Effects of tidal forces on the beam energy in LEP

The e⁺e^- collider LEP is used to investigate the Z particle and to measure its energy and width. This requires energy calibrations with ~20 ppm precision achieved by measuring the frequency of a resonance which destroys the transverse beam polarization established by synchrotron radiation. To make this calibration valid over a longer period all effects causing an energy change have to be corrected for. Among those are the terrestrial tides due to the Moon and Sun. They move the Earth surface up and down by as much as ~0.25 m which represents a relative local change of the Earth radius of 0.04 ppm. This motion has also lateral components resulting in a change of the LEP circumference (C_c=26.7 km) by a similar relative amount. Since the length of the beam orbit is fixed by the constant RF-frequency the change of the machine circumference will force the beam to go off-center through the quadrupoles and receive an extra, deflection leading to an energy change given by ΔC_c/C_c~-(α_cΔ_c E/E. With the momentum compaction α_c=1.85 10^-4 for the present LEP optics this gives tide-driven p.t.p. Energy excursion up to about 220 ppm, corresponding to ~18.5 MeV for the Z energy. A beam energy measurement carried out over a 24 hour period perfectly confirmed the effects expected from a more detailed calculation of the tides. A corresponding correction can be applied to energy calibrations