  Dark energy is frequently modelled as an additional dynamical scalar field
component in the Universe, referred to as "quintessence", which drives the
late-time acceleration. Furthermore, the quintessence field may be coupled to
dark matter and/or baryons, leading to a fifth force. In this paper we explore
the consequences for non-linear cosmological structure formation arising from a
momentum coupling between the quintessence field and dark matter only. The
coupling leads to a modified Euler equation, which we implement in an N-body
cosmological simulation. We then analyse the effects of the coupling on the
non-linear power spectrum and the properties of the dark matter halos. We find
that, for certain quintessence potentials, a positive coupling can lead to
significantly reduced structure on small scales and somewhat enhanced structure
on large scales, as well as reduced halo density profiles and increased
velocity dispersions.
