The spherically symmetric alpha2-dynamo and some of its spectral peculiarities

Uwe Guenther, Oleg N. Kirillov, Boris F. Samsonov, Frank Stefani

Submitted on 13 March 2007


A brief overview is given over 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.


Comment: 8 pages, 5 figures, Conf. Proc., 1st DI micro-conference "Analytic and algebraic methods in physics", Doppler Institute for mathematical physics and applied mathematics, Prague, February 20, 2007

Subjects: Mathematical Physics; Astrophysics; Quantum Physics