PREPRINT
B39F2153-4C92-4D6E-A008-61C5404136B0

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

Uwe Guenther, Oleg N. Kirillov, Boris F. Samsonov, Frank Stefani
arXiv:math-ph/0703041

Submitted on 13 March 2007

Abstract

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.

Preprint

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

URL: https://arxiv.org/abs/math-ph/0703041