Consequences of the discontinuous replacement of radiated energy on the performance of LEP 200

It is pointed out that, owing to synchrotron radiation, electrons and positrons circulating in a storage ring lose energy almost uniformly along the arcs of the machine, while this radiated energy is replaced only by a few localized RF stations. Therefore, even for a machine without imperfections, the orbits of electrons and positrons are different: the maximum orbit separation scales with the cube of the particle energy and is inversely proportional to the number of RF stations. Some tracing results are presented showing the consequent reduction of dynamic aperture in the case of LEP (Large Electron Positron collider) for different combinations of particle energy and numbers of RF stations. The conclusion is that, with four RF stations symmetrically installed around the ring, there is no appreciable reduction of dynamic aperture and, therefore, no deterioration of the machine performance up to a particle energy of 100 GeV. With only two RF stations, however, the aperture of the standard LEP lattice with a 90° phase advance per cell is reduced by nearly 50% above 70 GeV. The strong dependence of this reduction of dynamic aperture on the choice of machine tunes is analyzed, and the example of a modified 90° lattice whose aperture is reduced only by 20% at 100 GeV with two RF-stations is discussed