Hart, T.L. Acosta, J.G. Cremaldi, L.M. Neuffer, D.V. Oliveros, S.J. Summers, D.J. JACoW Geneva, Switzerland 978-3-95450-180-9 10.18429/JACoW-NAPAC2016-TUPOB44 English 592-595 TUPOB44 ion emittance quadrupole betatron collider Contribution to a conference proceedings 2017 2017-01 http://dx.doi.org/10.18429/JACoW-NAPAC2016-TUPOB44 https://jacow.org/napac2016/papers/tupob44.pdf Low emittance muon beam lines and muon colliders are potentially a rich source of BSM physics for future experimenters. A normalized transverse muon emittance of 280 microns has been achieved in simulation with short solenoids and a betatron function of 3 cm. Here we use ICOOL, G4Beamline, and MAD-X to explore using a flat 400 MeV/c muon beam and strong focusing quadrupoles to achieve a normalized transverse emittance of 100 microns and finish 6D cooling. The low beta regions, as low as 5 mm, produced by the quadrupoles are occupied by dense, low Z absorbers, such as lithium hydride or beryllium, that cool the beam. Equilibrium transverse emittance is linearly proportional to the beta function. Reverse emittance exchange with septa and/or wedges is then used to decrease transverse emittance from 100 to 25 microns at the expense of longitudinal emittance for a high energy lepton collider. Cooling challenges include chromaticity correction, momentum passband overlap, quadrupole acceptance, and staying in phase with RF.