TY - JOUR AU - Günther, U. AU - Kirillov, O. N. AU - Samsonov, B. F. AU - Stefani, F. PY - 2007/01/02 Y2 - 2024/03/29 TI - The Spherically Symmetric a2–dynamo and Some of its Spectral Peculiarities JF - Acta Polytechnica JA - Acta Polytech VL - 47 IS - 2-3 SE - Articles DO - 10.14311/946 UR - https://ojs.cvut.cz/ojs/index.php/ap/article/view/946 SP - AB - A brief overview is given of recent results on the spectral properties of spherically symmetric MHD α<sup>2</sup>-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<br />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. ER -