  We describe three-dimensional magnetohydrodynamical modelling of powerful
radio galaxies in realistic poor cluster environments. This modelling extends
our earlier work on the hydrodynamics of radio galaxies as a function of their
cluster environment to consider the magnetic field configuration in the lobes
and its observational consequences, using a realistic model for the magnetic
field in the intracluster medium, very high density contrast in the lobes and
high numerical resolution. We confirm, now with a realistic magnetic field
model, that lobes have characteristic trajectories in the radio power/linear
size diagram which depend strongly on their environment. We investigate the
detailed evolution of polarized emission, showing that the lobes evolve from
the initially ordered field configuration imposed by our boundary conditions to
one in which the longitudinal field comes to dominate. We obtain simulated
observations of polarization whose properties are quantitatively consistent
with observations. The highly spatially intermittent magnetic field also
reproduces the observation that inverse-Compton emission from lobes is much
smoother than synchrotron. Our simulations allow us to study the depolarizing
effect of the external medium on the lobes, and so to demonstrate that Faraday
depolarization from environments of the type we consider can reproduce the
integrated fractional polarization properties of large samples and the observed
preferential depolarization of the receding lobe.
