dorsal/arxiv
View SchemaMultiple resonance compensation for betatron coupling and its equivalence with matrix method
| Authors | G. De Ninno, D. Fanelli |
|---|---|
| Categories | |
| ArXiv ID | physics/9907040 |
| URL | https://arxiv.org/abs/physics/9907040 |
Abstract
Analyses of betatron coupling can be broadly divided into two categories: the matrix approach that decouples the single-turn matrix to reveal the normal modes and the hamiltonian approach that evaluates the coupling in terms of the action of resonances in perturbation theory. The latter is often regarded as being less exact but good for physical insight. The common opinion is that the correction of the two closest sum and difference resonances to the working point is sufficient to reduce the off-axis terms in the 4X4 single-turn matrix, but this is only partially true. The reason for this is explained, and a method is developed that sums to infinity all coupling resonances and, in this way, obtains results equivalent to the matrix approach. The two approaches is discussed with reference to the dynamic aperture. Finally, the extension of the summation method to resonances of all orders is outlined and the relative importance of a single resonance compared to all resonances of a given order is analytically described as a function of the working point.
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"abstract": "Analyses of betatron coupling can be broadly divided into two categories: the\nmatrix approach that decouples the single-turn matrix to reveal the normal\nmodes and the hamiltonian approach that evaluates the coupling in terms of the\naction of resonances in perturbation theory. The latter is often regarded as\nbeing less exact but good for physical insight. The common opinion is that the\ncorrection of the two closest sum and difference resonances to the working\npoint is sufficient to reduce the off-axis terms in the 4X4 single-turn matrix,\nbut this is only partially true. The reason for this is explained, and a method\nis developed that sums to infinity all coupling resonances and, in this way,\nobtains results equivalent to the matrix approach. The two approaches is\ndiscussed with reference to the dynamic aperture. Finally, the extension of the\nsummation method to resonances of all orders is outlined and the relative\nimportance of a single resonance compared to all resonances of a given order is\nanalytically described as a function of the working point.",
"arxiv_id": "physics/9907040",
"authors": [
"G. De Ninno",
"D. Fanelli"
],
"categories": [
"physics.acc-ph"
],
"title": "Multiple resonance compensation for betatron coupling and its equivalence with matrix method",
"url": "https://arxiv.org/abs/physics/9907040"
},
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