Stephan I Tzenov and Ronald C Davidson 2003 New J. Phys. 5 67 doi:10.1088/1367-2630/5/1/367
Renormalization group reduction of the Hénon map and application to the transverse betatron motion in cyclic accelerators
Stephan I Tzenov and Ronald C Davidson
Show affiliationsThe renormalization group (RG) method is applied to the study of discrete dynamical systems. As a particular example, the Hénon map is considered as being applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring possessing a FODO-cell structure with a single thin sextupole. A powerful RG method is developed that is valid correct to fourth order in the perturbation amplitude, and a technique for resolving the resonance structure of the Hénon map is also presented. This calculation represents an application of the RG method to the study of discrete dynamical systems in a unified manner capable of reducing the dynamics of the system both far from and close to resonances, thus preserving the symplectic symmetry of the original map.
- PACS
- Subjects
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Accelerators, beams and electromagnetism
- Dates
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Issue 1 (June 2003)
Received 18 February 2003
Published 11 June 2003
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Renormalization group reduction of the Hénon map and application to the transverse betatron motion in cyclic accelerators
Stephan I Tzenov and Ronald C Davidson 2003 New J. Phys. 5 67
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