This book provides a comprehensive treatment of intensity dependent particle beam instabilities in accelerating rings. Written for researchers, the material is also suitable for use as a textbook in an advanced graduate course for students studying accelerator physics.The presentation starts with a brief review of the basic concept of wake potentials and coupling impedances in the vacuum chamber followed by a discussion on static and dynamic solutions of their effects on the particle beams. Special emphasis is placed separately on proton and electron machines. Other special topics of interest covered include Landau damping, Balakin-Novokhatsky-Smirnov damping, Sacherer's integral equations, Landau cavity, saw-tooth instability, Robinson stability criteria, beam loading, transition crossing, two-stream instabilities, and collective instability issues of isochronous rings. After the formulation of an instability, readers are provided a thorough description of one or more experimental observations together with a discussion of the cures for the instability.Although the book is theory oriented, the use of mathematics has been minimized. The presentation is intended to be rigorous and self-contained with nearly all the formulas and equations derived.

Systems to damp radial and vertical instabilities of individual rf bunches in the Fermilab Booster are being implemented. The positions of individual bunches are derived from stripline pickups. The position information is transmitted over a variable delay, amplified, and applied to deflectors after one almost complete revolution, 6.25 horizontal and 6.75 vertical betatron wavelengths downstream of the pickup. Motivation, system concepts, design considerations, and initial operating experience are described.

This paper presents results of experimental and theoretical investigations of transverse beam stability at injection to Fermilab Booster and discusses a novel scheme for transition crossing allowing to avoid the longitudinal emittance growth related to the transition. At reduced chromaticity a multibunch high order head-tail mode develops with growth time of 12 turns at fractional part of tune close to zero. An estimate of the growth rate based on known sources of impedance results in significantly smaller value and cannot explain observed instability growth rate.

The Fermilab Booster - built more than 40 years ago - operates well above the design proton beam intensity of 4 · 1012 ppp. Still, the Fermilab neutrino experiments call for even higher intensity exceeding 5.5 · 1012 ppp. A multitude of intensity related effects must be overcome in order to meet this goal including suppression of coherent dipole instabilities of transverse oscillations which manifest themselves as a sudden drop in the beam current. In this report we present the results of observation of these instabilities at different tune, coupling and chromaticity settings and discuss possible cures.

This thesis presents profound insights into the origins and dynamics of beam instabilities using both experimental observations and numerical simulations. When the Recycler Ring, a high-intensity proton beam accelerator at Fermi National Accelerator Laboratory, was commissioned, it became evident that the Recycler beam experiences a very fast instability of unknown nature. This instability was so fast that the existing dampers were ineffective at suppressing it. The nature of this phenomenon, alongside several other poorly understood features of the beam, became one of the biggest puzzles in the accelerator community. The author investigated a hypothesis that the instability arises from an interaction with a dense cloud of electrons accompanying the proton beam. He studied the phenomena experimentally by comparing the dynamics of stable and unstable beams, by numerically simulating the build-up of the electron cloud and its interaction with the beam, and by constructing an analytical model of an electron cloud-driven instability with the electrons trapped in combined-function dipole magnets. He has devised a method to stabilize the beam by a clearing bunch, which conclusively revealed that the instability is caused by the electron cloud, trapped in a strong magnetic field. Finally, he conducted measurements of the microwave propagation through a single dipole magnet. These measurements have confirmed the presence of the electron cloud in combined-function magnets.