  Spin waves in non-collinear magnets with $C_{nv}$ symmetry are discussed in
the context of inelastic neutron scattering in small-angle scattering geometry.
In the framework of a minimal model including exchange coupling,
Dzayloshinskii-Moriya interaction (DMI), and single-ion anisotropy, we consider
the system properties at moderate external magnetic fields and in the
high-field fully polarized phase. In the latter case, the magnon spectrum is
gapped and non-reciprocal due to DMI with the minimum perpendicular to the
field direction for the in-plane field and is ferromagnetic-like for the field
along the high-symmetry axis. Inelastic small-angle neutron scattering in the
fully polarized phase (SWSANS) is considered in four different geometries. It
is shown that analysis of the field dependence of the SWSANS cutoff feature in
these geometries allows determining all important parameters of the model. The
possibility of the proposed method utilization in thin films with interfacial
DMI is also discussed.
