In this Chapter we will derive expressions for general field and alignment errors to be used in the Hamiltonian perturbation theory. Pure electromagnetic multipole fields have been derived in [2.1] from the Laplace equation while ignoring kinematic terms as well as higher-order field perturbations. In preparation for more sophisticated beam transport systems and accelerator designs aiming, for example, at ever smaller beam emittances it becomes imperative to consider higher-order perturbations to preserve desired beam characteristics. We will therefore derive the general electromagnetic fields from the curvilinear Laplace equation and formulate the general equations of motion in both planes with all higher-order geometric and chromatic perturbations up to third order. To meet also the increasing use of wiggler magnets and superconducting magnets, we discuss magnetic parameters of both magnet types.
KeywordsCurrent Sheet Deflection Angle Curvilinear Coordinate System Fringe Field Beam Transport
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