Abstract
The subject of local wave energy in plasmas is treated via quasilinear theory from the dual perspectives of the action-angle formalism and gyrokinetic analysis. This work presents an extension to all orders in the gyroradius of the self-consistent wave-propagation/quasilinear-absorption problem using gyrokinetics. Questions of when and under what conditions local energy should be of definite sign are answered using the action-angle formalism. An important result is that the 'dielectric operators' of the linearized wave equation and of the local energy are not the same, a fact which is obscured when the eikonal or WKB assumption is invoked. This study was originally motivated by concern over the question of local energy for RF-heating of plasmas, where in certain instances, full-wave effects such as refraction, strong absorption, and mode conversion are of primary importance. Fundamentally, the RF-absorption must equate with the energy moment of the quasilinear term to achieve a correct energy balance.
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