Exact matched-beam envelopes for undepressed transport in a quadrupole lattice with unequal drift lengths and arbitrary field strength

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In 1958, Courant and Snyder analyzed the problem of alternating-gradient beam transport and treated a model without focusing gaps or space charge. Recently we revisited their work and found the exactsolution for matched-beam envelopes in a linear quadrupole lattice [O.A. Anderson and L.L. LoDestro, Phys. Rev. ST Accel. Beams, 2009]. We extend that work here to include the effect of gaps. We derive the exact envelopes and show results for various field strengths, occupancies eta,and gap-length ratios. We find the peak envelope excursion. It has a broad minimum as a function of the phase advance sigma (typically around 34o) over ... continued below

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Anderson, O. A. & LoDestro, L. L. April 29, 2009.

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In 1958, Courant and Snyder analyzed the problem of alternating-gradient beam transport and treated a model without focusing gaps or space charge. Recently we revisited their work and found the exactsolution for matched-beam envelopes in a linear quadrupole lattice [O.A. Anderson and L.L. LoDestro, Phys. Rev. ST Accel. Beams, 2009]. We extend that work here to include the effect of gaps. We derive the exact envelopes and show results for various field strengths, occupancies eta,and gap-length ratios. We find the peak envelope excursion. It has a broad minimum as a function of the phase advance sigma (typically around 34o) over which it varies less than +-1percent. The phase-advance numbers also change little over the full range of gap ratios. However, the required field strengths vary appreciably. In the second stable band, the higher field strength necessitated by the lower occupancy accentuates the remarkable compression effect predicted for the FD (gapless) model.

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  • Report No.: LBNL-1812E
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.2172/953778 | External Link
  • Office of Scientific & Technical Information Report Number: 953778
  • Archival Resource Key: ark:/67531/metadc932135

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  • April 29, 2009

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Oct. 4, 2017, 3:29 p.m.

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Anderson, O. A. & LoDestro, L. L. Exact matched-beam envelopes for undepressed transport in a quadrupole lattice with unequal drift lengths and arbitrary field strength, report, April 29, 2009; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc932135/: accessed October 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.