Magnetic-field generation in helical turbulence*

We investigate analytically the amplification of a weak magnetic field in a homogeneous and isotropic turbulent flow lacking reflectional symmetry (helical turbulence). We propose that spectral distributions of magnetic energy and magnetic helicity can be found as eigenmodes of the self-adjoint, Schr\"odinger-type system of evolution equations. This implies that large-scale and small-scale magnetic fluctuations cannot be effectively separated, and that the conventional $\alpha$-model is, in general, not an adequate description of the large-scale magnetic-dynamo mechanism. As a consequence, the correct numerical modeling of such processes should resolve magnetic fluctuations down to very small, resistive scales.