Atmospheric Electricity of

Planetary Environments

Schumann Resonances

F. Simões, J.-J. Berthelier, M. Hamelin

CETP-IPSL, Saint Maur, France

TLE Workshop, Corte, 27 June 2008 1/18

Outline

TLE Workshop, Corte, 27 June 2008

• Introduction(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 2008 2/18

Schumann Resonance Theory

• Earth surface and ionosphere form a cavity where resonant electromagnetic waves can develop (2R)

• Lightning is a good candidate to excite these waves

• The frequencies fall in the ELF range and are given by

Where R is Earth radius, c the velocity of light in vacuum and n=1,2,…

… Balser and Wagner, Nature (1960) detected such waves.

R

c)n(nn 1

Schumann, Z. Naturforsch. (1952)

TLE Workshop, Corte, 27 June 2008 3/18

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

t BE

t DEH

ED o

HB o sn JHH 21 )(2

0)(2 21 EEn

E

k

H

The objective is solving Maxwell equations in a specific configuration:

TLE Workshop, Corte, 27 June 2008 4/18

Schumann Resonances on Earth

5 10 15 20 25 30 35 40 45 50

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

x 108

Frequency [Hz]

Ele

ctri

c F

ield

Am

pli

tud

e [1

]

Schumann spectrum measured on the surface – 5 peaks

The ‘World Record’ of Schumann peaks is:

8 14 20 26 32 38 44 Hz

Schumann spectrum at altitude of ~20 km (balloon) – 7 peaks

13 ! Füllekrug, GRL (2005)TLE Workshop, Corte, 27 June 2008 5/18

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 2008 6/18

Generalization to Other Planets

hcpp

Rcnnn )1(

Atmosphere:

atm

atm

Interior:

s

s

Environmental parameters: Geometric parameters:

R

Outer boundary:

iono, h

Inner boundary:

in, d

d

Simões et al., PSS (2007)

R

Transverse mode

TLE Workshop, Corte, 27 June 2008 7/18

Venus

16.22+1.01i

23.22+1.32i

9.13+0.62i

10.61+0.19i

9.28+0.34i

15.53+0.62i

17.28+0.23i

17.93+0.52i

25.07+0.61i24.93+0.87i

24.71+0.64i

21.48+0.95i

Highly asymmetric cavity:

• Day lasts longer

• No intrinsic magnetic field

• Specific atmospheric chemistry

“Similar” to the Stark and Zeeman effects in Quantum Mechanics

f > 1Hz

Simões et al., JGR (2008)

Eigenfrequency

Splitting

TLE Workshop, Corte, 27 June 2008 8/18

VenusHigh atmospheric density is responsible for refractivity phenomena N = (n-1)x10-6.

Analytical approximation using Maxwell equations and an exponential permittivity profile h29.6 km

Numerical model h31.5 km

h31.5 km

dense atmosphere

vacuum

Fermat principle – ray tracing h31.9 km

(for high frequencies and light)

E shows a maximum at specific altitude

Simões et al., JGR (2008)

TLE Workshop, Corte, 27 June 2008 9/18

Venus

Venera 11 and 12 data

Ksanfomaliti et al., Kosmich.Issled. (1979)TLE Workshop, Corte, 27 June 2008 10/18

Mars

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=2.2-12.5 Christensen and Moore, in ‘Mars’

(1993)

=10-10-10-12 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 2008 11/18

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] Q f3 [Hz] Q

Jupiter 0.68 8.5 1.21 8.6 1.74 8.7

Saturn 0.93 7.8 1.63 6.8 2.34 6.5TLE Workshop, Corte, 27 June 2008 12/18

Uranus and Neptune

Simões et al., Icarus (2008)

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)]And:• Conductivity is driven by water content in the gaseous envelope - Liu, PhD Thesis, Caltech (2006)

15% H2O

H2O depleted

Planet f1 [Hz]

Q F2 [Hz]

Q F3 [Hz]

Q

Uranus 2.44 20.3 4.24 19.3 6.00 20.0

Uranus 1.02 2.0 1.99 2.0 3.03 2.3

Neptune 2.33 9.7 4.12 9.4 5.90 9.5

Neptune 1.10 1.0 2.03 1.1 2.96 0.9

TLE Workshop, Corte, 27 June 2008 13/18

Earth Titan

Radius ~ 6370 km

Ionospheric Layer height ~ 90 km

Radius ~ 2575 km

Ionospheric Layer height ~ 700 km

TLE Workshop, Corte, 27 June 2008 14/18

TitanHuygens Probe - ELF spectra recorded with the PWA analyzer

Simões et al., PSS (2007)

36 Hz spectral line

This signal can not be the lowest eigenmode but is consistent to the second eigenfrequency TLE Workshop, Corte, 27 June 2008 15/18

TitanCavity Parameterization:• Radius 2575 km

• Height of the ionosphere ~ 1200 km (cavity upper boundary ~700 km)

• Low surface conductivity (10-10-10-9 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 2008 16/18

2D axisymmetric and 3D models of ELF-VLF electromagnetic wave propagation

The finite element model includes transient, eigenfrequency, harmonic propagation, and parametric analysis

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()

And now back to Earth…

We can apply the same numerical model to improve studies of the Earth cavity

Currently:

• Modelling eigenfrequency splitting

Near future:

• Model may be used to study TLEs

3D modelE(t), E()

H(t), H()Sources and medium properties

TLE Workshop, Corte, 27 June 2008 17/18

• 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

Summary

TLE Workshop, Corte, 27 June 2008 18/18

The model can run under specific configurations that might be useful for TLE investigations – current contact: Fernando.Simoes@cetp.ipsl.fr

A comparative planetology review of Schumann resonances is expected to be available soon – Simões et al., SSR (in press)