A kinetic energy principle for a tokamak allowing for bounce and transit resonances

Most of kinetic energy principles used in the theory of MHD instabilities in tokamaks are based on the assumption that the ratio of the wave frequency ω to the characteristic particle circulation frequency along the torus ωc is either small ω/ωc → 0 or large ω/ωc → ∞. In a number of problems the above ratio is finite, so it is necessary to have a kinetic energy principle which is valid for arbitrary ω/ωc. Derivation and analysis of such an energy principle is the object of the present paper. (orig.)