Full 3‐D TLM simulations of the Earth‐ionosphere cavity: Effect of conductivity on the Schumann resonances

Abstract

Schumann resonances can be found in planetary atmospheres, inside the cavity formed by the conducting surface of the planet and the lower ionosphere. They are a powerful tool to investigate both the electric processes that occur in the atmosphere and the characteristics of the surface and the lower ionosphere. Results from a full 3‐D model of the Earth‐ionosphere electromagnetic cavity based on the Transmission‐Line Modeling (TLM) method are presented. A Cartesian scheme with homogeneous cell size of 10 km is used to minimize numerical dispersion present in spherical schemes. Time and frequency domain results have been obtained to study the resonance phenomenon. The effect of conductivity on the Schumann resonances in the cavity is investigated by means of numerical simulations, studying the transition from resonant to nonresonant response and setting the conductivity limit for the resonances to develop inside the cavity. It is found that the transition from resonant to nonresonant behavior occurs for conductivity values above roughly 10−9 S/m. For large losses in the cavity, the resonances are damped, but, in addition, the peak frequencies change according to the local distance to the source and with the particular electromagnetic field component. These spatial variations present steep variations around each mode's nodal position, covering distances around 1/4 of the mode wavelength, the higher modes being more sensitive to this effect than the lower ones. The dependence of the measured frequency on the distance to the source and particular component of the electric field offers information on the source generating these resonances.

Exploration of a Composite Index to Describe Magnetospheric Activity: Reduction of the Magnetospheric State Vector to a Single Scalar

“…Magnetospheric measures that certainly would be of interest if they became available for extended periods of time are measures of the state of the plasmasphere, the state of the electron plasma sheet, the area of the polar cap, the dayside reconnection rate (measured from dayside ionospheric radars), the total radiation belt content (C.-L. Huang, private communication, August 31, 2015;Forsyth et al, 2016), a nightside stretching index (S. Wing, private communication, June 18, 2014), the mass composition of the magnetospheric plasmas, and the intensities of plasma waves in the magnetosphere (in particular electromagnetic ion cyclotron waves and whistler-mode chorus waves). Ionospheric measures that would be of interest if they became available are the ionospheric ion outflow rates from the polar cap and from the auroral zone (Welling et al, 2015;Wilson et al, 2004), the global total electron content (Emmert et al, 2017;Lin et al, 2017), the global Joule heating rate (Weimer, 2005;Zhang et al, 2005), and the Q-value of the Schumann resonance cavity (Fullenkrug et al, 2002;Toledo-Redondo et al, 2016). A storm time atmospheric measure that would be of interest for atmospheric drag if it became available is the thermospheric density (Rhoden et al, 2000;Vallardo & Finkleman, 2014).…”

Schumann resonances at Mars: Effects of the day‐night asymmetry and the dust‐loaded ionosphere

“…TLM is a time domain numerical method based on discretizing time and space and solves the involved differential equations by approximating the derivatives to differences. Details of the algorithm used can be found in Toledo‐Redondo et al [, ]. The algorithm has been adapted to the size of Mars (radius of 3390 km).…”

“…Different methods can be applied to approach the Schumann resonance cavity problem, like, for instance, finite differences in time domain [ Yang et al , ], 2‐D telegraph equations [ Pechony and Price , ], full wave solution [ Galuk et al , ], or the knee model [ Nickolaenko and Hayakawa , ]. We make use of the 3‐D TLM method [ Toledo‐Redondo et al , , ], which can be easily adapted to model the large day‐night asymmetry of the Martian cavity. This work considers two kinds of simulations: neglecting the day‐night differences (symmetric cavity) and accounting for them (asymmetric cavity).…”

“…The spectrum of this Gaussian current is approximately flat in the SR band. More details on the source used can be found in Toledo‐Redondo et al [s]. We use the same source for all the simulations, i.e., we inject the same amount of energy, and so the SR amplitudes can be compared among simulations.…”

ELF Electromagnetic Waves from Lightning: The Schumann Resonances

“…Methods of introducing more complicated ionosphere structure include two-layer [41] and multi-layer models [42][43][44][45], and the more realistic two-exponential [46], "knee" [47], and "multi-knee" [24] profiles. In recent years, more complicated 3-D transmission line modeling of the SR has been attempted [48] as well as 3-D finite difference time For other locations on the sphere, the relative intensity of the electric and magnetic fields depends uniquely on the source-observer distance (SOD). In Figure 2, the theoretical spectra for the vertical electric field, as a function of different SODs, are shown.…”