  The spectrum of the spherically symmetric alpha-2 dynamo is studied in the
case of idealized boundary conditions. Starting from the exact analytical
solutions of models with constant alpha-profiles a perturbation theory and a
Galerkin technique are developed in a Krein-space approach. With the help of
these tools a very pronounced alpha-resonance pattern is found in the
deformations of the spectral mesh as well as in the unfolding of the diabolical
points located at the nodes of this mesh. Non-oscillatory as well as
oscillatory dynamo regimes are obtained. A Fourier component based estimation
technique is developed for obtaining the critical alpha-profiles at which the
eigenvalues enter the right spectral half-plane with non-vanishing imaginary
components (at which overcritical oscillatory dynamo regimes form). Finally,
Frechet derivative (gradient) based methods are developed, suitable for further
numerical investigations of Krein-space related setups like MHD alpha-2-dynamos
or models of PT-symmetric quantum mechanics.
