  We model the population of AM CVn systems in the Galaxy and discuss the
detectability of these systems with optical, X-ray and gravitational wave
detectors. We concentrate on the short period (P < 1500 s) systems, some of
which are expected to be in a phase of direct impact accretion. Using a
self-consistent model for the star formation history and radial distribution of
stars in the Galaxy plus simple models for the emission of optical and X-ray
radiation from the AM CVn systems and interstellar absorption, we derive the
sample of short-period AM CVn systems that can be detected in the optical
and/or X-ray bands. At the shortest periods the detectable systems are all
X-ray sources, some with periods as short as three minutes. At periods above 10
minutes most detectable systems are optical sources. About one third of the
X-ray sources are also detectable in the optical band. We also calculate the
gravitational wave signal of the short-period AM CVn systems. We find that
potentially several thousand AM CVn systems can be resolved by the
gravitational wave detector LISA, comparable to the expected number of detached
double white dwarfs that can be resolved. We estimate that several hundreds of
the AM CVn systems resolvable by LISA, are also detectable in the optical
and/or X-ray bands.
