Krein space related perturbation theory for MHD α²-dynamos and resonant unfolding of diabolical points
Krein space related perturbation theory for MHD α²-dynamos and resonant unfolding of diabolical points
Günther, U.; Kirillov, O.
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. Finally, Fréchet derivative (gradient) based methods are developed, suitable for further numerical investigations of Krein-space related setups like MHD α²-dynamos or models of PT-symmetric quantum mechanics.
Keywords: Krein space; MHD dynamo; diabolical point; exceptional point; spectral deformation; perturbation theory; resonance; Galerkin method
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Journal of Physics A 39(2006)32, 10057-10076
DOI: 10.1088/0305-4470/39/32/S08
ISSN: 0305-4470, 1361-6447
Cited 40 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ-8201