  Irregular galaxies are usually smaller and less massive than their spiral,
S0, and elliptical counterparts. Radio observations indicate that a magnetic
field is present in irregular galaxies whose value is similar to that in spiral
galaxies. However, the conditions in the interstellar medium of an irregular
galaxy are unfavorable for amplification of the magnetic field because of the
slow rotation and low shearing rate. We investigate the cosmic-ray driven
dynamo in the interstellar medium of an irregular galaxy. We study its
efficiency under the conditions of slow rotation and weak shear. The star
formation is also taken into account in our model and is parametrized by the
frequency of explosions and modulations of activity. The numerical model
includes a magnetohydrodynamical dynamo driven by cosmic rays that is injected
into the interstellar medium by randomly exploding supernovae. In the model, we
also include essential elements such as vertical gravity of the disk,
differential rotation approximated by the shearing box, and resistivity leading
to magnetic reconnection. We find that even slow galactic rotation with a low
shearing rate amplifies the magnetic field, and that rapid rotation with a low
value of the shear enhances the efficiency of the dynamo. Our simulations have
shown that a high amount of magnetic energy leaves the simulation box becoming
an efficient source of intergalactic magnetic fields.
