Controlling Turbulence in Present and Future Stellarators

Turbulence is widely expected to limit the confinement and, thus, the overall performance of modern neoclassically optimized stellarators. We employ novel petaflop-scale gyrokinetic simulations to predict the distribution of turbulence fluctuations and the related transport scaling on entire stellarator magnetic surfaces and reveal striking differences to tokamaks. Using a stochastic global-search optimization method, we derive the first turbulence-optimized stellarator configuration stemming from an existing quasiomnigenous design.

Figure 1

Root-mean-squared electrostatic potential fluctuations caused by ion-temperature-gradient-driven turbulence in units of $T_i{\rho }^{*}/e$, where $T_i$ is the ion temperature, $e$ is the electron charge, and ${\rho }^{*}=1/125$ is the normalized ion gyroradius. The strongest fluctuations are contained in the red stripe on the outboard side of the surface. The resolution for the five-dimensional simulation box reads $({\widehat{L}}_r/N_r,{\widehat{L}}_y/N_y,{\widehat{L}}_z/N_z,{\widehat{L}}_v/N_v,{\widehat{L}}_{\mu }/N_{\mu })=(177/128,128/480,2\pi /128,3/64,9/8)$, where $r$, $y$, $z$ are the spatial (radial, binormal, parallel) dimensions, $v$ is the velocity parallel to the magnetic field, and $\mu$ is the magnetic moment. ${\widehat{L}}_r$ is the dimensionless length, and $N_r$ is the number of discretization points in the radial direction, etc. The normalized ion temperature gradient is $-a/T_{i}d{T}_i/dr=2$.

Figure 2

Ion-heat-flux scaling for different ${\rho }^{*}$ values from flux-surface gene simulations. Here $P_i$ is the ion pressure, $a$ is the minor radius of the torus, $r$ denotes the radial coordinate, $c_i$ is the ion sound speed, and ${\rho }_i$ is the ion gyroradius.

Figure 3

The turbulence-optimized MPX stellarator design. Shown is the magnetic field strength (tesla) over a magnetic surface. MPX is the first example of a quasiomnigenous stellarator, similar to W7-X, but with reduced turbulent transport. For this proof-of-principle configuration no attempt has been made to minimize the bootstrap current (which, however, takes acceptable values) or the alpha-particle losses.

Figure 4

The MPX configuration was produced during a stellopt run equipped with the Differential Evolution algorithm. The fluctuations in the cost function represent the stochastic evolution of the population and diminish as the algorithm converges. MPX was singled out before the collisional transport (not shown here) started to increase.

Figure 5

(a) Comparison of the ion-heat-flux scaling between MPX and W7-X with flux-surface gene simulations. (b) Comparison of the neoclassical confinement between MPX and W7-X over the plasma radius.

Figure 6

Comparison of the ion-heat-flux scaling between two W7-X configurations with different elongations. Similar to MPX, the less elongated configuration is associated with a weaker transport scaling.