Accelerator Physics Challenges for an Energy Frontier Muon Collider*

Muon colliders offer a unique path to multi-TeV, high-luminosity lepton collisions.  Muon collisions with a center-of-mass energy of 10 TeV or above would offer significant discovery potential where the constituent collision energies exceed those of the LHC program by an order of magnitude.  Significant progress on the fundamental R&D and design concepts for such a machine has led to a new international effort to assemble a conceptual design within the next few years.  This effort will assess the viability of such a machine as a successor to the LHC program.  The remaining challenges and the R&D required to deliver a complete machine description will be described.