Final Focus Challenges for Muon Colliders at Highest Energies

This report discusses challenges in developing final-focus systems for muon colliders at 10-100 TeV. The optics design is impeded by limited quadrupoles gradients and the large beam emittances. Of interest are also spot-size dilutions accumulating over several turns. Tolerances on magnet vibration and field stability are comparable to those at future electron-positron linear colliders. While at 10 TeV nonlinear kinematic terms are still important at 100 TeV synchrotron radiation may complicate the design. In view of the high charge per bunch and the multiple passes, wake fields and space-charge effects must be looked at carefully. For multi-TeV energies a single-pass muon collider is a promising option, since it poses no neutrino radiation hazard, can accommodate ultracold muon beams, and lends itself more easily to novel focusing techniques such as plasma lenses or dynamic focusing, thereby avoiding the gradient limitations of conventional quadrupoles.