# Function of dipoles in particle accelerators

I know now that quadrupoles are used to focus the beam in a particle accelerator, but what about dipoles? Are they used to center or accelerate the beam? The number for the LHC magnets I think it is B~8 T, are those dipole magnets? The maximum energy reached by a proton in those conditions is only dependent on B and R (27km/$\pi$)?

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 ($C_c$ of 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 $\Delta C_c = -(\alpha_c \Delta E/E)$. With the momentum compaction $\alpha_c =1.85 \times 10^{-4}$ 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.