We simulate an isolated, magnetised Milky Way-like disc galaxy using a self-consistent model of unresolved star formation and feedback, evolving the system until it reaches statistical steady state. We show that the quasi-steady-state structure is distinctly layered in galactocentric height $z$, with an innermost region having comparable gas and magnetic pressures (plasma beta $beta sim 1$), an outermost region having dominant gas pressures ($beta gg 1$), and an intermediate region between $300$ pc $lesssim |z| lesssim 3$ kpc that is dynamically dominated by magnetic fields ($beta ll 1$). We find field strengths, gas surface densities, and star formation rates that agree well with those observed both in the Galactic centre and in the Solar neighbourhood. The most significant dynamical effect of magnetic fields on the global properties of the disc is a reduction of the star formation rate by a factor of 1.5-2 with respect to an unmagnetised control simulation. At fixed star formation rate, there is no significant difference in the mass outflow rates or profiles between the magnetised and non-magnetised simulations. Our results for the global structure of the magnetic field have significant implications for models of cosmic ray-driven winds and cosmic-ray propagation in the Galaxy, and can be tested against observations with the forthcoming Square Kilometre Array and other facilities. Finally, we report the discovery of a physical error in the implementation of neutral gas heating and cooling in the popular GIZMO code, which may lead to qualitatively incorrect phase structures if not corrected.
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