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 $\pm 8\%$ down to the order of $\pm 1\%$. 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.

中文翻译：

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非能量闭合轨道的非线性光学

本文介绍了一种校正二阶（彩色六极）磁体晶格的新方案及其在第四代多弯曲消色差电子存储环上的部署。该方法类似于来自封闭轨道方案的行之有效的线性光学器件，但是使用能量不足的轨道响应矩阵来表征晶格的二阶光学器件。该矩阵由在偏离标称能量下测量的两个轨道响应矩阵之间的差异构成，并且与色六极场强度近似线性。在最小二乘最小化中利用它来找到一个模型，该模型可以最小化被测能量模型和模型的离能轨道响应矩阵之间的差异。根据该模型，可以计算出机器的色六极。实际上，对于MAX IV 3 GeV环，$\pm 8％$ 下降到 $\pm \mathrm{1个}％$。对称地设置了色度仪功能，测得的色度接近标称值，并且在相同的发射耦合水平下，在发射条件下光束的寿命从以前使用的六极杆设置的11 h增加到19 h。