# Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 41. no. 4. pp. 66–88. ISSN 2079-6641

Contents of this issue

MSC 78A40, 65M06

Research Article

Mathematical modeling of the propagation of a plane electromagnetic wave in a strip waveguide with inhomogeneous boundary conductivity

D. A. Tverdyi, E. I. Malkin, R. I. Parovik

Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034, Paratunka, Mirnaya st., 7, Russia

E-mail: dimsolid95@gmail.com

In the article, mathematical modeling of the electromagnetic dynamics of an atmosferic is carried out. Atmospheric is a broadband signal with a maximum intensity in the frequency range of 8-10 kHz, which propagates in the form of a plane electromagnetic wave in the complex structure of the conducting space of the waveguide formed by the Earth’s surface and the ionosphere. The mathematical model of the process is described by a boundary value problem for the system of Maxwell equations. The boundary conditions of the problem determine the structure of the waveguide (Perfectly matched layer), the parameters of the conducting volume, and the interaction with inhomogeneities in the waveguide, either temporarily arising (local change in conductivity) or existing permanently (coastal line of the oceans). The mathematical model is solved by the Finite-Difference Time-domain numerical method. To solve the problem, a software package was developed in the MATLAB environment. As a result of computer simulations, it is shown that the presence of distortions of the main electromagnetic wave is caused by the mutual interference of the main wave and the reflected wave from the inhomogeneity. As a result, by observing the parameters of the atmospheric, it is possible to establish the presence of inhomogeneity along the path of its propagation. Simulation of the process of interaction of electromagnetic radiation with an inhomogeneity in a waveguide can establish a relationship between
the radiation parameters and its inhomogeneities.

Key words: atmospheric, whistler, EM plane wave, conduction inhomogeneity, PML, ABC, interference, Maxwell equations, FDTD, MATLAB

DOI: 10.26117/2079-6641-2022-41-4-66-88

Original article submitted: 03.12.2022

Revision submitted: 06.12.2022

For citation. Tverdyi D. A., Malkin E. I., Parovik R. I. Mathematical modeling of the propagation of a plane electromagnetic wave in a strip waveguide with inhomogeneous boundary conductivity. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 41: 4, 66-88. DOI: 10.26117/2079-6641-2022-41-4-66-88

Funding. The research was carried out within the framework of the state task of IKIR FEB RAS on the topic AAAA-A21-121011290003-0.

Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

© Tverdyi D. A., Malkin E. I., Parovik R. I., 2022

References

1. Koronczay D., Lichtenberger J., Clilverd M. A., Rodger C. J., Lotz S. I., Sannikov D. V., et al. The source regions of whistlers, Journal of Geophysical Research: SpacePhysics, 2019, vol. 124, pp. 5082–5096. DOI: 10.1029/2019JA026559.
2.  Lichtenberger J., Ferencz C., Bodnar L., Hamar D., Steinbach P. Automatic whistler detector and analyzer system: Automatic whistler detector, J. Geophys. Res., 2008, vol. 113, no. A12. DOI: 10.1029/2008JA01346.
3. Storey L. R. O. An investigation of whistling atmospherics, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1953, vol. 246, no. 908, pp. 113–141. DOI: 10.1098/rsta.1953.0011.
4. Elsherbeni A. Z., Demir V. The finite-difference time-domain method for electromagnetics with MATLAB simulations. Raleigh, USA, SciTech Publishing, 2015, 560 pp., isbn: 978-1-61353-175-4.
5. Nickelson L. Electromagnetic Theory and Plasmonics for Engineers. Singapore, Springer, 2018, 749 pp., isbn: 9789811323522.
6. Yee K. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media, IEEE Transactions on Antennas and Propagation, 1966, vol. 14, no. 3, pp. 302–307. DOI: 10.1109/TAP.1966.1138693.
7. Taflove A., Hagness S. C. Computational Electrodynamics: The Finite-difference Timedomain Method. Massachusetts, USA, Artech House, 2005, 1038 pp., isbn: 9781580538329.
8. Chen W. K. The Electrical Engineering Handbook. Amsterdam, Elsevier, 2005, 1018 pp., isbn: 978-0-12-170960-0.
9. Courant R., Friedrichs K., Lewy H. On the partial difference equations of mathematical physics, IBM journal of Research and Development, 1967, vol. 11, no. 2, pp. 215–234. DOI: 10.1147/rd.112.0215.
10. Bachman G., Narici L., Beckenstein E. Fourier and Wavelet Analysis. New York, Springer, 1999, 516 pp., isbn: 978-0387988993.
11. Lindell I. V., Sihvola A. H. Perfect Electromagnetic Conductor, Journal of Electromagnetic Waves and Applications, 2005, vol. 19, no. 7, pp. 861–869. DOI: 10.1163/156939305775468741.
12. Berenger J.P. A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, 1994, vol. 114, no. 2, pp. 185–200. DOI: 10.1006/jcph.1994.1159.
13. Berenger J.P. Perfectly matched layer for the FDTD solution of wave-structure interaction problems, IEEE Transactions on Antennas and Propagation, 1996, vol. 44, no. 1, pp. 110–117. DOI: 10.1109/8.477535.
14. Andrew W. V., Balanis C. A. Tirkas P. A. Comparison of the Berenger perfectly matched layer and the Lindman higher-order ABC’s for the FDTD method, IEEE Microwave and Guided Wave Letters, 1995, vol. 5, no. 6, pp. 192–194. DOI: 10.1109/75.386128.
15. Veihl J. C., Mittra R. Efficient implementation of Berenger’s perfectly matched layer (PML) for finite-difference time-domain mesh truncation, IEEE Transactions on Antennas and Propagation, 1996, vol. 6, no. 2, pp. 94–96. DOI: 10.1109/75.482000.
16. Gedney S. D. An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices, IEEE Transactions on Antennas and Propagation, 1996, vol. 44, no. 12, pp. 1630–1639. DOI: 10.1109/8.546249.

Tverdyi Dmitrii Alexsandrovich – Ph. D. (Phys. & Math.), Lead programmer laboratory of electromagnetic propogation Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Russia, ORCID 0000-0001-6983-5258.

Malkin Evgeniy Ilich – Junior Researcher, Laboratory of Electromagnetic Radiation Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Russia, ORCID 0000-0001-8037-1335.

Parovik Roman Ivanovich – D. Sci. (Phys. & Math.), Associate Professor, Leading researcher laboratory of modeling physical processes Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Russia, ORCID 0000-0002-1576-1860.