On the energetic particle-induced geodesic acoustic modes with finite-orbit-width effects

Abstract

This study presents an analytical investigation of energetic particle-induced geodesic acoustic modes (EGAMs) within a gyro-kinetic model, incorporating finite-orbit-width (FOW) effects up to the second order. The inclusion of second-order FOW effects introduces two distinct types of energetic particle-wave resonances, occurring at $\omega = \omega_t^h$ and $\omega = 2\omega_t^h$ , respectively, where $\omega_t^h$ denotes the transit frequency of energetic particles (EPs). It is found that two unstable EGAM branches coexist: a low frequency branch (LFB) characterized by $0 \lt \omega_\textrm{LFB} \lt \omega_{t,\textrm{max}}^h$ , and a high frequency branch (HFB) marked by $\omega_{t,\textrm{max}}^h \lt \omega_\textrm{HFB} \lt 2\omega_{t,\textrm{max}}^h$ . The instability of LFB primarily arises from the resonance $\omega = \omega_t^h$ , mainly introduced by first-order FOW effects. As a result, the instability of LFB always exists regardless of the presence or absence of second-order FOW effects, and is barely modified by these effects. In contrast, the instability of HFB is exclusively attributed to the resonance $\omega = 2\omega_t^h$ induced by second-order FOW effects. Consequently, the HFB exhibits instability in the presence of these effects.

Keywords

• finite orbit width
• energetic particle
• geodesic acoustic mode
• instability
• tokamak