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Altering the optics in one section of a linear accelerator beamline will ingeneral cause an alteration of the optics in all downstream sections. Incircular accelerators, changing the optical properties of any beamline elementwill have an impact on the optical functions throughout the whole machine. Inmany cases, however, it is desirable to change the optics in a certain beamlinesection without disturbing any other parts of the machine. Such a local opticsmanipulation can be achieved by adjusting a number of additional correctormagnets that restore the initial optics after the manipulated section. In thatcase, the effect of the manipulation is confined in the region between themanipulated and the correcting beamline elements. Introducing a manipulationcontinuously, while the machine is operating, therefore requires continuouscorrection functions to be applied to the correcting quadrupole magnets.  In this paper we present an analytic approach to calculate such continuouscorrection functions for six quadrupole magnets by means of a homotopy method.Besides a detailed derivation of the method, we present its application to analgebraic example, as well as its implementation at the seeding experimentsFLASH at the free-electron laser FLASH located at DESY in Hamburg.

Confining continuous manipulations of accelerator beamline optics