Local and global Fokker–Planck neoclassical calculations showing flow and bootstrap current modification in a pedestal

Abstract

In transport barriers, particularly H-mode edge pedestals, radial scale lengths can become comparable to the ion orbit width, causing neoclassical physics to become radially nonlocal. In this work, the resulting changes to neoclassical flow and current are examined both analytically and numerically. Steep density gradients are considered, with scale lengths comparable to the poloidal ion gyroradius, together with strong radial electric fields sufficient to electrostatically confine the ions. Attention is restricted to relatively weak ion temperature gradients (but permitting arbitrary electron temperature gradients), since in this limit a δf (small departures from a Maxwellian distribution) rather than full-f approach is justified. This assumption is in fact consistent with measured inter-ELM H-Mode edge pedestal density and ion temperature profiles in many present experiments, and is expected to be increasingly valid in future lower collisionality experiments. In the numerical analysis, the distribution function and Rosenbluth potentials are solved for simultaneously, allowing use of the exact field term in the linearized Fokker-Planck-Landau collision operator.In the pedestal, the parallel and poloidal flows are found to deviate strongly from the best available conventional neoclassical prediction, with large poloidal variation of a different form than in the local theory. These predicted effects may be observable experimentally. In the local limit, the Sauter bootstrap current formulae appear accurate at low collisionality, but they can overestimate the bootstrap current near the plateau regime. In the pedestal ordering, ion contributions to the bootstrap and Pfirsch-Schlüter currents are also modified. a) landrema@mit.edu

Poloidal asymmetries in edge transport barriers

“…The poloidal variation of the parallel ion flow obtained (not shown) is qualitatively similar to the variation obtained with the PERFECT code 23 , for a steep pedestal density gradient.…”

“…Already important simulation and theoretical work are forthcoming, focused on including the non-local transport effects caused by large gradients in the density and temperature 17,23,[44][45][46] .…”

Comparison of edge turbulence imaging at two different poloidal locations in the scrape-off layer of Alcator C-Mod

“…Flow along B may appear on the cameras as either toward or away from the X-point depending on whether the pitch of the camera view is greater or less than the pitch of the field. Average parallel flow arises in the edge due to several factors, including Pfirsch-Schlüter effects [18], collisional (neoclassical) flow [39], and sources and sinks [36]. More detailed discussion of the relationship between this theory and the present experimental results is given in Sec.…”

Diamagnetic drift effects on the low-n magnetohydrodynamic modes at the high mode pedestal with plasma rotation

“…19 For parameters typical of QH mode pedestals with normalized collision frequency ν * = 0.05 and inverse aspect ratio r/R = 0.3, the bootstrap current is approximately 80%-90% of the collisionless limit. 20 In addition, numerical calculations find that there are modest modifications due to finite poloidal gyroradius 20 (which 3 have yet to be evaluated for QH modes). Our equilibrium results are consistent to the previous calculations with other codes as given in Ref.…”