Analytic Solution of the Envelope Equations for an Undepressed Matched Beam in a FODO Quadrupole Channel

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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 exact solution for matchedbeam 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 asymmetric drift spaces. We derive the solution and show exact envelopes for the first two solution bands and the peak envelope excursions as a function of the phase advancesigma up to 360o. In the second stable band, decreased occupancy ... continued below

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Anderson, Oscar & 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 exact solution for matchedbeam 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 asymmetric drift spaces. We derive the solution and show exact envelopes for the first two solution bands and the peak envelope excursions as a function of the phase advancesigma up to 360o. In the second stable band, decreased occupancy requires higher focus field-strength and accentuates the remarkable compression effect predicted for the FD (gapless) model.

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  • PAC09 Conference, Vancouver, Canada , May 4-8, 2009

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  • Report No.: LBNL-1832E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 957043
  • Archival Resource Key: ark:/67531/metadc931641

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  • April 29, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Jan. 4, 2017, 3:03 p.m.

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Anderson, Oscar & LoDestro, L. L. Analytic Solution of the Envelope Equations for an Undepressed Matched Beam in a FODO Quadrupole Channel, article, April 29, 2009; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc931641/: accessed January 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.