IONIZATION COOLING AND MUON COLLIDERS*

New inventions are rapidly improving the prospects for a high luminosity muon collider at the energy frontier. Recent analytical calculations, numerical simulations, and experimental measurements are coming together to make a strong case for a series of machines to be built, where each one is a precursor to the next, with its own unique experimental and accelerator physics programs. The ultimate machine is an energy-frontier muon collider. In about 4 years, the LHC and Tevatron will tell us the desired energy of the next lepton collider. At that time we must understand the needed technology and be ready to design, cost, and build the appropriate muon collider