The beam envelope equation -- Systematic solution for a FODO lattice with space charge

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Many approximate solutions for matched beam envelope functions with space charge have been developed; they generally have efforts of 2--10% for the parameters of interest and cannot be reliably improved. The new, systematic approach described here provides the K-V envelope functions to arbitrarily high accuracy as a power series in the quadrupole gradient. A useful simplification results from defining the sum and difference of the envelope radii; S = (a+b)/2 varies only slightly with distance z along the system axis, and D = (a-b)/2 contains most of the envelope oscillations. To solve the coupled equations for S and D, the ... continued below

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3 p.

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Lee, E.P. May 1, 1995.

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  • Lee, E.P. Lawrence Berkeley Lab., CA (United States). Accelerator and Fusion Research Div.

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Description

Many approximate solutions for matched beam envelope functions with space charge have been developed; they generally have efforts of 2--10% for the parameters of interest and cannot be reliably improved. The new, systematic approach described here provides the K-V envelope functions to arbitrarily high accuracy as a power series in the quadrupole gradient. A useful simplification results from defining the sum and difference of the envelope radii; S = (a+b)/2 varies only slightly with distance z along the system axis, and D = (a-b)/2 contains most of the envelope oscillations. To solve the coupled equations for S and D, the quadrupole strength K(z) is turned on by replacing K with {alpha}K{sub 1} and letting {alpha} increase continuously from 0 to 1. It is found that S and D may be expanded in even and odd powers of {alpha}, respectively. Equations for the coefficients of powers of {alpha} are then solved successively by integration in z. The periodicity conditions and tune integration close the calculation. Simple low order results are typically accurate to 1% or better.

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3 p.

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INIS; OSTI as DE96000132

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  • 16. Institute of Electrical and Electronic Engineers (IEEE) particle accelerator conference, Dallas, TX (United States), 1-5 May 1995

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  • Other: DE96000132
  • Report No.: LBL--36458
  • Report No.: CONF-950512--323
  • Grant Number: AC03-76SF00098
  • DOI: 10.2172/70711 | External Link
  • Office of Scientific & Technical Information Report Number: 106629
  • Archival Resource Key: ark:/67531/metadc621468

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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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  • May 1, 1995

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  • June 16, 2015, 7:43 a.m.

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  • April 4, 2016, 9:04 p.m.

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Lee, E.P. The beam envelope equation -- Systematic solution for a FODO lattice with space charge, article, May 1, 1995; California. (digital.library.unt.edu/ark:/67531/metadc621468/: accessed October 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.