  The self-consistent interaction between energetic particles and
self-generated hydromagnetic waves in a cosmic-ray pressure dominated plasma is
considered. Using a three-dimensional hybrid MHD-kinetic code, which utilises a
spherical harmonic expansion of the Vlasov-Fokker-Planck equation, high
resolution simulations of the magnetic field growth including feedback on the
cosmic rays are carried out. It is found that for shocks with high cosmic-ray
acceleration efficiency, the magnetic fields become highly disorganised,
resulting in near isotropic diffusion, independent of the initial orientation
of the ambient magnetic field. The possibility of sub-Bohm diffusion is
demonstrated for parallel shocks, while the diffusion coefficient approaches
the Bohm limit from below for oblique shocks. This universal behaviour suggests
that Bohm diffusion in the root mean squared field inferred from observation
may provide a realistic estimate for the maximum energy acceleration timescale
in young supernova remnants. Although disordered, the magnetic field is not
self-similar suggesting non-uniform energy dependent behaviour of the energetic
particle transport in the precursor. Possible indirect radiative signatures of
cosmic-ray driven magnetic field amplification are discussed.
