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A Study of the Propagation of Electromagnetic Waves in Titan's Available online at www.sciencedirect.com R Icarus 162 (2003) 374–384 www.elsevier.com/locate/icarus A study of the propagation of electromagnetic waves in Titan’s atmosphere with the TLM numerical method Juan A. Morente,a,* Gregorio J. Molina-Cuberos,b Jorge A. Portı´,a Korand Schwingenschuh,c and Bruno P. Besserc a Department of Applied Physics, University of Granada, E-18071 Granada, Spain b Department of Physics, Applied Electromagnetic Group, University of Murcia, E-30100 Murcia, Spain c Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, A-8042 Graz, Austria Received 13 May 2002; revised 11 November 2002 Abstract A numerical modeling of the electromagnetic characteristics of Titan’s atmosphere is carried out by means of the TLM numerical method, with the aim of calculating the Schumann resonant frequencies of Saturn’s satellite. The detection and measurement of these resonances by the Huygens probe, which will enter Titan’s atmosphere at the beginning of 2005, is expected to show the existence of electric activity with lightning discharges in the atmosphere of this satellite. As happens with the Schumann frequencies on Earth, losses associated with electric conductivity will make these frequencies lower than theoretically expected, the fundamental frequency being located between 11 and 15 Hz. This numerical study also shows that the strong losses associated to the high conductivity make it impossible for an electromagnetic wave with a frequency of 10 MHz or lower, generated near the surface, to reach the outer part of Titan’s atmosphere. © 2003 Elsevier Science (USA). All rights reserved. Keywords: Resonances; Titan; Radio observations; Ionospheres I. Introduction the cloud able to produce a temporary maximum electric field of Ϫ2 ϫ 106 V/m, which would be enough to cause Titan, the largest satellite of Saturn, is one of the main lightning in Titan’s lower troposphere. Grard et al. (1995) targets of the NASA–ESA Cassini–Huygens mission. proposed that the nondetection of lightning activity by Voy- Among the multiple questions that this mission will attempt ager could be due to the existence of a hidden ionospheric to answer is the likelihood of electric discharges in Titan’s layer produced by meteoric ionization. Using terrestrial atmosphere. Although no lightning was observed during the ionization rates and assuming that waves below the plasma Voyager flybys of Titan in 1980 and 1981, this negative frequency cannot propagate, they estimated that the mini- result does not remove the possibility of lightning phenom- mum frequency of waves able to propagate through this ena. There is recent evidence showing that lightning dis- layer is around 3 MHz. charges could occur in the lower atmosphere: (A) Griffith et If lightning in fact occurs, this electric discharge would al. (2000) detected the presence of methane condensation produce electromagnetic waves over a broad frequency clouds in the troposphere (15 Ϯ 10 km) through a pro- range that would propagate through the atmosphere and be nounced flux enhancement in the narrow spectral windows attenuated or reflected depending on the wave frequency of Titan, where the atmosphere is transparent. (B) Tokano et and plasma characteristics. Several instruments on the al. (2001) realized a one-dimensional time-dependent thun- Cassini–Huygens mission are devoted to the detection of dercloud model of Titan and obtained a negative charge in electromagnetic waves produced near Titan’s surface, which could indicate the presence of lightning. The radio * Corresponding author. Fax: ϩ34-958-243214. and plasma wave science (RPWS) instrument on board the E-mail address: [email protected] (J.A. Morente). Cassini Orbiter will measure electromagnetic waves during 0019-1035/03/$ – see front matter © 2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0019-1035(03)00025-3 J.A. Morente et al. / Icarus 162 (2003) 374–384 375 the Titan flybys at distances greater than 900 km. The Titan descent probe includes the permittivity, wave, and altimeter (PWA) instrument, as a part of the Huygens atmospheric structure instrument (HASI), devoted to investigating elec- tric properties and electric field fluctuations during the de- scent (from 170 km to the ground) (Fulchignoni et al., 1997). Lammer et al. (2001) investigated the most probable location of Titan’s cloud-to-ground lightning stroke and its characteristics in order to check the remote observation capabilities of the RPWS instrument. Based on the cloud formation model by Tokano et al. (2001), cloud-to-ground lightning strokes should be associated only with regions of strong convection near Titan’s subsolar regions, where the solar energy input is large. Using a simple propagation Fig. 1. Three possible conductivity profiles for Titan’s lower atmo- model, in which waves with frequencies lower than the