Time-dependent scalar Beltrami-Hertz potentials in free space |
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Authors: | W S Weiglhofer and A Lakhtakia |
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Institution: | (1) Department of Mathematics, University of Glasgow, G12 8QW Glasgow, Scotland, Great Britain;(2) Department of Engineering Science and Mechnics, Pennsylvania State University, 16802-1401 University Park, Pennsylvania |
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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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Keywords: | Time-dependent electromagnetism Beltrami fields Beltrami-Maxwell equations scalar Beltrami-Hertz potentials unidirectional source densities |
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