  We study the evolution of galactic magnetic fields using 3D smoothed particle
magnetohydrodynamics (SPMHD) simulations of galaxies with an imposed spiral
potential. We consider the appearance of reversals of the field, and
amplification of the field. We find magnetic field reversals occur when the
velocity jump across the spiral shock is above $\approx$20km s$^{-1}$,
occurring where the velocity change is highest, typically at the inner Lindblad
resonance (ILR) in our models. Reversals also occur at corotation, where the
direction of the velocity field reverses in the co-rotating frame of a spiral
arm. They occur earlier with a stronger amplitude spiral potential, and later
or not at all with weaker or no spiral arms. The presence of a reversal at a
radii of around 4--6 kpc in our fiducial model is consistent with a reversal
identified in the Milky Way, though we caution that alternative Galaxy models
could give a similar reversal. We find that relatively high resolution, a few
million particles in SPMHD, is required to produce consistent behaviour of the
magnetic field. Amplification of the magnetic field occurs in the models, and
while some may be genuinely attributable to differential rotation or spiral
arms, some may be a numerical artefact. We check our results using Athena,
finding reversals but less amplification of the field, suggesting that some of
the amplification of the field with SPMHD is numerical.
