  Galactic encounters are usually marked by a substantial increase of
synchrotron emission of the interacting galaxies compared to the typical
emission from similar isolated galaxies. This is believed to be associated with
an increase of the star formation rate and the associated turbulent magnetic
fields. The regular magnetic field is usually believed to decrease. We consider
a simple, however rather realistic, mean-field galactic dynamo model where the
effects of small-scale generation are represented by random injections of
magnetic field from star forming regions. We represent an encounter by the
introduction of large-scale streaming velocities and by an increase in
small-scale magnetic field injections. The latter describes the effect of an
increase of the star formation rate caused by the encounter. We demonstrate
that large-scale streaming, with associated deviations in the rotation curve,
can result in an enhancement of the anisotropic turbulent (ordered) magnetic
field strength, mainly along the azimuthal direction, leading to a significant
temporary increase of the total magnetic energy during the encounter; the
representation of an increase in star formation rate has an additional strong
effect. In contrast to expectations, the large-scale (regular) magnetic field
structure is not significantly destroyed by the encounter. It may be somewhat
weakened for a relatively short period, and its direction after the encounter
may be reversed. The encounter causes enhanced total and polarized emission
without increase of the regular magnetic field strength. The increase of
synchrotron emission caused by the large-scale streaming can be comparable to
the effect of the increase of the star formation rate, depending on the choice
of parameters.The effects of the encounter on the total magnetic field energy
last only slightly longer than the duration of the encounter (ca. 1 Gyr).
