The current fixed target (FT) experiments at CERN are a complementary approach to the Large Hadron Collider (LHC) and play a crucial role in the investigation of fundamental questions in particle physics. Within the scope of the LHC Injectors Upgrade (LIU), aiming to improve the LHC
beam production, the injector complex will be significantly upgraded during the second Long Shutdown (LS2). All nonLHC beams are expected to benefit from these upgrades. In this paper, we focus on the studies of the transverse instability in the Proton Synchrotron (PS), currently limiting the intensity of Time-Of-Flight (ToF) type beams, as well as the prediction of the impact of envisaged hardware modifications. A first discussion on the effect of space charge on the observed instability is also being presented
