Stellarators Resist Turbulent Transport on the Electron Larmor Scale

Electron temperature gradient (ETG)-driven turbulence, despite its ultrafine scale, is thought to drive significant thermal losses in magnetic fusion devices—but what role does it play in stellarators? The first numerical simulations of ETG turbulence for the Wendelstein 7-X stellarator, together with power balance analysis from its initial experimental operation phase, suggest that the associated transport should be negligible compared to other channels. The effect, we argue, originates essentially from the geometric constraint of multiple field periods, a generic feature of stellarators.

Figure 1

Density and temperature profiles (left column) with associated gradients (middle and right columns, bottom) and electron thermal diffusivities, for a W7-X OP1.1 discharge, versus normalized radial coordinate; here $n_i\approx n_e$ is assumed, neglecting impurity density. The hydrogen plasma was ECRH-heated by three gyrotrons with a total power of 2 MW. Electron heat diffusivities (middle and right columns, top) from power balance analysis (${\chi }_e^{\mathrm{eff}}$) and gyrokinetic simulations (${\chi }_e^{\mathrm{gk}}$) are presented for comparison. The electron density, electron temperature, and ion temperature were measured by Thomsen scattering, ECE radiometry, and an XICS diagnostic, respectively, assuming equal argon and hydrogen ion temperatures [20].

Figure 2

Comparison of heat fluxes from gene simulations; ${\rho }_s$ is the ion gyroradius, $c_s$ the sound speed, $P$ the ion pressure, and $a$ the minor radius. The heat flux caused by electron-scale turbulence for the W7-X stellarator (W7-X:ETG) and the negative-shear tokamak ($\mathrm{TO}\mathrm{K}-:\mathrm{ETG}$) are compared to the heat flux caused by equally driven ion-scale turbulence (W7-X:ITG), i.e., $a/L_{T_{i,e}}=3$.

Figure 3

Mode variation along the magnetic field line for linear modes in the positive-shear tokamak ($\mathrm{TOK}+$), the negative-shear tokamak ($\mathrm{TO}\mathrm{K}-$), and the stellarator (W7-X). For each case, the wave number chosen corresponds to the peak of the nonlinear heat flux spectrum.

Figure 4

Density fluctuations from gene simulations of electron-scale turbulence plotted in the plane perpendicular to the magnetic field. (a) The positive-shear tokamak ($\mathrm{TOK}+$), (b) the negative-shear tokamak ($\mathrm{TO}\mathrm{K}-$), and (c) the stellarator Wendelstein-7X are compared. Here, $x$ denotes the radial coordinate and $y$ the binormal coordinate.

Figure 5

Fluctuation spectra for electron-scale turbulence compared against power laws. The negative-shear tokamak ($\mathrm{TO}\mathrm{K}-$) and W7-X configurations are compared with $k_y^{-8/3}$, which is slightly steeper than the slab limit $k_y^{-7/3}$, while the positive-shear tokamak ($\mathrm{TOK}+$) matches the theoretical law $k_y^{-11/3}$, corresponding to two-dimensional (toroidal) turbulence. Note that these power laws apply for wave numbers larger than the injection scale and less than $k_y{\rho }_e=1$ (vertical line).