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Combined action of helical motions of plasma (the $\alpha$ effect) andnon-uniform (differential) rotation is a key dynamo mechanism of solar andgalactic large-scale magnetic fields. Dynamics of magnetic helicity ofsmall-scale fields is a crucial mechanism in a nonlinear dynamo saturationwhere turbulent magnetic helicity fluxes allow to avoid catastrophic quenchingof the $\alpha$ effect. The convective zone of the Sun and solar-like stars aswell as galactic discs are the source for production of turbulent magnetichelicity fluxes. In the framework of the mean-field approach and the spectral$\tau$ approximation, we derive turbulent magnetic helicity fluxes using theCoulomb gauge in a density-stratified turbulence. The turbulent magnetichelicity fluxes include non-gradient and gradient contributions. Thenon-gradient magnetic helicity flux is proportional to a nonlinear effectivevelocity (which vanishes in the absence of the density stratification)multiplied by small-scale magnetic helicity, while the gradient contributionsdescribe turbulent magnetic diffusion of the small-scale magnetic helicity. Inaddition, the turbulent magnetic helicity fluxes contain source termsproportional to the kinetic $\alpha$ effect or its gradients, and alsocontributions caused by the large-scale shear (solar differential rotation). Wehave demonstrated that the turbulent magnetic helicity fluxes due to thekinetic $\alpha$ effect and its radial derivative in combination with thenonlinear magnetic diffusion of the small-scale magnetic helicity are dominantin the solar convective zone.

Turbulent magnetic helicity fluxes in solar convective zone