Progress in RF theory: a sketch of recent evolution in selected areas

This review of recent developments in radio-frequency (RF) theory focusses on the lower (ion-cyclotron) frequency range, although the methods described could be applied to other frequency ranges. The basic RF problem is to solve the wave propagation problem jointly with the evolution of the distribution functions (generally speaking non-Maxwellian) of the particles heated by the RF. We describe the two traditional paths towards such a solution, namely the quasi-uniform magnetic field approach and the Hamiltonian approach. We show that a theory based on the guiding-centre description of the unperturbed particle orbits can unify the two approaches and lead to a fully consistent description of the complete problem, the wave propagation and RF-induced velocity-space diffusion (quasi-linear) parts resting on identical assumptions. This guarantees that basic properties of the wave-particle interactions are preserved and that the power balance between waves and particles is automatically satisfied. The recent evolution of full-wave codes and their comparison is reviewed, and some recent puzzles are pointed out. Recent work on coupling codes is also briefly reviewed.