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On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator

Authors
  • Guenther, Uwe
  • Langer, Heinz
  • Tretter, Christiane
Type
Published Article
Publication Date
Apr 01, 2010
Submission Date
Apr 01, 2010
Identifiers
DOI: 10.1137/100782024
Source
arXiv
License
Yellow
External links

Abstract

The existence of magnetohydrodynamic mean-field alpha^2-dynamos with spherically symmetric, isotropic helical turbulence function alpha is related to a non-self-adjoint spectral problem for a coupled system of two singular second order ordinary differential equations. We establish global estimates for the eigenvalues of this system in terms of the turbulence function alpha and its derivative alpha'. They allow us to formulate an anti-dynamo theorem and a non-oscillation theorem. The conditions of these theorems, which again involve alpha and alpha', must be violated in order to reach supercritical or oscillatory regimes.

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