One of the focal points of the present tokamak experiments is to gain better understanding and control of the interaction between fast particles and magnetohydrodynamical (MHD) waves and instabilities.A new model has been developed that takes toroidal rotation into account in a consistent manner. This model has been implemented in a new code suite, FINESSE–PHOENIX–HAGIS, to study the effect of flow on the interaction numerically. The model and the code suite have been applied to an n = 2 toroidal Alfvén eigenmode (TAE) occurring in a tokamak with a circular cross-section and to an n = 1 TAE mode supported by a JET-like equilibrium. These two applications show that the non-zero growth rate of the TAE mode has a complex dependence on plasma rotation which can be either stabilizing or destabilizing. Furthermore, the results show that the pitch angle distribution of the fast particles' velocity direction also plays an important role in determining the growth rate of the TAE mode in the presence of flow. The complex dependence upon rotation is also seen in the resulting radial particle flux density.In general, there is no rule of thumb to predict the influence of the toroidal flow on the interaction between fast particles and TAE modes. A detailed analysis, as presented in this paper, is required to accurately determine the growth rate of the TAEs in the presence of flow. This also holds for other types of shear Alfvén waves, such as the beta-induced Alfvén eigenmode and the ellipticity induced Alfvén eigenmode.
Double-resonant fast particle-wave interaction