Plasma elongation effects on energetic particle-induced geodesic acoustic modes in tokamaks

Abstract

Plasma elongation effects on energetic particle-induced geodesic acoustic modes (EGAMs) are theoretically investigated by using gyro-kinetic equations and the Miller local equilibrium model. Including an arbitrary elongation κ and a finite radial derivative sκ=r∂rκ/κ , a general EGAM dispersion relation is obtained for an arbitrary energetic particle (EP) distribution. In particular, we obtain analytical EGAM dispersion relations for both the double-shifted Maxwellian distribution and the standard slowing-down distribution of EPs. In both cases, the frequency of the unstable EGAM branch decreases slowly with increasing elongation, while its growth rate decreases rapidly with κ when the ratio of the EP to the bulk ion density, nh/ni⩾0.1 . These trends agree well with previous GENE and ORB5 simulations (Di Siena et al 2018 Nucl. Fusion 58 106014), but differ significantly from the elongation effects on geodesic acoustic modes (GAMs) (Gao et al 2009 Nucl. Fusion 49 045014). The portion of the EGAM dispersion relation accounting for the first-order finite-orbit-width shows greater sensitivity to frequency compared to that of GAM, which explains the smaller variations in the frequency of EGAM as κ changes. When the EP number is small (typically, nh/ni≈5% ) in the double-shifted Maxwellian case, the growth rate of EGAMs first increases with the increasing elongation and then decreases, while it monotonically increases with κ in the slowing-down case. Furthermore, the effects of s κ on EGAMs are similar to the elongation κ effects but weaker.