The role of curvature and stretching on the existence of fast dynamo plasma in Riemannian space
Abstract
Vishik's antidynamo 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 Re{sub m}{>=}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 antidynamomore »
 Authors:
 Departamento de Fisica TeoricaIFUniversidade do Estado do Rio de JaneiroUERJ, Rua Sao Francisco Xavier, 524 Cep 20550003, Maracana, Rio de Janeiro, RJ (Brazil)
 Publication Date:
 OSTI Identifier:
 21259700
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 15; Journal Issue: 12; Other Information: DOI: 10.1063/1.3041158; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 58 GEOSCIENCES; HELIOTRON; LAMINAR FLOW; MAGNETIC FLUX; PLASMA; RIEMANN SPACE
Citation Formats
Garcia de Andrade, L. C. The role of curvature and stretching on the existence of fast dynamo plasma in Riemannian space. United States: N. p., 2008.
Web. doi:10.1063/1.3041158.
Garcia de Andrade, L. C. The role of curvature and stretching on the existence of fast dynamo plasma in Riemannian space. United States. doi:10.1063/1.3041158.
Garcia de Andrade, L. C. 2008.
"The role of curvature and stretching on the existence of fast dynamo plasma in Riemannian space". United States.
doi:10.1063/1.3041158.
@article{osti_21259700,
title = {The role of curvature and stretching on the existence of fast dynamo plasma in Riemannian space},
author = {Garcia de Andrade, L. C.},
abstractNote = {Vishik's antidynamo 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 Re{sub m}{>=}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 antidynamo theorem. It is also shown that curvature and stretching are fundamental for the existence of fast dynamos in plasmas.},
doi = {10.1063/1.3041158},
journal = {Physics of Plasmas},
number = 12,
volume = 15,
place = {United States},
year = 2008,
month =
}

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