The Fermilab Recycler Ring is a high-vacuum fixed energy antiproton storage ring with both stochastic (at present) and the future electron cooling systems. In this paper the technique for diffusion rate measurement, beam parameters and the analysis of data are presented, as well as the effect of intra-beam scattering on the operational considerations for the storage and cooling of the antiproton beam in the Recycler.

High-energy particle accelerators are as diverse as their uses, which range from scientific research in fields such as high-energy physics, materials science and the life sciences, to applications in industry and medicine. Despite the diversity of accelerators, the particle beams that they are designed to produce behave in ways that share many common features. Beam Dynamics in High Energy Particle Accelerators aims to provide an introduction to phenomena regularly encountered when working with beams in accelerators; from the basic principles of motion of relativistic particles in electromagnetic fields, to instabilities that can affect beam quality in machines operating at high current. This book assumes no prior experience with accelerator physics and develops the subject in a way that provides a solid foundation for more advanced study of specific topics.As well as including numerous revisions and improvements in the text, this second edition features substantial new material, including sections on fringe fields in multipole magnets, Verlet integration for particle tracking, and measurement of beam emittances. References and discussions of current topics have been updated. As with the first edition, the aim is to provide practical and powerful tools and techniques for the study of beam dynamics, while emphasizing the elegance of the subject and helping the reader develop a deep understanding of the relevant physics.

Galena, Illinois, 18-23 September 2005

The Recycler Ring (RR) is a new 8Gev antiproton storage ring at Fermilab. Presently, this machine is being commissioned using protons from the Booster. It uses barrier buckets for stacking, un-stacking and storing the beam. At any given time, the RR is capable of storing proton or antiproton beams in multiple segments azimuthally. These segments of the beam may have widely differing longitudinal emittance and beam intensities and bunch lengths. It is highly essential to be able to measure the longitudinal emittance and keep track of the longitudinal dynamics at various stages of the operation of the RR. In this paper, the authors discuss a few methods of longitudinal emittance measurements in barrier buckets and discuss their merits and demerits.

The Fermilab Recycler Ring (permanent magnets) will be built on top of the Fermilab Main Injector sharing the same tunnel; its main function is to recycle the anti-protons after a store in the Tevatron and to provide storage for them after after accumulation and cooling in the Accumulator. Estimates of coupling impedances show domination by space charge. Examination of longitudinal instabilities shows that microwave instability will not occur if there are only N = 2.53 x 1012 anti-protons in the beam. Longitudinal coupling-bunch instability during injection stacking does not appear possible because of long bunch lengths/short bunch gaps and lack of sharp resonances. Transverse instability, on the other hand, cannot be Landau damped by the momentum spread in the beam, but it can be cured by a small spread in the betatron tunes (either from space charge or an octupole).

We investigate processes contributing to emittance growth in the Fermilab Recycler Ring. In addition to beam-gas multiple scattering, we also examine other external factors such as Main Injector ramping affecting the emittance growth.