Gyrokinetic investigation of the nonlinear interaction of Alfvén instabilities and energetic-particle driven geodesic acoustic modes

This paper presents a study of the interaction between Alfvén modes and zonal structures, considering a realistic ASDEX Upgrade equilibrium. The results of gyrokinetic simulations with the global, electromagnetic, particle-in-cell code ORB5 are presented, where the modes are driven unstable by energetic particles with a bump-on-tail equilibrium distribution function, with radial density gradient. Two regimes have been observed: at low energetic particles concentration, the Alfvén mode saturates at much higher level in presence of zonal structures; on the other hand at high energetic particles concentration the difference is less pronounced. The former regime is characterized by the zonal structure (identified as an energetic particle driven geodesic acoustic mode), being more unstable than the Alfvén mode. In the latter regime the Alfvén mode is more unstable than the zonal structure. The theoretical explanation is given in terms of a 3-wave coupling of the energetic particle driven geodesic acoustic mode and Alfvén mode, mediated by the curvature-pressure coupling term of the energetic particles.