Longitudinal instabilities and stability criteria

‘‘This paper is a short course on longitudinal instabilities and stability requirements for particle beams of circular accelerators which was presented at the 1987 U.S. Particle Accelerator School at Fermilab. The discussion includes criteria for longitudinal instability, stability limits, a longitudinal impedance estimation, a wire measurement (simulation) experiment, and results of an experiment to measure impedance by debunching. (AIP)