A Krein space related perturbation theory for MHD α2-dynamos and resonant unfolding of diabolical points

Günther, Uwe and Kirillov, Oleg (2006) A Krein space related perturbation theory for MHD α2-dynamos and resonant unfolding of diabolical points. Journal of Physics A: Mathematical and General, 39 (32). pp. 10057-10076. ISSN 0305-4470

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Abstract

The spectrum of the spherically symmetric α2-dynamo is studied in the case of idealized boundary conditions. Starting from the exact analytical solutions of models with constant α-profiles, a perturbation theory and a Galerkin technique are developed in a Krein space approach. With the help of these tools, a very pronounced α-resonance pattern is found in the deformations of the spectral mesh as well as in the unfolding of the diabolical points located at the nodes of this mesh. Non-oscillatory as well as oscillatory dynamo regimes are obtained. An estimation technique is developed for obtaining the critical α-profiles at which the eigenvalues enter the right spectral half-plane with non-vanishing imaginary components (at which overcritical oscillatory dynamo regimes form). Finally, Fréchet derivative (gradient) based methods are developed, suitable for further numerical investigations of Krein space related setups such as MHD α2-dynamos or models of {\cal P}{\cal T} -symmetric quantum mechanics.

Item Type:	Article
Subjects:	F300 Physics G100 Mathematics
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Oleg Kirillov
Date Deposited:	23 Jan 2017 11:50
Last Modified:	12 Oct 2019 22:27
URI:	http://nrl.northumbria.ac.uk/id/eprint/29300

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