  A three-dimensional (3D) MHD model is applied to simulate the evolution of a
large-scale magnetic field in a barred galaxy possessing a gaseous halo
extending to about 2.8 kpc above the galactic plane. As the model input we use
a time-dependent velocity field of molecular gas resulting from self-consistent
3D N-body simulations of a galactic disk. We assume that the gaseous halo
rotates differentially co-rotating with the disk or decreasing its velocity in
the Z direction. The dynamo process included in the model yields the
amplification of the magnetic field as well as the formation of field
structures high above the galactic disk. The simulated magnetic fields are used
to construct the models of a high-frequency (Faraday rotation-free) polarized
radio emission that accounts for effects of projection and limited resolution,
and is thus suitable for direct comparison with observations. We found that the
resultant magnetic field correctly reproduces the observed structures of
polarization B-vectors, forming coherent patterns well aligned with spiral arms
and with the bar. The process initializing a wave-like behavior of the magnetic
field, which efficiently forms magnetic maxima between the spiral arms, is
demonstrated. The inclusion of the galactic halo constitutes a step towards a
realistic model of galactic magnetic fields that includes as many dynamical
components as needed for a realistic description.
