Abstract
The large electron–positron collider LEP at CERN provides a beautiful example of our conceptual limits concerning the problem of dynamic aperture (short term stability of the transverse oscillations of particle trajectories) in circular machines. For the operation at 45 GeV (Z0 peak) the dynamic aperture did not pose any problem although its measurement gave a value much smaller than that predicted up to the end of 1993. After this date the measurements gave the same result as predicted but it was not possible to trace back the origin of the discrepancy. At high energy (the maximum operating energy foreseen is 100 GeV) the beam emittance increases with the square of the beam energy. Therefore, low emittance optics were proposed. These optics suffer from large anharmonicities because of the increased sextupole strengths. This led to an unexpected limitation of the beam lifetime.
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