Transport Barriers in Plasmas and Fluids

Doktorsavhandling, 2003

In the present work different mechanisms for generation and suppression of turbulence are studied. The suppression of nonlinearly generated turbulence stabilized by temperature boundary conditions as well as turbulence generated by linear instabilities and suppressed by nonlinearly generated secondary flows are treated. Linear stability analysis shows that in the edge of a tokamak, the two dimensional fluid description of plasma can support one high and one low frequency mode, resulting in high resp low transport. When the high frequency mode is stabilized the low frequency modes can still be unstable for short wavelengths. Quasilinear analysis yields that the low frequency mode can drive counter gradient particle transport on the H-mode barrier. Renormalizing the collision frequency extend the application of linear stability theory to regions where the plasma is not well described by ordinary quasi linear analysis. The renormalized collision frequency accounts for nonlinearly generated structures. It is shown that in realistic parameter regimes the renormalized frequency can produce resistive instabilities of frequencies relevant to the edge turbulence. A mechanism for generation of zonal flows is considered by means of the reductive perturbation method. The obtained Zakharov like equations then self-consistently describe the dynamics of zonal flows and ITG turbulence. Coefficients of the equations imply that zonal flows are resonantly excited through the nonlinearity in the ion energy equation. The resonance is found to be sensitive to the closure of the fluid hierarchy. The pressure driven flow between two infinite plates with a stabilizing temperature difference on the plates is studied using direct numerical simulations (DNS). Increasing the temperature difference between the plates gives decreased turbulent transport of heat, resulting in a thermocline solution. Although turbulent fluctuations of both the vertical velocity and temperature fields increase, the transport decreases indicating excitation of linear gravity waves. A numerical code for two dimensional fluid dynamics is developed and used to study the difference in nonlinear behavior of the Charney-Hasegawa-Mima (CHM) equation and the vortex equation. Numerical simulations of fluid equations in flux tube geometry show the central importance of zonal flow impact on the turbulent transport of heat and particles in tokamaks.