In this work, a comparison of the global gyrokinetic codes EUTERPE and GENE-3D in stellarator configurations of the Large Helical Device (LHD) and the Wendelstein 7-X (W7-X) is carried out. In linear simulations with adiabatic electrons, excellent agreement is found in the mode numbers, growth rate, frequency, mode structure, and spatial localization of the most unstable mode in LHD. In W7-X, the dependence of the growth rate and frequency with the mode number is well reproduced by both codes. The codes are also compared in linear simulations with kinetic ions and electrons in W7-X using model profiles, and reasonable agreement is found in the wavenumber of the most unstable modes. A stabilization of small-scale modes in kinetic-electron simulations with respect to the adiabatic-electron case is consistently found in both codes. Nonlinear simulations using adiabatic electrons and model profiles are also studied and the heat fluxes are compared. Very good agreement is found in the turbulent ion heat fluxes in both LHD and W7-X. Two problems that cannot be properly accounted for in local flux tube codes are studied: the localization of instabilities and turbulence over the flux surface and the influence of a background long-wavelength electric field. Good agreement between codes is found with respect to the spatial localization of instabilities and turbulence over the flux surface. The localization of saturated turbulence is found in both codes to be much smaller than that of the linear instabilities and smaller than previously reported in full-surface radially-local simulations. The influence of the electric field on the localization is also found to be smaller in the developed turbulent sate that in the linear phase, and smaller than in previous works. A stabilizing effect of a constant electric field on the linearly unstable modes is found in both codes. A moderate reduction of turbulent transport by the radial electric field, with small dependence with the sign of the electric field, is also found.
Advances in stellarator gyrokinetics