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

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

2010-04-01

arxiv.org/abs/1004.0231v1

SIAM J. Math. Anal. Volume 42, Issue 3, pp. 1413-1447 (2010)

Physics

Mathematical Physics

35 pages, 4 figures, to be published in SIAM J. Math. Anal.

Scientific paper

10.1137/100782024

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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