Generalized quenching of large-scale magnetic dynamos in anisotropic flows

The buildup of small-scale magnetic helicity which accompanies the oppositely signed growth on large scales is central to conventional dynamical quenching theories of mean-field dynamos. However, the conventional formalism presumes isotropic turbulence and thereby excludes part of the magnetic Lorentz back-reaction. This renders it insufficient to predict the full quenching for general anisotropic flows. To overcome this deficiency, we derive a new generalized quenching formalism that includes the full back-reacting Lorentz force, and a new "selective-damping-$\tau$" closure which conserves magnetic helicity. We apply the formalism to examples of $\bm\alpha^2$ dynamos and show its predicted quenching for different cases of turbulence---isotropic helical, anisotropic helical, and anisotropic non-helical. It predicts stronger-than-conventional quenching in general, but reduces to the conventional case in the helical isotropic limit.