(Abridged) We use new multi-wavelength radio observations, made with the VLA
and Effelsberg telescopes, to study the magnetic field of the nearby galaxy M51
on scales from 200\pc to several \kpc. Interferometric and single dish data
are combined to obtain new maps at \wwav{3}{6} in total and polarized emission,
and earlier \wav{20} data are re-reduced. We compare the spatial distribution
of the radio emission with observations of the neutral gas, derive radio
spectral index and Faraday depolarization maps, and model the large-scale
variation in Faraday rotation in order to deduce the structure of the regular
magnetic field. We find that the \wav{20} emission from the disc is severely
depolarized and that a dominating fraction of the observed polarized emission
at \wav{6} must be due to anisotropic small-scale magnetic fields. Taking this
into account, we derive two components for the regular magnetic field in this
galaxy: the disc is dominated by a combination of azimuthal modes, m=0+2, but
in the halo only an m=1 mode is required to fit the observations. We disuss
how the observed arm-interarm contrast in radio intensities can be reconciled
with evidence for strong gas compression in the spiral shocks. The average
arm--interam contrast, representative of the radii r>2\kpc where the spiral
arms are broader, is not compatible with straightforward compression: lower
arm--interarm contrasts than expected may be due to resolution effects and
\emph{decompression} of the magnetic field as it leaves the arms. We suggest a
simple method to estimate the turbulent scale in the magneto-ionic medium from
the dependence of the standard deviation of the observed Faraday rotation
measure on resolution. We thus obtain an estimate of 50\pc for the size of
the turbulent eddies.Comment: 21 pages, 18 figures (some at lower resolution than submitted
version), accepted for publication in MNRA
