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This monograph presents research on the transversal beam dynamics
of accelerators and evaluates and describes the respective magnetic
field homogeneity. The widely used cylindrical circular multipoles
have disadvantages for elliptical apertures or curved trajectories,
and the book also introduces new types of advanced multipole
magnets, detailing their application, as well as the numerical data
and measurements obtained. The research presented here provides
more precise descriptions of the field and better estimates of the
beam dynamics. Moreover, the effects of field inhomogeneity can be
estimated with higher precision than before. These findings are
further elaborated to demonstrate their usefulness for real magnets
and accelerator set ups, showing their advantages over cylindrical
circular multipoles. The research findings are complemented with
data obtained from the new superconducting beam guiding magnet
models (SIS100) for the FAIR (Facility for Antiproton and Ion
Research) project. Lastly, the book offers a comprehensive survey
of error propagation in multipole measurements and an appendix with
Mathematica scripts to calculate advanced magnetic coil designs.
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