Overlap Knock-Out Effects in the CERN Intersecting Storage Rings (ISR)

Overlap knock-out arises from an overlap between frequencies present in a bunched beam and the betatron frequencies in a stack. The "single ring" effect is the interaction of a bunched beam with a stack in the same ring. Here the coupling forces are fairly linear and are transmitted by machine elements. The "two-ring" effect is the interaction of a bunched beam with a stack in the other ring. Here the coupling forces are nonlinear since they are produced by the beam-beam interaction. A brief outline of the general theory of these effects is given. The single ring and two-ring dipole effects have been observed and shown to cause a large increase in the transverse size of the stacked beam. These observations are explained well by theoretical considerations. A special stacking program has greatly reduced the transverse blow-up, giving a smaller beam effective height and hence higher luminosity. Two-ring higher order effects have also been identified and explained by theory. The effects are small for the present ISR but can be an important consideration in the design of future machines.