Neoclassical transport processes are important to the understanding of plasma confinement physics in doubly periodic magnetized toroidal plasmas, especially, after the impact of the momentum confinement on the particle and energy confinement is recognized. Real doubly periodic tori in general are non-axisymmetric, with symmetric tori as a special case. An eight-moment approach to transport theory with plasma density N, plasma pressure p, mass flow velocity V and heat flow q as independent variables is adopted. Transport processes are dictated by the solutions of the momentum and heat flux balance equations. For toroidal plasma confinement devices, the first order (in the gyro-radius ordering) plasma flows are on the magnetic surface to guarantee good plasma confinement and are thus two-dimensional. Two linearly independent components of the momentum equation are required to determine the flows completely. Once this two-dimensional flow is relaxed, i.e. the momentum equation reaches a steady state, plasmas become ambipolar, and all the transport fluxes are determined through the flux–force relation. The flux–force relation is derived both from the kinetic definitions for the transport fluxes and from the manipulation of the momentum and heat flux balance equations to illustrate the nature of the transport fluxes by examining their corresponding driven forces and their roles in the momentum and heat flux balance equations. Steady-state plasma flows are determined by the components of the stress and heat stress tensors in the momentum and heat flux balance equations. This approach emphasizes the pivotal role of the momentum equation in the transport processes and is particularly useful in modelling plasma flows in experiments. The methodology for neoclassical transport theory is applied to fluctuation-driven transport fluxes in the quasilinear theory to unify these two theories. Experimental observations in tokamaks and stellarators for the physics discussed are presented.
Plasma flux motion in a toroidal plasma guide