Turbulent Origin of the Edge Radial Electric Field Asymmetry between Favourable and Unfavourable Drift Configurations

We study the influence of the ion magnetic-drift direction relative to the active X-point (favourable and unfavourable configurations) on edge turbulence, transport, and the radial electric field $E_r$ in ASDEX Upgrade and TCV. First-principles gyrokinetic simulations of the edge and scrape-off layer are performed in diverted X-point geometry using the spectral full-$f$ GENE-X code. Two matched pairs of L-mode discharges are simulated and validated against the available measurements in all four cases, showing good agreement, in particular for the $E_r$ profiles. A radial force-balance analysis shows that the deeper $E_r$ well in the favourable configuration is determined by the larger poloidal ion flow near the separatrix, which cannot be reproduced by neoclassical solvers and is identified in axisymmetric simulations as turbulence-driven. We then derive an exact evolution equation for the mean poloidal-flow acceleration from the full-$f$ gyrokinetic vorticity equation, which identifies the radial gradient of the total velocity stress as its nonlinear drive. The observed asymmetry is found to arise from stronger nonlinear energy transfer into the mean flow in the favourable configuration, associated with enhanced nonlinear $E\times B$ advection of vorticity near the separatrix and X-point. Flux-driven TCV simulations further show that the asymmetry persists at matched power more than six times the L-mode value. Assuming a critical $E_r$ at the L-H transition, this yields an estimated ratio of approximately 1.7 between the unfavourable and favourable L-H power thresholds, close to the experimental factor of two. Overall, the unfavourable configuration exhibits larger fluctuation amplitudes, a weaker $E_r$ well, stronger geodesic acoustic modes, and shorter energy confinement times for the same profiles, which may explain the observed difference in access to high-confinement regimes.