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Refined theory of tearing growth rates. Part 1. Plasma model without stability threshold

Published online by Cambridge University Press:  13 March 2009

W. Barbulla  and
E. Rebhan
W. Barbulla
Affiliation:
Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
E. Rebhan
Affiliation:
Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
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Abstract

In the theory of tearing modes analytical expressions for the growth rate y are only known for large y > 1/TR. However, since resistive instabilities cannot be externally stabilized, they will rather be observed at small growth rates, which are also the ones that matter in a bifurcation analysis. In this paper the described gap in the tearing theory is closed for the model of a convected resistivity in a sheet pinch. The analytical expressions obtained from an asymptotic perturbation analysis for small growth rates are as simple as those for large growth rates. However, they differ from them appreciably, and also show a marked difference between symmetric and asymmetric perturbations. Specifically, for asymmetric modes in contrast to the symmetric ones, no stability threshold exists, i.e. all asymmetric modes are at least weakly unstable. In addition to the results for small growth rates, an implicit analytical formula is presented that bridges the regime between small and large growth rates. The high quality of the analytical results is confirmed by numerical solution of the full tearing equations

Type
Research Article
Information
Journal of Plasma Physics , Volume 51 , Issue 1 , February 1994 , pp. 29 - 41
Copyright
Copyright © Cambridge University Press 1994

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References

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