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Subionospheric VLF propagation
Prepared by Morris Cohen, Benjamin Cotts, Forrest FoustStanford University, Stanford, CA
IHY Workshop on Advancing VLF through the Global AWESOME Network
2N. Lehtinen
Radio waves on the ionosphere
MicrowaveMF-HF Waves
LF Waves
Earth
Ionosphere
Atmosphere
Magnetosphere
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Ideal parallel-plate waveguide
Reflection Height
Earth
Ionosphere
Transmitter Receiver
Perfect Reflections
(reflection coefficient is 1)
Perfect Reflections
Flat Earth
Isotropic Ionosphere
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Basic waveguide analysis
~80 km
Transverse Electric (TE)
Transverse Magnetic (TM)
Magnetic Field (B)Electric Field (E)
Radial direction (propagation)
Azimuthal direction
Fields within waveguide
Modal components of propagating waves
Vertical direction
Above ~1.8 kHz
Below ~1.8 kHz
Earth
Ionosphere
Propagation
Transmitter
Receiver
Transverse Electromagnetic (TEM)
All Frequencies
22
a
njk
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Typical conductivities
Salt water = 4 S/m
Fresh water = 10-2 S/m
Dry soil = 10-4 to 10-2 S/m
Wet soil = 10-3 to 10-2 S/m
= 10-7 to 10-5 S/m
Daytime Ionosphere
~70-75 km
~80-90 km
Nighttime Ionosphere
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Basic plasma conductivity
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
Applied electric field
e-
e-
e-
e-
e-
Electron response
Polarization field
Debye Shielding• Applied electric field forced rearranging of
electrons• Polarization opposes field, shields it from
propagating further• Characteristic plasma response time ~ 1/p
p2 ~ Ne
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Ionospheric Conductivity
BvqF e
xy
z• Electrons in motion
forced to orbit magnetic field
• Applied electric field can generate currents in other directions
• Anisotropic conductivity
• “Gyrofrequency” is a function of magnetic field and e- mass
e
ece m
Bq 0
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Mode conversion
• Incident fields are “rotated” by electron response
• TE and TM waves can be converted into each other
Incident Wave Reflected Wave
Pure TM wave Mixed TM and TE wave
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Anisotropic Conductivity
• Direction of wave incidence matters
• Different reflection coefficients
Incident Wave Reflected Wave
Incident Wave
Reflected Wave
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Sharp ionospheric boundary
E
k
Perpendicular incidence
Ek
Parallel incidence
E
k
Perpendicular reflection
E
k
Parallel reflection
Reflection coefficients
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The Effect of Collisions
• Electrons lose energy via collisions
• Electron-neutral collisions are most prominent
• Wave energy can be absorbed via collisions
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Collisions and Magnetic Field
• Lower D-region, collision frequency much higher than gyrofrequency• Higher altitudes, collisions rare, magnetic field dominates
• Plasma frequency (electron density) increasing rapidly
Dominated by Collisions
Dominated by Magnetic Field
p= c
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Ionospheric Parameters
• Measures how strongly electron density affects wave propagation2
2
peX
ceY
effZ
• Measures how strongly geomagnetic field affects wave propagation
• Measures how strongly electron-neutral collisions affect wave propagation
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Plasma Terms
X=1 X=Z
• X=1 = p
• Plasma debye shielding fast enough to block wave
• Z>>X, so collisions suppress the shielding
• X=Z c = p
• Collision frequency weakens, Debye shielding wins out
• VLF waves reflected• Daytime reflection ~65 km• Nightime reflection ~85 km
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Conductivity Tensor
EEJ
Par
PedHall
HallPed
e
00
0
0
222
Ped )( cep j
j
22
22
Hall )( ce
cep j
jp
12Par
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Ionospheric Changes
Daytime Ionosphere
~70-75 km
~80-90 km
Nighttime Ionosphere
TransmitterReceiver
Earth
Scattered Wave
Incident Wave
Reflected Wave
Mode conversion
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Refractive Index
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4222
2
cos)1(4
sin)1(2
sin1
1
jZXY
YjZX
YjZ
Xn
B
Appleton-Hartree Equation Refractive index, n
Depends on , angle between wave and magnetic field
Depends on X, Y, and Z For Collision-less plasma (such
as magnetosphere) Z 0 When Collisions dominate
(Y>>Z), Y can be ignored
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“Helliwell” Absorption assumption Normal incidence Wavelength is much smaller than the size of any variation in the medium.
Loss () is proportional to the imaginary part of the refractive index
(in dB)
Ionospheric Absorption
1
1)Im(69.8 dzc
n
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Daytime vs. Nightime
Nightime reflection
Daytime reflection
• Higher reflection height at nightime• Absorption dominated by collisions at reflection height• Lower collisions less attenuation at night
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References
• K.G. Budden, The Wave-Guide Mode Theory of Wave Propagation, 1961, Prentice Hall
• J.R. Wait, Electromagnetic Waves in Stratified Media, 1962, Pergamon Press.
• J. Galejs, Terrestrial Propagation of Long Electromagnetic Waves,1972 Pergamon Press
• R.A. Helliwell, Whistlers and Related Ionospheric Phenomena, 1965
• R. Barr et al., ELF and VLF Radio Waves, J. Atmos. Sol.-Terr. Phy., Vol.2,1689-1719, 2000.