Impact of Magnetic Field Configuration on Heat Transport in Stellarators and Heliotrons

We assess the magnetic field configuration in modern fusion devices by comparing experiments with the same heating power, between a stellarator and a heliotron. The key role of turbulence is evident in the optimized stellarator, while neoclassical processes largely determine the transport in the heliotron device. Gyrokinetic simulations elucidate the underlying mechanisms promoting stronger ion scale turbulence in the stellarator. Similar plasma performances in these experiments suggests that neoclassical and turbulent transport should both be optimized in next step reactor designs.

Figure 1

(Left) The large helical device is a heliotron, featuring an elliptic plasma cross section that rotates around the torus for a total of 10 field periods, with major radius $R=3.6\mathrm{m}$ and aspect ratio $A=5.5$. (Right) The Wendelstein 7-X (W7-X) stellarator has a helical plasma axis with a varying cross section in the toroidal direction for a total of 5 field periods, with major radius $R=5.5\mathrm{m}$ and aspect ratio $A=10$. The plasma volume in both configurations measures approximately 30 cubic meters.

Figure 2

Rotational transform $\iota /2\pi$ (left) and effective helical ripple ${\epsilon }_{\mathrm{eff}}$ (right) along the plasma radius, for the W7-X stellarator in its standard vacuum configuration and the LHD heliotron in its inward shifted vacuum configuration.

Figure 3

Profiles of electron density $n_e$, electron temperature $T_e$, ion temperature $T_i$, and absorbed ECR heating power along the plasma radius for the LHD experiment No. 152264 at $t=4.47\mathrm{s}\text{ec}$ and the W7-X program No. 20180821.017 at $t=4.30\mathrm{s}\text{ec}$. $T_e$ and $n_e$ were measured with Thomson scattering diagnostics [20, 21]. In LHD, $n_e$ was also measured using a multichannel far infrared interferometer system [22]. $T_i$ and the radial electric field $E_r$ in LHD were measured with active charge exchange recombination spectroscopy (CXRS), using short 20 ms blips of perpendicular neutral beam injection [23]. In W7-X, $T_i$ was also measured with a CXRS system [24].

Figure 4

Experimental (dashed dotted lines) and neoclassical (solid lines) ion heat conductivities for W7-X (left) and LHD (middle), and anomalous heat conductivities (diamonds, right), as extracted from the power balance analysis. The squares (right) correspond to the simulated values of the heat transport. The experimental heat conductivities (dashed dotted lines) are repeated in the right panel for comparison. The shaded areas reflect uncertainties stemming from the error bars of the plasma profiles.

Figure 5

Ion heat fluxes, normalized to gyroBohm units $Q_{GB}={\rho }_s^2{c}_s{P}_i/a^2$, inferred from turbulence simulations for W7-X and LHD, according to the measured profiles ($P_i$ is the ion pressure, $a$ is the minor radius, ${\rho }_s=c_s/{\mathrm{\Omega }}_i$ is the ion gyroradius, $c_s=\sqrt{T_i/m_i}$ is the ion sound speed, ${\mathrm{\Omega }}_i=qB/m_{i}c$ is the ion gyrofrequency, $B$ is the magnetic field, $q$ is the ion charge and $m_i$ is the ion mass). The inset figure shows the growth rates of the ITG instability as a function of the binormal wave number normalized to the ion gyroradius.

Figure 6

Ion heat fluxes, normalized to gyroBohm units (for definitions, see Fig. 5), inferred from turbulence simulations for W7-X and LHD. For the ITG simulations, we have used the same normalized ion temperature gradient $a/L_{T_i}=3$ and adiabatic electrons, whereas for the ETG simulations, we have used the same electron temperature gradient $a/L_{T_e}=3$ and adiabatic ions. For all simulations, $a/L_n=0$ and $T_e/T_i=1$ is assumed.