Valerij V. Pipin, Norbert Seehafer

• Context. The standard dynamo model for the solar and stellar magnetic fields is based on the $alphaOmega$ mechanism, namely, an interplay between differential rotation (the $Omega$ effect) and a mean electromotive force generated by helical turbulent convection flows (the $alpha$ effect). There are, however, a number of problems with the $alpha$ effect and $alphaOmega$ dynamo models. Two of them are that, in the case of the Sun, the obtained cycle periods are too short and the magnetic activity is not sufficiently concentrated at low latitudes. Aims. We explore the role of turbulent induction effects that may appear in addition to the $alpha$ effect. The additional effects result from the combined action of rotation and an inhomogeneity of the large-scale magnetic field. The best known of them is the $vec{Omega} imesvec{J}$ effect. We also include anisotropic diffusion and a new dynamo term that is of third order in the rotation vector $vec{Omega}$. Methods. We studied axisymmetric mean-field dynamo models containing differentialContext. The standard dynamo model for the solar and stellar magnetic fields is based on the $alphaOmega$ mechanism, namely, an interplay between differential rotation (the $Omega$ effect) and a mean electromotive force generated by helical turbulent convection flows (the $alpha$ effect). There are, however, a number of problems with the $alpha$ effect and $alphaOmega$ dynamo models. Two of them are that, in the case of the Sun, the obtained cycle periods are too short and the magnetic activity is not sufficiently concentrated at low latitudes. Aims. We explore the role of turbulent induction effects that may appear in addition to the $alpha$ effect. The additional effects result from the combined action of rotation and an inhomogeneity of the large-scale magnetic field. The best known of them is the $vec{Omega} imesvec{J}$ effect. We also include anisotropic diffusion and a new dynamo term that is of third order in the rotation vector $vec{Omega}$. Methods. We studied axisymmetric mean-field dynamo models containing differential rotation, the $alpha$ effect, and the additional turbulent induction effects. The model calculations were carried out using the rotation profile of the Sun as obtained from helioseismic measurements and radial profiles of other quantities according to a standard model of the solar interior. In addition, we consider a dynamo model for a full sphere that is based solely on the joint induction effects of rotation and an inhomogeneity of the large-scale magnetic field, without differential rotation and the $alpha$ effect (a $delta^{2}$ dynamo model). This kind of dynamo model may be relevant for fully convective stars. Results. With respect to the solar dynamo, the inclusion of the additional turbulent induction effects increases the period of the dynamo and brings the large-scale toroidal field closer to the equator, thus improving the agreement of the models with the observations. For the $delta^{2}$ dynamo working in a full sphere, we find dynamo modes that are steady if the effect of anisotropic diffusion is not included. The inclusion of anisotropic diffusion yields a magnetic field oscillating with a period close to the turbulent magnetic diffusion time.…