Measurements of tune shifts with amplitude at LEP

The beam orbit system of the LEP electron-positron collider is able to store the beam position over 1000 turns following a deflection by a horizontal kicker. A precise analysis of such 1000-turn data for many beam position monitors was used to study the dependence of the tune on the horizontal amplitude. The horizontal tune shift with amplitude was determined from the decay of the beam oscillation for various LEP optics. This parameter turned out to be an important issue for the LEP high energy optics.