Studies of Anomalous Dispersion in the Slc Second Order Achromat’

certain coherent displacements did indeed linearly perturb the dispersion. This observation led to several studies of systematic’ and random8 errors with the conclusion that this effect stems from the fact that the dispersion in the Arcs is not always matched (especially in the vertical plane) due to the necessity of rolling the achromats about the beam axis to follow the site terrain. We will now review these findings in simple form. Certain causes of anomalois dispersion in the second order achromats of the SLC arcs are investigated. For matched dispersion, transverse displacements of combined function magnets do not introduce anomalous dispersion. This is shown by deriving-a’non-dispersive condition connecting the average of the matched dispersion function with the quadrupole and sextupole components of the field. In the SLC Arcs, however, the achromats are rolled producing a dispersion mismatch. In this case, the horizontal (vertical) dispersion is affected linearly by vertical (horizontal) displacement of magnets. The integral condition connecting the dipole and quadrupole fields and the matched disperstan is also derived. Combining this with the non-dispersive condition and the analytic expression of the matched dispersion gives two simple relationships for the fields of second order achromats constructed of combined function magnets. -3’h.e effects of the dispersion mismatch in the SLC Arcs is investigated using computer simulations. The results show that this mismatch will increase the sensitivity to transverse errors. We report the effects of certain systematic errors. Consider a differential slice of an Arc magnet with length ds. The transverse field components can be expressed as follows, Non-Dispersive Condition