  Antiprotons, stored and cooled at low energies in a storage ring or at rest
in traps, are highly desirable for the investigation of a large number of basic
questions on fundamental interactions. This includes the static structure of
antiprotonic atomic systems and the time-dependent quantum dynamics of
correlated systems. The Antiproton Decelerator (AD) at CERN is currently the
worlds only low energy antiproton factory dedicated to antimatter experiments.
New antiproton facilities, such as the Extra Low ENergy Antiproton ring (ELENA)
at CERN and the Ultra-low energy Storage Ring (USR) at FLAIR, will open unique
possibilities. They will provide cooled, high quality beams of extra-low energy
antiprotons at intensities exceeding those achieved presently at the AD by
factors of ten to one hundred. These facilities, operating in the energy regime
between 100 keV down to 20 keV, face several design and beam dynamics
challenges, for example nonlinearities, space charge and scattering effects
limiting beam life time. Detailed investigations into the low energy and long
term beam dynamics have been carried out to address many of those challenges
towards the design optimisation. Results from these studies are presented in
this contribution, showing some examples for ELENA.
