Discrete Alfvén eigenmodes excited by energetic particles in high-β toroidal plasmas

Resonant excitations of Alfvén eigenmodes by energetic particles in high-β (ratio of plasma to magnetic pressures) second ballooning-mode stable toroidal plasmas are investigated employing a gyrokinetic-magnetohydrodynamic (MHD) hybrid simulation code. The new type of high-n (toroidal wavenumber) discrete Alfvén eigenmodes correspond to bound states trapped in the α-induced potential wells and, hence, are termed αTAE (α-induced Alfvén eigenmode); where α denotes the ballooning drive due to pressure gradient and curvature (Hu S and Chen L 2004 Phys. Plasmas 11 1). These MHD-stable eigenmodes can be kinetically excited, in the present studies, by magnetically trapped energetic particles via bounce–precessional drift resonances. A dense αTAE spectrum has been found due to the existence of multiple potential wells and, correspondingly, the eigenmodes can either be quasi-marginally stable or experience small but finite Alfvén-continuum damping. Furthermore, these αTAEs exist independently of the toroidal Alfvén frequency gap, in contrast to the usual low-β TAE (toroidicity-induced Alfvén eigenmode) (Cheng C Z, Chen L and Chance M S 1985 Ann. Phys. 161 21). For negative magnetic shear, the αTAE is also shown to extend into the small-α domain and evolve into the low-β TAE. A two-dimensional eigenmode analysis, employing WKB approximation in the radial direction, demonstrates that global αTAEs can be radially localized around the maximal α values.