STUDIES OF ANOMALOUS DISPERSION IN THE SLC SECOND ORDER ACHROMAT

Summary Certain causes of anomalous 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 dispersion 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. The effects of the dispersion mismatch in the SLC Arcs is