Residual zonal flows in tokamaks and stellarators at arbitrary wavelengths

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...

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Bibliographic Details
Published in:Plasma physics and controlled fusion 2016-04, Vol.58 (4), p.45018-45032
Main Authors: Monreal, Pedro, Calvo, Iván, Sánchez, Edilberto, Parra, Félix I, Bustos, Andrés, Könies, Axel, Kleiber , Ralf, Görler , Tobias
Format: Article
Language:English
Subjects:
CAS3D-K
Controlled fusion
EUTERPE
Genes
Mathematical analysis
Particle trajectories
Perturbation methods
residual
stellarator
Stellarators
tokamak
Tokamaks
Wavelengths
zonal flow
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Summary: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.
ISSN:0741-3335
1361-6587
DOI:10.1088/0741-3335/58/4/045018