Dynamical quenching with non-local alpha and downward pumping
  In light of new results, the one-dimensional mean-field dynamo model of Brandenburg & Kapyla (2007) with dynamical quenching and a nonlocal Babcock-Leighton alpha effect is re-examined for the solar dynamo. We extend the one-dimensional model to include the effects of turbulent downward pumping (Kitchatinov & Olemskoy 2011), and to combine dynamical quenching with shear. We use both the conventional dynamical quenching model of Kleeorin & Ruzmaikin (1982) and the alternate one of Hubbard & Brandenburg (2011), and confirm that with varying levels of non-locality in the alpha effect, and possibly shear as well, the saturation field strength can be independent of the magnetic Reynolds number. 
A. Brandenburg (1,2), A. Hubbard (3,1), and P. J. K\"apyl\"a (4,5,1)   ((1) Nordita, (2) Stockholm University, (3) American ...
astro-ph.SR