We present three-dimensional global numerical simulations of the cosmic-ray ( CR ) driven dynamo in barred galaxies .
We study the evolution of the interstellar medium of the barred galaxy in the presence of non-axisymmetric component of the potential , i.e .
the bar .
The magnetohydrodynamical dynamo is driven by CRs , which are continuously supplied to the disk by supernova ( SN ) remnants .
No magnetic field is present at the beginning of simulations but one-tenth of SN explosions is a source of a small-scale randomly oriented dipolar magnetic field .
In all models we assume that 10 % of 10 ^ { 51 } erg SN kinetic energy output is converted into CR energy .

To compare our results directly with the observed properties of galaxies we construct realistic maps of polarized radio emission .
The main result is that the CR-driven dynamo can amplify weak magnetic fields up to a few \mu { G } within a few Gyr in barred galaxies .
The obtained e -folding time is equal to 300 Myr and the magnetic field reaches equipartition at time t \sim 4.0 Gyr .
Initially , completely random magnetic field evolves into large-scale structures .
An even ( quadrupole-type ) configuration of the magnetic field with respect to the galactic plane can be observed .
Additionally , the modeled magnetic field configuration resembles maps of the polarized intensity observed in barred galaxies .
Polarization vectors are distributed along the bar and between spiral arms .
Moreover , the drift of magnetic arms with respect to the spiral pattern in the gas density distribution is observed during the whole simulation time .