  In this work, we report on systematic Monte Carlo (MC) studies for the FRACAS
apparatus, a large acceptance mass spectrometer that will be used to measure
the fragmentation cross sections of $^{12}$C ions for hadrontherapy. The
apparatus placed, in a 100 mbar reaction chamber, will be made of a beam
monitor, trackers surrounding a magnet and a Time-Of-Flight (TOF) wall. In
order to determine the required performances of the trackers, Geant4
simulations of the whole system and in-house developed algorithms were used.
While keeping the beam monitor and TOF-wall positions fixed, the effects of the
tracker positions and spatial resolutions on the trajectory reconstruction and
mass identification efficiencies have been extracted. An optimal configuration
was found where the upstream trackers should be located 6 cm away from the
target and spaced 4 cm apart whereas their spatial resolutions should be close
to 100 $\mu$m. The positions of the downstream trackers will have to be changed
according to the beam energy to preserve high identification efficiencies.
Their spatial resolutions, even though of a lesser importance compared to the
upstream trackers, should be around 1 mm or better. In this optimal
configuration, an overall fragment identification efficiency above 90% has been
obtained for beam energies ranging from 100 to 400 MeV/nucleon.
