A new, very fast code, SSFPQL, which solves the steady state quasi-linear kinetic equation describing the ion distribution function during ion cyclotron heating in two velocity variables has been written. It uses an expansion of the distribution function in Legendre polynomials in pitch angle and cubic finite elements in the velocity variable. The success of the Legendre expansion for the ion cyclotron heating problem depends on a non-conventional representation of the quasi-linear diffusion coefficient based on the addition theorem of Bessel functions. By omitting toroidal trapping of energetic ions but otherwise including finite Larmor radius effects to all orders, SSFPQL offers a very efficient complement to wave codes and tokamak radial transport codes in view of the ultimate goals of a self-consistent modelling of ion cyclotron heating. In particular, the velocity space information supplied by SSFPQL can easily be used to take into account quasi-linear effects in the description of wave propagation and absorption with a reasonably modest numerical effort. A few applications of SSFPQL to first harmonic ion cyclotron heating of tritium in a typical ITER plasma are presented. At the power levels to be expected in ITER, the suprathermal ion population is strongly anisotropic: the parallel energy increase is typically only 20% of the total. The total energy in the ion tail is never very high, and its effects on the heating rate are rather modest; in particular, self-boosting of first harmonic heating by finite Larmor radius effects can hardly compensate for the poor efficiency of this heating method at ohmic temperatures. A reduction of the density at the beginning of the heating pulse, or the introduction of a low concentration 3He minority, might be needed to overcome this unfavourable situation. On the other hand, near ignition the quasi-linear increase of the fusion reactivity by first harmonic heating of tritium is not negligible and could lower the ignition temperature by a few keV
Fast-wave ion-cyclotron and first-harmonic heating of large tokamaks