Quadrupole Doublet Channel and Septa Emittance Exchange for Muon Collider Final Cooling

The Muon Collider requires a low emittance $\epsilon_{6D}=0.044mm^{3}$ muon beam to get a luminosity of $\mathcal{L} \simeq10^{34}cm^{-2}s^{-1}$ to produce enough rare events. The muons are generated from pion decays that produce a muon beam with a very high emittance. To reduce the emittance two ionization cooling channels have been simulated that reduce the 6D normalized emittance to as low as $\epsilon_{6D}=0.123mm^{3}$, almost a factor of a million. However, the 6D emittance required by a muon collider is $\epsilon_{6D}=0.044mm^{3}$. We propose a final cooling channel composed of quadrupole doublets limited to 14 Tesla that provide strong focusing. The low $\beta^{*}$ regions, as low as 5 mm, are occupied by dense, low Z absorbers that cool the beam. Quadrupole channel emittances are based on calculations rather than full simulations at this point. After final cooling, normalized xyz emittances of (0.071, 0.141, 2.4) mm-rad are exchanged into (0.025, 0.025, 70) mm-rad as required by a collider. The beam is divided by 16 electrostatic septa into 17 channels.After that, a series of RF deflector cavities, as used in CLIC tests, form a 3.7 m long bunch train. Snap bunch coalescence combines the 17 bunches into one in a 21 GeV ring in 55 microseconds.