We discuss the mean-field dynamo action in protoneutron stars that are subject to instabilities during the early evolutionary phase. The mean field is generated in the neutron-finger unstable region where the Rossby number is ∼ 1 and mean-field dynamo is efficient. Depending on the rotation rate, the mean-field dynamo can lead to the formation of three different types of pulsars. If the initial period of the protoneutron star is short, then the generated large-scale field is very strong (${>} 3 \times 10^{13}$ G) and exceeds the small-scale field at the neutron star surface. If rotation is moderate, then the pulsars are formed with more or less standard dipole fields (${<} 3 \times 10^{13}$ G) but with surface small-scale magnetic fields stronger than the dipole field. If rotation is very slow, then the mean-field dynamo does not operate, and the neutron star has no global field. Nevertheless, strong small-scale fields are generated in such pulsars, and they can manifest themselves as objects with very low spin-down rate but with a strong magnetic field inferred from the spectral features.

Most probably the sunspot cycle period is ruled by a meridional flow located near the base of the convection zone (Hathaway et al. 2003). On the other hand, if the eddy diffusivity is low enough, dramatic modification of the standard alpha(2) Omega-dynamo by the meridional flow are expected. In this paper we shall discuss the dependence of periods, dynamo numbers and the sign of the current helicity as a function of the magnetic Reynolds number for a double cell meridional circulation and for a positive a-effect at the base of the convection zone. The dynamo action occurs at lower latitudes and its location is at the interface between equatorward and poleward motions near the base of the convection zone. In spite of the complexity of the flow pattern, our simulations show that the resulting dynamo action reproduces several observed features of the solar cycle. (c) 2006 WILEY-VCH Verlag GmbH& Co. KGaA, Weinheim.

We have investigated the turbulent mean-field dynamo action in protoneutron stars that are subject to convective and neutron finger instabilities during the early evolutionary phase. While the first one develops mostly in the inner regions of the star, the second one is favored in the outer regions, where the Rossby number is much smaller and a mean-field dynamo action is more efficient. By solving the mean-field induction equation we have computed the critical spin period below which no dynamo action is possible and found it to be similar to 1 s for a wide range of stellar models and for both axisymmetric and non-axisymmetric magnetic fields. Because this critical period is substantially longer than the characteristic spin period of very young pulsars, we expect that a mean-field dynamo will be effective for most protoneutron stars. The saturation dipole field estimated by making use of the model of "global" quenching fits well the pulsar magnetic fields inferred from the spin-down data. Apart from the large-scale magnetic field, our model also predicts a generation of small-scale fields which are typically stronger than the poloidal field and can survive during the lifetime of pulsars. Extremely rapidly rotating protoneutron stars (P similar to 1 ms) may have a dipole field similar to(3- 6) x 10(14) G.

We discuss the effect of a non-trivial meridional circulation pattern on a flux-transport type of solar dynamo. The critical value of the turbulent helicity and the periods are calculated as a function of the meridional flow strength. We found that the dynamo mechanism is mainly determined by the global topology of the meridional flow. In particular the equatorwards migration in the butterfly diagram can be easily obtained by the combined action of two cells of meridional circulation.

We have developed a high-precision code which solves the kinematic dynamo problem both for given rotation law and meridional flow in the case of a low eddy diffusivity of the order of 10(11) cm(2) s(-1) known from the sunspot decay. All our models work with an alpha-effect which is positive (negative) in the northern (southern) hemisphere. It is concentrated in radial layers located either at the top or at the bottom of the convection zone. We have also considered an alpha-effect uniformly distributed in all the convection zone. In the present paper the main attention is focused on i) the parity of the solution, ii) the form of the butterfly diagram and iii) the phase relation of the resulting field components. If the helioseismologically derived internal solar rotation law is considered, a model without meridional flow of high magnetic Reynolds number (corresponding to low eddy diffusivity) fails in all the three issues in comparison with the observations. However, a meridional flow with equatorial drift at the bottom of the convection zone of few meters by second can indeed enforce the equatorward migration of the toroidal magnetic field belts similar to the observed butterfly diagram but, the solution has only a dipolar parity if the (positive) alpha-effect is located at the base of the convection zone rather than at the top. We can, therefore, confirm the main results of a similar study by Dikpati Gilman (2001).