Solving electromagnetic boundary problems with equivalence methods

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Doctoral thesis (article-based)
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23, [104]
Electromagnetics Laboratory report series, 434
A basic problem in electromagnetics involves solving the Maxwell equations in a non-empty space, i.e. in a space with interfaces or boundaries. In this dissertation the wanted electromagnetic fields are searched via equivalence methods: a full electromagnetic problem is transformed to a simpler solvable form, or the solution is an equivalent source, or both. The chosen transformations result to two slightly different transmission line formulations or to Kelvin inversion (inversion in a sphere). The equivalent source is typically an image source. The included cases are 1) a planar multilayer chiral structure, 2) a conducting earth under a current source, 3) a sphere in an isotropic or bi-isotropic space, and 4) three types of anisotropic half-space-planar boundary or half-space problems. The first two cases (three papers) are time-dependent problems and the latter two (four papers) statics or quasi-statics. In each case the solution methodology is presented, the solutions are written, and the implications and limitations are discussed.
equivalence method, equivalent source, electromagnetic image principle, Kelvin inversion, bi-isotropic medium, anisotropic medium, exact image theory (EIT), geomagnetically induced currents (GIC), transmission line, electrostatics
Other note
  • Oksanen M. I., Hänninen J. and Tretyakov S. A., 1991. Vector circuit method for calculating reflection and transmission of electromagnetic waves in multilayer chiral structures. IEE Proceedings H – Microwaves, Antennas and Propagation 138, number 6, pages 513-520.
  • Lindell I. V. and Hänninen J. J., 2000. Static image principle for the sphere in isotropic or bi-isotropic space. Radio Science 35, number 3, pages 653-660.
  • Lindell I. V., Hänninen J. J. and Pirjola R., 2000. Wait's complex-image principle generalized to arbitrary sources. IEEE Transactions on Antennas and Propagation 48, number 10, pages 1618-1624.
  • Hänninen J. J., Pirjola R. J. and Lindell I. V., 2002. Application of the exact image theory to studies of ground effects of space weather. Geophysical Journal International 151, number 2, pages 534-542.
  • Lindell I. V., Hänninen J. J. and Nikoskinen K. I., Electrostatic image theory for an anisotropic boundary. IEE Proceedings – Science, Measurement and Technology, accepted for publication.
  • Hänninen J. J., Lindell I. V. and Nikoskinen K. I., 2004. Electrostatic image theory for an anisotropic boundary of an anisotropic half-space. Progress in Electromagnetics Research 47, pages 235-262.
  • Hänninen J. J., Nikoskinen K. I. and Lindell I. V., 2004. Electrostatic image theory for two anisotropic half-spaces. Helsinki University of Technology, Electromagnetics Laboratory Report Series, Report 428. Submitted in shorter form to Electrical Engineering (Archiv für Elektrotechnik).
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