The Spherically Symmetric a2–dynamo and Some of its Spectral Peculiarities
DOI:
https://doi.org/10.14311/946Keywords:
MHD dynamo, operator spectrum, Krein space, boundary conditions, supersymmetric Quantum Mechanics, diabolical points, resonance, KdV soliton potentialAbstract
A brief overview is given of recent results on the spectral properties of spherically symmetric MHD α2-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 α-profile embedded in a conducting surrounding can be mode decoupled by a diagonalization ofthe 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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Published
2007-01-02
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Articles
How to Cite
Günther, U., Kirillov, O. N., Samsonov, B. F., & Stefani, F. (2007). The Spherically Symmetric a2–dynamo and Some of its Spectral Peculiarities. Acta Polytechnica, 47(2-3). https://doi.org/10.14311/946