We investigate the dynamics of magnetic fields in spiral galaxies by performing 3D MHD simulations of galactic discs subject to a spiral potential. Recent hydrodynamic simulations have demonstrated the formation of inter-arm spurs as well as spiral arm molecular clouds provided the ISM model includes a cold HI phase. We find that the main effect of adding a magnetic field to these calculations is to inhibit the formation of structure in the disc. However, provided a cold phase is included, spurs and spiral arm clumps are still present if $beta gtrsim 0.1$ in the cold gas. A caveat to two phase calculations though is that by assuming a uniform initial distribution, $beta gtrsim 10$ in the warm gas, emphasizing that models with more consistent initial conditions and thermodynamics are required. Our simulations with only warm gas do not show such structure, irrespective of the magnetic field strength. Furthermore, we find that the introduction of a cold HI phase naturally produces the observed degree of disorder in the magnetic field, which is again absent from simulations using only warm gas. Whilst the global magnetic field follows the large scale gas flow, the magnetic field also contains a substantial random component that is produced by the velocity dispersion induced in the cold gas during the passage through a spiral shock. Without any cold gas, the magnetic field in the warm phase remains relatively well ordered apart from becoming compressed in the spiral shocks. Our results provide a natural explanation for the observed high proportions of disordered magnetic field in spiral galaxies and we thus predict that the relative strengths of the random and ordered components of the magnetic field observed in spiral galaxies will depend on the dynamics of spiral shocks.
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