Galactic dynamo with helicity fluxes

We construct an approximation for the magnetic field of galaxies that takes into account the magnetic helicity conservation law. In our calculations, we use the fact that the galactic disk is fairly thin and, therefore, the magnetic field component perpendicular to the galactic disk can be neglected (the so-called no-z approximation). However, an averaging of the magnetic field over the entire galaxy, as was done in previous works, is not performed. Our results are compared both with the approximation that disregards the helicity flux and with the results obtained in models with helicity fluxes but without averaging. We show that, compared to the classical model, there are a number of new effects (for example, magnetic field oscillations) and, compared to the model with averaging, the behavior of the magnetic field "softens": its stationary value is reached more slowly and the oscillation amplitude decreases. This is because the dissipative processes changing the magnetic field growth rate are taken into account in our model. In contrast to the model with averaging, here it becomes possible to construct the dependence of the magnetic field and helicity on the distance from the galactic center.