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Measurements and analysis of orbit response matrix have been providing fordecades a formidable tool in the detection of linear lattice imperfections andtheir correction. Basically all storage-ring-based synchrotron light sourcesacross the world make routinely use of this technique in their daily operation,reaching in some cases a correction of linear optics down to 1% beta beatingand 0.1% coupling. During the design phase of a new storage ring it is alsoapplied in simulations for the evaluation of magnetic and mechanicaltolerances. However, this technique is known for its intrinsic slownesscompared to other methods based on turn-by-turn beam position data, both in themeasurement and in the data analysis. In this paper analytic formulas arederived and discussed that shall greatly speed up this second part. Themathematical formalism based on the Lie algebra and the resonance driving termsis extended to the off-momentum regime and explicit analytic formulas for theevaluation of chromatic functions from lattice parameters are also derived. Therobustness of these formulas, which are linear in the magnet strengths, istested with different lattice configurations.

Analytic formulas for the rapid evaluation of the orbit response matrix and chromatic functions from lattice parameters in circular accelerators