Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models
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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024438?viewType=HTML |
| _version_ | 1797261928091877376 |
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| author | Geoffrey Beck Akram Beni Hamad |
| author_facet | Geoffrey Beck Akram Beni Hamad |
| author_sort | Geoffrey Beck |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T23:49:00Z |
| format | Article |
| id | doaj.art-b83568f6cde24bd39ef585138566dd2b |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T23:49:00Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-b83568f6cde24bd39ef585138566dd2b2024-03-15T01:25:19ZengAIMS PressAIMS Mathematics2473-69882024-03-01948981901910.3934/math.2024438Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D modelsGeoffrey Beck 0Akram Beni Hamad 11. Rennes University, IRMAR UMR 6625, INRIA centre at Rennes University (MINGuS project-team), ENS Rennes-École normale supérieure, Rennes, France2. INRIA Paris, 2 Rue Simone Iff, 75012 Paris. CERMICS, Ecole des Ponts, 77455 Marne-la-Vallée, FranceThis 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.https://www.aimspress.com/article/doi/10.3934/math.2024438?viewType=HTMLcoaxial cablesmaxwell's equationstelegrapher's modelsfinite elementsasymptotic analysis |
| spellingShingle | Geoffrey Beck Akram Beni Hamad Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models AIMS Mathematics coaxial cables maxwell's equations telegrapher's models finite elements asymptotic analysis |
| title | Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models |
| title_full | Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models |
| title_fullStr | Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models |
| title_full_unstemmed | Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models |
| title_short | Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models |
| title_sort | electromagnetic waves propagation in thin heterogenous coaxial cables comparison between 3d and 1d models |
| topic | coaxial cables maxwell's equations telegrapher's models finite elements asymptotic analysis |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024438?viewType=HTML |
| work_keys_str_mv | AT geoffreybeck electromagneticwavespropagationinthinheterogenouscoaxialcablescomparisonbetween3dand1dmodels AT akrambenihamad electromagneticwavespropagationinthinheterogenouscoaxialcablescomparisonbetween3dand1dmodels |