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A new simulation set-up is proposed for studying mean field dynamo action.The model combines the computational advantages of local cartesian geometrywith the ability to include a shear profile that resembles the sun'sdifferential rotation at low latitudes. It is shown that in a two-dimensionalmean field model this geometry produces cyclic solutions with dynamo wavestraveling away from the equator -- as expected for a positive alpha effect inthe northern hemisphere. In three dimensions with turbulence driven by ahelical forcing function, an alpha effect is self-consistently generated in thepresence of a finite imposed toroidal magnetic field. The results suggest that,due to a finite flux of current helicity out of the domain, alpha quenchingappears to be non-catastrophic -- at least for intermediate values of themagnetic Reynolds number. For larger values of the magnetic Reynolds number,however, there is evidence for a reversal of the trend and that $\alpha$ maydecrease with increasing magnetic Reynolds number. Control experiments withclosed boundaries confirm that in the absence of a current helicity flux, butwith shear as before, alpha quenching is always catastrophic and alphadecreases inversely proportional to the magnetic Reynolds number. For solarparameters, our results suggest a current helicity flux of about 0.001 G^2/s.This corresponds to a magnetic helicity flux, integrated over the northernhemisphere and over the 11 year solar cycle, of about 10^{46}Mx^2.Comment: 9 pages, 10 figures, A&A (in press

Catastrophic alpha quenching alleviated by helicity flux and shear