We analytically derive the structures of the low-frequency shear Alfvén continuous spectrum due to resonant wave-particle interactions with magnetically trapped thermal particles in tokamaks. Our theoretical description asymptotically recovers known results in the relevant limits at both high and low frequencies; furthermore, it is relevant for assessing the accurate kinetic structures that are due to shear Alfvén and acoustic wave spectra in toroidal geometry. Since there is a continuous transition between various shear Alfvén wave and MHD fluctuation branches in many situations of experimental interest, the results reported in this work are of practical relevance for their interpretation when used in the theoretical framework of the general 'fishbone-like' dispersion relation.

The properties of the low frequency shear Alfvén and acoustic wave spectra in toroidal geometry are examined analytically and numerically considering wave particle interactions with magnetically trapped and circulating particles, using the theoretical model described in [I. Chavdarovski and F. Zonca, Plasma Phys. Controlled Fusion 51, 115001 (2009)] and following the framework of the generalized fishbone-like dispersion relation. Effects of trapped particles as well as diamagnetic effects on the frequencies and damping rates of the beta-induced Alfvén eigenmodes, kinetic ballooning modes and beta-induced Alfvén-acoustic eigenmodes are discussed and shown to be crucial to give a proper assessment of mode structure and stability conditions. Present results also demonstrate the mutual coupling of these various branches and suggest that frequency as well as mode polarization are crucial for their identification on the basis of experimental evidence.

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 analytical 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. As a main result, the formula for the saturation level is provided. 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.

We present a general theoretical framework for discussing the physics of low frequency fluctuation spectra of shear Alfvén and acoustic waves in toroidal plasmas of fusion interest. This framework helps identifying the relevant dynamics and, thus, interpreting experimental observations. We also discuss the roles of such general theoretical framework for verification and validation of numerical simulation codes vs. analytic predictions and experimental results.