On the radiofrequency response of tokamak plasmas

Using standard guiding centre (gc) variables, we have obtained general expressions for the contributions of individual gc orbits to the linear radiofrequency response of a tokamak plasma. The theory is therefore valid for general equilibrium distribution functions (namely, arbitrary functions of the constants of the motion). Particle motion is described to first order inclusive in the drift approximation. Particular emphasis is put on the importance of wave-particle phase decorrelation; a simplified model of decorrelation due to the effect of Coulomb collisions, based on other authors' work, is incorporated. This allows, for instance, the description of the transition from correlated to uncorrelated resonance crossings occurring near tangent resonance. Two successive asymptotic expansions, based on the important inhomogeneity along the trajectory induced by toroidicity and rotational transform, allow drastic analytical simplifications for a broad class of orbits and interactions; these situations generally coincide with a rapid phase decorrelation. Special attention is paid therein to a realistic description of tangent resonance phenomena. The opposite regime, where the inhomogeneity is weak along the gc orbit, lends itself to direct numerical investigation, and is generally associated with stronger non-local effects such as resonances between the gyromotion, the gc bounce motion and the Doppler-shifted wave frequency. Our results allow the self-consistent (full-wave) study of many radiofrequency wave propagation and absorption scenarios, as well as instabilities; we have indeed applied a common mathematical treatment to these various mechanisms. The present work has been carried out with a marked orientation toward practical applications, which will follow in future publications.