Cross-coupling of gyrokinetic turbulence and the neoclassical equilibrium in tokamak plasmas

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 flux in terms of the flow. The scaling law provides a good approximation of the intrinsic rotation due to the neoclassical corrections, but does not perfectly reproduce the momentum flux as there is a significant amount of scatter in the data. Thirdly, a new damping mechanism for zonal flows is discovered. Zonal flows are toroidally symmetric poloidal shear flows and are not considered a neoclassical phenomena; however, they can be seen as a background flow that couples with the turbulence and has a critical impact on its regulation. It is shown that the radial transport of parallel momentum provides a damping mechanism for the zonal flow relevant for plasmas turbulence close to the nonlinear threshold. The damping mechanism is confirmed by a "Rosenbluth-Hinton" test with a model radial momentum diffusion, in which the decay rate of the residual potential is found to be proportional to the model diffusion coefficient and in good agreement with the analytic result. Nonlinear simulations show that stronger long wavelength zonal flow shearing occurs when momentum transport is suppressed. This is relevant for the spontaneously occurring meso-scale structures in the E×B shear, known as staircases, which critically impact the nonlinear stability at experimentally relevant turbulence levels. The suppression of momentum transport allows for the development of fully developed staircase structures in the E×B shear, which can suppress turbulence completely for a finite time window. No impact on shorter wavelength zonal flows is observed, in contrast to the analytic prediction which suggests a high damping rate. The latter result raises questions about the relevance of the residual zonal flow for turbulence saturation. Finally, the interplay between an external torque and staircase structures in the E×B shear is investigated. Gyrokinetic simulations show that the E×B shear connected with the external torque does not simply add to the shear of the meso-scale structures. A positive (negative) externally forced E×B shear leads to a broadening of the corresponding region of the staircase, but does not significantly change the plateau value or the narrow layer of zero shear. In consequence, while the space and time averaged shearing rate is enhanced by the external torque, there is little or no effect on the turbulent transport. This raises doubts about the importance of driven or intrinsic rotation as a means to improve plasma confinement close to the stability threshold.