  A number of studies suggest that shock acceleration with particle feedback
and very efficient magnetic-field amplification combined with Alfv\'{e}nic
drift are needed to explain the rather soft radio spectrum and the narrow rims
observed for Tycho's SNR. We show that the broadband spectrum of Tycho's SNR
can alternatively be well explained when accounting for stochastic acceleration
as a secondary process. The re-acceleration of particles in the turbulent
region immediately downstream of the shock should be efficient enough to impact
particle spectra over several decades in energy. The so-called Alfv\'{e}nic
drift and particle feedback on the shock structure are not required in this
scenario. Additionally, we investigate whether synchrotron losses or
magnetic-field damping play a more profound role in the formation of the
non-thermal filaments. We solve the full particle transport equation in
test-particle mode using hydrodynamic simulations of the SNR plasma flow. The
background magnetic field is either computed from the induction equation or
follows analytic profiles, depending on the model considered. Fast-mode waves
in the downstream region provide the diffusion of particles in momentum space.
We show that the broadband spectrum of Tycho can be well explained if
magnetic-field damping and stochastic re-acceleration of particles are taken
into account. Although not as efficient as standard DSA, stochastic
acceleration leaves its imprint on the particle spectra, which is especially
notable in the emission at radio wavelengths. We find a lower limit for the
post-shock magnetic-field strength $\sim330\,\mathrm{\mu G}$, implying
efficient amplification even for the magnetic-field damping scenario. For the
formation of the filaments in the radio range magnetic-field damping is
necessary, while the X-ray filaments are shaped by both the synchrotron losses
and magnetic-field damping.
