Erik Hansen Final Defense

Turbulence in a plasma is responsible for an enhancement of particle transport, which has important consequences for magnetically confined fusion systems and astrophysical dynamics. A crucial idea in the Kolmogorov turbulent cascade is that external energy drives the system before being spread and dissipated among length scales in the system.  On the other hand, many plasma configurations contain instabilities which do not require external input for the plasma to become turbulent. In this work, we analyze the energy transfer that occurs in turbulent systems, at the source of instability and between scales. We begin with an analysis of the incompressible Hall MHD system. By assuming that strong wave interactions modify the linear dispersion relation of the system, we may find nonlinear corrections to the wave frequency. This results in a growth or damping rate representing energy exchange between scales. While growth rates in this analysis originate within the Hamiltonian structure of incompressible Hall MHD, the anti-diffusive forcing of the famed Kuramoto-Sivashinsky (KS) equation is shown to be thermodynamically inconsistent. When unstable linear modes of the KS equation are removed to build a system following the metriplectic framework for thermodynamically consistent systems, all solutions tend toward their average value and no chaos is recovered. The selective reintroduction of forcing shows how chaotic solutions to the KS equation are driven by the nonlinear interaction of many instabilities. Unlike the KS equation, however, the Hazeltine three-field model and modified Hasegawa-Wakatani models for drift wave turbulence are formally metriplectic. These results warrant further study of the conditions allowing a non-equilibrium turbulent state to emerge from the second law of thermodynamics.