This paper presents a study of the interaction between Alfvén modes and zonal structures, considering a realistic ASDEX Upgrade equilibrium. The results of gyrokinetic simulations with the global, electromagnetic, particle-in-cell code ORB5 are presented, where the modes are driven unstable by energetic particles with a bump-on-tail equilibrium distribution function, with radial density gradient. Two regimes have been observed. At low energetic particle concentration, the zonal structure (identified as an energetic particle-driven geodesic acoustic mode) is more unstable than the Alfvén mode. In the regime at high energetic particle concentration, the Alfvén mode is more unstable than the zonal structure. The interplay between the modes leads to a modification of their growth rates as well as to a modification of their saturation levels. The theoretical explanation of the mode interaction is given in terms of three-wave coupling of the energetic particle-driven geodesic acoustic mode and Alfvén mode, mediated by the curvature–pressure coupling term of the energetic particles.

中文翻译：

---

阿尔文不稳定性和高能粒子驱动测地线声学模式非线性相互作用的陀螺动力学研究

考虑到现实的 ASDEX 升级平衡，本文介绍了阿尔芬模式和带状结构之间相互作用的研究。介绍了使用全局、电磁、细胞内粒子代码 ORB5 进行的陀螺动力学模拟的结果，其中模式由具有碰撞尾部平衡分布函数和径向密度梯度的高能粒子驱动而不稳定。已观察到两种制度。在低能粒子浓度下，带状结构（被识别为高能粒子驱动的测地线声学模式）比 Alfvén 模式更不稳定。在高能粒子浓度的状态下，阿尔文模式比带状结构更不稳定。模式之间的相互作用导致它们的增长率的修改以及它们的饱和水平的修改。