Search

We present a stellarator configuration optimized for a large threshold ('critical gradient') for the onset of the ion temperature gradient (ITG) driven mode, which achieves the largest critical gradient we have seen in any stellarator. Above this threshold, gyrokinetic simulations show that the configuration has low turbulence levels over an experimentally relevant range of the drive strength. The applied optimization seeks to maximize the drift curvature, leading to enhanced local-shear stabilization of toroidal ITG modes, and the associated turbulence. These benefits are combined with excellent quasi-symmetry, yielding low neoclassical transport and vanishingly small alpha particle losses. Analysis of the resulting configuration suggests a trade-off between magnetohydrodynamic (MHD) and ITG stability, as the new configuration possesses a vacuum magnetic hill. [ABSTRACT FROM AUTHOR]

First experimental observations in the Wendelstein 7-X stellarator indicate that the impurity confinement can be explained by turbulent processes. In particular, plasma discharges with increased ion to electron temperature ratio are accompanied by reduced electron density fluctuation amplitudes and anomalous impurity diffusion, suggesting a lower turbulent transport. Employing gyro-kinetic numerical simulations, we argue that the temperature ratio plays a key role for reducing the ion temperature gradient instability in Wendelstein 7-X, leading to an enhanced impurity confinement. [ABSTRACT FROM AUTHOR]

We study the effect of turbulent transport in different magnetic configurations of the Weldenstein 7-X stellarator. In particular, we performed direct numerical simulations with the global gyrokinetic code GENE-3D, modeling the behavior of Ion Temperature Gradient turbulence in the Standard, High-Mirror and Low-Mirror configurations of W7-X. We found that the Low-Mirror configuration produces more transport than both the High-Mirror and the Standard configurations. By comparison with radially local simulations, we have demonstrated the importance of performing global non-linear simulations to predict the turbulent fluxes quantitatively. [ABSTRACT FROM AUTHOR]

A non-perturbative analysis for the study non-axisymmetric (3D) effects on the linear ion-temperature-gradient driven mode is introduced. Perturbations and equilibria are considered to be global on the flux surface, yet radially local. The analysis is valid for systems arbitrarily far from axisymmetry. It is found that finite Larmor radius effects can suppress the global (on the surface) instability, in analogy with the local analysis but shift its poloidal location from the position of the greatest local instability. Fourier spectra of the instability whose width grow for increasingly non-axisymmetric systems are predicted. Results are in qualitative agreement with numerical global (on the surface) gyrokinetic simulations. [ABSTRACT FROM AUTHOR]

Turbulence induced by the ion temperature gradient (ITG) is investigated in the helical and axisymmetric plasma states of a reversed field pinch device by means of gyrokinetic calculations. The two magnetic configurations are systematically compared, both linearly and nonlinearly, in order to evaluate the impact of the geometry on the instability and its ensuing transport, as well as on the production of zonal flows. Despite its enhanced confinement, the high-current helical state demonstrates a lower ITG stability threshold compared to the axisymmetric state, and ITG turbulence is expected to become an important contributor to the total heat transport. [ABSTRACT FROM AUTHOR]

We investigate the linear theory of the ion-temperature-gradient (ITG) mode, with the goal of developing a general understanding that may be applied to stellarators. We highlight the Wendelstein 7X (W7-X) device. Simple fluid and kinetic models that follow closely from existing literature are reviewed and two new first-principle models are presented and compared with results from direct numerical simulation. One model investigates the effect of regions of strong localized shear, which are generic to stellarator equilibria. These "shear spikes" are found to have a potentially significant stabilizing affect on the mode; however, the effect is strongest at short wavelengths perpendicular to the magnetic field, and it is found to be significant only for the fastest growing modes in W7-X. A second model investigates the long-wavelength limit for the case of negligible global magnetic shear. The analytic calculation reveals that the effect of the curvature drive enters at second order in the drift frequency, confirming conventional wisdom that the ITG mode is slab-like at long wavelengths. Using flux tube simulations of a zero-shear W7-X configuration, we observe a close relationship to an axisymmetric configuration at a similar parameter point. It is concluded that scale lengths of the equilibrium gradients constitute a good parameter space to characterize the ITG mode. Thus, to optimize the magnetic geometry for ITG mode stability, it may be fruitful to focus on local parameters, such as the magnitude of bad curvature, connection length, and local shear at locations of bad curvature (where the ITG mode amplitude peaks). [ABSTRACT FROM AUTHOR]

The threshold for the resonant destabilisation of ion-temperature-gradient (ITG) driven instabilities that render the modes ubiquitous in both tokamaks and stellarators is investigated. We discover remarkably similar results for both confinement concepts if care is taken in the analysis of the effect of the global shear ${\hat{s}}$. We revisit, analytically and by means of gyrokinetic simulations, accepted tokamak results and discover inadequacies of some aspects of their theoretical interpretation. In particular, for standard tokamak configurations, we find that global shear effects on the critical gradient cannot be attributed to the wave–particle resonance destabilising mechanism of Hahm & Tang (Phys. Plasmas, vol. 1, 1989, pp. 1185–1192), but are consistent with a stabilising contribution predicted by Biglari et al. (Phys. Plasmas, vol. 1, 1989, pp. 109–118). Extensive analytical and numerical investigations show that virtually no previous tokamak theoretical predictions capture the temperature dependence of the mode frequency at marginality, thus leading to incorrect instability thresholds. In the asymptotic limit ${\hat{s}}\unicode[STIX]{x1D704}\ll 1$, where $\unicode[STIX]{x1D704}$ is the rotational transform, and such a threshold should be solely determined by the resonant toroidal branch of the ITG mode, we discover a family of unstable solutions below the previously known threshold of instability. This is true for a tokamak case described by a local ${\hat{s}}-\unicode[STIX]{x1D6FC}$ local equilibrium, and for the stellarator Wendelstein 7-X, where these unstable solutions are present even for configurations with a small trapped-particle population. We conjecture they are of the Floquet type and derive their properties from the Fourier analysis of toroidal drift modes of Connor & Taylor (Phys. Fluids, vol. 30, 1987, pp. 3180–3185), and to Hill’s theory of the motion of the lunar perigee (Acta Math., vol. 8, 1886, pp. 1–36). The temperature dependence of the newly determined threshold is given for both confinement concepts. In the first case, the new temperature-gradient threshold is found to be rather insensitive to the temperature ratio $T_{i}/T_{e}$, at least for $T_{i}/T_{e}\lesssim 1$, and to be a growing function of the density gradient scale for $T_{i}/T_{e}\gtrsim 1$. For Wendelstein 7-X, the new critical temperature gradient is a growing function of the temperature ratio. The importance of these findings for the assessment of turbulence in stellarators and low-shear tokamak configurations is discussed. [ABSTRACT FROM AUTHOR]