Neoclassical momentum transport in a collisional stellarator and a rippled tokamak

Abstract

Short mean-free path two-fluid equations are employed to evaluate the lowest order non-ambipolar radial current in plasma confined by a three-dimensional toroidal magnetic field. The result is used to obtain a necessary condition for intrinsic ambipolarity of plasma transport in such a field and to derive a criterion for the importance of the toroidal field ripple for collisional tokamak plasma rotation. The ripple effects on toroidal plasma rotation are found to be negligible if the characteristic perpendicular length scale is determined by the pedestal width of order the poloidal ion gyroradius (as may be the case in the H-mode regime), but may conceivably become important for more shallow plasma gradients.

Pfirsch–Schlüter impurity transport in stellarators

“…In the limit Z eff − 1 1, the radial electric field is equal to that in a pure plasma and is given in Ref. [5]. In the opposite, Lorentz limit (Z eff 1), the ion collision operator reduces to a simple pitch-angle scattering operator,…”

“…II. The pressure anisotropy of a pure plasma has been calculated before [5], and, in the notation used in this paper, reads…”

“…The present calculation, which is based on the direct expansion of the drift kinetic equation by Hazeltine and Hinton [4], retains some terms of geometrical nature that are otherwise neglected, see, e.g. [5], and is used here to derive explicit transport coefficients.…”

Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas

“…In the momentum-conserving calculations, these transport coefficients are inversely proportional to ν, whereas they are proportional to ν if the collisions are approximated by pure pitchangle scattering. To understand why, it is useful to recall that the Pfirsch-Schlüter particle flux consists of two terms: one related to the parallel friction force and one related to parallel viscosity [46,47]. This is most easily seen by taking the scalar product of the lowest-order plasma current, which satisfies J × B = cp ′ (ψ)∇ψ, with the momentum equation,…”

“…In the short-mean-free-path limit ν ′ ≫ 1, the ion transport and flow can be computed analytically in terms of the parallel current [46]. The transport matrix elements associated with the Fokker-Planck collision operator may therefore be extracted from Ref.…”