Controlled longitudinal emittance blow-up using band-limited phase noise in CERN PSB

Controlled longitudinal emittance blow-up (from 1 eVs to 1.4 eVs) for LHC beams in the CERN PS Booster is currently achievied using sinusoidal phase modulation of a dedicated high-harmonic RF system. In 2021, after the LHC injectors upgrade, 3 eVs should be extracted to the PS. Even if the current method may satisfy the new requirements, it relies on low-power level RF improvements. In this paper another method of blow-up was considered, that is the injection of band-limited phase noise in the main RF system (h=1), never tried in PSB but already used in CERN SPS and LHC, under different conditions (longer cycles). This technique, which lowers the peak line density and therefore the impact of intensity effects in the PSB and the PS, can also be complementary to the present method. The longitudinal space charge, dominant in the PSB, causes significant synchrotron frequency shifts with intensity, and its effect should be taken into account. Another complication arises from the interaction of the phase loop with the injected noise, since both act on the RF phase. All these elements were studied in simulations of the PSB cycle with the BLonD code, and the required blow-up was achieved.