Longitudinal instability of a continuous beam in a proton synchrotron

Abstract

The results of a calculation of the threshold for longitudinal coherent instability of a continuous beam circulating in a proton synchrotron and constant energy are presented. A beam in an intermediate state — not bunched into bunches but not uniform over the azimuth — is said to be continuous. Such a beam moves outside (possibly, near) empty rf separatrices of the longitudinal sinusoidal electric field and has a ribbon portrait in the longitudinal phase plane. The computational method is used for the U-70 synchrotron at the Institute of High Energy Physics, where in the course of stochastic slow extraction of a circulating beam is continuous in the sense indicated. It bends around empty separatrices of the 200-MHz accelerating field and for several seconds interacts with the electromagnetic fields of the working oscillations of the disconnected resonators of the main accelerating system with frequency 5.5–6 MHz, which can result in a loss of longitudinal stability.