Abstract
Altering the optics in one section of a linear accelerator beamline will in general cause an alteration of the optics in all downstream sections. In circular accelerators, changing the optical properties of any beamline element will have an impact on the optical functions throughout the whole machine. In many cases, however, it is desirable to change the optics in a certain beamline section without disturbing any other parts of the machine. Such a local optics manipulation can be achieved by adjusting a number of additional corrector magnets that restore the initial optics after the manipulated section. In that case, the effect of the manipulation is confined in the region between the manipulated and the correcting beamline elements. Introducing a manipulation continuously, while the machine is operating, therefore requires continuous correction functions to be applied to the correcting quadrupole magnets. In this paper we present an analytic approach to calculate such continuous correction functions for six quadrupole magnets by means of a homotopy method. Besides a detailed derivation of the method, we present its application to an algebraic example, as well as its implementation at the seeding experiment sFLASH at the free-electron laser FLASH located at DESY in Hamburg.
Highlights
Introducing a manipulation continuously, while the machine is operating, requires continuous correction functions to be applied to the correcting quadrupole magnets
We present an approach to calculate such continuous correction functions for six quadrupole magnets by means of a homotopy method
Besides a detailed derivation of the method, we present its application to an algebraic example, as well as its demonstration at the seeding experiment sFLASH at the free-electron laser FLASH located at DESY in Hamburg
Summary
Many applications of particle accelerators require the dynamical manipulation of the optical functions in certain regions of the beam line during operation as, for example, minimizing the β-function at the interaction point of a collider experiment, or closing a variable-gap undulator in a synchrotron light source or a free-electron laser (FEL). Accelerator simulation codes such as ELEGANT [2] or MAD-X [3] can perform this matching and determine a suitable correction by numerically solving minimization problems Such an approach, is ill-suited for calculating continuous correction functions, which are required to compensate a manipulation that is being introduced continuously, as we will discuss later. Undulator the sFLASH experiment is located, which, since its installation in 2010, utilizes a variable-gap undulator system to generate seeded FEL radiation using different seeding techniques [5] By closing this undulator in order to start seeded operation, the optics in the following FLASH1 main undulator is altered, which results in a deteriorated FEL performance. The precise restoration of the initial optics could be verified by beam size measurements along the FLASH1 main undulator, which are presented in the final section of this paper
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