The 3D Vector Potential, Magnetic Field and Stored Energy in a Thin cos2 theta Coil Array

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The vector potential and the magnetic field have been derived for an arrays of quadrupole magnets with thin Cos(2{theta}) current sheet placed at r = R.{sup bc}. The field strength of each coil within the array, varies purely as a Fourier sinusoidal series of the longidutinal coordinate z in proportion to {omega}{sub m}z, where {omega}{sub m} = (2m-1){pi}/L, L denotes the half-period, and m = 1,2,3 etc. The analysis is based on the expansion of the vector potential in the region external to the windings of a linear 3D quad, and a revision of that expansion by the application of ... continued below

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Caspi, S. July 9, 1997.

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The vector potential and the magnetic field have been derived for an arrays of quadrupole magnets with thin Cos(2{theta}) current sheet placed at r = R.{sup bc}. The field strength of each coil within the array, varies purely as a Fourier sinusoidal series of the longidutinal coordinate z in proportion to {omega}{sub m}z, where {omega}{sub m} = (2m-1){pi}/L, L denotes the half-period, and m = 1,2,3 etc. The analysis is based on the expansion of the vector potential in the region external to the windings of a linear 3D quad, and a revision of that expansion by the application of the 'Addition Theorem' from that around the coil center to that around any arbitrary point in space.

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  • Report No.: LBNL-40564
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.2172/1011371 | External Link
  • Office of Scientific & Technical Information Report Number: 1011371
  • Archival Resource Key: ark:/67531/metadc831263

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  • July 9, 1997

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  • May 19, 2016, 3:16 p.m.

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  • June 15, 2016, 6:40 p.m.

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Caspi, S. The 3D Vector Potential, Magnetic Field and Stored Energy in a Thin cos2 theta Coil Array, report, July 9, 1997; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc831263/: accessed November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.