  Star-forming dwarf galaxies can be seen as the local proxies of the
high-redshift building blocks of more massive galaxies according to the current
paradigm of the hierarchical galaxy formation. They are low-mass objects, and
therefore their rotation speed is very low. Several galaxies are observed to
show quite strong magnetic fields. These cases of strong ordered magnetic
fields seem to correlate with a high, but not extremely high, star formation
rate. We investigate whether these magnetic fields could be generated by the
cosmic-ray-driven dynamo. The environment of a dwarf galaxy is unfavourable for
the large-scale dynamo action because of the very slow rotation that is
required to create the regular component of the magnetic field. We built a 3D
global model of a dwarf galaxy that consists of two gravitational components:
the stars and the dark-matter halo described by the purely phenomenological
profile proposed previously. We solved a system of magnetohydrodynamic (MHD)
equations that include an additional cosmic-ray component described by the
fluid approximation. We found that the cosmic-ray-driven dynamo can amplify the
magnetic field with an exponential growth rate. The $e$-folding time is
correlated with the initial rotation speed. The final mean value of the
azimuthal flux for our models is of the order of few $\mu$G and the system
reaches its equipartition level. The results indicate that the
cosmic-ray-driven dynamo is a process that can explain the magnetic fields in
dwarf galaxies.
