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Dynamos in the Sun and other bodies tend to produce magnetic fields thatpossess magnetic helicity of opposite sign at large and small scales,respectively. The build-up of magnetic helicity at small scales provides animportant saturation mechanism. In order to understand the nature of the solardynamo we need to understand the details of the saturation mechanism inspherical geometry. In particular, we want to understand the effects ofmagnetic helicity fluxes from turbulence and meridional circulation. Weconsider a model with just radial shear confined to a thin layer (tachocline)at the bottom of the convection zone. The kinetic alpha owing to helicalturbulence is assumed to be localized in a region above the convection zone.The dynamical quenching formalism is used to describe the build-up of meanmagnetic helicity in the model, which results in a magnetic alpha effect thatfeeds back on the kinetic alpha effect. In some cases we compare with resultsobtained using a simple algebraic alpha quenching formula. In agreement withearlier findings, the magnetic alpha effect in the dynamical alpha quenchingformalism has the opposite sign compared with the kinetic alpha effect andleads to a catastrophic decrease of the saturation field strength withincreasing magnetic Reynolds numbers. However, at high latitudes this quenchingeffect can lead to secondary dynamo waves that propagate poleward due to theopposite sign of alpha. Magnetic helicity fluxes both from turbulent mixing andfrom meridional circulation alleviate catastrophic quenching.

Magnetic helicity fluxes in interface and flux transport dynamos