TITLE

The role of curvature and stretching on the existence of fast dynamo plasma in Riemannian space

AUTHOR(S)
Garcia de Andrade, L. C.
PUB. DATE
December 2008
SOURCE
Physics of Plasmas;Dec2008, Vol. 15 Issue 12, p122106
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Vishik’s anti-dynamo theorem is applied to a nonstretched twisted magnetic flux tube in Riemannian space. Marginal or slow dynamos along curved (folded), torsioned (twisted), and nonstretching flux tubes plasma flows are obtained. Riemannian curvature of the twisted magnetic flux tube is computed in terms of the Frenet curvature in the thin tube limit. It is shown that, for nonstretched filaments, fast dynamo action in the diffusive case cannot be obtained, in agreement with Vishik’s argument that fast dynamos cannot be obtained in nonstretched flows. Instead of a fast dynamo, a nonuniform stretching slow dynamo is obtained. An example is given, which generalizes plasma dynamo laminar flows, recently presented by Wang et al. [Phys Plasmas 9, 1491 (2002)], in the case of low magnetic Reynolds number Rem>=210. Curved and twisting Riemannian heliotrons, where nondynamo modes are found even when stretching is present, shows that the simple presence of stretching is not enough for the existence of dynamo action. In this paper, folding plays the role of Riemannian curvature and can be used to cancel magnetic fields, not enhancing the dynamo action. Nondynamo modes are found for certain values of torsion, or Frenet curvature (folding) in the spirit of the anti-dynamo theorem. It is also shown that curvature and stretching are fundamental for the existence of fast dynamos in plasmas.
ACCESSION #
35982554

 

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