  Euclid is the second M-class mission of the ESA Cosmic Vision programme, with
the principal science goal of studying dark energy. Euclid is also expected to
undertake additional Legacy Science programmes. One proposal is the Exoplanet
Euclid Legacy Survey (ExELS) which will be the first survey able to measure the
abundance of exoplanets down to Earth mass for host separations from ~1AU out
to the free-floating (unbound) regime. The cold and free-floating exoplanet
regimes represent a crucial discovery space for testing planet formation
theories. ExELS will use the gravitational microlensing technique and will
detect 1000 microlensing events per month over 1.6 deg^2 of the Galactic bulge.
We assess how many of these events will have detectable planetary signatures
using a detailed multi-wavelength microlensing simulator (MABuLS) which
incorporates the Besancon Galactic model with 3D extinction. MABuLS is the
first theoretical simulation of microlensing to treat the effects of point
spread function (PSF) blending self-consistently with the underlying Galactic
model. We use MABuLS, together with current numerical models for the Euclid
PSFs, to explore a number of designs and de-scope options for ExELS, including
the exoplanet yield as a function of filter choice and slewing time, and the
effect of systematic photometry errors. Using conservative extrapolations of
current empirical exoplanet mass functions determined from ground-based
microlensing and radial velocity surveys, ExELS can expect to detect a few
hundred cold exoplanets around mainly G, K and M-type stellar hosts, including
~45 Earth-mass planets and ~6 Mars-mass planets for an observing programme
totalling 10 months. ExELS will be capable of measuring the cold exoplanet mass
function down to Earth mass or below, with orbital separations from ~1AU to the
free-floating regime. (Abridged)
