Extension of gyrokinetics to transport time scales

Abstract

In the last decade, gyrokinetic simulations have greatly improved our theoretical understanding of turbulent transport in fusion devices. Most gyrokinetic models in use are [sigma]f simulations in which the slowly varying radial profiles of density and temperature are assumed to be constant for turbulence saturation times, and only the turbulent electromagnetic fluctuations are calculated. Due to the success of these models, new massive simulations are being built to self-consistently determine the radial profiles of density and temperature. However, these new codes have failed to realize that modern gyrokinetic formulations, composed of a gyrokinetic Fokker-Planck equation and a gyrokinetic quasineutrality equation, are only valid for [sigma]f simulations that do not reach the longer transport time scales necessary to evolve radial profiles. In tokamaks, due to axisymmetry, the evolution of the axisymmetric radial electric field is a challenging problem requiring substantial modifications to gyrokinetic treatments. The radial electric field, closely related to plasma flow, is known to have a considerable impact on turbulence saturation, and any self-consistent global simulation of turbulent transport needs an accurate procedure to determine it. In this thesis, I study the effect of turbulence on the global electric field and plasma flows. By studying the current conservation equation, or vorticity equation, I prove that the long wavelength, axisymmetric flow must remain neoclassical and I show that the tokamak is intrinsically ambipolar, i.e., the radial current is zero to a very high order for any long wavelength radial electric field.

(cont.) Intrinsic ambipolarity is the origin of the problems with the modern gyrokinetic approach since the lower order gyrokinetic quasineutrality (if properly evaluated) is effectively independent of the radial electric field. I propose a new gyrokinetic formalism in which, instead of a quasineutrality equation, a current conservation equation or vorticity equation is solved. The vorticity equation makes the time scales in the problem explicit and shows that the radial electric field is determined by the conservation of toroidal angular momentum.