Title:

Multiscale gyrokinetics for rotating tokamak plasmas

This thesis presents a complete theoretical framework for turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding orderby order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gra dients in the equilibrium quantities, and the transporttimescale evolu tion of mean profiles of these quantities driven by the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. Largescale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the highflow gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local cascade of free energy. Transport equations for the evolution of the mean density, temperature and flow ve locity profiles are derived. These transport equations show how the neo classical corrections and the fluctuations act back upon the mean profiles through fluxes and heating. This framework is further developed by exploiting the scale separation between ions and the electrons. The gyrokinetic equation is expanded in powers of the electron to ion mass ratio, which provides a rigorous method for deriving the electron response to ionscale turbulence. We prove that such turbulence cannot change the magnetic topology, and ar gue that, therefore, the magnetic field lies on fluctuating flux surfaces. These flux surfaces are used to construct magnetic coordinates, and in these coordinates a closed system of equations for the electron response is derived. All fast electron timescales have been eliminated from these equations. Simplified transport equations for electrons in this limit are also derived.
