Choice of tune and aperture of a circular collider

At low energies the considerations in the choice of the focusing strength (choice of nu) are the beam size and the orbit distortion due to field errors which, together, generate a geometrical requirement on the size of the beam pipe and the good field aperture. Indeed, the strong focusing principle was invented to reduce the necessary magnet aperture, thereby the cost of the magnets. But, at high energies this is no longer true. The beam size is, generally, negligibly small and the orbit distortion is corrected to arbitrary desired accuracy. With properly designed trim dipole system the correction is straightforward. Other types of geometrical demands on the aperture arise from beam manipulations such as stacking and resonant extraction. These requirements tend to be local and can usually be satisfied by local lattice insertions. The excitation of higher order resonances by magnet field errors is small and negligible beyond the octupole. However, in colliders the excitation by beam-beam forces is large and resonances up to the 7th order must be avoided. (This severely limits the allowable tune spread Δnu, hence the available Landau damping of beam instabilities.) But this excitation depends only on the orbit functions at the collision point and not on the overall focusing strength