Variational bounds for transport coefficients in three-dimensional toroidal plasmas

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 28, 157 (1988)] are used to demonstrate the application of this procedure.

Formation of Electron-Root Radial Electric Field and its Effect on Thermal Transport in LHD High <i>T</i>_ePlasma

“…In referring to the FOW effect in this paper, we mean the whole effect caused by neglecting the particle radial drift. This comes from the convention of the local neoclassical transport adopted in many numerical neoclassical transport codes, such as DKES [12]. In the local codes, not only the radial drift but also the ∇B and curvature drifts in poloidal and toroidal directions included in the drift kinetic equation are neglected as a consequence of the assumption of |v E×B | |v B |, where v E×B is the E × B drifts and v B represents the drift arising from the ∇B and the curvature.…”

Momentum correction techniques for neoclassical transport in stellarators

“…are the thermal transport coefficients with direct energy convolution (see [1,2]), i.e. without momentum correction included.…”

“…This assumption of mainly neoclassical transport leads to an upper limit for the temperatures and, consequently, for the bootstrap currents. The neoclassical particle and heat fluxes are evaluated from precalculated databases of mono-energetic transport coefficients (from DKES [1,2]) by energy convolution with and without momentum correction included. The correction technique described in Sec.…”

“…Several numerical tools are available: DKES [1,2], which is based on the Fourier-Legendre expansion of the linearised drift-kinetic equation, and quite different Monte Carlo techniques; see Refs. [3][4][5][6][7].…”

Moment approach to the bootstrap current in nonaxisymmetric toroidal plasmas using δf Monte Carlo methods

“…They showed that parallel viscosities ͗B · ٌ͑ · a ͒͘ and ͗B · ٌ͑ · ⌰ a ͒͘ can be evaluated numerically using the drift-kinetic equation solver ͑DKES͒ code; 14,15 substituting these viscosity terms into the moment equations, 16 the bootstrap current is determined algebraically without breaking the conservation laws. While based on the pitchangle scattering approximation, the important feature of the DKES code is that all the elements of the monoenergetic transport matrix D ij ͑i , j =1,3͒ can be calculated by the variational principle.…”