The spherically symmetric alpha2-dynamo and some of its spectral peculiarities
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.
Keywords
Cite
@article{arxiv.math-ph/0703041,
title = {The spherically symmetric alpha2-dynamo and some of its spectral peculiarities},
author = {Uwe Guenther and Oleg N. Kirillov and Boris F. Samsonov and Frank Stefani},
journal= {arXiv preprint arXiv:math-ph/0703041},
year = {2008}
}
Comments
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