1. Atmospheric Electricity of Planetary Environments
Schumann Resonances
F. Simões, J.-J. Berthelier, M. Hamelin
CETP-IPSL, Saint Maur, France
TLE Workshop, Corte, 27 June /18

2. Outline Introduction Schumann resonances on Earth
(what are Schumann resonances?)
Schumann resonances on Earth
(what can we learn from such phenomenon?)
Schumann resonances on planetary environments
(what are the expected similarities/differences on other planets and moons?)
Schumann resonances and TLEs
(which modelling improvements are required?)
Summary
TLE Workshop, Corte, 27 June /18
TLE Workshop, Corte, 27 June 2008

3. Schumann Resonance Theory
Earth surface and ionosphere form a cavity where resonant electromagnetic waves can develop (2R)
Lightning is a good candidate to excite these waves
The frequencies fall in the ELF range and are given by
Schumann, Z. Naturforsch. (1952)
Where R is Earth radius, c the velocity of light in vacuum and n=1,2,…
… Balser and Wagner, Nature (1960) detected such waves.
TLE Workshop, Corte, 27 June /18

4. Schumann Resonance Theory
The initial assumptions were:
Surface is a Perfect Electric Conductor (PEC)
Ionosphere is a PEC boundary
Cavity thichness is much smaller than radius
Lossless cavity with =1 k  E H
The objective is solving Maxwell equations in a specific configuration:
TLE Workshop, Corte, 27 June /18

5. Schumann Resonances on Earth
Schumann spectrum measured on the surface – 5 peaks
Schumann spectrum at altitude of ~20 km (balloon) – 7 peaks Hz
The ‘World Record’ of Schumann peaks is:
13 !
Füllekrug, GRL (2005)
TLE Workshop, Corte, 27 June /18

6. Schumann Resonances on Earth
Daily variation of Schumann peaks -Balser and Wagner, Nature (1960)
Schumann resonance spectrum is modulated over the solar cycle and responds to solar flares -Reid, in ‘Study in Geophysics: the earth's electrical environment’ (1986)
Seasonal variation - ‘global tropical thermometer’ -Williams, Nature (1992)
Connection between Schumann resonance and lightning variability, sprites -Boccippio et al., Science (1995)
Used to monitoring tropospheric water vapour -Price, Nature (2000)
Many other contributions can be find in the book ‘Resonances in the Earth-ionosphere cavity’ of Nickolaenko and Hayakawa (2002)
Remark: Schumann resonances respond to sources distribution and ionospheric variability
TLE Workshop, Corte, 27 June /18

7. Generalization to Other Planets
Environmental parameters:
Geometric parameters: R
Atmosphere:
atm
atm
Outer boundary:
iono, h
Inner boundary:
in, d R
Interior: s s d
Transverse mode
Simões et al., PSS (2007)
TLE Workshop, Corte, 27 June /18

8. Venus
“Similar” to the Stark and Zeeman effects in Quantum Mechanics i i
f > 1Hz i i i i i i i
Simões et al., JGR (2008)
Highly asymmetric cavity:
Day lasts longer
No intrinsic magnetic field
Specific atmospheric chemistry i
Eigenfrequency
Splitting i i
TLE Workshop, Corte, 27 June /18

9. Venus h31.5 km Fermat principle – ray tracing  h31.9 km
High atmospheric density is responsible for refractivity phenomena  N = (n-1)x10-6.
Analytical approximation using Maxwell equations and an exponential permittivity profile  h29.6 km
Numerical model  h31.5 km
 dense atmosphere
h31.5 km
 vacuum
Simões et al., JGR (2008)
Fermat principle – ray tracing  h31.9 km
(for high frequencies and light)
E shows a maximum at specific altitude
TLE Workshop, Corte, 27 June /18

10. Venus
Venera 11 and 12 data
Ksanfomaliti et al., Kosmich.Issled. (1979)
TLE Workshop, Corte, 27 June /18

11. Mars r=2.2-12.5 Christensen and Moore, in ‘Mars’ (1993)
Cavity Conditions:
Models predict significant atmospheric conductivity down to the surface
Surface highly heterogeneous
Unknown surface permittivity and conductivity
Electric discharging:
Lightning – unlikely
Triboelectricity from dust storms – likely
Surface properties:
r= Christensen and Moore, in ‘Mars’ (1993)
= Sm-1 Berthelier et al., PSS (2000)
Schumann resonances can be used to:
Investigating the sporadic meteor layer – Molina-Cuberos et al., RadSci (2006)
Assessing atmospheric propagation conditions - Soriano et al., JGR (2007)
Studying triboelectricity
But
Strong attenuation is expected if the atmospheric conductivity models are confirmed; evanescent modes may occur.
TLE Workshop, Corte, 27 June /18

