The Spherically Symmetric a2–dynamo and Some of its Spectral Peculiarities
Keywords:MHD dynamo, operator spectrum, Krein space, boundary conditions, supersymmetric Quantum Mechanics, diabolical points, resonance, KdV soliton potential
AbstractA 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 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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