  Methods.There are no experimental data about the background experienced by
microcalorimeters in the L2 orbit, and thus the particle background levels were
calculated by means of Monte Carlo simulations: we considered the original
design configuration and an improved configuration aimed to reduce the
unrejected background, and tested them in the L2 orbit and in the low Earth
orbit, comparing the results with experimental data reported by other X-ray
instruments.To show the results obtainable with the improved configuration we
simulated the observation of a faint, high-redshift, point source (F[0.5-10
keV]~6.4E-16 erg cm-2 s-1, z=3.7), and of a hot galaxy cluster at R200
(Sb[0.5-2 keV]=8.61E-16 erg cm-2 s-1 arcmin-2,T=6.6 keV). Results.First we
confirm that implementing an active cryogenic anticoincidence reduces the
particle background by an order of magnitude and brings it close to the
required level.The implementation and test of several design solutions can
reduce the particle background level by a further factor of 6 with respect to
the original configuration.The best background level achievable in the L2 orbit
with the implementation of ad-hoc passive shielding for secondary particles is
similar to that measured in the more favorable LEO environment without the
passive shielding, allowing us to exploit the advantages of the L2 orbit.We
define a reference model for the diffuse background and collect all the
available information on its variation with epoch and pointing direction.With
this background level the ATHENA mission with the X-IFU instrument is able to
detect ~4100 new obscured AGNs with F>6.4E-16 erg cm-2 s-1 during three years,
to characterize cluster of galaxies with Sb(0.5-2 keV)>9.4E-16 erg cm-2 s-1
sr-1 on timescales of 50 ks (500 ks) with errors <40% (<12%) on
metallicity,<16% (4.8%) on temperature,2.6% (0.72%) on the gas density, and
several single-element abundances.
