Difference in Neoclassical Edge Flows Between Strongly Negative and Positive Triangularities in the XGC Gyrokinetic Simulation

TL;DR

The paper analyzes edge neoclassical flows in strongly negative triangularity (NT) versus a manufactured positive triangularity (PT) edge equilibrium for a DIII-D-like discharge using the edge-focused gyrokinetic code XGC. By mirroring the NT equilibrium to create PT with matched profiles, the authors isolate the effect of triangularity sign and quantify the impact of X-point ion orbit loss and Pfirsch-Schluter flows on edge toroidal rotation, including carbon impurities self-consistently. Neoclassical simulations reproduce NT carbon rotation reasonably well in the mid-pedestal but fail near the separatrix, indicating that edge turbulence must be included to capture far-edge behavior. The results provide a neoclassical baseline for NT vs PT and motivate future multiphysics studies that couple turbulence with edge kinetic effects in negative triangularity plasmas.

Abstract

The neoclassical baseline study of a strongly negative triangularity (NT) plasma and the corresponding positive triangularity plasma is performed using the edge-specialized, total-f gyrokinetic code XGC. A DIII-D-like plasma is used, based on the negative triangularity discharge of DIII-D \#193793. An artificial positive triangularity (PT) equilibrium has been constructed to compare the edge rotation physics at the same triangularity strength, but with opposite sign, while keeping the same elongation and other geometric parameters. Carbon(+6) ions are added to the deuterium plasma at an experimentally relevant level. By using the experimental profile of carbon toroidal rotation profile as an input, XGC finds that the deuteron rotation is significantly different from the carbon rotation at the inboard and outboard midplanes, mostly caused by the difference in the Pfirsch-Schluter rotation. More importantly, significant difference in the X-point orbit loss physics, thus the rotation source, is found between the positive and negative triangularity equilibrium models. However, it is also found that the agreement between the present neoclassical simulation and the experimental NT data is validated only within the middle of pedestal slope, indicating the importance of edge turbulence. This study could establish baseline for the multiphysics, multiscale studies that include turbulence of negative triangularity plasmas.

Figures (7)

• Figure 1: (a) poloidal flux, (b) pressure, (c) safety factor, (d) pressure gradient (P'), and (e) the product of poloidal current function and its derivative (FF') from Grad-Shafranov equation of NT (black) and PT (red).
• Figure 2: Initial profiles of density (top), temperature (middle), and toroidal rotation (bottom). Carbon density is multiplied by the charge number, 6. Initial temperature of deuterium and carbon are identical. The toroidal rotations are identical for all species.
• Figure 3: Toroidal flow ($u_\phi$) structure from test particle simulations of PT (left) and NT (right) plasmas without electric field. The color represents the direction and magnitude of toroidal flow, with red indicating positive toroidal (co-current) flow and blue indicating negative toroidal (counter-current) flow. The far scrape-off-layer is not displayed for better visualization. The curved arrows illustrate cartoon picture of ion particle trajectories projected to the poloidal planes accounting for the parallel motion and the $\nabla B$ drift ($V_{\nabla B}$). Particles with opposite parallel direction to the direction of cartoon trajectory on the side of strong flux surface curvature have a higher probability of being lost. The magnitude of the curvature determines how large the radial component of the $\nabla B$ drift is on the above or below the midplane. $\psi$ is the poloidal flux.
• Figure 4: Velocity space hole from the test particles simulations without radial E-field. Top (bottom) graphs are from negative (positive) triangularity. Left (right) graphs are measured at high (low) field side midplane with $\psi_N$ = 0.985. $v_0$ is thermal velocity with flat 2 keV profile, which is for better visualization. The wiggles are from particle noises and limited resolution of velocity space grid, 33 by 31
• Figure 5: Toroidal flow of deuterium (solid lines) and carbon impurities (dashed lines) at the low-field-side midplane (top) and high-field-side midplane (bottom) from neoclassical simulations of PT (blue) and NT (orange) geometries. Black dash dot line in the top figure represent experimental measurements of carbon impurities.