Local magnetic shear and drift waves in stellarators

Abstract

A study of the effect of local magnetic shear on the drift wave stability is presented. The eigenvalue problem for the drift wave equation is solved numerically in fully three-dimensional stellarator plasma using the ballooning mode formalism. It is found that negative local magnetic shear has a stabilizing effect on the drift wave instability and positive local shear is destabilizing. This is in agreement with the effect of negative global magnetic shear in tokamaks and also agrees with the simple estimates. As a consequence the highly unstable modes found on a specific magnetic surface are localized in the region of positive local magnetic shear.

Gyrokinetic simulations of microinstabilities in stellarator geometry

“…Therefore, both the normal curvature and the local magnetic shear favor a more unstable mode in the case of ( t , h ) = (0.1, 0.12) than for the case of ( t , h ) = (0.1, 0.0), in agreement with Fig.11. The detrimental influence of a large, positive local magnetic shear on drift wave stability in realistic 3D stellararator geometries has been noted by Nadeem and co-workers [22]; these authors also discuss the case of large, negative local magnetic shear which appears to have a stabilizing influence on the drift mode. This is in agreement with our observations, although the MHD model equilibrium used here is far simpler than the fully 3D stellarator equilibrium used in the work of Nadeem et al…”

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

“…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].…”

Resistive Drift Waves in a Bumpy Torus

“…Note that in the case of Figure 9 the bulk of the drift mode amplitude experiences a positive global shear away from the θ = 0; therefore, we expect the linear growth rate to be larger for the case of Figure 9 as compared to the case of Figure 8. The detrimental influence of a large, positive local magnetic shear on drift wave stability in realistic 3D stellararator geometries has been noted by Nadeem and co-workers [8]; these authors also discuss the case of large, negative local magnetic shear which appears to have a stabilizing influence on the drift mode. This is in agreement with our observations, although our model equilibrium is far simpler than the fully 3D stellarator equilibrium used in the work of Nadeem et al…”

“…Drift waves represent a special class of gradient instabilities which are driven unstable by a source of free energy in the density and/or temperature gradients. In order to determine the linear properties of drift waves (and other drift-type modes satisfying k || /k ⊥ 1, where k || and k ⊥ are the parallel and perpendicular wavevectors, respectively) in toroidal geometry, the model equations can be solved using the ballooning representation of Connor et al [2] as an eigenvalue [8] or as initial-value problem [7] for a set of representative field lines. Although some understanding of the drift wave dynamics can be gained using the so-called iδ model (for which the parameter δ is used as a tuning parameter for the drive of the instability), more realistic models usually require the solution of two or more coupled partial differential equations to be solved on a given field line.…”