This paper presents a study of the interaction between Alfven 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 prese
nted, 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 Alfven 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 Alfven mode. In the latter regime the Alfven 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 Alfven mode, mediated by the curvature-pressure coupling term of the energetic particles.
The nonlinear dynamics of beta-induced Alfven Eigenmodes (BAE) driven by energetic particles (EP) in the presence of ion-temperature-gradient (ITG) turbulence is investigated, by means of selfconsistent global gyrokinetic simulations and analytical t
heory. A tokamak magnetic equilibrium with large aspect ratio and reversed shear is considered. A previous study of this configuration has shown that the electron species plays an important role in determining the nonlinear saturation level of a BAE in the absence of turbulence [A. Biancalani, et al., J. Plasma Phys. (2020)]. Here, we extend the study to a turbulent plasma. The EPs are found modify the heat fluxes by introducing energy at the large spatial scales, mainly at the toroidal mode number of the dominant BAE and its harmonics. In this regime, BAEs are found to carry a strong electron heat flux. The feed-back of the global relaxation of the temperature profiles induced by the BAE, and on the turbulence dynamics, is also discussed.
The global and electromagnetic gyrokinetic particle-in-cell code ORB5 is employed to investigate the self-consistent interactions between Alfven modes (AM) and ion temperature gradient (ITG) turbulence in a magnetically confined plasma. Here, an axis
ymmetric magnetic equilibrium with reversed shear and large aspect ratio is considered. An AM with toroidal mode number n=5 is driven unstable by introducing a population of suprathermal ions. Once the AM saturates in the presence of the fully developed turbulence, the ion heat flux is dominated by the AM and its main harmonics. ITG-induced transport is found to also be enhanced in the presence of the unstable AM.
Turbulence in tokamaks generates radially sheared zonal flows. Their oscillatory counterparts, geodesic acoustic modes (GAMs), appear due to the action of the magnetic field curvature. The GAMs can be driven unstable by an anisotropic energetic parti
cle (EP) population leading to the formation of global radial structures, called EGAMs. The EGAMs can redistribute EP energy to the bulk plasma through collisionless wave-particle interaction. In such a way, the EGAMs might contribute to the plasma heating. Thus, investigation of EGAM properties, especially in the velocity space, is necessary for precise understanding of the transport phenomena in tokamak plasmas. In this work, the nonlinear dynamics of EGAMs without considering the mode interaction with the turbulence is investigated with the help of a Mode-Particle-Resonance (MPR) diagnostic implemented in the global gyrokinetic particle-in-cell code ORB5. An ASDEX Upgrade discharge is chosen as a reference case for this investigation due to its rich EP nonlinear dynamics. An experimentally relevant magnetic field configuration, thermal species profiles and an EP density profile are taken for EGAM chirping modelling and its comparison with available empirical data. The same magnetic configuration is used to explore energy transfer by the mode from the energetic particles to the thermal plasma including kinetic electron effects. For a given EGAM level the plasma heating by the mode can be significantly enhanced by varying the EP parameters. Electron dynamics decreases the EGAM saturation amplitude and consequently reduces the plasma heating, even though the mode transfers its energy to thermal ions much more than to electrons.
The linear destabilization and nonlinear saturation of energetic-particle driven Alfvenic instabilities in tokamaks strongly depend on the damping channels. In this work, the collisionless damping mechanisms of Alfvenic modes are investigated within
a gyrokinetic framework, by means of global simulations with the particle-in-cell code ORB5, and compared with the eigenvalue code LIGKA and reduced models. In particular, the continuum damping and the Landau damping (of ions and electrons) are considered. The electron Landau damping is found to be dominant on the ion Landau damping for experimentally relevant cases. As an application, the linear and nonlinear dynamics of toroidicity induced Alfven eigenmodes and energetic-particle driven modes in ASDEX Upgrade is investigated theoretically and compared with experimental measurements.
The nonlinear dynamics of energetic particle (EP) driven geodesic acoustic modes (EGAM) in tokamaks is investigated, and compared with the beam-plasma system (BPS). The EGAM is studied with the global gyrokinetic (GK) particle-in-cell code ORB5, trea
ting the thermal ions and EP (in this case, fast ions) as GK and neglecting the kinetic effects of the electrons. The wave-particle nonlinearity only is considered in the EGAM nonlinear dynamics. The BPS is studied with a 1D code where the thermal plasma is treated as a linear dielectric, and the EP (in this case, fast electrons) with an n-body hamiltonian formulation. A one-to-one mapping between the EGAM and the BPS is described. The focus is on understanding and predicting the EP redistribution in phase space. We identify here two distint regimes for the mapping: in the low-drive regime, the BPS mapping with the EGAM is found to be complete, and in the high-drive regime, the EGAM dynamics and the BPS dynamics are found to differ. The transition is described with the presence of a non-negligible frequency chirping, which affects the EGAM but not the BPS, above the identified drive threshold. The difference can be resolved by adding an ad-hoc frequency modification to the BPS model. As a main result, the formula for the prediction of the nonlinear width of the velocity redistribution around the resonance velocity is provided.
The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytica
l theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave-particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. The EP bounce frequency is calculated as a function of the EGAM frequency, and shown not to depend on the value of the bulk temperature. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e., the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.
Geodesic acoustic modes (GAMs) are studied by means of the gyrokinetic global particle-in-cell code ORB5. Linear electromagnetic simulations in the low electron beta limit have been performed, in order to separate acoustic and Alfvenic time scales an
d obtain more accurate measurements. The dependence of the frequency and damping rate on several parameters such as the safety factor, the GAM radial wavenumber and the plasma elongation is studied. All simulations have been performed with kinetic electrons with realistic electron/ion mass ratio. Interpolating formulae for the GAM frequency and damping rate, based on the results of the gyrokinetic simulations, have been derived. Using these expressions, the influence of the temperature gradient on the damping rate is also investigated. Finally, the results are applied to the study of a real discharge of the ASDEX Upgrade tokamak.
The linear properties of the geodesic acoustic modes (GAM) in tokamaks are investigated by means of the comparison of analytical theory and gyrokinetic numerical simulations. The dependence on the value of the safety factor, finite-orbit-width of the
ions in relation to the radial mode width, magnetic-flux-surface shaping, and electron/ion mass ratio are considered. Nonuniformities in the plasma profiles (such as density, temperature, or safety factor), electro-magnetic effects, collisions and presence of minority species are neglected. Also, only linear simulations are considered, focusing on the local dynamics. We use three different gyrokinetic codes: the lagrangian (particle-in-cell) code ORB5, the eulerian code GENE and semi-lagrangian code GYSELA. One of the main aims of this paper is to provide a detailed comparison of the numerical results and analytical theory, in the regimes where this is possible. This helps understanding better the behavior of the linear GAM dynamics in these different regimes, the behavior of the codes, which is crucial in the view of a future work where more physics is present, and the regimes of validity of each specific analytical dispersion relation.
