Unstable ion-temperature-gradient modes in the Wendelstein 7-X stellarator configuration

Abstract

The linear stability of the ion-temperature-gradient modes (ITG) in the electrostatic limit is examined in the short wavelength region by using a two fluid reactive model in fully three-dimensional Wendelstein 7-X (W7-X) stellarator [G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] geometry. The spectrum of stable and unstable modes and their real frequencies and eigenfunctions are calculated. The effects of density gradients, temperature gradients, temperature ratios, wavevector, ballooning angle, curvature and local magnetic shear on the ITG mode are also investigated. The frequency and growth rate of the most unstable ITG mode is calculated and visualized for a specific magnetic flux surface. For the equilibrium under investigation both localized and extended eigenmodes are found. The effect of small and large temperature ratios, small and large density gradients as well as large local magnetic shear are all found to be stabilizing. The highest growth rates are found at the outer part of the surface where the local magnetic shear is small and normal curvature is unfavorable.

Turbulent transport in the scrape-off layer of Wendelstein 7-X

“…While the normal curvature in W7-X has strong, fine-scale variations along a magnetic flux tube [14,28], previous work has indicated that due to the fast dynamics parallel to the ambient magnetic field, the averaged normal curvature along a field line dominates the formation and behaviour of turbulent filaments [14,29]. Since the magnetic configurations of W7-X considered here mostly differ with respect to the rotational transform, the magnetic curvature profile along a field line starting from the probe does not change more than a few % between configurations.…”

Spatial structure of drift-wave turbulence and transport in a stellarator

“…This suggests the stabilizing role of local magnetic shear described in Refs. [15,14]. Comparing Fig.…”

“…Especially in complex stellarator configurations, the local properties of the magnetic field, like curvatures and field-line shear, have to be included into the models in order to describe the structure and dynamics of turbulence appropriately. Different approaches like a ballooning-mode formalism [6,7,8,9,10,11], a full three-dimensional analysis of unstable modes on a flux surface [12,13,14,15] and non-linear fluid [16,17,18] or gyrokinetic [19,4,20,21] simulations point to significant effects of the local magnetic field geometry on the spatial structure and the stability of drift modes. Theoretical studies indicate that turbulent transport can be reduced by more than a factor of 2 if an appropriate shaping procedure considering local magnetic field properties is applied [22].…”

Gyrokinetic global electrostatic ion-temperature-gradient modes in finite β equilibria of Wendelstein 7-X

“…There are numerous studies of ITG instabilities for tokamaks and a few for stellarators (see, e.g. [10,11]), using fluid or gyrokinetic approaches based on the ballooning approximation. While the ballooning approximation offers a computationally fast and easy way to gain some insight into the dependence of the growth rate on physical parameters and to extend the physical set of equations, it is, nevertheless, only a local calculation performed for each field line which (in its simplest form) gives only very restricted information on the real spatial structure of a mode.…”