UC San Diego

In this dissertation, we present advances in turbulence modeling for magnetically confined plasmas. We investigate the ecology of microscopic drift wave turbulence and the self-generated macroscopic flows in magnetically confined plasmas. We formulate reduced models that self-consistently describe the evolution of turbulence and mean plasma profiles (including flows) and recover trends obtained from the CSDX device and HL-2A tokamak. The dissertation is divided to three parts. The first part presents a reduced model that describes the interplay between drift wave turbulence and zonal and axial flows in the adiabatic plasma of CSDX, where the electron response is Boltzmann. The model explains how free energy released from the density gradient accelerates both axial and azimuthal flows in CSDX. A description of the interactions between the disparate scales of the plasma via the parallel and perpendicular Reynolds stresses $\langle \tilde v_x \tilde v_z \rangle $ and $\langle \tilde v_x \tilde v_y \rangle $ is presented. Expressions for these stresses are decomposed into a diffusive component that relaxes the flow profile, and a residual stress responsible for accelerating the corresponding flow. Moreover, parallel and perpendicular flow dynamics are described using an extended mixing length approach. This accounts for the degree of symmetry breaking in the parallel direction and parametrizes the efficiency of $\nabla n$ in driving the axial flow. In the second part of the dissertation, the relationship between drift waves and zonal flows is examined in depth via a more specific model. Analytical results obtained from this model confirm the published experimental data showing a suppression of turbulence with the increase in magnitude of the magnetic field \textbf{B}. A new criterion for access to enhanced confinement is introduced. This criterion captured by the dimensionless quantity $R_{DT}$, compares the production rate of turbulent enstrophy due to relaxation of the mean profiles, to the corresponding destruction rate via coupling to the mean flow. When $R_{DT} >1$, the profiles steepen and enhanced confinement is accessible. In the third paper, a novel idea for understanding the physics of the density limit problem in low $\beta$ tokamaks is presented. The collapse of the zonal shear flow when the electron response transitions from Boltzmann to hydrodynamic scaling, along with cooling of the edge and the onset of MHD activity is predicted by the observation that the zonal flow drive will drop as the electron parallel diffusion time increases with density. This leads to a simple, verified understanding of the density limit phenomenon in $L$-modes.