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

Guenther, Uwe, Kirillov, Oleg, Samsonov, Boris and Stefani, Frank (2007) The spherically-symmetric α2-dynamo and some of its spectral peculiarities. Acta Polytechnica, 47 (2-3). pp. 75-81. ISSN 1210-2709

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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.

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