Analysis of a model for resonant extraction of intense beams by normal forms and frequency map
A simple 1D model is proposed to explore the resonant extraction of intense beams from a synchrotron as performed in the SIS synchrotron in GSI (Darmstadt). The model Hamiltonian consists of a constant focusing, a thin sextupole, and a smooth space charge field. Hyperbolic normal forms are used to e...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2001-11-01
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| Series: | Physical Review Special Topics. Accelerators and Beams |
| Online Access: | http://doi.org/10.1103/PhysRevSTAB.4.114201 |
| _version_ | 1818988252734947328 |
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| author | L. Bongini A. Bazzani G. Turchetti I. Hofmann |
| author_facet | L. Bongini A. Bazzani G. Turchetti I. Hofmann |
| author_sort | L. Bongini |
| collection | DOAJ |
| description | A simple 1D model is proposed to explore the resonant extraction of intense beams from a synchrotron as performed in the SIS synchrotron in GSI (Darmstadt). The model Hamiltonian consists of a constant focusing, a thin sextupole, and a smooth space charge field. Hyperbolic normal forms are used to estimate the extraction times and the emittance of the extracted beam; the quality of the reconstruction is tested in absence of space charge. The effect of space charge on the dynamical behavior of the beam near the 1/3 betatron resonance is numerically investigated using the frequency map analysis and qualitatively explained with perturbation theory. A polynomial approximation to the one turn map is obtained by replacing the exact space charge force with a sequence of polynomial kicks, and the resonant normal forms reproduce quite accurately the nonlinear tunes and the fixed points position. At low order an analytical estimate of the area of the stable region is proposed to recover the self-consistency of the model. |
| first_indexed | 2024-12-20T19:19:38Z |
| format | Article |
| id | doaj.art-872baf90498c4637acb61a15c06f79c0 |
| institution | Directory Open Access Journal |
| issn | 1098-4402 |
| language | English |
| last_indexed | 2024-12-20T19:19:38Z |
| publishDate | 2001-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Special Topics. Accelerators and Beams |
| spelling | doaj.art-872baf90498c4637acb61a15c06f79c02022-12-21T19:29:02ZengAmerican Physical SocietyPhysical Review Special Topics. Accelerators and Beams1098-44022001-11-0141111420110.1103/PhysRevSTAB.4.114201Analysis of a model for resonant extraction of intense beams by normal forms and frequency mapL. BonginiA. BazzaniG. TurchettiI. HofmannA simple 1D model is proposed to explore the resonant extraction of intense beams from a synchrotron as performed in the SIS synchrotron in GSI (Darmstadt). The model Hamiltonian consists of a constant focusing, a thin sextupole, and a smooth space charge field. Hyperbolic normal forms are used to estimate the extraction times and the emittance of the extracted beam; the quality of the reconstruction is tested in absence of space charge. The effect of space charge on the dynamical behavior of the beam near the 1/3 betatron resonance is numerically investigated using the frequency map analysis and qualitatively explained with perturbation theory. A polynomial approximation to the one turn map is obtained by replacing the exact space charge force with a sequence of polynomial kicks, and the resonant normal forms reproduce quite accurately the nonlinear tunes and the fixed points position. At low order an analytical estimate of the area of the stable region is proposed to recover the self-consistency of the model.http://doi.org/10.1103/PhysRevSTAB.4.114201 |
| spellingShingle | L. Bongini A. Bazzani G. Turchetti I. Hofmann Analysis of a model for resonant extraction of intense beams by normal forms and frequency map Physical Review Special Topics. Accelerators and Beams |
| title | Analysis of a model for resonant extraction of intense beams by normal forms and frequency map |
| title_full | Analysis of a model for resonant extraction of intense beams by normal forms and frequency map |
| title_fullStr | Analysis of a model for resonant extraction of intense beams by normal forms and frequency map |
| title_full_unstemmed | Analysis of a model for resonant extraction of intense beams by normal forms and frequency map |
| title_short | Analysis of a model for resonant extraction of intense beams by normal forms and frequency map |
| title_sort | analysis of a model for resonant extraction of intense beams by normal forms and frequency map |
| url | http://doi.org/10.1103/PhysRevSTAB.4.114201 |
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