Plasma transport coefficients for nonsymmetric toroidal confinement systems

Abstract

A variational principle is developed for computing accurate values of local plasma transport coefficients in nonsymmetric toroidal confinement configurations. Numerical solutions of the linearized drift Fokker–Planck equation are used to obtain the thermodynamic fluxes as functions of collision frequency and the radial electric field. Effects resulting from the variation of the longitudinal adiabatic invariant J along an orbit (resulting from particle transitions from helically trapped to toroidally trapped orbits) are treated. The velocity-space distribution resulting from trapped, circulating, and transition particle orbits is well represented by a Legendre polynomial expansion in the pitch angle coordinate. The computational effort is significantly reduced from that required with Monte Carlo methods through use of an efficient treatment of the disparity between the time scales of collisionless and collisional particle dynamics. Numerical computations for a stellarator configuration are presented.

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.…”

“…Ref. [1]. Splitting this DKE with respect to the driving forces leads to two 1st-order distribution functions, .…”

“…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].…”

ECRH scenarios with selective heating of trapped/passing electrons in the W7-X Stellarator

“…The magnetic equilibriums with finite-β effects accounted were precalculated by the VMEC code [17] as well as the transport coefficients calculated by the DKES code [18]. The present understanding and all theoretical assumptions that adopted for modeling are based on the substantial experience from W7-AS and other experiments [8,9,11,19].…”