Multiple geodesic acoustic modes destabilization in the presence of energetic particles with finite orbit width effects

Finite orbit width (FOW) effects on energetic particle induced geodesic acoustic modes (EGAMs) are investigated using gyrokinetic theory. A dispersion relation is derived, accounting for the FOW effects and assuming a double-shifted Maxwellian distribution in parallel velocity for energetic particles. Numerical solutions of the dispersion relation show good agreement with gyrokinetic simulations. The FOW effects are shown to enhance EGAM damping, consistent with their conventional role in GAM dynamics. Interestingly, when the FOW becomes large enough, a new unstable EGAM branch, referred to as delta EGAM, emerges at a higher frequency than the GAM. This phenomenon is consistent with recent analytic EGAM results obtained using a slowing-down distribution for energetic particles. Depending on the safety factor and the parallel velocity shift of energetic particles, the delta EGAM shows two distinct destabilization patterns and its relationship with the GAM. Based on these characteristics, the delta EGAM is classified into two types, each showing a distinct energetic particle density threshold and frequency range. If energetic particles exhibit a positive slope at the FOW-induced transit resonance, their kinetic energy is transferred to the delta EGAM via inverse Landau damping.