Variational bounds for transport coefficients in three-dimensional toroidal plasmas

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Abstract
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 2 8, 157 (1988)] are used to demonstrate the application of this procedure.