Nonlinear optics from off-energy closed orbits

This paper describes a novel scheme for correcting the second order (chromatic sextupole) magnet lattice and its deployment on a fourth generation multibend achromat electron storage ring. The method is analogous to the well-established linear optics from closed orbits scheme, but uses an off-energy orbit response matrix to characterize the second order optics of a lattice. The matrix is constructed from the difference between two orbit response matrices measured at off-nominal energy, and is approximately linear with chromatic sextupole field strengths. This is utilized in a least squares minimization to find a model which minimizes the difference between the measured and model off-energy orbit response matrix. From this model corrections to the chromatic sextupoles of the machine can be calculated. In effect, for the MAX IV 3 GeV ring, the proposed scheme, NOECO (nonlinear optics from off-energy closed orbits), brings initial sextupole strength variations between achromats in the order of $\ifmmode\pm\else\textpm\fi{}8%$ down to the order of $\ifmmode\pm\else\textpm\fi{}1%$. The chromatic machine functions were symmetrized, the measured chromaticities approached the nominal values, and the lifetime of the beam at delivery conditions, with the same level of emittance coupling, increased to 19 h from 11 h at previously used sextupole settings.