  This paper presents a complete theoretical framework for plasma 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 order-by-order in this
expansion, a framework for plasma turbulence is developed. It comprises an
instantaneous equilibrium, the fluctuations driven by gradients in the
equilibrium quantities, and the transport-timescale evolution 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. The magnetic equillibrium is obtained from the Grad-Shafranov
equation for a rotating plasma and the slow (resistive) evolution of the
magnetic field is given by an evolution equation for the safety factor q.
Large-scale deviations of the distribution function from a Maxwellian are given
by neoclassical theory. The fluctuations are determined by the high-flow
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 velocity profiles are derived. These transport equations show how the
neoclassical corrections and the fluctuations act back upon the mean profiles
through fluxes and heating. The energy and entropy conservation laws for the
mean profiles are derived. Total energy is conserved and there is no net
turbulent heating. Entropy is produced by the action of fluxes flattening
gradients, Ohmic heating, and the equilibration of mean temperatures. Finally,
this framework is condensed, in the low-Mach-number limit, to a concise set of
equations suitable for numerical implementation.
