Kinetic Neoclassical Transport in the H-mode Pedestal*

This paper presents the first quantitative comparison between the multi-species transport rates in H-mode pedestals on DIII-D and NSTX and the kinetic neoclassical transport calculated using XGC0, a full-f particle-in-cell drift-kinetic solver with self-consistent neutral recycling and sheath potentials. The best quantitative agreement between the simulation and measurement of the pedestal density, temperature and flow profiles during the ELM-free period following the L-H transition is achieved when assuming ion transport is reduced to the kinetic neoclassical level within the steep-gradient region while additional turbulent transport ($D \sim 0.5\,$m$^2$/s) exists in regions of low $E_r\times B$ shear such as the pedestal top and in the scrape-off layer (SOL). The non-Maxwellian ion distributions from kinetic effects lead to a co-$I_p$ intrinsic torque that matches the measurements in the pedestal on DIII-D. The kinetic neoclassical mean $E_r\times B$ shear is strongly dependent on the plasma boundary shape, and the predicted dependence of L-H transition conditions versus X-point radius is consistent with experiments on NSTX. In QH-modes on DIII-D, $T_i$ is larger than in the early ELM-free H-modes, and the drift-kinetic effects that are absent in fluid models become more pronounced. The ion distributions are calculated to be non-Maxwellian through the entire pedestal, driving $T_i$ anisotropy, poloidal asymmetries and intrinsic flows. For example, $T_i^{\perp} > T_i^{||}$ in the pedestal, consistent with the orthogonal measurements of $T_i^{C6+}$. Also, the observation that $T_i^{C6+} \geq T_{i,ped}$ in the far-SOL is reproduced in the simulations and attributed to long-lived collisionless ion orbits at low SOL densities. These studies indicate that kinetic neoclassical transport will play an important role in the L-H transition, H-mode transport and interpretation of measurements in the high-$T_i$ pedestals expected in ITER.