Non-linear gyro-kinetic equations via action variational lie perturbation method

Abstract

We derive a self-consistent, non-linear gyro-kinetic Vlasov-Poisson system which is suitable for particle simulation studies of finite $\beta$ tokamak microturbulence and its associated anomalous transport. This formalism is based on the Action variational Lie perturbation method, and preserve the Hamiltonian structure of original Vlasov-Poisson system. In this thesis, we consider only electrostatic perturbation; however, this method can be extended to the electromagnetic perturbation, while preserving its advantages.