The beam envelope equation-systematic solution for a periodic quadrupole lattice with space charge

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Description

Many approximate solutions for matched beam envelope functions with space charge have been developed; they generally have errors 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 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 ... continued below

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22 p.

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Lee, E.P. April 1, 1995.

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This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 18 times . More information about this report can be viewed below.

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Description

Many approximate solutions for matched beam envelope functions with space charge have been developed; they generally have errors 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 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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22 p.

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INIS; OSTI as DE95012761

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  • Other Information: PBD: Apr 1995

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  • Other: DE95012761
  • Report No.: LBL--37050
  • Grant Number: AC03-76SF00098
  • DOI: 10.2172/70711 | External Link
  • Office of Scientific & Technical Information Report Number: 70711
  • Archival Resource Key: ark:/67531/metadc704473

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  • April 1, 1995

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  • Sept. 12, 2015, 6:31 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 periodic quadrupole lattice with space charge, report, April 1, 1995; California. (digital.library.unt.edu/ark:/67531/metadc704473/: accessed August 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.