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.
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