Function of dipoles in particle accelerators

Question

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/$\pi$)?

Answer 1

Dipoles bend the beam. If you have enough of them, they bend the beam in a circle.

The strength of the dipole magnets sets the energy of the beam if it's traveling along the nominal orbit axis, which is essentially the design centerline for the machine. That's the one energy where all those dipoles will bend the beam by 360 degrees.

But if you want to be really, really precise about the energy, it can get complicated. If the beam is running off-axis for some reason, then it gets additional bending contributions from the focusing magnets (quadupoles, sextapoles, octapoles) so it has to have a different energy. The beam has to go around in a very specific amount of time set by the RF acceleration (each turn of the beam has to line up with the RF), so if that's too short or too long the beam will deviate from the nominal path and change energy.

With LEP, the predecessor of the LHC in the same tunnel, all this led to some interesting effects (from "Effects of tidal forces on the beam energy in LEP", Arnaudon et al, 1993):

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.