  Collisionless plasma shocks are efficient sources of non-thermal particle
acceleration in space and astrophysical systems. We use hybrid (kinetic ions --
fluid electrons) simulations to examine the non-linear feedback of the
self-generated energetic particles (cosmic rays, CRs) on the shock
hydrodynamics. When CR acceleration is efficient, we find evidence of both an
upstream precursor, where the inflowing plasma is compressed and heated, and a
downstream postcursor, where the energy flux in CRs and amplified magnetic
fields play a dynamical role. For the first time, we assess how non-linear
magnetic fluctuations in the postcursor preferentially travel away from the
shock at roughly the local Alfv\'en speed with respect to the downstream
plasma. The drift of both magnetic and CR energy with respect to the thermal
plasma substantially increases the shock compression ratio with respect to the
standard prediction, in particular exceeding 4 for strong shocks. Such
modifications also have implications for the spectrum of the particles
accelerated via diffusive shock acceleration, a significant result detailed in
a companion paper, Caprioli, Haggerty & Blasi 2020, arXiv:2009.00007
[astro-ph.HE].
