  Type Ibn supernovae (SNe) are a mysterious class of transients whose spectra
exhibit persistently narrow HeI lines, and whose bolometric light curves are
typically fast evolving and overluminous at peak relative to standard Type Ibc
SNe. We explore the interaction scenario of such Type Ibn SNe by performing
radiation-hydrodynamics and radiative-transfer calculations. We find that
standard-energy helium-star explosions within dense wind-like circumstellar
material (CSM) can reach on day timescales a peak luminosity of a few 10^44
erg/s, reminiscent of exceptional events like AT2018cow. Similar interactions
but with weaker winds can lead to Type Ibc SNe with double-peak light curves
and peak luminosities in the range ~10^42.2 to ~10^43 erg/s. In contrast, the
narrow spectral lines and modest peak luminosities of most Type Ibn SNe are
suggestive of a low-energy explosion in an initially <~5 Msun helium star, most
likely arising from interacting binaries, and colliding with a massive
helium-rich, probably ejecta-like, CSM at ~10^15 cm. Nonlocal thermodynamic
equilibrium radiative-transfer simulations of a slow-moving dense shell born
out and powered by the interaction compare favorably to Type Ibn SNe like
2006jc, 2011hw, or 2018bcc at late times and suggest a composition made of
about 50% helium, a solar metallicity, and a total ejecta/CSM mass of 1-2Msun.
A lower fractional helium abundance leads to weak or absent HeI lines and thus
excludes more massive configurations for observed Type Ibn SNe. Further, the
dominance of FeII emission below 5500A seen in Type Ibn SNe at late times is
not predicted at low metallicity. Hence, despite their promising properties,
Type Ibn SNe from pulsational-pair instability in very massive stars, which
requires low metallicity, have probably not yet been observed.
