Linear kinetic effects of core plasma on low frequency Alfven and acoustic eigenmodes in tokamaks

The resonant and non-resonant effects of core plasma on the excitation of low frequency modes with $\omega < \omega_{BAE}$, such as Beta-induced Alfv\'en Acoustic Eigenmodes (BAAEs) and Kinetic Ballooning Modes (KBMs) are examined in the framework of the generalized fishbone-like dispersion relation. The formalism of the fishbone-like equation contains all the necessary ingredients to describe the features of these low frequency fluctuations, and explain experimental findings. Core plasma properties (diamagnetic frequency and precession resonance with trapped ions) strongly affect the excitation of the modes, and in the case of BAAEs more effectively than the energetic particles. The diamagnetic frequency of the core plasma also contributes to the coupling of the BAAEs with the KBMs, thus affecting the excitation and polarization of both modes. Energetic particles can still provide a non-resonant drive to some of the low frequency modes.