Nonlinear Saturation of Kinetic Ballooning Modes by Zonal Fields in Toroidal Plasmas*

The nonlinear evolution of the kinetic ballooning modes (KBM) has been a subject of great interest for eruptive phenomena in space and fusion plasmas. While the nonlinear evolution of ballooning modes has been proposed as a mechanism for detonation in tokamak plasmas, the role of kinetic effects in such nonlinear dynamics remains largely unexplored. In this work, global gyrokinetic PIC simulation results of nonlinear KBM are presented for the cyclone base case with plasma beta ranging from 1.5% (near KBM marginality) to 2% (strong KBM instability). We find that instead of detonating, the nonlinear KBM continues to grow exponentially in an "intermediate" regime, followed by nonlinear saturation regulated by spontaneously generated zonal fields. The origin of the zonal fields can be attributed to three-wave coupling processes. In the intermediate regime, localized current sheets develop that are prone to secondary tearing instabilities, but the growth rate of the resistive tearing instabilities appear to be subdominant to KBM growth. Additional simulation results using DIII-D pedestal equilibrium with unstable KBM show the same saturation mechanism.