Non-linear galactic dynamos: A toolbox
  We compare various models and approximations for non-linear mean-field
dynamos in disc galaxies to assess their applicability and accuracy, and thus
to suggest a set of simple solutions suitable to model the large-scale galactic
magnetic fields in various contexts. The dynamo saturation mechanisms
considered are the magnetic helicity balance involving helicity fluxes (the
dynamical $\alpha$-quenching) and an algebraic $\alpha$-quenching. The
non-linear solutions are then compared with the marginal kinematic and
asymptotic solutions. We also discuss the accuracy of the no-$z$ approximation.
Although these tools are very different in the degree of approximation and
hence complexity, they all lead to remarkably similar solutions for the mean
magnetic field. In particular, we show that the algebraic $\alpha$-quenching
non-linearity can be obtained from a more physical dynamical $\alpha$-quenching
model in the limit of nearly azimuthal magnetic field. This suggests, for
instance, that earlier results on galactic disc dynamos based on the simple
algebraic non-linearity are likely to be reliable, and that estimates based on
simple, even linear models are often a good starting point. We suggest improved
no-$z$ and algebraic $\alpha$-quenching models, and also incorporate galactic
outflows into a simple analytical dynamo model to show that the outflow can
produce leading magnetic spirals near the disc surface. The simple dynamo
models developed are applied to estimate the magnetic pitch angle and the
arm-interarm contrast in the saturated magnetic field strength for realistic
parameter values.
