Ann. Geophys., 38, 207–230, 2020 https://doi.org/10.5194/angeo-38-207-2020 © Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License. Model of the propagation of very low-frequency beams in the Earth–ionosphere waveguide: principles of the tensor impedance method in multi-layered gyrotropic waveguides Yuriy Rapoport1,6, Vladimir Grimalsky2, Viktor Fedun3, Oleksiy Agapitov1,4, John Bonnell4, Asen Grytsai1, Gennadi Milinevsky1,5, Alex Liashchuk6, Alexander Rozhnoi7, Maria Solovieva7, and Andrey Gulin1 1Faculty of Physics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine 2IICBA, CIICAp, Autonomous University of the State of Morelos (UAEM), Cuernavaca, Morelos, Mexico 3Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, UK 4Space Science Laboratory, University of California, Berkeley, Berkeley, California, USA 5International Center of Future Science, College of Physics, Jilin University, Changchun, China 6National Space Facilities Control and Test Center, State Space Agency of Ukraine, Kyiv, Ukraine 7Shmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia Correspondence: Yuriy Rapoport (
[email protected]) Received: 20 March 2019 – Discussion started: 7 May 2019 Revised: 25 November 2019 – Accepted: 17 December 2019 – Published: 10 February 2020 Abstract. The modeling of very low-frequency (VLF) elec- 1 Introduction tromagnetic (EM) beam propagation in the Earth–ionosphere waveguide (WGEI) is considered. A new tensor impedance The results of the analytical and numerical study of very method for modeling the propagation of electromagnetic low-frequency (VLF) electromagnetic (EM) wave/beam beams in a multi-layered and inhomogeneous waveguide is propagation in the lithosphere–atmosphere–ionosphere– presented.