Theorem on magnet fringe field

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Transverse particle motion in particle accelerators is governed almost totally by non-solenoidal magnets for which the body magnetic field can be expressed as a series expansion of the normal (b{sub n}) and skew (a{sub n}) multipoles, B{sub y} + iB{sub x} = {summation}(b{sub n} + ia{sub n})(x + iy){sup n}, where x, y, and z denote horizontal, vertical, and longitudinal (along the magnet) coordinates. Since the magnet length L is necessarily finite, deflections are actually proportional to ``field integrals`` such as {bar B}L {equivalent_to} {integral} B(x,y,z)dz where the integration range starts well before the magnet and ends well after it. ... continued below

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5 p.

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Wei, Jie & Talman, R. December 31, 1995.

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  • Wei, Jie Brookhaven National Lab., Upton, NY (United States)
  • Talman, R. Cornell Univ., Ithaca, NY (United States). Lab. of Nuclear Studies

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Transverse particle motion in particle accelerators is governed almost totally by non-solenoidal magnets for which the body magnetic field can be expressed as a series expansion of the normal (b{sub n}) and skew (a{sub n}) multipoles, B{sub y} + iB{sub x} = {summation}(b{sub n} + ia{sub n})(x + iy){sup n}, where x, y, and z denote horizontal, vertical, and longitudinal (along the magnet) coordinates. Since the magnet length L is necessarily finite, deflections are actually proportional to ``field integrals`` such as {bar B}L {equivalent_to} {integral} B(x,y,z)dz where the integration range starts well before the magnet and ends well after it. For {bar a}{sub n}, {bar b}{sub n}, {bar B}{sub x}, and {bar B}{sub y} defined this way, the same expansion Eq. 1 is valid and the ``standard`` approximation is to neglect any deflections not described by this expansion, in spite of the fact that Maxwell`s equations demand the presence of longitudinal field components at the magnet ends. The purpose of this note is to provide a semi-quantitative estimate of the importance of {vert_bar}{Delta}p{sub {proportional_to}}{vert_bar}, the transverse deflection produced by the ion-gitudinal component of the fringe field at one magnet end relative to {vert_bar}{Delta}p{sub 0}{vert_bar}, the total deflection produced by passage through the whole magnet. To emphasize the generality and simplicity of the result it is given in the form of a theorem. The essence of the proof is an evaluation of the contribution of the longitudinal field B{sub x} from the vicinity of one magnet end since, along a path parallel to the magnet axis such as path BC.

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5 p.

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INIS; OSTI as DE96007743

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  • LHC `95: international workshop on single particle effects in large hadron colliders, Montreux (Switzerland), 15-21 Oct 1995

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  • Other: DE96007743
  • Report No.: BNL--62610
  • Report No.: CONF-9510138--4
  • Grant Number: AC02-76CH00016
  • Office of Scientific & Technical Information Report Number: 220539
  • Archival Resource Key: ark:/67531/metadc672488

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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.

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  • December 31, 1995

Added to The UNT Digital Library

  • June 29, 2015, 9:42 p.m.

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  • Nov. 25, 2015, 5:29 p.m.

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Wei, Jie & Talman, R. Theorem on magnet fringe field, article, December 31, 1995; Upton, New York. (digital.library.unt.edu/ark:/67531/metadc672488/: accessed September 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.