Nonlinear Dynamics of the Kinetic Ballooning Modes

Abstract

Kinetic ballooning modes (KBM) are widely believed to play a critical role in explosive and disruptive dynamics in laboratory and space plasmas. While the nonlinear evolution of ballooning modes has been proposed as a mechanism for the eruptive events in the tokamak edge, known as edge localized modes (ELMs), and magnetospheric substorms, the role of kinetic effects in such nonlinear dynamics with potentially impulsive behavior remains largely unexplored. Detailed studies of the KBM nonlinear dynamics can help in understanding the cause and properties of the eruptive behavior and large turbulent transport in ELMs, and potentially contribute in our ability to predict and even control them in experiments. In this thesis nonlinear dynamics and saturation mechanism of KBM are presented using primarily global gyrokinetic particle-in-cell simulation results. The compressional component of magnetic perturbation δB∥ can be important for KBM in high β plasmas. A numerical scheme that includes δB∥ in first-principles gyrokinetic simulations has been formulated, implemented and benchmarked as a first step. With the perturbed electrostatic potential, and both the perpendicular and the parallel magnetic perturbations, KBM nonlinear evolution is studied for the Cyclone Base Case (CBC) parameters. In contrast to the finite-time singularity predicted by ideal MHD theory, the kinetic instability is shown to develop into an intermediate nonlinear regime of exponential growth, followed by a nonlinear saturation regulated by spontaneously generated zonal fields. The zonal fields, including both the zonal flow (flux-surface averaged electrostatic potential) and the zonal current (flux-surface averaged parallel vector potential), are shown to be important in governing the nonlinear mode structure, and in suppressing trans- port. The kinetic intermediate nonlinear regime resembles the intermediate regime already discovered in the full MHD simulations. During this regime, rapid growth of localized current sheet, which can induce tearing mode and magnetic reconnection, is observed. In the KBM simulations using experimentally measured equilibrium at the DIII-D tokamak edge, the nonlinear convective motion appears to compete with the shearing effect produced by zonal fields, which is weaker in the narrow pedestal steep gradient region compared with that in the core plasma. The effects of the zonal fields and the nonlinear non-zonal convection together regulate the KBM nonlinear saturation level in the DIII-D steep gradient region.