matrix seen by the driving circuits. The problem is couched in generalized coordinates in a fashion amenable to computational implementation. The energy is absorbed in boundary layers which straddle those magnetic surfaces corresponding to continuum eigenfunctions resonant with the driving frequency. The contribution of these resonant surfaces to the extremal value of the variational functional is given explicitly in terms of quantities which must be found by solving the problem in the regions external to the resonant surfaces. The structure of the theory suggests optimum ways of implementing the method.