  We study cosmic-ray acceleration in young Type Ia Supernova Remnants (SNRs)
by means of test-particle diffusive shock acceleration theory and 1-D
hydrodynamical simulations of their evolution. In addition to acceleration at
the forward shock, we explore the particle acceleration at the reverse shock in
the presence of a possible substantial magnetic field, and consequently the
impact of this acceleration on the particle spectra in the remnant. We
investigate the time evolution of the spectra for various time-dependent
profiles of the magnetic field in the shocked region of the remnant. We test a
possible influence on particle spectra of the Alfv\'enic drift of scattering
centers in the precursor regions of the shocks. In addition, we study the
radiation spectra and morphology in a broad band from radio to gamma-rays. It
is demonstrated that the reverse shock contribution to the cosmic-ray particle
population of young Type Ia SNRs may be significant, modifying the spatial
distribution of particles and noticeably affecting the volume-integrated
particle spectra in young SNRs. In particular spectral structures may arise in
test-particle calculations that are often discussed as signatures of non-linear
cosmic-ray modification of shocks. Therefore, the spectrum and morphology of
emission, and their time evolution, differ from pure forward-shock solutions.
