Fast symplectic mapping and long-term stability near broad resonances

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Fast symplectic mapping, based on a canonical generator of the full-turn map in polar coordinates (I, {Phi}), is a powerful tool to study long-term stability in large hadron storage rings. Accurate maps for realistic lattices can be constructed in a few hours on a workstation computer, and can be iterated to follow orbits for 10{sup 7} turns in less than 4 hours. Orbits of the map can also be used in a non-perturbative construction of quasi-invariant actions. By bounding the small changes in quasi-invariants along many short orbits, one can derive conservative estimates of survival time for long orbits, for ... continued below

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24 p.

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Warnock, R.L. & Berg, J.S. April 1, 1997.

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  • Warnock, R.L. Stanford Linear Accelerator Center, CA (United States)
  • Berg, J.S. European Organization for High-Energy Physics (CERN), Geneva (Switzerland)

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Fast symplectic mapping, based on a canonical generator of the full-turn map in polar coordinates (I, {Phi}), is a powerful tool to study long-term stability in large hadron storage rings. Accurate maps for realistic lattices can be constructed in a few hours on a workstation computer, and can be iterated to follow orbits for 10{sup 7} turns in less than 4 hours. Orbits of the map can also be used in a non-perturbative construction of quasi-invariant actions. By bounding the small changes in quasi-invariants along many short orbits, one can derive conservative estimates of survival time for long orbits, for any initial condition in a region of phase space. A first quasi-invariant vector, J, arises from a canonical transformation (1, {Phi}) {r_arrow} (J, {Psi}), based on interpolation of invariant tori surrounding the origin. The variation of J is relatively large near a broad resonance. In such a region a second canonical transformation, associated with pendulum-like motion in appropriate variables, is required to produce a good quasi-invariant. This quasi-invariant is used to set a long-term bound on motion near a broad, large-amplitude resonance in a realistic model of the Large Hadron Collider (LHC). Interesting general properties of the pseudo-pendulum motion are studied.

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24 p.

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INIS; OSTI as DE97006469

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  • 12. advanced ICFA beam dynamics workshop on nonlinear and collective phenomena in beam physics, Arcidosso (Italy), 2-6 Sep 1996

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  • Other: DE97006469
  • Report No.: SLAC-PUB--7464
  • Report No.: CONF-9609198--6
  • Grant Number: AC03-76SF00515
  • Office of Scientific & Technical Information Report Number: 489627
  • Archival Resource Key: ark:/67531/metadc677407

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  • April 1, 1997

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  • July 25, 2015, 2:21 a.m.

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  • Feb. 2, 2016, 5:30 p.m.

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Warnock, R.L. & Berg, J.S. Fast symplectic mapping and long-term stability near broad resonances, article, April 1, 1997; Menlo Park, California. (digital.library.unt.edu/ark:/67531/metadc677407/: accessed November 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.