INTRODUCTION

There has recently been a number of controversies [1,2] over which model to trust when predicting the stability of fusion plasmas, where the inhomogeneity of super-Alfvénic (NBI, ICRF, $\alpha$) particles drive Alfvén eigenmodes (AEs) that could in turn trigger unacceptable losses of confinement.

Theoretical models are clearly required to extrapolate into thermonuclear conditions that are not accessible today from experimental scalings; meaningful comparisons with measurements are nevertheless possible using the tokamaks that are now in operation to test the ingredients and the parametric dependencies of the underlying physics. Increasingly sophisticated models have been implemented in global wave codes and are categorized as shear-Alfvén wave models (LION [3], NOVA-K [4], CASTOR-K [5], the Frascati code [6], KIN-2DEM [9]), a two-fluid model (TASK-WM [7]) and a gyrokinetic model for the bulk species (PENN [8]); they treat the fast particles either perturbatively (LION, TASK-WM, PENN, NOVA-K, CASTOR-K) or not (Frascati code, KIN-2DEM).

To understand the orders of magnitude discrepancies between various predictions of growth / damping rates and to resolve the argument in terms of toroidal mode conversion, this paper starts with a number of basic considerations in sect.2. The different models are then described and compared on theoretical ground in sect.3, giving a few references to the tests that have been carried out against experimental measurements. The conclusions in sect.4 highlight the present understanding of the mode conversion and the AE stability in tokamaks.