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A unified approach to the Darwin approximation

Phys. Plasmas 14, 102112 (2007); doi:10.1063/1.2799346

Published 30 October 2007

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Todd B. Krause
Institute for Fusion Studies and Physics Department, The University of Texas at Austin, Austin, Texas 78712, USA

A. Apte
Centre for Applied Mathematics, Tata Institute of Fundamental Research, Bangalore, India

P. J. Morrison
Physics Department and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712, USA
There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting. ©2007 American Institute of Physics
History: Received 9 July 2007; accepted 25 September 2007; published 30 October 2007
Permalink: http://link.aip.org/link/?PHPAEN/14/102112/1
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KEYWORDS and PACS

Keywords
PACS
  • 02.30.Mv
    Approximations and expansions
  • 03.50.De
    Classical electromagnetism, Maxwell equations
  • YEAR: 2007

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ISSN:
1070-664X (print)   1089-7674 (online)
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