Accurate iterative analytic solution of theKapchinskij-Vladimirskij equations for the case of a matched beam

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The well-known Kapchinskij-Vladimirskij (KV) equations are difficult to solve in general, but the problem is simplified for the matched-beam case with sufficient symmetry. They show that the interdependence of the two KV equations is eliminated, so that only one needs to be solved--a great simplification. They present an iterative method of solution which can potentially yield any desired level of accuracy. The lowest level, the well-known smooth approximation, yields simple, explicit results with good accuracy for weak or moderate focusing fields. The next level improves the accuracy for high fields; they previously showed how to maintain a simple explicit format ... continued below

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Anderson, Oscar A. August 6, 2006.

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The well-known Kapchinskij-Vladimirskij (KV) equations are difficult to solve in general, but the problem is simplified for the matched-beam case with sufficient symmetry. They show that the interdependence of the two KV equations is eliminated, so that only one needs to be solved--a great simplification. They present an iterative method of solution which can potentially yield any desired level of accuracy. The lowest level, the well-known smooth approximation, yields simple, explicit results with good accuracy for weak or moderate focusing fields. The next level improves the accuracy for high fields; they previously showed how to maintain a simple explicit format for the results. That paper used expansion in a small parameter to obtain the second level. The present paper, using straightforward iteration, obtains equations of first, second, and third levels of accuracy. For a periodic lattice with beam matched to lattice, they use the lattice and beam parameters as input and solve for phase advances and envelope waveforms. They find excellent agreement with numerical solutions over a wide range of beam emittances and intensities.

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  • Report No.: LBNL--61171
  • Report No.: HIFAN 1369
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.2172/920259 | External Link
  • Office of Scientific & Technical Information Report Number: 920259
  • Archival Resource Key: ark:/67531/metadc897393

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  • August 6, 2006

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

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  • Sept. 29, 2016, 1:36 p.m.

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Anderson, Oscar A. Accurate iterative analytic solution of theKapchinskij-Vladimirskij equations for the case of a matched beam, report, August 6, 2006; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc897393/: accessed September 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.