Resonant normal forms, interpolating Hamiltonians and stability analysis of area preserving maps

Bazzani, Armando; Giovannozzi, M.; Servizi, G.; Todesco, E.; Turchetti, G.

doi:10.1016/0167-2789(93)90249-z

Cited by 75 publications

(92 citation statements)

References 13 publications

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“…Normal forms and RDT have been proven in [10,15,16] to be a powerful tool to investigate lattice nonlinearities. This formalism is used here to describe betatron coupling close to the difference resonance.…”

Section: Resonance Driving Term Description Of the Emittance Sharmentioning

confidence: 99%

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Emittance sharing and exchange driven by linear betatron coupling in circular accelerators

Franchi

Métral

Tomás

2007

Phys. Rev. ST Accel. Beams

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The influence of linear betatron coupling due to constant-in-time skew quadrupolar fields on the transverse emittances is discussed using both a simplified model of a smooth circular accelerator and a more realistic strong-focusing lattice with localized sources of coupling (thin lens). New formulas for the coupled transverse emittances are derived that include the initial emittances, the coupling strengths, and the tune distance from the resonance. By using the more powerful Lie algebra and the resonance driving terms formalism, equivalent formulas are derived that provide a better understanding of some counterintuitive effects, otherwise not understandable in the smooth approximation. The new formulas have been tested both numerically and experimentally by using data of the CERN Proton Synchrotron showing a remarkable agreement.

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Section: Resonance Driving Term Description Of the Emittance Sharmentioning

confidence: 99%

“…where h x x ÿ ip x and h y ŷ ÿ ip y are the same complex Courant-Snyder coordinates of [15]. substitutes s as independent variable and is defined as follows:…”

Section: New Theory Of Emittance Exchange In the Smooth Approximmentioning

confidence: 99%

Emittance sharing and exchange driven by linear betatron coupling in circular accelerators

Franchi

Métral

Tomás

2007

Phys. Rev. ST Accel. Beams

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“…This however does not influence the derivation of our final results, since all the observables are eventually related to the canonical coordinatesx;p x (ŷ;p y ). For a detailed analysis of the effect of the nonsymplectic transformation, see [6]. The nonlinear tunes x;y appear in the above expression instead of Q x;y since this approach takes into account possible amplitude dependent detuning.…”

Section: A Hamiltonian Coefficients and Magnet Strengthmentioning

confidence: 99%

Magnet strength measurement in circular accelerators from beam position monitor data

Franchi

Tomás

Schmidt

2007

Phys. Rev. ST Accel. Beams

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Recent measurements of resonance terms suggested the extension of the existing technique to measure magnet strengths from turn-by-turn beam position monitor data. This article describes the algorithm to infer the magnet strength from the variation along the ring of the resonance terms and reports on the first measurement. Both the algorithm and the software written for the analysis of the data can be particularly useful in the commissioning period of an accelerator in order to find magnets with wrong strengths or polarities as well as magnets with large magnetic errors.

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“…A simple model representing the horizontal betatron motion in a circular machine under the influence of sextupole and octupole magnets was used (the motion in the vertical plane can be safely neglected). By assuming that the nonlinear magnets are located at the same place and the single-kick approximation [10] is used, the one-turn transfer map can be expressed as x n+1 = M n (x n ):…”

Section: The Novel Multiturn Extractionmentioning

confidence: 99%

Multiturn Extraction Based on Trapping in Stable Islands

Cappi¹,

Gilardoni²,

Giovannozzi³

et al. 2005

AIP Conference Proceedings

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For some applications an intermediate extraction mode between fast (one turn) and slow (several thousand turns) is needed. This is the case of the five-turn extraction used to transfer the proton beam from the CERN Proton Synchrotron (PS) to the Super Proton Synchrotron (SPS). Unavoidable losses and poor betatronic matching with the receiving machine affect the present approach, which is based on beam slicing by means of an electrostatic septum. These features are rather serious obstacles to an intensity upgrade of the PS/SPS Complex. To overcome these difficulties, a novel extraction technique was proposed recently. By using nonlinear magnetic elements, stable islands can be generated in the transverse phase space. Furthermore, provided the linear tune is varied slowly, it is possible to trap the charged particles inside the stable islands in order to split the beam into different beamlets. Once generated, the distance between these beamlets can be tailored to the extraction needs by simply increasing the distance of the tune from the resonance value. The results of numerical simulations for the novel technique are presented and discussed in detail together with the outcome of the intense experimental studies performed to assess the validity of this approach. Abstract. For some applications an intermediate extraction mode between fast (one turn) and slow (several thousand turns) is needed. This is the case of the five-turn extraction used to transfer the proton beam from the CERN Proton Synchrotron (PS) to the Super Proton Synchrotron (SPS). Unavoidable losses and poor betatronic matching with the receiving machine affect the present approach, which is based on beam slicing by means of an electrostatic septum. These features are rather serious obstacles to an intensity upgrade of the PS/SPS Complex. To overcome these difficulties, a novel extraction technique was proposed recently. By using nonlinear magnetic elements, stable islands can be generated in the transverse phase space. Furthermore, provided the linear tune is varied slowly, it is possible to trap the charged particles inside the stable islands in order to split the beam into different beamlets. Once generated, the distance between these beamlets can be tailored to the extraction needs by simply increasing the distance of the tune from the resonance value. The results of numerical simulations for the novel technique are presented and discussed in detail together with the outcome of the intense experimental studies performed to assess the validity of this approach.

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Resonant normal forms, interpolating Hamiltonians and stability analysis of area preserving maps

Cited by 75 publications

References 13 publications

Emittance sharing and exchange driven by linear betatron coupling in circular accelerators

Emittance sharing and exchange driven by linear betatron coupling in circular accelerators

Magnet strength measurement in circular accelerators from beam position monitor data

Multiturn Extraction Based on Trapping in Stable Islands

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