For several decades now, wide-field coded mask cameras have been used with success to localise Gamma-ray bursts (GRBs). In these instruments, the event count rate is dominated by the photon background due to their large field of view and large effective area. It is therefore essential to estimate the instrument background expected in orbit during the early phases of the instrument design in order to optimise the scientific performances of the mission. We present here a detailed study of the instrument background and sensitivity of the coded-mask camera for X- and Gamma-rays (CXG) to be used in the detection and localisation of high-redshift GRBs on-board the international GRB mission SVOM. To compute the background spectrum, a Monte-Carlo approach was used to simulate the primary and secondary interactions between particles from the main components of the space environment that SVOM will encounter along its Low Earth Orbit (LEO) (with an altitude of 600 km and an inclination of ~ 30 deg) and the body of the CXG. We consider the detailed mass model of the CXG in its latest design. According to our results, i) the design of the passive shield of the camera ensures that in the 4-50 keV imaging band the cosmic X-Gamma-ray background is dominant whilst the internal background should start to become dominant above 70-90 keV; ii) the current camera design ensures that the CXG camera will be more sensitive to high-redshift GRBs than the Swift Burst Alert Telescope thanks to a low-energy threshold of 4 keV.
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