Extension of gyrokinetics to transport time scales

TL;DR

This paper extends gyrokinetic theory to include transport time scales by addressing the limitations of current models in evolving radial profiles and electric fields in tokamaks, proposing a new formalism for this purpose.

Contribution

It introduces a novel gyrokinetic formalism capable of modeling transport time scales and the evolution of the radial electric field in tokamaks.

Findings

Proves that the long wavelength, axisymmetric flow must remain neoclassical.

Shows that tokamaks are intrinsically ambipolar, with zero radial current for any long wavelength electric field.

Identifies limitations of current gyrokinetic models in evolving radial profiles over transport time scales.

Abstract

Gyrokinetic simulations have greatly improved our theoretical understanding of turbulent transport in fusion devices. Most gyrokinetic models in use are delta-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. 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 delta-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. 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. 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 to solve for the global radial electric field.