Longitudinal parameters of the LHC beam in the SPS: 25 ns/50 ns/75 ns bunch spacing

This Note describes some of the studies in 2008 concerning the longitudinal plane of the LHC beam in the SPS. These studies were carried out for different bunch spacing and different beam intensities, aiming to verify the ability to deliver to the LHC a stable beam with the desired emittance despite the different injected beam parameters. Controlled emittance blow up and a second RF system (800 MHz) are used to stabilise the nominal intensity beam and to increase the emittance of low intensity beams. The bunch length at extraction is verified for different cases: emittance blow-up applied or not, different settings of the relative phase between the 200 MHz and the 800 MHz systems, different bunch spacing (25 ns, 50 ns or 75 ns), different intensity per bunch and different number of PS batches. A range of phases for the 800 MHz system (acceptable in bunch shortening mode) allows guaranteeing the beam stability and the amplitude of the applied noise allows tuning the beam emittance. Figures of merit are used that allow rapid evaluation and comparison of the quality of the beam at extraction as for example stability and bunch length uniformity across batches.