Global gyrokinetic simulations with kinetic electrons of microturbulent transport in LHD and W7-X stellarators*

Global gyrokinetic simulations using the GTC code of the ion temperature gradient (ITG) and trapped electron mode (TEM) turbulence in LHD and W7-X are reported.This full flux-surface simulations with kinetic electrons only become feasible thanks to the GTC global field-aligned mesh in real space, which reduces the number of parallel grid points by a factor of 150. GTC simulations show that electrostatic ITG eigenmode structure is extended in the magnetic field direction but narrow in the perpendicular direction and peaks in bad curvature regions in both the LHD and W7-X. The ITG eigenmode structure is localized at the outer mid-plane in the LHD, similar to that in a tokamak but in the W7-X is strongly localized to some magnetic fieldlines at the corners of W7-X due to the mirror-like magnetic fields varying strongly in the toroidal direction. Nonlinear simualtions show that the main saturation mechanism for ITG is the self-generated zonal flows. For the TEM eigemode, LHD also exhibits similar characteristic to Tokamaks (localized on the outer mid-plane side where the curvature is bad). However, GTC code finds a new electrostatic helically trapped electron mode (HTEM) driven by a realistic density gradient in the W7-X. The HTEM is excited by helically trapped electrons at the toroidal section with a weak magnetic field. The linear eigenmode is localized to discrete field lines on the inner side of the torus where the curvature becomes unfavorable in the so-called 'straight' section in W7-X. Nonlinear simulations indicate that zonal flow play a secondary role in TEM and HTEM saturation. Finally, GTC simualtions of microturublence in LHD are validated using an LHD discharge.