Determination of the effective permittivity of dielectric mixtures with the transmission line matrix methodDetermination of the effective permittivity of dielectric mixtures with the transmission line matrix method

In this article, the effective permittivity of two-phase dielectric mixtures is calculated by applying the transmission line matrix (TLM) method. Two slightly different TLM algorithms are considered: a hybrid approach, which combines the TLM method with a subgriding technique based on dual capacitor circuits, to allow a refined description of the material, and a standard or pure TLM approach, which uses a mesh size smaller than the typical dimension of insertions in order to appropriately describe details of the geometry. A study of the statistical distribution of permittivity for insertions in random positions is also presented, showing that the effective permittivity of the mixture tends …

Transmission line meshes for computational simulation of electromagnetic modes in the Earth's atmosphere

PurposeTwo transmission line meshes to simulate electromagnetic waves in the Earth's atmosphere are developed, one with the link transmission lines connected in parallel and the other with connections in series.Design/methodology/approachThe equations describing propagation of waves through these parallel or series meshes are equivalent to the Maxwell equations for TEr or TMr modes in a spherical cavity with lossy dielectric material between the external conducting surfaces, respectively.FindingsThe transmission line meshes are used for a numerical study of the natural electromagnetic noise due to lightning discharges in the Earth‐ionosphere cavity.Originality/valueThe numerical algorithm f…

A numerical study of atmospheric signals in the Earth-ionosphere electromagnetic cavity with the Transmission Line Matrix method

[1] The effect of the Earth-ionosphere electromagnetic cavity on the spectrum of an atmospheric signal generated by a broadband electrical current source is analyzed numerically by means of the Transmission Line Matrix (TLM) method. Two new TLM meshes are developed, one with transmission lines connected in parallel and the other with connections in series. The equations describing propagation through these parallel or series meshes are equivalent to the Maxwell equations for TEr or TMr modes in the spherical Earth-ionosphere cavity, respectively. The numerical algorithm obtains Schumann resonance frequencies very close to the experimental ones, confirming that this methodology is a valid nu…

An analysis of VLF electric field spectra measured in Titan's atmosphere by the Huygens probe

[1] A numerical simulation of Titan's electromagnetic cavity in the VLF band is carried out using the Transmission Line Matrix (TLM) method, with the aim of assessing the VLF electric field spectra sent by the Huygens probe. In an Earth-like model, successive peaks would be expected in the spectra, associated with multiple reflections of the electromagnetic wave on the external surfaces of Titan's electromagnetic cavity, formed by the ionosphere and a conductive ground or underground surface. However, owing to high losses conferred by the electrical conductivity to Titan's atmosphere, the direct numerical and experimental spectra are decreasing functions of the frequency without resonances …

Evidence of electrical activity on Titan drawn from the Schumann resonances sent by Huygens probe

Abstract A procedure is shown for extracting weak resonances from the responses of electromagnetic systems excited by electric discharges. The procedure, based on analysis of the late-time system response, is first checked using an analytical function and later with the data for the electric field generated by the computational simulation of Titan's atmosphere using the Transmission Line Matrix (TLM) method. Finally, the low frequency spectrum of the natural electric field in Titan's atmosphere sent by the mutual impedance sensor (MIP) included in the Huygens probe is analyzed employing this technique. The MIP sensor was initially designed to measure the horizontal component of the electric…

Rebuttal to “Comment on “Evidence of electrical activity on Titan drawn from the Schumann resonances sent by Huygens probe” by J.A. Morente, J.A. Portí, A. Salinas, and E.A. Navarro [2008, Icarus, 195, 802–811]”

Abstract Hamelin et al. criticize some conclusions of our paper [Morente, J.A., Porti, J.A., Salinas, A., Navarro, E.A., 2008. Icarus 195, 802–811]. This rebuttal is our response to their criticism. In our view, their comments are contradictory and not based on scientific argument. Our paper presents a comprehensible methodology for extracting weak resonances from the late-time response of systems with high losses and our conclusions are derived from and supported by this methodology, which was first checked using an analytical function and later with the data from a numerical simulation of Titan’s atmosphere. Conversely, the Comment of Hamelin et al. does not contain any mathematical proof…

A finite difference time domain model for the Titan ionosphere Schumann resonances

[1] This paper presents a numerical approach to model the electrical properties of Titan's atmosphere. The finite difference time domain technique is applied to model the atmosphere of Saturn's satellite in order to determine Schumann resonant frequencies and electromagnetic field distributions at the extremely low frequency range. Spherical coordinates are employed, and periodic boundary conditions are implemented in order to exploit the symmetry in rotation of the celestial body. Results are compared with a previous model using the transmission line matrix method up to 180 km altitude. For the first time a numerical FDTD model up to 800 km altitude is carried out, and we report lower freq…

Reply to comment by R. Grard et al. on “An analysis of VLF electric field spectra measured in Titan's atmosphere by the Huygens probe”

Numerical analysis of ionosphere disturbances and Schumann mode splitting in the Earth-ionosphere cavity

[1] The variability of ionosphere properties plays an important role in the Schumann resonances (SR), amplitudes, frequencies, and Q factor. Therefore, as atmosphere ionization is related to solar activity, SR could be devised as a source of indirect parameters that locally from the surface of the Earth could provide space weather information. A proper understanding of this link to SR parameters can be obtained through finite difference time domain (FDTD) simulations, specifically with the numerically obtained modes and frequencies that relate frequency shifts to the day-night asymmetry and polar inhomogeneities. Day-Night asymmetry is observed to have a minor influence in SR; however, larg…

A numerical study of the Schumann resonances in Mars with the FDTD method

[1] Natural electromagnetic waves generated near the surface by electrostatic discharges in dust storms (dust devils) or by geological activity could be trapped in the resonant cavity formed by the surface and lower ionosphere of Mars, as it occurs on Earth giving rise to Schumann resonances. The finite difference time-domain technique (FDTD) is applied to model the atmosphere of Mars in order to determine Schumann resonant frequencies, and natural electromagnetic fields at the extremely low frequency range (ELF). A numerical tool is provided to analyze the electrical conductivity profile of the Martian atmosphere, with the aim of obtaining Schumann resonance frequencies and their dependenc…