Width of nonlinear resonance

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Two approximations are made, one essential and the other not so essential but convenient to keep the analytical treatment manageable: (1) Only one nonlinear resonance is considered at a time so that the treatment is best suited when the tune is close to one resonance only. To improve this approximation, one must go to the next order which involves a canonical transformation of dynamical variables. Analytical treatment of more than one resonance is not possible for general cases. (2) In the formalism using the action-angle variables, the Hamiltonian can have terms which are independent of the angle variables. These terms ... continued below

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Pages: 2

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Ohnuma, S. March 1, 1984.

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Description

Two approximations are made, one essential and the other not so essential but convenient to keep the analytical treatment manageable: (1) Only one nonlinear resonance is considered at a time so that the treatment is best suited when the tune is close to one resonance only. To improve this approximation, one must go to the next order which involves a canonical transformation of dynamical variables. Analytical treatment of more than one resonance is not possible for general cases. (2) In the formalism using the action-angle variables, the Hamiltonian can have terms which are independent of the angle variables. These terms are called phase-independent terms or shear terms. The tune is then a function of the oscillation amplitudes. In the lowest-order treatment, the (4N)-pole components but not the (4N + 2)-pole components contribute to this dependence. In deriving the resonance width analytically, one ignores these terms in the Hamiltonian for the sake of simplicity. If these are retained, one needs at least three extra parameters and the analytical treatment becomes rather unwieldy.

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Pages: 2

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NTIS, PC A02/MF A01; 1.

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  • Other Information: 1

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  • Other: DE84009862
  • Report No.: FERMILAB/TM-1247
  • Grant Number: AC02-76CH03000
  • DOI: 10.2172/5179339 | External Link
  • Office of Scientific & Technical Information Report Number: 5179339
  • Archival Resource Key: ark:/67531/metadc1062016

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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Creation Date

  • March 1, 1984

Added to The UNT Digital Library

  • Jan. 22, 2018, 7:23 a.m.

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  • Feb. 1, 2018, 8:33 p.m.

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Ohnuma, S. Width of nonlinear resonance, report, March 1, 1984; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc1062016/: accessed November 13, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.