Analytical expressions for the smear due to nonlinear multipoles

An analytical derivation of the horizontal smear due to sextupoles and octupoles is presented. A generalized expression for the horizontal smear due to all multipoles is derived. A two-degree-of-freedom calculation yields the smear due to sextupoles and octupoles. Experimental observations of the smear induced by special sextupoles have been made at the Fermilab Tevatron, and the present calculations agree very well with data over a wide range of conditions. The smear due to random and systematic multiple errors in the dipoles, before and after the insertion of lumped correctors, is calculated for the SSC (Superconducting Super Collider) lattice. The smear due to random and systematic multipole errors in the Tevatron dipoles is computed.<>