Long-Term Landau-Fluid Simulation of Alfvén Eigenmode Instabilities∗)

An energetic particle Landau-fluid closure model (TAEFL) is applied to a case where both RSAE (Reversed Shear Alfvén Eigenmode) and TAE (Toroidal Alfvén Eigenmode) modes are destabilized by beam ions. The nonlinear evolution of the coupled modes are followed for about 104 Alfvén times under the simplifying assumptions that a density source is present that exactly balances the quasi-linear fast ion profile changes driven by the instabilities. Saturation is achieved via self-regulation/organization through zonal flows and currents. A quasi-stationary nonlinear state persists, which is characterized by repetitive predator-prey phenomena. As the mode grows, it drives zonal flows/currents, these quench its amplitude until the linear mode structure sets in again and grows, driving further zonal flows/currents, etc. This capability of following nonlinear fast ion-driven instabilities over longer time intervals (achieved here by using a higher order time-stepping method) is an important requirement for future integrated models of burning plasmas.