  High-brightness muon beams of energy comparable to those produced by
state-of-the-art electron, proton and ion accelerators have yet to be realised.
Such beams have the potential to carry the search for new phenomena in
lepton-antilepton collisions to extremely high energy and also to provide
uniquely well-characterised neutrino beams. A muon beam may be created through
the decay of pions produced in the interaction of a proton beam with a target.
To produce a high-brightness beam from such a source requires that the phase
space volume occupied by the muons be reduced (cooled). Ionization cooling is
the novel technique by which it is proposed to cool the beam. The Muon
Ionization Cooling Experiment collaboration has constructed a section of an
ionization cooling cell and used it to provide the first demonstration of
ionization cooling. We present these ground-breaking measurements.
