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Time-dependent scalar Beltrami-Hertz potentials in free space

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Abstract

We have solved the Beltrami-Maxwell equations for free space in terms of time-dependent scalar functions, the so-called scalar Beltrami-Hertz potentials. The two Beltrami fields have been represented in terms of scalar Beltrami-Hertz potentials. While the method is formulated for general sources, it is at its most powerful when the impressed source current densities are unidirectional: each Beltrami field, a complex-valued vector, can then be derived from a single scalar Beltrami-Hertz potential. We have calculated the corresponding scalar Green function explicity and given closed-form solutions for dipolar sources. Finally, the connection between the Beltrami-Maxwell formalism and conventional electromagnetic theory has been re-affirmed.

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Authors and Affiliations

  1. Department of Mathematics, University of Glasgow, G12 8QW, Glasgow, Scotland, Great Britain

    W. S. Weiglhofer

  2. Department of Engineering Science and Mechnics, Pennsylvania State University, 16802-1401, University Park, Pennsylvania

    A. Lakhtakia

Authors
  1. W. S. Weiglhofer
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  2. A. Lakhtakia
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Weiglhofer, W.S., Lakhtakia, A. Time-dependent scalar Beltrami-Hertz potentials in free space. Int J Infrared Milli Waves 15, 1015–1026 (1994). https://doi.org/10.1007/BF02096132

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  • DOI: https://doi.org/10.1007/BF02096132

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