The spherically-symmetric α2-dynamo and some of its spectral peculiarities

Uwe Guenther, Oleg Kirillov, Boris Samsonov, Frank Stefani

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Abstract

A brief overview is given of recent results on the spectral properties of spherically symmetric MHD alpha2-dynamos. In particular, the spectra of sphere-confined fluid or plasma configurations with physically realistic boundary conditions (BCs) (surrounding vacuum) and with idealized BCs (super-conducting surrounding) are discussed. The subjects comprise third-order branch points of the spectrum, self-adjointness of the dynamo operator in a Krein space as well as the resonant unfolding of diabolical points. It is sketched how certain classes of dynamos with a strongly localized alpha-profile embedded in a conducting surrounding can be mode decoupled by a diagonalization of the dynamo operator matrix. A mapping of the dynamo eigenvalue problem to that of a quantum mechanical Hamiltonian with energy dependent potential is used to obtain qualitative information about the spectral behavior. Links to supersymmetric Quantum Mechanics and to the Dirac equation are indicated.
Original languageEnglish
Pages (from-to)75-81
JournalActa Polytechnica
Volume47
Issue number2-3
Publication statusPublished - 13 Mar 2007

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