Variational bounds for transport coefficients in three-dimensional toroidal plasmas

A variational principle is developed for the linearized drift-kinetic, Fokker–Planck equation, from which both upper and lower bounds for neoclassical transport coefficients can be calculated for plasmas in three-dimensional toroidal confinement geometries. These bounds converge monotonically with the increasing phase-space dimensionality of the assumed trial function. This property may be used to identify those portions of phase space that make dominant contributions to the transport process. A computer code based on this principle has been developed that uses Fourier–Legendre expansions for the poloidal, toroidal, and pitch-angle dependences of the distribution function. Numerical calculations of transport coefficients for a plasma in the TJ-II flexible heliac [Nucl. Fusion 28, 157 (1988)] are used to demonstrate the application of this procedure.