Erratum: Available Energy of Trapped Electrons and Its Relation to Turbulent Transport [Phys. Rev. Lett. 128, 175001 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.128.175001.

Enhanced Transport at High Plasma Pressure and Subthreshold Kinetic Ballooning Modes in Wendelstein 7-X.

High-performance fusion plasmas, requiring high pressure ß, are not well understood in stellarator-type experiments. Here, the effect of ß on ion-temperature-gradient-driven (ITG) turbulence is studied in Wendelstein 7-X (W7-X), showing that subdominant kinetic ballooning modes (KBMs) are unstable well below the ideal MHD threshold and get strongly excited in the turbulence. By zonal-flow erosion, these subthreshold KBMs (stKBMs) affect ITG saturation and enable higher heat fluxes. Controlling stKBMs will be essential to allow W7-X and future stellarators to achieve maximum performance.

Available Energy of Trapped Electrons and Its Relation to Turbulent Transport.

Any collisionless plasma possesses some "available energy" (AE), defined as that part of the thermal energy that can be converted into instabilities and turbulence. Here, we present a calculation of the AE carried by magnetically trapped electrons in a flux tube of collisionless plasma. The AE is compared with nonlinear simulations of the energy flux resulting from collisionless turbulence driven by trapped-electron modes in various magnetic geometries. The numerical calculation of AE is rapid and shows a strong correlation with the simulated energy fluxes, which can be expressed as a power law and understood in terms of a simple model.

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.

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.

Resilience of quasi-isodynamic stellarators against trapped-particle instabilities.

It is shown that in perfectly quasi-isodynamic stellarators, trapped particles with a bounce frequency much higher than the frequency of the instability are stabilizing in the electrostatic and collisionless limit. The collisionless trapped-particle instability is therefore stable as well as the ordinary electron-density-gradient-driven trapped-electron mode. This result follows from the energy balance of electrostatic instabilities and is thus independent of all other details of the magnetic geometry.