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 …

Extremely low frequency band station for natural electromagnetic noise measurement

A new permanent ELF measurement station has been deployed in Sierra Nevada, Spain. It is composed of two magnetometers, oriented NS and EW, respectively. At 10 Hz, their sensitivity is 19 μV/pT and the signal-to-noise ratio (SNR) is 28 dB for a time-varying signal of 1 pT, the expected field amplitude in Sierra Nevada. The station operates for frequencies below 24 Hz. The magnetometers, together with their corresponding electronics, have been specifically designed to achieve such an SNR for small signals. They are based on high-resolution search coils with ferromagnetic core and 106 turns, operating in limited geometry configuration. Different system noise sources are considered, and a stud…

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…

Solar storm effects during Saint Patrick's Days in 2013 and 2015 on the Schumann resonances measured by the ELF station at Sierra Nevada (Spain)

TLM Nodes: A New Look at an Old Problem

In this paper, an alternative perspective on the transmission line modeling (TLM) method concepts to unify previous work is presented. The procedure begins by discretizing Maxwell’s equations and proposing TLM equivalent models. Node voltage and mesh current definitions are provided in terms of link line contributions, compatible with stub currents and voltages. They allow obtaining an expression that relates incident and reflected pulses with no other condition required. With this unified approach, modeling of other situations is straightforward. 2-D cases, source implementation, and anisotropic media are described and numerically tested.

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 …

Analysis of the finite difference time domain technique to solve the Schrödinger equation for quantum devices

An extension of the finite difference time domain is applied to solve the Schrödinger equation. A systematic analysis of stability and convergence of this technique is carried out in this article. The numerical scheme used to solve the Schrödinger equation differs from the scheme found in electromagnetics. Also, the unit cell employed to model quantum devices is different from the Yee cell used by the electrical engineering community. A bound for the time step is derived to ensure stability. Several numerical experiments in quantum structures demonstrate the accuracy of a second order, comparable to the analysis of electromagnetic devices with the Yee cell. a!Electronic mail: Antonio.Sorian…

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…

Design & Optimization of Large Cylindrical Radomes with Subcell and Non-Orthogonal FDTD Meshes Combined with Genetic Algorithms

The word radome is a contraction of radar and dome. The function of radomes is to protect antennas from atmospheric agents. Radomes are closed structures that protect the antennas from environmental factors such as wind, rain, ice, sand, and ultraviolet rays, among others. The radomes are passive structures that introduce return losses, and whose proper design would relax the requirement of complex front-end elements such as amplifiers. The radome consists mostly in a thin dielectric curved shape cover and sometimes needs to be tuned using metal inserts to cancel the capacitive performance of the dielectric. Radomes are in the near field region of the antennas and a full wave analysis of th…

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…

Kinetic Interaction of Cold and Hot Protons With an Oblique EMIC Wave Near the Dayside Reconnecting Magnetopause

STR acknowledges support from the ISSI international team Cold plasma of ionospheric origin in the Earth's magnetosphere and of the Ministry of Economy and Competitiveness (MINECO) of Spain (grant FIS2017-90102-R). Research at IRAP was supported by CNRS, CNES and the University of Toulouse. JHL and DLT acknowledge support from NASA Grant 80NSSC18K1378. RED was supported by NASA grants 80NSSC19K070 and 80NSSC19K0254. MA was supported by SNSA Grant 56/18. SKV and RCA acknowledge support from NASA Grant 80NSSC19K0270. Work performed by MMS team members is supported by NASA contract NNG04EB99C.

Graphical Schemes Designed to Display and Study the Long-term Variations of Schumann Resonance

This work proposes and illustrates a graphical approach aimed at studying a wide range of features of the ELF horizontal magnetic field signal recorded at the Sierra Nevada station (Spain). In addition to the traditional long-term variations in the parameters of the first three Schumann resonances (their amplitudes, central frequencies and widths), many other properties such as the saturations of the magnetometers, anomalous values for the parameters or spectra with any kind of particularities are taken into consideration in this work. These features can provide us with complementary information about the long-term variation of Schumann resonances, give an estimation of the extent up to whi…

A New Approach to the Modeling of Anisotropic Media with the Transmission Line Matrix Method

A reformulation of the Transmission Line Matrix (TLM) method is presented to model non-dispersive anisotropic media. Two TLM-based solutions to solve this problem can already be found in the literature, each one with an interesting feature. One can be considered a more conceptual approach, close to the TLM fundamentals, which identifies each TLM in Maxwell’s equations with a specific line. But this simplicity is achieved at the expense of an increase in the memory storage requirements of a general situation. The second existing solution is a more powerful and general formulation that avoids this increase in memory storage. However, it is based on signal processing techniques and considerabl…

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…