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

TL;DR

This paper investigates how neoclassical flow and bootstrap current are modified in the edge pedestal of tokamaks due to nonlocal effects, using analytical and numerical methods that account for steep gradients and finite orbit widths.

Contribution

It introduces a combined analytical and numerical approach to evaluate nonlocal neoclassical effects on flow and current in the pedestal, extending beyond traditional local theories.

Findings

Parallel and poloidal flows deviate from local predictions with strong poloidal variation.

Bootstrap current estimates can be overestimated by conventional formulas near the plateau regime.

Ion contributions to currents are significantly modified in the pedestal regime.

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 delta-f (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 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-Schluter currents are also modified.