Boundary turbulence simulations of the optimized HSX stellarator and comparison with experiments

We present the first-ever full-$f$, three-dimensional, two-fluid simulation of plasma turbulence based on the drift-reduced Braginskii equations in the optimized HSX stellarator in its quasi-helical configuration. The simulation is carried out by using the \texttt{GBS} code, adapted to simulate 3D magnetic fields with large torsion and ellipticity. The simulation results are compared with edge measurements performed by \textit{Guttenfelder et al.} (2009) using Langmuir probes and Thomson scattering. The comparison shows good agreement in time-averaged density, electron temperature, and electrostatic potential profiles. A good match is also observed in turbulent properties, namely in the frequency spectra of fluctuations and in spatial correlation measurements. Field-aligned turbulence is found to be curvature driven and developing at finite $k_\parallel$, as proposed in a quasi-linear theory by \textit{Rafiq et al.} (2010). Frequency spectra of $E\times B$ turbulent transport is consistent with experimental results. Fluctuations levels are underestimated by the simulation. For the first time in stellarator edge turbulent modelling, the effective transport coefficients in the HSX edge are provided.