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Kinetic ion gradient instability: bifurcation properties of a simple, kinetic ηi-unstable slab model

Published online by Cambridge University Press:  29 May 2001

O. SIEKS
Affiliation:
Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
K. H. SPATSCHEK
Affiliation:
Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany

Extract

The so-called ηi instability is driven by the ion-temperature gradient and affects both particle and energy transport. Using a simple kinetic model, first the onset of the instability is investigated by linear theory. In contrast to most treatments in the literature, a non-local analysis is performed. It turns out that the local approximation is only a very rough approximation, and may drastically overestimate the instability conditions. A numerical solution of the full model confirms the non-local stability analysis. In addition, it allows one to follow the nonlinear development of the instability. Using a numerical scheme based on the Lagrange structure of the equations of motion, the saturation values are obtained. A constriction of the density profile is accompanied by a broadening of the ion-temperature profile. The normal form of the bifurcation is obtained, together with the scaling of the anomalous transport (in terms of the deviation from the marginal condition).

Type
Research Article
Copyright
© 2000 Cambridge University Press

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