Abstract-Beam instabilities cover a wide range of effects in particle accelerators and they have been the subject of intense research for several decades. As the machines performance was pushed new mechanisms were revealed and nowadays the challenge consists in studying the interplays between all this intricate phenomena, as it is very often not possible to treat the different effects separately. The aim of this paper is to review the main mechanisms, discussing in particular the recent developments of beam instability theories and simulations.

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The SIS100 synchrotron as a part of the new FAIR accelerator facility at GSI should be operated at the "space charge limit" for light and heavy-ion beams. Losses due to space charge induced resonance crossing should not exceed a few percent during a full cycle. Detailed magnet field measurements are now available for 72 out of the total 108 main SIS100 dipole magnets. Particle tracking studies including nonlinear field errors up to 7 th order in the main magnets together with different space charge models are performed. Because of the long time scales reduced space charge models are employed for tune scans. First comparisons with simulations using a self-consistent space charge solver are discussed as well as potential measures to further improve the options in tune space for the reference intensities and beyond. K: Accelerator modelling and simulations (multi-particle dynamics; single-particle dynamics); Beam dynamics; Beam Optics 1Corresponding author.

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