This work deals with wave propagation into a coaxial cable, which can be modelled by the 3D Maxwell equations or 1D simplified models. The usual model, called the telegrapher's model, is a 1D wave equation of the electrical voltage and current. We derived a more accurate model from the Maxwell equations that takes into account dispersive effects. These two models aim to be a good approximation of the 3D electromagnetic fields in the case where the thickness of the cable is small. We perform some numerical simulations of the 3D Maxwell equations and of the 1D simplified models in order to validate the usual model and the new one. Moreover, we show that, while the usual telegrapher model is of order one with respect to the thickness of the cable, the dispersive 1D model is of order two.
Citation: Geoffrey Beck, Akram Beni Hamad. Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models[J]. AIMS Mathematics, 2024, 9(4): 8981-9019. doi: 10.3934/math.2024438
This work deals with wave propagation into a coaxial cable, which can be modelled by the 3D Maxwell equations or 1D simplified models. The usual model, called the telegrapher's model, is a 1D wave equation of the electrical voltage and current. We derived a more accurate model from the Maxwell equations that takes into account dispersive effects. These two models aim to be a good approximation of the 3D electromagnetic fields in the case where the thickness of the cable is small. We perform some numerical simulations of the 3D Maxwell equations and of the 1D simplified models in order to validate the usual model and the new one. Moreover, we show that, while the usual telegrapher model is of order one with respect to the thickness of the cable, the dispersive 1D model is of order two.
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Geoffrey Beck, Akram Beni Hamad. Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models[J]. AIMS Mathematics, 2024, 9(4): 8981-9019. doi: 10.3934/math.2024438
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