12. Jupiter and Saturn Cavity Parameterization:
Radius is one order of magnitude larger than Earth
Inner boundary is significantly lower than planetary radius
Interior conductivity is required - Liu, PhD Thesis, Caltech (2006)
Permittivity profile must be used because gas density cannot be neglected – range [1, ~1.25 (liquid hydrogen)]
Strong intrinsic magnetic field – effect is neglected though
Eigenfrequencies:
Simões et al., Icarus (2008)
Planet
f1 [Hz] Q
f2 [Hz]
f3 [Hz]
Jupiter
0.68
8.5
1.21
8.6
1.74
8.7
Saturn
0.93
7.8
1.63
6.8
2.34
6.5
TLE Workshop, Corte, 27 June /18

13. Uranus and Neptune Cavity Parameterization: And:
Planet
f1 [Hz] Q
F2 [Hz]
F3 [Hz]
Uranus
2.44
20.3
4.24
19.3
6.00
20.0
1.02
2.0
1.99
3.03
2.3
Neptune
2.33
9.7
4.12
9.4
5.90
9.5
1.10
1.0
2.03
1.1
2.96
0.9
Cavity Parameterization:
Radius is smaller than in the Jovian planets
Inner boundary is significantly lower than the radius
Interior permittivity profile must be used because gas density cannot be neglected – range [1, ~1.25 (liquid hydrogen)]
Simões et al., Icarus (2008)
And:
Conductivity is driven by water content in the gaseous envelope - Liu, PhD Thesis, Caltech (2006)
15% H2O
H2O depleted
TLE Workshop, Corte, 27 June /18

14. Earth Titan Radius ~ 2575 km Ionospheric Layer height ~ 700 km
TLE Workshop, Corte, 27 June /18

15. Huygens Probe - ELF spectra recorded with the PWA analyzer
Titan
Huygens Probe - ELF spectra recorded with the PWA analyzer
36 Hz spectral line
Simões et al., PSS (2007)
This signal can not be the lowest eigenmode but is consistent to the second eigenfrequency
TLE Workshop, Corte, 27 June /18

16. Titan Cavity Parameterization: Data: Interpretation: Radius 2575 km
Height of the ionosphere ~ 1200 km (cavity upper boundary ~700 km)
Low surface conductivity ( Sm-1) – Grard et al., PSS (2006)  skin depth >103 km
Theoretical models predict buried ocean - Lunine and Stevenson, Icarus (1987)
Data:
Huygens Probe provided ELF data – Fulchignoni et al., Nature (2005); Grard et al., PSS (2006)
Cassini Orbiter did not detect lightning - Fischer et al., Icarus (2007)
Conductivity measurements below 140 km – Hamelin et al., PSS (2006); López-Moreno et al., GRL (submitted)
Interpretation:
If the signal detected by Huygens is natural, the Schumann resonance is likely excited by an interaction with the magnetosphere of Saturn - Béghin et al., Icarus (2007)
Schumann resonances can be used to investigate the interior of Titan and assess the depth of the buried ocean - Simões et al., PSS (2007)
TLE Workshop, Corte, 27 June /18

17. And now back to Earth…
2D axisymmetric and 3D models of ELF-VLF electromagnetic wave propagation
We can apply the same numerical model to improve studies of the Earth cavity
The finite element model includes transient, eigenfrequency, harmonic propagation, and parametric analysis
Currently:
Modelling eigenfrequency splitting
Near future:
Model may be used to study TLEs
Cavity Parameterization:
Inner boundary (Earth radius)
Outer boundary (D-layer)
3D Ionospheric data
3D Atmospheric data
3D Geomagnetic field
Sources are Hertz dipoles S(t) or S()
E(t), E()
H(t), H()
Sources and medium properties
3D model
TLE Workshop, Corte, 27 June /18

18. Summary
Schumann resonances respond to sources distribution and ionospheric variability
Schumann resonances can be used to investigate atmospheric electricity through the Solar System, including rocky planets, icy moons, and the giant planets
The eigenmodes can be used to investigate Venus atmospheric turbulence and refractivity phenomena
Venus cavity asymmetry is expected to induce line splitting larger than 1 Hz
Schumann resonance monitoring can be used to investigate the sporadic meteor layer of Mars
The water content of the gaseous envelope of Uranus and Neptune can be investigated by means of Schumann resonance measurements
Schumann resonances can be used to investigate the interior of Titan and estimate the depth o the buried ocean
The model can run under specific configurations that might be useful for TLE investigations – current contact:
A comparative planetology review of Schumann resonances is expected to be available soon – Simões et al., SSR (in press)
TLE Workshop, Corte, 27 June /18