Numerical simulation of collisionless kinetic plasma turbulence

Abstract

Hot plasma dissipates energy on scales comparable to the modes of collective oscillation through a turbulent cascade of the distribution function in its phase space. This phase space turbulence is responsible for augmenting fluid transport coefficients beyond predictions from collisional theories, a phenomenon termed anomalous transport. This work studies collisionless kinetic phase space turbulence using spectral and high-order discontinuous Galerkin numerical methods to produce highly resolved simulations of the kinetic equation. Based on these simulations intuition is built for the physics of anomalously enhanced transport, critical studies are performed on reduced models such as quasilinear theory, and mechanisms are identified by which macroscopic plasma properties are altered by microscopic turbulence. Novel results on discontinuous Galerkin method can be found within, such as a new way of thinking about the discrete differential operators of finite element methods as partial sums of orthogonal polynomial completeness theorems. Phase space eigenfunctions are studied in detail for both the electrostatic and electromagnetic pictures in the unmagnetized and strongly magnetized regimes, and utilized in a novel way to produce the initial conditions of continuum kinetic simulations. The nonlinear phase space structures of electron cyclotron instabilities are studied for loss-cone distributions. In addition, highly resolved simulations are presented for Langmuir and Weibel turbulence in two-dimensional configuration space.