Abstract
The field distributions in magnetic and electric quadrupoles as well as trajectories of charged particles in these fields are derived. Transformations of positions and inclinations of particle trajectories are described for quadrupole multiplets. Relations for point-to-parallel, point-to-point, and more complex transformations are outlined, and the properties of systems that can achieve such relations are discussed. Different methods for obtaining numerical solutions for the trajectories of charged particles through quadrupole multiplets are presented including solutions for relativistically fast charged particles.
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