Abstract
At the CERN accelerator complex, it seems that only the highest energy machine in the sequence, the LHC, with space charge (SC) parameter close to one, sees the predicted beneficial effect of SC on transverse coherent instabilities. In the other circular machines of the LHC injector chain (PSB, PS and SPS), where the SC parameter is much bigger than one, SC does not seem to play a major (stabilising) role, and it is maybe the opposite in the SPS. All the measurements and simulations performed so far in both the SPS and LHC will be reviewed and analysed in detail.
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