Variational theory of ion cyclotron resonance heating in tokamak plasmas

Abstract

The electromagnetic perturbation produced through a set of antennas in a tokamak plasma is studied near the ion cyclotron resonances and the two-ion hybrid resonance. Using an appropriate variational principle, it is possible to derive ' the perturbed field (the compressional wave and the converted torsional wave) with the help of relatively smooth test functions of the compressional type. The method produces conditions under which the variational functional L, an extremum with respect to the perturbation, can be written in a suitable manner for computer handling. Moreover, this functional provides an expression for the power damped by the thermal motion of particles, and in the two-ion hybrid regime it provides the power coupled to the converted wave. The ion cyclotron resonance leads to different regimes for the ratio of the parallel scalelength, λ, of the field and the intrinsic parallel scale of the resonance, λc, with λc ≈|v‖/∇‖ωc|1/2 The usual WKB formulas used by previous authors appear to be limited to the case λ < λc only, and new formulas are given for λ ≥ λc. In the mode conversion case, the method generalizes Budden's results, with restrictions taking into account the non-uniformity effects along the resonance surface.