Abstract
An optimisation study of a periodic structure of superconducting solenoids used as a focusing system for a muon cooling channel is presented. In order to optimise the field quality of these focusing solenoids, the general solution of the axi-symmetric Laplace equation with periodic boundary conditions in the longitudinal direction is calculated. The objective function for the field optimisation has been derived from the equation of motion of a charged particle inside the periodic decay channel. A coil cross-section has been found that reduces the first order non-linearity of the focusing system by 27% (with respect to a coil with rectangular cross-section) while keeping the linear focusing power constant.
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