A proton driver for the Muon Collider source with a tunable momentum compaction lattice

The future Muon Collider will have a luminosity of the order of 10 ³⁵ cm^-2-1 during 1000 turns when the muons decay. This requires 10¹² muons per bunch. The muon source is a 30 GeV proton driver with 2.5 10¹³ protons per pulse. The proton bunch length should be of the order of 1 ns. Short bunches could be created by a tunable momentum compaction lattice which would bring the momentum compaction to zero in a short time. This isochronous condition would allow bunches to shear and become very short in time. We present a lattice where the momentum compaction is a tunable parameter at fixed horizontal and vertical betatron tunes. The values of the maxima of the dispersion function are kept small. We examine two kinds of lattices, with combined function as well as normal dipole and quadrupole magnets