First order variation of the dispersion function with particle energy deviation

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The variation of the dispersion function with the particle energy deviation can presently be calculated from second order transfer matrices; its periodic solution is determined numerically. The general differential equations for the dispersion function deduced from the complete equation of motion to second order are solved, using Green's function integral leading to an analytical expression of the periodic solution of the dispersion function D/sub 0/ and of the first order perturbation, D/sub 1/, with respect to energy deviation. The same method can be extended to higher order perturbations of the dispersion function. The determination of the periodic solution as well ... continued below

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Pages: 24

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Delahaye, J.P. & Jaeger, J. December 1, 1984.

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Description

The variation of the dispersion function with the particle energy deviation can presently be calculated from second order transfer matrices; its periodic solution is determined numerically. The general differential equations for the dispersion function deduced from the complete equation of motion to second order are solved, using Green's function integral leading to an analytical expression of the periodic solution of the dispersion function D/sub 0/ and of the first order perturbation, D/sub 1/, with respect to energy deviation. The same method can be extended to higher order perturbations of the dispersion function. The determination of the periodic solution as well as the transportation of these two dispersion functions through any element depends only on two particular integrals. These integrals are derived for the general case of a combined function magnet, with up to second order components. The derivation includes the contribution from the edges. Chapter 2 and 3 deal with closed machines, chapter 4 applies these results to beam transport lines. These analytical expressions are then applied to a typical machine in order to illustrate the most important driving terms; the results do agree with those obtained by optics programs like MAD or DIMAT based on second order transfer matrices.

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Pages: 24

Notes

NTIS, PC A02/MF A01.

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  • Other: DE85007740
  • Report No.: SLAC/AP-40
  • Grant Number: AC03-76SF00515
  • DOI: 10.2172/6104210 | External Link
  • Office of Scientific & Technical Information Report Number: 6104210
  • Archival Resource Key: ark:/67531/metadc1109772

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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

  • December 1, 1984

Added to The UNT Digital Library

  • Feb. 22, 2018, 7:45 p.m.

Description Last Updated

  • March 23, 2018, 4:22 p.m.

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Delahaye, J.P. & Jaeger, J. First order variation of the dispersion function with particle energy deviation, report, December 1, 1984; United States. (digital.library.unt.edu/ark:/67531/metadc1109772/: accessed May 28, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.