Beam Dynamics Studies and Design Optimisation of New Low Energy Antiproton Facilities

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.Comment: 6 pages, 4 figures, 12th International Conference on Low Energy Antiproton Physics, LEAP 2016. Submitted to JPS Conference Proceeding

When all solutions of x′ = −∑ qi(t) x(t − Ti(t)) oscillate

AbstractIn this paper the long-term behavior of solutions to the equation in the title are examined, where qi(t) and Ti(t) are positive. In particular, it is shown that if lim inft → ∝ ∑i = 1n Ti(t) qi(t) > 1/e, all solutions oscillate about 0 infinitely often