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- W1567277313 abstract "We describe the motion of a particle in the lattice of a hadron accelerator using the formalism of symplectic maps. We revisit the Courant-Snyder’s theory and we stress that the reduction to normal form of a symplectic map is just the natural generalization of the linear theory. We show that a simple FODO cell (formed by linear elements and a sextupole) can be reduced to a quadratic map, for which some results are presented. We show also that it is possible to recover a continuum limit from a discrete description of the lattice. Finally a study of a one-dimensional model for LHC is made. The normal forms are used to compute the tune shifts and smear in various configurations. A comparison is made with the tracking results and an excellent agreement is found in a region whose boundary is close to the dynamical aperture. This suggests that the two-dimensional extension of the method is well suited to treat the coupled betatron nonlinear oscillations." @default.
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- W1567277313 date "1988-07-01" @default.
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- W1567277313 title "Normal forms for Hamiltonian maps and nonlinear effects in a particle accelerator" @default.
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- W1567277313 doi "https://doi.org/10.1007/bf02728793" @default.
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