Cross-Coupling of Gyrokinetic Turbulence and the Neoclassical Equilibrium in Tokamak Plasmas

Abstract

Small scale turbulence in a magnetically confined fusion plasma is the major loss channel for energy and critically limits the confinement. This thesis investigates the interactions between the turbulence and the neoclassical equilibrium background in a tokamak fusion plasma and conducts various numerical investigations using the nonlinear gyrokinetic code gkw. It is conventionally assumed that the neoclassical and turbulent description of a plasma can be treated separately. This is, in many cases, a reasonable approximation because of the large separation of the respective length and time scales. Moreover, different aspects of plasma behaviour are well described by employing just the relevant one of these two descriptions. However, cross-coupling can be important in some cases and in this thesis several aspects of turbulence-background cross-coupling are examined. Firstly, the influence of turbulent dynamics on the neoclassical equilibrium with an emphasis on the turbulence driven stationary electric current is investigated. The neoclassical solution is evaluated using the Hirschmann-Sigmar formalism into which the turbulent dynamics enter as driving terms. These driving terms are evaluated through time averages of gyrokinetic turbulence simulations and are linked with the velocity nonlinearity in the gyrokinetic equation. The time averaged turbulent driving terms provide a non-negligible current drive, despite being a correction of second order in the normalised Larmor radius. For ion temperature gradient mode turbulence, the force exerted due to the heat flux balance is the dominant contribution to the current, which is mostly driven by the electrons, namely by the parallel fluctuations of electron density/temperature and the electrostatic potential. The current is in magnitude comparable to the bootstrap current in the kinetic cyclone base case and increases the total current by a few percent in cases with an experimentally relevant heat flux. A symmetry breaking mechanism for the mode structure along the magnetic field is required for the turbulent current drive. In this study the symmetry breaking is provided by a background rotation or rotation gradient. Consequently the current is nearly linear in the plasma rotation or its gradient. Additional current generation is of great economic interest for tokamaks as the inductive current drive for the poloidal magnetic field naturally limits the operation time. Secondly, a large scale parameter study of the intrinsic rotation caused by neoclassical modifications to the Maxwellian background in turbulent simulations is performed and a simple scaling model using the first order neoclassical flow and its gradient is developed. The results show that the toroidal angular momentum flux is roughly linear in the parallel flow velocity obtained by the neoclassical theory. This suggests that the parallel flow in the neoclassical equilibrium provides the most important symmetry breaking mechanism required for momentum transport, and allows for a simple scaling law for the…