Residual zonal flows in tokamaks and stellarators at arbitrary wavelengths

Abstract

In the linear collisionless limit, a zonal potential perturbation in a toroidal plasma relaxes, in general, to a non-zero residual value. Expressions for the residual value in tokamak and stellarator geometries, and for arbitrary wavelengths, are derived. These expressions involve averages over the lowest order particle trajectories, that typically cannot be evaluated analytically. In this work, an efficient numerical method for the evaluation of such expressions is reported. It is shown that this method is faster than direct gyrokinetic simulations performed with the GENE and EUTERPE codes. Calculations of the residual value in stellarators are provided for much shorter wavelengths than previously available in the literature. Electrons must be treated kinetically in stellarators because, unlike in tokamaks, kinetic electrons modify the residual value even at long wavelengths. This effect, that had already been predicted theoretically, is confirmed by gyrokinetic simulations.

31 pages, 15 figures

References in corpus (1)

• Less constrained omnigeneous stellarators

Cited by in corpus (15)

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• The Parallel Boundary Condition for Turbulence Simulations in Low Magnetic Shear Devices
• Impurity effects on residual zonal flow in deuterium (D)-tritium (T) plasmas
• Nonlinear gyrokinetic PIC simulations in stellarators with the code EUTERPE
• Semianalytical calculation of the zonal-flow oscillation frequency in stellarators
• Electrostatic gyrokinetic simulations in Wendelstein 7-X geometry: benchmark between the codes stella and GENE
• Effects of anisotropic energetic particles on zonal flow residual level
• Oscillatory relaxation of zonal flows in a multi-species stellarator plasma
• Comparison of local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators
• The residual flow in well-optimized stellarators
• Collisionless zonal-flow dynamics in quasisymmetric stellarators
• Electromagnetic zonal flow residual responses
• The zonal-flow residual does not tend to zero in the limit of small mirror ratio
• Near-axis quasi-isodynamic database
• Gyrokinetic simulations in stellarators using different computational domains