  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.
