Energetic particles produced by neutral beams are observed to excite energetic-particle-driven geodesic acoustic modes (EGAMs) in tokamaks. We study the effects of anisotropy of distribution function of the energetic particles on the excitation of such instabilities with ORB5, a gyrokinetic particle-in-cell code. Numerical results are shown for linear electrostatic simulations with ORB5. The growth rate is found to be sensitively dependent on the phase-space shape of the distribution function. The behavior of the instability is qualitatively compared to the theoretical analysis of dispersion relations. Realistic neutral beam energetic particle anisotropic distributions are obtained from the heating solver RABBIT and are introduced into ORB5 as input distribution function. Results show a dependence of the growth rate on the injection angle. A qualitative comparison between the numerical results and experimental measurements is presented. An explanation for the differences is advanced.

In the present paper, the evolution of the Alfvén modes is studied in a realistic ASDEX Upgrade equilibrium by analyzing the results of simulations with the global, electromagnetic, gyrokinetic particle-in-cell code ORB5. The energetic particles are modelled both via the newly implemented isotropic slowing-down and with Maxwellian distribution functions. The comparison of the numerical results shows that modelling the energetic particles with the equivalent Maxwellian rather than with the slowing-down, does not significantly affect the frequency of the driven Alfvén mode, while its growth rate appears to be underestimated with a quantitative difference as large as almost 30 %. Additionally the choice of the isotropic slowing-down allows a better description of the nonlinear modification of the dominant Alfvén mode frequency, while an equivalent Maxwellian underestimates it. A good comparison with the experimental spectrogram is found.

Phase Space Zonal Structures (PSZSs), obtained by averaging out dependencies on angle-like variables in the energetic particle (EP) distribution function, play a fundamental role in regulating EP transport induced by Alfvén instabilities in burning plasmas, acting as a slowly varying nonlinear equilibrium state. Therefore, they are of great interest for the development of reduced models for the description of EP heat and particle transport on long time scales, comparable with the energy confinement time, for future burning plasma experiments. In this work, we propose an efficient finite element based projection of the time evolution of the PSZS, suited for global particle-in-cell (PIC) gyrokinetic (GK) codes. The resulting algorithm has been implemented in the global GK PIC code ORB5. PSZSs can not only be used for validating reduced models, but also as a diagnostic tool for characterizing the nonlinear interaction in phase space between Alfvén instabilities and EPs in global GK simulations.

Energetic particles present in tokamak machines can drive through resonant wave-particle interaction different plasma instabilities, e.g Alfvén modes and energetic particle-driven geodesic acoustic modes (EGAMs). While the former are potentially detrimental as they can enhance the energetic particle transport and damage the machine wall, the latter are axisymmetric, possibly benign modes that can act to regulate turbulence. A unique scenario, the so-called NLED-AUG case, has been developed in ASDEX Upgrade by tuning the plasma parameters so that the energetic particle kinetic energy is 100 times higher than that of the background plasma, like in ITER. An intense energetic particle-driven activity is observed, most prominently various Alfvén mode bursts triggering chirping EGAMs. The present work reports studies on the Alfvén mode and EGAM dynamics showing, for the first time, many toroidal mode gyrokinetic simulations with ORB5 where the NLED-AUG case scenario is considered. We study the mode dynamics modelling the energetic particles with different equilibrium distribution functions, such as: isotropic slowing-down, double-bump-on-tail and equivalent Maxwellian. We retain, at the beginning, the nonlinearities only in the energetic particle dynamics. Later, also the background plasma species nonlinearities are taken into account.