J. H. E. Proll

Collisionless microinstabilities in stellarators. II. Numerical simulations

Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-J geometry) are partly resilient to trapped-particle instabilities, because fast-bouncing particles tend to extract energy from these modes near marginal stability. In reality, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here, the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with the National Compact Stellarator Experiment and the DIII-D tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, ion-temperature-gradient modes, trapped-electron modes, and mixed-type instabilities are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilizing in the energy budget. These results suggest that imperfectly optimized stellarators can retain most of the stabilizing properties predicted for perfect maximum-J configurations.

Gyrokinetic studies of trapped electron mode turbulence in the Helically Symmetric eXperiment stellarator

Gyrokinetic simulations of plasma microturbulence in the Helically Symmetric eXperiment are presented. Using plasma profiles relevant to experimental operation, four dominant drift wave regimes are observed in the ion wavenumber range, which are identified as different flavors of density-gradient-driven trapped electron modes. For the most part, the heat transport exhibits properties associated with turbulence driven by these types of modes. Additionally, long-wavelength, radially localized, nonlinearly excited coherent structures near the resonant central flux surface, not predicted by linear simulations, can further enhance flux levels. Integrated heat fluxes are compatible with experimental observations in the corresponding density gradient range. Despite low shearing rates, zonal flows are observed to regulate turbulence but can be overwhelmed at higher density gradients by the long-wavelength coherent structures.

Gyrokinetic TEM stability calculations for quasi-isodynamic stellarators

Recent theoretical findings suggest that in perfectly quasi-isodynamic stellarators, the trapped-particle instability as well as the ordinary electron-density-gradient-driven trapped-electron mode are stable in the electrostatic and collisionless approximation. In these configurations contours of constant magnetic field strength B are poloidally closed, the second adiabatic invariant J is constant on flux surfaces and peaks in the centre. It follows that the diamagnetic drift frequency ?*? and the bounce-averaged magnetic drift frequency are in opposite directions, 0, everywhere on the flux surface. This is the signature of average good curvature for trapped particles and, thanks to this property, particles that bounce faster than the frequency of any unstable mode must draw energy from it near marginal stability. Consequently, the point of marginal stability cannot exist for the collisionless trapped-particle mode, and hence this mode will be absent. By a similar argument, the ordinary trapped-electron mode is also stable. Because perfect quasi-isodynamicity can never be reached, it is necessary to test configurations approaching quasi-isodynamicity numerically in order to probe their resilience against trapped-particle modes. Progress has been made to extend gyrokinetic simulations to stellarator geometries, enabling us to perform the first linear gyrokinetic simulations of density-gradient-driven modes in stellarator configurations approaching quasi-isodynamicity, such as Wendelstein 7-X and more recently found configurations. These simulations appear to confirm the analytical predictions.