sphere. plasma frequency cannot propagate and higher frequencies propagate freely, they concluded that the RPWS should be Ѩ ជ Ѩ ϭ ␻␧ ជ ␴ Ն Ϫ7 able to detect electromagnetic signals above the ionospheric D/ t j 0E, provided 10 S/m. In these equa- ͌ cut-off frequencies of about 500 kHz or 1 MHz, depending tions, j ϭ Ϫ 1 is the imaginary unity and ␴ stands for the on the ionospheric plasma density caused by meteoroids conductivity, which for this low frequency range equals the ␴ (Molina-Cuberos et al., 2001a). The approximation that DC conductivity, 0. Therefore, the outer concentric spher- plasma frequency is the minimum frequency for wave prop- ical surface will be located at the distance for which this agation and that waves above this limit propagate without value of electric conductivity occurs. The three conductivity attenuation is only valid for a medium without collisions. profiles shown in Fig. 1 for Titan’s lower atmosphere have The collision frequency in Titan’s atmosphere is higher than been used in this paper. The medium or nominal model the plasma frequency at altitudes below around 550 km. considers the present knowledge of Titan’s aeronomy to Schwingenschuh et al. (2001) developed a propagation calculate the concentration of electrons and ions (Molina- model considering both factors and concluded that 1 MHz Cuberos et al., 1999). Due to the uncertainties regarding the waves are almost completely absorbed, while propagation is atmospheric composition of Titan, especially in the lower possible for frequencies above 10 MHz. part of the atmosphere, we have also considered some ex- In this paper, numerical modeling of electromagnetic treme cases in order to estimate maximum and minimum waves propagation in Titan’s atmosphere is presented in limits in the expected conductivity. Lines labeled maximum order to study the possibility of wave detection, and there- and minimum represent the range of change in conductivity; fore lightning detection, by the RPWS and PWA/HASI the minimum was calculated assuming the existence of instruments. The numerical model proposed for this study is negative ions and a high electron recombination rate and the the transmission line modeling (TLM) method, which has maximum a low rate of recombination (Molina-Cuberos et been effectively used in the simulation of especially com- al., 1999, 2000). In the three profiles, the electric conduc- Ϫ plex electromagnetic systems (Port´ı et al., 1998a). tivity reaches the value of approximately 10 7 S/m for a height of about 180 km, which is therefore the distance at which the outer conducting sphere has been located. II. Titan as a resonant cavity: Schumann resonances In the simplest model for Titan, ohmic losses in the dielectric have been neglected, and the surface and upper Titan’s Schumann resonances are the resonant frequen- ionosphere are considered as perfectly conducting, which cies of the electromagnetic cavity formed by Titan’s surface means that the system is a lossless spherical resonant cavity. as conducting one boundary surface and the other its iono- This model is simple enough to be analytically solved, with sphere. These resonant frequencies were predicted for the the result that transverse electromagnetic (TEM) waves, terrestrial atmosphere by Schumann (1952) and detected by TEr, and TMr (transverse electric and magnetic to r) modes Balser and Wagner (1960). The lowest resonant modes of can propagate in this cavity. TEM modes have spatial struc- such a system are obviously very low frequency modes, ture similar to that of static fields due to the fact that the two since their characteristic wavelength must be on the order of conducting surfaces are separated by a dielectric region, ϭ magnitude of Titan’s radius, r0 2575 km. That is to say, which impedes the transfer of electric charge between them. Schumann frequencies will be lower than 300 Hz, i.e., in the Regarding the TEr modes in spherical coordinates, they extremely low frequency range. For these frequencies, the are described by the electric and magnetic fields, Eជ and Hជ , conduction current, Jជ ϭ ␴Eជ, is predominant, at least one which can be derived from potentials, Fជ and Aជ, in the form order of magnitude greater, over the displacement current, (Balanis, 1989) 376 J.A. Morente et al. / Icarus 162 (2003) 374–384 Table 1 Roots and resonant frequencies, theoretical and numerical (TLM resonances), for the electromagnetic cavity model of Titan’s atmosphere n 123456 k (rad/m) (theoretical roots) 5.31 ϫ 10Ϫ7 9.20 ϫ 10Ϫ7 13.01 ϫ 10Ϫ7 16.79 ϫ 10Ϫ7 20.56 ϫ 10Ϫ7 24.33 ϫ 10Ϫ7 f (Hz) (theoretical resonances) 25.33 43.88 62.06 80.11 98.12 116.09 f(Hz) (TLM resonances) 25.36 43.86 62.04 80.38 98.57 116.91 Error (%) between theoretical and 0.1 0.05 0.03 0.3 0.5 0.7 numerical 1 1 This equation does not depend on m, a great number of (Eជ ϭ ٌ ϫ ٌ ϫ Aជ Ϫ ٌ ϫ Fជ , (1a j␻␮␧ ␧ degenerate modes being observed as n increases.
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