Stability boundary and diffusion in 2D maps describing a magnetic lattice
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Polymilis, C
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Servizi, G
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Bazzani, A
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Turchetti, G
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Hizanidis, K
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We consider the non-linear map describing the basic cell of a circular accelerator. The dependence of the stability basin on the non-linearity is investigated by considering increasing multipolar orders. A model for the diffusion induced by a periodic ripple is derived; for a quadratic non-linearity it is the Hénon map with a modulated linear frequency. For slow modulation the diffusion process is conveniently described by the adiabatic theory, which gives a diffusion time proportional to the cube of the modulation period. Unlike the case of noise modulation, the diffusion takes place in the bounded region, near a resonance, swept by the separatrices.
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