The Spherically Symmetric a2–dynamo and Some of its Spectral Peculiarities

Authors

  • U. Günther
  • O. N. Kirillov
  • B. F. Samsonov
  • F. Stefani

DOI:

https://doi.org/10.14311/946

Keywords:

MHD dynamo, operator spectrum, Krein space, boundary conditions, supersymmetric Quantum Mechanics, diabolical points, resonance, KdV soliton potential

Abstract

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 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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Published

2007-01-02

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Section

Articles