  Supernova remnants are believed to be the major contributors to Galactic
cosmic rays. In this paper, we explore how the non-thermal emission from young
remnants can be used to probe the production of energetic particles at the
shock (both protons and electrons). Our model couples hydrodynamic simulations
of a supernova remnant with a kinetic treatment of particle acceleration. We
include two important back-reaction loops upstream of the shock: energetic
particles can (i) modify the flow structure and (ii) amplify the magnetic
field. As the latter process is not fully understood, we use different limit
cases that encompass a wide range of possibilities. We follow the history of
the shock dynamics and of the particle transport downstream of the shock, which
allows us to compute the non-thermal emission from the remnant at any given
age. We do this in 3D, in order to generate projected maps that can be compared
with observations. We observe that completely different recipes for the
magnetic field can lead to similar modifications of the shock structure,
although to very different configurations of the field and particles. We show
how this affects the emission patterns in different energy bands, from radio to
X-rays and $\gamma$-rays. High magnetic fields ($>100 \mu$G) directly impact
the synchrotron emission from electrons, by restricting their emission to thin
rims, and indirectly impact the inverse Compton emission from electrons and
also the pion decay emission from protons, mostly by shifting their cut-off
energies to respectively lower and higher energies.
