Turbulence Mechanisms of Enhanced Performance Stellarator Plasmas

We theoretically assess two mechanisms thought to be responsible for the enhanced performance observed in plasma discharges of the Wendelstein 7-X stellarator experiment fueled by pellet injection. The effects of the ambipolar radial electric field and the electron density peaking on the turbulent ion heat transport are separately evaluated using large-scale gyrokinetic simulations. The essential role of the stellarator magnetic geometry is demonstrated, by comparison with a tokamak.

Figure 1

Time traces of the W7-X program 20181016.037 for heating power ($P$), electron density ($n_e$), electron and ion temperatures ($T_e$, $T_i$), and diamagnetic energy ($W_{\mathrm{dia}}$). In the bottom panel, the normalized gradients and radial electric field for the ECR and PEP phases, derived from dkes calculations, are shown. The black line marks the radial location where the simulations are conducted.

Figure 2

Comparison of simulated ion heat diffusivities for the ECR and PEP phases of the W7-X pellet discharge, and an artificial case ($E_r=0$), isolating the role of the radial electric field ($a/L_{n_e}=0$). The Mach number for the ECR and PEP phases is 0.8% and 2%, respectively. The discretization of the five-dimensional computational box reads $(n_x,n_y,n_z,n_{v_{\parallel }},n_{\mu })=64\times 64\times 102\times 30\times 8$. The size of the computational domain in the radial and binormal directions is $L_x=L_y=125$ in units of ${\rho }_s=c_s/a$, with $c_s$ the ion sound speed, and for the parallel direction is $L_z=2\pi a$. The extent for the parallel velocity is $-3\le v_{\parallel }\le 3$ in units of ion thermal velocity, and for the magnetic moment $0\le \mu \le 9T_i/B_0$. Here, $B_0=2{\mathrm{\Phi }}_0/a^2$, where ${\mathrm{\Phi }}_0$ is the toroidal magnetic flux within the last closed flux surface. Also shown are the experimental diffusivities [ECR(exp), PEP(exp)] for the corresponding phases of the discharge (the error bars reflect uncertainties in the measured profiles).

Figure 3

Time-averaged density fluctuations on the magnetic surface of the W7-X stellarator from the simulations corresponding to Fig. 2 (rescaled with respect to their individual maximum value to facilitate inspection). The magnetic field line $a=0$ is shown in black.

Figure 4

Comparison of simulated ion heat diffusivities for the ECR and PEP phases of the W7-X pellet discharge, isolating the role of the density peaking ($E_r=0$). The time-averaged diffusivities for the two phases along the magnetic field line are found in the inset. Also shown are the experimental diffusivities [ECR(exp), PEP(exp)] for the corresponding phases (the error bars reflect uncertainties in the measured profiles). In the bottom panel, the real frequency ($\omega$) and growth rate ($\gamma$) spectra for various linear modes, related to the experimental conditions, are displayed. The ITG mode characterizes the ECR phase, while the ITEM the PEP phase. Both modes propagate in the ion diamagnetic direction ($\omega >0$). The TEM, on the other hand, driven by the density gradient alone, propagates in the electron diamagnetic direction.

Figure 5

Comparison of simulated ion heat diffusivities for a tokamak configuration, applying parameters similar to the two phases of the W7-X pellet discharge. In the bottom panel, the real frequency ($\omega$) and growth rate ($\gamma$) spectra for the linear modes are shown (see Fig. 4 for details).