Systematic multipoles and the linear aperture for the SSC

The Superconducting Supercollider (SSC) requires an adequate linear aperture for reliable operation. Linear motion is required over a working region in amplitude and momentum space sufficient to include the beam size and momentum spread, closed-orbit deviations, and injection errors. For the SSC, the linearity requirement has been translated into a limit on orbit distortion or ''smear'' of 10% and a limit on amplitude and momentum dependent tune shifts Δν < 0.005 at betatron amplitudes Ax, Ay up to 0.005 m (maximum) in the SSC arcs over the momentum spread δ = Δp/p = ± 1.0 x 10-3, and at amplitudes up to 0.007 m at pΔ p/p = 0. The implications of these tune-shift criteria on the tolerances for systematic and random multipole components of SSC magnets are discussed in this paper. The large circumference of the SSC makes it sensitive to effects that add coherently around the ring. The amplitude- and momentum-dependent tune shifts due to systematic multipole components in the SSC dipoles are particularly important. The linearity criteria set strict tolerances on SSC dipole systematic multipole components. The tolerances are strongly dependent on the strength of focusing in the SSC lattice, as discussed in this paper