We present our results of a three-dimensional, fully nonlinear MHD simulations of a large-scale magnetic field evolution in a barred galaxy with the back reaction of magnetic field to gas. In our simulations we consider the time evolution of an isothermal galactic disk which is in initial magnetodynamic equilibrium. We assume that the total gravitational potential consists of the superposition of a disk (isochrone), halo and bulge (elliptical) as well as of the bar (Ferrers).
For each of the models we made a series of numerical calculations for, among others, different values of a bar radius, an axial ratio, bar pattern speed and initial toroidal magnetic field. In order to compare our modeling results with observations we also construct models of a high-frequency polarized radio emission from the simulated magnetic fields.
We found that the obtained magnetic field configurations are highly similar to the observed maps of the polarized intensity of barred galaxies, because the modeled vectors form coherent structures along the bar and spiral arms. Due to the dynamical influence of the bar the gas forms spiral waves which go radially outward. Each spiral arm forms the magnetic arm which stays much longer in the disk, than the gaseous spiral structure. The modeled total energy of magnetic field grows due to strong compression and shear of non-axisymmetrical bar flows and differential rotation, respectively.