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The existence of magnetohydrodynamic mean-field alpha^2-dynamos withspherically symmetric, isotropic helical turbulence function alpha is relatedto a non-self-adjoint spectral problem for a coupled system of two singularsecond order ordinary differential equations. We establish global estimates forthe eigenvalues of this system in terms of the turbulence function alpha andits derivative alpha'. They allow us to formulate an anti-dynamo theorem and anon-oscillation theorem. The conditions of these theorems, which again involvealpha and alpha', must be violated in order to reach supercritical oroscillatory regimes.

On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator