Review of Dynamic Instabilities in Circular Accelerators

The coherent electromagnetic self-forces of a beam of particles in an accelerator can render unstable the motion of individual particles, or give rise to unstable coherent motion of the beam. The latter is the subject of this work. Coherent longitudinal bunching of an azimuthally uniform beam can result from the negative mass instability or interaction of the beam with the accelerating cavities. The negative mass instability can be suppressed by a sufficient spread in circulation frequency or by surrounding the beam with appropriate walls. The beam-cavity interaction can be overcome by careful design of the rf system. The interaction of the self-fields with the surrounding walls can lead to unstable coherent transverse motion through the finite resistance of the wall material. This instability may be suppressed by a sufficient spread in betatron frequencies. The relatively slow growth rate also allows stabilization by means of electronic feedback, and the stabilizing effect of passive structures has also been investigated. Experimental and theoretical investigation has led to an understanding of these effects to the extent that accelerators can be designed to overcome the instabilities.