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 , 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, . These trends agree well with previous GENE and ORB5 simulations (Di Siena et al 2018 Nucl. Fusion58 106014), but differ significantly from the elongation effects on geodesic acoustic modes (GAMs) (Gao et al 2009 Nucl. Fusion49 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, ) 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 sκ on EGAMs are similar to the elongation κ effects but weaker.
プラズマ伸長度が高エネルギー粒子誘起測地線音響モード（EGAMs）に及ぼす影響を、ジャイロ運動論方程式とミラー局所平衡モデルを用いて理論的に調べた。任意の伸長度κと有限動径微分 , を含めて、任意の高エネルギー粒子（EP）分布に対する一般的なEGAM分散関係が得られる。特に、二重シフトマクスウェル分布と標準的な減速分布の両方について、解析的なEGAM分散関係を導出する。どちらの場合も、不安定EGAM分枝の周波数は伸長度の増加とともにゆっくり減少し、一方、その成長率は、EPとバルクイオン密度の比 , のときκとともに急速に減少する。これらの傾向は、以前のGENEおよびORB5シミュレーション（Di Siena et