  Ultracompact cataclysmic variables (CVs) of the AM CVn type are deemed to be
important verification sources for the future space gravitational wave
detectors such as the Laser Interferometer Space Antenna (LISA). We model the
present-day Galactic population of AM CVn stars with He-star donors. Such a
population has long expected to exist, though only a couple of candidates are
known. We applied the hybrid method of binary population synthesis (BPS) which
combines a simulation of the population of immediate precursors of AM CVn stars
by a fast BPS code with subsequent tracking of their evolution by a full
evolutionary code. The model predicts that the present birthrate of He-donor AM
CVn stars in the Galaxy is $4.6\times 10^{-4}$ per yr and the Galaxy may
harbour about 112000 objects of this class which have orbital periods less than
42-43 min. The foreground confusion limit and instrumental noise of LISA
prevent the discovery of longer periods systems in gravitational waves. We find
that about 500 He-star AM CVns may be detected by LISA with signal-to-noise
ratio (S/N)>5 during a 4 yr mission. Within 1 Kpc from the Sun, there may exist
up to 130 He-star AM CVns with the periods in the same range, which may serve
as verification binaries, if detected in the electromagnetic spectrum. In the
Milky Way, there are also about 14800 immediate precursors of AM CVn stars.
They are detached systems with a stripped low-mass He-star and a white dwarf
companion, out of which about 75 may potentially be observed by LISA during its
mission.
