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.
