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Some relevant aspects of the instability of Geodesic Acoustic Modes (GAMs) driven by Neutral Beam (NB) injection are studied, in particular its dependence on the injection direction, that is, co- or counter-injection, and on the pitch angle distribution of the beam particles in velocity space. In this paper, we further investigate these and other related issues considering the excitation of GAMs by energetic ions created during NB injection and modeled by a bump-on-tail distribution function with a sharp Gaussian dependence over the pitch angle at the injection angle. The bump is considered to have an energetic ion tail with temperature of the order of the third part of the critical energy that appears due to the slowing down effect on electrons. It is found that the maximum frequency of the GAM instability stays below the particle circulation frequency at the critical energy, and it is substantially reduced to be closer to parallel injection conditions. The instability may be preferentially driven for counter NB injection due to the interaction of plasma rotation and/or diamagnetic drift with electron current velocity.

Geodesic Acoustic Modes (GAM) are M=0, N=0 axisymmetric toroidal modes combined with M=±1, ±2 poloidal side-bands and driven by the electron and anisotropic ion pressure perturbations with the frequency

Energetic-particle-induced geodesic acoustic modes, EGAMs (Fu, Phys. Rev. Let., vol. 101, 2008, pp. 185002), driven by neutral beam injection (NBI), have been observed in many DIII-D tokamak experiments (Nazikian et al., Phys. Rev. Lett., vol. 101, 2008, pp. 185001). This mechanism has been theoretically investigated in (Qiu et al., Plasma Phys. Control. Fusion, vol. 52, 2010, pp. 095003), using a sharp energetic particle distribution function, and in (Qu et al., Plasma Phys. Control. Fusion, vol. 59, 2017, pp. 055018), where the dispersion relation and eigenmode behaviour were obtained for the situation of early beam scenario, that is, for times smaller than the beam slowing down time. In this work, we extend these studies determining the eigenmode for beyond the slowing down time, in a scenario with reverse safety factor $q$ profile, where a small concentration of energetic ions can produce an off-axis maximum in the GAM dispersion relation. The characteristics of EGAM are analytically studied with the drift kinetic equation together with the MHD code NOVA. The toroidal energetic ion transit frequency, coupled with the GAM frequency, produces the maximum in the dispersion relation where the eigenmode can be found. The quantitative correspondence of experimental results with the predictions of the proposed model is analysed.

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